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## spptrf()

subroutine spptrf | ( | character | uplo,
|  | integer | n,
|  | real, dimension( * ) | ap,
|  | integer | info )

SPPTRF

Download SPPTRF + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> SPPTRF computes the Cholesky factorization of a real symmetric
      !> positive definite matrix A stored in packed format.
      !>
      !> The factorization has the form
      !>    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 lower triangular.
      !>

Parameters

  [in]

  UPLO

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

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix A.  N >= 0.
      !>

  [in,out]

  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 triangular factor U or L from the
      !>          Cholesky factorization A = U**T*U or A = L*L**T, in the same
      !>          storage format as A.
      !>

  [out]

  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
      !>                is not positive, and the factorization could not be
      !>                completed.
      !>

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 = aji)
      !>                 a44
      !>
      !>  Packed storage of the upper triangle of A:
      !>
      !>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
      !>