CSPFA(3)

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

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

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2C1

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

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

AUTHOR
Bunch, J., (UCSD)

DESCRIPTION
CSPFA factors a complex symmetric matrix stored in packed form by elimination with symmetric pivoting. To solve A*X = B , follow CSPFA by CSPSL. To compute INVERSE(A)*C , follow CSPFA by CSPSL. To compute DETERMINANT(A) , follow CSPFA by CSPDI. To compute INVERSE(A) , follow CSPFA by CSPDI. On Entry AP COMPLEX (N*(N+1)/2) the packed form of a symmetric 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 . On Return 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*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. 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 CSPSL or CSPDI may divide by zero if called. Packed Storage The following program segment will pack the upper triangle of a symmetric 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 Corrected category and 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)