dtrsyl(3)

NAME

DTRSYL - solve the real Sylvester matrix equation

SYNOPSIS

SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N,  A,  LDA,  B,
LDB, C, LDC, SCALE, INFO )
    CHARACTER      TRANA, TRANB
    INTEGER        INFO, ISGN, LDA, LDB, LDC, M, N
    DOUBLE         PRECISION SCALE
    DOUBLE          PRECISION A( LDA, * ), B( LDB, * ), C(
LDC, * )

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 ele

ments 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 = Trans

pose)

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 = Trans

pose)

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 over

flow in X.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value
= 1: A and B have common or very close eigenval

ues; perturbed values were used to solve the equation (but the

matrices A and B are unchanged).

LAPACK version 3.0 15 June 2000

DTRSYL(3)