double_blas_level3(3)

NAME
double_blas_level3 - double

SYNOPSIS

  Functions
subroutine dgemm (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
subroutine dsymm (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
DSYMM
subroutine dsyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DSYR2K
subroutine dsyrk (uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
DSYRK
subroutine dtrmm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRMM
subroutine dtrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRSM

Detailed Description

This is the group of double LEVEL 3 BLAS routines.

Function Documentation

  subroutine dgemm (character transa, character transb, integer m, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)

DGEMM

Purpose:

     DGEMM  performs one of the matrix-matrix operations
        C := alpha*op( A )*op( B ) + beta*C,
     where  op( X ) is one of
        op( X ) = X   or   op( X ) = X**T,
     alpha and beta are scalars, and A, B and C are matrices, with op( A )
     an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.

Parameters
    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.

    TRANSB

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

    M

              M is INTEGER
               On entry,  M  specifies  the number  of rows  of the  matrix
               op( A )  and of the  matrix  C.  M  must  be at least  zero.

    N

              N is INTEGER
               On entry,  N  specifies the number  of columns of the matrix
               op( B ) and the number of columns of the matrix C. N must be
               at least zero.

    K

              K is INTEGER
               On entry,  K  specifies  the number of columns of the matrix
               op( A ) and the number of rows of the matrix op( B ). K must
               be at least  zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    A

              A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
               k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
               Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by m  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. When  TRANSA = 'N' or 'n' then
               LDA must be at least  max( 1, m ), otherwise  LDA must be at
               least  max( 1, k ).

    B

              B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is
               n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
               Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  n by k  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in the calling (sub) program. When  TRANSB = 'N' or 'n' then
               LDB must be at least  max( 1, k ), otherwise  LDB must be at
               least  max( 1, n ).

    BETA

              BETA is DOUBLE PRECISION.
               On entry,  BETA  specifies the scalar  beta.  When  BETA  is
               supplied as zero then C need not be set on input.

    C

              C is DOUBLE PRECISION array, dimension ( LDC, N )
               Before entry, the leading  m by n  part of the array  C must
               contain the matrix  C,  except when  beta  is zero, in which
               case C need not be set on entry.
               On exit, the array  C  is overwritten by the  m by n  matrix
               ( alpha*op( A )*op( B ) + beta*C ).

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  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 186 of file dgemm.f.

  subroutine dsymm (character side, character uplo, integer m, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)

DSYMM

Purpose:

     DSYMM  performs one of the matrix-matrix operations
        C := alpha*A*B + beta*C,
     or
        C := alpha*B*A + beta*C,
     where alpha and beta are scalars,  A is a symmetric matrix and  B and
     C are  m by n matrices.

Parameters
    SIDE

              SIDE is CHARACTER*1
               On entry,  SIDE  specifies whether  the  symmetric matrix  A
               appears on the  left or right  in the  operation as follows:
                  SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
                  SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of  the  symmetric  matrix   A  is  to  be
               referenced as follows:
                  UPLO = 'U' or 'u'   Only the upper triangular part of the
                                      symmetric matrix is to be referenced.
                  UPLO = 'L' or 'l'   Only the lower triangular part of the
                                      symmetric matrix is to be referenced.

    M

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

    N

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

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    A

              A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
               m  when  SIDE = 'L' or 'l'  and is  n otherwise.
               Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
               the array  A  must contain the  symmetric matrix,  such that
               when  UPLO = 'U' or 'u', the leading m by m upper triangular
               part of the array  A  must contain the upper triangular part
               of the  symmetric matrix and the  strictly  lower triangular
               part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
               the leading  m by m  lower triangular part  of the  array  A
               must  contain  the  lower triangular part  of the  symmetric
               matrix and the  strictly upper triangular part of  A  is not
               referenced.
               Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
               the array  A  must contain the  symmetric matrix,  such that
               when  UPLO = 'U' or 'u', the leading n by n upper triangular
               part of the array  A  must contain the upper triangular part
               of the  symmetric matrix and the  strictly  lower triangular
               part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
               the leading  n by n  lower triangular part  of the  array  A
               must  contain  the  lower triangular part  of the  symmetric
               matrix and the  strictly upper triangular part of  A  is not
               referenced.

    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 ), otherwise  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 matrix B.

    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 ).

    BETA

              BETA is DOUBLE PRECISION.
               On entry,  BETA  specifies the scalar  beta.  When  BETA  is
               supplied as zero then C need not be set on input.

    C

              C is DOUBLE PRECISION array, dimension ( LDC, N )
               Before entry, the leading  m by n  part of the array  C must
               contain the matrix  C,  except when  beta  is zero, in which
               case C need not be set on entry.
               On exit, the array  C  is overwritten by the  m by n updated
               matrix.

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  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 188 of file dsymm.f.

  subroutine dsyr2k (character uplo, character trans, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)

DSYR2K

Purpose:

     DSYR2K  performs one of the symmetric rank 2k operations
        C := alpha*A*B**T + alpha*B*A**T + beta*C,
     or
        C := alpha*A**T*B + alpha*B**T*A + beta*C,
     where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
     and  A and B  are  n by k  matrices  in the  first  case  and  k by n
     matrices in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   C := alpha*A*B**T + alpha*B*A**T +
                                            beta*C.
                  TRANS = 'T' or 't'   C := alpha*A**T*B + alpha*B**T*A +
                                            beta*C.
                  TRANS = 'C' or 'c'   C := alpha*A**T*B + alpha*B**T*A +
                                            beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns  of the  matrices  A and B,  and on  entry  with
               TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
               of rows of the matrices  A and B.  K must be at least  zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    A

              A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    B

              B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  k by n  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDB must be at least  max( 1, n ), otherwise  LDB must
               be at least  max( 1, k ).

    BETA

              BETA is DOUBLE PRECISION.
               On entry, BETA specifies the scalar beta.

    C

              C is DOUBLE PRECISION array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  symmetric matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  symmetric matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.

    LDC

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

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 191 of file dsyr2k.f.

  subroutine dsyrk (character uplo, character trans, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision beta, double precision, dimension(ldc,*) c, integer ldc)

DSYRK

Purpose:

     DSYRK  performs one of the symmetric rank k operations
        C := alpha*A*A**T + beta*C,
     or
        C := alpha*A**T*A + beta*C,
     where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
     and  A  is an  n by k  matrix in the first case and a  k by n  matrix
     in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   C := alpha*A*A**T + beta*C.
                  TRANS = 'T' or 't'   C := alpha*A**T*A + beta*C.
                  TRANS = 'C' or 'c'   C := alpha*A**T*A + beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns   of  the   matrix   A,   and  on   entry   with
               TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
               of rows of the matrix  A.  K must be at least zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    A

              A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    BETA

              BETA is DOUBLE PRECISION.
               On entry, BETA specifies the scalar beta.

    C

              C is DOUBLE PRECISION array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  symmetric matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  symmetric matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.

    LDC

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

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 168 of file dsyrk.f.

  subroutine dtrmm (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)

DTRMM

Purpose:

     DTRMM  performs one of the matrix-matrix operations
        B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
     where  alpha  is a scalar,  B  is an m by n matrix,  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.

Parameters
    SIDE

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

    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 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 matrix  B,  and  on exit  is overwritten  by the
               transformed matrix.

    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 176 of file dtrmm.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.

Author

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