SSIDI(3)

SYNOPSIS
SUBROUTINE SSIDI (A, LDA, N, KPVT, DET, INERT, WORK, JOB)

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

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1A, D3B1A

TYPE
SINGLE PRECISION (SSIDI-S, DSIDI-D, CHIDI-C, CSIDI-C)

KEYWORDS
DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, SYMMETRIC

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
SSIDI computes the determinant, inertia and inverse of a real symmetric matrix using the factors from SSIFA. On Entry A REAL(LDA,N) the output from SSIFA. LDA INTEGER the leading dimension of the array A. N INTEGER the order of the matrix A. KPVT INTEGER(N) the pivot vector from SSIFA. WORK REAL(N) work vector. Contents destroyed. JOB INTEGER JOB has the decimal expansion ABC where If C .NE. 0, the inverse is computed, If B .NE. 0, the determinant is computed, If A .NE. 0, the inertia is computed. For example, JOB = 111 gives all three. On Return Variables not requested by JOB are not used. A contains the upper triangle of the inverse of the original matrix. The strict lower triangle is never referenced. DET REAL(2) determinant of original matrix. Determinant = DET(1) * 10.0**DET(2) with 1.0 .LE. ABS(DET(1)) .LT. 10.0 or DET(1) = 0.0. INERT INTEGER(3) the inertia of the original matrix. INERT(1) = number of positive eigenvalues. INERT(2) = number of negative eigenvalues. INERT(3) = number of zero eigenvalues. Error Condition A division by zero may occur if the inverse is requested and SSICO has set RCOND .EQ. 0.0 or SSIFA has set INFO .NE. 0 .

REFERENCES
J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979.

ROUTINES CALLED
SAXPY, SCOPY, SDOT, SSWAP

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
891107 Modified routine equivalence list. (WRB)
891107 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)