CPPSV(3)              LAPACK driver routine (version 3.1)             CPPSV(3)



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

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

           CHARACTER     UPLO

           INTEGER       INFO, LDB, N, NRHS

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

PURPOSE
       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  fac-
               torization 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 ]




 LAPACK driver routine (version 3.N1o)vember 2006                        CPPSV(3)