Functions/Subroutines
subroutine	chetrf (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
	CHETRF

Function/Subroutine Documentation

subroutine chetrf	(	character	UPLO,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		integer, dimension( * )	IPIV,
		complex, dimension( * )	WORK,
		integer	LWORK,
		integer	INFO
	)

CHETRF

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Purpose:

 CHETRF computes the factorization of a complex Hermitian matrix A
 using the Bunch-Kaufman diagonal pivoting method.  The form of the
 factorization is

    A = U*D*U**H  or  A = L*D*L**H

 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 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]	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.
[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.

Date:: November 2011

Further Details:

  If UPLO = 'U', then A = U*D*U**H, where
     U = P(n)*U(n)* ... <em>P(k)U(k)</em> ...,
  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**H, where
     L = P(1)*L(1)* ... <em>P(k)*L(k)</em> ...,
  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).

Definition at line 178 of file chetrf.f.

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