1ZTRSYL(1)                LAPACK routine (version 3.1)                ZTRSYL(1)
2
3
4

NAME

6       ZTRSYL - the complex Sylvester matrix equation
7

SYNOPSIS

9       SUBROUTINE ZTRSYL( TRANA,  TRANB,  ISGN,  M, N, A, LDA, B, LDB, C, LDC,
10                          SCALE, INFO )
11
12           CHARACTER      TRANA, TRANB
13
14           INTEGER        INFO, ISGN, LDA, LDB, LDC, M, N
15
16           DOUBLE         PRECISION SCALE
17
18           COMPLEX*16     A( LDA, * ), B( LDB, * ), C( LDC, * )
19

PURPOSE

21       ZTRSYL solves the complex Sylvester matrix equation:
22
23          op(A)*X + X*op(B) = scale*C or
24          op(A)*X - X*op(B) = scale*C,
25
26       where op(A) = A or A**H, and A and B are both upper triangular. A is M-
27       by-M  and  B is N-by-N; the right hand side C and the solution X are M-
28       by-N; and scale is an output scale factor, set <= 1 to  avoid  overflow
29       in X.
30
31

ARGUMENTS

33       TRANA   (input) CHARACTER*1
34               Specifies the option op(A):
35               = 'N': op(A) = A    (No transpose)
36               = 'C': op(A) = A**H (Conjugate transpose)
37
38       TRANB   (input) CHARACTER*1
39               Specifies the option op(B):
40               = 'N': op(B) = B    (No transpose)
41               = 'C': op(B) = B**H (Conjugate transpose)
42
43       ISGN    (input) INTEGER
44               Specifies the sign in the equation:
45               = +1: solve op(A)*X + X*op(B) = scale*C
46               = -1: solve op(A)*X - X*op(B) = scale*C
47
48       M       (input) INTEGER
49               The order of the matrix A, and the number of rows in the matri‐
50               ces X and C. M >= 0.
51
52       N       (input) INTEGER
53               The order of the matrix B, and the number  of  columns  in  the
54               matrices X and C. N >= 0.
55
56       A       (input) COMPLEX*16 array, dimension (LDA,M)
57               The upper triangular matrix A.
58
59       LDA     (input) INTEGER
60               The leading dimension of the array A. LDA >= max(1,M).
61
62       B       (input) COMPLEX*16 array, dimension (LDB,N)
63               The upper triangular matrix B.
64
65       LDB     (input) INTEGER
66               The leading dimension of the array B. LDB >= max(1,N).
67
68       C       (input/output) COMPLEX*16 array, dimension (LDC,N)
69               On  entry,  the M-by-N right hand side matrix C.  On exit, C is
70               overwritten by the solution matrix X.
71
72       LDC     (input) INTEGER
73               The leading dimension of the array C. LDC >= max(1,M)
74
75       SCALE   (output) DOUBLE PRECISION
76               The scale factor, scale, set <= 1 to avoid overflow in X.
77
78       INFO    (output) INTEGER
79               = 0: successful exit
80               < 0: if INFO = -i, the i-th argument had an illegal value
81               = 1: A and B have common or very close  eigenvalues;  perturbed
82               values  were used to solve the equation (but the matrices A and
83               B are unchanged).
84
85
86
87 LAPACK routine (version 3.1)    November 2006                       ZTRSYL(1)