
DTRSYL(l) ) DTRSYL(l)
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 MbyM and B
is NbyN; the right hand side C and the solution X are MbyN; 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 tri
angular with 1by1 and 2by2 diagonal blocks; each 2by2 diagonal block has its diago
nal elements equal and its offdiagonal 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 quasitriangular 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 quasitriangular 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 MbyN 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 ith 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 3.0 15 June 2000 DTRSYL(l) 
