.Modelica.Math.Matrices.LAPACK.dtrsm

Information

Lapack documentation
    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'.

    The matrix X is overwritten on B.

    Arguments
    ==========

    SIDE   - 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.

             Unchanged on exit.

    UPLO   - 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.

             Unchanged on exit.

    TRANSA - 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'.

                TRANSA = 'C' or 'c'   op( A ) = A'.

             Unchanged on exit.

    DIAG   - 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.

             Unchanged on exit.

    M      - INTEGER.
             On entry, M specifies the number of rows of B. M must be at
             least zero.
             Unchanged on exit.

    N      - INTEGER.
             On entry, N specifies the number of columns of B.  N must be
             at least zero.
             Unchanged on exit.

    ALPHA  - 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.
             Unchanged on exit.

    A      - DOUBLE PRECISION array of 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.
             Unchanged on exit.

    LDA    - 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 ).
             Unchanged on exit.

    B      - DOUBLE PRECISION array of 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    - 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 ).
             Unchanged on exit.

    Level 3 Blas routine.

Interface

pure function dtrsm
  extends Modelica.Icons.Function;
  input Real A[:, :] "Input matrix A";
  input Real B[:, :] "Input matrix B";
  input Real alpha = 1 "Factor alpha";
  input Boolean right = true "= true, if A is right multiplication";
  input Boolean upper = true "= true, if A is upper triangular";
  input Boolean trans = false "= true, if op(A) means transposed(A)";
  input Boolean unitTriangular = false "= true, if A is unit triangular, i.e., all diagonal elements of A are equal to 1";
  output Real X[size(B, 1), size(B, 2)] = B "Matrix Bout=alpha*op( A )*B, or B := alpha*B*op( A )";
end dtrsm;