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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, * )



     #include <sunperf.h>

     void dppsv(char uplo, int n, int nrhs,  double  *ap,  double
               *db, int ldb, int *info) ;

PURPOSE
     DPPSV computes the solution to a real system of linear equa-
     tions
        A * X = B, where A is an N-by-N symmetric positive defin-
     ite 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  tri-
     angular  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  sym-
               metric  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**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 ille-
               gal 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 ]

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