csytrf_rook.f man page on Cygwin

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csytrf_rook.f(3)		    LAPACK		      csytrf_rook.f(3)

NAME
       csytrf_rook.f -

SYNOPSIS
   Functions/Subroutines
       subroutine csytrf_rook (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
	   CSYTRF_ROOK

Function/Subroutine Documentation
   subroutine csytrf_rook (characterUPLO, integerN, complex, dimension( lda, *
       )A, integerLDA, integer, dimension( * )IPIV, complex, dimension( *
       )WORK, integerLWORK, integerINFO)
       CSYTRF_ROOK

       Purpose:

	    CSYTRF_ROOK computes the factorization of a complex symmetric matrix A
	    using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
	    The form of the factorization is

	       A = U*D*U**T  or	 A = L*D*L**T

	    where U (or L) is a product of permutation and unit upper (lower)
	    triangular matrices, and D is symmetric and block diagonal with
	    1-by-1 and 2-by-2 diagonal blocks.

	    This is the blocked version of the algorithm, calling Level 3 BLAS.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  Upper triangle of A is stored;
		     = 'L':  Lower triangle of A is stored.

	   N

		     N is INTEGER
		     The order of the matrix A.	 N >= 0.

	   A

		     A is COMPLEX array, dimension (LDA,N)
		     On entry, the symmetric matrix A.	If UPLO = 'U', the leading
		     N-by-N upper triangular part of A contains the upper
		     triangular part of the matrix A, and the strictly lower
		     triangular part of A is not referenced.  If UPLO = 'L', the
		     leading N-by-N lower triangular part of A contains the lower
		     triangular part of the matrix A, and the strictly upper
		     triangular part of A is not referenced.

		     On exit, the block diagonal matrix D and the multipliers used
		     to obtain the factor U or L (see below for further details).

	   LDA

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

	   IPIV

		     IPIV is INTEGER array, dimension (N)
		     Details of the interchanges and the block structure of D.

		     If UPLO = 'U':
			  If IPIV(k) > 0, then rows and columns k and IPIV(k)
			  were interchanged and D(k,k) is a 1-by-1 diagonal block.

			  If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
			  columns k and -IPIV(k) were interchanged and rows and
			  columns k-1 and -IPIV(k-1) were inerchaged,
			  D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

		     If UPLO = 'L':
			  If IPIV(k) > 0, then rows and columns k and IPIV(k)
			  were interchanged and D(k,k) is a 1-by-1 diagonal block.

			  If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
			  columns k and -IPIV(k) were interchanged and rows and
			  columns k+1 and -IPIV(k+1) were inerchaged,
			  D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

	   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 length of WORK.  LWORK >=1.  For best performance
		     LWORK >= N*NB, where NB is the block size returned by ILAENV.

		     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.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  if INFO = i, D(i,i) is exactly zero.	 The factorization
			   has been completed, but the block diagonal matrix D is
			   exactly singular, and division by zero will occur if it
			   is used to solve a system of equations.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     If UPLO = 'U', then A = U*D*U**T, where
		U = P(n)*U(n)* ... *P(k)U(k)* ...,
	     i.e., U is a product of terms P(k)*U(k), where k decreases from n to
	     1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
	     and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
	     defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
	     that if the diagonal block D(k) is of order s (s = 1 or 2), then

			(   I	 v    0	  )   k-s
		U(k) =	(   0	 I    0	  )   s
			(   0	 0    I	  )   n-k
			   k-s	 s   n-k

	     If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
	     If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
	     and A(k,k), and v overwrites A(1:k-2,k-1:k).

	     If UPLO = 'L', then A = L*D*L**T, where
		L = P(1)*L(1)* ... *P(k)*L(k)* ...,
	     i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
	     n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
	     and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
	     defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
	     that if the diagonal block D(k) is of order s (s = 1 or 2), then

			(   I	 0     0   )  k-1
		L(k) =	(   0	 I     0   )  s
			(   0	 v     I   )  n-k-s+1
			   k-1	 s  n-k-s+1

	     If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
	     If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
	     and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

       Contributors:

	      November 2011, Igor Kozachenko,
			     Computer Science Division,
			     University of California, Berkeley

	     September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
			     School of Mathematics,
			     University of Manchester

       Definition at line 209 of file csytrf_rook.f.

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

Version 3.4.2			Sat Nov 16 2013		      csytrf_rook.f(3)
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