Man page - tbtrs(3)

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Manual

tbtrs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctbtrs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integerldab, complex, dimension( ldb, * ) b, integer ldb, integer info)
subroutine dtbtrs (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,integer info)
subroutine stbtrs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integerldab, real, dimension( ldb, * ) b, integer ldb, integer info)
subroutine ztbtrs (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, integerinfo)
Author

NAME

tbtrs - tbtrs: triangular solve

SYNOPSIS

Functions

subroutine ctbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
CTBTRS
subroutine dtbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
DTBTRS
subroutine stbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
STBTRS
subroutine ztbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
ZTBTRS

Detailed Description

Function Documentation

subroutine ctbtrs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integerldab, complex, dimension( ldb, * ) b, integer ldb, integer info)

CTBTRS

Purpose:

CTBTRS solves a triangular system of the form

A * X = B, A**T * X = B, or A**H * X = B,

where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

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 matrix B. 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 AB. 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)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

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

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dtbtrs (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,integer info)

DTBTRS

Purpose:

DTBTRS solves a triangular system of the form

A * X = B or A**T * X = B,

where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

Parameters

UPLO

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

TRANS

TRANS is CHARACTER*1
Specifies the form 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 matrix B. 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 AB. 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)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

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

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine stbtrs (character uplo, character trans, character diag, integern, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integerldab, real, dimension( ldb, * ) b, integer ldb, integer info)

STBTRS

Purpose:

STBTRS solves a triangular system of the form

A * X = B or A**T * X = B,

where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

Parameters

UPLO

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

TRANS

TRANS is CHARACTER*1
Specifies the form 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 matrix B. 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 AB. 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)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

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

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ztbtrs (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, integerinfo)

ZTBTRS

Purpose:

ZTBTRS solves a triangular system of the form

A * X = B, A**T * X = B, or A**H * X = B,

where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

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 matrix B. 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 AB. 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)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

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

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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