SSICO(3)

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

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

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1A

TYPE
SINGLE PRECISION (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
SSICO factors a real symmetric matrix by elimination with symmetric pivoting and estimates the condition of the matrix. If RCOND is not needed, SSIFA is slightly faster. To solve A*X = B , follow SSICO by SSISL. To compute INVERSE(A)*C , follow SSICO by SSISL. To compute INVERSE(A) , follow SSICO by SSIDI. To compute DETERMINANT(A) , follow SSICO by SSIDI. To compute INERTIA(A), follow SSICO by SSIDI. On Entry A REAL(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 . Output 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. KPVT 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 REAL(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
SASUM, SAXPY, SDOT, SSCAL, SSIFA

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)