cspsv.f(3)							      LAPACK								cspsv.f(3)

NAME

       cspsv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cspsv (UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
	    CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation
   subroutine cspsv (characterUPLO, integerN, integerNRHS, complex, dimension( * )AP, integer, dimension( * )IPIV, complex, dimension( ldb, * )B,
       integerLDB, integerINFO)
	CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

       Purpose:

	    CSPSV computes the solution to a complex system of linear equations
	       A * X = B,
	    where A is an N-by-N symmetric matrix stored in packed format and X
	    and B are N-by-NRHS matrices.

	    The diagonal pivoting method is used to factor A as
	       A = U * D * U**T,  if UPLO = 'U', or
	       A = L * D * L**T,  if UPLO = 'L',
	    where U (or L) is a product of permutation and unit upper (lower)
	    triangular matrices, D is symmetric and block diagonal with 1-by-1
	    and 2-by-2 diagonal blocks.  The factored form of A is then used to
	    solve the system of equations A * X = B.

       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 number of linear equations, i.e., the order of the
		     matrix A.	N >= 0.

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of columns
		     of the matrix B.  NRHS >= 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.
		     See below for further details.

		     On exit, the block diagonal matrix D and the multipliers used
		     to obtain the factor U or L from the factorization
		     A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as
		     a packed triangular matrix in the same storage format as A.

	   IPIV

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

	   B

		     B is COMPLEX array, dimension (LDB,NRHS)
		     On entry, the N-by-NRHS right hand side matrix B.
		     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

	   LDB

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

	   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, so the solution could not be
			   computed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     The packed storage scheme is illustrated by the following example
	     when N = 4, UPLO = 'U':

	     Two-dimensional storage of the symmetric matrix A:

		a11 a12 a13 a14
		    a22 a23 a24
			a33 a34     (aij = aji)
			    a44

	     Packed storage of the upper triangle of A:

	     AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

       Definition at line 163 of file cspsv.f.

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

Version 3.4.1							  Sun May 26 2013							cspsv.f(3)