csptrf.f(3)							      LAPACK							       csptrf.f(3)

NAME

       csptrf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine csptrf (UPLO, N, AP, IPIV, INFO)
	   CSPTRF

Function/Subroutine Documentation
   subroutine csptrf (characterUPLO, integerN, complex, dimension( * )AP, integer, dimension( * )IPIV, integerINFO)
       CSPTRF

       Purpose:

	    CSPTRF computes the factorization of a complex symmetric matrix A
	    stored in packed format using the Bunch-Kaufman diagonal pivoting
	    method:

	       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.

       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.

	   AP

		     AP is COMPLEX array, dimension (N*(N+1)/2)
		     On entry, the upper or lower triangle of the symmetric matrix
		     A, packed columnwise in a linear array.  The j-th column of A
		     is stored in the array AP as follows:
		     if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
		     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

		     On exit, the block diagonal matrix D and the multipliers used
		     to obtain the factor U or L, stored as a packed triangular
		     matrix overwriting A (see below for further details).

	   IPIV

		     IPIV is INTEGER array, dimension (N)
		     Details of the interchanges and the block structure of D.
		     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 UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
		     columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
		     is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
		     IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
		     interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

	   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:

	     5-96 - Based on modifications by J. Lewis, Boeing Computer Services
		    Company

	     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).

       Definition at line 159 of file csptrf.f.

Author
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Version 3.4.1							  Sun May 26 2013						       csptrf.f(3)