DGECO(3)

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

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

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2A1

TYPE
DOUBLE PRECISION (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
DGECO factors a double precision matrix by Gaussian elimination and estimates the condition of the matrix. If RCOND is not needed, DGEFA is slightly faster. To solve A*X = B , follow DGECO by DGESL. To compute INVERSE(A)*C , follow DGECO by DGESL. To compute DETERMINANT(A) , follow DGECO by DGEDI. To compute INVERSE(A) , follow DGECO by DGEDI. On Entry A DOUBLE PRECISION(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 DOUBLE PRECISION 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 DOUBLE PRECISION(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
DASUM, DAXPY, DDOT, DGEFA, DSCAL

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)