SPTRF - 5.2 English - 68552

SPTRF computes the factorization of a real symmetric matrix A.

Purpose:

  SPTRF computes the factorization of a real symmetric matrix A stored
  in packed format using the Bunch-Kaufman diagonal pivoting method:

     A = U*D*U**T  or  A = L*D*L**T

  where U (or L) is a product of permutation and unit upper (lower)
  triangular matrices, and D is symmetric and block diagonal with
  1-by-1 and 2-by-2 diagonal blocks.

Parameters:

• UPLO – [in]

  UPLO is CHARACTER*1

  = ‘U’: Upper triangle of A is stored;

  = ‘L’: Lower triangle of A is stored.

• N – [in]

  N is INTEGER

  The order of the matrix A. N >= 0.

• AP – [inout]

  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.

  On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix overwriting A (see below for further details).

• IPIV – [out]

  IPIV is INTEGER array, dimension (N)

  Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.

  If UPLO = ‘U’ and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ‘L’ and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit

  < 0: if INFO = -i, the i-th argument had an illegal value

  > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.