chetf2-f(3)

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 Bunch-Kaufman 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 1-by-1 and 2-by-2 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 is INTEGER
 The order of the matrix A. N >= 0.

 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 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.

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -k, the k-th 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:

 09-29-06 - 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
 01-01-96 - 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 = H(n)*H(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 chetf2.f.

Author

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