
zsytf2.f(3) LAPACK zsytf2.f(3)
NAME
zsytf2.f 
SYNOPSIS
Functions/Subroutines
subroutine zsytf2 (UPLO, N, A, LDA, IPIV, INFO)
ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the
diagonal pivoting method (unblocked algorithm).
Function/Subroutine Documentation
subroutine zsytf2 (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA,
integer, dimension( * )IPIV, integerINFO)
ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the
diagonal pivoting method (unblocked algorithm).
Purpose:
ZSYTF2 computes the factorization of a complex symmetric matrix A
using the BunchKaufman 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, U**T is the transpose of U, and D is symmetric 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
symmetric 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*16 array, dimension (LDA,N)
On entry, the symmetric 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:
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 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**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 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).
Contributors:
092906  patch from
Bobby Cheng, MathWorks
Replace l.209 and l.377
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
by
IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
196  Based on modifications by J. Lewis, Boeing Computer Services
Company
Definition at line 183 of file zsytf2.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 zsytf2.f(3) 
