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NAME DPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, SYNOPSIS SUBROUTINE DPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS INTEGER IWORK( * ) DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * ) PURPOSE DPORFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error esti- mates for the solution. ARGUMENTS UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 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 symmetric matrix A. If UPLO = 'U', 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 = 'L', 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. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). AF (input) DOUBLE PRECISION array, dimension (LDAF,N) The triangular factor U or L from the Cholesky fac- torization A = U**T*U or A = L*L**T, as computed by DPOTRF. LDAF (input) INTEGER The leading dimension of the array AF. LDAF >= max(1,N). 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). (LDX,NRHS) X (input/output) DOUBLE PRECISION array, dimension On entry, the solution matrix X, as computed by DPOTRS. 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 bounds for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution, FERR(j) bounds the magnitude of the largest entry in (X(j) - XTRUE) divided by the magnitude of the largest entry in X(j). The quality of the error bound depends on the quality of the estimate of norm(inv(A)) computed in the code; if the estimate of norm(inv(A)) is accu- rate, the error bound is guaranteed. 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 entry 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 refine- ment.