1CTRSYL(1)                LAPACK routine (version 3.2)                CTRSYL(1)
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NAME

6       CTRSYL - solves the complex Sylvester matrix equation
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SYNOPSIS

9       SUBROUTINE CTRSYL( TRANA,  TRANB,  ISGN,  M, N, A, LDA, B, LDB, C, LDC,
10                          SCALE, INFO )
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12           CHARACTER      TRANA, TRANB
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14           INTEGER        INFO, ISGN, LDA, LDB, LDC, M, N
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16           REAL           SCALE
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18           COMPLEX        A( LDA, * ), B( LDB, * ), C( LDC, * )
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PURPOSE

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

30       TRANA   (input) CHARACTER*1
31               Specifies the option op(A):
32               = 'N': op(A) = A    (No transpose)
33               = 'C': op(A) = A**H (Conjugate transpose)
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35       TRANB   (input) CHARACTER*1
36               Specifies the option op(B):
37               = 'N': op(B) = B    (No transpose)
38               = 'C': op(B) = B**H (Conjugate transpose)
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40       ISGN    (input) INTEGER
41               Specifies the sign in the equation:
42               = +1: solve op(A)*X + X*op(B) = scale*C
43               = -1: solve op(A)*X - X*op(B) = scale*C
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45       M       (input) INTEGER
46               The order of the matrix A, and the number of rows in the matri‐
47               ces X and C. M >= 0.
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49       N       (input) INTEGER
50               The order of the matrix B, and the number  of  columns  in  the
51               matrices X and C. N >= 0.
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53       A       (input) COMPLEX array, dimension (LDA,M)
54               The upper triangular matrix A.
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56       LDA     (input) INTEGER
57               The leading dimension of the array A. LDA >= max(1,M).
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59       B       (input) COMPLEX array, dimension (LDB,N)
60               The upper triangular matrix B.
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62       LDB     (input) INTEGER
63               The leading dimension of the array B. LDB >= max(1,N).
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65       C       (input/output) COMPLEX array, dimension (LDC,N)
66               On  entry,  the M-by-N right hand side matrix C.  On exit, C is
67               overwritten by the solution matrix X.
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69       LDC     (input) INTEGER
70               The leading dimension of the array C. LDC >= max(1,M)
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72       SCALE   (output) REAL
73               The scale factor, scale, set <= 1 to avoid overflow in X.
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75       INFO    (output) INTEGER
76               = 0: successful exit
77               < 0: if INFO = -i, the i-th argument had an illegal value
78               = 1: A and B have common or very close  eigenvalues;  perturbed
79               values  were used to solve the equation (but the matrices A and
80               B are unchanged).
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84 LAPACK routine (version 3.2)    November 2008                       CTRSYL(1)