- 15-POINT GAUSS-KRONROD RULES
- 21-POINT GAUSS-KRONROD RULES
- 25-POINT CLENSHAW-CURTIS INTEGRATION
- 31-POINT GAUSS-KRONROD RULES
- 3J COEFFICIENTS
- 3J SYMBOLS
- 41-POINT GAUSS-KRONROD RULES
- 51-POINT GAUSS-KRONROD RULES
- 61-POINT GAUSS-KRONROD RULES
- 6J COEFFICIENTS
- 6J SYMBOLS
- ABORT PROGRAM EXECUTION
- ABSOLUTE VALUE
- ABSOLUTE VALUE OF THE LOGARITHM OF THE GAMMA FUNCTION
- ACOSH
- ADAMS METHOD
- ADAMS-BASHFORTH METHOD
- ADAPTIVE QUADRATURE
- AIRY FUNCTION
- ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES
- ALGEBRAICO-LOGARITHMIC
- ANALYSIS OF COVARIANCE
- APPLICATION OF PERMUTATION TO DATA VECTOR
- ARC COSINE
- ARC HYPERBOLIC COSINE
- ARC HYPERBOLIC SINE
- ARC HYPERBOLIC TANGENT
- ARC SINE
- ARC TANGENT
- ARGUMENT OF A COMPLEX NUMBER
- ASINH
- ATANH
- AUTOMATIC INTEGRATOR
- B-SPLINE
- B-SPLINES
- BACKWARD DIFFERENTIATION FORMULAS
- BAIRY FUNCTION
- BANDED
- BANDED MATRIX
- BASE TEN LOGARITHM
- BESSEL FUNCTION
- BESSEL FUNCTION OF ORDER ONE THIRD
- BESSEL FUNCTION OF ORDER TWO THIRDS
- BESSEL FUNCTIONS OF COMPLEX ARGUMENT
- BESSEL FUNCTIONS OF SECOND KIND
- BESSEL FUNCTIONS OF THE FIRST KIND
- BESSEL FUNCTIONS OF THE THIRD KIND
- BICKLEY FUNCTIONS
- BICONJUGATE GRADIENT
- BICONJUGATE GRADIENT SQUARED
- BINOMIAL COEFFICIENTS
- BISECTION
- BLAS
- BOUNDS
- BROWN'S METHOD
- CARTESIAN
- CAUCHY PRINCIPAL VALUE
- CHARACTER COMPARISON
- CHEBYSHEV
- CHEBYSHEV SERIES
- CHEBYSHEV SERIES EXPANSION
- CHOLESKY DECOMPOSITION
- CLEBSCH-GORDAN COEFFICIENTS
- CLENSHAW-CURTIS METHOD
- COEFFICIENTS
- COMPLEMENTARY ERROR FUNCTION
- COMPLEMENTARY INCOMPLETE GAMMA FUNCTION
- COMPLETE BETA FUNCTION
- COMPLETE ELLIPTIC INTEGRAL
- COMPLETE GAMMA FUNCTION
- COMPLEX HERMITIAN
- COMPLEX LINEAR EQUATIONS
- COMPLEX POLYNOMIAL
- COMPLEX VALUED
- COMPLEX VECTORS
- CONDITION NUMBER
- CONSTRAINED LEAST SQUARES
- CONSTRAINTS
- CONVERGENCE ACCELERATION
- CONVERSION
- COPY
- CORRECTION TERM
- COS OR SIN IN WEIGHT FUNCTION
- COSINE
- COSINE FOURIER TRANSFORM
- COTANGENT
- COVARIANCE MATRIX
- CUBE ROOT
- CUBIC HERMITE DIFFERENTIATION
- CUBIC HERMITE EVALUATION
- CUBIC HERMITE INTERPOLATION
- CUBIC POLYNOMIAL EVALUATION
- CUBIC SPLINES
- CURVE FITTING
- CYCLIC REDUCTION
- CYLINDRICAL
- DASSL
- DATA FITTING
- DAWSON'S FUNCTION
- DEGREES
- DEPAC
- DERIVATIVES OF THE GAMMA FUNCTION
- DETERMINANT
- DIAGNOSTICS
- DIAGONAL
- DIFFERENTIAL/ALGEBRAIC
- DIFFERENTIATION OF B-SPLINE
- DIFFERENTIATION OF SPLINES
- DIGAMMA FUNCTION
- DISCLAIMER
- DOCUMENTATION
- DOT PRODUCT
- DOUBLE PRECISION
- DOWNDATE
- DUPLICATION THEOREM
- E1 FUNCTION
- EASY-TO-USE
- EI FUNCTION
- EIGENVALUES
- EIGENVALUES OF A REAL SYMMETRIC MATRIX
- EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX
- EIGENVECTORS
- EIGENVECTORS OF A REAL SYMMETRIC MATRIX
- EISPACK
- ELEMENTARY FUNCTIONS
- ELLIPTIC
- ELLIPTIC INTEGRAL
- ELLIPTIC PDE
- END POINT SINGULARITIES
- EPSILON ALGORITHM
- EQUALITY CONSTRAINTS
- ERF
- ERFC
- ERROR
- ERROR CHECKING
- ERROR FUNCTION
- ERROR MESSAGE
- ERROR MESSAGES
- ERROR NUMBER
- EUCLIDEAN LENGTH
- EUCLIDEAN NORM
- EVALUATION OF B-SPLINE
- EXCHANGE
- EXPONENTIAL
- EXPONENTIAL INTEGRAL
- EXPONENTIALLY SCALED
- EXPONENTIALLY SCALED AIRY FUNCTION
- EXTENDED-RANGE DOUBLE-PRECISION ARITHMETIC
- EXTENDED-RANGE SINGLE-PRECISION ARITHMETIC
- EXTRAPOLATION
- FACTORIAL
- FAST FOURIER TRANSFORM
- FFT
- FFTPACK
- FIRST KIND
- FIRST ORDER
- FISHPACK
- FNLIB
- FOURIER INTEGRALS
- FOURIER TRANSFORM
- FRACTIONAL ORDER
- GAMMA FUNCTION
- GAUSS QUADRATURE
- GAUSS-KRONROD RULES
- GAUSS-KRONROD(PATTERSON) RULES
- GAUSSIAN
- GEAR'S METHOD
- GENERAL MATRIX
- GENERAL SYSTEM OF LINEAR EQUATIONS
- GENERAL-PURPOSE
- GENERALIZED MINIMUM RESIDUAL
- GIVENS ROTATION
- GIVENS TRANSFORMATION
- GLOBALLY ADAPTIVE
- GMRES
- GRADIENTS
- GUIDELINES FOR SELECTION
- H BESSEL FUNCTIONS
- HANKEL FUNCTIONS
- HELMHOLTZ
- HERMITE INTERPOLATION
- HERMITIAN
- HYPERBOLIC BESSEL FUNCTION
- HYPERBOLIC COSINE
- HYPERBOLIC SINE
- HYPERBOLIC TANGENT
- I BESSEL FUNCTION
- I BESSEL FUNCTIONS
- IMPLICIT DIFFERENTIAL SYSTEMS
- INCOMPLETE BETA FUNCTION
- INCOMPLETE CHOLESKY
- INCOMPLETE CHOLESKY FACTORIZATION
- INCOMPLETE ELLIPTIC INTEGRAL
- INCOMPLETE FACTORIZATION
- INCOMPLETE GAMMA FUNCTION
- INCOMPLETE LU FACTORIZATION
- INEQUALITY
- INEQUALITY CONSTRAINTS
- INFINITE INTERVALS
- INITIAL VALUE PROBLEMS
- INITIALIZE
- INNER PRODUCT
- INTEGRAL OF B-SPLINE
- INTEGRAL OF B-SPLINES
- INTEGRAL OF THE FIRST KIND
- INTEGRAL OF THE SECOND KIND
- INTEGRAL OF THE THIRD KIND
- INTEGRALS OF BESSEL FUNCTIONS
- INTEGRAND EXAMINATOR
- INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR
- INTEGRATION
- INTEGRATION BETWEEN ZEROS
- INTEGRATION RULES FOR FUNCTIONS WITH COS OR SIN FACTOR
- INTERCHANGE
- INTERPOLATION
- INVERSE
- INVERSE COSINE FOURIER TRANSFORM
- INVERSE HYPERBOLIC COSINE
- INVERSE HYPERBOLIC SINE
- INVERSE HYPERBOLIC TANGENT
- ITERATIVE IMPROVEMENT
- ITERATIVE INCOMPLETE LU PRECONDITION
- ITERATIVE PRECONDITION
- J BESSEL FUNCTION
- J BESSEL FUNCTIONS
- JACOBIAN
- K BESSEL FUNCTION
- K BESSEL FUNCTIONS
- K-ZERO BESSEL FUNCTION
- L2
- LARGE X
- LEAST SQUARES
- LEGENDRE FUNCTIONS
- LEVEL 2 BLAS
- LEVEL 3 BLAS
- LEVENBERG-MARQUARDT
- LIMITS
- LINEAR
- LINEAR ALGEBRA
- LINEAR CONSTRAINTS
- LINEAR EQUATIONS
- LINEAR LEAST SQUARES
- LINEAR OPTIMIZATION
- LINEAR PROGRAMMING
- LINEAR SYSTEM
- LINEAR SYSTEM SOLVE
- LINPACK
- LOG GAMMA
- LOGARITHM
- LOGARITHM OF GAMMA FUNCTION
- LOGARITHM OF THE COMPLETE BETA FUNCTION
- LOGARITHMIC CONFLUENT HYPERGEOMETRIC FUNCTION
- LOGARITHMIC INTEGRAL
- LOWER TRIANGLE
- LP
- LQ FACTORIZATION
- LR METHOD
- MACHINE CONSTANTS
- MATRIX
- MATRIX FACTORIZATION
- MATRIX READ
- MATRIX TRANSPOSE VECTOR MULTIPLY
- MATRIX VECTOR MULTIPLY
- MAXIMUM COMPONENT
- MINPACK
- MODIFIED BESSEL FUNCTION
- MODIFIED BESSEL FUNCTIONS
- MODIFIED CHEBYSHEV MOMENTS
- MODIFIED GIVENS ROTATION
- MODULUS
- MONOTONE INTERPOLATION
- NEWTON'S METHOD
- NEWTON-COTES
- NON-SYMMETRIC LINEAR SYSTEM
- NON-SYMMETRIC LINEAR SYSTEM SOLVE
- NONADAPTIVE
- NONLINEAR
- NONLINEAR DATA FITTING
- NONLINEAR EQUATIONS
- NONLINEAR LEAST SQUARES
- NONLINEAR SQUARE SYSTEM
- NONNEGATIVITY CONSTRAINTS
- NONSYMMETRIC
- NORMAL
- NORMAL EQUATIONS
- NORMAL EQUATIONS.
- NUMBER SORTING
- NUMERICAL INTEGRATION
- ODE
- ORDER ONE
- ORDER ZERO
- ORDINARY DIFFERENTIAL EQUATIONS
- ORTHOGONAL POLYNOMIAL
- ORTHOGONAL SERIES
- ORTHOGONAL TRIANGULAR
- ORTHOMIN
- ORTHONORMALIZATION
- PACK
- PACKED
- PASSIVE SORTING
- PCHIP
- PDE
- PERMUTATION
- PERRON'S CONTINUED FRACTION
- PHASE
- PIECEWISE CUBIC EVALUATION
- PIECEWISE CUBIC INTERPOLATION
- PIECEWISE POLYNOMIAL
- PLANE ROTATION
- POCHHAMMER
- POISSON
- POLAR
- POLAR ANGEL
- POLYGAMMA FUNCTION
- POLYNOMIAL
- POLYNOMIAL APPROXIMATION
- POLYNOMIAL EVALUATION
- POLYNOMIAL FIT
- POLYNOMIAL INTERPOLATION
- POLYNOMIAL ROOTS
- POLYNOMIAL ZEROS
- POSITIVE DEFINITE
- POWELL HYBRID METHOD
- PRECONDITIONED CONJUGATE GRADIENT
- PREDICTOR-CORRECTOR
- PRINTING
- PSI FUNCTION
- QL METHOD
- QR DECOMPOSITION
- QR FACTORIZATION
- QUADPACK
- QUADRANT
- QUADRATIC PROGRAMMING
- QUADRATURE
- RACAH COEFFICIENTS
- RANDOM NUMBER
- REAL ROOTS
- REARRANGEMENT
- RECALL
- RECIPROCAL GAMMA FUNCTION
- RELATIVE ADDRESS DETERMINATION FUNCTION
- RKF
- ROOTS
- RUNGE-KUTTA-FEHLBERG METHODS
- SAVE
- SCALE
- SDRIVE
- SECOND KIND
- SECOND ORDER
- SEPARABLE
- SEQUENCE OF BESSEL FUNCTIONS
- SEQUENTIAL SORTING
- SHAPE-PRESERVING INTERPOLATION
- SHOOTING
- SINE
- SINGLE PRECISION
- SINGLETON QUICKSORT
- SINGULAR VALUE DECOMPOSITION
- SINGULARITIES AT USER SPECIFIED POINTS
- SLAP
- SLAP SPARSE
- SLATEC
- SMALL X
- SMOOTH INTEGRAND
- SMOOTH INTERPOLANT
- SOLUTIONS
- SOLVE
- SORT
- SORTING
- SPARSE
- SPARSE CONSTRAINTS
- SPARSE ITERATIVE METHODS
- SPECIAL FUNCTIONS
- SPECIAL-PURPOSE
- SPECIAL-PURPOSE INTEGRAL
- SPENCE'S INTEGRAL
- SPHERICAL
- SPLINE INTERPOLATION
- SPLINES
- STIFF
- STOP TEST
- STRING SORTING
- SUM OF MAGNITUDES OF A VECTOR
- SURVEY OF INTEGRATORS
- SYMMETRIC
- SYMMETRIC LINEAR SYSTEM
- SYMMETRIC LINEAR SYSTEM SOLVE
- TABULATED DATA
- TANGENT
- TAYLOR SERIES
- THIRD KIND
- TRANSFORMATION
- TRIAD
- TRIANGULAR
- TRIANGULAR LINEAR SYSTEM
- TRIANGULAR MATRIX
- TRICOMI
- TRIDIAGONAL
- TRIDIAGONAL LINEAR SYSTEM
- TRIGONOMETRIC
- TWO-POINT BOUNDARY VALUE PROBLEM
- UNDERDETERMINED LINEAR SYSTEM
- UNDERDETERMINED LINEAR SYSTEMS
- UNIFORM
- UNITARY
- UNPACK
- UPDATE
- UTILITY ROUTINE
- VECTOR
- VECTOR ADDITION COEFFICIENTS
- VERSION
- WEBER'S FUNCTION
- WEIGHT FUNCTION
- WEIGHTED LEAST SQUARES
- WIGNER COEFFICIENTS
- WORKSPACE CHECKING
- XERMSG
- XERROR
- Y BESSEL FUNCTION
- Y BESSEL FUNCTIONS
- ZEROS
### 15-POINT GAUSS-KRONROD RULES

- dqk15
To compute I = Integral of F over (A,B), with error estimate J = integral of ABS(F) over (A,B)

- dqk15i
The original (infinite integration range is mapped onto the interval (0,1) and (A,B) is a part of (0,1). it is the purpose to compute I = Integral of transformed integrand over (A,B), J = Integral of ABS(Transformed Integrand) over (A,B).

- dqk15w
To compute I = Integral of F*W over (A,B), with error estimate J = Integral of ABS(F*W) over (A,B)

- qk15
To compute I = Integral of F over (A,B), with error estimate J = integral of ABS(F) over (A,B)

- qk15i
The original (infinite integration range is mapped onto the interval (0,1) and (A,B) is a part of (0,1). it is the purpose to compute I = Integral of transformed integrand over (A,B), J = Integral of ABS(Transformed Integrand) over (A,B).

- qk15w
To compute I = Integral of F*W over (A,B), with error estimate J = Integral of ABS(F*W) over (A,B)

### 21-POINT GAUSS-KRONROD RULES

- dqk21
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- qk21
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

### 25-POINT CLENSHAW-CURTIS INTEGRATION

- dqc25c
To compute I = Integral of F*W over (A,B) with error estimate, where W(X) = 1/(X-C)

- dqc25s
To compute I = Integral of F*W over (BL,BR), with error estimate, where the weight function W has a singular behaviour of ALGEBRAICO-LOGARITHMIC type at the points A and/or B. (BL,BR) is a part of (A,B).

- qc25c
To compute I = Integral of F*W over (A,B) with error estimate, where W(X) = 1/(X-C)

- qc25s
To compute I = Integral of F*W over (BL,BR), with error estimate, where the weight function W has a singular behaviour of ALGEBRAICO-LOGARITHMIC type at the points A and/or B. (BL,BR) is a part of (A,B).

### 31-POINT GAUSS-KRONROD RULES

- dqk31
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qk31
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

### 3J COEFFICIENTS

- drc3jj
Evaluate the 3j symbol f(L1) = ( L1 L2 L3) (-M2-M3 M2 M3) for all allowed values of L1, the other parameters being held fixed.

- drc3jm
Evaluate the 3j symbol g(M2) = (L1 L2 L3 ) (M1 M2 -M1-M2) for all allowed values of M2, the other parameters being held fixed.

- rc3jj
Evaluate the 3j symbol f(L1) = ( L1 L2 L3) (-M2-M3 M2 M3) for all allowed values of L1, the other parameters being held fixed.

- rc3jm
Evaluate the 3j symbol g(M2) = (L1 L2 L3 ) (M1 M2 -M1-M2) for all allowed values of M2, the other parameters being held fixed.

### 3J SYMBOLS

- drc3jj
Evaluate the 3j symbol f(L1) = ( L1 L2 L3) (-M2-M3 M2 M3) for all allowed values of L1, the other parameters being held fixed.

- drc3jm
Evaluate the 3j symbol g(M2) = (L1 L2 L3 ) (M1 M2 -M1-M2) for all allowed values of M2, the other parameters being held fixed.

- rc3jj
- rc3jm

### 41-POINT GAUSS-KRONROD RULES

- dqk41
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- qk41
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

### 51-POINT GAUSS-KRONROD RULES

- dqk51
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qk51
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

### 61-POINT GAUSS-KRONROD RULES

- dqk61
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qk61
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

### 6J COEFFICIENTS

- drc6j
Evaluate the 6j symbol h(L1) = {L1 L2 L3} {L4 L5 L6} for all allowed values of L1, the other parameters being held fixed.

- rc6j
Evaluate the 6j symbol h(L1) = {L1 L2 L3} {L4 L5 L6} for all allowed values of L1, the other parameters being held fixed.

### 6J SYMBOLS

- drc6j
Evaluate the 6j symbol h(L1) = {L1 L2 L3} {L4 L5 L6} for all allowed values of L1, the other parameters being held fixed.

- rc6j

### ABORT PROGRAM EXECUTION

- xerhlt
Abort program execution and print error message.

### ABSOLUTE VALUE

- alngam
Compute the logarithm of the absolute value of the Gamma function.

- clngam
Compute the logarithm of the absolute value of the Gamma function.

- dlngam
Compute the logarithm of the absolute value of the Gamma function.

### ABSOLUTE VALUE OF THE LOGARITHM OF THE GAMMA FUNCTION

- algams
Compute the logarithm of the absolute value of the Gamma function.

- dlgams
Compute the logarithm of the absolute value of the Gamma function.

### ACOSH

- acosh
Compute the arc hyperbolic cosine.

- cacosh
Compute the arc hyperbolic cosine.

- dacosh
Compute the arc hyperbolic cosine.

### ADAMS METHOD

- dintp
Approximate the solution at XOUT by evaluating the polynomial computed in DSTEPS at XOUT. Must be used in conjunction with DSTEPS.

- dsteps
Integrate a system of first order ordinary differential equations one step.

- sintrp
Approximate the solution at XOUT by evaluating the polynomial computed in STEPS at XOUT. Must be used in conjunction with STEPS.

- steps
Integrate a system of first order ordinary differential equations one step.

### ADAMS-BASHFORTH METHOD

- ddeabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- deabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

### ADAPTIVE QUADRATURE

- dgaus8
Integrate a real function of one variable over a finite interval using an adaptive 8-point Legendre-Gauss algorithm. Intended primarily for high accuracy integration or integration of smooth functions.

- dqnc79
Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.

- gaus8
Integrate a real function of one variable over a finite interval using an adaptive 8-point Legendre-Gauss algorithm. Intended primarily for high accuracy integration or integration of smooth functions.

- qnc79
Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.

### AIRY FUNCTION

- ai
Evaluate the Airy function.

- cairy
Compute the Airy function Ai(z) or its derivative dAi/dz for complex argument z. A scaling option is available to help avoid underflow and overflow.

- cbiry
Compute the Airy function Bi(z) or its derivative dBi/dz for complex argument z. A scaling option is available to help avoid overflow.

- d9aimp
Evaluate the Airy modulus and phase.

- dai
Evaluate the Airy function.

- r9aimp
Evaluate the Airy modulus and phase.

- zairy
Compute the Airy function Ai(z) or its derivative dAi/dz for complex argument z. A scaling option is available to help avoid underflow and overflow.

- zbiry
Compute the Airy function Bi(z) or its derivative dBi/dz for complex argument z. A scaling option is available to help avoid overflow.

### ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES

- dqaws
The routine calculates an approximation result to a given definite integral I = Integral of F*W over (A,B), (where W shows a singular behaviour at the end points see parameter INTEGR). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqawse
The routine calculates an approximation result to a given definite integral I = Integral of F*W over (A,B), (where W shows a singular behaviour at the end points, see parameter INTEGR). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qaws
The routine calculates an approximation result to a given definite integral I = Integral of F*W over (A,B), (where W shows a singular behaviour at the end points see parameter INTEGR). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qawse
The routine calculates an approximation result to a given definite integral I = Integral of F*W over (A,B), (where W shows a singular behaviour at the end points, see parameter INTEGR). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

### ALGEBRAICO-LOGARITHMIC

- dqwgts
This function subprogram is used together with the routine DQAWS and defines the WEIGHT function.

- qwgts
This function subprogram is used together with the routine QAWS and defines the WEIGHT function.

### ANALYSIS OF COVARIANCE

- cv
Evaluate the variance function of the curve obtained by the constrained B-spline fitting subprogram FC.

- dcv
Evaluate the variance function of the curve obtained by the constrained B-spline fitting subprogram DFC.

### APPLICATION OF PERMUTATION TO DATA VECTOR

- hpperm
Rearrange a given array according to a prescribed permutation vector.

- ipperm
Rearrange a given array according to a prescribed permutation vector.

- spperm
Rearrange a given array according to a prescribed permutation vector.

### ARC COSINE

- cacos
Compute the complex arc cosine.

### ARC HYPERBOLIC COSINE

- acosh
Compute the arc hyperbolic cosine.

- cacosh
Compute the arc hyperbolic cosine.

- dacosh
Compute the arc hyperbolic cosine.

### ARC HYPERBOLIC SINE

- asinh
Compute the arc hyperbolic sine.

- casinh
Compute the arc hyperbolic sine.

- dasinh
Compute the arc hyperbolic sine.

### ARC HYPERBOLIC TANGENT

- atanh
Compute the arc hyperbolic tangent.

- catanh
Compute the arc hyperbolic tangent.

- datanh
Compute the arc hyperbolic tangent.

### ARC SINE

- casin
Compute the complex arc sine.

### ARC TANGENT

- catan
Compute the complex arc tangent.

- catan2
Compute the complex arc tangent in the proper quadrant.

- d9atn1
Evaluate DATAN(X) from first order relative accuracy so that DATAN(X) = X + X**3*D9ATN1(X).

- r9atn1
Evaluate ATAN(X) from first order relative accuracy so that ATAN(X) = X + X**3*R9ATN1(X).

### ARGUMENT OF A COMPLEX NUMBER

- carg
Compute the argument of a complex number.

### ASINH

- asinh
Compute the arc hyperbolic sine.

- casinh
Compute the arc hyperbolic sine.

- dasinh
Compute the arc hyperbolic sine.

### ATANH

- atanh
Compute the arc hyperbolic tangent.

- catanh
Compute the arc hyperbolic tangent.

- datanh
Compute the arc hyperbolic tangent.

### AUTOMATIC INTEGRATOR

- dgaus8
Integrate a real function of one variable over a finite interval using an adaptive 8-point Legendre-Gauss algorithm. Intended primarily for high accuracy integration or integration of smooth functions.

- dqag
The routine calculates an approximation result to a given definite integral I = integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqage
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqagi
The routine calculates an approximation result to a given INTEGRAL I = Integral of F over (BOUND,+INFINITY) OR I = Integral of F over (-INFINITY,BOUND) OR I = Integral of F over (-INFINITY,+INFINITY) Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqagie
The routine calculates an approximation result to a given integral I = Integral of F over (BOUND,+INFINITY) or I = Integral of F over (-INFINITY,BOUND) or I = Integral of F over (-INFINITY,+INFINITY), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

- dqagp
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy break points of the integration interval, where local difficulties of the integrand may occur (e.g. SINGULARITIES, DISCONTINUITIES), are provided by the user.

- dqagpe
Approximate a given definite integral I = Integral of F over (A,B), hopefully satisfying the accuracy claim: ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)). Break points of the integration interval, where local difficulties of the integrand may occur (e.g. singularities or discontinuities) are provided by the user.

- dqags
The routine calculates an approximation result to a given Definite integral I = Integral of F over (A,B), Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqagse
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqawc
The routine calculates an approximation result to a Cauchy principal value I = INTEGRAL of F*W over (A,B) (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

- dqawce
The routine calculates an approximation result to a CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B) (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

- dqawf
The routine calculates an approximation result to a given Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- dqawfe
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- dqawo
Calculate an approximation to a given definite integral I= Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqawoe
Calculate an approximation to a given definite integral I = Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqaws
The routine calculates an approximation result to a given definite integral I = Integral of F*W over (A,B), (where W shows a singular behaviour at the end points see parameter INTEGR). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqawse
The routine calculates an approximation result to a given definite integral I = Integral of F*W over (A,B), (where W shows a singular behaviour at the end points, see parameter INTEGR). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqng
The routine calculates an approximation result to a given definite integral I = integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- gaus8
- qag
The routine calculates an approximation result to a given definite integral I = integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

- qage
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qagi
The routine calculates an approximation result to a given INTEGRAL I = Integral of F over (BOUND,+INFINITY) OR I = Integral of F over (-INFINITY,BOUND) OR I = Integral of F over (-INFINITY,+INFINITY) Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qagie
The routine calculates an approximation result to a given integral I = Integral of F over (BOUND,+INFINITY) or I = Integral of F over (-INFINITY,BOUND) or I = Integral of F over (-INFINITY,+INFINITY), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

- qagp
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy break points of the integration interval, where local difficulties of the integrand may occur(e.g. SINGULARITIES, DISCONTINUITIES), are provided by the user.

- qagpe
Approximate a given definite integral I = Integral of F over (A,B), hopefully satisfying the accuracy claim: ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)). Break points of the integration interval, where local difficulties of the integrand may occur (e.g. singularities or discontinuities) are provided by the user.

- qags
The routine calculates an approximation result to a given Definite integral I = Integral of F over (A,B), Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qagse
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qawc
The routine calculates an approximation result to a Cauchy principal value I = INTEGRAL of F*W over (A,B) (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

- qawce
The routine calculates an approximation result to a CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B) (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

- qawf
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- qawfe
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- qawo
Calculate an approximation to a given definite integral I = Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qawoe
Calculate an approximation to a given definite integral I = Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qaws
- qawse
- qng
The routine calculates an approximation result to a given definite integral I = integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

### B-SPLINE

- bint4
Compute the B-representation of a cubic spline which interpolates given data.

- bintk
Compute the B-representation of a spline which interpolates given data.

- bspdoc
Documentation for BSPLINE, a package of subprograms for working with piecewise polynomial functions in B-representation.

- bspdr
Use the B-representation to construct a divided difference table preparatory to a (right) derivative calculation.

- bspev
Calculate the value of the spline and its derivatives from the B-representation.

- bsppp
Convert the B-representation of a B-spline to the piecewise polynomial (PP) form.

- cv
Evaluate the variance function of the curve obtained by the constrained B-spline fitting subprogram FC.

- dbint4
Compute the B-representation of a cubic spline which interpolates given data.

- dbintk
Compute the B-representation of a spline which interpolates given data.

- dbspdr
Use the B-representation to construct a divided difference table preparatory to a (right) derivative calculation.

- dbspev
Calculate the value of the spline and its derivatives from the B-representation.

- dbsppp
Convert the B-representation of a B-spline to the piecewise polynomial (PP) form.

- dcv
Evaluate the variance function of the curve obtained by the constrained B-spline fitting subprogram DFC.

- defc
Fit a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense.

- dfc
Fit a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. Equality and inequality constraints can be imposed on the fitted curve.

- dintrv
Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT such that XT(ILEFT) .LE. X where XT(*) is a subdivision of the X interval.

- dpfqad
Compute the integral on (X1,X2) of a product of a function F and the ID-th derivative of a B-spline, (PP-representation).

- dppqad
Compute the integral on (X1,X2) of a K-th order B-spline using the piecewise polynomial (PP) representation.

- dppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

- efc
Fit a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense.

- fc
Fit a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. Equality and inequality constraints can be imposed on the fitted curve.

- intrv
Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT such that XT(ILEFT) .LE. X where XT(*) is a subdivision of the X interval.

- pfqad
Compute the integral on (X1,X2) of a product of a function F and the ID-th derivative of a B-spline, (PP-representation).

- ppqad
Compute the integral on (X1,X2) of a K-th order B-spline using the piecewise polynomial (PP) representation.

- ppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

### B-SPLINES

- dpchbs
Piecewise Cubic Hermite to B-Spline converter.

- pchbs
Piecewise Cubic Hermite to B-Spline converter.

### BACKWARD DIFFERENTIATION FORMULAS

- ddassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

- ddebdf
Solve an initial value problem in ordinary differential equations using backward differentiation formulas. It is intended primarily for stiff problems.

- debdf
Solve an initial value problem in ordinary differential equations using backward differentiation formulas. It is intended primarily for stiff problems.

- sdassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

### BAIRY FUNCTION

- bi
Evaluate the Bairy function (the Airy function of the second kind).

- bie
Calculate the Bairy function for a negative argument and an exponentially scaled Bairy function for a non-negative argument.

- dbi
Evaluate the Bairy function (the Airy function of the second kind).

- dbie
Calculate the Bairy function for a negative argument and an exponentially scaled Bairy function for a non-negative argument.

### BANDED

- cgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- cgbdi
Compute the determinant of a complex band matrix using the factors from CGBCO or CGBFA.

- cgbfa
Factor a band matrix using Gaussian elimination.

- cgbsl
Solve the complex band system A*X=B or CTRANS(A)*X=B using the factors computed by CGBCO or CGBFA.

- cnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- cnbdi
Compute the determinant of a band matrix using the factors computed by CNBCO or CNBFA.

- cnbfa
Factor a band matrix by elimination.

- cnbfs
Solve a general nonsymmetric banded system of linear equations.

- cnbir
Solve a general nonsymmetric banded system of linear equations. Iterative refinement is used to obtain an error estimate.

- cnbsl
Solve a complex band system using the factors computed by CNBCO or CNBFA.

- cpbco
Factor a complex Hermitian positive definite matrix stored in band form and estimate the condition number of the matrix.

- cpbdi
Compute the determinant of a complex Hermitian positive definite band matrix using the factors computed by CPBCO or CPBFA.

- cpbfa
Factor a complex Hermitian positive definite matrix stored in band form.

- cpbsl
Solve the complex Hermitian positive definite band system using the factors computed by CPBCO or CPBFA.

- dgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- dgbdi
Compute the determinant of a band matrix using the factors computed by DGBCO or DGBFA.

- dgbfa
Factor a band matrix using Gaussian elimination.

- dgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by DGBCO or DGBFA.

- dnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- dnbdi
Compute the determinant of a band matrix using the factors computed by DNBCO or DNBFA.

- dnbfa
Factor a band matrix by elimination.

- dnbfs
Solve a general nonsymmetric banded system of linear equations.

- dnbsl
Solve a real band system using the factors computed by DNBCO or DNBFA.

- dpbco
Factor a real symmetric positive definite matrix stored in band form and estimate the condition number of the matrix.

- dpbdi
Compute the determinant of a symmetric positive definite band matrix using the factors computed by DPBCO or DPBFA.

- dpbfa
Factor a real symmetric positive definite matrix stored in in band form.

- dpbsl
Solve a real symmetric positive definite band system using the factors computed by DPBCO or DPBFA.

- sgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- sgbdi
Compute the determinant of a band matrix using the factors computed by SGBCO or SGBFA.

- sgbfa
Factor a band matrix using Gaussian elimination.

- sgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by SGBCO or SGBFA.

- snbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- snbdi
Compute the determinant of a band matrix using the factors computed by SNBCO or SNBFA.

- snbfa
Factor a real band matrix by elimination.

- snbfs
Solve a general nonsymmetric banded system of linear equations.

- snbir
Solve a general nonsymmetric banded system of linear equations. Iterative refinement is used to obtain an error estimate.

- snbsl
Solve a real band system using the factors computed by SNBCO or SNBFA.

- spbco
Factor a real symmetric positive definite matrix stored in band form and estimate the condition number of the matrix.

- spbdi
Compute the determinant of a symmetric positive definite band matrix using the factors computed by SPBCO or SPBFA.

- spbfa
Factor a real symmetric positive definite matrix stored in band form.

- spbsl
Solve a real symmetric positive definite band system using the factors computed by SPBCO or SPBFA.

### BANDED MATRIX

- bndacc
Compute the LU factorization of a banded matrices using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

- bndsol
Solve the least squares problem for a banded matrix using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

- dbndac
Compute the LU factorization of a banded matrices using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

- dbndsl
Solve the least squares problem for a banded matrix using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

### BASE TEN LOGARITHM

- clog10
Compute the principal value of the complex base 10 logarithm.

### BESSEL FUNCTION

- besj0
Compute the Bessel function of the first kind of order zero.

- besj1
Compute the Bessel function of the first kind of order one.

- besy0
Compute the Bessel function of the second kind of order zero.

- besy1
Compute the Bessel function of the second kind of order one.

- d9b0mp
Evaluate the modulus and phase for the J0 and Y0 Bessel functions.

- d9b1mp
Evaluate the modulus and phase for the J1 and Y1 Bessel functions.

- d9knus
Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)* K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

- dbesj0
Compute the Bessel function of the first kind of order zero.

- dbesj1
Compute the Bessel function of the first kind of order one.

- dbesy0
Compute the Bessel function of the second kind of order zero.

- dbesy1
Compute the Bessel function of the second kind of order one.

- r9knus
Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)* K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

### BESSEL FUNCTION OF ORDER ONE THIRD

- cairy
Compute the Airy function Ai(z) or its derivative dAi/dz for complex argument z. A scaling option is available to help avoid underflow and overflow.

- cbiry
Compute the Airy function Bi(z) or its derivative dBi/dz for complex argument z. A scaling option is available to help avoid overflow.

- zairy
- zbiry

### BESSEL FUNCTION OF ORDER TWO THIRDS

- cairy
- cbiry
- zairy
- zbiry

### BESSEL FUNCTIONS OF COMPLEX ARGUMENT

- cbesh
Compute a sequence of the Hankel functions H(m,a,z) for superscript m=1 or 2, real nonnegative orders a=b, b+1,... where b>0, and nonzero complex argument z. A scaling option is available to help avoid overflow.

- cbesi
Compute a sequence of the Bessel functions I(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- cbesj
Compute a sequence of the Bessel functions J(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- cbesk
Compute a sequence of the Bessel functions K(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- cbesy
Compute a sequence of the Bessel functions Y(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesh
Compute a sequence of the Hankel functions H(m,a,z) for superscript m=1 or 2, real nonnegative orders a=b, b+1,... where b>0, and nonzero complex argument z. A scaling option is available to help avoid overflow.

- zbesi
Compute a sequence of the Bessel functions I(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesj
Compute a sequence of the Bessel functions J(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesk
Compute a sequence of the Bessel functions K(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesy
Compute a sequence of the Bessel functions Y(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

### BESSEL FUNCTIONS OF SECOND KIND

- cbesy
Compute a sequence of the Bessel functions Y(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesy

### BESSEL FUNCTIONS OF THE FIRST KIND

- cbesj
Compute a sequence of the Bessel functions J(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesj

### BESSEL FUNCTIONS OF THE THIRD KIND

- cbesh
Compute a sequence of the Hankel functions H(m,a,z) for superscript m=1 or 2, real nonnegative orders a=b, b+1,... where b>0, and nonzero complex argument z. A scaling option is available to help avoid overflow.

- zbesh

### BICKLEY FUNCTIONS

- bskin
Compute repeated integrals of the K-zero Bessel function.

- dbskin
Compute repeated integrals of the K-zero Bessel function.

### BICONJUGATE GRADIENT

- dbcg
Preconditioned BiConjugate Gradient Sparse Ax = b Solver. Routine to solve a Non-Symmetric linear system Ax = b using the Preconditioned BiConjugate Gradient method.

- dcgs
Preconditioned BiConjugate Gradient Squared Ax=b Solver. Routine to solve a Non-Symmetric linear system Ax = b using the Preconditioned BiConjugate Gradient Squared method.

- sbcg
Preconditioned BiConjugate Gradient Sparse Ax = b Solver. Routine to solve a Non-Symmetric linear system Ax = b using the Preconditioned BiConjugate Gradient method.

- scgs
Preconditioned BiConjugate Gradient Squared Ax=b Solver. Routine to solve a Non-Symmetric linear system Ax = b using the Preconditioned BiConjugate Gradient Squared method.

### BICONJUGATE GRADIENT SQUARED

- dlpdoc
Sparse Linear Algebra Package Version 2.0.2 Documentation. Routines to solve large sparse symmetric and nonsymmetric positive definite linear systems, Ax = b, using precondi- tioned iterative methods.

- slpdoc
Sparse Linear Algebra Package Version 2.0.2 Documentation. Routines to solve large sparse symmetric and nonsymmetric positive definite linear systems, Ax = b, using precondi- tioned iterative methods.

### BINOMIAL COEFFICIENTS

### BISECTION

- dfzero
Search for a zero of a function F(X) in a given interval (B,C). It is designed primarily for problems where F(B) and F(C) have opposite signs.

- fzero
Search for a zero of a function F(X) in a given interval (B,C). It is designed primarily for problems where F(B) and F(C) have opposite signs.

### BLAS

- caxpy
Compute a constant times a vector plus a vector.

- ccopy
Copy a vector.

- cdcdot
Compute the inner product of two vectors with extended precision accumulation.

- cdotc
Dot product of two complex vectors using the complex conjugate of the first vector.

- cdotu
Compute the inner product of two vectors.

- crotg
Construct a Givens transformation.

- cscal
Multiply a vector by a constant.

- csrot
Apply a plane Givens rotation.

- csscal
Scale a complex vector.

- cswap
Interchange two vectors.

- dasum
Compute the sum of the magnitudes of the elements of a vector.

- daxpy
Compute a constant times a vector plus a vector.

- dcdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dcopy
Copy a vector.

- dcopym
Copy the negative of a vector to a vector.

- ddot
Compute the inner product of two vectors.

- dnrm2
Compute the Euclidean length (L2 norm) of a vector.

- drot
Apply a plane Givens rotation.

- drotg
Construct a plane Givens rotation.

- drotm
Apply a modified Givens transformation.

- drotmg
Construct a modified Givens transformation.

- dscal
Multiply a vector by a constant.

- dsdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dswap
Interchange two vectors.

- icamax
Find the smallest index of the component of a complex vector having the maximum sum of magnitudes of real and imaginary parts.

- icopy
Copy a vector.

- idamax
Find the smallest index of that component of a vector having the maximum magnitude.

- isamax
Find the smallest index of that component of a vector having the maximum magnitude.

- iswap
Interchange two vectors.

- sasum
Compute the sum of the magnitudes of the elements of a vector.

- saxpy
Compute a constant times a vector plus a vector.

- scasum
Compute the sum of the magnitudes of the real and imaginary elements of a complex vector.

- scnrm2
Compute the unitary norm of a complex vector.

- scopy
Copy a vector.

- scopym
Copy the negative of a vector to a vector.

- sdot
Compute the inner product of two vectors.

- sdsdot
Compute the inner product of two vectors with extended precision accumulation.

- snrm2
Compute the Euclidean length (L2 norm) of a vector.

- srot
Apply a plane Givens rotation.

- srotg
Construct a plane Givens rotation.

- srotm
Apply a modified Givens transformation.

- srotmg
Construct a modified Givens transformation.

- sscal
Multiply a vector by a constant.

- sswap
Interchange two vectors.

### BOUNDS

- dbocls
Solve the bounded and constrained least squares problem consisting of solving the equation E*X = F (in the least squares sense) subject to the linear constraints C*X = Y.

- dbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

- sbocls
Solve the bounded and constrained least squares problem consisting of solving the equation E*X = F (in the least squares sense) subject to the linear constraints C*X = Y.

- sbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

### BROWN'S METHOD

- dsos
Solve a square system of nonlinear equations.

- sos
Solve a square system of nonlinear equations.

### CARTESIAN

- hw3crt
Solve the standard seven-point finite difference approximation to the Helmholtz equation in Cartesian coordinates.

- hwscrt
Solves the standard five-point finite difference approximation to the Helmholtz equation in Cartesian coordinates.

### CAUCHY PRINCIPAL VALUE

- dqawc
The routine calculates an approximation result to a Cauchy principal value I = INTEGRAL of F*W over (A,B) (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

- dqawce
The routine calculates an approximation result to a CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B) (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

- dqwgtc
This function subprogram is used together with the routine DQAWC and defines the WEIGHT function.

- qawc
- qawce
- qwgtc
This function subprogram is used together with the routine QAWC and defines the WEIGHT function.

### CHARACTER COMPARISON

- lsame
Test two characters to determine if they are the same letter, except for case.

### CHEBYSHEV

- initds
Determine the number of terms needed in an orthogonal polynomial series so that it meets a specified accuracy.

- inits
Determine the number of terms needed in an orthogonal polynomial series so that it meets a specified accuracy.

### CHEBYSHEV SERIES

### CHEBYSHEV SERIES EXPANSION

- dqcheb
This routine computes the CHEBYSHEV series expansion of degrees 12 and 24 of a function using A FAST FOURIER TRANSFORM METHOD F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)), F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)), Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

- qcheb
This routine computes the CHEBYSHEV series expansion of degrees 12 and 24 of a function using A FAST FOURIER TRANSFORM METHOD F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)), F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)), Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

### CHOLESKY DECOMPOSITION

- cchdc
Compute the Cholesky decomposition of a positive definite matrix. A pivoting option allows the user to estimate the condition number of a positive definite matrix or determine the rank of a positive semidefinite matrix.

- cchdd
Downdate an augmented Cholesky decomposition or the triangular factor of an augmented QR decomposition.

- cchex
Update the Cholesky factorization A=TRANS(R)*R of a positive definite matrix A of order P under diagonal permutations of the form TRANS(E)*A*E, where E is a permutation matrix.

- cchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- dchdc
Compute the Cholesky decomposition of a positive definite matrix. A pivoting option allows the user to estimate the condition number of a positive definite matrix or determine the rank of a positive semidefinite matrix.

- dchdd
Downdate an augmented Cholesky decomposition or the triangular factor of an augmented QR decomposition.

- dchex
Update the Cholesky factorization A=TRANS(R)*R of a positive definite matrix A of order P under diagonal permutations of the form TRANS(E)*A*E, where E is a permutation matrix.

- dchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- schdc
Compute the Cholesky decomposition of a positive definite matrix. A pivoting option allows the user to estimate the condition number of a positive definite matrix or determine the rank of a positive semidefinite matrix.

- schdd
Downdate an augmented Cholesky decomposition or the triangular factor of an augmented QR decomposition.

- schex
Update the Cholesky factorization A=TRANS(R)*R of A positive definite matrix A of order P under diagonal permutations of the form TRANS(E)*A*E, where E is a permutation matrix.

- schud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

### CLEBSCH-GORDAN COEFFICIENTS

- drc3jj
- drc3jm
- drc6j
- rc3jj
- rc3jm
- rc6j

### CLENSHAW-CURTIS METHOD

- dqawc
- dqawce
- dqawo
Calculate an approximation to a given definite integral I= Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqawoe
Calculate an approximation to a given definite integral I = Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqaws
- dqawse
- dqc25f
To compute the integral I=Integral of F(X) over (A,B) Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to compute J = Integral of ABS(F) over (A,B). For small value of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO Rule is used. Otherwise a generalized CLENSHAW-CURTIS method is used.

- qawc
- qawce
- qawo
Calculate an approximation to a given definite integral I = Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qawoe
- qaws
- qawse
- qc25f
To compute the integral I=Integral of F(X) over (A,B) Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X) and to compute J=Integral of ABS(F) over (A,B). For small value of OMEGA or small intervals (A,B) 15-point GAUSS- KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

### COEFFICIENTS

- dpolcf
Compute the coefficients of the polynomial fit (including Hermite polynomial fits) produced by a previous call to POLINT.

- polcof
Compute the coefficients of the polynomial fit (including Hermite polynomial fits) produced by a previous call to POLINT.

### COMPLEMENTARY ERROR FUNCTION

### COMPLEMENTARY INCOMPLETE GAMMA FUNCTION

- d9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and X small.

- d9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- d9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- dgamic
Calculate the complementary incomplete Gamma function.

- dgamit
Calculate Tricomi's form of the incomplete Gamma function.

- gamic
Calculate the complementary incomplete Gamma function.

- gamit
Calculate Tricomi's form of the incomplete Gamma function.

- r9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and for small X.

- r9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- r9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

### COMPLETE BETA FUNCTION

- beta
Compute the complete Beta function.

- cbeta
Compute the complete Beta function.

- dbeta
Compute the complete Beta function.

### COMPLETE ELLIPTIC INTEGRAL

- drd
Compute the incomplete or complete elliptic integral of the 2nd kind. For X and Y nonnegative, X+Y and Z positive, DRD(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -3/2 (3/2)(t+X) (t+Y) (t+Z) dt. If X or Y is zero, the integral is complete.

- drf
Compute the incomplete or complete elliptic integral of the 1st kind. For X, Y, and Z non-negative and at most one of them zero, RF(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -1/2 (1/2)(t+X) (t+Y) (t+Z) dt. If X, Y or Z is zero, the integral is complete.

- drj
Compute the incomplete or complete (X or Y or Z is zero) elliptic integral of the 3rd kind. For X, Y, and Z non- negative, at most one of them zero, and P positive, RJ(X,Y,Z,P) = Integral from zero to infinity of -1/2 -1/2 -1/2 -1 (3/2)(t+X) (t+Y) (t+Z) (t+P) dt.

- rd
Compute the incomplete or complete elliptic integral of the 2nd kind. For X and Y nonnegative, X+Y and Z positive, RD(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -3/2 (3/2)(t+X) (t+Y) (t+Z) dt. If X or Y is zero, the integral is complete.

- rf
Compute the incomplete or complete elliptic integral of the 1st kind. For X, Y, and Z non-negative and at most one of them zero, RF(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -1/2 (1/2)(t+X) (t+Y) (t+Z) dt. If X, Y or Z is zero, the integral is complete.

- rj
Compute the incomplete or complete (X or Y or Z is zero) elliptic integral of the 3rd kind. For X, Y, and Z non- negative, at most one of them zero, and P positive, RJ(X,Y,Z,P) = Integral from zero to infinity of -1/2 -1/2 -1/2 -1 (3/2)(t+X) (t+Y) (t+Z) (t+P) dt.

### COMPLETE GAMMA FUNCTION

- alngam
Compute the logarithm of the absolute value of the Gamma function.

- c9lgmc
Compute the log gamma correction factor so that LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z + C9LGMC(Z).

- cgamma
Compute the complete Gamma function.

- clngam
Compute the logarithm of the absolute value of the Gamma function.

- d9lgmc
Compute the log Gamma correction factor so that LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X + D9LGMC(X).

- dgamlm
Compute the minimum and maximum bounds for the argument in the Gamma function.

- dgamma
Compute the complete Gamma function.

- dlngam
Compute the logarithm of the absolute value of the Gamma function.

- gamlim
Compute the minimum and maximum bounds for the argument in the Gamma function.

- gamma
Compute the complete Gamma function.

- r9lgmc
Compute the log Gamma correction factor so that LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X + R9LGMC(X).

### COMPLEX HERMITIAN

- chiev
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- ssiev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

### COMPLEX LINEAR EQUATIONS

- cgefs
Solve a general system of linear equations.

- cgeir
Solve a general system of linear equations. Iterative refinement is used to obtain an error estimate.

- dgefs
Solve a general system of linear equations.

- sgefs
Solve a general system of linear equations.

- sgeir
Solve a general system of linear equations. Iterative refinement is used to obtain an error estimate.

### COMPLEX POLYNOMIAL

- cpqr79
Find the zeros of a polynomial with complex coefficients.

- rpqr79
Find the zeros of a polynomial with real coefficients.

### COMPLEX VALUED

- cdriv1
The function of CDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. CDRIV1 allows complex-valued differential equations.

- cdriv2
The function of CDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. CDRIV2 allows complex-valued differential equations.

- cdriv3
The function of CDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. CDRIV3 allows complex-valued differential equations.

### COMPLEX VECTORS

- dcdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dsdot
Compute the inner product of two vectors with extended precision accumulation and result.

### CONDITION NUMBER

- cgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- cgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- chico
Factor a complex Hermitian matrix by elimination with sym- metric pivoting and estimate the condition of the matrix.

- chpco
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- cpbco
Factor a complex Hermitian positive definite matrix stored in band form and estimate the condition number of the matrix.

- cpoco
Factor a complex Hermitian positive definite matrix and estimate the condition number of the matrix.

- cppco
Factor a complex Hermitian positive definite matrix stored in packed form and estimate the condition number of the matrix.

- csico
Factor a complex symmetric matrix by elimination with symmetric pivoting and estimate the condition number of the matrix.

- cspco
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- ctrco
Estimate the condition number of a triangular matrix.

- dgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- dgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- dpbco
Factor a real symmetric positive definite matrix stored in band form and estimate the condition number of the matrix.

- dpoco
Factor a real symmetric positive definite matrix and estimate the condition of the matrix.

- dppco
Factor a symmetric positive definite matrix stored in packed form and estimate the condition number of the matrix.

- dsico
Factor a symmetric matrix by elimination with symmetric pivoting and estimate the condition number of the matrix.

- dspco
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- dtrco
Estimate the condition number of a triangular matrix.

- sgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- sgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- spbco
- spoco
Factor a real symmetric positive definite matrix and estimate the condition number of the matrix.

- sppco
Factor a symmetric positive definite matrix stored in packed form and estimate the condition number of the matrix.

- ssico
Factor a symmetric matrix by elimination with symmetric pivoting and estimate the condition number of the matrix.

- sspco
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- strco
Estimate the condition number of a triangular matrix.

### CONSTRAINED LEAST SQUARES

- cv
Evaluate the variance function of the curve obtained by the constrained B-spline fitting subprogram FC.

- dcv
Evaluate the variance function of the curve obtained by the constrained B-spline fitting subprogram DFC.

- defc
Fit a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense.

- dfc
Fit a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. Equality and inequality constraints can be imposed on the fitted curve.

- dlsei
Solve a linearly constrained least squares problem with equality and inequality constraints, and optionally compute a covariance matrix.

- dwnnls
Solve a linearly constrained least squares problem with equality constraints and nonnegativity constraints on selected variables.

- fc
- lsei
Solve a linearly constrained least squares problem with equality and inequality constraints, and optionally compute a covariance matrix.

- wnnls
Solve a linearly constrained least squares problem with equality constraints and nonnegativity constraints on selected variables.

### CONSTRAINTS

- dbocls
Solve the bounded and constrained least squares problem consisting of solving the equation E*X = F (in the least squares sense) subject to the linear constraints C*X = Y.

- dbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

- sbocls
- sbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

### CONVERGENCE ACCELERATION

- dqawf
The routine calculates an approximation result to a given Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- dqawfe
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- dqelg
The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P.Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved.

- qawf
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- qawfe
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- qelg
The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P. Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved.

### CONVERSION

- dpchbs
Piecewise Cubic Hermite to B-Spline converter.

- pchbs
Piecewise Cubic Hermite to B-Spline converter.

### COPY

- ccopy
Copy a vector.

- dcopy
Copy a vector.

- dcopym
Copy the negative of a vector to a vector.

- icopy
Copy a vector.

- scopy
Copy a vector.

- scopym
Copy the negative of a vector to a vector.

### CORRECTION TERM

- c9lgmc
Compute the log gamma correction factor so that LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z + C9LGMC(Z).

- d9lgmc
Compute the log Gamma correction factor so that LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X + D9LGMC(X).

- r9lgmc
Compute the log Gamma correction factor so that LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X + R9LGMC(X).

### COS OR SIN IN WEIGHT FUNCTION

- dqwgtf
This function subprogram is used together with the routine DQAWF and defines the WEIGHT function.

- qwgtf
This function subprogram is used together with the routine QAWF and defines the WEIGHT function.

### COSINE

- cosdg
Compute the cosine of an argument in degrees.

- dcosdg
Compute the cosine of an argument in degrees.

### COSINE FOURIER TRANSFORM

- cosqf
Compute the forward cosine transform with odd wave numbers.

- cosqi
Initialize a work array for COSQF and COSQB.

- cost
Compute the cosine transform of a real, even sequence.

- costi
Initialize a work array for COST.

### COTANGENT

### COVARIANCE MATRIX

- dcov
Calculate the covariance matrix for a nonlinear data fitting problem. It is intended to be used after a successful return from either DNLS1 or DNLS1E.

- scov
Calculate the covariance matrix for a nonlinear data fitting problem. It is intended to be used after a successful return from either SNLS1 or SNLS1E.

### CUBE ROOT

### CUBIC HERMITE DIFFERENTIATION

- chfdv
Evaluate a cubic polynomial given in Hermite form and its first derivative at an array of points. While designed for use by PCHFD, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. If only function values are required, use CHFEV instead.

- dchfdv
Evaluate a cubic polynomial given in Hermite form and its first derivative at an array of points. While designed for use by DPCHFD, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. If only function values are required, use DCHFEV instead.

- dpchfd
Evaluate a piecewise cubic Hermite function and its first derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC. If only function values are required, use DPCHFE instead.

- pchfd
Evaluate a piecewise cubic Hermite function and its first derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC. If only function values are required, use PCHFE instead.

### CUBIC HERMITE EVALUATION

- chfdv
Evaluate a cubic polynomial given in Hermite form and its first derivative at an array of points. While designed for use by PCHFD, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. If only function values are required, use CHFEV instead.

- chfev
Evaluate a cubic polynomial given in Hermite form at an array of points. While designed for use by PCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.

- dchfdv
Evaluate a cubic polynomial given in Hermite form and its first derivative at an array of points. While designed for use by DPCHFD, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. If only function values are required, use DCHFEV instead.

- dchfev
Evaluate a cubic polynomial given in Hermite form at an array of points. While designed for use by DPCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.

- dpchfd
Evaluate a piecewise cubic Hermite function and its first derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC. If only function values are required, use DPCHFE instead.

- dpchfe
Evaluate a piecewise cubic Hermite function at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC.

- pchfd
Evaluate a piecewise cubic Hermite function and its first derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC. If only function values are required, use PCHFE instead.

- pchfe
Evaluate a piecewise cubic Hermite function at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC.

### CUBIC HERMITE INTERPOLATION

- dpchbs
Piecewise Cubic Hermite to B-Spline converter.

- dpchcm
Check a cubic Hermite function for monotonicity.

- dpchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- dpchic
Set derivatives needed to determine a piecewise monotone piecewise cubic Hermite interpolant to given data. User control is available over boundary conditions and/or treatment of points where monotonicity switches direction.

- dpchid
Evaluate the definite integral of a piecewise cubic Hermite function over an interval whose endpoints are data points.

- dpchim
Set derivatives needed to determine a monotone piecewise cubic Hermite interpolant to given data. Boundary values are provided which are compatible with monotonicity. The interpolant will have an extremum at each point where mono- tonicity switches direction. (See DPCHIC if user control is desired over boundary or switch conditions.)

- dpchsp
Set derivatives needed to determine the Hermite represen- tation of the cubic spline interpolant to given data, with specified boundary conditions.

- pchbs
Piecewise Cubic Hermite to B-Spline converter.

- pchcm
Check a cubic Hermite function for monotonicity.

- pchdoc
Documentation for PCHIP, a Fortran package for piecewise cubic Hermite interpolation of data.

- pchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- pchic
Set derivatives needed to determine a piecewise monotone piecewise cubic Hermite interpolant to given data. User control is available over boundary conditions and/or treatment of points where monotonicity switches direction.

- pchid
Evaluate the definite integral of a piecewise cubic Hermite function over an interval whose endpoints are data points.

- pchim
Set derivatives needed to determine a monotone piecewise cubic Hermite interpolant to given data. Boundary values are provided which are compatible with monotonicity. The interpolant will have an extremum at each point where mono- tonicity switches direction. (See PCHIC if user control is desired over boundary or switch conditions.)

- pchsp
Set derivatives needed to determine the Hermite represen- tation of the cubic spline interpolant to given data, with specified boundary conditions.

### CUBIC POLYNOMIAL EVALUATION

- chfdv
Evaluate a cubic polynomial given in Hermite form and its first derivative at an array of points. While designed for use by PCHFD, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. If only function values are required, use CHFEV instead.

- chfev
Evaluate a cubic polynomial given in Hermite form at an array of points. While designed for use by PCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.

- dchfdv
Evaluate a cubic polynomial given in Hermite form and its first derivative at an array of points. While designed for use by DPCHFD, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. If only function values are required, use DCHFEV instead.

- dchfev
Evaluate a cubic polynomial given in Hermite form at an array of points. While designed for use by DPCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.

### CUBIC SPLINES

- bint4
Compute the B-representation of a cubic spline which interpolates given data.

- dbint4
Compute the B-representation of a cubic spline which interpolates given data.

### CURVE FITTING

- bndacc
Compute the LU factorization of a banded matrices using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

- bndsol
Solve the least squares problem for a banded matrix using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

- cv
- dbndac
- dbndsl
- dcv
- defc
- dfc
- dhfti
Solve a least squares problem for banded matrices using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

- dlsei
Solve a linearly constrained least squares problem with equality and inequality constraints, and optionally compute a covariance matrix.

- dp1vlu
Use the coefficients generated by DPOLFT to evaluate the polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.

- dpcoef
Convert the DPOLFT coefficients to Taylor series form.

- dpolft
Fit discrete data in a least squares sense by polynomials in one variable.

- dwnnls
Solve a linearly constrained least squares problem with equality constraints and nonnegativity constraints on selected variables.

- efc
- fc
- hfti
Solve a linear least squares problems by performing a QR factorization of the matrix using Householder transformations.

- lsei
- pcoef
Convert the POLFIT coefficients to Taylor series form.

- polfit
Fit discrete data in a least squares sense by polynomials in one variable.

- pvalue
Use the coefficients generated by POLFIT to evaluate the polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.

- wnnls

### CYCLIC REDUCTION

- cmgnbn
Solve a complex block tridiagonal linear system of equations by a cyclic reduction algorithm.

### CYLINDRICAL

- hstcyl
Solve the standard five-point finite difference approximation on a staggered grid to the modified Helmholtz equation in cylindrical coordinates.

- hwscyl
Solve a standard finite difference approximation to the Helmholtz equation in cylindrical coordinates.

### DASSL

- ddassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

- sdassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

### DATA FITTING

- bint4
Compute the B-representation of a cubic spline which interpolates given data.

- bintk
Compute the B-representation of a spline which interpolates given data.

- bspdr
Use the B-representation to construct a divided difference table preparatory to a (right) derivative calculation.

- bspev
Calculate the value of the spline and its derivatives from the B-representation.

- dbint4
Compute the B-representation of a cubic spline which interpolates given data.

- dbintk
Compute the B-representation of a spline which interpolates given data.

- dbspdr
- dbspev
Calculate the value of the spline and its derivatives from the B-representation.

- dintrv
Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT such that XT(ILEFT) .LE. X where XT(*) is a subdivision of the X interval.

- dlsei
- dpcoef
Convert the DPOLFT coefficients to Taylor series form.

- dpfqad
Compute the integral on (X1,X2) of a product of a function F and the ID-th derivative of a B-spline, (PP-representation).

- dpolft
Fit discrete data in a least squares sense by polynomials in one variable.

- dppqad
Compute the integral on (X1,X2) of a K-th order B-spline using the piecewise polynomial (PP) representation.

- dppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

- dwnnls
- intrv
- lsei
- pcoef
Convert the POLFIT coefficients to Taylor series form.

- pfqad
- polfit
Fit discrete data in a least squares sense by polynomials in one variable.

- ppqad
- ppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

- wnnls

### DAWSON'S FUNCTION

### DEGREES

- cosdg
Compute the cosine of an argument in degrees.

- dcosdg
Compute the cosine of an argument in degrees.

- dsindg
Compute the sine of an argument in degrees.

- sindg
Compute the sine of an argument in degrees.

### DEPAC

- ddeabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- ddebdf
Solve an initial value problem in ordinary differential equations using backward differentiation formulas. It is intended primarily for stiff problems.

- dderkf
Solve an initial value problem in ordinary differential equations using a Runge-Kutta-Fehlberg scheme.

- deabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- debdf
- derkf
Solve an initial value problem in ordinary differential equations using a Runge-Kutta-Fehlberg scheme.

- dintp
Approximate the solution at XOUT by evaluating the polynomial computed in DSTEPS at XOUT. Must be used in conjunction with DSTEPS.

- dsteps
Integrate a system of first order ordinary differential equations one step.

- sintrp
Approximate the solution at XOUT by evaluating the polynomial computed in STEPS at XOUT. Must be used in conjunction with STEPS.

- steps
Integrate a system of first order ordinary differential equations one step.

### DERIVATIVES OF THE GAMMA FUNCTION

### DETERMINANT

- cgbdi
Compute the determinant of a complex band matrix using the factors from CGBCO or CGBFA.

- cgedi
Compute the determinant and inverse of a matrix using the factors computed by CGECO or CGEFA.

- chidi
Compute the determinant, inertia and inverse of a complex Hermitian matrix using the factors obtained from CHIFA.

- chpdi
Compute the determinant, inertia and inverse of a complex Hermitian matrix stored in packed form using the factors obtained from CHPFA.

- cnbdi
Compute the determinant of a band matrix using the factors computed by CNBCO or CNBFA.

- cpbdi
Compute the determinant of a complex Hermitian positive definite band matrix using the factors computed by CPBCO or CPBFA.

- cpodi
Compute the determinant and inverse of a certain complex Hermitian positive definite matrix using the factors computed by CPOCO, CPOFA, or CQRDC.

- cppdi
Compute the determinant and inverse of a complex Hermitian positive definite matrix using factors from CPPCO or CPPFA.

- csidi
Compute the determinant and inverse of a complex symmetric matrix using the factors from CSIFA.

- cspdi
Compute the determinant and inverse of a complex symmetric matrix stored in packed form using the factors from CSPFA.

- ctrdi
Compute the determinant and inverse of a triangular matrix.

- dgbdi
Compute the determinant of a band matrix using the factors computed by DGBCO or DGBFA.

- dgedi
Compute the determinant and inverse of a matrix using the factors computed by DGECO or DGEFA.

- dnbdi
Compute the determinant of a band matrix using the factors computed by DNBCO or DNBFA.

- dpbdi
Compute the determinant of a symmetric positive definite band matrix using the factors computed by DPBCO or DPBFA.

- dpodi
Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by DPOCO, DPOFA or DQRDC.

- dppdi
Compute the determinant and inverse of a real symmetric positive definite matrix using factors from DPPCO or DPPFA.

- dsidi
Compute the determinant, inertia and inverse of a real symmetric matrix using the factors from DSIFA.

- dspdi
Compute the determinant, inertia, inverse of a real symmetric matrix stored in packed form using the factors from DSPFA.

- dtrdi
Compute the determinant and inverse of a triangular matrix.

- sgbdi
Compute the determinant of a band matrix using the factors computed by SGBCO or SGBFA.

- sgedi
Compute the determinant and inverse of a matrix using the factors computed by SGECO or SGEFA.

- snbdi
Compute the determinant of a band matrix using the factors computed by SNBCO or SNBFA.

- spbdi
Compute the determinant of a symmetric positive definite band matrix using the factors computed by SPBCO or SPBFA.

- spodi
Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by SPOCO, SPOFA or SQRDC.

- sppdi
Compute the determinant and inverse of a real symmetric positive definite matrix using factors from SPPCO or SPPFA.

- ssidi
Compute the determinant, inertia and inverse of a real symmetric matrix using the factors from SSIFA.

- sspdi
Compute the determinant, inertia, inverse of a real symmetric matrix stored in packed form using the factors from SSPFA.

- strdi
Compute the determinant and inverse of a triangular matrix.

### DIAGNOSTICS

- dcpplt
Printer Plot of SLAP Column Format Matrix. Routine to print out a SLAP Column format matrix in a "printer plot" graphical representation.

- dtin
Read in SLAP Triad Format Linear System. Routine to read in a SLAP Triad format matrix and right hand side and solution to the system, if known.

- dtout
Write out SLAP Triad Format Linear System. Routine to write out a SLAP Triad format matrix and right hand side and solution to the system, if known.

- scpplt
Printer Plot of SLAP Column Format Matrix. Routine to print out a SLAP Column format matrix in a "printer plot" graphical representation.

- stin
Read in SLAP Triad Format Linear System. Routine to read in a SLAP Triad format matrix and right hand side and solution to the system, if known.

- stout
Write out SLAP Triad Format Linear System. Routine to write out a SLAP Triad format matrix and right hand side and solution to the system, if known.

### DIAGONAL

- dsd2s
Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up. Routine to compute the inverse of the diagonal of the matrix A*A', where A is stored in SLAP-Column format.

- dsds
Diagonal Scaling Preconditioner SLAP Set Up. Routine to compute the inverse of the diagonal of a matrix stored in the SLAP Column format.

- dsdscl
Diagonal Scaling of system Ax = b. This routine scales (and unscales) the system Ax = b by symmetric diagonal scaling.

- ssd2s
Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up. Routine to compute the inverse of the diagonal of the matrix A*A', where A is stored in SLAP-Column format.

- ssds
Diagonal Scaling Preconditioner SLAP Set Up. Routine to compute the inverse of the diagonal of a matrix stored in the SLAP Column format.

- ssdscl
Diagonal Scaling of system Ax = b. This routine scales (and unscales) the system Ax = b by symmetric diagonal scaling.

### DIFFERENTIAL/ALGEBRAIC

- ddassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

- sdassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

### DIFFERENTIATION OF B-SPLINE

- bspvd
Calculate the value and all derivatives of order less than NDERIV of all basis functions which do not vanish at X.

- bvalu
Evaluate the B-representation of a B-spline at X for the function value or any of its derivatives.

- dbspvd
Calculate the value and all derivatives of order less than NDERIV of all basis functions which do not vanish at X.

- dbvalu
Evaluate the B-representation of a B-spline at X for the function value or any of its derivatives.

### DIFFERENTIATION OF SPLINES

- bspdr
- dbspdr

### DIGAMMA FUNCTION

- cpsi
Compute the Psi (or Digamma) function.

- dpsi
Compute the Psi (or Digamma) function.

- psi
Compute the Psi (or Digamma) function.

### DISCLAIMER

- aaaaaa
SLATEC Common Mathematical Library disclaimer and version.

### DOCUMENTATION

- aaaaaa
SLATEC Common Mathematical Library disclaimer and version.

- bspdoc
Documentation for BSPLINE, a package of subprograms for working with piecewise polynomial functions in B-representation.

- dlpdoc
Sparse Linear Algebra Package Version 2.0.2 Documentation. Routines to solve large sparse symmetric and nonsymmetric positive definite linear systems, Ax = b, using precondi- tioned iterative methods.

- fftdoc
Documentation for FFTPACK, a collection of Fast Fourier Transform routines.

- fundoc
Documentation for FNLIB, a collection of routines for evaluating elementary and special functions.

- pchdoc
Documentation for PCHIP, a Fortran package for piecewise cubic Hermite interpolation of data.

- qpdoc
Documentation for QUADPACK, a package of subprograms for automatic evaluation of one-dimensional definite integrals.

- slpdoc

### DOT PRODUCT

- cdcdot
Compute the inner product of two vectors with extended precision accumulation.

- dcdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dqdota
Compute the inner product of two vectors with extended precision accumulation and result.

- dqdoti
Compute the inner product of two vectors with extended precision accumulation and result.

- dsdot
Compute the inner product of two vectors with extended precision accumulation and result.

- sdsdot
Compute the inner product of two vectors with extended precision accumulation.

### DOUBLE PRECISION

- ddriv1
The function of DDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. DDRIV1 uses double precision arithmetic.

- ddriv2
The function of DDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. DDRIV2 uses double precision arithmetic.

- ddriv3
The function of DDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. DDRIV3 uses double precision arithmetic.

### DOWNDATE

- cchdd
- dchdd
- schdd

### DUPLICATION THEOREM

- drc
Calculate a double precision approximation to DRC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.

- drd
Compute the incomplete or complete elliptic integral of the 2nd kind. For X and Y nonnegative, X+Y and Z positive, DRD(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -3/2 (3/2)(t+X) (t+Y) (t+Z) dt. If X or Y is zero, the integral is complete.

- drf
Compute the incomplete or complete elliptic integral of the 1st kind. For X, Y, and Z non-negative and at most one of them zero, RF(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -1/2 (1/2)(t+X) (t+Y) (t+Z) dt. If X, Y or Z is zero, the integral is complete.

- drj
Compute the incomplete or complete (X or Y or Z is zero) elliptic integral of the 3rd kind. For X, Y, and Z non- negative, at most one of them zero, and P positive, RJ(X,Y,Z,P) = Integral from zero to infinity of -1/2 -1/2 -1/2 -1 (3/2)(t+X) (t+Y) (t+Z) (t+P) dt.

- rc
Calculate an approximation to RC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.

- rd
Compute the incomplete or complete elliptic integral of the 2nd kind. For X and Y nonnegative, X+Y and Z positive, RD(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -3/2 (3/2)(t+X) (t+Y) (t+Z) dt. If X or Y is zero, the integral is complete.

- rf
- rj

### E1 FUNCTION

### EASY-TO-USE

- dnls1e
An easy-to-use code which minimizes the sum of the squares of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm.

- dnsqe
An easy-to-use code to find a zero of a system of N nonlinear functions in N variables by a modification of the Powell hybrid method.

- snls1e
An easy-to-use code which minimizes the sum of the squares of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm.

- snsqe
An easy-to-use code to find a zero of a system of N nonlinear functions in N variables by a modification of the Powell hybrid method.

### EI FUNCTION

### EIGENVALUES

- bandr
Reduce a real symmetric band matrix to symmetric tridiagonal matrix and, optionally, accumulate orthogonal similarity transformations.

- bisect
Compute the eigenvalues of a symmetric tridiagonal matrix in a given interval using Sturm sequencing.

- bqr
Compute some of the eigenvalues of a real symmetric matrix using the QR method with shifts of origin.

- cg
Compute the eigenvalues and, optionally, the eigenvectors of a complex general matrix.

- ch
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- cgeev
Compute the eigenvalues and, optionally, the eigenvectors of a complex general matrix.

- chiev
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- cinvit
Compute the eigenvectors of a complex upper Hessenberg associated with specified eigenvalues using inverse iteration.

- combak
Form the eigenvectors of a complex general matrix from the eigenvectors of a upper Hessenberg matrix output from COMHES.

- comhes
Reduce a complex general matrix to complex upper Hessenberg form using stabilized elementary similarity transformations.

- comlr
Compute the eigenvalues of a complex upper Hessenberg matrix using the modified LR method.

- comlr2
Compute the eigenvalues and eigenvectors of a complex upper Hessenberg matrix using the modified LR method.

- comqr
Compute the eigenvalues of complex upper Hessenberg matrix using the QR method.

- comqr2
Compute the eigenvalues and eigenvectors of a complex upper Hessenberg matrix.

- cortb
Form the eigenvectors of a complex general matrix from eigenvectors of upper Hessenberg matrix output from CORTH.

- corth
Reduce a complex general matrix to complex upper Hessenberg form using unitary similarity transformations.

- eisdoc
Documentation for EISPACK, a collection of subprograms for solving matrix eigen-problems.

- elmbak
Form the eigenvectors of a real general matrix from the eigenvectors of the upper Hessenberg matrix output from ELMHES.

- elmhes
Reduce a real general matrix to upper Hessenberg form using stabilized elementary similarity transformations.

- eltran
Accumulates the stabilized elementary similarity transformations used in the reduction of a real general matrix to upper Hessenberg form by ELMHES.

- figi
Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

- figi2
Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

- hqr
Compute the eigenvalues of a real upper Hessenberg matrix using the QR method.

- hqr2
Compute the eigenvalues and eigenvectors of a real upper Hessenberg matrix using QR method.

- htrib3
Compute the eigenvectors of a complex Hermitian matrix from the eigenvectors of a real symmetric tridiagonal matrix output from HTRID3.

- htribk
Form the eigenvectors of a complex Hermitian matrix from the eigenvectors of a real symmetric tridiagonal matrix output from HTRIDI.

- htrid3
Reduce a complex Hermitian (packed) matrix to a real symmetric tridiagonal matrix by unitary similarity transformations.

- htridi
Reduce a complex Hermitian matrix to a real symmetric tridiagonal matrix using unitary similarity transformations.

- imtql1
Compute the eigenvalues of a symmetric tridiagonal matrix using the implicit QL method.

- imtql2
Compute the eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the implicit QL method.

- imtqlv
Compute the eigenvalues of a symmetric tridiagonal matrix using the implicit QL method. Eigenvectors may be computed later.

- invit
Compute the eigenvectors of a real upper Hessenberg matrix associated with specified eigenvalues by inverse iteration.

- minfit
Compute the singular value decomposition of a rectangular matrix and solve the related linear least squares problem.

- ortbak
Form the eigenvectors of a general real matrix from the eigenvectors of the upper Hessenberg matrix output from ORTHES.

- orthes
Reduce a real general matrix to upper Hessenberg form using orthogonal similarity transformations.

- ortran
Accumulate orthogonal similarity transformations in the reduction of real general matrix by ORTHES.

- qzhes
The first step of the QZ algorithm for solving generalized matrix eigenproblems. Accepts a pair of real general matrices and reduces one of them to upper Hessenberg and the other to upper triangular form using orthogonal transformations. Usually followed by QZIT, QZVAL, QZVEC.

- qzit
The second step of the QZ algorithm for generalized eigenproblems. Accepts an upper Hessenberg and an upper triangular matrix and reduces the former to quasi-triangular form while preserving the form of the latter. Usually preceded by QZHES and followed by QZVAL and QZVEC.

- qzval
The third step of the QZ algorithm for generalized eigenproblems. Accepts a pair of real matrices, one in quasi-triangular form and the other in upper triangular form and computes the eigenvalues of the associated eigenproblem. Usually preceded by QZHES, QZIT, and followed by QZVEC.

- qzvec
The optional fourth step of the QZ algorithm for generalized eigenproblems. Accepts a matrix in quasi-triangular form and another in upper triangular and computes the eigenvectors of the triangular problem and transforms them back to the original coordinates Usually preceded by QZHES, QZIT, and QZVAL.

- ratqr
Compute the largest or smallest eigenvalues of a symmetric tridiagonal matrix using the rational QR method with Newton correction.

- rebak
Form the eigenvectors of a generalized symmetric eigensystem from the eigenvectors of derived matrix output from REDUC or REDUC2.

- rebakb
Form the eigenvectors of a generalized symmetric eigensystem from the eigenvectors of derived matrix output from REDUC2.

- reduc
Reduce a generalized symmetric eigenproblem to a standard symmetric eigenproblem using Cholesky factorization.

- reduc2
Reduce a certain generalized symmetric eigenproblem to a standard symmetric eigenproblem using Cholesky factorization.

- rg
Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

- rgg
Compute the eigenvalues and eigenvectors for a real generalized eigenproblem.

- rs
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

- rsb
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric band matrix.

- rsg
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsgab
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsgba
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsp
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix packed into a one dimensional array.

- rst
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric tridiagonal matrix.

- rt
Compute the eigenvalues and eigenvectors of a special real tridiagonal matrix.

- sgeev
Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

- ssiev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

- sspev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix stored in packed form.

- tql2
Compute the eigenvalues and eigenvectors of symmetric tridiagonal matrix.

- tred1
Reduce a real symmetric matrix to symmetric tridiagonal matrix using orthogonal similarity transformations.

- tred2
Reduce a real symmetric matrix to a symmetric tridiagonal matrix using and accumulating orthogonal transformations.

- tred3
Reduce a real symmetric matrix stored in packed form to symmetric tridiagonal matrix using orthogonal transformations.

- tsturm
Find those eigenvalues of a symmetric tridiagonal matrix in a given interval and their associated eigenvectors by Sturm sequencing.

### EIGENVALUES OF A REAL SYMMETRIC MATRIX

- tridib
Compute the eigenvalues of a symmetric tridiagonal matrix in a given interval using Sturm sequencing.

### EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX

- tql1
Compute the eigenvalues of symmetric tridiagonal matrix by the QL method.

- tqlrat
Compute the eigenvalues of symmetric tridiagonal matrix using a rational variant of the QL method.

### EIGENVECTORS

- bakvec
Form the eigenvectors of a certain real non-symmetric tridiagonal matrix from a symmetric tridiagonal matrix output from FIGI.

- balanc
Balance a real general matrix and isolate eigenvalues whenever possible.

- balbak
Form the eigenvectors of a real general matrix from the eigenvectors of matrix output from BALANC.

- bandr
Reduce a real symmetric band matrix to symmetric tridiagonal matrix and, optionally, accumulate orthogonal similarity transformations.

- bandv
Form the eigenvectors of a real symmetric band matrix associated with a set of ordered approximate eigenvalues by inverse iteration.

- cbabk2
Form the eigenvectors of a complex general matrix from the eigenvectors of matrix output from CBAL.

- cbal
Balance a complex general matrix and isolate eigenvalues whenever possible.

- cg
Compute the eigenvalues and, optionally, the eigenvectors of a complex general matrix.

- ch
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- cgeev
Compute the eigenvalues and, optionally, the eigenvectors of a complex general matrix.

- chiev
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- cinvit
Compute the eigenvectors of a complex upper Hessenberg associated with specified eigenvalues using inverse iteration.

- combak
Form the eigenvectors of a complex general matrix from the eigenvectors of a upper Hessenberg matrix output from COMHES.

- comhes
Reduce a complex general matrix to complex upper Hessenberg form using stabilized elementary similarity transformations.

- comlr2
Compute the eigenvalues and eigenvectors of a complex upper Hessenberg matrix using the modified LR method.

- comqr
Compute the eigenvalues of complex upper Hessenberg matrix using the QR method.

- comqr2
Compute the eigenvalues and eigenvectors of a complex upper Hessenberg matrix.

- cortb
Form the eigenvectors of a complex general matrix from eigenvectors of upper Hessenberg matrix output from CORTH.

- corth
Reduce a complex general matrix to complex upper Hessenberg form using unitary similarity transformations.

- eisdoc
Documentation for EISPACK, a collection of subprograms for solving matrix eigen-problems.

- elmbak
Form the eigenvectors of a real general matrix from the eigenvectors of the upper Hessenberg matrix output from ELMHES.

- elmhes
Reduce a real general matrix to upper Hessenberg form using stabilized elementary similarity transformations.

- eltran
Accumulates the stabilized elementary similarity transformations used in the reduction of a real general matrix to upper Hessenberg form by ELMHES.

- figi
Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

- figi2
Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

- hqr
Compute the eigenvalues of a real upper Hessenberg matrix using the QR method.

- hqr2
Compute the eigenvalues and eigenvectors of a real upper Hessenberg matrix using QR method.

- htrib3
Compute the eigenvectors of a complex Hermitian matrix from the eigenvectors of a real symmetric tridiagonal matrix output from HTRID3.

- htribk
Form the eigenvectors of a complex Hermitian matrix from the eigenvectors of a real symmetric tridiagonal matrix output from HTRIDI.

- htrid3
Reduce a complex Hermitian (packed) matrix to a real symmetric tridiagonal matrix by unitary similarity transformations.

- htridi
Reduce a complex Hermitian matrix to a real symmetric tridiagonal matrix using unitary similarity transformations.

- imtql1
Compute the eigenvalues of a symmetric tridiagonal matrix using the implicit QL method.

- imtql2
Compute the eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the implicit QL method.

- imtqlv
Compute the eigenvalues of a symmetric tridiagonal matrix using the implicit QL method. Eigenvectors may be computed later.

- invit
Compute the eigenvectors of a real upper Hessenberg matrix associated with specified eigenvalues by inverse iteration.

- minfit
Compute the singular value decomposition of a rectangular matrix and solve the related linear least squares problem.

- ortbak
Form the eigenvectors of a general real matrix from the eigenvectors of the upper Hessenberg matrix output from ORTHES.

- orthes
Reduce a real general matrix to upper Hessenberg form using orthogonal similarity transformations.

- ortran
Accumulate orthogonal similarity transformations in the reduction of real general matrix by ORTHES.

- qzhes
The first step of the QZ algorithm for solving generalized matrix eigenproblems. Accepts a pair of real general matrices and reduces one of them to upper Hessenberg and the other to upper triangular form using orthogonal transformations. Usually followed by QZIT, QZVAL, QZVEC.

- qzit
The second step of the QZ algorithm for generalized eigenproblems. Accepts an upper Hessenberg and an upper triangular matrix and reduces the former to quasi-triangular form while preserving the form of the latter. Usually preceded by QZHES and followed by QZVAL and QZVEC.

- qzval
The third step of the QZ algorithm for generalized eigenproblems. Accepts a pair of real matrices, one in quasi-triangular form and the other in upper triangular form and computes the eigenvalues of the associated eigenproblem. Usually preceded by QZHES, QZIT, and followed by QZVEC.

- qzvec
The optional fourth step of the QZ algorithm for generalized eigenproblems. Accepts a matrix in quasi-triangular form and another in upper triangular and computes the eigenvectors of the triangular problem and transforms them back to the original coordinates Usually preceded by QZHES, QZIT, and QZVAL.

- ratqr
Compute the largest or smallest eigenvalues of a symmetric tridiagonal matrix using the rational QR method with Newton correction.

- rebak
Form the eigenvectors of a generalized symmetric eigensystem from the eigenvectors of derived matrix output from REDUC or REDUC2.

- rebakb
Form the eigenvectors of a generalized symmetric eigensystem from the eigenvectors of derived matrix output from REDUC2.

- reduc
Reduce a generalized symmetric eigenproblem to a standard symmetric eigenproblem using Cholesky factorization.

- reduc2
Reduce a certain generalized symmetric eigenproblem to a standard symmetric eigenproblem using Cholesky factorization.

- rg
Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

- rgg
Compute the eigenvalues and eigenvectors for a real generalized eigenproblem.

- rs
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

- rsb
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric band matrix.

- rsg
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsgab
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsgba
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsp
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix packed into a one dimensional array.

- rst
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric tridiagonal matrix.

- rt
Compute the eigenvalues and eigenvectors of a special real tridiagonal matrix.

- sgeev
Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

- ssiev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

- sspev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix stored in packed form.

- tinvit
Compute the eigenvectors of symmetric tridiagonal matrix corresponding to specified eigenvalues, using inverse iteration.

- tql2
Compute the eigenvalues and eigenvectors of symmetric tridiagonal matrix.

- tred1
Reduce a real symmetric matrix to symmetric tridiagonal matrix using orthogonal similarity transformations.

- tred2
Reduce a real symmetric matrix to a symmetric tridiagonal matrix using and accumulating orthogonal transformations.

- tred3
Reduce a real symmetric matrix stored in packed form to symmetric tridiagonal matrix using orthogonal transformations.

- tsturm
Find those eigenvalues of a symmetric tridiagonal matrix in a given interval and their associated eigenvectors by Sturm sequencing.

### EIGENVECTORS OF A REAL SYMMETRIC MATRIX

- trbak1
Form the eigenvectors of real symmetric matrix from the eigenvectors of a symmetric tridiagonal matrix formed by TRED1.

- trbak3
Form the eigenvectors of a real symmetric matrix from the eigenvectors of a symmetric tridiagonal matrix formed by TRED3.

### EISPACK

- bakvec
Form the eigenvectors of a certain real non-symmetric tridiagonal matrix from a symmetric tridiagonal matrix output from FIGI.

- balanc
Balance a real general matrix and isolate eigenvalues whenever possible.

- balbak
Form the eigenvectors of a real general matrix from the eigenvectors of matrix output from BALANC.

- bandr
Reduce a real symmetric band matrix to symmetric tridiagonal matrix and, optionally, accumulate orthogonal similarity transformations.

- bandv
Form the eigenvectors of a real symmetric band matrix associated with a set of ordered approximate eigenvalues by inverse iteration.

- bisect
Compute the eigenvalues of a symmetric tridiagonal matrix in a given interval using Sturm sequencing.

- bqr
Compute some of the eigenvalues of a real symmetric matrix using the QR method with shifts of origin.

- cbabk2
Form the eigenvectors of a complex general matrix from the eigenvectors of matrix output from CBAL.

- cbal
Balance a complex general matrix and isolate eigenvalues whenever possible.

- cg
Compute the eigenvalues and, optionally, the eigenvectors of a complex general matrix.

- ch
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- cinvit
Compute the eigenvectors of a complex upper Hessenberg associated with specified eigenvalues using inverse iteration.

- combak
Form the eigenvectors of a complex general matrix from the eigenvectors of a upper Hessenberg matrix output from COMHES.

- comhes
Reduce a complex general matrix to complex upper Hessenberg form using stabilized elementary similarity transformations.

- comlr
Compute the eigenvalues of a complex upper Hessenberg matrix using the modified LR method.

- comlr2
Compute the eigenvalues and eigenvectors of a complex upper Hessenberg matrix using the modified LR method.

- comqr
Compute the eigenvalues of complex upper Hessenberg matrix using the QR method.

- comqr2
Compute the eigenvalues and eigenvectors of a complex upper Hessenberg matrix.

- cortb
Form the eigenvectors of a complex general matrix from eigenvectors of upper Hessenberg matrix output from CORTH.

- corth
Reduce a complex general matrix to complex upper Hessenberg form using unitary similarity transformations.

- eisdoc
Documentation for EISPACK, a collection of subprograms for solving matrix eigen-problems.

- elmbak
Form the eigenvectors of a real general matrix from the eigenvectors of the upper Hessenberg matrix output from ELMHES.

- elmhes
Reduce a real general matrix to upper Hessenberg form using stabilized elementary similarity transformations.

- eltran
Accumulates the stabilized elementary similarity transformations used in the reduction of a real general matrix to upper Hessenberg form by ELMHES.

- figi
Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

- figi2
Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

- hqr
Compute the eigenvalues of a real upper Hessenberg matrix using the QR method.

- hqr2
Compute the eigenvalues and eigenvectors of a real upper Hessenberg matrix using QR method.

- htrib3
Compute the eigenvectors of a complex Hermitian matrix from the eigenvectors of a real symmetric tridiagonal matrix output from HTRID3.

- htribk
Form the eigenvectors of a complex Hermitian matrix from the eigenvectors of a real symmetric tridiagonal matrix output from HTRIDI.

- htrid3
Reduce a complex Hermitian (packed) matrix to a real symmetric tridiagonal matrix by unitary similarity transformations.

- htridi
Reduce a complex Hermitian matrix to a real symmetric tridiagonal matrix using unitary similarity transformations.

- imtql1
Compute the eigenvalues of a symmetric tridiagonal matrix using the implicit QL method.

- imtql2
Compute the eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the implicit QL method.

- imtqlv
Compute the eigenvalues of a symmetric tridiagonal matrix using the implicit QL method. Eigenvectors may be computed later.

- invit
Compute the eigenvectors of a real upper Hessenberg matrix associated with specified eigenvalues by inverse iteration.

- minfit
Compute the singular value decomposition of a rectangular matrix and solve the related linear least squares problem.

- ortbak
Form the eigenvectors of a general real matrix from the eigenvectors of the upper Hessenberg matrix output from ORTHES.

- orthes
Reduce a real general matrix to upper Hessenberg form using orthogonal similarity transformations.

- ortran
Accumulate orthogonal similarity transformations in the reduction of real general matrix by ORTHES.

- qzhes
The first step of the QZ algorithm for solving generalized matrix eigenproblems. Accepts a pair of real general matrices and reduces one of them to upper Hessenberg and the other to upper triangular form using orthogonal transformations. Usually followed by QZIT, QZVAL, QZVEC.

- qzit
The second step of the QZ algorithm for generalized eigenproblems. Accepts an upper Hessenberg and an upper triangular matrix and reduces the former to quasi-triangular form while preserving the form of the latter. Usually preceded by QZHES and followed by QZVAL and QZVEC.

- qzval
The third step of the QZ algorithm for generalized eigenproblems. Accepts a pair of real matrices, one in quasi-triangular form and the other in upper triangular form and computes the eigenvalues of the associated eigenproblem. Usually preceded by QZHES, QZIT, and followed by QZVEC.

- qzvec
The optional fourth step of the QZ algorithm for generalized eigenproblems. Accepts a matrix in quasi-triangular form and another in upper triangular and computes the eigenvectors of the triangular problem and transforms them back to the original coordinates Usually preceded by QZHES, QZIT, and QZVAL.

- ratqr
Compute the largest or smallest eigenvalues of a symmetric tridiagonal matrix using the rational QR method with Newton correction.

- rebak
Form the eigenvectors of a generalized symmetric eigensystem from the eigenvectors of derived matrix output from REDUC or REDUC2.

- rebakb
Form the eigenvectors of a generalized symmetric eigensystem from the eigenvectors of derived matrix output from REDUC2.

- reduc
Reduce a generalized symmetric eigenproblem to a standard symmetric eigenproblem using Cholesky factorization.

- reduc2
Reduce a certain generalized symmetric eigenproblem to a standard symmetric eigenproblem using Cholesky factorization.

- rg
Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

- rgg
Compute the eigenvalues and eigenvectors for a real generalized eigenproblem.

- rs
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

- rsb
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric band matrix.

- rsg
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsgab
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsgba
Compute the eigenvalues and, optionally, the eigenvectors of a symmetric generalized eigenproblem.

- rsp
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix packed into a one dimensional array.

- rst
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric tridiagonal matrix.

- rt
Compute the eigenvalues and eigenvectors of a special real tridiagonal matrix.

- sspev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix stored in packed form.

- tinvit
Compute the eigenvectors of symmetric tridiagonal matrix corresponding to specified eigenvalues, using inverse iteration.

- tql1
Compute the eigenvalues of symmetric tridiagonal matrix by the QL method.

- tql2
Compute the eigenvalues and eigenvectors of symmetric tridiagonal matrix.

- tqlrat
Compute the eigenvalues of symmetric tridiagonal matrix using a rational variant of the QL method.

- trbak1
Form the eigenvectors of real symmetric matrix from the eigenvectors of a symmetric tridiagonal matrix formed by TRED1.

- trbak3
Form the eigenvectors of a real symmetric matrix from the eigenvectors of a symmetric tridiagonal matrix formed by TRED3.

- tred1
Reduce a real symmetric matrix to symmetric tridiagonal matrix using orthogonal similarity transformations.

- tred2
Reduce a real symmetric matrix to a symmetric tridiagonal matrix using and accumulating orthogonal transformations.

- tred3
Reduce a real symmetric matrix stored in packed form to symmetric tridiagonal matrix using orthogonal transformations.

- tridib
- tsturm
Find those eigenvalues of a symmetric tridiagonal matrix in a given interval and their associated eigenvectors by Sturm sequencing.

### ELEMENTARY FUNCTIONS

- acosh
Compute the arc hyperbolic cosine.

- alnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- asinh
Compute the arc hyperbolic sine.

- atanh
Compute the arc hyperbolic tangent.

- c9ln2r
Evaluate LOG(1+Z) from second order relative accuracy so that LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

- cacos
Compute the complex arc cosine.

- cacosh
Compute the arc hyperbolic cosine.

- carg
Compute the argument of a complex number.

- casin
Compute the complex arc sine.

- casinh
Compute the arc hyperbolic sine.

- catan
Compute the complex arc tangent.

- catan2
Compute the complex arc tangent in the proper quadrant.

- catanh
Compute the arc hyperbolic tangent.

- cbrt
Compute the cube root.

- ccbrt
Compute the cube root.

- ccosh
Compute the complex hyperbolic cosine.

- ccot
Compute the cotangent.

- cexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- clnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- clog10
Compute the principal value of the complex base 10 logarithm.

- cosdg
Compute the cosine of an argument in degrees.

- cot
Compute the cotangent.

- csinh
Compute the complex hyperbolic sine.

- ctan
Compute the complex tangent.

- ctanh
Compute the complex hyperbolic tangent.

- d9atn1
Evaluate DATAN(X) from first order relative accuracy so that DATAN(X) = X + X**3*D9ATN1(X).

- d9ln2r
Evaluate LOG(1+X) from second order relative accuracy so that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

- dacosh
Compute the arc hyperbolic cosine.

- dasinh
Compute the arc hyperbolic sine.

- datanh
Compute the arc hyperbolic tangent.

- dcbrt
Compute the cube root.

- dcosdg
Compute the cosine of an argument in degrees.

- dcot
Compute the cotangent.

- dexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- dlnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- drc
Calculate a double precision approximation to DRC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.

- dsindg
Compute the sine of an argument in degrees.

- exprel
Calculate the relative error exponential (EXP(X)-1)/X.

- fundoc
Documentation for FNLIB, a collection of routines for evaluating elementary and special functions.

- r9atn1
Evaluate ATAN(X) from first order relative accuracy so that ATAN(X) = X + X**3*R9ATN1(X).

- r9ln2r
Evaluate LOG(1+X) from second order relative accuracy so that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

- rc
Calculate an approximation to RC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.

- sindg
Compute the sine of an argument in degrees.

### ELLIPTIC

- genbun
Solve by a cyclic reduction algorithm the linear system of equations that results from a finite difference approximation to certain 2-d elliptic PDE's on a centered grid .

- hstcrt
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in Cartesian coordinates.

- hstcsp
Solve the standard five-point finite difference approximation on a staggered grid to the modified Helmholtz equation in spherical coordinates assuming axisymmetry (no dependence on longitude).

- hstcyl
Solve the standard five-point finite difference approximation on a staggered grid to the modified Helmholtz equation in cylindrical coordinates.

- hstplr
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in polar coordinates.

- hstssp
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in spherical coordinates and on the surface of the unit sphere (radius of 1).

- hw3crt
Solve the standard seven-point finite difference approximation to the Helmholtz equation in Cartesian coordinates.

- hwscrt
Solves the standard five-point finite difference approximation to the Helmholtz equation in Cartesian coordinates.

- hwscsp
Solve a finite difference approximation to the modified Helmholtz equation in spherical coordinates assuming axisymmetry (no dependence on longitude).

- hwscyl
Solve a standard finite difference approximation to the Helmholtz equation in cylindrical coordinates.

- hwsplr
Solve a finite difference approximation to the Helmholtz equation in polar coordinates.

- hwsssp
Solve a finite difference approximation to the Helmholtz equation in spherical coordinates and on the surface of the unit sphere (radius of 1).

- poistg
Solve a block tridiagonal system of linear equations that results from a staggered grid finite difference approximation to 2-D elliptic PDE's.

- sepeli
Discretize and solve a second and, optionally, a fourth order finite difference approximation on a uniform grid to the general separable elliptic partial differential equation on a rectangle with any combination of periodic or mixed boundary conditions.

- sepx4
Solve for either the second or fourth order finite difference approximation to the solution of a separable elliptic partial differential equation on a rectangle. Any combination of periodic or mixed boundary conditions is allowed.

### ELLIPTIC INTEGRAL

- drc
Calculate a double precision approximation to DRC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.

- rc
Calculate an approximation to RC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.

### ELLIPTIC PDE

- blktri
Solve a block tridiagonal system of linear equations (usually resulting from the discretization of separable two-dimensional elliptic equations).

- cblktr
Solve a block tridiagonal system of linear equations (usually resulting from the discretization of separable two-dimensional elliptic equations).

- cmgnbn
Solve a complex block tridiagonal linear system of equations by a cyclic reduction algorithm.

- pois3d
Solve a three-dimensional block tridiagonal linear system which arises from a finite difference approximation to a three-dimensional Poisson equation using the Fourier transform package FFTPAK written by Paul Swarztrauber.

### END POINT SINGULARITIES

- dqags
The routine calculates an approximation result to a given Definite integral I = Integral of F over (A,B), Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqagse
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqwgts
This function subprogram is used together with the routine DQAWS and defines the WEIGHT function.

- qags
- qagse
- qwgts
This function subprogram is used together with the routine QAWS and defines the WEIGHT function.

### EPSILON ALGORITHM

- dqelg
The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P.Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved.

- qelg
The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P. Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved.

### EQUALITY CONSTRAINTS

- dlsei
- dwnnls
- lsei
- wnnls

### ERF

### ERFC

### ERROR

- fdump
Symbolic dump (should be locally written).

- xerclr
Reset current error number to zero.

- xercnt
Allow user control over handling of errors.

- xerdmp
Print the error tables and then clear them.

- xerhlt
Abort program execution and print error message.

- xermax
Set maximum number of times any error message is to be printed.

- xersve
Record that an error has occurred.

- xgetf
Return the current value of the error control flag.

- xgetua
Return unit number(s) to which error messages are being sent.

- xgetun
Return the (first) output file to which error messages are being sent.

- xsetf
Set the error control flag.

- xsetua
Set logical unit numbers (up to 5) to which error messages are to be sent.

- xsetun
Set output file to which error messages are to be sent.

### ERROR CHECKING

- dchkw
SLAP WORK/IWORK Array Bounds Checker. This routine checks the work array lengths and interfaces to the SLATEC error handler if a problem is found.

- schkw
SLAP WORK/IWORK Array Bounds Checker. This routine checks the work array lengths and interfaces to the SLATEC error handler if a problem is found.

### ERROR FUNCTION

### ERROR MESSAGE

- xerbla
Error handler for the Level 2 and Level 3 BLAS Routines.

- xermsg
Process error messages for SLATEC and other libraries.

### ERROR MESSAGES

- j4save
Save or recall global variables needed by error handling routines.

- xerprn
Print error messages processed by XERMSG.

### ERROR NUMBER

- j4save
Save or recall global variables needed by error handling routines.

- numxer
Return the most recent error number.

### EUCLIDEAN LENGTH

- dnrm2
Compute the Euclidean length (L2 norm) of a vector.

- scnrm2
Compute the unitary norm of a complex vector.

- snrm2
Compute the Euclidean length (L2 norm) of a vector.

### EUCLIDEAN NORM

- dnrm2
Compute the Euclidean length (L2 norm) of a vector.

- scnrm2
Compute the unitary norm of a complex vector.

- snrm2
Compute the Euclidean length (L2 norm) of a vector.

### EVALUATION OF B-SPLINE

- bspvd
Calculate the value and all derivatives of order less than NDERIV of all basis functions which do not vanish at X.

- bspvn
Calculate the value of all (possibly) nonzero basis functions at X.

- bvalu
Evaluate the B-representation of a B-spline at X for the function value or any of its derivatives.

- dbspvd
- dbspvn
Calculate the value of all (possibly) nonzero basis functions at X.

- dbvalu
Evaluate the B-representation of a B-spline at X for the function value or any of its derivatives.

### EXCHANGE

- cchex
Update the Cholesky factorization A=TRANS(R)*R of a positive definite matrix A of order P under diagonal permutations of the form TRANS(E)*A*E, where E is a permutation matrix.

- dchex
- schex
Update the Cholesky factorization A=TRANS(R)*R of A positive definite matrix A of order P under diagonal permutations of the form TRANS(E)*A*E, where E is a permutation matrix.

### EXPONENTIAL

- cexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- dexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- exprel
Calculate the relative error exponential (EXP(X)-1)/X.

### EXPONENTIAL INTEGRAL

- bskin
Compute repeated integrals of the K-zero Bessel function.

- dbskin
Compute repeated integrals of the K-zero Bessel function.

- de1
Compute the exponential integral E1(X).

- dei
Compute the exponential integral Ei(X).

- dexint
Compute an M member sequence of exponential integrals E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

- e1
Compute the exponential integral E1(X).

- ei
Compute the exponential integral Ei(X).

- exint
Compute an M member sequence of exponential integrals E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

### EXPONENTIALLY SCALED

- besi0e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero.

- besi1e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one.

- besk0e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero.

- besk1e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one.

- beskes
Compute a sequence of exponentially scaled modified Bessel functions of the third kind of fractional order.

- bie
Calculate the Bairy function for a negative argument and an exponentially scaled Bairy function for a non-negative argument.

- dbie
- dbsi0e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero.

- dbsi1e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one.

- dbsk0e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero.

- dbsk1e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one.

- dbskes
Compute a sequence of exponentially scaled modified Bessel functions of the third kind of fractional order.

### EXPONENTIALLY SCALED AIRY FUNCTION

- aie
Calculate the Airy function for a negative argument and an exponentially scaled Airy function for a non-negative argument.

- daie
Calculate the Airy function for a negative argument and an exponentially scaled Airy function for a non-negative argument.

### EXTENDED-RANGE DOUBLE-PRECISION ARITHMETIC

- dxadd
To provide double-precision floating-point arithmetic with an extended exponent range.

- dxadj
To provide double-precision floating-point arithmetic with an extended exponent range.

- dxc210
To provide double-precision floating-point arithmetic with an extended exponent range.

- dxcon
To provide double-precision floating-point arithmetic with an extended exponent range.

- dxred
To provide double-precision floating-point arithmetic with an extended exponent range.

- dxset
To provide double-precision floating-point arithmetic with an extended exponent range.

### EXTENDED-RANGE SINGLE-PRECISION ARITHMETIC

- xadd
To provide single-precision floating-point arithmetic with an extended exponent range.

- xadj
To provide single-precision floating-point arithmetic with an extended exponent range.

- xc210
To provide single-precision floating-point arithmetic with an extended exponent range.

- xcon
To provide single-precision floating-point arithmetic with an extended exponent range.

- xred
To provide single-precision floating-point arithmetic with an extended exponent range.

- xset
To provide single-precision floating-point arithmetic with an extended exponent range.

### EXTRAPOLATION

- dqagi
The routine calculates an approximation result to a given INTEGRAL I = Integral of F over (BOUND,+INFINITY) OR I = Integral of F over (-INFINITY,BOUND) OR I = Integral of F over (-INFINITY,+INFINITY) Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqagie
The routine calculates an approximation result to a given integral I = Integral of F over (BOUND,+INFINITY) or I = Integral of F over (-INFINITY,BOUND) or I = Integral of F over (-INFINITY,+INFINITY), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

- dqagp
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy break points of the integration interval, where local difficulties of the integrand may occur (e.g. SINGULARITIES, DISCONTINUITIES), are provided by the user.

- dqagpe
Approximate a given definite integral I = Integral of F over (A,B), hopefully satisfying the accuracy claim: ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)). Break points of the integration interval, where local difficulties of the integrand may occur (e.g. singularities or discontinuities) are provided by the user.

- dqags
- dqagse
- dqawo
Calculate an approximation to a given definite integral I= Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqawoe
Calculate an approximation to a given definite integral I = Integral of F(X)*W(X) over (A,B), where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X), hopefully satisfying the following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqelg
The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P.Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved.

- qagi
- qagie
- qagp
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy break points of the integration interval, where local difficulties of the integrand may occur(e.g. SINGULARITIES, DISCONTINUITIES), are provided by the user.

- qagpe
- qags
- qagse
- qawo
- qawoe
- qelg
The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P. Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved.

### FACTORIAL

### FAST FOURIER TRANSFORM

- dqcheb
This routine computes the CHEBYSHEV series expansion of degrees 12 and 24 of a function using A FAST FOURIER TRANSFORM METHOD F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)), F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)), Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

- fftdoc
Documentation for FFTPACK, a collection of Fast Fourier Transform routines.

- qcheb

### FFT

- fftdoc
Documentation for FFTPACK, a collection of Fast Fourier Transform routines.

### FFTPACK

- cfftb
Compute the unnormalized inverse of CFFTF.

- cfftb1
Compute the unnormalized inverse of CFFTF1.

- cfftf
Compute the forward transform of a complex, periodic sequence.

- cfftf1
Compute the forward transform of a complex, periodic sequence.

- cffti
Initialize a work array for CFFTF and CFFTB.

- cffti1
Initialize a real and an integer work array for CFFTF1 and CFFTB1.

- cosqb
Compute the unnormalized inverse cosine transform.

- cosqb1
Compute the unnormalized inverse of COSQF1.

- cosqf
Compute the forward cosine transform with odd wave numbers.

- cosqf1
Compute the forward cosine transform with odd wave numbers.

- cosqi
Initialize a work array for COSQF and COSQB.

- cost
Compute the cosine transform of a real, even sequence.

- costi
Initialize a work array for COST.

- ezfftb
A simplified real, periodic, backward fast Fourier transform.

- ezfftf
Compute a simplified real, periodic, fast Fourier forward transform.

- ezffti
Initialize a work array for EZFFTF and EZFFTB.

- rfftb
Compute the backward fast Fourier transform of a real coefficient array.

- rfftb1
Compute the backward fast Fourier transform of a real coefficient array.

- rfftf
Compute the forward transform of a real, periodic sequence.

- rfftf1
Compute the forward transform of a real, periodic sequence.

- rffti
Initialize a work array for RFFTF and RFFTB.

- rffti1
Initialize a real and an integer work array for RFFTF1 and RFFTB1.

- sinqb
Compute the unnormalized inverse of SINQF.

- sinqf
Compute the forward sine transform with odd wave numbers.

- sinqi
Initialize a work array for SINQF and SINQB.

- sint
Compute the sine transform of a real, odd sequence.

- sinti
Initialize a work array for SINT.

### FIRST KIND

- besi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- besi0e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero.

- besi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- besi1e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one.

- besj0
Compute the Bessel function of the first kind of order zero.

- besj1
Compute the Bessel function of the first kind of order one.

- dbesi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- dbesi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- dbesj0
Compute the Bessel function of the first kind of order zero.

- dbesj1
Compute the Bessel function of the first kind of order one.

- dbsi0e
- dbsi1e

### FIRST ORDER

- cexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- d9atn1
Evaluate DATAN(X) from first order relative accuracy so that DATAN(X) = X + X**3*D9ATN1(X).

- dexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- dpoch1
Calculate a generalization of Pochhammer's symbol starting from first order.

- exprel
Calculate the relative error exponential (EXP(X)-1)/X.

- poch1
Calculate a generalization of Pochhammer's symbol starting from first order.

- r9atn1
Evaluate ATAN(X) from first order relative accuracy so that ATAN(X) = X + X**3*R9ATN1(X).

### FISHPACK

- blktri
Solve a block tridiagonal system of linear equations (usually resulting from the discretization of separable two-dimensional elliptic equations).

- cblktr
- cmgnbn
Solve a complex block tridiagonal linear system of equations by a cyclic reduction algorithm.

- genbun
Solve by a cyclic reduction algorithm the linear system of equations that results from a finite difference approximation to certain 2-d elliptic PDE's on a centered grid .

- hstcrt
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in Cartesian coordinates.

- hstcsp
Solve the standard five-point finite difference approximation on a staggered grid to the modified Helmholtz equation in spherical coordinates assuming axisymmetry (no dependence on longitude).

- hstcyl
Solve the standard five-point finite difference approximation on a staggered grid to the modified Helmholtz equation in cylindrical coordinates.

- hstplr
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in polar coordinates.

- hstssp
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in spherical coordinates and on the surface of the unit sphere (radius of 1).

- hw3crt
Solve the standard seven-point finite difference approximation to the Helmholtz equation in Cartesian coordinates.

- hwscrt
Solves the standard five-point finite difference approximation to the Helmholtz equation in Cartesian coordinates.

- hwscsp
Solve a finite difference approximation to the modified Helmholtz equation in spherical coordinates assuming axisymmetry (no dependence on longitude).

- hwscyl
Solve a standard finite difference approximation to the Helmholtz equation in cylindrical coordinates.

- hwsplr
Solve a finite difference approximation to the Helmholtz equation in polar coordinates.

- hwsssp
Solve a finite difference approximation to the Helmholtz equation in spherical coordinates and on the surface of the unit sphere (radius of 1).

- pois3d
Solve a three-dimensional block tridiagonal linear system which arises from a finite difference approximation to a three-dimensional Poisson equation using the Fourier transform package FFTPAK written by Paul Swarztrauber.

- poistg
Solve a block tridiagonal system of linear equations that results from a staggered grid finite difference approximation to 2-D elliptic PDE's.

- sepeli
Discretize and solve a second and, optionally, a fourth order finite difference approximation on a uniform grid to the general separable elliptic partial differential equation on a rectangle with any combination of periodic or mixed boundary conditions.

- sepx4
Solve for either the second or fourth order finite difference approximation to the solution of a separable elliptic partial differential equation on a rectangle. Any combination of periodic or mixed boundary conditions is allowed.

### FNLIB

- acosh
Compute the arc hyperbolic cosine.

- ai
Evaluate the Airy function.

- aie
Calculate the Airy function for a negative argument and an exponentially scaled Airy function for a non-negative argument.

- albeta
Compute the natural logarithm of the complete Beta function.

- algams
Compute the logarithm of the absolute value of the Gamma function.

- ali
Compute the logarithmic integral.

- alngam
Compute the logarithm of the absolute value of the Gamma function.

- alnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- asinh
Compute the arc hyperbolic sine.

- atanh
Compute the arc hyperbolic tangent.

- besi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- besi0e
- besi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- besi1e
- besj0
Compute the Bessel function of the first kind of order zero.

- besj1
Compute the Bessel function of the first kind of order one.

- besk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- besk0e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero.

- besk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- besk1e
Compute the exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one.

- beskes
Compute a sequence of exponentially scaled modified Bessel functions of the third kind of fractional order.

- besks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- besy0
Compute the Bessel function of the second kind of order zero.

- besy1
Compute the Bessel function of the second kind of order one.

- beta
Compute the complete Beta function.

- betai
Calculate the incomplete Beta function.

- bi
Evaluate the Bairy function (the Airy function of the second kind).

- bie
- binom
Compute the binomial coefficients.

- c0lgmc
Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative accuracy.

- c9lgmc
Compute the log gamma correction factor so that LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z + C9LGMC(Z).

- c9ln2r
Evaluate LOG(1+Z) from second order relative accuracy so that LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

- cacos
Compute the complex arc cosine.

- cacosh
Compute the arc hyperbolic cosine.

- carg
Compute the argument of a complex number.

- casin
Compute the complex arc sine.

- casinh
Compute the arc hyperbolic sine.

- catan
Compute the complex arc tangent.

- catan2
Compute the complex arc tangent in the proper quadrant.

- catanh
Compute the arc hyperbolic tangent.

- cbeta
Compute the complete Beta function.

- cbrt
Compute the cube root.

- ccbrt
Compute the cube root.

- ccosh
Compute the complex hyperbolic cosine.

- ccot
Compute the cotangent.

- cexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- cgamma
Compute the complete Gamma function.

- cgamr
Compute the reciprocal of the Gamma function.

- chu
Compute the logarithmic confluent hypergeometric function.

- clbeta
Compute the natural logarithm of the complete Beta function.

- clngam
Compute the logarithm of the absolute value of the Gamma function.

- clnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- clog10
Compute the principal value of the complex base 10 logarithm.

- cosdg
Compute the cosine of an argument in degrees.

- cot
Compute the cotangent.

- cpsi
Compute the Psi (or Digamma) function.

- csevl
Evaluate a Chebyshev series.

- csinh
Compute the complex hyperbolic sine.

- ctan
Compute the complex tangent.

- ctanh
Compute the complex hyperbolic tangent.

- d9aimp
Evaluate the Airy modulus and phase.

- d9atn1
Evaluate DATAN(X) from first order relative accuracy so that DATAN(X) = X + X**3*D9ATN1(X).

- d9b0mp
Evaluate the modulus and phase for the J0 and Y0 Bessel functions.

- d9b1mp
Evaluate the modulus and phase for the J1 and Y1 Bessel functions.

- d9chu
Evaluate for large Z Z**A * U(A,B,Z) where U is the logarithmic confluent hypergeometric function.

- d9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and X small.

- d9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- d9knus
Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)* K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

- d9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- d9lgit
Compute the logarithm of Tricomi's incomplete Gamma function with Perron's continued fraction for large X and A .GE. X.

- d9lgmc
Compute the log Gamma correction factor so that LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X + D9LGMC(X).

- d9ln2r
Evaluate LOG(1+X) from second order relative accuracy so that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

- d9pak
Pack a base 2 exponent into a floating point number.

- d9upak
Unpack a floating point number X so that X = Y*2**N.

- dai
Evaluate the Airy function.

- dacosh
Compute the arc hyperbolic cosine.

- daie
- dasinh
Compute the arc hyperbolic sine.

- datanh
Compute the arc hyperbolic tangent.

- daws
Compute Dawson's function.

- dbesi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- dbesi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- dbesj0
Compute the Bessel function of the first kind of order zero.

- dbesj1
Compute the Bessel function of the first kind of order one.

- dbesk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- dbesk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- dbesks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbesy0
Compute the Bessel function of the second kind of order zero.

- dbesy1
Compute the Bessel function of the second kind of order one.

- dbeta
Compute the complete Beta function.

- dbetai
Calculate the incomplete Beta function.

- dbi
Evaluate the Bairy function (the Airy function of the second kind).

- dbie
- dbinom
Compute the binomial coefficients.

- dbsi0e
- dbsi1e
- dbsk0e
- dbsk1e
- dbskes
- dcbrt
Compute the cube root.

- dchu
Compute the logarithmic confluent hypergeometric function.

- dcosdg
Compute the cosine of an argument in degrees.

- dcot
Compute the cotangent.

- dcsevl
Evaluate a Chebyshev series.

- ddaws
Compute Dawson's function.

- de1
Compute the exponential integral E1(X).

- dei
Compute the exponential integral Ei(X).

- derf
Compute the error function.

- derfc
Compute the complementary error function.

- dexprl
Calculate the relative error exponential (EXP(X)-1)/X.

- dfac
Compute the factorial function.

- dgami
Evaluate the incomplete Gamma function.

- dgamic
Calculate the complementary incomplete Gamma function.

- dgamit
Calculate Tricomi's form of the incomplete Gamma function.

- dgamlm
Compute the minimum and maximum bounds for the argument in the Gamma function.

- dgamma
Compute the complete Gamma function.

- dgamr
Compute the reciprocal of the Gamma function.

- dlbeta
Compute the natural logarithm of the complete Beta function.

- dlgams
Compute the logarithm of the absolute value of the Gamma function.

- dli
Compute the logarithmic integral.

- dlngam
Compute the logarithm of the absolute value of the Gamma function.

- dlnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- dpoch
Evaluate a generalization of Pochhammer's symbol.

- dpoch1
Calculate a generalization of Pochhammer's symbol starting from first order.

- dpsi
Compute the Psi (or Digamma) function.

- dsindg
Compute the sine of an argument in degrees.

- dspenc
Compute a form of Spence's integral due to K. Mitchell.

- e1
Compute the exponential integral E1(X).

- ei
Compute the exponential integral Ei(X).

- erf
Compute the error function.

- erfc
Compute the complementary error function.

- exprel
Calculate the relative error exponential (EXP(X)-1)/X.

- fac
Compute the factorial function.

- gami
Evaluate the incomplete Gamma function.

- gamic
Calculate the complementary incomplete Gamma function.

- gamit
Calculate Tricomi's form of the incomplete Gamma function.

- gamlim
Compute the minimum and maximum bounds for the argument in the Gamma function.

- gamma
Compute the complete Gamma function.

- gamr
Compute the reciprocal of the Gamma function.

- initds
Determine the number of terms needed in an orthogonal polynomial series so that it meets a specified accuracy.

- inits
- psi
Compute the Psi (or Digamma) function.

- poch
Evaluate a generalization of Pochhammer's symbol.

- poch1
Calculate a generalization of Pochhammer's symbol starting from first order.

- r9aimp
Evaluate the Airy modulus and phase.

- r9atn1
Evaluate ATAN(X) from first order relative accuracy so that ATAN(X) = X + X**3*R9ATN1(X).

- r9chu
Evaluate for large Z Z**A * U(A,B,Z) where U is the logarithmic confluent hypergeometric function.

- r9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and for small X.

- r9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- rand
Generate a uniformly distributed random number.

- r9knus
Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)* K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

- r9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- r9lgit
Compute the logarithm of Tricomi's incomplete Gamma function with Perron's continued fraction for large X and A .GE. X.

- r9lgmc
Compute the log Gamma correction factor so that LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X + R9LGMC(X).

- r9ln2r
Evaluate LOG(1+X) from second order relative accuracy so that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

- r9pak
Pack a base 2 exponent into a floating point number.

- r9upak
Unpack a floating point number X so that X = Y*2**N.

- rgauss
Generate a normally distributed (Gaussian) random number.

- runif
Generate a uniformly distributed random number.

- sindg
Compute the sine of an argument in degrees.

- spenc
Compute a form of Spence's integral due to K. Mitchell.

### FOURIER INTEGRALS

- dqawf
The routine calculates an approximation result to a given Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- dqawfe
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- qawf
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

- qawfe
The routine calculates an approximation result to a given Fourier integral I = Integral of F(X)*W(X) over (A,INFINITY) where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.EPSABS.

### FOURIER TRANSFORM

- cfftb
Compute the unnormalized inverse of CFFTF.

- cfftb1
Compute the unnormalized inverse of CFFTF1.

- cfftf
Compute the forward transform of a complex, periodic sequence.

- cfftf1
Compute the forward transform of a complex, periodic sequence.

- cffti
Initialize a work array for CFFTF and CFFTB.

- cffti1
Initialize a real and an integer work array for CFFTF1 and CFFTB1.

- cosqb1
Compute the unnormalized inverse of COSQF1.

- cosqf1
Compute the forward cosine transform with odd wave numbers.

- ezfftb
A simplified real, periodic, backward fast Fourier transform.

- ezfftf
Compute a simplified real, periodic, fast Fourier forward transform.

- ezffti
Initialize a work array for EZFFTF and EZFFTB.

- rfftb
Compute the backward fast Fourier transform of a real coefficient array.

- rfftb1
Compute the backward fast Fourier transform of a real coefficient array.

- rfftf
Compute the forward transform of a real, periodic sequence.

- rfftf1
Compute the forward transform of a real, periodic sequence.

- rffti
Initialize a work array for RFFTF and RFFTB.

- rffti1
Initialize a real and an integer work array for RFFTF1 and RFFTB1.

- sinqb
Compute the unnormalized inverse of SINQF.

- sinqf
Compute the forward sine transform with odd wave numbers.

- sinqi
Initialize a work array for SINQF and SINQB.

- sint
Compute the sine transform of a real, odd sequence.

- sinti
Initialize a work array for SINT.

### FRACTIONAL ORDER

- beskes
- besks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbesks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbskes

### GAMMA FUNCTION

- c0lgmc
Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative accuracy.

### GAUSS QUADRATURE

- dgaus8
- gaus8

### GAUSS-KRONROD RULES

- dqag
The routine calculates an approximation result to a given definite integral I = integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqage
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- dqc25f
To compute the integral I=Integral of F(X) over (A,B) Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to compute J = Integral of ABS(F) over (A,B). For small value of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO Rule is used. Otherwise a generalized CLENSHAW-CURTIS method is used.

- qag
- qage
- qc25f
To compute the integral I=Integral of F(X) over (A,B) Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X) and to compute J=Integral of ABS(F) over (A,B). For small value of OMEGA or small intervals (A,B) 15-point GAUSS- KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

### GAUSS-KRONROD(PATTERSON) RULES

- dqng
The routine calculates an approximation result to a given definite integral I = integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

- qng

### GAUSSIAN

- rgauss
Generate a normally distributed (Gaussian) random number.

### GEAR'S METHOD

- cdriv1
The function of CDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. CDRIV1 allows complex-valued differential equations.

- cdriv2
The function of CDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. CDRIV2 allows complex-valued differential equations.

- cdriv3
The function of CDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. CDRIV3 allows complex-valued differential equations.

- ddriv1
The function of DDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. DDRIV1 uses double precision arithmetic.

- ddriv2
The function of DDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. DDRIV2 uses double precision arithmetic.

- ddriv3
The function of DDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. DDRIV3 uses double precision arithmetic.

- sdriv1
The function of SDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. SDRIV1 uses single precision arithmetic.

- sdriv2
The function of SDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. SDRIV2 uses single precision arithmetic.

- sdriv3
The function of SDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. SDRIV3 uses single precision arithmetic.

### GENERAL MATRIX

- cgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- cgeev
Compute the eigenvalues and, optionally, the eigenvectors of a complex general matrix.

- cgefa
Factor a matrix using Gaussian elimination.

- cgefs
Solve a general system of linear equations.

- cgeir
Solve a general system of linear equations. Iterative refinement is used to obtain an error estimate.

- dgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- dgefa
Factor a matrix using Gaussian elimination.

- dgefs
Solve a general system of linear equations.

- sgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- sgeev
Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

- sgefa
Factor a matrix using Gaussian elimination.

- sgefs
Solve a general system of linear equations.

- sgeir

### GENERAL SYSTEM OF LINEAR EQUATIONS

- cgefs
Solve a general system of linear equations.

- cgeir
- dgefs
Solve a general system of linear equations.

- sgefs
Solve a general system of linear equations.

- sgeir

### GENERAL-PURPOSE

- dqag
- dqage
- dqagi
- dqagie
- dqagp
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy break points of the integration interval, where local difficulties of the integrand may occur (e.g. SINGULARITIES, DISCONTINUITIES), are provided by the user.

- dqagpe
- dqags
- dqagse
- qag
- qage
- qagi
- qagie
- qagp
The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy break points of the integration interval, where local difficulties of the integrand may occur(e.g. SINGULARITIES, DISCONTINUITIES), are provided by the user.

- qagpe
- qags
- qagse

### GENERALIZED MINIMUM RESIDUAL

- dgmres
Preconditioned GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with preconditioning to solve non-symmetric linear systems of the form: Ax = b.

- dhels
Internal routine for DGMRES.

- dheqr
Internal routine for DGMRES.

- dlpdoc
- dorth
Internal routine for DGMRES.

- dpigmr
Internal routine for DGMRES.

- drlcal
Internal routine for DGMRES.

- dsdgmr
Diagonally scaled GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with diagonal scaling to solve possibly non-symmetric linear systems of the form: Ax = b.

- dslugm
Incomplete LU GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with incomplete LU factorization for preconditioning to solve possibly non-symmetric linear systems of the form: Ax = b.

- dxlcal
Internal routine for DGMRES.

- sgmres
Preconditioned GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with preconditioning to solve non-symmetric linear systems of the form: Ax = b.

- shels
Internal routine for SGMRES.

- sheqr
Internal routine for SGMRES.

- slpdoc
- sorth
Internal routine for SGMRES.

- spigmr
Internal routine for SGMRES.

- srlcal
Internal routine for SGMRES.

- ssdgmr
Diagonally Scaled GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with diagonal scaling to solve possibly non-symmetric linear systems of the form: Ax = b.

- sslugm
Incomplete LU GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with incomplete LU factorization for preconditioning to solve possibly non-symmetric linear systems of the form: Ax = b.

- sxlcal
Internal routine for SGMRES.

### GIVENS ROTATION

- crotg
Construct a Givens transformation.

- csrot
Apply a plane Givens rotation.

- drot
Apply a plane Givens rotation.

- drotg
Construct a plane Givens rotation.

- srot
Apply a plane Givens rotation.

- srotg
Construct a plane Givens rotation.

### GIVENS TRANSFORMATION

- crotg
Construct a Givens transformation.

- csrot
Apply a plane Givens rotation.

- drot
Apply a plane Givens rotation.

- drotg
Construct a plane Givens rotation.

- srot
Apply a plane Givens rotation.

- srotg
Construct a plane Givens rotation.

### GLOBALLY ADAPTIVE

- dqag
- dqage
- dqagi
- dqagie
- dqagp
- dqagpe
- dqags
- dqagse
- dqawc
- dqawo
- dqawoe
- dqaws
- qag
- qage
- qagi
- qagie
- qagp
- qagpe
- qags
- qagse
- qawc
- qawo
- qawoe
- qaws

### GMRES

- isdgmr
Generalized Minimum Residual Stop Test. This routine calculates the stop test for the Generalized Minimum RESidual (GMRES) iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- issgmr
Generalized Minimum Residual Stop Test. This routine calculates the stop test for the Generalized Minimum RESidual (GMRES) iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

### GRADIENTS

- chkder
Check the gradients of M nonlinear functions in N variables, evaluated at a point X, for consistency with the functions themselves.

- dckder
Check the gradients of M nonlinear functions in N variables, evaluated at a point X, for consistency with the functions themselves.

### GUIDELINES FOR SELECTION

- qpdoc
Documentation for QUADPACK, a package of subprograms for automatic evaluation of one-dimensional definite integrals.

### H BESSEL FUNCTIONS

- cbesh
- zbesh

### HANKEL FUNCTIONS

- cbesh
- zbesh

### HELMHOLTZ

- hstcrt
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in Cartesian coordinates.

- hstcsp
Solve the standard five-point finite difference approximation on a staggered grid to the modified Helmholtz equation in spherical coordinates assuming axisymmetry (no dependence on longitude).

- hstcyl
- hstplr
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in polar coordinates.

- hstssp
Solve the standard five-point finite difference approximation on a staggered grid to the Helmholtz equation in spherical coordinates and on the surface of the unit sphere (radius of 1).

- hw3crt
- hwscrt
- hwscsp
Solve a finite difference approximation to the modified Helmholtz equation in spherical coordinates assuming axisymmetry (no dependence on longitude).

- hwscyl
- hwsplr
Solve a finite difference approximation to the Helmholtz equation in polar coordinates.

- hwsssp
Solve a finite difference approximation to the Helmholtz equation in spherical coordinates and on the surface of the unit sphere (radius of 1).

- pois3d
Solve a three-dimensional block tridiagonal linear system which arises from a finite difference approximation to a three-dimensional Poisson equation using the Fourier transform package FFTPAK written by Paul Swarztrauber.

- poistg
Solve a block tridiagonal system of linear equations that results from a staggered grid finite difference approximation to 2-D elliptic PDE's.

- sepeli
Discretize and solve a second and, optionally, a fourth order finite difference approximation on a uniform grid to the general separable elliptic partial differential equation on a rectangle with any combination of periodic or mixed boundary conditions.

- sepx4
Solve for either the second or fourth order finite difference approximation to the solution of a separable elliptic partial differential equation on a rectangle. Any combination of periodic or mixed boundary conditions is allowed.

### HERMITE INTERPOLATION

- dpchfd
Evaluate a piecewise cubic Hermite function and its first derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC. If only function values are required, use DPCHFE instead.

- dpchfe
Evaluate a piecewise cubic Hermite function at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC.

- pchfd
Evaluate a piecewise cubic Hermite function and its first derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC. If only function values are required, use PCHFE instead.

- pchfe
Evaluate a piecewise cubic Hermite function at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC.

### HERMITIAN

- chico
Factor a complex Hermitian matrix by elimination with sym- metric pivoting and estimate the condition of the matrix.

- chidi
Compute the determinant, inertia and inverse of a complex Hermitian matrix using the factors obtained from CHIFA.

- chifa
Factor a complex Hermitian matrix by elimination (symmetric pivoting).

- chisl
Solve the complex Hermitian system using factors obtained from CHIFA.

- chpco
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- chpdi
Compute the determinant, inertia and inverse of a complex Hermitian matrix stored in packed form using the factors obtained from CHPFA.

- chpfa
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting.

- chpsl
Solve a complex Hermitian system using factors obtained from CHPFA.

- cpofs
Solve a positive definite symmetric complex system of linear equations.

- cpoir
Solve a positive definite Hermitian system of linear equations. Iterative refinement is used to obtain an error estimate.

- dpofs
Solve a positive definite symmetric system of linear equations.

- spofs
Solve a positive definite symmetric system of linear equations.

- spoir
Solve a positive definite symmetric system of linear equations. Iterative refinement is used to obtain an error estimate.

### HYPERBOLIC BESSEL FUNCTION

- besi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- besi0e
- besi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- besi1e
- besk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- besk0e
- besk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- besk1e
- dbesi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- dbesi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- dbesk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- dbesk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- dbsi0e
- dbsi1e
- dbsk0e
- dbsk1e

### HYPERBOLIC COSINE

- ccosh
Compute the complex hyperbolic cosine.

### HYPERBOLIC SINE

- csinh
Compute the complex hyperbolic sine.

### HYPERBOLIC TANGENT

- ctanh
Compute the complex hyperbolic tangent.

### I BESSEL FUNCTION

- besi
Compute an N member sequence of I Bessel functions I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X.

- dbesi
Compute an N member sequence of I Bessel functions I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for nonnegative ALPHA and X.

### I BESSEL FUNCTIONS

- cbesi
Compute a sequence of the Bessel functions I(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesi

### IMPLICIT DIFFERENTIAL SYSTEMS

- ddassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

- sdassl
This code solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0.

### INCOMPLETE BETA FUNCTION

### INCOMPLETE CHOLESKY

- dsiccg
Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the incomplete Cholesky Preconditioned Conjugate Gradient method.

- ssiccg
Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the incomplete Cholesky Preconditioned Conjugate Gradient method.

### INCOMPLETE CHOLESKY FACTORIZATION

- dsics
Incompl. Cholesky Decomposition Preconditioner SLAP Set Up. Routine to generate the Incomplete Cholesky decomposition, L*D*L-trans, of a symmetric positive definite matrix, A, which is stored in SLAP Column format. The unit lower triangular matrix L is stored by rows, and the inverse of the diagonal matrix D is stored.

- ssics
Incompl. Cholesky Decomposition Preconditioner SLAP Set Up. Routine to generate the Incomplete Cholesky decomposition, L*D*L-trans, of a symmetric positive definite matrix, A, which is stored in SLAP Column format. The unit lower triangular matrix L is stored by rows, and the inverse of the diagonal matrix D is stored.

### INCOMPLETE ELLIPTIC INTEGRAL

- drd
Compute the incomplete or complete elliptic integral of the 2nd kind. For X and Y nonnegative, X+Y and Z positive, DRD(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -3/2 (3/2)(t+X) (t+Y) (t+Z) dt. If X or Y is zero, the integral is complete.

- drf
- drj
- rd
Compute the incomplete or complete elliptic integral of the 2nd kind. For X and Y nonnegative, X+Y and Z positive, RD(X,Y,Z) = Integral from zero to infinity of -1/2 -1/2 -3/2 (3/2)(t+X) (t+Y) (t+Z) dt. If X or Y is zero, the integral is complete.

- rf
- rj

### INCOMPLETE FACTORIZATION

- dllti2
SLAP Backsolve routine for LDL' Factorization. Routine to solve a system of the form L*D*L' X = B, where L is a unit lower triangular matrix and D is a diagonal matrix and ' means transpose.

- sllti2
SLAP Backsolve routine for LDL' Factorization. Routine to solve a system of the form L*D*L' X = B, where L is a unit lower triangular matrix and D is a diagonal matrix and ' means transpose.

### INCOMPLETE GAMMA FUNCTION

- d9lgit
Compute the logarithm of Tricomi's incomplete Gamma function with Perron's continued fraction for large X and A .GE. X.

- dgami
Evaluate the incomplete Gamma function.

- gami
Evaluate the incomplete Gamma function.

- r9lgit

### INCOMPLETE LU FACTORIZATION

- dsilus
Incomplete LU Decomposition Preconditioner SLAP Set Up. Routine to generate the incomplete LDU decomposition of a matrix. The unit lower triangular factor L is stored by rows and the unit upper triangular factor U is stored by columns. The inverse of the diagonal matrix D is stored. No fill in is allowed.

- ssilus
Incomplete LU Decomposition Preconditioner SLAP Set Up. Routine to generate the incomplete LDU decomposition of a matrix. The unit lower triangular factor L is stored by rows and the unit upper triangular factor U is stored by columns. The inverse of the diagonal matrix D is stored. No fill in is allowed.

### INEQUALITY

- dbocls
- dbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

- sbocls
- sbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

### INEQUALITY CONSTRAINTS

- dlsei
- dwnnls
- lsei
- wnnls

### INFINITE INTERVALS

- dqagi
- dqagie
- qagi
- qagie

### INITIAL VALUE PROBLEMS

- cdriv1
The function of CDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. CDRIV1 allows complex-valued differential equations.

- cdriv2
The function of CDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. CDRIV2 allows complex-valued differential equations.

- cdriv3
The function of CDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. CDRIV3 allows complex-valued differential equations.

- ddeabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- ddebdf
- dderkf
Solve an initial value problem in ordinary differential equations using a Runge-Kutta-Fehlberg scheme.

- ddriv1
The function of DDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. DDRIV1 uses double precision arithmetic.

- ddriv2
The function of DDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. DDRIV2 uses double precision arithmetic.

- ddriv3
The function of DDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. DDRIV3 uses double precision arithmetic.

- deabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- debdf
- derkf
- dintp
Approximate the solution at XOUT by evaluating the polynomial computed in DSTEPS at XOUT. Must be used in conjunction with DSTEPS.

- dsteps
Integrate a system of first order ordinary differential equations one step.

- sdriv1
The function of SDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. SDRIV1 uses single precision arithmetic.

- sdriv2
The function of SDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. SDRIV2 uses single precision arithmetic.

- sdriv3
The function of SDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. SDRIV3 uses single precision arithmetic.

- sintrp
Approximate the solution at XOUT by evaluating the polynomial computed in STEPS at XOUT. Must be used in conjunction with STEPS.

- steps
Integrate a system of first order ordinary differential equations one step.

### INITIALIZE

- initds
- inits

### INNER PRODUCT

- cdcdot
Compute the inner product of two vectors with extended precision accumulation.

- cdotc
Dot product of two complex vectors using the complex conjugate of the first vector.

- cdotu
Compute the inner product of two vectors.

- dcdot
Compute the inner product of two vectors with extended precision accumulation and result.

- ddot
Compute the inner product of two vectors.

- dqdota
Compute the inner product of two vectors with extended precision accumulation and result.

- dqdoti
Compute the inner product of two vectors with extended precision accumulation and result.

- dsdot
Compute the inner product of two vectors with extended precision accumulation and result.

- sdot
Compute the inner product of two vectors.

- sdsdot
Compute the inner product of two vectors with extended precision accumulation.

### INTEGRAL OF B-SPLINE

- bfqad
Compute the integral of a product of a function and a derivative of a B-spline.

- dbfqad
Compute the integral of a product of a function and a derivative of a K-th order B-spline.

### INTEGRAL OF B-SPLINES

- bsqad
Compute the integral of a K-th order B-spline using the B-representation.

- dbsqad
Compute the integral of a K-th order B-spline using the B-representation.

### INTEGRAL OF THE FIRST KIND

- drf
- rf

### INTEGRAL OF THE SECOND KIND

- drd
- rd

### INTEGRAL OF THE THIRD KIND

- drj
- rj

### INTEGRALS OF BESSEL FUNCTIONS

- bskin
Compute repeated integrals of the K-zero Bessel function.

- dbskin
Compute repeated integrals of the K-zero Bessel function.

### INTEGRAND EXAMINATOR

- dqag
- dqage
- qag
- qage

### INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR

- dqawo
- dqawoe
- qawo
- qawoe

### INTEGRATION

- avint
Integrate a function tabulated at arbitrarily spaced abscissas using overlapping parabolas.

- davint
Integrate a function tabulated at arbitrarily spaced abscissas using overlapping parabolas.

- dqnc79
Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.

- qnc79
Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.

### INTEGRATION BETWEEN ZEROS

- dqawf
- dqawfe
- qawf
- qawfe

### INTEGRATION RULES FOR FUNCTIONS WITH COS OR SIN FACTOR

- dqc25f
To compute the integral I=Integral of F(X) over (A,B) Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to compute J = Integral of ABS(F) over (A,B). For small value of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO Rule is used. Otherwise a generalized CLENSHAW-CURTIS method is used.

- qc25f
To compute the integral I=Integral of F(X) over (A,B) Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X) and to compute J=Integral of ABS(F) over (A,B). For small value of OMEGA or small intervals (A,B) 15-point GAUSS- KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

### INTERCHANGE

- cswap
Interchange two vectors.

- dswap
Interchange two vectors.

- iswap
Interchange two vectors.

- sswap
Interchange two vectors.

### INTERPOLATION

- bint4
Compute the B-representation of a cubic spline which interpolates given data.

- bintk
Compute the B-representation of a spline which interpolates given data.

- bspdr
- bspev
Calculate the value of the spline and its derivatives from the B-representation.

- dbint4
Compute the B-representation of a cubic spline which interpolates given data.

- dbintk
Compute the B-representation of a spline which interpolates given data.

- dbspdr
- dbspev
Calculate the value of the spline and its derivatives from the B-representation.

- dintrv
- dpfqad
- dppqad
- dppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

- intrv
- pfqad
- ppqad
- ppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

### INVERSE

- cgbdi
Compute the determinant of a complex band matrix using the factors from CGBCO or CGBFA.

- cgedi
Compute the determinant and inverse of a matrix using the factors computed by CGECO or CGEFA.

- chidi
Compute the determinant, inertia and inverse of a complex Hermitian matrix using the factors obtained from CHIFA.

- chpdi
Compute the determinant, inertia and inverse of a complex Hermitian matrix stored in packed form using the factors obtained from CHPFA.

- cpbdi
Compute the determinant of a complex Hermitian positive definite band matrix using the factors computed by CPBCO or CPBFA.

- cpodi
Compute the determinant and inverse of a certain complex Hermitian positive definite matrix using the factors computed by CPOCO, CPOFA, or CQRDC.

- cppdi
Compute the determinant and inverse of a complex Hermitian positive definite matrix using factors from CPPCO or CPPFA.

- csidi
Compute the determinant and inverse of a complex symmetric matrix using the factors from CSIFA.

- cspdi
Compute the determinant and inverse of a complex symmetric matrix stored in packed form using the factors from CSPFA.

- ctrdi
Compute the determinant and inverse of a triangular matrix.

- dgbdi
Compute the determinant of a band matrix using the factors computed by DGBCO or DGBFA.

- dgedi
Compute the determinant and inverse of a matrix using the factors computed by DGECO or DGEFA.

- dpbdi
Compute the determinant of a symmetric positive definite band matrix using the factors computed by DPBCO or DPBFA.

- dpodi
Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by DPOCO, DPOFA or DQRDC.

- dppdi
Compute the determinant and inverse of a real symmetric positive definite matrix using factors from DPPCO or DPPFA.

- dsidi
Compute the determinant, inertia and inverse of a real symmetric matrix using the factors from DSIFA.

- dspdi
Compute the determinant, inertia, inverse of a real symmetric matrix stored in packed form using the factors from DSPFA.

- dtrdi
Compute the determinant and inverse of a triangular matrix.

- sgbdi
Compute the determinant of a band matrix using the factors computed by SGBCO or SGBFA.

- sgedi
Compute the determinant and inverse of a matrix using the factors computed by SGECO or SGEFA.

- spbdi
Compute the determinant of a symmetric positive definite band matrix using the factors computed by SPBCO or SPBFA.

- spodi
Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by SPOCO, SPOFA or SQRDC.

- sppdi
Compute the determinant and inverse of a real symmetric positive definite matrix using factors from SPPCO or SPPFA.

- ssidi
Compute the determinant, inertia and inverse of a real symmetric matrix using the factors from SSIFA.

- sspdi
Compute the determinant, inertia, inverse of a real symmetric matrix stored in packed form using the factors from SSPFA.

- strdi
Compute the determinant and inverse of a triangular matrix.

### INVERSE COSINE FOURIER TRANSFORM

- cosqb
Compute the unnormalized inverse cosine transform.

### INVERSE HYPERBOLIC COSINE

- acosh
Compute the arc hyperbolic cosine.

- cacosh
Compute the arc hyperbolic cosine.

- dacosh
Compute the arc hyperbolic cosine.

### INVERSE HYPERBOLIC SINE

- asinh
Compute the arc hyperbolic sine.

- casinh
Compute the arc hyperbolic sine.

- dasinh
Compute the arc hyperbolic sine.

### INVERSE HYPERBOLIC TANGENT

- atanh
Compute the arc hyperbolic tangent.

- catanh
Compute the arc hyperbolic tangent.

- datanh
Compute the arc hyperbolic tangent.

### ITERATIVE IMPROVEMENT

- dlpdoc
- slpdoc

### ITERATIVE INCOMPLETE LU PRECONDITION

- dslubc
Incomplete LU BiConjugate Gradient Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient method with Incomplete LU decomposition preconditioning.

- dslucn
Incomplete LU CG Sparse Ax=b Solver for Normal Equations. Routine to solve a general linear system Ax = b using the incomplete LU decomposition with the Conjugate Gradient method applied to the normal equations, viz., AA'y = b, x = A'y.

- dslucs
Incomplete LU BiConjugate Gradient Squared Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient Squared method with Incomplete LU decomposition preconditioning.

- dsluom
Incomplete LU Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Orthomin method with Incomplete LU decomposition.

- sslubc
Incomplete LU BiConjugate Gradient Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient method with Incomplete LU decomposition preconditioning.

- sslucn
Incomplete LU CG Sparse Ax=b Solver for Normal Equations. Routine to solve a general linear system Ax = b using the incomplete LU decomposition with the Conjugate Gradient method applied to the normal equations, viz., AA'y = b, x = A'y.

- sslucs
Incomplete LU BiConjugate Gradient Squared Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient Squared method with Incomplete LU decomposition preconditioning.

- ssluom
Incomplete LU Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Orthomin method with Incomplete LU decomposition.

### ITERATIVE PRECONDITION

- dbcg
Preconditioned BiConjugate Gradient Sparse Ax = b Solver. Routine to solve a Non-Symmetric linear system Ax = b using the Preconditioned BiConjugate Gradient method.

- dcg
Preconditioned Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the Preconditioned Conjugate Gradient method.

- dcgn
Preconditioned CG Sparse Ax=b Solver for Normal Equations. Routine to solve a general linear system Ax = b using the Preconditioned Conjugate Gradient method applied to the normal equations AA'y = b, x=A'y.

- dcgs
Preconditioned BiConjugate Gradient Squared Ax=b Solver. Routine to solve a Non-Symmetric linear system Ax = b using the Preconditioned BiConjugate Gradient Squared method.

- dgmres
Preconditioned GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with preconditioning to solve non-symmetric linear systems of the form: Ax = b.

- dhels
Internal routine for DGMRES.

- dheqr
Internal routine for DGMRES.

- dir
Preconditioned Iterative Refinement Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using iterative refinement with a matrix splitting.

- dllti2
SLAP Backsolve routine for LDL' Factorization. Routine to solve a system of the form L*D*L' X = B, where L is a unit lower triangular matrix and D is a diagonal matrix and ' means transpose.

- domn
Preconditioned Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Preconditioned Orthomin method.

- dorth
Internal routine for DGMRES.

- dpigmr
Internal routine for DGMRES.

- drlcal
Internal routine for DGMRES.

- dsdbcg
Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient method with diagonal scaling.

- dsdcg
Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the Preconditioned Conjugate Gradient method. The preconditioner is diagonal scaling.

- dsdcgn
Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's. Routine to solve a general linear system Ax = b using diagonal scaling with the Conjugate Gradient method applied to the the normal equations, viz., AA'y = b, where x = A'y.

- dsdcgs
Diagonally Scaled CGS Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient Squared method with diagonal scaling.

- dsdgmr
Diagonally scaled GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with diagonal scaling to solve possibly non-symmetric linear systems of the form: Ax = b.

- dsdi
Diagonal Matrix Vector Multiply. Routine to calculate the product X = DIAG*B, where DIAG is a diagonal matrix.

- dsdomn
Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Orthomin method with diagonal scaling.

- dsgs
Gauss-Seidel Method Iterative Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using Gauss-Seidel iteration.

- dsiccg
Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the incomplete Cholesky Preconditioned Conjugate Gradient method.

- dsics
Incompl. Cholesky Decomposition Preconditioner SLAP Set Up. Routine to generate the Incomplete Cholesky decomposition, L*D*L-trans, of a symmetric positive definite matrix, A, which is stored in SLAP Column format. The unit lower triangular matrix L is stored by rows, and the inverse of the diagonal matrix D is stored.

- dsilur
Incomplete LU Iterative Refinement Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using the incomplete LU decomposition with iterative refinement.

- dsilus
Incomplete LU Decomposition Preconditioner SLAP Set Up. Routine to generate the incomplete LDU decomposition of a matrix. The unit lower triangular factor L is stored by rows and the unit upper triangular factor U is stored by columns. The inverse of the diagonal matrix D is stored. No fill in is allowed.

- dsjac
Jacobi's Method Iterative Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using Jacobi iteration.

- dsli
SLAP MSOLVE for Lower Triangle Matrix. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes L B = X.

- dsli2
SLAP Lower Triangle Matrix Backsolve. Routine to solve a system of the form Lx = b , where L is a lower triangular matrix.

- dsllti
SLAP MSOLVE for LDL' (IC) Factorization. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes (LDL') B = X.

- dslugm
Incomplete LU GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with incomplete LU factorization for preconditioning to solve possibly non-symmetric linear systems of the form: Ax = b.

- dslui
SLAP MSOLVE for LDU Factorization. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes (LDU) B = X.

- dslui2
SLAP Backsolve for LDU Factorization. Routine to solve a system of the form L*D*U X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix.

- dslui4
SLAP Backsolve for LDU Factorization. Routine to solve a system of the form (L*D*U)' X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix and ' denotes transpose.

- dsluti
SLAP MTSOLV for LDU Factorization. This routine acts as an interface between the SLAP generic MTSOLV calling convention and the routine that actually -T computes (LDU) B = X.

- dsmmi2
SLAP Backsolve for LDU Factorization of Normal Equations. To solve a system of the form (L*D*U)*(L*D*U)' X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix and ' denotes transpose.

- dsmmti
SLAP MSOLVE for LDU Factorization of Normal Equations. This routine acts as an interface between the SLAP generic MMTSLV calling convention and the routine that actually -1 computes [(LDU)*(LDU)'] B = X.

- dxlcal
Internal routine for DGMRES.

- isdbcg
Preconditioned BiConjugate Gradient Stop Test. This routine calculates the stop test for the BiConjugate Gradient iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdcgn
Preconditioned CG on Normal Equations Stop Test. This routine calculates the stop test for the Conjugate Gradient iteration scheme applied to the normal equations. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdcgs
Preconditioned BiConjugate Gradient Squared Stop Test. This routine calculates the stop test for the BiConjugate Gradient Squared iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdomn
Preconditioned Orthomin Stop Test. This routine calculates the stop test for the Orthomin iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- issbcg
Preconditioned BiConjugate Gradient Stop Test. This routine calculates the stop test for the BiConjugate Gradient iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isscgn
Preconditioned CG on Normal Equations Stop Test. This routine calculates the stop test for the Conjugate Gradient iteration scheme applied to the normal equations. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isscgs
Preconditioned BiConjugate Gradient Squared Stop Test. This routine calculates the stop test for the BiConjugate Gradient Squared iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- issomn
Preconditioned Orthomin Stop Test. This routine calculates the stop test for the Orthomin iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- sbcg
- scg
Preconditioned Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the Preconditioned Conjugate Gradient method.

- scgn
Preconditioned CG Sparse Ax=b Solver for Normal Equations. Routine to solve a general linear system Ax = b using the Preconditioned Conjugate Gradient method applied to the normal equations AA'y = b, x=A'y.

- scgs
- sir
Preconditioned Iterative Refinement Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using iterative refinement with a matrix splitting.

- sgmres
Preconditioned GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with preconditioning to solve non-symmetric linear systems of the form: Ax = b.

- shels
Internal routine for SGMRES.

- sheqr
Internal routine for SGMRES.

- sllti2
- somn
Preconditioned Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Preconditioned Orthomin method.

- sorth
Internal routine for SGMRES.

- spigmr
Internal routine for SGMRES.

- srlcal
Internal routine for SGMRES.

- ssdbcg
Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient method with diagonal scaling.

- ssdcg
Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the Preconditioned Conjugate Gradient method. The preconditioner is diagonal scaling.

- ssdcgn
Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's. Routine to solve a general linear system Ax = b using diagonal scaling with the Conjugate Gradient method applied to the the normal equations, viz., AA'y = b, where x = A'y.

- ssdcgs
Diagonally Scaled CGS Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient Squared method with diagonal scaling.

- ssdgmr
Diagonally Scaled GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with diagonal scaling to solve possibly non-symmetric linear systems of the form: Ax = b.

- ssdi
Diagonal Matrix Vector Multiply. Routine to calculate the product X = DIAG*B, where DIAG is a diagonal matrix.

- ssdomn
Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Orthomin method with diagonal scaling.

- ssgs
Gauss-Seidel Method Iterative Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using Gauss-Seidel iteration.

- ssiccg
- ssics
- ssilur
Incomplete LU Iterative Refinement Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using the incomplete LU decomposition with iterative refinement.

- ssilus
- ssjac
Jacobi's Method Iterative Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using Jacobi iteration.

- ssli
SLAP MSOLVE for Lower Triangle Matrix. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes L B = X.

- ssli2
SLAP Lower Triangle Matrix Backsolve. Routine to solve a system of the form Lx = b , where L is a lower triangular matrix.

- ssllti
SLAP MSOLVE for LDL' (IC) Factorization. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes (LDL') B = X.

- sslugm
Incomplete LU GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with incomplete LU factorization for preconditioning to solve possibly non-symmetric linear systems of the form: Ax = b.

- sslui
SLAP MSOLVE for LDU Factorization. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes (LDU) B = X.

- sslui2
SLAP Backsolve for LDU Factorization. Routine to solve a system of the form L*D*U X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix.

- sslui4
SLAP Backsolve for LDU Factorization. Routine to solve a system of the form (L*D*U)' X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix and ' denotes transpose.

- ssluti
SLAP MTSOLV for LDU Factorization. This routine acts as an interface between the SLAP generic MTSOLV calling convention and the routine that actually -T computes (LDU) B = X.

- ssmmi2
SLAP Backsolve for LDU Factorization of Normal Equations. To solve a system of the form (L*D*U)*(L*D*U)' X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix and ' denotes transpose.

- ssmmti
SLAP MSOLVE for LDU Factorization of Normal Equations. This routine acts as an interface between the SLAP generic MMTSLV calling convention and the routine that actually -1 computes [(LDU)*(LDU)'] B = X.

- sxlcal
Internal routine for SGMRES.

### J BESSEL FUNCTION

- besj
Compute an N member sequence of J Bessel functions J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X.

- dbesj
Compute an N member sequence of J Bessel functions J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X.

### J BESSEL FUNCTIONS

- cbesj
- zbesj

### JACOBIAN

- chkder
Check the gradients of M nonlinear functions in N variables, evaluated at a point X, for consistency with the functions themselves.

- dckder

### K BESSEL FUNCTION

- besk
Implement forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive X and non-negative orders FNU.

- dbesk
Implement forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive X and non-negative orders FNU.

### K BESSEL FUNCTIONS

- cbesk
Compute a sequence of the Bessel functions K(a,z) for complex argument z and real nonnegative orders a=b,b+1, b+2,... where b>0. A scaling option is available to help avoid overflow.

- zbesk

### K-ZERO BESSEL FUNCTION

- bskin
Compute repeated integrals of the K-zero Bessel function.

- dbskin
Compute repeated integrals of the K-zero Bessel function.

### L2

- dnrm2
Compute the Euclidean length (L2 norm) of a vector.

- scnrm2
Compute the unitary norm of a complex vector.

- snrm2
Compute the Euclidean length (L2 norm) of a vector.

### LARGE X

- d9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- r9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

### LEAST SQUARES

- bndacc
- bndsol
- dbndac
- dbndsl
- dbocls
- dbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

- dhfti
Solve a least squares problem for banded matrices using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

- dp1vlu
Use the coefficients generated by DPOLFT to evaluate the polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.

- dpcoef
Convert the DPOLFT coefficients to Taylor series form.

- dpolft
Fit discrete data in a least squares sense by polynomials in one variable.

- pcoef
Convert the POLFIT coefficients to Taylor series form.

- polfit
Fit discrete data in a least squares sense by polynomials in one variable.

- pvalue
Use the coefficients generated by POLFIT to evaluate the polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.

- sbocls
- sbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

### LEGENDRE FUNCTIONS

- dxlegf
Compute normalized Legendre polynomials and associated Legendre functions.

- dxnrmp
Compute normalized Legendre polynomials.

- dxpmu
To compute the values of Legendre functions for DXLEGF. Method: backward mu-wise recurrence for P(-MU,NU,X) for fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ..., P(-MU1,NU1,X) and store in ascending mu order.

- dxpmup
To compute the values of Legendre functions for DXLEGF. This subroutine transforms an array of Legendre functions of the first kind of negative order stored in array PQA into Legendre functions of the first kind of positive order stored in array PQA. The original array is destroyed.

- dxpnrm
To compute the values of Legendre functions for DXLEGF. This subroutine transforms an array of Legendre functions of the first kind of negative order stored in array PQA into normalized Legendre polynomials stored in array PQA. The original array is destroyed.

- dxpqnu
To compute the values of Legendre functions for DXLEGF. This subroutine calculates initial values of P or Q using power series, then performs forward nu-wise recurrence to obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise recurrence is stable for P for all mu and for Q for mu=0,1.

- dxqmu
To compute the values of Legendre functions for DXLEGF. Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).

- dxqnu
To compute the values of Legendre functions for DXLEGF. Method: backward nu-wise recurrence for Q(MU,NU,X) for fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ..., Q(MU1,NU2,X).

- xlegf
Compute normalized Legendre polynomials and associated Legendre functions.

- xnrmp
Compute normalized Legendre polynomials.

- xpmu
To compute the values of Legendre functions for XLEGF. Method: backward mu-wise recurrence for P(-MU,NU,X) for fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ..., P(-MU1,NU1,X) and store in ascending mu order.

- xpmup
To compute the values of Legendre functions for XLEGF. This subroutine transforms an array of Legendre functions of the first kind of negative order stored in array PQA into Legendre functions of the first kind of positive order stored in array PQA. The original array is destroyed.

- xpnrm
To compute the values of Legendre functions for XLEGF. This subroutine transforms an array of Legendre functions of the first kind of negative order stored in array PQA into normalized Legendre polynomials stored in array PQA. The original array is destroyed.

- xpqnu
To compute the values of Legendre functions for XLEGF. This subroutine calculates initial values of P or Q using power series, then performs forward nu-wise recurrence to obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise recurrence is stable for P for all mu and for Q for mu=0,1.

- xqmu
To compute the values of Legendre functions for XLEGF. Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).

- xqnu
To compute the values of Legendre functions for XLEGF. Method: backward nu-wise recurrence for Q(MU,NU,X) for fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ..., Q(MU1,NU2,X).

### LEVEL 2 BLAS

- cgbmv
Multiply a complex vector by a complex general band matrix.

- cgemv
Multiply a complex vector by a complex general matrix.

- cgerc
Perform conjugated rank 1 update of a complex general matrix.

- cgeru
Perform unconjugated rank 1 update of a complex general matrix.

- chbmv
Multiply a complex vector by a complex Hermitian band matrix.

- chemv
Multiply a complex vector by a complex Hermitian matrix.

- cher
Perform Hermitian rank 1 update of a complex Hermitian matrix.

- cher2
Perform Hermitian rank 2 update of a complex Hermitian matrix.

- chpmv
Perform the matrix-vector operation.

- chpr
Perform the hermitian rank 1 operation.

- chpr2
Perform the hermitian rank 2 operation.

- ctbmv
Multiply a complex vector by a complex triangular band matrix.

- ctbsv
Solve a complex triangular banded system of equations.

- ctpmv
Perform one of the matrix-vector operations.

- ctpsv
Solve one of the systems of equations.

- ctrmv
Multiply a complex vector by a complex triangular matrix.

- ctrsv
Solve a complex triangular system of equations.

- dgbmv
Perform one of the matrix-vector operations.

- dgemv
Perform one of the matrix-vector operations.

- dger
Perform the rank 1 operation.

- dsbmv
Perform the matrix-vector operation.

- dspmv
Perform the matrix-vector operation.

- dspr
Perform the symmetric rank 1 operation.

- dspr2
Perform the symmetric rank 2 operation.

- dsymv
Perform the matrix-vector operation.

- dsyr
Perform the symmetric rank 1 operation.

- dsyr2
Perform the symmetric rank 2 operation.

- dtbmv
Perform one of the matrix-vector operations.

- dtbsv
Solve one of the systems of equations.

- dtpmv
Perform one of the matrix-vector operations.

- dtpsv
Solve one of the systems of equations.

- dtrmv
Perform one of the matrix-vector operations.

- dtrsv
Solve one of the systems of equations.

- lsame
Test two characters to determine if they are the same letter, except for case.

- sgbmv
Multiply a real vector by a real general band matrix.

- sgemv
Multiply a real vector by a real general matrix.

- sger
Perform rank 1 update of a real general matrix.

- ssbmv
Multiply a real vector by a real symmetric band matrix.

- sspmv
Perform the matrix-vector operation.

- sspr
Performs the symmetric rank 1 operation.

- sspr2
Perform the symmetric rank 2 operation.

- ssymv
Multiply a real vector by a real symmetric matrix.

- ssyr
Perform symmetric rank 1 update of a real symmetric matrix.

- ssyr2
Perform symmetric rank 2 update of a real symmetric matrix.

- stbmv
Multiply a real vector by a real triangular band matrix.

- stbsv
Solve a real triangular banded system of linear equations.

- stpmv
Perform one of the matrix-vector operations.

- stpsv
Solve one of the systems of equations.

- strmv
Multiply a real vector by a real triangular matrix.

- strsv
Solve a real triangular system of linear equations.

### LEVEL 3 BLAS

- cgemm
Multiply a complex general matrix by a complex general matrix.

- chemm
Multiply a complex general matrix by a complex Hermitian matrix.

- cher2k
Perform Hermitian rank 2k update of a complex.

- cherk
Perform Hermitian rank k update of a complex Hermitian matrix.

- csymm
Multiply a complex general matrix by a complex symmetric matrix.

- csyr2k
Perform symmetric rank 2k update of a complex symmetric matrix.

- csyrk
Perform symmetric rank k update of a complex symmetric matrix.

- ctrmm
Multiply a complex general matrix by a complex triangular matrix.

- ctrsm
Solve a complex triangular system of equations with multiple right-hand sides.

- dgemm
Perform one of the matrix-matrix operations.

- dsymm
Perform one of the matrix-matrix operations.

- dsyr2k
Perform one of the symmetric rank 2k operations.

- dsyrk
Perform one of the symmetric rank k operations.

- dtrmm
Perform one of the matrix-matrix operations.

- dtrsm
Solve one of the matrix equations.

- lsame
Test two characters to determine if they are the same letter, except for case.

- sgemm
Multiply a real general matrix by a real general matrix.

- ssymm
Multiply a real general matrix by a real symmetric matrix.

- ssyr2k
Perform symmetric rank 2k update of a real symmetric matrix

- ssyrk
Perform symmetric rank k update of a real symmetric matrix.

- strmm
Multiply a real general matrix by a real triangular matrix.

- strsm
Solve a real triangular system of equations with multiple right-hand sides.

### LEVENBERG-MARQUARDT

- dnls1
Minimize the sum of the squares of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm.

- dnls1e
An easy-to-use code which minimizes the sum of the squares of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm.

- snls1
Minimize the sum of the squares of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm.

- snls1e

### LIMITS

- dgamlm
Compute the minimum and maximum bounds for the argument in the Gamma function.

- gamlim
Compute the minimum and maximum bounds for the argument in the Gamma function.

### LINEAR

- dbocls
- dbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

- sbocls
- sbols
Solve the problem E*X = F (in the least squares sense) with bounds on selected X values.

### LINEAR ALGEBRA

- caxpy
Compute a constant times a vector plus a vector.

- cchdc
- cchdd
- cchex
- cchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- ccopy
Copy a vector.

- cdcdot
Compute the inner product of two vectors with extended precision accumulation.

- cdotc
Dot product of two complex vectors using the complex conjugate of the first vector.

- cdotu
Compute the inner product of two vectors.

- cgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- cgbdi
Compute the determinant of a complex band matrix using the factors from CGBCO or CGBFA.

- cgbfa
Factor a band matrix using Gaussian elimination.

- cgbmv
Multiply a complex vector by a complex general band matrix.

- cgbsl
Solve the complex band system A*X=B or CTRANS(A)*X=B using the factors computed by CGBCO or CGBFA.

- cgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- cgedi
Compute the determinant and inverse of a matrix using the factors computed by CGECO or CGEFA.

- cgefa
Factor a matrix using Gaussian elimination.

- cgemm
Multiply a complex general matrix by a complex general matrix.

- cgemv
Multiply a complex vector by a complex general matrix.

- cgerc
Perform conjugated rank 1 update of a complex general matrix.

- cgeru
Perform unconjugated rank 1 update of a complex general matrix.

- cgesl
Solve the complex system A*X=B or CTRANS(A)*X=B using the factors computed by CGECO or CGEFA.

- cgtsl
Solve a tridiagonal linear system.

- chbmv
Multiply a complex vector by a complex Hermitian band matrix.

- chemm
Multiply a complex general matrix by a complex Hermitian matrix.

- chemv
Multiply a complex vector by a complex Hermitian matrix.

- cher
Perform Hermitian rank 1 update of a complex Hermitian matrix.

- cher2
Perform Hermitian rank 2 update of a complex Hermitian matrix.

- cher2k
Perform Hermitian rank 2k update of a complex.

- cherk
Perform Hermitian rank k update of a complex Hermitian matrix.

- chico
Factor a complex Hermitian matrix by elimination with sym- metric pivoting and estimate the condition of the matrix.

- chidi
- chifa
Factor a complex Hermitian matrix by elimination (symmetric pivoting).

- chisl
Solve the complex Hermitian system using factors obtained from CHIFA.

- chpco
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- chpdi
- chpfa
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting.

- chpmv
Perform the matrix-vector operation.

- chpr
Perform the hermitian rank 1 operation.

- chpr2
Perform the hermitian rank 2 operation.

- chpsl
Solve a complex Hermitian system using factors obtained from CHPFA.

- cpbco
Factor a complex Hermitian positive definite matrix stored in band form and estimate the condition number of the matrix.

- cpbdi
- cpbfa
Factor a complex Hermitian positive definite matrix stored in band form.

- cpbsl
Solve the complex Hermitian positive definite band system using the factors computed by CPBCO or CPBFA.

- cpoco
Factor a complex Hermitian positive definite matrix and estimate the condition number of the matrix.

- cpodi
Compute the determinant and inverse of a certain complex Hermitian positive definite matrix using the factors computed by CPOCO, CPOFA, or CQRDC.

- cpofa
Factor a complex Hermitian positive definite matrix.

- cposl
Solve the complex Hermitian positive definite linear system using the factors computed by CPOCO or CPOFA.

- cppco
Factor a complex Hermitian positive definite matrix stored in packed form and estimate the condition number of the matrix.

- cppdi
Compute the determinant and inverse of a complex Hermitian positive definite matrix using factors from CPPCO or CPPFA.

- cppfa
Factor a complex Hermitian positive definite matrix stored in packed form.

- cppsl
Solve the complex Hermitian positive definite system using the factors computed by CPPCO or CPPFA.

- cptsl
Solve a positive definite tridiagonal linear system.

- cqrdc
Use Householder transformations to compute the QR factorization of an N by P matrix. Column pivoting is a users option.

- cqrsl
Apply the output of CQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- crotg
Construct a Givens transformation.

- cscal
Multiply a vector by a constant.

- csico
Factor a complex symmetric matrix by elimination with symmetric pivoting and estimate the condition number of the matrix.

- csidi
Compute the determinant and inverse of a complex symmetric matrix using the factors from CSIFA.

- csifa
Factor a complex symmetric matrix by elimination with symmetric pivoting.

- csisl
Solve a complex symmetric system using the factors obtained from CSIFA.

- cspco
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- cspdi
Compute the determinant and inverse of a complex symmetric matrix stored in packed form using the factors from CSPFA.

- cspfa
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting.

- cspsl
Solve a complex symmetric system using the factors obtained from CSPFA.

- csrot
Apply a plane Givens rotation.

- csscal
Scale a complex vector.

- csvdc
Perform the singular value decomposition of a rectangular matrix.

- cswap
Interchange two vectors.

- csymm
Multiply a complex general matrix by a complex symmetric matrix.

- csyr2k
Perform symmetric rank 2k update of a complex symmetric matrix.

- csyrk
Perform symmetric rank k update of a complex symmetric matrix.

- ctbmv
Multiply a complex vector by a complex triangular band matrix.

- ctbsv
Solve a complex triangular banded system of equations.

- ctpmv
Perform one of the matrix-vector operations.

- ctpsv
Solve one of the systems of equations.

- ctrco
Estimate the condition number of a triangular matrix.

- ctrdi
Compute the determinant and inverse of a triangular matrix.

- ctrmm
Multiply a complex general matrix by a complex triangular matrix.

- ctrmv
Multiply a complex vector by a complex triangular matrix.

- ctrsl
Solve a system of the form T*X=B or CTRANS(T)*X=B, where T is a triangular matrix. Here CTRANS(T) is the conjugate transpose.

- ctrsm
Solve a complex triangular system of equations with multiple right-hand sides.

- ctrsv
Solve a complex triangular system of equations.

- dasum
Compute the sum of the magnitudes of the elements of a vector.

- daxpy
Compute a constant times a vector plus a vector.

- dcdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dchdc
- dchdd
- dchex
- dchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- dcopy
Copy a vector.

- ddot
Compute the inner product of two vectors.

- dgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- dgbdi
Compute the determinant of a band matrix using the factors computed by DGBCO or DGBFA.

- dgbfa
Factor a band matrix using Gaussian elimination.

- dgbmv
Perform one of the matrix-vector operations.

- dgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by DGBCO or DGBFA.

- dgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- dgedi
Compute the determinant and inverse of a matrix using the factors computed by DGECO or DGEFA.

- dgefa
Factor a matrix using Gaussian elimination.

- dgemm
Perform one of the matrix-matrix operations.

- dgemv
Perform one of the matrix-vector operations.

- dger
Perform the rank 1 operation.

- dgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors computed by DGECO or DGEFA.

- dgtsl
Solve a tridiagonal linear system.

- dnrm2
Compute the Euclidean length (L2 norm) of a vector.

- dpbco
- dpbdi
- dpbfa
Factor a real symmetric positive definite matrix stored in in band form.

- dpbsl
Solve a real symmetric positive definite band system using the factors computed by DPBCO or DPBFA.

- dpoco
Factor a real symmetric positive definite matrix and estimate the condition of the matrix.

- dpodi
Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by DPOCO, DPOFA or DQRDC.

- dpofa
Factor a real symmetric positive definite matrix.

- dposl
Solve the real symmetric positive definite linear system using the factors computed by DPOCO or DPOFA.

- dppco
Factor a symmetric positive definite matrix stored in packed form and estimate the condition number of the matrix.

- dppdi
Compute the determinant and inverse of a real symmetric positive definite matrix using factors from DPPCO or DPPFA.

- dppfa
Factor a real symmetric positive definite matrix stored in packed form.

- dppsl
Solve the real symmetric positive definite system using the factors computed by DPPCO or DPPFA.

- dptsl
Solve a positive definite tridiagonal linear system.

- dqrdc
Use Householder transformations to compute the QR factorization of an N by P matrix. Column pivoting is a users option.

- dqrsl
Apply the output of DQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- drot
Apply a plane Givens rotation.

- drotg
Construct a plane Givens rotation.

- drotm
Apply a modified Givens transformation.

- drotmg
Construct a modified Givens transformation.

- dsbmv
Perform the matrix-vector operation.

- dscal
Multiply a vector by a constant.

- dsdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dsico
Factor a symmetric matrix by elimination with symmetric pivoting and estimate the condition number of the matrix.

- dsidi
Compute the determinant, inertia and inverse of a real symmetric matrix using the factors from DSIFA.

- dsifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- dsisl
Solve a real symmetric system using the factors obtained from SSIFA.

- dspco
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- dspdi
Compute the determinant, inertia, inverse of a real symmetric matrix stored in packed form using the factors from DSPFA.

- dspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- dspmv
Perform the matrix-vector operation.

- dspr
Perform the symmetric rank 1 operation.

- dspr2
Perform the symmetric rank 2 operation.

- dspsl
Solve a real symmetric system using the factors obtained from DSPFA.

- dsvdc
Perform the singular value decomposition of a rectangular matrix.

- dswap
Interchange two vectors.

- dsymm
Perform one of the matrix-matrix operations.

- dsymv
Perform the matrix-vector operation.

- dsyr
Perform the symmetric rank 1 operation.

- dsyr2
Perform the symmetric rank 2 operation.

- dsyr2k
Perform one of the symmetric rank 2k operations.

- dsyrk
Perform one of the symmetric rank k operations.

- dtbmv
Perform one of the matrix-vector operations.

- dtbsv
Solve one of the systems of equations.

- dtpmv
Perform one of the matrix-vector operations.

- dtpsv
Solve one of the systems of equations.

- dtrco
Estimate the condition number of a triangular matrix.

- dtrdi
Compute the determinant and inverse of a triangular matrix.

- dtrmm
Perform one of the matrix-matrix operations.

- dtrmv
Perform one of the matrix-vector operations.

- dtrsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

- dtrsm
Solve one of the matrix equations.

- dtrsv
Solve one of the systems of equations.

- icamax
Find the smallest index of the component of a complex vector having the maximum sum of magnitudes of real and imaginary parts.

- icopy
Copy a vector.

- idamax
Find the smallest index of that component of a vector having the maximum magnitude.

- isamax
Find the smallest index of that component of a vector having the maximum magnitude.

- iswap
Interchange two vectors.

- sasum
Compute the sum of the magnitudes of the elements of a vector.

- saxpy
Compute a constant times a vector plus a vector.

- scasum
Compute the sum of the magnitudes of the real and imaginary elements of a complex vector.

- schdc
- schdd
- schex
Update the Cholesky factorization A=TRANS(R)*R of A positive definite matrix A of order P under diagonal permutations of the form TRANS(E)*A*E, where E is a permutation matrix.

- schud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- scnrm2
Compute the unitary norm of a complex vector.

- scopy
Copy a vector.

- sdot
Compute the inner product of two vectors.

- sdsdot
Compute the inner product of two vectors with extended precision accumulation.

- sgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- sgbdi
Compute the determinant of a band matrix using the factors computed by SGBCO or SGBFA.

- sgbfa
Factor a band matrix using Gaussian elimination.

- sgbmv
Multiply a real vector by a real general band matrix.

- sgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by SGBCO or SGBFA.

- sgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- sgedi
Compute the determinant and inverse of a matrix using the factors computed by SGECO or SGEFA.

- sgefa
Factor a matrix using Gaussian elimination.

- sgemm
Multiply a real general matrix by a real general matrix.

- sgemv
Multiply a real vector by a real general matrix.

- sger
Perform rank 1 update of a real general matrix.

- sgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors of SGECO or SGEFA.

- sgtsl
Solve a tridiagonal linear system.

- snrm2
Compute the Euclidean length (L2 norm) of a vector.

- spbco
- spbdi
- spbfa
Factor a real symmetric positive definite matrix stored in band form.

- spbsl
Solve a real symmetric positive definite band system using the factors computed by SPBCO or SPBFA.

- spoco
Factor a real symmetric positive definite matrix and estimate the condition number of the matrix.

- spodi
Compute the determinant and inverse of a certain real symmetric positive definite matrix using the factors computed by SPOCO, SPOFA or SQRDC.

- spofa
Factor a real symmetric positive definite matrix.

- sposl
Solve the real symmetric positive definite linear system using the factors computed by SPOCO or SPOFA.

- sppco
- sppdi
Compute the determinant and inverse of a real symmetric positive definite matrix using factors from SPPCO or SPPFA.

- sppfa
Factor a real symmetric positive definite matrix stored in packed form.

- sppsl
Solve the real symmetric positive definite system using the factors computed by SPPCO or SPPFA.

- sptsl
Solve a positive definite tridiagonal linear system.

- sqrdc
Use Householder transformations to compute the QR factorization of an N by P matrix. Column pivoting is a users option.

- sqrsl
Apply the output of SQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- srot
Apply a plane Givens rotation.

- srotg
Construct a plane Givens rotation.

- srotm
Apply a modified Givens transformation.

- srotmg
Construct a modified Givens transformation.

- ssbmv
Multiply a real vector by a real symmetric band matrix.

- sscal
Multiply a vector by a constant.

- ssico
- ssidi
Compute the determinant, inertia and inverse of a real symmetric matrix using the factors from SSIFA.

- ssifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- ssisl
Solve a real symmetric system using the factors obtained from SSIFA.

- sspco
- sspdi
Compute the determinant, inertia, inverse of a real symmetric matrix stored in packed form using the factors from SSPFA.

- sspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- sspmv
Perform the matrix-vector operation.

- sspr
Performs the symmetric rank 1 operation.

- sspr2
Perform the symmetric rank 2 operation.

- sspsl
Solve a real symmetric system using the factors obtained from SSPFA.

- ssvdc
Perform the singular value decomposition of a rectangular matrix.

- sswap
Interchange two vectors.

- ssymm
Multiply a real general matrix by a real symmetric matrix.

- ssymv
Multiply a real vector by a real symmetric matrix.

- ssyr
Perform symmetric rank 1 update of a real symmetric matrix.

- ssyr2
Perform symmetric rank 2 update of a real symmetric matrix.

- ssyr2k
Perform symmetric rank 2k update of a real symmetric matrix

- ssyrk
Perform symmetric rank k update of a real symmetric matrix.

- stbmv
Multiply a real vector by a real triangular band matrix.

- stbsv
Solve a real triangular banded system of linear equations.

- stpmv
Perform one of the matrix-vector operations.

- stpsv
Solve one of the systems of equations.

- strco
Estimate the condition number of a triangular matrix.

- strdi
Compute the determinant and inverse of a triangular matrix.

- strmm
Multiply a real general matrix by a real triangular matrix.

- strmv
Multiply a real vector by a real triangular matrix.

- strsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

- strsm
Solve a real triangular system of equations with multiple right-hand sides.

- strsv
Solve a real triangular system of linear equations.

### LINEAR CONSTRAINTS

- dsplp
Solve linear programming problems involving at most a few thousand constraints and variables. Takes advantage of sparsity in the constraint matrix.

- splp
Solve linear programming problems involving at most a few thousand constraints and variables. Takes advantage of sparsity in the constraint matrix.

### LINEAR EQUATIONS

- cnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- cnbdi
Compute the determinant of a band matrix using the factors computed by CNBCO or CNBFA.

- cnbfa
Factor a band matrix by elimination.

- cnbfs
Solve a general nonsymmetric banded system of linear equations.

- cnbir
Solve a general nonsymmetric banded system of linear equations. Iterative refinement is used to obtain an error estimate.

- cnbsl
Solve a complex band system using the factors computed by CNBCO or CNBFA.

- cpofs
Solve a positive definite symmetric complex system of linear equations.

- cpoir
Solve a positive definite Hermitian system of linear equations. Iterative refinement is used to obtain an error estimate.

- dnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- dnbdi
Compute the determinant of a band matrix using the factors computed by DNBCO or DNBFA.

- dnbfa
Factor a band matrix by elimination.

- dnbfs
Solve a general nonsymmetric banded system of linear equations.

- dnbsl
Solve a real band system using the factors computed by DNBCO or DNBFA.

- dpofs
Solve a positive definite symmetric system of linear equations.

- snbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- snbdi
Compute the determinant of a band matrix using the factors computed by SNBCO or SNBFA.

- snbfa
Factor a real band matrix by elimination.

- snbfs
Solve a general nonsymmetric banded system of linear equations.

- snbir
- snbsl
Solve a real band system using the factors computed by SNBCO or SNBFA.

- spofs
Solve a positive definite symmetric system of linear equations.

- spoir
Solve a positive definite symmetric system of linear equations. Iterative refinement is used to obtain an error estimate.

### LINEAR LEAST SQUARES

- dglss
Solve a linear least squares problems by performing a QR factorization of the input matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- dllsia
Solve linear least squares problems by performing a QR factorization of the input matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- dulsia
Solve an underdetermined linear system of equations by performing an LQ factorization of the matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- hfti
Solve a linear least squares problems by performing a QR factorization of the matrix using Householder transformations.

- llsia
Solve a linear least squares problems by performing a QR factorization of the matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- sglss
Solve a linear least squares problems by performing a QR factorization of the matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- ulsia
Solve an underdetermined linear system of equations by performing an LQ factorization of the matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

### LINEAR OPTIMIZATION

- dsplp
Solve linear programming problems involving at most a few thousand constraints and variables. Takes advantage of sparsity in the constraint matrix.

- splp

### LINEAR PROGRAMMING

- dsplp
- splp

### LINEAR SYSTEM

- dbhin
Read a Sparse Linear System in the Boeing/Harwell Format. The matrix is read in and if the right hand side is also present in the input file then it too is read in. The matrix is then modified to be in the SLAP Column format.

- dcpplt
Printer Plot of SLAP Column Format Matrix. Routine to print out a SLAP Column format matrix in a "printer plot" graphical representation.

- dir
Preconditioned Iterative Refinement Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using iterative refinement with a matrix splitting.

- ds2lt
Lower Triangle Preconditioner SLAP Set Up. Routine to store the lower triangle of a matrix stored in the SLAP Column format.

- ds2y
SLAP Triad to SLAP Column Format Converter. Routine to convert from the SLAP Triad to SLAP Column format.

- dsgs
Gauss-Seidel Method Iterative Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using Gauss-Seidel iteration.

- dsics
- dsilur
Incomplete LU Iterative Refinement Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using the incomplete LU decomposition with iterative refinement.

- dsjac
Jacobi's Method Iterative Sparse Ax = b Solver. Routine to solve a general linear system Ax = b using Jacobi iteration.

- dsmmi2
SLAP Backsolve for LDU Factorization of Normal Equations. To solve a system of the form (L*D*U)*(L*D*U)' X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix and ' denotes transpose.

- dtin
Read in SLAP Triad Format Linear System. Routine to read in a SLAP Triad format matrix and right hand side and solution to the system, if known.

- dtout
Write out SLAP Triad Format Linear System. Routine to write out a SLAP Triad format matrix and right hand side and solution to the system, if known.

- isdcg
Preconditioned Conjugate Gradient Stop Test. This routine calculates the stop test for the Conjugate Gradient iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdgmr
Generalized Minimum Residual Stop Test. This routine calculates the stop test for the Generalized Minimum RESidual (GMRES) iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdir
Preconditioned Iterative Refinement Stop Test. This routine calculates the stop test for the iterative refinement iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isscg
Preconditioned Conjugate Gradient Stop Test. This routine calculates the stop test for the Conjugate Gradient iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- issgmr
- issir
Preconditioned Iterative Refinement Stop Test. This routine calculates the stop test for the iterative refinement iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- sbhin
Read a Sparse Linear System in the Boeing/Harwell Format. The matrix is read in and if the right hand side is also present in the input file then it too is read in. The matrix is then modified to be in the SLAP Column format.

- sir
- scpplt
- ss2lt
Lower Triangle Preconditioner SLAP Set Up. Routine to store the lower triangle of a matrix stored in the SLAP Column format.

- ss2y
SLAP Triad to SLAP Column Format Converter. Routine to convert from the SLAP Triad to SLAP Column format.

- ssgs
- ssics
- ssilur
- ssjac
- ssmmi2
- stin
- stout

### LINEAR SYSTEM SOLVE

- dsdi
Diagonal Matrix Vector Multiply. Routine to calculate the product X = DIAG*B, where DIAG is a diagonal matrix.

- dsli
SLAP MSOLVE for Lower Triangle Matrix. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes L B = X.

- dsli2
SLAP Lower Triangle Matrix Backsolve. Routine to solve a system of the form Lx = b , where L is a lower triangular matrix.

- dsllti
SLAP MSOLVE for LDL' (IC) Factorization. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes (LDL') B = X.

- dsluti
SLAP MTSOLV for LDU Factorization. This routine acts as an interface between the SLAP generic MTSOLV calling convention and the routine that actually -T computes (LDU) B = X.

- dsmmti
SLAP MSOLVE for LDU Factorization of Normal Equations. This routine acts as an interface between the SLAP generic MMTSLV calling convention and the routine that actually -1 computes [(LDU)*(LDU)'] B = X.

- ssdi
- ssli
- ssli2
- ssllti
- ssluti
- ssmmti

### LINPACK

- cchdc
- cchdd
- cchex
- cchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- cgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- cgbdi
Compute the determinant of a complex band matrix using the factors from CGBCO or CGBFA.

- cgbfa
Factor a band matrix using Gaussian elimination.

- cgbsl
Solve the complex band system A*X=B or CTRANS(A)*X=B using the factors computed by CGBCO or CGBFA.

- cgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- cgedi
Compute the determinant and inverse of a matrix using the factors computed by CGECO or CGEFA.

- cgefa
Factor a matrix using Gaussian elimination.

- cgesl
Solve the complex system A*X=B or CTRANS(A)*X=B using the factors computed by CGECO or CGEFA.

- cgtsl
Solve a tridiagonal linear system.

- chico
- chidi
- chifa
Factor a complex Hermitian matrix by elimination (symmetric pivoting).

- chisl
Solve the complex Hermitian system using factors obtained from CHIFA.

- chpco
- chpdi
- chpfa
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting.

- chpsl
Solve a complex Hermitian system using factors obtained from CHPFA.

- cpbco
- cpbdi
- cpbfa
Factor a complex Hermitian positive definite matrix stored in band form.

- cpbsl
Solve the complex Hermitian positive definite band system using the factors computed by CPBCO or CPBFA.

- cpoco
Factor a complex Hermitian positive definite matrix and estimate the condition number of the matrix.

- cpodi
- cpofa
Factor a complex Hermitian positive definite matrix.

- cposl
Solve the complex Hermitian positive definite linear system using the factors computed by CPOCO or CPOFA.

- cppco
Factor a complex Hermitian positive definite matrix stored in packed form and estimate the condition number of the matrix.

- cppdi
- cppfa
Factor a complex Hermitian positive definite matrix stored in packed form.

- cppsl
Solve the complex Hermitian positive definite system using the factors computed by CPPCO or CPPFA.

- cptsl
Solve a positive definite tridiagonal linear system.

- cqrdc
- cqrsl
Apply the output of CQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- csico
Factor a complex symmetric matrix by elimination with symmetric pivoting and estimate the condition number of the matrix.

- csidi
Compute the determinant and inverse of a complex symmetric matrix using the factors from CSIFA.

- csifa
Factor a complex symmetric matrix by elimination with symmetric pivoting.

- csisl
Solve a complex symmetric system using the factors obtained from CSIFA.

- cspco
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

- cspdi
- cspfa
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting.

- cspsl
Solve a complex symmetric system using the factors obtained from CSPFA.

- csvdc
Perform the singular value decomposition of a rectangular matrix.

- ctrco
Estimate the condition number of a triangular matrix.

- ctrdi
Compute the determinant and inverse of a triangular matrix.

- ctrsl
Solve a system of the form T*X=B or CTRANS(T)*X=B, where T is a triangular matrix. Here CTRANS(T) is the conjugate transpose.

- dchdc
- dchdd
- dchex
- dchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- dgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- dgbdi
Compute the determinant of a band matrix using the factors computed by DGBCO or DGBFA.

- dgbfa
Factor a band matrix using Gaussian elimination.

- dgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by DGBCO or DGBFA.

- dgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- dgedi
Compute the determinant and inverse of a matrix using the factors computed by DGECO or DGEFA.

- dgefa
Factor a matrix using Gaussian elimination.

- dgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors computed by DGECO or DGEFA.

- dgtsl
Solve a tridiagonal linear system.

- dpbco
- dpbdi
- dpbfa
Factor a real symmetric positive definite matrix stored in in band form.

- dpbsl
Solve a real symmetric positive definite band system using the factors computed by DPBCO or DPBFA.

- dpoco
Factor a real symmetric positive definite matrix and estimate the condition of the matrix.

- dpodi
- dpofa
Factor a real symmetric positive definite matrix.

- dposl
Solve the real symmetric positive definite linear system using the factors computed by DPOCO or DPOFA.

- dppco
- dppdi
- dppfa
Factor a real symmetric positive definite matrix stored in packed form.

- dppsl
Solve the real symmetric positive definite system using the factors computed by DPPCO or DPPFA.

- dptsl
Solve a positive definite tridiagonal linear system.

- dqrdc
- dqrsl
Apply the output of DQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- dsico
- dsidi
- dsifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- dsisl
Solve a real symmetric system using the factors obtained from SSIFA.

- dspco
- dspdi
- dspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- dspsl
Solve a real symmetric system using the factors obtained from DSPFA.

- dsvdc
Perform the singular value decomposition of a rectangular matrix.

- dtrco
Estimate the condition number of a triangular matrix.

- dtrdi
Compute the determinant and inverse of a triangular matrix.

- dtrsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

- schdc
- schdd
- schex
- schud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- sgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- sgbdi
Compute the determinant of a band matrix using the factors computed by SGBCO or SGBFA.

- sgbfa
Factor a band matrix using Gaussian elimination.

- sgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by SGBCO or SGBFA.

- sgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- sgedi
Compute the determinant and inverse of a matrix using the factors computed by SGECO or SGEFA.

- sgefa
Factor a matrix using Gaussian elimination.

- sgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors of SGECO or SGEFA.

- sgtsl
Solve a tridiagonal linear system.

- spbco
- spbdi
- spbfa
Factor a real symmetric positive definite matrix stored in band form.

- spbsl
Solve a real symmetric positive definite band system using the factors computed by SPBCO or SPBFA.

- spoco
Factor a real symmetric positive definite matrix and estimate the condition number of the matrix.

- spodi
- spofa
Factor a real symmetric positive definite matrix.

- sposl
Solve the real symmetric positive definite linear system using the factors computed by SPOCO or SPOFA.

- sppco
- sppdi
- sppfa
Factor a real symmetric positive definite matrix stored in packed form.

- sppsl
Solve the real symmetric positive definite system using the factors computed by SPPCO or SPPFA.

- sptsl
Solve a positive definite tridiagonal linear system.

- sqrdc
- sqrsl
Apply the output of SQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- ssico
- ssidi
- ssifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- ssisl
Solve a real symmetric system using the factors obtained from SSIFA.

- sspco
- sspdi
- sspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- sspsl
Solve a real symmetric system using the factors obtained from SSPFA.

- ssvdc
Perform the singular value decomposition of a rectangular matrix.

- strco
Estimate the condition number of a triangular matrix.

- strdi
Compute the determinant and inverse of a triangular matrix.

- strsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

### LOG GAMMA

- c9lgmc
- d9lgmc
- r9lgmc

### LOGARITHM

- alngam
Compute the logarithm of the absolute value of the Gamma function.

- alnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- c9lgmc
- c9ln2r
Evaluate LOG(1+Z) from second order relative accuracy so that LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

- clngam
Compute the logarithm of the absolute value of the Gamma function.

- clnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- d9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- d9lgit
- d9lgmc
- d9ln2r
Evaluate LOG(1+X) from second order relative accuracy so that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

- dlngam
Compute the logarithm of the absolute value of the Gamma function.

- dlnrel
Evaluate ln(1+X) accurate in the sense of relative error.

- r9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- r9lgit
- r9lgmc
- r9ln2r
Evaluate LOG(1+X) from second order relative accuracy so that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

### LOGARITHM OF GAMMA FUNCTION

- dgamln
Compute the logarithm of the Gamma function

- gamln
Compute the logarithm of the Gamma function

### LOGARITHM OF THE COMPLETE BETA FUNCTION

- albeta
Compute the natural logarithm of the complete Beta function.

- clbeta
Compute the natural logarithm of the complete Beta function.

- dlbeta
Compute the natural logarithm of the complete Beta function.

### LOGARITHMIC CONFLUENT HYPERGEOMETRIC FUNCTION

- chu
Compute the logarithmic confluent hypergeometric function.

- d9chu
Evaluate for large Z Z**A * U(A,B,Z) where U is the logarithmic confluent hypergeometric function.

- dchu
Compute the logarithmic confluent hypergeometric function.

- r9chu
Evaluate for large Z Z**A * U(A,B,Z) where U is the logarithmic confluent hypergeometric function.

### LOGARITHMIC INTEGRAL

### LOWER TRIANGLE

- ds2lt
Lower Triangle Preconditioner SLAP Set Up. Routine to store the lower triangle of a matrix stored in the SLAP Column format.

- ss2lt

### LP

- dsplp
- splp

### LQ FACTORIZATION

- dglss
Solve a linear least squares problems by performing a QR factorization of the input matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- dulsia
Solve an underdetermined linear system of equations by performing an LQ factorization of the matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- sglss
Solve a linear least squares problems by performing a QR factorization of the matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- ulsia

### LR METHOD

- comlr
Compute the eigenvalues of a complex upper Hessenberg matrix using the modified LR method.

- comlr2

### MACHINE CONSTANTS

- d1mach_IRIX
Return floating point machine dependent constants.

- i1mach_IRIX
Return integer machine dependent constants.

- d1mach_GENERIC
Return floating point machine dependent constants.

- d1mach_IRIX6
Return floating point machine dependent constants.

- d1mach_Linux
Return floating point machine dependent constants.

- d1mach_OSF1
Return floating point machine dependent constants.

- i1mach_GENERIC
Return integer machine dependent constants.

- i1mach_IRIX6
Return integer machine dependent constants.

- i1mach_Linux
Return integer machine dependent constants.

- i1mach_OSF1
Return integer machine dependent constants.

- r1mach_IRIX
Return floating point machine dependent constants.

- r1mach_GENERIC
Return floating point machine dependent constants.

- r1mach_IRIX6
Return floating point machine dependent constants.

- r1mach_Linux
Return floating point machine dependent constants.

- r1mach_OSF1
Return floating point machine dependent constants.

### MATRIX

- cchdc
- cchdd
- cchex
- cchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- cgbdi
Compute the determinant of a complex band matrix using the factors from CGBCO or CGBFA.

- cgbsl
Solve the complex band system A*X=B or CTRANS(A)*X=B using the factors computed by CGBCO or CGBFA.

- cgedi
Compute the determinant and inverse of a matrix using the factors computed by CGECO or CGEFA.

- cgesl
Solve the complex system A*X=B or CTRANS(A)*X=B using the factors computed by CGECO or CGEFA.

- cgtsl
Solve a tridiagonal linear system.

- chidi
- chiev
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- chisl
Solve the complex Hermitian system using factors obtained from CHIFA.

- chpdi
- chpsl
Solve a complex Hermitian system using factors obtained from CHPFA.

- cpbdi
- cpbsl
- cpodi
- cposl
Solve the complex Hermitian positive definite linear system using the factors computed by CPOCO or CPOFA.

- cppdi
- cppsl
Solve the complex Hermitian positive definite system using the factors computed by CPPCO or CPPFA.

- cptsl
Solve a positive definite tridiagonal linear system.

- cqrdc
- cqrsl
Apply the output of CQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- csidi
Compute the determinant and inverse of a complex symmetric matrix using the factors from CSIFA.

- csisl
Solve a complex symmetric system using the factors obtained from CSIFA.

- cspdi
- cspsl
Solve a complex symmetric system using the factors obtained from CSPFA.

- csvdc
Perform the singular value decomposition of a rectangular matrix.

- dchdc
- dchdd
- dchex
- dchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- dgbdi
Compute the determinant of a band matrix using the factors computed by DGBCO or DGBFA.

- dgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by DGBCO or DGBFA.

- dgedi
Compute the determinant and inverse of a matrix using the factors computed by DGECO or DGEFA.

- dgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors computed by DGECO or DGEFA.

- dgtsl
Solve a tridiagonal linear system.

- dpbdi
- dpbsl
Solve a real symmetric positive definite band system using the factors computed by DPBCO or DPBFA.

- dpodi
- dposl
Solve the real symmetric positive definite linear system using the factors computed by DPOCO or DPOFA.

- dppdi
- dppsl
Solve the real symmetric positive definite system using the factors computed by DPPCO or DPPFA.

- dptsl
Solve a positive definite tridiagonal linear system.

- dqrdc
- dqrsl
Apply the output of DQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- dsidi
- dsisl
Solve a real symmetric system using the factors obtained from SSIFA.

- dspdi
- dspsl
Solve a real symmetric system using the factors obtained from DSPFA.

- dsvdc
Perform the singular value decomposition of a rectangular matrix.

- schdc
- schdd
- schex
- schud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- sgbdi
Compute the determinant of a band matrix using the factors computed by SGBCO or SGBFA.

- sgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by SGBCO or SGBFA.

- sgedi
Compute the determinant and inverse of a matrix using the factors computed by SGECO or SGEFA.

- sgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors of SGECO or SGEFA.

- sgtsl
Solve a tridiagonal linear system.

- spbdi
- spbsl
Solve a real symmetric positive definite band system using the factors computed by SPBCO or SPBFA.

- spodi
- sposl
Solve the real symmetric positive definite linear system using the factors computed by SPOCO or SPOFA.

- sppdi
- sppsl
Solve the real symmetric positive definite system using the factors computed by SPPCO or SPPFA.

- sptsl
Solve a positive definite tridiagonal linear system.

- sqrdc
- sqrsl
Apply the output of SQRDC to compute coordinate transfor- mations, projections, and least squares solutions.

- ssidi
- ssiev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

- ssisl
Solve a real symmetric system using the factors obtained from SSIFA.

- sspdi
- sspsl
Solve a real symmetric system using the factors obtained from SSPFA.

- ssvdc
Perform the singular value decomposition of a rectangular matrix.

- strdi
Compute the determinant and inverse of a triangular matrix.

### MATRIX FACTORIZATION

- cgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- cgbfa
Factor a band matrix using Gaussian elimination.

- cgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- cgefa
Factor a matrix using Gaussian elimination.

- chico
- chifa
Factor a complex Hermitian matrix by elimination (symmetric pivoting).

- chpco
- chpfa
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting.

- cnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- cnbfa
Factor a band matrix by elimination.

- cpbco
- cpbfa
Factor a complex Hermitian positive definite matrix stored in band form.

- cpoco
Factor a complex Hermitian positive definite matrix and estimate the condition number of the matrix.

- cpofa
Factor a complex Hermitian positive definite matrix.

- cppco
- cppfa
Factor a complex Hermitian positive definite matrix stored in packed form.

- csico
- csifa
Factor a complex symmetric matrix by elimination with symmetric pivoting.

- cspco
- cspfa
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting.

- dgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- dgbfa
Factor a band matrix using Gaussian elimination.

- dgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- dgefa
Factor a matrix using Gaussian elimination.

- dnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- dnbfa
Factor a band matrix by elimination.

- dpbco
- dpbfa
Factor a real symmetric positive definite matrix stored in in band form.

- dpoco
Factor a real symmetric positive definite matrix and estimate the condition of the matrix.

- dpofa
Factor a real symmetric positive definite matrix.

- dppco
- dppfa
Factor a real symmetric positive definite matrix stored in packed form.

- dsico
- dsifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- dspco
- dspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- sgbco
Factor a band matrix by Gaussian elimination and estimate the condition number of the matrix.

- sgbfa
Factor a band matrix using Gaussian elimination.

- sgeco
Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

- sgefa
Factor a matrix using Gaussian elimination.

- snbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- snbfa
Factor a real band matrix by elimination.

- spbco
- spbfa
Factor a real symmetric positive definite matrix stored in band form.

- spoco
Factor a real symmetric positive definite matrix and estimate the condition number of the matrix.

- spofa
Factor a real symmetric positive definite matrix.

- sppco
- sppfa
Factor a real symmetric positive definite matrix stored in packed form.

- ssico
- ssifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- sspco
- sspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

### MATRIX READ

- dbhin
Read a Sparse Linear System in the Boeing/Harwell Format. The matrix is read in and if the right hand side is also present in the input file then it too is read in. The matrix is then modified to be in the SLAP Column format.

- sbhin

### MATRIX TRANSPOSE VECTOR MULTIPLY

- dsmtv
SLAP Column Format Sparse Matrix Transpose Vector Product. Routine to calculate the sparse matrix vector product: Y = A'*X, where ' denotes transpose.

- ssmtv
SLAP Column Format Sparse Matrix Transpose Vector Product. Routine to calculate the sparse matrix vector product: Y = A'*X, where ' denotes transpose.

### MATRIX VECTOR MULTIPLY

- dsmv
SLAP Column Format Sparse Matrix Vector Product. Routine to calculate the sparse matrix vector product: Y = A*X.

- ssmv
SLAP Column Format Sparse Matrix Vector Product. Routine to calculate the sparse matrix vector product: Y = A*X.

### MAXIMUM COMPONENT

- icamax
Find the smallest index of the component of a complex vector having the maximum sum of magnitudes of real and imaginary parts.

- idamax
Find the smallest index of that component of a vector having the maximum magnitude.

- isamax
Find the smallest index of that component of a vector having the maximum magnitude.

### MINPACK

- chkder
- dckder

### MODIFIED BESSEL FUNCTION

- besi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- besi0e
- besi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- besi1e
- besk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- besk0e
- besk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- besk1e
- beskes
- besks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbesi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- dbesi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- dbesk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- dbesk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- dbesks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbsi0e
- dbsi1e
- dbsk0e
- dbsk1e
- dbskes

### MODIFIED BESSEL FUNCTIONS

- cbesi
- cbesk
- zbesi
- zbesk

### MODIFIED CHEBYSHEV MOMENTS

- dqmomo
This routine computes modified Chebyshev moments. The K-th modified Chebyshev moment is defined as the integral over (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev polynomial of degree K.

- qmomo
This routine computes modified Chebyshev moments. The K-th modified Chebyshev moment is defined as the integral over (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev polynomial of degree K.

### MODIFIED GIVENS ROTATION

- drotm
Apply a modified Givens transformation.

- drotmg
Construct a modified Givens transformation.

- srotm
Apply a modified Givens transformation.

- srotmg
Construct a modified Givens transformation.

### MODULUS

- d9aimp
Evaluate the Airy modulus and phase.

- d9b0mp
Evaluate the modulus and phase for the J0 and Y0 Bessel functions.

- d9b1mp
Evaluate the modulus and phase for the J1 and Y1 Bessel functions.

- r9aimp
Evaluate the Airy modulus and phase.

### MONOTONE INTERPOLATION

- dpchcm
Check a cubic Hermite function for monotonicity.

- dpchic
Set derivatives needed to determine a piecewise monotone piecewise cubic Hermite interpolant to given data. User control is available over boundary conditions and/or treatment of points where monotonicity switches direction.

- dpchim
Set derivatives needed to determine a monotone piecewise cubic Hermite interpolant to given data. Boundary values are provided which are compatible with monotonicity. The interpolant will have an extremum at each point where mono- tonicity switches direction. (See DPCHIC if user control is desired over boundary or switch conditions.)

- pchcm
Check a cubic Hermite function for monotonicity.

- pchdoc
Documentation for PCHIP, a Fortran package for piecewise cubic Hermite interpolation of data.

- pchic
- pchim
Set derivatives needed to determine a monotone piecewise cubic Hermite interpolant to given data. Boundary values are provided which are compatible with monotonicity. The interpolant will have an extremum at each point where mono- tonicity switches direction. (See PCHIC if user control is desired over boundary or switch conditions.)

### NEWTON'S METHOD

- dsos
Solve a square system of nonlinear equations.

- sos
Solve a square system of nonlinear equations.

### NEWTON-COTES

- dqnc79
Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.

- qnc79
Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.

### NON-SYMMETRIC LINEAR SYSTEM

- dbcg
- dcgs
- dgmres
Preconditioned GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with preconditioning to solve non-symmetric linear systems of the form: Ax = b.

- dhels
Internal routine for DGMRES.

- dheqr
Internal routine for DGMRES.

- domn
Preconditioned Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Preconditioned Orthomin method.

- dorth
Internal routine for DGMRES.

- dpigmr
Internal routine for DGMRES.

- drlcal
Internal routine for DGMRES.

- dsdbcg
Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient method with diagonal scaling.

- dsdcgs
Diagonally Scaled CGS Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient Squared method with diagonal scaling.

- dsdgmr
Diagonally scaled GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with diagonal scaling to solve possibly non-symmetric linear systems of the form: Ax = b.

- dsilus
- dslubc
Incomplete LU BiConjugate Gradient Sparse Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient method with Incomplete LU decomposition preconditioning.

- dslucn
Incomplete LU CG Sparse Ax=b Solver for Normal Equations. Routine to solve a general linear system Ax = b using the incomplete LU decomposition with the Conjugate Gradient method applied to the normal equations, viz., AA'y = b, x = A'y.

- dslucs
Incomplete LU BiConjugate Gradient Squared Ax=b Solver. Routine to solve a linear system Ax = b using the BiConjugate Gradient Squared method with Incomplete LU decomposition preconditioning.

- dslugm
Incomplete LU GMRES iterative sparse Ax=b solver. This routine uses the generalized minimum residual (GMRES) method with incomplete LU factorization for preconditioning to solve possibly non-symmetric linear systems of the form: Ax = b.

- dsluom
Incomplete LU Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Orthomin method with Incomplete LU decomposition.

- dxlcal
Internal routine for DGMRES.

- isdbcg
Preconditioned BiConjugate Gradient Stop Test. This routine calculates the stop test for the BiConjugate Gradient iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdcgn
Preconditioned CG on Normal Equations Stop Test. This routine calculates the stop test for the Conjugate Gradient iteration scheme applied to the normal equations. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdcgs
Preconditioned BiConjugate Gradient Squared Stop Test. This routine calculates the stop test for the BiConjugate Gradient Squared iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdomn
Preconditioned Orthomin Stop Test. This routine calculates the stop test for the Orthomin iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- issbcg
- isscgn
- isscgs
- issomn
- sbcg
- scgs
- sgmres
Preconditioned GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with preconditioning to solve non-symmetric linear systems of the form: Ax = b.

- shels
Internal routine for SGMRES.

- sheqr
Internal routine for SGMRES.

- somn
- sorth
Internal routine for SGMRES.

- spigmr
Internal routine for SGMRES.

- srlcal
Internal routine for SGMRES.

- ssdbcg
- ssdcgs
- ssdgmr
Diagonally Scaled GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with diagonal scaling to solve possibly non-symmetric linear systems of the form: Ax = b.

- ssilus
- sslubc
- sslucn
- sslucs
- sslugm
Incomplete LU GMRES Iterative Sparse Ax=b Solver. This routine uses the generalized minimum residual (GMRES) method with incomplete LU factorization for preconditioning to solve possibly non-symmetric linear systems of the form: Ax = b.

- ssluom
- sxlcal
Internal routine for SGMRES.

### NON-SYMMETRIC LINEAR SYSTEM SOLVE

- dcgn
Preconditioned CG Sparse Ax=b Solver for Normal Equations. Routine to solve a general linear system Ax = b using the Preconditioned Conjugate Gradient method applied to the normal equations AA'y = b, x=A'y.

- dsdcgn
Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's. Routine to solve a general linear system Ax = b using diagonal scaling with the Conjugate Gradient method applied to the the normal equations, viz., AA'y = b, where x = A'y.

- dsdomn
Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver. Routine to solve a general linear system Ax = b using the Orthomin method with diagonal scaling.

- dslui
SLAP MSOLVE for LDU Factorization. This routine acts as an interface between the SLAP generic MSOLVE calling convention and the routine that actually -1 computes (LDU) B = X.

- dslui2
SLAP Backsolve for LDU Factorization. Routine to solve a system of the form L*D*U X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix.

- dslui4
SLAP Backsolve for LDU Factorization. Routine to solve a system of the form (L*D*U)' X = B, where L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix and ' denotes transpose.

- scgn
- ssdcgn
- ssdomn
- sslui
- sslui2
- sslui4

### NONADAPTIVE

- dqng
- qng

### NONLINEAR

- chkder
- dckder
- dfzero
Search for a zero of a function F(X) in a given interval (B,C). It is designed primarily for problems where F(B) and F(C) have opposite signs.

### NONLINEAR DATA FITTING

- dcov
Calculate the covariance matrix for a nonlinear data fitting problem. It is intended to be used after a successful return from either DNLS1 or DNLS1E.

- dnls1
Minimize the sum of the squares of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm.

- dnls1e
- scov
Calculate the covariance matrix for a nonlinear data fitting problem. It is intended to be used after a successful return from either SNLS1 or SNLS1E.

- snls1
- snls1e

### NONLINEAR EQUATIONS

- dsos
Solve a square system of nonlinear equations.

- fzero
- sos
Solve a square system of nonlinear equations.

### NONLINEAR LEAST SQUARES

- dcov
Calculate the covariance matrix for a nonlinear data fitting problem. It is intended to be used after a successful return from either DNLS1 or DNLS1E.

- dnls1
- dnls1e
- scov
Calculate the covariance matrix for a nonlinear data fitting problem. It is intended to be used after a successful return from either SNLS1 or SNLS1E.

- snls1
- snls1e

### NONLINEAR SQUARE SYSTEM

- dnsq
Find a zero of a system of a N nonlinear functions in N variables by a modification of the Powell hybrid method.

- dnsqe
An easy-to-use code to find a zero of a system of N nonlinear functions in N variables by a modification of the Powell hybrid method.

- snsq
Find a zero of a system of a N nonlinear functions in N variables by a modification of the Powell hybrid method.

- snsqe

### NONNEGATIVITY CONSTRAINTS

- dwnnls
- wnnls

### NONSYMMETRIC

- cnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- cnbdi
Compute the determinant of a band matrix using the factors computed by CNBCO or CNBFA.

- cnbfa
Factor a band matrix by elimination.

- cnbfs
Solve a general nonsymmetric banded system of linear equations.

- cnbir
- cnbsl
Solve a complex band system using the factors computed by CNBCO or CNBFA.

- dnbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- dnbdi
Compute the determinant of a band matrix using the factors computed by DNBCO or DNBFA.

- dnbfa
Factor a band matrix by elimination.

- dnbfs
Solve a general nonsymmetric banded system of linear equations.

- dnbsl
Solve a real band system using the factors computed by DNBCO or DNBFA.

- snbco
Factor a band matrix using Gaussian elimination and estimate the condition number.

- snbdi
Compute the determinant of a band matrix using the factors computed by SNBCO or SNBFA.

- snbfa
Factor a real band matrix by elimination.

- snbfs
Solve a general nonsymmetric banded system of linear equations.

- snbir
- snbsl
Solve a real band system using the factors computed by SNBCO or SNBFA.

### NORMAL

- rgauss
Generate a normally distributed (Gaussian) random number.

### NORMAL EQUATIONS

- dlpdoc
- isdcgn
- isscgn
- slpdoc

### NORMAL EQUATIONS.

- dcgn
- scgn

### NUMBER SORTING

- dpsort
Return the permutation vector generated by sorting a given array and, optionally, rearrange the elements of the array. The array may be sorted in increasing or decreasing order. A slightly modified quicksort algorithm is used.

- ipsort
Return the permutation vector generated by sorting a given array and, optionally, rearrange the elements of the array. The array may be sorted in increasing or decreasing order. A slightly modified quicksort algorithm is used.

- spsort
Return the permutation vector generated by sorting a given array and, optionally, rearrange the elements of the array. The array may be sorted in increasing or decreasing order. A slightly modified quicksort algorithm is used.

### NUMERICAL INTEGRATION

- dgaus8
- dpchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- dpchid
Evaluate the definite integral of a piecewise cubic Hermite function over an interval whose endpoints are data points.

- gaus8
- pchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- pchid

### ODE

- cdriv1
- cdriv2
- cdriv3
- ddeabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- ddebdf
- dderkf
- ddriv1
- ddriv2
- ddriv3
- deabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- debdf
- derkf
- dintp
- dsteps
Integrate a system of first order ordinary differential equations one step.

- sdriv1
The function of SDRIV1 is to solve N (200 or fewer) ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. SDRIV1 uses single precision arithmetic.

- sdriv2
The function of SDRIV2 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. SDRIV2 uses single precision arithmetic.

- sdriv3
The function of SDRIV3 is to solve N ordinary differential equations of the form dY(I)/dT = F(Y(I),T), given the initial conditions Y(I) = YI. The program has options to allow the solution of both stiff and non-stiff differential equations. Other important options are available. SDRIV3 uses single precision arithmetic.

- sintrp
- steps
Integrate a system of first order ordinary differential equations one step.

### ORDER ONE

- besi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- besi1e
- besj1
Compute the Bessel function of the first kind of order one.

- besk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- besk1e
- besy1
Compute the Bessel function of the second kind of order one.

- dbesi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- dbesj1
Compute the Bessel function of the first kind of order one.

- dbesk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- dbesy1
Compute the Bessel function of the second kind of order one.

- dbsi1e
- dbsk1e

### ORDER ZERO

- besi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- besi0e
- besj0
Compute the Bessel function of the first kind of order zero.

- besk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- besk0e
- besy0
Compute the Bessel function of the second kind of order zero.

- dbesi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- dbesj0
Compute the Bessel function of the first kind of order zero.

- dbesk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- dbesy0
Compute the Bessel function of the second kind of order zero.

- dbsi0e
- dbsk0e

### ORDINARY DIFFERENTIAL EQUATIONS

- cdriv1
- cdriv2
- cdriv3
- ddeabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- ddebdf
- dderkf
- ddriv1
- ddriv2
- ddriv3
- deabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- debdf
- derkf
- dintp
- dsteps
Integrate a system of first order ordinary differential equations one step.

- sdriv1
- sdriv2
- sdriv3
- sintrp
- steps
Integrate a system of first order ordinary differential equations one step.

### ORTHOGONAL POLYNOMIAL

- initds
- inits

### ORTHOGONAL SERIES

- initds
- inits

### ORTHOGONAL TRIANGULAR

- cqrdc
- cqrsl
- dqrdc
- dqrsl
- sqrdc
- sqrsl

### ORTHOMIN

- dlpdoc
- domn
- isdomn
- issomn
- slpdoc
- somn

### ORTHONORMALIZATION

- bvsup
Solve a linear two-point boundary value problem using superposition coupled with an orthonormalization procedure and a variable-step integration scheme.

- dbvsup
Solve a linear two-point boundary value problem using superposition coupled with an orthonormalization procedure and a variable-step integration scheme.

### PACK

- d9pak
Pack a base 2 exponent into a floating point number.

- r9pak
Pack a base 2 exponent into a floating point number.

### PACKED

- chpco
- chpdi
- chpfa
Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting.

- chpsl
Solve a complex Hermitian system using factors obtained from CHPFA.

- cppco
- cppdi
- cppfa
Factor a complex Hermitian positive definite matrix stored in packed form.

- cppsl
Solve the complex Hermitian positive definite system using the factors computed by CPPCO or CPPFA.

- cspco
- cspdi
- cspfa
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting.

- cspsl
Solve a complex symmetric system using the factors obtained from CSPFA.

- dppco
- dppdi
- dppfa
Factor a real symmetric positive definite matrix stored in packed form.

- dppsl
Solve the real symmetric positive definite system using the factors computed by DPPCO or DPPFA.

- dspco
- dspdi
- dspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- dspsl
Solve a real symmetric system using the factors obtained from DSPFA.

- sppco
- sppdi
- sppfa
Factor a real symmetric positive definite matrix stored in packed form.

- sppsl
Solve the real symmetric positive definite system using the factors computed by SPPCO or SPPFA.

- sspco
- sspdi
- sspev
- sspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- sspsl
Solve a real symmetric system using the factors obtained from SSPFA.

### PASSIVE SORTING

- dpsort
- hpsort
Return the permutation vector generated by sorting a substring within a character array and, optionally, rearrange the elements of the array. The array may be sorted in forward or reverse lexicographical order. A slightly modified quicksort algorithm is used.

- ipsort
- spsort

### PCHIP

- chfdv
- chfev
Evaluate a cubic polynomial given in Hermite form at an array of points. While designed for use by PCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.

- dchfdv
- dchfev
Evaluate a cubic polynomial given in Hermite form at an array of points. While designed for use by DPCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.

- dpchcm
Check a cubic Hermite function for monotonicity.

- dpchfd
- dpchfe
Evaluate a piecewise cubic Hermite function at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC.

- dpchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- dpchic
- dpchid
- dpchim
Set derivatives needed to determine a monotone piecewise cubic Hermite interpolant to given data. Boundary values are provided which are compatible with monotonicity. The interpolant will have an extremum at each point where mono- tonicity switches direction. (See DPCHIC if user control is desired over boundary or switch conditions.)

- dpchsp
Set derivatives needed to determine the Hermite represen- tation of the cubic spline interpolant to given data, with specified boundary conditions.

- pchcm
Check a cubic Hermite function for monotonicity.

- pchdoc
Documentation for PCHIP, a Fortran package for piecewise cubic Hermite interpolation of data.

- pchfd
- pchfe
Evaluate a piecewise cubic Hermite function at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC.

- pchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- pchic
- pchid
- pchim
Set derivatives needed to determine a monotone piecewise cubic Hermite interpolant to given data. Boundary values are provided which are compatible with monotonicity. The interpolant will have an extremum at each point where mono- tonicity switches direction. (See PCHIC if user control is desired over boundary or switch conditions.)

- pchsp

### PDE

- genbun
Solve by a cyclic reduction algorithm the linear system of equations that results from a finite difference approximation to certain 2-d elliptic PDE's on a centered grid .

- hstcrt
- hstcsp
- hstcyl
- hstplr
- hstssp
- hw3crt
- hwscrt
- hwscsp
- hwscyl
- hwsplr
Solve a finite difference approximation to the Helmholtz equation in polar coordinates.

- hwsssp
- poistg
- sepeli
- sepx4

### PERMUTATION

- dpperm
Rearrange a given array according to a prescribed permutation vector.

### PERRON'S CONTINUED FRACTION

- d9lgit
- r9lgit

### PHASE

- d9aimp
Evaluate the Airy modulus and phase.

- d9b0mp
Evaluate the modulus and phase for the J0 and Y0 Bessel functions.

- d9b1mp
Evaluate the modulus and phase for the J1 and Y1 Bessel functions.

- r9aimp
Evaluate the Airy modulus and phase.

### PIECEWISE CUBIC EVALUATION

- dpchfd
- dpchfe
- pchfd
- pchfe

### PIECEWISE CUBIC INTERPOLATION

- dpchbs
Piecewise Cubic Hermite to B-Spline converter.

- dpchcm
Check a cubic Hermite function for monotonicity.

- dpchic
- dpchim
- dpchsp
- pchbs
Piecewise Cubic Hermite to B-Spline converter.

- pchcm
Check a cubic Hermite function for monotonicity.

- pchdoc
Documentation for PCHIP, a Fortran package for piecewise cubic Hermite interpolation of data.

- pchic
- pchim
- pchsp

### PIECEWISE POLYNOMIAL

- bsppp
Convert the B-representation of a B-spline to the piecewise polynomial (PP) form.

- dbsppp
Convert the B-representation of a B-spline to the piecewise polynomial (PP) form.

### PLANE ROTATION

- csrot
Apply a plane Givens rotation.

- drot
Apply a plane Givens rotation.

- srot
Apply a plane Givens rotation.

### POCHHAMMER

- dpoch
Evaluate a generalization of Pochhammer's symbol.

- dpoch1
Calculate a generalization of Pochhammer's symbol starting from first order.

- poch
Evaluate a generalization of Pochhammer's symbol.

- poch1
Calculate a generalization of Pochhammer's symbol starting from first order.

### POISSON

- pois3d

### POLAR

- hstplr
- hwsplr
Solve a finite difference approximation to the Helmholtz equation in polar coordinates.

### POLAR ANGEL

- catan2
Compute the complex arc tangent in the proper quadrant.

### POLYGAMMA FUNCTION

### POLYNOMIAL

- dpolcf
Compute the coefficients of the polynomial fit (including Hermite polynomial fits) produced by a previous call to POLINT.

- polcof

### POLYNOMIAL APPROXIMATION

- dp1vlu
Use the coefficients generated by DPOLFT to evaluate the polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.

- pvalue
Use the coefficients generated by POLFIT to evaluate the polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.

### POLYNOMIAL EVALUATION

- dpolvl
Calculate the value of a polynomial and its first NDER derivatives where the polynomial was produced by a previous call to DPLINT.

- polyvl
Calculate the value of a polynomial and its first NDER derivatives where the polynomial was produced by a previous call to POLINT.

### POLYNOMIAL FIT

- dpcoef
Convert the DPOLFT coefficients to Taylor series form.

- dpolft
Fit discrete data in a least squares sense by polynomials in one variable.

- pcoef
Convert the POLFIT coefficients to Taylor series form.

- polfit
Fit discrete data in a least squares sense by polynomials in one variable.

### POLYNOMIAL INTERPOLATION

- dplint
Produce the polynomial which interpolates a set of discrete data points.

- polint
Produce the polynomial which interpolates a set of discrete data points.

### POLYNOMIAL ROOTS

- cpqr79
Find the zeros of a polynomial with complex coefficients.

- cpzero
Find the zeros of a polynomial with complex coefficients.

- rpqr79
Find the zeros of a polynomial with real coefficients.

- rpzero
Find the zeros of a polynomial with real coefficients.

### POLYNOMIAL ZEROS

- cpqr79
Find the zeros of a polynomial with complex coefficients.

- cpzero
Find the zeros of a polynomial with complex coefficients.

- rpqr79
Find the zeros of a polynomial with real coefficients.

- rpzero
Find the zeros of a polynomial with real coefficients.

### POSITIVE DEFINITE

- cchdc
- cchex
- cpbco
- cpbdi
- cpbfa
Factor a complex Hermitian positive definite matrix stored in band form.

- cpbsl
- cpoco
Factor a complex Hermitian positive definite matrix and estimate the condition number of the matrix.

- cpodi
- cpofa
Factor a complex Hermitian positive definite matrix.

- cpofs
Solve a positive definite symmetric complex system of linear equations.

- cpoir
Solve a positive definite Hermitian system of linear equations. Iterative refinement is used to obtain an error estimate.

- cposl
- cppco
- cppdi
- cppfa
Factor a complex Hermitian positive definite matrix stored in packed form.

- cppsl
Solve the complex Hermitian positive definite system using the factors computed by CPPCO or CPPFA.

- cptsl
Solve a positive definite tridiagonal linear system.

- dchdc
- dchex
- dpbco
- dpbdi
- dpbfa
Factor a real symmetric positive definite matrix stored in in band form.

- dpbsl
Solve a real symmetric positive definite band system using the factors computed by DPBCO or DPBFA.

- dpoco
Factor a real symmetric positive definite matrix and estimate the condition of the matrix.

- dpodi
- dpofa
Factor a real symmetric positive definite matrix.

- dpofs
Solve a positive definite symmetric system of linear equations.

- dposl
- dppco
- dppdi
- dppfa
Factor a real symmetric positive definite matrix stored in packed form.

- dppsl
Solve the real symmetric positive definite system using the factors computed by DPPCO or DPPFA.

- dptsl
Solve a positive definite tridiagonal linear system.

- schdc
- schex
- spbco
- spbdi
- spbfa
Factor a real symmetric positive definite matrix stored in band form.

- spbsl
Solve a real symmetric positive definite band system using the factors computed by SPBCO or SPBFA.

- spoco
Factor a real symmetric positive definite matrix and estimate the condition number of the matrix.

- spodi
- spofa
Factor a real symmetric positive definite matrix.

- spofs
Solve a positive definite symmetric system of linear equations.

- spoir
Solve a positive definite symmetric system of linear equations. Iterative refinement is used to obtain an error estimate.

- sposl
- sppco
- sppdi
- sppfa
Factor a real symmetric positive definite matrix stored in packed form.

- sppsl
Solve the real symmetric positive definite system using the factors computed by SPPCO or SPPFA.

- sptsl
Solve a positive definite tridiagonal linear system.

### POWELL HYBRID METHOD

- dnsq
Find a zero of a system of a N nonlinear functions in N variables by a modification of the Powell hybrid method.

- dnsqe
- snsq
- snsqe

### PRECONDITIONED CONJUGATE GRADIENT

- dlpdoc
- slpdoc

### PREDICTOR-CORRECTOR

- ddeabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- deabm
Solve an initial value problem in ordinary differential equations using an Adams-Bashforth method.

- dintp
- dsteps
Integrate a system of first order ordinary differential equations one step.

- sintrp
- steps
Integrate a system of first order ordinary differential equations one step.

### PRINTING

- xerprn
Print error messages processed by XERMSG.

### PSI FUNCTION

- cpsi
Compute the Psi (or Digamma) function.

- dpsi
Compute the Psi (or Digamma) function.

- dpsifn
Compute derivatives of the Psi function.

- dxpsi
To compute values of the Psi function for DXLEGF.

- psifn
Compute derivatives of the Psi function.

- psi
Compute the Psi (or Digamma) function.

- xpsi
To compute values of the Psi function for XLEGF.

### QL METHOD

- tql1
Compute the eigenvalues of symmetric tridiagonal matrix by the QL method.

- tqlrat
Compute the eigenvalues of symmetric tridiagonal matrix using a rational variant of the QL method.

### QR DECOMPOSITION

- cqrdc
- dqrdc
- sqrdc

### QR FACTORIZATION

- dglss
Solve a linear least squares problems by performing a QR factorization of the input matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- dllsia
Solve linear least squares problems by performing a QR factorization of the input matrix using Householder transformations. Emphasis is put on detecting possible rank deficiency.

- hfti
Solve a linear least squares problems by performing a QR factorization of the matrix using Householder transformations.

- llsia
- sglss

### QUADPACK

- dqag
- dqage
- dqagi
- dqagie
- dqagp
- dqagpe
- dqags
- dqagse
- dqawc
- dqawce
- dqawf
- dqawfe
- dqawo
- dqawoe
- dqaws
- dqawse
- dqc25c
To compute I = Integral of F*W over (A,B) with error estimate, where W(X) = 1/(X-C)

- dqc25f
- dqc25s
To compute I = Integral of F*W over (BL,BR), with error estimate, where the weight function W has a singular behaviour of ALGEBRAICO-LOGARITHMIC type at the points A and/or B. (BL,BR) is a part of (A,B).

- dqk15
To compute I = Integral of F over (A,B), with error estimate J = integral of ABS(F) over (A,B)

- dqk15i
The original (infinite integration range is mapped onto the interval (0,1) and (A,B) is a part of (0,1). it is the purpose to compute I = Integral of transformed integrand over (A,B), J = Integral of ABS(Transformed Integrand) over (A,B).

- dqk15w
To compute I = Integral of F*W over (A,B), with error estimate J = Integral of ABS(F*W) over (A,B)

- dqk21
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- dqk31
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- dqk41
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- dqk51
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- dqk61
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- dqmomo
This routine computes modified Chebyshev moments. The K-th modified Chebyshev moment is defined as the integral over (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev polynomial of degree K.

- dqng
- qag
- qage
- qagi
- qagie
- qagp
- qagpe
- qags
- qagse
- qawc
- qawce
- qawf
- qawfe
- qawo
- qawoe
- qaws
- qawse
- qc25c
To compute I = Integral of F*W over (A,B) with error estimate, where W(X) = 1/(X-C)

- qc25f
- qc25s
- qk15
To compute I = Integral of F over (A,B), with error estimate J = integral of ABS(F) over (A,B)

- qk15i
- qk15w
To compute I = Integral of F*W over (A,B), with error estimate J = Integral of ABS(F*W) over (A,B)

- qk21
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- qk31
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qk41
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- qk51
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qk61
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qmomo
- qng
- qpdoc
Documentation for QUADPACK, a package of subprograms for automatic evaluation of one-dimensional definite integrals.

### QUADRANT

- catan2
Compute the complex arc tangent in the proper quadrant.

### QUADRATIC PROGRAMMING

- dlsei
- dwnnls
- lsei
- wnnls

### QUADRATURE

- avint
Integrate a function tabulated at arbitrarily spaced abscissas using overlapping parabolas.

- bfqad
Compute the integral of a product of a function and a derivative of a B-spline.

- bsqad
Compute the integral of a K-th order B-spline using the B-representation.

- davint
Integrate a function tabulated at arbitrarily spaced abscissas using overlapping parabolas.

- dbfqad
Compute the integral of a product of a function and a derivative of a K-th order B-spline.

- dbsqad
Compute the integral of a K-th order B-spline using the B-representation.

- dpchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- dpchid
- dpfqad
- dppqad
- dqag
- dqage
- dqagi
- dqagie
- dqagp
- dqagpe
- dqags
- dqagse
- dqawc
- dqawce
- dqawf
- dqawfe
- dqawo
- dqawoe
- dqaws
- dqawse
- dqc25c
To compute I = Integral of F*W over (A,B) with error estimate, where W(X) = 1/(X-C)

- dqc25f
- dqc25s
- dqk15
To compute I = Integral of F over (A,B), with error estimate J = integral of ABS(F) over (A,B)

- dqk15i
- dqk15w
To compute I = Integral of F*W over (A,B), with error estimate J = Integral of ABS(F*W) over (A,B)

- dqk21
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- dqk31
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- dqk41
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- dqk51
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- dqk61
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- dqmomo
- dqng
- pchia
Evaluate the definite integral of a piecewise cubic Hermite function over an arbitrary interval.

- pchid
- pfqad
- ppqad
- qag
- qage
- qagi
- qagie
- qagp
- qagpe
- qags
- qagse
- qawc
- qawce
- qawf
- qawfe
- qawo
- qawoe
- qaws
- qawse
- qc25c
To compute I = Integral of F*W over (A,B) with error estimate, where W(X) = 1/(X-C)

- qc25f
- qc25s
- qk15
To compute I = Integral of F over (A,B), with error estimate J = integral of ABS(F) over (A,B)

- qk15i
- qk15w
To compute I = Integral of F*W over (A,B), with error estimate J = Integral of ABS(F*W) over (A,B)

- qk21
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- qk31
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qk41
To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B)

- qk51
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qk61
To compute I = Integral of F over (A,B) with error estimate J = Integral of ABS(F) over (A,B)

- qmomo
- qng
- qpdoc

### RACAH COEFFICIENTS

- drc3jj
- drc3jm
- drc6j
- rc3jj
- rc3jm
- rc6j

### RANDOM NUMBER

- rand
Generate a uniformly distributed random number.

- rgauss
Generate a normally distributed (Gaussian) random number.

- runif
Generate a uniformly distributed random number.

### REAL ROOTS

- cpzero
Find the zeros of a polynomial with complex coefficients.

- rpzero
Find the zeros of a polynomial with real coefficients.

### REARRANGEMENT

- dpperm
Rearrange a given array according to a prescribed permutation vector.

### RECALL

- j4save
Save or recall global variables needed by error handling routines.

### RECIPROCAL GAMMA FUNCTION

- cgamr
Compute the reciprocal of the Gamma function.

- dgamr
Compute the reciprocal of the Gamma function.

- gamr
Compute the reciprocal of the Gamma function.

### RELATIVE ADDRESS DETERMINATION FUNCTION

### RKF

- dderkf
- derkf

### ROOTS

- cbrt
Compute the cube root.

- ccbrt
Compute the cube root.

- dcbrt
Compute the cube root.

- dfzero
- dsos
Solve a square system of nonlinear equations.

- fzero
- sos
Solve a square system of nonlinear equations.

### RUNGE-KUTTA-FEHLBERG METHODS

- dderkf
- derkf

### SAVE

- j4save
Save or recall global variables needed by error handling routines.

### SCALE

- cscal
Multiply a vector by a constant.

- csscal
Scale a complex vector.

- dscal
Multiply a vector by a constant.

- sscal
Multiply a vector by a constant.

### SDRIVE

- cdriv1
- cdriv2
- cdriv3
- ddriv1
- ddriv2
- ddriv3
- sdriv1
- sdriv2
- sdriv3

### SECOND KIND

- besy0
Compute the Bessel function of the second kind of order zero.

- besy1
Compute the Bessel function of the second kind of order one.

- dbesy0
Compute the Bessel function of the second kind of order zero.

- dbesy1
Compute the Bessel function of the second kind of order one.

### SECOND ORDER

- c9ln2r
- d9ln2r
Evaluate LOG(1+X) from second order relative accuracy so that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

- r9ln2r

### SEPARABLE

- sepeli
- sepx4

### SEQUENCE OF BESSEL FUNCTIONS

- beskes
- besks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbesks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbskes

### SEQUENTIAL SORTING

- dqpsrt
This routine maintains the descending ordering in the list of the local error estimated resulting from the interval subdivision process. At each call two error estimates are inserted using the sequential search method, top-down for the largest error estimate and bottom-up for the smallest error estimate.

- qpsrt
Subsidiary to QAGE, QAGIE, QAGPE, QAGSE, QAWCE, QAWOE and QAWSE

### SHAPE-PRESERVING INTERPOLATION

- dpchic
- pchic

### SHOOTING

- bvsup
Solve a linear two-point boundary value problem using superposition coupled with an orthonormalization procedure and a variable-step integration scheme.

- dbvsup

### SINE

- dsindg
Compute the sine of an argument in degrees.

- sindg
Compute the sine of an argument in degrees.

### SINGLE PRECISION

- sdriv1
- sdriv2
- sdriv3

### SINGLETON QUICKSORT

- dpsort
- dsort
Sort an array and optionally make the same interchanges in an auxiliary array. The array may be sorted in increasing or decreasing order. A slightly modified QUICKSORT algorithm is used.

- hpsort
Return the permutation vector generated by sorting a substring within a character array and, optionally, rearrange the elements of the array. The array may be sorted in forward or reverse lexicographical order. A slightly modified quicksort algorithm is used.

- ipsort
- isort
Sort an array and optionally make the same interchanges in an auxiliary array. The array may be sorted in increasing or decreasing order. A slightly modified QUICKSORT algorithm is used.

- qs2i1d
Sort an integer array, moving an integer and DP array. This routine sorts the integer array IA and makes the same interchanges in the integer array JA and the double pre- cision array A. The array IA may be sorted in increasing order or decreasing order. A slightly modified QUICKSORT algorithm is used.

- qs2i1r
Sort an integer array, moving an integer and real array. This routine sorts the integer array IA and makes the same interchanges in the integer array JA and the real array A. The array IA may be sorted in increasing order or decreas- ing order. A slightly modified QUICKSORT algorithm is used.

- spsort
- ssort
Sort an array and optionally make the same interchanges in an auxiliary array. The array may be sorted in increasing or decreasing order. A slightly modified QUICKSORT algorithm is used.

### SINGULAR VALUE DECOMPOSITION

- csvdc
Perform the singular value decomposition of a rectangular matrix.

- dsvdc
Perform the singular value decomposition of a rectangular matrix.

- ssvdc
Perform the singular value decomposition of a rectangular matrix.

### SINGULARITIES AT USER SPECIFIED POINTS

- dqagp
- dqagpe
- qagp
- qagpe

### SLAP

- dbcg
- dcg
Preconditioned Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the Preconditioned Conjugate Gradient method.

- dcgn
- dcgs
- dchkw
SLAP WORK/IWORK Array Bounds Checker. This routine checks the work array lengths and interfaces to the SLATEC error handler if a problem is found.

- dgmres
- dhels
Internal routine for DGMRES.

- dheqr
Internal routine for DGMRES.

- dir
- dllti2
- dlpdoc
- domn
- dorth
Internal routine for DGMRES.

- dpigmr
Internal routine for DGMRES.

- drlcal
Internal routine for DGMRES.

- dsdbcg
- dsdcg
Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver. Routine to solve a symmetric positive definite linear system Ax = b using the Preconditioned Conjugate Gradient method. The preconditioner is diagonal scaling.

- dsdcgn
- dsdcgs
- dsdgmr
- dsdi
- dsdomn
- dsgs
- dsiccg
- dsilur
- dsilus
- dsjac
- dsli
- dsli2
- dsllti
- dslubc
- dslucn
- dslucs
- dslugm
- dslui
- dslui2
- dslui4
- dsluom
- dsluti
- dsmmi2
- dsmmti
- dsmtv
SLAP Column Format Sparse Matrix Transpose Vector Product. Routine to calculate the sparse matrix vector product: Y = A'*X, where ' denotes transpose.

- dsmv
SLAP Column Format Sparse Matrix Vector Product. Routine to calculate the sparse matrix vector product: Y = A*X.

- dxlcal
Internal routine for DGMRES.

- isdbcg
- isdcg
Preconditioned Conjugate Gradient Stop Test. This routine calculates the stop test for the Conjugate Gradient iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdcgn
- isdcgs
- isdgmr
- isdir
Preconditioned Iterative Refinement Stop Test. This routine calculates the stop test for the iterative refinement iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

- isdomn
- issbcg
- isscg
- isscgn
- isscgs
- issgmr
- issir
- issomn
- qs2i1d
Sort an integer array, moving an integer and DP array. This routine sorts the integer array IA and makes the same interchanges in the integer array JA and the double pre- cision array A. The array IA may be sorted in increasing order or decreasing order. A slightly modified QUICKSORT algorithm is used.

- qs2i1r
Sort an integer array, moving an integer and real array. This routine sorts the integer array IA and makes the same interchanges in the integer array JA and the real array A. The array IA may be sorted in increasing order or decreas- ing order. A slightly modified QUICKSORT algorithm is used.

- sbcg
- scg
- scgn
- scgs
- schkw
- sir
- sgmres
- shels
Internal routine for SGMRES.

- sheqr
Internal routine for SGMRES.

- sllti2
- slpdoc
- somn
- sorth
Internal routine for SGMRES.

- spigmr
Internal routine for SGMRES.

- srlcal
Internal routine for SGMRES.

- ssdbcg
- ssdcg
- ssdcgn
- ssdcgs
- ssdgmr
- ssdi
- ssdomn
- ssgs
- ssiccg
- ssilur
- ssilus
- ssjac
- ssli
- ssli2
- ssllti
- sslubc
- sslucn
- sslucs
- sslugm
- sslui
- sslui2
- sslui4
- ssluom
- ssluti
- ssmmi2
- ssmmti
- ssmtv
- ssmv
- sxlcal
Internal routine for SGMRES.

### SLAP SPARSE

- dbhin
- dcpplt
- ds2lt
- ds2y
SLAP Triad to SLAP Column Format Converter. Routine to convert from the SLAP Triad to SLAP Column format.

- dsd2s
Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up. Routine to compute the inverse of the diagonal of the matrix A*A', where A is stored in SLAP-Column format.

- dsds
Diagonal Scaling Preconditioner SLAP Set Up. Routine to compute the inverse of the diagonal of a matrix stored in the SLAP Column format.

- dsdscl
Diagonal Scaling of system Ax = b. This routine scales (and unscales) the system Ax = b by symmetric diagonal scaling.

- dsics
- dtin
- dtout
- sbhin
- scpplt
- ss2lt
- ss2y
- ssd2s
- ssds
- ssdscl
- ssics
- stin
- stout

### SLATEC

### SMALL X

- d9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and X small.

- d9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- r9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and for small X.

- r9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

### SMOOTH INTEGRAND

- dqng
- qng

### SMOOTH INTERPOLANT

- dintp
- sintrp

### SOLUTIONS

- dsos
Solve a square system of nonlinear equations.

- sos
Solve a square system of nonlinear equations.

### SOLVE

- cgbsl
Solve the complex band system A*X=B or CTRANS(A)*X=B using the factors computed by CGBCO or CGBFA.

- cgesl
Solve the complex system A*X=B or CTRANS(A)*X=B using the factors computed by CGECO or CGEFA.

- cgtsl
Solve a tridiagonal linear system.

- chisl
Solve the complex Hermitian system using factors obtained from CHIFA.

- chpsl
Solve a complex Hermitian system using factors obtained from CHPFA.

- cnbsl
Solve a complex band system using the factors computed by CNBCO or CNBFA.

- cpbsl
- cposl
- cppsl
Solve the complex Hermitian positive definite system using the factors computed by CPPCO or CPPFA.

- cptsl
Solve a positive definite tridiagonal linear system.

- cqrsl
- csisl
Solve a complex symmetric system using the factors obtained from CSIFA.

- cspsl
Solve a complex symmetric system using the factors obtained from CSPFA.

- dgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by DGBCO or DGBFA.

- dgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors computed by DGECO or DGEFA.

- dgtsl
Solve a tridiagonal linear system.

- dnbsl
Solve a real band system using the factors computed by DNBCO or DNBFA.

- dpbsl
Solve a real symmetric positive definite band system using the factors computed by DPBCO or DPBFA.

- dposl
- dppsl
Solve the real symmetric positive definite system using the factors computed by DPPCO or DPPFA.

- dptsl
Solve a positive definite tridiagonal linear system.

- dqrsl
- dsisl
Solve a real symmetric system using the factors obtained from SSIFA.

- dspsl
Solve a real symmetric system using the factors obtained from DSPFA.

- sgbsl
Solve the real band system A*X=B or TRANS(A)*X=B using the factors computed by SGBCO or SGBFA.

- sgesl
Solve the real system A*X=B or TRANS(A)*X=B using the factors of SGECO or SGEFA.

- sgtsl
Solve a tridiagonal linear system.

- snbsl
Solve a real band system using the factors computed by SNBCO or SNBFA.

- spbsl
Solve a real symmetric positive definite band system using the factors computed by SPBCO or SPBFA.

- sposl
- sppsl
Solve the real symmetric positive definite system using the factors computed by SPPCO or SPPFA.

- sptsl
Solve a positive definite tridiagonal linear system.

- sqrsl
- ssisl
Solve a real symmetric system using the factors obtained from SSIFA.

- sspsl
Solve a real symmetric system using the factors obtained from SSPFA.

### SORT

- dpsort
- dsort
- hpsort
Return the permutation vector generated by sorting a substring within a character array and, optionally, rearrange the elements of the array. The array may be sorted in forward or reverse lexicographical order. A slightly modified quicksort algorithm is used.

- ipsort
- isort
- qs2i1d
Sort an integer array, moving an integer and DP array. This routine sorts the integer array IA and makes the same interchanges in the integer array JA and the double pre- cision array A. The array IA may be sorted in increasing order or decreasing order. A slightly modified QUICKSORT algorithm is used.

- qs2i1r
Sort an integer array, moving an integer and real array. This routine sorts the integer array IA and makes the same interchanges in the integer array JA and the real array A. The array IA may be sorted in increasing order or decreas- ing order. A slightly modified QUICKSORT algorithm is used.

- spsort
- ssort

### SORTING

- dsort
- isort
- qs2i1d
- qs2i1r
- ssort

### SPARSE

- dbcg
- dcg
- dcgn
- dcgs
- dgmres
- dhels
Internal routine for DGMRES.

- dheqr
Internal routine for DGMRES.

- dir
- dllti2
- domn
- dorth
Internal routine for DGMRES.

- dpigmr
Internal routine for DGMRES.

- drlcal
Internal routine for DGMRES.

- dsdbcg
- dsdcg
- dsdcgn
- dsdcgs
- dsdgmr
- dsdi
- dsdomn
- dsgs
- dsiccg
- dsilur
- dsilus
- dsjac
- dsli
- dsli2
- dsllti
- dslubc
- dslucn
- dslucs
- dslugm
- dslui
- dslui2
- dslui4
- dsluom
- dsluti
- dsmmi2
- dsmmti
- dsmtv
- dsmv
- dxlcal
Internal routine for DGMRES.

- isdbcg
- isdcg
- isdcgn
- isdcgs
- isdgmr
- isdir
- isdomn
- issbcg
- isscg
- isscgn
- isscgs
- issgmr
- issir
- issomn
- sbcg
- scg
- scgn
- scgs
- sir
- sgmres
- shels
Internal routine for SGMRES.

- sheqr
Internal routine for SGMRES.

- sllti2
- somn
- sorth
Internal routine for SGMRES.

- spigmr
Internal routine for SGMRES.

- srlcal
Internal routine for SGMRES.

- ssdbcg
- ssdcg
- ssdcgn
- ssdcgs
- ssdgmr
- ssdi
- ssdomn
- ssgs
- ssiccg
- ssilur
- ssilus
- ssjac
- ssli
- ssli2
- ssllti
- sslubc
- sslucn
- sslucs
- sslugm
- sslui
- sslui2
- sslui4
- ssluom
- ssluti
- ssmmi2
- ssmmti
- ssmtv
- ssmv
- sxlcal
Internal routine for SGMRES.

### SPARSE CONSTRAINTS

- dsplp
- splp

### SPARSE ITERATIVE METHODS

- dlpdoc
- slpdoc

### SPECIAL FUNCTIONS

- ai
Evaluate the Airy function.

- aie
- albeta
Compute the natural logarithm of the complete Beta function.

- algams
Compute the logarithm of the absolute value of the Gamma function.

- ali
Compute the logarithmic integral.

- alngam
Compute the logarithm of the absolute value of the Gamma function.

- besi
Compute an N member sequence of I Bessel functions I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X.

- besi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- besi0e
- besi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- besi1e
- besj
Compute an N member sequence of J Bessel functions J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X.

- besj0
Compute the Bessel function of the first kind of order zero.

- besj1
Compute the Bessel function of the first kind of order one.

- besk
Implement forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive X and non-negative orders FNU.

- besk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- besk0e
- besk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- besk1e
- beskes
- besks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- besy
Implement forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive X and non-negative orders FNU.

- besy0
Compute the Bessel function of the second kind of order zero.

- besy1
Compute the Bessel function of the second kind of order one.

- beta
Compute the complete Beta function.

- betai
Calculate the incomplete Beta function.

- bi
Evaluate the Bairy function (the Airy function of the second kind).

- bie
- binom
Compute the binomial coefficients.

- c0lgmc
Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative accuracy.

- c9lgmc
- cbeta
Compute the complete Beta function.

- cgamma
Compute the complete Gamma function.

- cgamr
Compute the reciprocal of the Gamma function.

- chu
Compute the logarithmic confluent hypergeometric function.

- clbeta
Compute the natural logarithm of the complete Beta function.

- clngam
Compute the logarithm of the absolute value of the Gamma function.

- cpsi
Compute the Psi (or Digamma) function.

- csevl
Evaluate a Chebyshev series.

- d9aimp
Evaluate the Airy modulus and phase.

- d9b0mp
Evaluate the modulus and phase for the J0 and Y0 Bessel functions.

- d9b1mp
Evaluate the modulus and phase for the J1 and Y1 Bessel functions.

- d9chu
Evaluate for large Z Z**A * U(A,B,Z) where U is the logarithmic confluent hypergeometric function.

- d9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and X small.

- d9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- d9knus
Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)* K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

- d9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- d9lgit
- d9lgmc
- dai
Evaluate the Airy function.

- daie
- daws
Compute Dawson's function.

- dbesi
Compute an N member sequence of I Bessel functions I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for nonnegative ALPHA and X.

- dbesi0
Compute the hyperbolic Bessel function of the first kind of order zero.

- dbesi1
Compute the modified (hyperbolic) Bessel function of the first kind of order one.

- dbesj
- dbesj0
Compute the Bessel function of the first kind of order zero.

- dbesj1
Compute the Bessel function of the first kind of order one.

- dbesk
- dbesk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- dbesk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- dbesks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbesy
Implement forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive X and non-negative orders FNU.

- dbesy0
Compute the Bessel function of the second kind of order zero.

- dbesy1
Compute the Bessel function of the second kind of order one.

- dbeta
Compute the complete Beta function.

- dbetai
Calculate the incomplete Beta function.

- dbi
Evaluate the Bairy function (the Airy function of the second kind).

- dbie
- dbinom
Compute the binomial coefficients.

- dbsi0e
- dbsi1e
- dbsk0e
- dbsk1e
- dbskes
- dchu
Compute the logarithmic confluent hypergeometric function.

- dcsevl
Evaluate a Chebyshev series.

- ddaws
Compute Dawson's function.

- de1
Compute the exponential integral E1(X).

- dei
Compute the exponential integral Ei(X).

- derf
Compute the error function.

- derfc
Compute the complementary error function.

- dexint
Compute an M member sequence of exponential integrals E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

- dfac
Compute the factorial function.

- dgami
Evaluate the incomplete Gamma function.

- dgamic
Calculate the complementary incomplete Gamma function.

- dgamit
Calculate Tricomi's form of the incomplete Gamma function.

- dgamlm
Compute the minimum and maximum bounds for the argument in the Gamma function.

- dgamma
Compute the complete Gamma function.

- dgamr
Compute the reciprocal of the Gamma function.

- dlbeta
Compute the natural logarithm of the complete Beta function.

- dlgams
Compute the logarithm of the absolute value of the Gamma function.

- dli
Compute the logarithmic integral.

- dlngam
Compute the logarithm of the absolute value of the Gamma function.

- dpoch
Evaluate a generalization of Pochhammer's symbol.

- dpoch1
Calculate a generalization of Pochhammer's symbol starting from first order.

- dpsi
Compute the Psi (or Digamma) function.

- dspenc
Compute a form of Spence's integral due to K. Mitchell.

- e1
Compute the exponential integral E1(X).

- ei
Compute the exponential integral Ei(X).

- erf
Compute the error function.

- erfc
Compute the complementary error function.

- exint
- fac
Compute the factorial function.

- fundoc
Documentation for FNLIB, a collection of routines for evaluating elementary and special functions.

- gami
Evaluate the incomplete Gamma function.

- gamic
Calculate the complementary incomplete Gamma function.

- gamit
Calculate Tricomi's form of the incomplete Gamma function.

- gamlim
Compute the minimum and maximum bounds for the argument in the Gamma function.

- gamma
Compute the complete Gamma function.

- gamr
Compute the reciprocal of the Gamma function.

- initds
- inits
- psi
Compute the Psi (or Digamma) function.

- poch
Evaluate a generalization of Pochhammer's symbol.

- poch1
Calculate a generalization of Pochhammer's symbol starting from first order.

- r9aimp
Evaluate the Airy modulus and phase.

- r9chu
Evaluate for large Z Z**A * U(A,B,Z) where U is the logarithmic confluent hypergeometric function.

- r9gmic
Compute the complementary incomplete Gamma function for A near a negative integer and for small X.

- r9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- rand
Generate a uniformly distributed random number.

- r9knus
Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)* K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

- r9lgic
Compute the log complementary incomplete Gamma function for large X and for A .LE. X.

- r9lgit
- r9lgmc
- rgauss
Generate a normally distributed (Gaussian) random number.

- runif
Generate a uniformly distributed random number.

- spenc
Compute a form of Spence's integral due to K. Mitchell.

### SPECIAL-PURPOSE

- dqawc
- dqawce
- dqawo
- dqawoe
- dqaws
- dqawse
- qawc
- qawce
- qawo
- qawoe
- qaws
- qawse

### SPECIAL-PURPOSE INTEGRAL

- dqawf
- dqawfe
- qawf
- qawfe

### SPENCE'S INTEGRAL

- dspenc
Compute a form of Spence's integral due to K. Mitchell.

- spenc
Compute a form of Spence's integral due to K. Mitchell.

### SPHERICAL

- hstcsp
- hstssp
- hwscsp
- hwsssp

### SPLINE INTERPOLATION

- dpchsp
- pchsp

### SPLINES

- bspdoc
Documentation for BSPLINE, a package of subprograms for working with piecewise polynomial functions in B-representation.

- bspev
Calculate the value of the spline and its derivatives from the B-representation.

- dbspev
Calculate the value of the spline and its derivatives from the B-representation.

- dintrv
- dpfqad
- dppqad
- dppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

- intrv
- pfqad
- ppqad
- ppval
Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

### STIFF

- cdriv1
- cdriv2
- cdriv3
- ddebdf
- ddriv1
- ddriv2
- ddriv3
- debdf
- sdriv1
- sdriv2
- sdriv3

### STOP TEST

- isdbcg
- isdcg
- isdcgs
- isdgmr
- isdir
- isdomn
- issbcg
- isscg
- isscgs
- issgmr
- issir
- issomn

### STRING SORTING

- hpsort

### SUM OF MAGNITUDES OF A VECTOR

- dasum
Compute the sum of the magnitudes of the elements of a vector.

- sasum
Compute the sum of the magnitudes of the elements of a vector.

- scasum
Compute the sum of the magnitudes of the real and imaginary elements of a complex vector.

### SURVEY OF INTEGRATORS

- qpdoc

### SYMMETRIC

- chiev
Compute the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix.

- cpofs
Solve a positive definite symmetric complex system of linear equations.

- cpoir
- csico
- csidi
Compute the determinant and inverse of a complex symmetric matrix using the factors from CSIFA.

- csifa
Factor a complex symmetric matrix by elimination with symmetric pivoting.

- csisl
Solve a complex symmetric system using the factors obtained from CSIFA.

- cspco
- cspdi
- cspfa
Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting.

- cspsl
Solve a complex symmetric system using the factors obtained from CSPFA.

- dpofs
Solve a positive definite symmetric system of linear equations.

- dsico
- dsidi
- dsifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- dsisl
Solve a real symmetric system using the factors obtained from SSIFA.

- dspco
- dspdi
- dspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- dspsl
Solve a real symmetric system using the factors obtained from DSPFA.

- spofs
Solve a positive definite symmetric system of linear equations.

- spoir
- ssico
- ssidi
- ssiev
Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric matrix.

- ssifa
Factor a real symmetric matrix by elimination with symmetric pivoting.

- ssisl
Solve a real symmetric system using the factors obtained from SSIFA.

- sspco
- sspdi
- sspev
- sspfa
Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting.

- sspsl
Solve a real symmetric system using the factors obtained from SSPFA.

### SYMMETRIC LINEAR SYSTEM

- dcg
- dsdcg
- dsiccg
- scg
- ssdcg
- ssiccg

### SYMMETRIC LINEAR SYSTEM SOLVE

- dllti2
- sllti2

### TABULATED DATA

- avint
Integrate a function tabulated at arbitrarily spaced abscissas using overlapping parabolas.

- davint
Integrate a function tabulated at arbitrarily spaced abscissas using overlapping parabolas.

### TANGENT

- ctan
Compute the complex tangent.

### TAYLOR SERIES

- drc
- drd
- drf
- drj
- rc
- rd
- rf
- rj

### THIRD KIND

- besk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- besk0e
- besk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- besk1e
- beskes
- besks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbesk0
Compute the modified (hyperbolic) Bessel function of the third kind of order zero.

- dbesk1
Compute the modified (hyperbolic) Bessel function of the third kind of order one.

- dbesks
Compute a sequence of modified Bessel functions of the third kind of fractional order.

- dbsk0e
- dbsk1e
- dbskes

### TRANSFORMATION

- dqagi
- dqagie
- qagi
- qagie

### TRIAD

- caxpy
Compute a constant times a vector plus a vector.

- daxpy
Compute a constant times a vector plus a vector.

- saxpy
Compute a constant times a vector plus a vector.

### TRIANGULAR

- strdi
Compute the determinant and inverse of a triangular matrix.

### TRIANGULAR LINEAR SYSTEM

- ctrsl
Solve a system of the form T*X=B or CTRANS(T)*X=B, where T is a triangular matrix. Here CTRANS(T) is the conjugate transpose.

- dtrsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

- strsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

### TRIANGULAR MATRIX

- ctrco
Estimate the condition number of a triangular matrix.

- ctrdi
Compute the determinant and inverse of a triangular matrix.

- ctrsl
- dtrco
Estimate the condition number of a triangular matrix.

- dtrdi
Compute the determinant and inverse of a triangular matrix.

- dtrsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

- strco
Estimate the condition number of a triangular matrix.

- strsl
Solve a system of the form T*X=B or TRANS(T)*X=B, where T is a triangular matrix.

### TRICOMI

- d9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- d9lgit
- dgamit
Calculate Tricomi's form of the incomplete Gamma function.

- gamit
Calculate Tricomi's form of the incomplete Gamma function.

- r9gmit
Compute Tricomi's incomplete Gamma function for small arguments.

- r9lgit

### TRIDIAGONAL

- cgtsl
Solve a tridiagonal linear system.

- cptsl
Solve a positive definite tridiagonal linear system.

- dgtsl
Solve a tridiagonal linear system.

- dptsl
Solve a positive definite tridiagonal linear system.

- genbun
- poistg
- sgtsl
Solve a tridiagonal linear system.

- sptsl
Solve a positive definite tridiagonal linear system.

### TRIDIAGONAL LINEAR SYSTEM

- blktri
- cblktr
- cmgnbn
Solve a complex block tridiagonal linear system of equations by a cyclic reduction algorithm.

### TRIGONOMETRIC

- cacos
Compute the complex arc cosine.

- casin
Compute the complex arc sine.

- catan
Compute the complex arc tangent.

- catan2
Compute the complex arc tangent in the proper quadrant.

- ccot
Compute the cotangent.

- cosdg
Compute the cosine of an argument in degrees.

- cot
Compute the cotangent.

- ctan
Compute the complex tangent.

- d9atn1
Evaluate DATAN(X) from first order relative accuracy so that DATAN(X) = X + X**3*D9ATN1(X).

- dcosdg
Compute the cosine of an argument in degrees.

- dcot
Compute the cotangent.

- dsindg
Compute the sine of an argument in degrees.

- r9atn1
Evaluate ATAN(X) from first order relative accuracy so that ATAN(X) = X + X**3*R9ATN1(X).

- sindg
Compute the sine of an argument in degrees.

### TWO-POINT BOUNDARY VALUE PROBLEM

- bvsup
- dbvsup

### UNDERDETERMINED LINEAR SYSTEM

- dulsia
- ulsia

### UNDERDETERMINED LINEAR SYSTEMS

- dglss
- sglss

### UNIFORM

- rand
Generate a uniformly distributed random number.

- runif
Generate a uniformly distributed random number.

### UNITARY

- dnrm2
Compute the Euclidean length (L2 norm) of a vector.

- scnrm2
Compute the unitary norm of a complex vector.

- snrm2
Compute the Euclidean length (L2 norm) of a vector.

### UNPACK

- d9upak
Unpack a floating point number X so that X = Y*2**N.

- r9upak
Unpack a floating point number X so that X = Y*2**N.

### UPDATE

- cchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- dchud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

- schud
Update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

### UTILITY ROUTINE

- dpchcm
Check a cubic Hermite function for monotonicity.

- pchcm
Check a cubic Hermite function for monotonicity.

### VECTOR

- caxpy
Compute a constant times a vector plus a vector.

- ccopy
Copy a vector.

- cdcdot
Compute the inner product of two vectors with extended precision accumulation.

- cdotc
Dot product of two complex vectors using the complex conjugate of the first vector.

- cdotu
Compute the inner product of two vectors.

- crotg
Construct a Givens transformation.

- cscal
Multiply a vector by a constant.

- csrot
Apply a plane Givens rotation.

- csscal
Scale a complex vector.

- cswap
Interchange two vectors.

- daxpy
Compute a constant times a vector plus a vector.

- dcdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dcopy
Copy a vector.

- dcopym
Copy the negative of a vector to a vector.

- ddot
Compute the inner product of two vectors.

- dnrm2
Compute the Euclidean length (L2 norm) of a vector.

- drot
Apply a plane Givens rotation.

- drotg
Construct a plane Givens rotation.

- drotm
Apply a modified Givens transformation.

- drotmg
Construct a modified Givens transformation.

- dscal
Multiply a vector by a constant.

- dsdot
Compute the inner product of two vectors with extended precision accumulation and result.

- dswap
Interchange two vectors.

- icamax
- icopy
Copy a vector.

- idamax
Find the smallest index of that component of a vector having the maximum magnitude.

- isamax
Find the smallest index of that component of a vector having the maximum magnitude.

- iswap
Interchange two vectors.

- saxpy
Compute a constant times a vector plus a vector.

- scnrm2
Compute the unitary norm of a complex vector.

- scopy
Copy a vector.

- scopym
Copy the negative of a vector to a vector.

- sdot
Compute the inner product of two vectors.

- sdsdot
Compute the inner product of two vectors with extended precision accumulation.

- snrm2
Compute the Euclidean length (L2 norm) of a vector.

- srot
Apply a plane Givens rotation.

- srotg
Construct a plane Givens rotation.

- srotm
Apply a modified Givens transformation.

- srotmg
Construct a modified Givens transformation.

- sscal
Multiply a vector by a constant.

- sswap
Interchange two vectors.

### VECTOR ADDITION COEFFICIENTS

- drc3jj
- drc3jm
- drc6j
- rc3jj
- rc3jm
- rc6j

### VERSION

- aaaaaa
SLATEC Common Mathematical Library disclaimer and version.

### WEBER'S FUNCTION

- cbesy
- zbesy

### WEIGHT FUNCTION

- dqwgtc
This function subprogram is used together with the routine DQAWC and defines the WEIGHT function.

- dqwgts
This function subprogram is used together with the routine DQAWS and defines the WEIGHT function.

- qwgtc
This function subprogram is used together with the routine QAWC and defines the WEIGHT function.

- qwgts
This function subprogram is used together with the routine QAWS and defines the WEIGHT function.

### WEIGHTED LEAST SQUARES

- dfc
- efc
- fc

### WIGNER COEFFICIENTS

- drc3jj
- drc3jm
- drc6j
- rc3jj
- rc3jm
- rc6j

### WORKSPACE CHECKING

- dchkw
- schkw

### XERMSG

- fdump
Symbolic dump (should be locally written).

### XERROR

- j4save
Save or recall global variables needed by error handling routines.

- numxer
Return the most recent error number.

- xerclr
Reset current error number to zero.

- xercnt
Allow user control over handling of errors.

- xerdmp
Print the error tables and then clear them.

- xerhlt
Abort program execution and print error message.

- xermax
Set maximum number of times any error message is to be printed.

- xermsg
Process error messages for SLATEC and other libraries.

- xerprn
Print error messages processed by XERMSG.

- xersve
Record that an error has occurred.

- xgetf
Return the current value of the error control flag.

- xgetua
Return unit number(s) to which error messages are being sent.

- xgetun
Return the (first) output file to which error messages are being sent.

- xsetf
Set the error control flag.

- xsetua
Set logical unit numbers (up to 5) to which error messages are to be sent.

- xsetun
Set output file to which error messages are to be sent.

### Y BESSEL FUNCTION

- besy
Implement forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive X and non-negative orders FNU.

- dbesy

### Y BESSEL FUNCTIONS

- cbesy
- zbesy

### ZEROS

- dfzero
- dnsq
- dnsqe
- fzero
- snsq
- snsqe

- dqk15