SPPSV(3)       LAPACK routine of NEC Numeric Library Collection       SPPSV(3)



NAME
       SPPSV

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



PURPOSE
            SPPSV 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)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The number of linear equations, i.e., the order of the
                     matrix A.  N >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           AP        (input/output)
                     AP is REAL 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
                     factorization A = U**T*U or A = L*L**T, in the same storage
                     format as A.

           B         (input/output)
                     B is 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)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           INFO      (output)
                     INFO is 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 routine                  31 October 2017                       SPPSV(3)