DTRSYL(3)      LAPACK routine of NEC Numeric Library Collection      DTRSYL(3)



NAME
       DTRSYL

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



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 elements equal and its
            off-diagonal elements of opposite sign.




ARGUMENTS
           TRANA     (input)
                     TRANA is 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)
                     TRANB is 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)
                     ISGN is 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)
                     M is INTEGER
                     The order of the matrix A, and the number of rows in the
                     matrices X and C. M >= 0.

           N         (input)
                     N is INTEGER
                     The order of the matrix B, and the number of columns in the
                     matrices X and C. N >= 0.

           A         (input)
                     A is DOUBLE PRECISION array, dimension (LDA,M)
                     The upper quasi-triangular matrix A, in Schur canonical form.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A. LDA >= max(1,M).

           B         (input)
                     B is DOUBLE PRECISION array, dimension (LDB,N)
                     The upper quasi-triangular matrix B, in Schur canonical form.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B. LDB >= max(1,N).

           C         (input/output)
                     C is 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)
                     LDC is INTEGER
                     The leading dimension of the array C. LDC >= max(1,M)

           SCALE     (output)
                     SCALE is DOUBLE PRECISION
                     The scale factor, scale, set <= 1 to avoid overflow in X.

           INFO      (output)
                     INFO is 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 routine                  31 October 2017                      DTRSYL(3)