.TH ZPORFS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZPORFS - the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, .SH SYNOPSIS .TP 19 SUBROUTINE ZPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS .TP 19 .ti +4 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) .TP 19 .ti +4 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * ) .SH PURPOSE ZPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and provides error bounds and backward error estimates for the solution. .br .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .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 Hermitian matrix A. If UPLO = \(aqU\(aq, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = \(aqL\(aq, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 AF (input) COMPLEX*16 array, dimension (LDAF,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF. .TP 8 LDAF (input) INTEGER The leading dimension of the array AF. LDAF >= 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/output) COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZPOTRS. On exit, the improved 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 .SH PARAMETERS ITMAX is the maximum number of steps of iterative refinement.