dgerfs (l) - Linux Manuals

dgerfs: improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution

NAME

DGERFS - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution

SYNOPSIS

SUBROUTINE DGERFS(
TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

    
CHARACTER TRANS

    
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS

    
INTEGER IPIV( * ), IWORK( * )

    
DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

DGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution.

ARGUMENTS

TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= aqNaq: A * X = B (No transpose)
= aqTaq: A**T * X = B (Transpose)
= aqCaq: A**H * X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The original N-by-N matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
The factors L and U from the factorization A = P*L*U as computed by DGETRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DGETRS. On exit, the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refinement.

Pages related to dgerfs

  • dgerfs (3)
  • dgerfsx (l) - DGERFSX improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
  • dger (l) - performs the rank 1 operation A := alpha*x*yaq + A,
  • dgerq2 (l) - computes an RQ factorization of a real m by n matrix A
  • dgerqf (l) - computes an RQ factorization of a real M-by-N matrix A
  • dgebak (l) - forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL
  • dgebal (l) - balances a general real matrix A
  • dgebd2 (l) - reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation