
chetf2.f(3) LAPACK chetf2.f(3)
NAME
chetf2.f 
SYNOPSIS
Functions/Subroutines
subroutine chetf2 (UPLO, N, A, LDA, IPIV, INFO)
CHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal
pivoting method (unblocked algorithm).
Function/Subroutine Documentation
subroutine chetf2 (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA,
integer, dimension( * )IPIV, integerINFO)
CHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal
pivoting method (unblocked algorithm).
Purpose:
CHETF2 computes the factorization of a complex Hermitian matrix A
using the BunchKaufman diagonal pivoting method:
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, U**H is the conjugate transpose of U, and D is
Hermitian and block diagonal with 1by1 and 2by2 diagonal blocks.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
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
nbyn 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 nbyn 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 IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1by1 diagonal block.
If UPLO = 'U' and IPIV(k) = IPIV(k1) < 0, then rows and
columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k)
is a 2by2 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 2by2 diagonal block.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = k, the kth argument had an illegal value
> 0: if INFO = k, D(k,k) 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:
September 2012
Further Details:
092906  patch from
Bobby Cheng, MathWorks
Replace l.210 and l.392
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
by
IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
010196  Based on modifications by
J. Lewis, Boeing Computer Services Company
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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 1by1
and 2by2 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 ) ks
U(k) = ( 0 I 0 ) s
( 0 0 I ) nk
ks s nk
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k).
If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k),
and A(k,k), and v overwrites A(1:k2,k1: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 1by1
and 2by2 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 ) k1
L(k) = ( 0 I 0 ) s
( 0 v I ) nks+1
k1 s nks+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 chetf2.f.
Author
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Version 3.4.2 Tue Sep 25 2012 chetf2.f(3) 
