SPPSV (3lapack)

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 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) 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 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) 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 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 ]