cgerfs(l) [redhat man page]
CGERFS(l) ) CGERFS(l) NAME
CGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solu- tion SYNOPSIS
SUBROUTINE CGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) CHARACTER TRANS INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS INTEGER IPIV( * ) REAL BERR( * ), FERR( * ), RWORK( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * ) PURPOSE
CGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solu- tion. ARGUMENTS
TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate 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) COMPLEX 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) COMPLEX array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF. LDAF (input) INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indices from CGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CGETRS. On exit, the improved solution matrix X. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). FERR (output) REAL 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) REAL 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) COMPLEX array, dimension (2*N) RWORK (workspace) REAL 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. LAPACK version 3.0 15 June 2000 CGERFS(l)
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ZGERFS(l) ) ZGERFS(l) NAME
ZGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solu- tion SYNOPSIS
SUBROUTINE ZGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) CHARACTER TRANS INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS INTEGER IPIV( * ) DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * ) PURPOSE
ZGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solu- tion. ARGUMENTS
TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate 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) COMPLEX*16 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) COMPLEX*16 array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF. LDAF (input) INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indices from ZGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). B (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZGETRS. 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) COMPLEX*16 array, dimension (2*N) RWORK (workspace) DOUBLE PRECISION 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. LAPACK version 3.0 15 June 2000 ZGERFS(l)