CXML
        	    
LAPACK version 3.0
cspsv(3)

PURPOSE
  CSPSV - compute the solution to a complex system of linear equations A * X
  = B,

SYNTAX
  SUBROUTINE CSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )

      CHARACTER	    UPLO

      INTEGER	    INFO, LDB, N, NRHS

      INTEGER	    IPIV( * )

      COMPLEX	    AP( * ), B( LDB, * )

DESCRIPTION
  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.

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

  N	  (input) INTEGER
	  The number of linear equations, i.e., the order of the matrix A.  N
	  >= 0.

  NRHS	  (input) INTEGER
	  The number of right hand sides, i.e., the number of columns of the
	  matrix B.  NRHS >= 0.

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

  INFO	  (output) 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.

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 ]