CXML
        	    
LAPACK version 3.0
cppsv(3)

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

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

      CHARACTER	    UPLO

      INTEGER	    INFO, LDB, N, NRHS

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

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

  The Cholesky decomposition is used to factor A as
     A = U**H* U,  if UPLO = 'U', or
     A = L * L**H,  if UPLO = 'L',
  where U is an upper triangular matrix and L is a lower triangular matrix.
  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 Hermitian 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, if INFO = 0, the factor U or L from the Cholesky
	  factorization A = U**H*U or A = L*L**H, in the same storage format
	  as A.

  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, the leading minor of order i of A is not
	  positive definite, so the factorization could not be completed, and
	  the solution has not been computed.

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

  Two-dimensional storage of the Hermitian matrix A:

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

  Packed storage of the upper triangle of A:

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