.Modelica_LinearSystems2.Math.Matrices.LAPACK.dtrsv

Information

Lapack documentation:

   Purpose
   =======

   DTRSV  solves one of the systems of equations
      A*x = b,   or   A'*x = b,
   where b and x are n element vectors and A is an n by n unit, or
   non-unit, upper or lower triangular matrix.
   No test for singularity or near-singularity is included in this
   routine. Such tests must be performed before calling this routine.
   Arguments
   ==========
   UPLO   - CHARACTER*1.
            On entry, UPLO specifies whether the matrix 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.
   TRANS  - CHARACTER*1.
            On entry, TRANS specifies the equations to be solved as
            follows:
               TRANS = 'N' or 'n'   A*x = b.
               TRANS = 'T' or 't'   A'*x = b.
               TRANS = 'C' or 'c'   A'*x = b.
            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.
   N      - INTEGER.
            On entry, N specifies the order of the matrix A.
            N must be at least zero.
            Unchanged on exit.
   A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
            Before entry with  UPLO = 'U' or 'u', the leading n by n
            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 n by n
            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. LDA must be at least
            max( 1, n ).
            Unchanged on exit.
   X      - DOUBLE PRECISION array of dimension at least
            ( 1 + ( n - 1 )*abs( INCX ) ).
            Before entry, the incremented array X must contain the n
            element right-hand side vector b. On exit, X is overwritten
            with the solution vector x.
   INCX   - INTEGER.
            On entry, INCX specifies the increment for the elements of
            X. INCX must not be zero.
            Unchanged on exit.

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

   Level 2 Blas routine.

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

Interface

function dtrsv
  input Real A[:, :] "Input matrix A";
  input Real b[size(A, 2)] "Input vector b";
  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)] = b "Solution x";
end dtrsv;