.Modelica_LinearSystems2.Math.Matrices.LAPACK.dtrsyl

Information

Lapack documentation:

   Purpose
   =======

   DTRSYL solves the real Sylvester matrix equation:

      op(A)*X + X*op(B) = scale*C or
      op(A)*X - X*op(B) = scale*C,

   where op(A) = A or A**T, and  A and B are both upper quasi-
   triangular. A is M-by-M and B is N-by-N; the right hand side C and
   the solution X are M-by-N; and scale is an output scale factor, set
   <= 1 to avoid overflow in X.

   A and B must be in Schur canonical form (as returned by DHSEQR), that
   is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
   each 2-by-2 diagonal block has its diagonal elements equal and its
   off-diagonal elements of opposite sign.

   Arguments
   =========

   TRANA   (input) CHARACTER*1
           Specifies the option op(A):
           = 'N': op(A) = A    (No transpose)
           = 'T': op(A) = A**T (Transpose)
           = 'C': op(A) = A**H (Conjugate transpose = Transpose)

   TRANB   (input) CHARACTER*1
           Specifies the option op(B):
           = 'N': op(B) = B    (No transpose)
           = 'T': op(B) = B**T (Transpose)
           = 'C': op(B) = B**H (Conjugate transpose = Transpose)

   ISGN    (input) INTEGER
           Specifies the sign in the equation:
           = +1: solve op(A)*X + X*op(B) = scale*C
           = -1: solve op(A)*X - X*op(B) = scale*C

   M       (input) INTEGER
           The order of the matrix A, and the number of rows in the
           matrices X and C. M >= 0.

   N       (input) INTEGER
           The order of the matrix B, and the number of columns in the
           matrices X and C. N >= 0.

   A       (input) DOUBLE PRECISION array, dimension (LDA,M)
           The upper quasi-triangular matrix A, in Schur canonical form.

   LDA     (input) INTEGER
           The leading dimension of the array A. LDA >= max(1,M).

   B       (input) DOUBLE PRECISION array, dimension (LDB,N)
           The upper quasi-triangular matrix B, in Schur canonical form.

   LDB     (input) INTEGER
           The leading dimension of the array B. LDB >= max(1,N).

   C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
           On entry, the M-by-N right hand side matrix C.
           On exit, C is overwritten by the solution matrix X.

   LDC     (input) INTEGER
           The leading dimension of the array C. LDC >= max(1,M)

   SCALE   (output) DOUBLE PRECISION
           The scale factor, scale, set <= 1 to avoid overflow in X.

   INFO    (output) INTEGER
           = 0: successful exit
           < 0: if INFO = -i, the i-th argument had an illegal value
           = 1: A and B have common or very close eigenvalues; perturbed
                values were used to solve the equation (but the matrices
                A and B are unchanged).

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

Interface

function dtrsyl
  input Real A[:, :];
  input Real B[:, :];
  input Real C[if tranA then size(A, 1) else size(A, 2), if tranB then size(B, 1) else size(B, 2)];
  input Boolean tranA = false;
  input Boolean tranB = false;
  input Integer isgn = 1;
  output Real X[size(C, 1), size(C, 2)] = C;
  output Real scale;
  output Integer info;
end dtrsyl;