SRC/sppsv.f(3)

NAME
SRC/sppsv.f

SYNOPSIS

  Functions/Subroutines
subroutine sppsv (uplo, n, nrhs, ap, b, ldb, info)
SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation

  subroutine sppsv (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)

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

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.

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 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

              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

              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 principal minor of order i
                    of A is not positive, 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.

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 143 of file sppsv.f.

Author

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