.Modelica_LinearSystems2.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.

   Further Details
   ===============

   Level 3 Blas routine.

   =====================================================================  

Interface

function dtrsm
  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 "Solution X";
end dtrsm;