Man page - porfs(3)

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Manual

porfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cporfs (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,integer ldaf, complex, dimension( ldb, * ) b, integer ldb, complex,dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,dimension( * ) berr, complex, dimension( * ) work, real, dimension( * )rwork, integer info)
subroutine dporfs (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldaf, * ) af, integer ldaf, double precision, dimension(ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x,integer ldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, double precision, dimension( * ) work, integer,dimension( * ) iwork, integer info)
subroutine sporfs (character uplo, integer n, integer nrhs, real,dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af,integer ldaf, real, dimension( ldb, * ) b, integer ldb, real,dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,dimension( * ) berr, real, dimension( * ) work, integer, dimension( * )iwork, integer info)
subroutine zporfs (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * )af, integer ldaf, complex*16, dimension( ldb, * ) b, integer ldb,complex*16, dimension( ldx, * ) x, integer ldx, double precision,dimension( * ) ferr, double precision, dimension( * ) berr, complex*16,dimension( * ) work, double precision, dimension( * ) rwork, integerinfo)
Author

NAME

porfs - porfs: iterative refinement

SYNOPSIS

Functions

subroutine cporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CPORFS
subroutine dporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DPORFS
subroutine sporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SPORFS
subroutine zporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZPORFS

Detailed Description

Function Documentation

subroutine cporfs (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,integer ldaf, complex, dimension( ldb, * ) b, integer ldb, complex,dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,dimension( * ) berr, complex, dimension( * ) work, real, dimension( * )rwork, integer info)

CPORFS

Purpose:

CPORFS 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.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 COMPLEX array, dimension (LDA,N)
The Hermitian matrix A. If UPLO = ā€™Uā€™, 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 = ā€™Lā€™, 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 COMPLEX 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 CPOTRF.

LDAF

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

B

B is COMPLEX 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 COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CPOTRS.
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 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

BERR is 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

WORK is COMPLEX array, dimension (2*N)

RWORK

RWORK is REAL 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.

subroutine dporfs (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldaf, * ) af, integer ldaf, double precision, dimension(ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x,integer ldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, double precision, dimension( * ) work, integer,dimension( * ) iwork, integer info)

DPORFS

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 estimates for the
solution.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, as computed by DPOTRF.

LDAF

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

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 DPOTRS.
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.

subroutine sporfs (character uplo, integer n, integer nrhs, real,dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af,integer ldaf, real, dimension( ldb, * ) b, integer ldb, real,dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,dimension( * ) berr, real, dimension( * ) work, integer, dimension( * )iwork, integer info)

SPORFS

Purpose:

SPORFS 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 estimates for the
solution.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 REAL array, dimension (LDA,N)
The symmetric matrix A. If UPLO = ā€™Uā€™, 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 = ā€™Lā€™, 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 REAL array, dimension (LDAF,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, as computed by SPOTRF.

LDAF

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

B

B is REAL 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 REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPOTRS.
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 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

BERR is 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

WORK is REAL 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.

subroutine zporfs (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * )af, integer ldaf, complex*16, dimension( ldb, * ) b, integer ldb,complex*16, dimension( ldx, * ) x, integer ldx, double precision,dimension( * ) ferr, double precision, dimension( * ) berr, complex*16,dimension( * ) work, double precision, dimension( * ) rwork, integerinfo)

ZPORFS

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.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 COMPLEX*16 array, dimension (LDA,N)
The Hermitian matrix A. If UPLO = ā€™Uā€™, 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 = ā€™Lā€™, 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 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.

LDAF

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

B

B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPOTRS.
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 COMPLEX*16 array, dimension (2*N)

RWORK

RWORK is DOUBLE PRECISION 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.

Author

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