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version 1.13, 2012/12/14 14:22:47
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*> \brief \b ZHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm). |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZHETF2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetf2.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetf2.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetf2.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, LDA, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* COMPLEX*16 A( LDA, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZHETF2 computes the factorization of a complex Hermitian matrix A |
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*> using the Bunch-Kaufman diagonal pivoting method: |
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*> |
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*> A = U*D*U**H or A = L*D*L**H |
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*> |
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*> where U (or L) is a product of permutation and unit upper (lower) |
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*> triangular matrices, U**H is the conjugate transpose of U, and D is |
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*> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. |
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*> |
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*> This is the unblocked version of the algorithm, calling Level 2 BLAS. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> Specifies whether the upper or lower triangular part of the |
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*> Hermitian matrix A is stored: |
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*> = 'U': Upper triangular |
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*> = 'L': Lower triangular |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension (LDA,N) |
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*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading |
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*> n-by-n upper triangular part of A contains the upper |
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*> triangular part of the matrix A, and the strictly lower |
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*> triangular part of A is not referenced. If UPLO = 'L', the |
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*> leading n-by-n lower triangular part of A contains the lower |
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*> triangular part of the matrix A, and the strictly upper |
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*> triangular part of A is not referenced. |
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*> |
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*> On exit, the block diagonal matrix D and the multipliers used |
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*> to obtain the factor U or L (see below for further details). |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] IPIV |
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*> \verbatim |
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*> IPIV is INTEGER array, dimension (N) |
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*> Details of the interchanges and the block structure of D. |
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*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were |
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*> interchanged and D(k,k) is a 1-by-1 diagonal block. |
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*> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and |
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*> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) |
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*> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = |
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*> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were |
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*> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -k, the k-th argument had an illegal value |
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*> > 0: if INFO = k, D(k,k) is exactly zero. The factorization |
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*> has been completed, but the block diagonal matrix D is |
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*> exactly singular, and division by zero will occur if it |
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*> is used to solve a system of equations. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date September 2012 |
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* |
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*> \ingroup complex16HEcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> If UPLO = 'U', then A = U*D*U**H, where |
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*> U = P(n)*U(n)* ... *P(k)U(k)* ..., |
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*> i.e., U is a product of terms P(k)*U(k), where k decreases from n to |
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*> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as |
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*> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such |
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*> that if the diagonal block D(k) is of order s (s = 1 or 2), then |
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*> |
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*> ( I v 0 ) k-s |
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*> U(k) = ( 0 I 0 ) s |
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*> ( 0 0 I ) n-k |
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*> k-s s n-k |
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*> |
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*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). |
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*> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), |
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*> and A(k,k), and v overwrites A(1:k-2,k-1:k). |
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*> |
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*> If UPLO = 'L', then A = L*D*L**H, where |
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*> L = P(1)*L(1)* ... *P(k)*L(k)* ..., |
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*> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to |
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*> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as |
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*> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such |
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*> that if the diagonal block D(k) is of order s (s = 1 or 2), then |
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*> |
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*> ( I 0 0 ) k-1 |
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*> L(k) = ( 0 I 0 ) s |
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*> ( 0 v I ) n-k-s+1 |
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*> k-1 s n-k-s+1 |
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*> |
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*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). |
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*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), |
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*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). |
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*> \endverbatim |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> \verbatim |
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*> 09-29-06 - patch from |
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*> Bobby Cheng, MathWorks |
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*> |
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*> Replace l.210 and l.393 |
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*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN |
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*> by |
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*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN |
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*> |
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*> 01-01-96 - Based on modifications by |
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*> J. Lewis, Boeing Computer Services Company |
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*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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*> \endverbatim |
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* |
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* ===================================================================== |
SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO ) |
SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO ) |
* |
* |
* -- LAPACK routine (version 3.3.1) -- |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- April 2011 -- |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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COMPLEX*16 A( LDA, * ) |
COMPLEX*16 A( LDA, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
|
* |
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* ZHETF2 computes the factorization of a complex Hermitian matrix A |
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* using the Bunch-Kaufman diagonal pivoting method: |
|
* |
|
* A = U*D*U**H or A = L*D*L**H |
|
* |
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* 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. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
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* UPLO (input) CHARACTER*1 |
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* Specifies whether the upper or lower triangular part of the |
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* Hermitian matrix A is stored: |
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* = 'U': Upper triangular |
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* = 'L': Lower triangular |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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* On entry, the Hermitian matrix A. If UPLO = 'U', the leading |
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* n-by-n upper triangular part of A contains the upper |
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* triangular part of the matrix A, and the strictly lower |
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* triangular part of A is not referenced. If UPLO = 'L', the |
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* leading n-by-n lower triangular part of A contains the lower |
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* triangular part of the matrix A, and the strictly upper |
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* triangular part of A is not referenced. |
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* |
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* On exit, the block diagonal matrix D and the multipliers used |
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* to obtain the factor U or L (see below for further details). |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* IPIV (output) INTEGER array, dimension (N) |
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* Details of the interchanges and the block structure of D. |
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* If IPIV(k) > 0, then rows and columns k and IPIV(k) were |
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* interchanged and D(k,k) is a 1-by-1 diagonal block. |
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* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and |
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* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) |
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* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = |
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* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were |
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* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -k, the k-th argument had an illegal value |
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* > 0: if INFO = k, D(k,k) is exactly zero. The factorization |
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* has been completed, but the block diagonal matrix D is |
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* exactly singular, and division by zero will occur if it |
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* is used to solve a system of equations. |
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* |
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* Further Details |
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* =============== |
|
* |
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* 09-29-06 - patch from |
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* Bobby Cheng, MathWorks |
|
* |
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* Replace l.210 and l.393 |
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* IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN |
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* by |
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* IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN |
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* |
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* 01-01-96 - Based on modifications by |
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* J. Lewis, Boeing Computer Services Company |
|
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
|
* |
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* If UPLO = 'U', then A = U*D*U**H, where |
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* U = P(n)*U(n)* ... *P(k)U(k)* ..., |
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* i.e., U is a product of terms P(k)*U(k), where k decreases from n to |
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* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as |
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* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such |
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* that if the diagonal block D(k) is of order s (s = 1 or 2), then |
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* |
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* ( I v 0 ) k-s |
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* U(k) = ( 0 I 0 ) s |
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* ( 0 0 I ) n-k |
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* k-s s n-k |
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* |
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* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). |
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* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), |
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* and A(k,k), and v overwrites A(1:k-2,k-1:k). |
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* |
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* If UPLO = 'L', then A = L*D*L**H, where |
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* L = P(1)*L(1)* ... *P(k)*L(k)* ..., |
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* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to |
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* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as |
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* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such |
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* that if the diagonal block D(k) is of order s (s = 1 or 2), then |
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* |
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* ( I 0 0 ) k-1 |
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* L(k) = ( 0 I 0 ) s |
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* ( 0 v I ) n-k-s+1 |
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* k-1 s n-k-s+1 |
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* |
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* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). |
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* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), |
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* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |