sgemm

single_blas_level3(3)               LAPACK               single_blas_level3(3)



NAME
       single_blas_level3

SYNOPSIS
   Functions
       subroutine sgemm (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA,
           C, LDC)
           SGEMM
       subroutine ssymm (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C,
           LDC)
           SSYMM
       subroutine ssyr2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C,
           LDC)
           SSYR2K
       subroutine ssyrk (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
           SSYRK
       subroutine strmm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B,
           LDB)
           STRMM
       subroutine strsm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B,
           LDB)
           STRSM

Detailed Description
       This is the group of real LEVEL 3 BLAS routines.

Function Documentation
   subroutine sgemm (character TRANSA, character TRANSB, integer M, integer N,
       integer K, real ALPHA, real, dimension(lda,*) A, integer LDA, real,
       dimension(ldb,*) B, integer LDB, real BETA, real, dimension(ldc,*) C,
       integer LDC)
       SGEMM

       Purpose:


            SGEMM  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 REAL
                      On entry, ALPHA specifies the scalar alpha.

           A

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

           C

                     C is REAL 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.

       Date
           December 2016

       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 sgemm.f.

   subroutine ssymm (character SIDE, character UPLO, integer M, integer N,
       real ALPHA, real, dimension(lda,*) A, integer LDA, real,
       dimension(ldb,*) B, integer LDB, real BETA, real, dimension(ldc,*) C,
       integer LDC)
       SSYMM

       Purpose:


            SSYMM  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 REAL
                      On entry, ALPHA specifies the scalar alpha.

           A

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

           C

                     C is REAL 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.

       Date
           December 2016

       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 190 of file ssymm.f.

   subroutine ssyr2k (character UPLO, character TRANS, integer N, integer K,
       real ALPHA, real, dimension(lda,*) A, integer LDA, real,
       dimension(ldb,*) B, integer LDB, real BETA, real, dimension(ldc,*) C,
       integer LDC)
       SSYR2K

       Purpose:


            SSYR2K  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 REAL
                      On entry, ALPHA specifies the scalar alpha.

           A

                     A is REAL 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 REAL 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 REAL
                      On entry, BETA specifies the scalar beta.

           C

                     C is REAL 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.

       Date
           December 2016

       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 193 of file ssyr2k.f.

   subroutine ssyrk (character UPLO, character TRANS, integer N, integer K,
       real ALPHA, real, dimension(lda,*) A, integer LDA, real BETA, real,
       dimension(ldc,*) C, integer LDC)
       SSYRK

       Purpose:


            SSYRK  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 REAL
                      On entry, ALPHA specifies the scalar alpha.

           A

                     A is REAL 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 REAL
                      On entry, BETA specifies the scalar beta.

           C

                     C is REAL 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.

       Date
           December 2016

       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 170 of file ssyrk.f.

   subroutine strmm (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)
       STRMM

       Purpose:


            STRMM  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 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 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 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.

       Date
           December 2016

       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 178 of file strmm.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.

       Date
           December 2016

       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 182 of file strsm.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.




Version 3.9.0                   Sat May 16 2020          single_blas_level3(3)