CGECO(3)

SYNOPSIS
SUBROUTINE CGECO (A, LDA, N, IPVT, RCOND, Z)

NAME
cgeco - Factor a matrix using Gaussian elimination and estimate the condition number of the matrix.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2C1

TYPE
COMPLEX (SGECO-S, DGECO-D, CGECO-C)

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

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

DESCRIPTION
CGECO factors a complex matrix by Gaussian elimination and estimates the condition of the matrix. If RCOND is not needed, CGEFA is slightly faster. To solve A*X = B , follow CGECO By CGESL. To Compute INVERSE(A)*C , follow CGECO by CGESL. To compute DETERMINANT(A) , follow CGECO by CGEDI. To compute INVERSE(A) , follow CGECO by CGEDI. On Entry A COMPLEX(LDA, N) the matrix to be factored. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . On Return A an upper triangular matrix and the multipliers which were used to obtain it. The factorization can be written A = L*U where L is a product of permutation and unit lower triangular matrices and U is upper triangular. IPVT 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, CDOTC, CGEFA, 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)