This information is part of the Modelica Standard Library maintained by the Modelica Association.

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).

(X, scale, info) = dtrsyl(A, B, C, tranA, tranB, isgn)

A	Type: Real[:,:] Description: Upper quasi-triangular matrix
B	Type: Real[:,:] Description: Upper quasi-triangular matrix
C	Type: Real[if tranA then size(A, 1) else size(A, 2),if tranB then size(B, 1) else size(B, 2)] Description: Right side of the Sylvester equation
tranA	Default Value: false Type: Boolean Description: = true, if op(A)=A'
tranB	Default Value: false Type: Boolean Description: = true, if op(B)=B'
isgn	Default Value: 1 Type: Integer Description: Specifies the sign in the equation, +1 or -1

X	Default Value: C Type: Real[size(C, 1),size(C, 2)] Description: Solution of the Sylvester equation
scale	Type: Real Description: Scale factor
info	Type: Integer