CPOCO(3)

SYNOPSIS
SUBROUTINE CPOCO (A, LDA, N, RCOND, Z, INFO)

NAME
cpoco - Factor a complex Hermitian positive definite matrix and estimate the condition number of the matrix.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2D1B

TYPE
COMPLEX (SPOCO-S, DPOCO-D, CPOCO-C)

KEYWORDS
CONDITION NUMBER, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, POSITIVE DEFINITE

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

DESCRIPTION
CPOCO factors a complex Hermitian positive definite matrix and estimates the condition of the matrix. If RCOND is not needed, CPOFA is slightly faster. To solve A*X = B , follow CPOCO by CPOSL. To compute INVERSE(A)*C , follow CPOCO by CPOSL. To compute DETERMINANT(A) , follow CPOCO by CPODI. To compute INVERSE(A) , follow CPOCO by CPODI. On Entry A COMPLEX(LDA, N) the Hermitian 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 an upper triangular matrix R so that A = CTRANS(R)*R where CTRANS(R) is the conjugate transpose. The strict lower triangle is unaltered. If INFO .NE. 0 , the factorization is not complete. 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. If INFO .NE. 0 , RCOND is unchanged. 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) . If INFO .NE. 0 , Z is unchanged. INFO INTEGER = 0 for normal return. = K signals an error condition. The leading minor of order K is not positive definite.

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

ROUTINES CALLED
CAXPY, CDOTC, CPOFA, CSSCAL, SCASUM

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
890831 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)