DGECO(3F)DGECO(3F)NAMEDGECO - 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.
SYNOPSYS
SUBROUTINE DGECO(A,LDA,N,IPVT,RCOND,Z)
DESCRIPTION
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) . LINPACK. This version dated
08/14/78 . Cleve Moler, University of New Mexico, Argonne National Lab.
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DGECO(3F)DGECO(3F)
Subroutines and Functions LINPACK DGEFA BLAS DAXPY,DDOT,DSCAL,DASUM
Fortran DABS,DMAX1,DSIGN
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