CHPFA(3)

SYNOPSIS
SUBROUTINE CHPFA (AP, N, KPVT, INFO)

NAME
chpfa - Factor a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2D1A

TYPE
COMPLEX (SSPFA-S, DSPFA-D, CHPFA-C, DSPFA-C)

KEYWORDS
HERMITIAN, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, PACKED

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
CHPFA factors a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting. To solve A*X = B , follow CHPFA by CHPSL. To compute INVERSE(A)*C , follow CHPFA by CHPSL. To compute DETERMINANT(A) , follow CHPFA by CHPDI. To compute INERTIA(A) , follow CHPFA by CHPDI. To compute INVERSE(A) , follow CHPFA by CHPDI. On Entry AP COMPLEX (N*(N+1)/2) the packed form of a Hermitian matrix A . The columns of the upper triangle are stored sequentially in a one-dimensional array of length N*(N+1)/2 . See comments below for details. N INTEGER the order of the matrix A . Output AP A block diagonal matrix and the multipliers which were used to obtain it stored in packed form. 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 CHPSL or CHPDI may divide by zero if called. Packed Storage The following program segment will pack the upper triangle of a Hermitian matrix. K = 0 DO 20 J = 1, N DO 10 I = 1, J K = K + 1 AP(K) = A(I,J) 10 CONTINUE 20 CONTINUE

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)