.TH ZTRRFS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZTRRFS - error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix .SH SYNOPSIS .TP 19 SUBROUTINE ZTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) .TP 19 .ti +4 CHARACTER DIAG, TRANS, UPLO .TP 19 .ti +4 INTEGER INFO, LDA, LDB, LDX, N, NRHS .TP 19 .ti +4 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) .TP 19 .ti +4 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * ) .SH PURPOSE ZTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by ZTRTRS or some other means before entering this routine. ZTRRFS does not do iterative refinement because doing so cannot improve the backward error. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: A is upper triangular; .br = \(aqL\(aq: A is lower triangular. .TP 8 TRANS (input) CHARACTER*1 .br Specifies the form of the system of equations: .br = \(aqN\(aq: A * X = B (No transpose) .br = \(aqT\(aq: A**T * X = B (Transpose) .br = \(aqC\(aq: A**H * X = B (Conjugate transpose) .TP 8 DIAG (input) CHARACTER*1 .br = \(aqN\(aq: A is non-unit triangular; .br = \(aqU\(aq: A is unit triangular. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. .TP 8 A (input) COMPLEX*16 array, dimension (LDA,N) The triangular matrix A. If UPLO = \(aqU\(aq, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = \(aqL\(aq, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = \(aqU\(aq, the diagonal elements of A are also not referenced and are assumed to be 1. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 B (input) COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B. .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 X (input) COMPLEX*16 array, dimension (LDX,NRHS) The solution matrix X. .TP 8 LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). .TP 8 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. .TP 8 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). .TP 8 WORK (workspace) COMPLEX*16 array, dimension (2*N) .TP 8 RWORK (workspace) DOUBLE PRECISION array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value