CHIFA(3)

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

NAME
chifa - Factor a complex Hermitian matrix by elimination (symmetric pivoting).

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2D1A

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

KEYWORDS
HERMITIAN, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
CHIFA factors a complex Hermitian matrix by elimination with symmetric pivoting. To solve A*X = B , follow CHIFA by CHISL. To compute INVERSE(A)*C , follow CHIFA by CHISL. To compute DETERMINANT(A) , follow CHIFA by CHIDI. To compute INERTIA(A) , follow CHIFA by CHIDI. To compute INVERSE(A) , follow CHIFA by CHIDI. On Entry A COMPLEX(LDA,N) the Hermitian 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*CTRANS(U) where U is a product of permutation and unit upper triangular matrices , CTRANS(U) is the conjugate transpose of U , and D is block diagonal with 1 by 1 and 2 by 2 blocks. KVPT 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 CHISL or CHIDI 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
CAXPY, CSWAP, ICAMAX

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)