NAME

STRSYL - solve the real Sylvester matrix equation

SYNOPSIS

SUBROUTINE STRSYL(
TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO )

CHARACTER TRANA, TRANB

INTEGER INFO, ISGN, LDA, LDB, LDC, M, N

REAL SCALE

REAL A( LDA, ∗ ), B( LDB, ∗ ), C( LDC, ∗ )

PURPOSE

STRSYL 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 SHSEQR), 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) REAL 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) REAL 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) REAL 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) REAL
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).

  —  LAPACK version 2.0  —  08 October 1994