trsm(3)

NAME
trsm - trsm: triangular matrix-matrix solve

SYNOPSIS

  Functions
subroutine ctrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRSM
subroutine dtrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRSM
subroutine strsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
STRSM
subroutine ztrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRSM

Detailed Description

Function Documentation

  subroutine ctrsm (character side, character uplo, character transa, character diag, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb)

CTRSM

Purpose:

     CTRSM  solves one of the matrix equations
        op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
     where alpha is a scalar, X and B are m by n matrices, A is a unit, or
     non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
        op( A ) = A   or   op( A ) = A**T   or   op( A ) = A**H.
     The matrix X is overwritten on B.

Parameters
    SIDE

              SIDE is CHARACTER*1
               On entry, SIDE specifies whether op( A ) appears on the left
               or right of X as follows:
                  SIDE = 'L' or 'l'   op( A )*X = alpha*B.
                  SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix A is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANSA

              TRANSA is CHARACTER*1
               On entry, TRANSA specifies the form of op( A ) to be used in
               the matrix multiplication as follows:
                  TRANSA = 'N' or 'n'   op( A ) = A.
                  TRANSA = 'T' or 't'   op( A ) = A**T.
                  TRANSA = 'C' or 'c'   op( A ) = A**H.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit triangular
               as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    M

              M is INTEGER
               On entry, M specifies the number of rows of B. M must be at
               least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of B.  N must be
               at least zero.

    ALPHA

              ALPHA is COMPLEX
               On entry,  ALPHA specifies the scalar  alpha. When  alpha is
               zero then  A is not referenced and  B need not be set before
               entry.

    A

              A is COMPLEX array, dimension ( LDA, k ),
               where k is m when SIDE = 'L' or 'l'
                 and k is n when SIDE = 'R' or 'r'.
               Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
               upper triangular part of the array  A must contain the upper
               triangular matrix  and the strictly lower triangular part of
               A is not referenced.
               Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
               lower triangular part of the array  A must contain the lower
               triangular matrix  and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u',  the diagonal elements of
               A  are not referenced either,  but are assumed to be  unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
               LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
               then LDA must be at least max( 1, n ).

    B

              B is COMPLEX array, dimension ( LDB, N )
               Before entry,  the leading  m by n part of the array  B must
               contain  the  right-hand  side  matrix  B,  and  on exit  is
               overwritten by the solution matrix  X.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   LDB  must  be  at  least
               max( 1, m ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 179 of file ctrsm.f.

  subroutine dtrsm (character side, character uplo, character transa, character diag, integer m, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb)

DTRSM

Purpose:

     DTRSM  solves one of the matrix equations
        op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
     where alpha is a scalar, X and B are m by n matrices, A is a unit, or
     non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
        op( A ) = A   or   op( A ) = A**T.
     The matrix X is overwritten on B.

Parameters
    SIDE

              SIDE is CHARACTER*1
               On entry, SIDE specifies whether op( A ) appears on the left
               or right of X as follows:
                  SIDE = 'L' or 'l'   op( A )*X = alpha*B.
                  SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix A is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANSA

              TRANSA is CHARACTER*1
               On entry, TRANSA specifies the form of op( A ) to be used in
               the matrix multiplication as follows:
                  TRANSA = 'N' or 'n'   op( A ) = A.
                  TRANSA = 'T' or 't'   op( A ) = A**T.
                  TRANSA = 'C' or 'c'   op( A ) = A**T.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit triangular
               as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    M

              M is INTEGER
               On entry, M specifies the number of rows of B. M must be at
               least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of B.  N must be
               at least zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry,  ALPHA specifies the scalar  alpha. When  alpha is
               zero then  A is not referenced and  B need not be set before
               entry.

    A

              A is DOUBLE PRECISION array, dimension ( LDA, k ),
               where k is m when SIDE = 'L' or 'l'
                 and k is n when SIDE = 'R' or 'r'.
               Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
               upper triangular part of the array  A must contain the upper
               triangular matrix  and the strictly lower triangular part of
               A is not referenced.
               Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
               lower triangular part of the array  A must contain the lower
               triangular matrix  and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u',  the diagonal elements of
               A  are not referenced either,  but are assumed to be  unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
               LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
               then LDA must be at least max( 1, n ).

    B

              B is DOUBLE PRECISION array, dimension ( LDB, N )
               Before entry,  the leading  m by n part of the array  B must
               contain  the  right-hand  side  matrix  B,  and  on exit  is
               overwritten by the solution matrix  X.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   LDB  must  be  at  least
               max( 1, m ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 180 of file dtrsm.f.

  subroutine strsm (character side, character uplo, character transa, character diag, integer m, integer n, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb)

STRSM

Purpose:

     STRSM  solves one of the matrix equations
        op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
     where alpha is a scalar, X and B are m by n matrices, A is a unit, or
     non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
        op( A ) = A   or   op( A ) = A**T.
     The matrix X is overwritten on B.

Parameters
    SIDE

              SIDE is CHARACTER*1
               On entry, SIDE specifies whether op( A ) appears on the left
               or right of X as follows:
                  SIDE = 'L' or 'l'   op( A )*X = alpha*B.
                  SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix A is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANSA

              TRANSA is CHARACTER*1
               On entry, TRANSA specifies the form of op( A ) to be used in
               the matrix multiplication as follows:
                  TRANSA = 'N' or 'n'   op( A ) = A.
                  TRANSA = 'T' or 't'   op( A ) = A**T.
                  TRANSA = 'C' or 'c'   op( A ) = A**T.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit triangular
               as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    M

              M is INTEGER
               On entry, M specifies the number of rows of B. M must be at
               least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of B.  N must be
               at least zero.

    ALPHA

              ALPHA is REAL
               On entry,  ALPHA specifies the scalar  alpha. When  alpha is
               zero then  A is not referenced and  B need not be set before
               entry.

    A

              A is REAL array, dimension ( LDA, k ),
               where k is m when SIDE = 'L' or 'l'
                 and k is n when SIDE = 'R' or 'r'.
               Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
               upper triangular part of the array  A must contain the upper
               triangular matrix  and the strictly lower triangular part of
               A is not referenced.
               Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
               lower triangular part of the array  A must contain the lower
               triangular matrix  and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u',  the diagonal elements of
               A  are not referenced either,  but are assumed to be  unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
               LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
               then LDA must be at least max( 1, n ).

    B

              B is REAL array, dimension ( LDB, N )
               Before entry,  the leading  m by n part of the array  B must
               contain  the  right-hand  side  matrix  B,  and  on exit  is
               overwritten by the solution matrix  X.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   LDB  must  be  at  least
               max( 1, m ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 180 of file strsm.f.

  subroutine ztrsm (character side, character uplo, character transa, character diag, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb)

ZTRSM

Purpose:

     ZTRSM  solves one of the matrix equations
        op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
     where alpha is a scalar, X and B are m by n matrices, A is a unit, or
     non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
        op( A ) = A   or   op( A ) = A**T   or   op( A ) = A**H.
     The matrix X is overwritten on B.

Parameters
    SIDE

              SIDE is CHARACTER*1
               On entry, SIDE specifies whether op( A ) appears on the left
               or right of X as follows:
                  SIDE = 'L' or 'l'   op( A )*X = alpha*B.
                  SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix A is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANSA

              TRANSA is CHARACTER*1
               On entry, TRANSA specifies the form of op( A ) to be used in
               the matrix multiplication as follows:
                  TRANSA = 'N' or 'n'   op( A ) = A.
                  TRANSA = 'T' or 't'   op( A ) = A**T.
                  TRANSA = 'C' or 'c'   op( A ) = A**H.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit triangular
               as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    M

              M is INTEGER
               On entry, M specifies the number of rows of B. M must be at
               least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of B.  N must be
               at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry,  ALPHA specifies the scalar  alpha. When  alpha is
               zero then  A is not referenced and  B need not be set before
               entry.

    A

              A is COMPLEX*16 array, dimension ( LDA, k ),
               where k is m when SIDE = 'L' or 'l'
                 and k is n when SIDE = 'R' or 'r'.
               Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
               upper triangular part of the array  A must contain the upper
               triangular matrix  and the strictly lower triangular part of
               A is not referenced.
               Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
               lower triangular part of the array  A must contain the lower
               triangular matrix  and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u',  the diagonal elements of
               A  are not referenced either,  but are assumed to be  unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
               LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
               then LDA must be at least max( 1, n ).

    B

              B is COMPLEX*16 array, dimension ( LDB, N )
               Before entry,  the leading  m by n part of the array  B must
               contain  the  right-hand  side  matrix  B,  and  on exit  is
               overwritten by the solution matrix  X.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   LDB  must  be  at  least
               max( 1, m ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 179 of file ztrsm.f.

Author

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