SSIFA(3)

SYNOPSIS
SUBROUTINE SSIFA (A, LDA, N, KPVT, INFO)

NAME
ssifa - Factor a real symmetric matrix by elimination with symmetric pivoting.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1A

TYPE
SINGLE PRECISION (SSIFA-S, DSIFA-D, CHIFA-C, CSIFA-C)

KEYWORDS
LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, SYMMETRIC

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
SSIFA factors a real symmetric matrix by elimination with symmetric pivoting. To solve A*X = B , follow SSIFA by SSISL. To compute INVERSE(A)*C , follow SSIFA by SSISL. To compute DETERMINANT(A) , follow SSIFA by SSIDI. To compute INERTIA(A) , follow SSIFA by SSIDI. To compute INVERSE(A) , follow SSIFA by SSIDI. On Entry A REAL(LDA,N) the symmetric matrix to be factored. Only the diagonal and upper triangle are used. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . On Return A a block diagonal matrix and the multipliers which were used to obtain it. The factorization can be written A = U*D*TRANS(U) where U is a product of permutation and unit upper triangular matrices , TRANS(U) is the transpose of U , and D is block diagonal with 1 by 1 and 2 by 2 blocks. KPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER = 0 normal value. = K if the K-th pivot block is singular. This is not an error condition for this subroutine, but it does indicate that SSISL or SSIDI may divide by zero if called.

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

ROUTINES CALLED
ISAMAX, SAXPY, 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)