strmm, dtrmm, ctrmm, ztrmm 

Matrix-matrix product for triangular matrix

FORMAT

  {S,D,C,Z}TRMM

  ( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )

Arguments

  side                character*1
                      On entry, specifies whether (op)A multiplies B on the
                      left or right in the operation:

                      If side = 'L' or 'l', the operation is B  =  alpha *
                      (op)A*B.

                      If side = 'R' or 'r', the operation is B  =  alpha * B
                      * (op)A .
                      On exit, side is unchanged.

  uplo                character*1
                      On entry, specifies whether the matrix A is an upper-
                      or lower-triangular matrix:

                      If uplo = 'U' or 'u', the matrix A is an upper-
                      triangular matrix.

                      If uplo = 'L' or 'l', the matrix A is a lower-
                      triangular matrix.
                      On exit, uplo is unchanged.

  transa              character*1
                      On entry, specifies the form of (op)A used in the
                      matrix multiplication:

                      If transa = 'N' or 'n', (op)A = A.

                      If transa = 'T' or 't', (op)A = transp(A).

                      If transa = 'C' or 'c', (op)A = conjug_transp(A).
                      On exit, transa is unchanged.

  diag                character*1
                      On entry, specifies whether the matrix A is unit-
                      triangular:

                      If diag = 'U' or 'u', A is a unit-triangular matrix.

                      If diag = 'N' or 'n', A is not a unit-triangular
                      matrix.
                      On exit, diag is unchanged.

  m                   integer*4
                      On entry, the number of rows of the matrix B; m >= 0
                      On exit, m is unchanged.

  n                   integer*4
                      On entry, the number of columns of the matrix B; n >= 0
                      On exit, n is unchanged.

  alpha               real*4 | real*8 | complex*8 | complex*16
                      On entry, specifies the scalar alpha.
                      On exit, alpha is unchanged.

  a                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array A with dimensions lda
                      by k.
                      If the multiplication is on the left side, k >= m and
                      the leading m by m part of the array contains the
                      matrix A.
                      If the multiplication is on the right side, k >= n and
                      the leading n by n part of the array A must contain the
                      matrix A.
                      In either case, when the leading part of the array is
                      specified as the  upper part, the upper triangular part
                      of array A contains the upper-triangular part of the
                      matrix A, and the lower-triangular part of matrix A is
                      not referenced.  When the lower part is specified, the
                      lower triangular part of the array A contains the lower
                      triangular part of the matrix  A, and the upper-
                      triangular part of A is not  referenced.

                      If matrix A is unit-triangular, its diagonal elements
                      are assumed to be unity and are not referenced.
                      On exit, a is unchanged.

  lda                 integer*4
                      On entry, the first dimension of A.  When
                      multiplication is on the left, lda >= MAX(1,m). When
                      multiplication is on the right, lda >= MAX(1,n).
                      On exit, lda is unchanged.

  b                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array B of dimensions ldb
                      by at least n.  The leading m by n part of the array B
                      must contain the matrix B.
                      On exit, b is overwritten by the m by n updated matrix.

  ldb                 integer*4
                      On entry, the first dimension of B; ldb >= MAX(1,m)
                      On exit, ldb is unchanged.

Description

  STRMM and DTRMM compute a matrix-matrix product for a real triangular
  matrix or its transpose.  CTRMM and ZTRMM compute a matrix-matrix product
  for a complex triangular matrix, its transpose, or its conjugate transpose.
  B  = alpha(op)A*B
    B  = alpha * B((op)A)

  where (op)A = A, transp(A),  or conjug_transp(A)

  alpha is a scalar, B is an m by n matrix, and A is a unit or non-unit,
  upper- or lower-triangular matrix.

Example

  REAL*8 A(25,40), B(30,35), alpha
  M = 15
  N = 18
  LDA = 25
  LDB = 30
  alpha = -1.0D0
  CALL DTRMM ('R','L','T','U',M,N,alpha,A,LDA,B,LDB)

  This FORTRAN code computes the product B  =  alpha * B*transp(A) where A is
  a lower-triangular real matrix with a unit diagonal.  A is an 18 by 18 real
  triangular matrix embedded in array A, and B is a 15 by 18 real rectangular
  matrix embedded in array B.  The leading 18 by 18 lower-triangular part of
  the array A must contain the lower-triangular matrix A.  The upper-
  triangular part of A and the diagonal are not referenced.

  COMPLEX*16 A(25,40), B(30,35), alpha
  M = 15
  N = 18
  LDA = 25
  LDB = 30
  alpha = (-1.0D0, 2.0D0)
  CALL ZTRMM ('R','L','T','U',M,N,alpha,A,LDA,B,LDB)

  This FORTRAN code computes the product B  =  alpha * B*transp(A) where A is
  a lower-triangular complex matrix with a unit diagonal.  A is an 18 by 18
  complex triangular matrix embedded in array A, and B is a 15 by 18 complex
  rectangular matrix embedded in array B.  The leading 18 by 18 lower-
  triangular part of the array A must contain the lower-triangular matrix A.
  The upper-triangular part of A and the diagonal are not referenced.