WOLFRAM SYSTEM MODELER

# dtrsyl

Solve the real Sylvester matrix equation op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C # Wolfram Language

In:= `SystemModel["Modelica.Math.Matrices.LAPACK.dtrsyl"]`
Out:= # Information

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
= +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).```

# Syntax

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

# Inputs (6)

A Type: Real[:,:] Description: Upper quais-triangular matrix Type: Real[:,:] Description: Upper quais-triangular matrix 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 Default Value: false Type: Boolean Description: True if op(A)=A' Default Value: false Type: Boolean Description: True if op(B)=B' Default Value: 1 Type: Integer Description: Specifies the sign in the equation, +1 or -1

# Outputs (3)

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