cgeco.f
SUBROUTINE CGECO (A, LDA, N, IPVT, RCOND, Z)
C***BEGIN PROLOGUE CGECO
C***PURPOSE Factor a matrix using Gaussian elimination and estimate
C the condition number of the matrix.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2C1
C***TYPE COMPLEX (SGECO-S, DGECO-D, CGECO-C)
C***KEYWORDS CONDITION NUMBER, GENERAL MATRIX, LINEAR ALGEBRA, LINPACK,
C MATRIX FACTORIZATION
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C CGECO factors a complex matrix by Gaussian elimination
C and estimates the condition of the matrix.
C
C If RCOND is not needed, CGEFA is slightly faster.
C To solve A*X = B , follow CGECO By CGESL.
C To Compute INVERSE(A)*C , follow CGECO by CGESL.
C To compute DETERMINANT(A) , follow CGECO by CGEDI.
C To compute INVERSE(A) , follow CGECO by CGEDI.
C
C On Entry
C
C A COMPLEX(LDA, N)
C the matrix to be factored.
C
C LDA INTEGER
C the leading dimension of the array A .
C
C N INTEGER
C the order of the matrix A .
C
C On Return
C
C A an upper triangular matrix and the multipliers
C which were used to obtain it.
C The factorization can be written A = L*U where
C L is a product of permutation and unit lower
C triangular matrices and U is upper triangular.
C
C IPVT INTEGER(N)
C an integer vector of pivot indices.
C
C RCOND REAL
C an estimate of the reciprocal condition of A .
C For the system A*X = B , relative perturbations
C in A and B of size EPSILON may cause
C relative perturbations in X of size EPSILON/RCOND .
C If RCOND is so small that the logical expression
C 1.0 + RCOND .EQ. 1.0
C is true, then A may be singular to working
C precision. In particular, RCOND is zero if
C exact singularity is detected or the estimate
C underflows.
C
C Z COMPLEX(N)
C a work vector whose contents are usually unimportant.
C If A is close to a singular matrix, then Z is
C an approximate null vector in the sense that
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED CAXPY, CDOTC, CGEFA, CSSCAL, SCASUM
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE CGECO