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


SYNOPSIS

       SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )

           CHARACTER     UPLO

           INTEGER       INFO, LDA, LDB, N, NRHS

           DOUBLE        PRECISION A( LDA, * ), B( LDB, * )


PURPOSE

       DPOSV computes the solution to a  real  system  of  linear
       equations  A * X = B, where A is an N-by-N symmetric posi­
       tive definite matrix 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.

       A       (input/output) DOUBLE PRECISION array, dimension
               (LDA,N)
               On  entry, the symmetric matrix A.  If UPLO = 'U',
               the leading N-by-N upper triangular part of A con­
               tains  the  upper triangular part of the matrix A,
               and the strictly lower triangular part of A is not
               referenced.   If  UPLO  =  'L', the leading N-by-N
               lower triangular part of A contains the lower tri­
               angular  part  of  the  matrix A, and the strictly
               upper triangular part of A is not referenced.

               On exit, if INFO = 0, the factor U or L  from  the
               Cholesky factorization A = U**T*U or A = L*L**T.

               The  leading  dimension  of  the  array A.  LDA >=
               max(1,N).

       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.


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