CSPCO(3)

SYNOPSIS
SUBROUTINE CSPCO (AP, N, KPVT, RCOND, Z)

NAME
cspco - Factor a complex symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2C1

TYPE
COMPLEX (SSPCO-S, DSPCO-D, CHPCO-C, CSPCO-C)

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

AUTHOR
Moler, C. B., (U. of New Mexico)

DESCRIPTION
CSPCO factors a complex symmetric matrix stored in packed form by elimination with symmetric pivoting and estimates the condition of the matrix. If RCOND is not needed, CSPFA is slightly faster. To solve A*X = B , follow CSPCO by CSPSL. To compute INVERSE(A)*C , follow CSPCO by CSPSL. To compute INVERSE(A) , follow CSPCO by CSPDI. To compute DETERMINANT(A) , follow CSPCO 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. RCOND REAL an estimate of the reciprocal condition of A . For the system A*X = B , relative perturbations in A and B of size EPSILON may cause relative perturbations in X of size EPSILON/RCOND . If RCOND is so small that the logical expression 1.0 + RCOND .EQ. 1.0 is true, then A may be singular to working precision. In particular, RCOND is zero if exact singularity is detected or the estimate underflows. Z COMPLEX(N) a work vector whose contents are usually unimportant. If A is close to a singular matrix, then Z is an approximate null vector in the sense that NORM(A*Z) = RCOND*NORM(A)*NORM(Z) . 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, CDOTU, CSPFA, CSSCAL, SCASUM

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)