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## chetrf_rook()

subroutine chetrf_rook | ( | character | uplo,
|  | integer | n,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | integer, dimension( * ) | ipiv,
|  | complex, dimension( * ) | work,
|  | integer | lwork,
|  | integer | info )

CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

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

Purpose:

      !>
      !> CHETRF_ROOK computes the factorization of a complex Hermitian matrix A
      !> using the bounded Bunch-Kaufman () diagonal pivoting method.
      !> The form of the factorization is
      !>
      !>    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 Hermitian and block diagonal with
      !> 1-by-1 and 2-by-2 diagonal blocks.
      !>
      !> This is the blocked version of the algorithm, calling Level 3 BLAS.
      !>

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]

  A

      !>          A is COMPLEX array, dimension (LDA,N)
      !>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
      !>          N-by-N upper triangular part of A contains the upper
      !>          triangular part of the matrix A, and the strictly lower
      !>          triangular part of A is not referenced.  If UPLO = 'L', the
      !>          leading N-by-N lower triangular part of A contains the lower
      !>          triangular part of the matrix A, and the strictly upper
      !>          triangular part of A is not referenced.
      !>
      !>          On exit, the block diagonal matrix D and the multipliers used
      !>          to obtain the factor U or L (see below for further details).
      !>

  [in]

  LDA

      !>          LDA is INTEGER
      !>          The leading dimension of the array A.  LDA >= max(1,N).
      !>

  [out]

  IPIV

      !>          IPIV is INTEGER array, dimension (N)
      !>          Details of the interchanges and the block structure of D.
      !>
      !>          If UPLO = 'U':
      !>             Only the last KB elements of IPIV are set.
      !>
      !>             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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
      !>             columns k and -IPIV(k) were interchanged and rows and
      !>             columns k-1 and -IPIV(k-1) were inerchaged,
      !>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
      !>
      !>          If UPLO = 'L':
      !>             Only the first KB elements of IPIV are set.
      !>
      !>             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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
      !>             columns k and -IPIV(k) were interchanged and rows and
      !>             columns k+1 and -IPIV(k+1) were inerchaged,
      !>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
      !>

  [out]

  WORK

      !>          WORK is COMPLEX array, dimension (MAX(1,LWORK)).
      !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
      !>

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The length of WORK.  LWORK >= 1.  For best performance
      !>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
      !>
      !>          If LWORK = -1, then a workspace query is assumed; the routine
      !>          only calculates the optimal size of the WORK array, returns
      !>          this value as the first entry of the WORK array, and no error
      !>          message related to LWORK is issued by XERBLA.
      !>

  [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:

      !>
      !>  June 2016,  Igor Kozachenko,
      !>                  Computer Science Division,
      !>                  University of California, Berkeley
      !>
      !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
      !>                  School of Mathematics,
      !>                  University of Manchester
      !>
      !>