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## dsptrf()

subroutine dsptrf | ( | character | uplo,
|  | integer | n,
|  | double precision, dimension( * ) | ap,
|  | integer, dimension( * ) | ipiv,
|  | integer | info )

DSPTRF

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

Purpose:

      !>
      !> DSPTRF 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

  [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 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.
      !>
      !>          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).
      !>

  [out]

  IPIV

      !>          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.
      !>

  [out]

  INFO

      !>          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.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Further Details:

      !>
      !>  If UPLO = 'U', then A = U*D*U**T, where
      !>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
      !>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
      !>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      !>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
      !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
      !>
      !>             (   I    v    0   )   k-s
      !>     U(k) =  (   0    I    0   )   s
      !>             (   0    0    I   )   n-k
      !>                k-s   s   n-k
      !>
      !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
      !>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
      !>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
      !>
      !>  If UPLO = 'L', then A = L*D*L**T, where
      !>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
      !>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
      !>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      !>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
      !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
      !>
      !>             (   I    0     0   )  k-1
      !>     L(k) =  (   0    I     0   )  s
      !>             (   0    v     I   )  n-k-s+1
      !>                k-1   s  n-k-s+1
      !>
      !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
      !>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
      !>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
      !>

Contributors:
  J. Lewis, Boeing Computer Services Company