Man page - tbrfs(3)

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Manual

tbrfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integerldab, 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 dtbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab,integer ldab, double precision, dimension( ldb, * ) b, integer ldb,double precision, dimension( ldx, * ) x, integer ldx, double precision,dimension( * ) ferr, double precision, dimension( * ) berr, doubleprecision, dimension( * ) work, integer, dimension( * ) iwork, integerinfo)
subroutine stbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integerldab, 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 ztbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab,integer ldab, 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

tbrfs - tbrfs: triangular iterative refinement

SYNOPSIS

Functions

subroutine ctbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CTBRFS
subroutine dtbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DTBRFS
subroutine stbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)
STBRFS
subroutine ztbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZTBRFS

Detailed Description

Function Documentation

subroutine ctbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integerldab, 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)

CTBRFS

Purpose:

CTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.

The solution matrix X must be computed by CTBTRS or some other
means before entering this routine. CTBRFS 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.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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.

AB

AB is COMPLEX array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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 dtbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab,integer ldab, double precision, dimension( ldb, * ) b, integer ldb,double precision, dimension( ldx, * ) x, integer ldx, double precision,dimension( * ) ferr, double precision, dimension( * ) berr, doubleprecision, dimension( * ) work, integer, dimension( * ) iwork, integerinfo)

DTBRFS

Purpose:

DTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.

The solution matrix X must be computed by DTBTRS or some other
means before entering this routine. DTBRFS 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.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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 stbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integerldab, 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)

STBRFS

Purpose:

STBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.

The solution matrix X must be computed by STBTRS or some other
means before entering this routine. STBRFS 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.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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.

AB

AB is REAL array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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 ztbrfs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab,integer ldab, 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)

ZTBRFS

Purpose:

ZTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.

The solution matrix X must be computed by ZTBTRS or some other
means before entering this routine. ZTBRFS 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.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 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.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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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