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CentOS 7.0 - man page for ctgsyl (centos section 3)

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ctgsyl.f(3)				      LAPACK				      ctgsyl.f(3)

NAME
       ctgsyl.f -

SYNOPSIS
   Functions/Subroutines
       subroutine ctgsyl (TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF,
	   SCALE, DIF, WORK, LWORK, IWORK, INFO)
	   CTGSYL

Function/Subroutine Documentation
   subroutine ctgsyl (characterTRANS, integerIJOB, integerM, integerN, complex, dimension( lda, *
       )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldc, * )C,
       integerLDC, complex, dimension( ldd, * )D, integerLDD, complex, dimension( lde, * )E,
       integerLDE, complex, dimension( ldf, * )F, integerLDF, realSCALE, realDIF, complex,
       dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)
       CTGSYL

       Purpose:

	    CTGSYL solves the generalized Sylvester equation:

			A * R - L * B = scale * C	     (1)
			D * R - L * E = scale * F

	    where R and L are unknown m-by-n matrices, (A, D), (B, E) and
	    (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
	    respectively, with complex entries. A, B, D and E are upper
	    triangular (i.e., (A,D) and (B,E) in generalized Schur form).

	    The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1
	    is an output scaling factor chosen to avoid overflow.

	    In matrix notation (1) is equivalent to solve Zx = scale*b, where Z
	    is defined as

		   Z = [ kron(In, A)  -kron(B**H, Im) ]        (2)
		       [ kron(In, D)  -kron(E**H, Im) ],

	    Here Ix is the identity matrix of size x and X**H is the conjugate
	    transpose of X. Kron(X, Y) is the Kronecker product between the
	    matrices X and Y.

	    If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b
	    is solved for, which is equivalent to solve for R and L in

			A**H * R + D**H * L = scale * C 	  (3)
			R * B**H + L * E**H = scale * -F

	    This case (TRANS = 'C') is used to compute an one-norm-based estimate
	    of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
	    and (B,E), using CLACON.

	    If IJOB >= 1, CTGSYL computes a Frobenius norm-based estimate of
	    Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
	    reciprocal of the smallest singular value of Z.

	    This is a level-3 BLAS algorithm.

       Parameters:
	   TRANS

		     TRANS is CHARACTER*1
		     = 'N': solve the generalized sylvester equation (1).
		     = 'C': solve the "conjugate transposed" system (3).

	   IJOB

		     IJOB is INTEGER
		     Specifies what kind of functionality to be performed.
		     =0: solve (1) only.
		     =1: The functionality of 0 and 3.
		     =2: The functionality of 0 and 4.
		     =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
			 (look ahead strategy is used).
		     =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
			 (CGECON on sub-systems is used).
		     Not referenced if TRANS = 'C'.

	   M

		     M is INTEGER
		     The order of the matrices A and D, and the row dimension of
		     the matrices C, F, R and L.

	   N

		     N is INTEGER
		     The order of the matrices B and E, and the column dimension
		     of the matrices C, F, R and L.

	   A

		     A is COMPLEX array, dimension (LDA, M)
		     The upper triangular matrix A.

	   LDA

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

	   B

		     B is COMPLEX array, dimension (LDB, N)
		     The upper triangular matrix B.

	   LDB

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

	   C

		     C is COMPLEX array, dimension (LDC, N)
		     On entry, C contains the right-hand-side of the first matrix
		     equation in (1) or (3).
		     On exit, if IJOB = 0, 1 or 2, C has been overwritten by
		     the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
		     the solution achieved during the computation of the
		     Dif-estimate.

	   LDC

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

	   D

		     D is COMPLEX array, dimension (LDD, M)
		     The upper triangular matrix D.

	   LDD

		     LDD is INTEGER
		     The leading dimension of the array D. LDD >= max(1, M).

	   E

		     E is COMPLEX array, dimension (LDE, N)
		     The upper triangular matrix E.

	   LDE

		     LDE is INTEGER
		     The leading dimension of the array E. LDE >= max(1, N).

	   F

		     F is COMPLEX array, dimension (LDF, N)
		     On entry, F contains the right-hand-side of the second matrix
		     equation in (1) or (3).
		     On exit, if IJOB = 0, 1 or 2, F has been overwritten by
		     the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
		     the solution achieved during the computation of the
		     Dif-estimate.

	   LDF

		     LDF is INTEGER
		     The leading dimension of the array F. LDF >= max(1, M).

	   DIF

		     DIF is REAL
		     On exit DIF is the reciprocal of a lower bound of the
		     reciprocal of the Dif-function, i.e. DIF is an upper bound of
		     Dif[(A,D), (B,E)] = sigma-min(Z), where Z as in (2).
		     IF IJOB = 0 or TRANS = 'C', DIF is not referenced.

	   SCALE

		     SCALE is REAL
		     On exit SCALE is the scaling factor in (1) or (3).
		     If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
		     to a slightly perturbed system but the input matrices A, B,
		     D and E have not been changed. If SCALE = 0, R and L will
		     hold the solutions to the homogenious system with C = F = 0.

	   WORK

		     WORK is COMPLEX array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK. LWORK > = 1.
		     If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the WORK array, and no error
		     message related to LWORK is issued by XERBLA.

	   IWORK

		     IWORK is INTEGER array, dimension (M+N+2)

	   INFO

		     INFO is INTEGER
		       =0: successful exit
		       <0: If INFO = -i, the i-th argument had an illegal value.
		       >0: (A, D) and (B, E) have common or very close
			   eigenvalues.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901
	   87 Umea, Sweden.

       References:
	   [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the
	   Generalized Sylvester Equation and Estimating the Separation between Regular Matrix
	   Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901
	   87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK Working Note 75. To
	   appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.
	    [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester Equation (AR -
	   LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. Appl., 15(4):1045-1060, 1994.
	    [3] B. Kagstrom and L. Westin, Generalized Schur Methods with Condition Estimators
	   for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic
	   Control, Vol. 34, No. 7, July 1989, pp 745-751.

       Definition at line 294 of file ctgsyl.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      ctgsyl.f(3)
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