SSPDI(3)

SYNOPSIS
SUBROUTINE SSPDI (AP, N, KPVT, DET, INERT, WORK, JOB)

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

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1A, D3B1A

TYPE
SINGLE PRECISION (SSPDI-S, DSPDI-D, CHPDI-C, CSPDI-C)

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

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
SSPDI computes the determinant, inertia and inverse of a real symmetric matrix using the factors from SSPFA, where the matrix is stored in packed form. On Entry AP REAL (N*(N+1)/2) the output from SSPFA. N INTEGER the order of the matrix A. KPVT INTEGER(N) the pivot vector from SSPFA. WORK REAL(N) work vector. Contents ignored. 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. AP contains the upper triangle of the inverse of the original matrix, stored in packed form. The columns of the upper triangle are stored sequentially in a one-dimensional array. 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 will occur if the inverse is requested and SSPCO has set RCOND .EQ. 0.0 or SSPFA 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)