CSICO(3)

SYNOPSIS
SUBROUTINE CSICO (A, LDA, N, KPVT, RCOND, Z)

NAME
csico - Factor a complex symmetric matrix by elimination with symmetric pivoting and estimate the condition number of the matrix.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2C1

TYPE
COMPLEX (SSICO-S, DSICO-D, CHICO-C, CSICO-C)

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

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

DESCRIPTION
CSICO factors a complex symmetric matrix by elimination with symmetric pivoting and estimates the condition of the matrix. If RCOND is not needed, CSIFA is slightly faster. To solve A*X = B , follow CSICO by CSISL. To compute INVERSE(A)*C , follow CSICO by CSISL. To compute INVERSE(A) , follow CSICO by CSIDI. To compute DETERMINANT(A) , follow CSICO by CSIDI. On Entry A COMPLEX(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. 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) .

REFERENCES
J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979.

ROUTINES CALLED
CAXPY, CDOTU, CSIFA, 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)