chetrf_rook.f man page

chetrf_rook.f —

Synopsis

Functions/Subroutines

subroutine chetrf_rook (UPLO, N, A, LDA, IPIV, WORK, LWORK, 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).

Function/Subroutine Documentation

subroutine chetrf_rook (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex, dimension( * )WORK, integerLWORK, integerINFO)

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).

Purpose:

CHETRF_ROOK computes the factorization of a comlex Hermitian matrix A
using the bounded Bunch-Kaufman ("rook") 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:

UPLO

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

N

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

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).

LDA

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

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.

WORK

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

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.

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.

Date:

November 2013

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:

November 2013,  Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                School of Mathematics,
                University of Manchester

Definition at line 213 of file chetrf_rook.f.

Author

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Referenced By

chetrf_rook(3) is an alias of chetrf_rook.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK