Man page - trrfs(3)

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Manual

trrfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctrrfs (character uplo, character trans, character diag, integern, integer nrhs, complex, dimension( lda, * ) a, integer lda, 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 dtrrfs (character uplo, character trans, character diag, integern, integer nrhs, double precision, dimension( lda, * ) a, integer lda,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 strrfs (character uplo, character trans, character diag, integern, integer nrhs, real, dimension( lda, * ) a, integer lda, 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 ztrrfs (character uplo, character trans, character diag, integern, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, complex*16, dimension( * ) work, doubleprecision, dimension( * ) rwork, integer info)
Author

NAME

trrfs - trrfs: triangular iterative refinement

SYNOPSIS

Functions

subroutine ctrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CTRRFS
subroutine dtrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DTRRFS
subroutine strrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
STRRFS
subroutine ztrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZTRRFS

Detailed Description

Function Documentation

subroutine ctrrfs (character uplo, character trans, character diag, integern, integer nrhs, complex, dimension( lda, * ) a, integer lda, 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)

CTRRFS

Purpose:

CTRRFS 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 CTRTRS or some other
means before entering this routine. CTRRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular matrix A. If UPLO = ’U’, 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 = ’L’, 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 = ’U’, the diagonal elements of A are
also not referenced and are assumed to be 1.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dtrrfs (character uplo, character trans, character diag, integern, integer nrhs, double precision, dimension( lda, * ) a, integer lda,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)

DTRRFS

Purpose:

DTRRFS 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 DTRTRS or some other
means before entering this routine. DTRRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular matrix A. If UPLO = ’U’, 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 = ’L’, 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 = ’U’, the diagonal elements of A are
also not referenced and are assumed to be 1.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine strrfs (character uplo, character trans, character diag, integern, integer nrhs, real, dimension( lda, * ) a, integer lda, 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)

STRRFS

Purpose:

STRRFS 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 STRTRS or some other
means before entering this routine. STRRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular matrix A. If UPLO = ’U’, 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 = ’L’, 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 = ’U’, the diagonal elements of A are
also not referenced and are assumed to be 1.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ztrrfs (character uplo, character trans, character diag, integern, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, complex*16, dimension( * ) work, doubleprecision, dimension( * ) rwork, integer info)

ZTRRFS

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.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular matrix A. If UPLO = ’U’, 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 = ’L’, 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 = ’U’, the diagonal elements of A are
also not referenced and are assumed to be 1.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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