dppsv.f(3)

NAME
dppsv.f -

SYNOPSIS

  Functions/Subroutines
subroutine dppsv (UPLO, N, NRHS, AP, B, LDB, INFO)
DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation

  subroutine dppsv (characterUPLO, integerN, integerNRHS, double precision, dimension( * )AP, double precision, dimension( ldb, * )B, integerLDB, integerINFO)

DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

     DPPSV 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.

Parameters:
    UPLO

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

    N

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

    NRHS

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

    AP

              AP is DOUBLE PRECISION 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

              B is 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

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

    INFO

              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.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

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 ]

Definition at line 145 of file dppsv.f.

Author

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