chetrf-f(3)

chetrf.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

CHETRF

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:

UPLO

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

 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.

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.

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 = 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 chetrf.f.

Author

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