dpoco.f
SUBROUTINE DPOCO (A, LDA, N, RCOND, Z, INFO)
C***BEGIN PROLOGUE DPOCO
C***PURPOSE Factor a real symmetric positive definite matrix
C and estimate the condition of the matrix.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2B1B
C***TYPE DOUBLE PRECISION (SPOCO-S, DPOCO-D, CPOCO-C)
C***KEYWORDS CONDITION NUMBER, LINEAR ALGEBRA, LINPACK,
C MATRIX FACTORIZATION, POSITIVE DEFINITE
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C DPOCO factors a double precision symmetric positive definite
C matrix and estimates the condition of the matrix.
C
C If RCOND is not needed, DPOFA is slightly faster.
C To solve A*X = B , follow DPOCO by DPOSL.
C To compute INVERSE(A)*C , follow DPOCO by DPOSL.
C To compute DETERMINANT(A) , follow DPOCO by DPODI.
C To compute INVERSE(A) , follow DPOCO by DPODI.
C
C On Entry
C
C A DOUBLE PRECISION(LDA, N)
C the symmetric matrix to be factored. Only the
C diagonal and upper triangle are used.
C
C LDA INTEGER
C the leading dimension of the array A .
C
C N INTEGER
C the order of the matrix A .
C
C On Return
C
C A an upper triangular matrix R so that A = TRANS(R)*R
C where TRANS(R) is the transpose.
C The strict lower triangle is unaltered.
C If INFO .NE. 0 , the factorization is not complete.
C
C RCOND DOUBLE PRECISION
C an estimate of the reciprocal condition of A .
C For the system A*X = B , relative perturbations
C in A and B of size EPSILON may cause
C relative perturbations in X of size EPSILON/RCOND .
C If RCOND is so small that the logical expression
C 1.0 + RCOND .EQ. 1.0
C is true, then A may be singular to working
C precision. In particular, RCOND is zero if
C exact singularity is detected or the estimate
C underflows. If INFO .NE. 0 , RCOND is unchanged.
C
C Z DOUBLE PRECISION(N)
C a work vector whose contents are usually unimportant.
C If A is close to a singular matrix, then Z is
C an approximate null vector in the sense that
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C If INFO .NE. 0 , Z is unchanged.
C
C INFO INTEGER
C = 0 for normal return.
C = K signals an error condition. The leading minor
C of order K is not positive definite.
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED DASUM, DAXPY, DDOT, DPOFA, DSCAL
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DPOCO