trtrs(3)

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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