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DPPSV(l)			       )			      DPPSV(l)

NAME
       DPPSV - compute the solution to a real system of linear equations A * X
       = B,

SYNOPSIS
       SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )

	   CHARACTER	 UPLO

	   INTEGER	 INFO, LDB, N, NRHS

	   DOUBLE	 PRECISION AP( * ), B( LDB, * )

PURPOSE
       DPPSV computes the solution to a real system of linear equations A *  X
       =  B, where A is an N-by-N symmetric 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**T* U,	if UPLO = 'U', or
	  A = L * L**T,	 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) DOUBLE PRECISION 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, if INFO = 0, the factor U or L from the Cholesky fac‐
	       torization A = U**T*U or A = L*L**T, in the same storage format
	       as A.

       B       (input/output) DOUBLE PRECISION 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 symmetric 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 ]

LAPACK version 3.0		 15 June 2000			      DPPSV(l)
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