DPOSV (3lapack)

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 positive 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 contains 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 triangular 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.

  LDA     (input) INTEGER
          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 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.