dsyrfs.f (3) Linux Manual Page

dsyrfs.f –

Synopsis

Functions/Subroutines

subroutine dsyrfs (UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DSYRFS

Function/Subroutine Documentation

subroutine dsyrfs (characterUPLO, integerN, integerNRHS, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldaf, * )AF, integerLDAF, integer, dimension( * )IPIV, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

DSYRFS

Purpose:

 DSYRFS improves the computed solution to a system of linear

 equations when the coefficient matrix is symmetric indefinite, and

 provides error bounds and backward error estimates for the solution.

 

Parameters:

UPLO

 UPLO is CHARACTER*1

 = ‘U’: Upper triangle of A is stored;

 = ‘L’: Lower triangle of A is stored.

N

 N is INTEGER

 The order of the matrix A. N >= 0.

NRHS

 NRHS is INTEGER

 The number of right hand sides, i.e., the number of columns

 of the matrices B and X. NRHS >= 0.

A

 A is 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

 LDA is INTEGER

 The leading dimension of the array A. LDA >= max(1,N).

AF

 AF is DOUBLE PRECISION array, dimension (LDAF,N)

 The factored form of the matrix A. AF contains the block

 diagonal matrix D and the multipliers used to obtain the

 factor U or L from the factorization A = U*D*U**T or

 A = L*D*L**T as computed by DSYTRF.

LDAF

 LDAF is INTEGER

 The leading dimension of the array AF. LDAF >= max(1,N).

IPIV

 IPIV is INTEGER array, dimension (N)

 Details of the interchanges and the block structure of D

 as determined by DSYTRF.

B

 B is DOUBLE PRECISION array, dimension (LDB,NRHS)

 The right hand side matrix B.

LDB

 LDB is INTEGER

 The leading dimension of the array B. LDB >= max(1,N).

X

 X is DOUBLE PRECISION array, dimension (LDX,NRHS)

 On entry, the solution matrix X, as computed by DSYTRS.

 On exit, the improved solution matrix X.

LDX

 LDX is INTEGER

 The leading dimension of the array X. LDX >= max(1,N).

FERR

 FERR is 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

 BERR is 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

 WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK

 IWORK is INTEGER array, dimension (N)

INFO

 INFO is INTEGER

 = 0: successful exit

 < 0: if INFO = -i, the i-th argument had an illegal value

 

Internal Parameters:

 ITMAX is the maximum number of steps of iterative refinement.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 191 of file dsyrfs.f.

Author

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