Provided by: liblapack-doc_3.12.1-2_all 
NAME
trtrs - trtrs: triangular solve
SYNOPSIS
Functions
subroutine ctrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
CTRTRS
subroutine dtrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
DTRTRS
subroutine strtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
STRTRS
subroutine ztrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
ZTRTRS
Detailed Description
Function Documentation
subroutine ctrtrs (character uplo, character trans, character diag, integer n, integer nrhs, complex,
dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)
CTRTRS
Purpose:
CTRTRS solves a triangular system of the form
A * X = B, A**T * X = B, or A**H * X = B,
where A is a triangular 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.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. 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)
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 dtrtrs (character uplo, character trans, character diag, integer n, integer nrhs, double
precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb,
integer info)
DTRTRS
Purpose:
DTRTRS solves a triangular system of the form
A * X = B or A**T * X = B,
where A is a triangular 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 = 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 matrix B. 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)
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 strtrs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension(
lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)
STRTRS
Purpose:
STRTRS solves a triangular system of the form
A * X = B or A**T * X = B,
where A is a triangular 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 = 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 matrix B. 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)
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 ztrtrs (character uplo, character trans, character diag, integer n, integer nrhs, complex*16,
dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)
ZTRTRS
Purpose:
ZTRTRS solves a triangular system of the form
A * X = B, A**T * X = B, or A**H * X = B,
where A is a triangular 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.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. 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)
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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