spodi.f
SUBROUTINE SPODI (A, LDA, N, DET, JOB)
C***BEGIN PROLOGUE SPODI
C***PURPOSE Compute the determinant and inverse of a certain real
C symmetric positive definite matrix using the factors
C computed by SPOCO, SPOFA or SQRDC.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2B1B, D3B1B
C***TYPE SINGLE PRECISION (SPODI-S, DPODI-D, CPODI-C)
C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX,
C POSITIVE DEFINITE
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C SPODI computes the determinant and inverse of a certain
C real symmetric positive definite matrix (see below)
C using the factors computed by SPOCO, SPOFA or SQRDC.
C
C On Entry
C
C A REAL(LDA, N)
C the output A from SPOCO or SPOFA
C or the output X from SQRDC.
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 JOB INTEGER
C = 11 both determinant and inverse.
C = 01 inverse only.
C = 10 determinant only.
C
C On Return
C
C A If SPOCO or SPOFA was used to factor A , then
C SPODI produces the upper half of INVERSE(A) .
C If SQRDC was used to decompose X , then
C SPODI produces the upper half of INVERSE(TRANS(X)*X),
C where TRANS(X) is the transpose.
C Elements of A below the diagonal are unchanged.
C If the units digit of JOB is zero, A is unchanged.
C
C DET REAL(2)
C determinant of A or of TRANS(X)*X if requested.
C Otherwise not referenced.
C Determinant = DET(1) * 10.0**DET(2)
C with 1.0 .LE. DET(1) .LT. 10.0
C or DET(1) .EQ. 0.0 .
C
C Error Condition
C
C A division by zero will occur if the input factor contains
C a zero on the diagonal and the inverse is requested.
C It will not occur if the subroutines are called correctly
C and if SPOCO or SPOFA has set INFO .EQ. 0 .
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 SAXPY, SSCAL
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
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 SPODI