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sppsv

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

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

          CHARACTER     UPLO

          INTEGER       INFO, LDB, N, NRHS

          REAL          AP( * ), B( LDB, * )

 PURPOSE
      SPPSV 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) REAL 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) REAL 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 com-
              puted.

 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 ]