DSIFA(3)

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

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

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1A

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

KEYWORDS
LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, SYMMETRIC

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
DSIFA factors a double precision symmetric matrix by elimination with symmetric pivoting. To solve A*X = B , follow DSIFA by DSISL. To compute INVERSE(A)*C , follow DSIFA by DSISL. To compute DETERMINANT(A) , follow DSIFA by DSIDI. To compute INERTIA(A) , follow DSIFA by DSIDI. To compute INVERSE(A) , follow DSIFA by DSIDI. On Entry A DOUBLE PRECISION(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 DSISL or DSIDI 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
DAXPY, DSWAP, IDAMAX

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)