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version 1.9, 2011/11/21 20:43:23
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*> \brief \b ZTZRZF |
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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 ZTZRZF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztzrzf.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/ztzrzf.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/ztzrzf.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 ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDA, LWORK, M, N |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
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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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*> ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A |
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*> to upper triangular form by means of unitary transformations. |
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*> |
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*> The upper trapezoidal matrix A is factored as |
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*> |
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*> A = ( R 0 ) * Z, |
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*> |
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*> where Z is an N-by-N unitary matrix and R is an M-by-M upper |
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*> triangular matrix. |
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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] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix A. M >= 0. |
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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 number of columns of the matrix A. N >= M. |
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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 leading M-by-N upper trapezoidal part of the |
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*> array A must contain the matrix to be factorized. |
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*> On exit, the leading M-by-M upper triangular part of A |
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*> contains the upper triangular matrix R, and elements M+1 to |
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*> N of the first M rows of A, with the array TAU, represent the |
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*> unitary matrix Z as a product of M elementary reflectors. |
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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,M). |
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*> \endverbatim |
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*> |
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*> \param[out] TAU |
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*> \verbatim |
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*> TAU is COMPLEX*16 array, dimension (M) |
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*> The scalar factors of the elementary reflectors. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LWORK |
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*> \verbatim |
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*> LWORK is INTEGER |
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*> The dimension of the array WORK. LWORK >= max(1,M). |
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*> For optimum performance LWORK >= M*NB, where NB is |
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*> the optimal blocksize. |
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*> |
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*> If LWORK = -1, then a workspace query is assumed; the routine |
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*> only calculates the optimal size of the WORK array, returns |
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*> this value as the first entry of the WORK array, and no error |
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*> message related to LWORK is issued by XERBLA. |
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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 = -i, the i-th argument had an illegal value |
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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 November 2011 |
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* |
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*> \ingroup complex16OTHERcomputational |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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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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*> The factorization is obtained by Householder's method. The kth |
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*> transformation matrix, Z( k ), which is used to introduce zeros into |
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*> the ( m - k + 1 )th row of A, is given in the form |
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*> |
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*> Z( k ) = ( I 0 ), |
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*> ( 0 T( k ) ) |
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*> |
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*> where |
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*> |
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*> T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), |
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*> ( 0 ) |
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*> ( z( k ) ) |
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*> |
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*> tau is a scalar and z( k ) is an ( n - m ) element vector. |
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*> tau and z( k ) are chosen to annihilate the elements of the kth row |
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*> of X. |
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*> |
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*> The scalar tau is returned in the kth element of TAU and the vector |
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*> u( k ) in the kth row of A, such that the elements of z( k ) are |
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*> in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in |
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*> the upper triangular part of A. |
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*> |
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*> Z is given by |
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*> |
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*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.3.1) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- 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 -- |
* November 2011 |
* @precisions normal z -> s d c |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, LWORK, M, N |
INTEGER INFO, LDA, LWORK, M, N |
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COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
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* ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A |
|
* to upper triangular form by means of unitary transformations. |
|
* |
|
* The upper trapezoidal matrix A is factored as |
|
* |
|
* A = ( R 0 ) * Z, |
|
* |
|
* where Z is an N-by-N unitary matrix and R is an M-by-M upper |
|
* triangular matrix. |
|
* |
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* Arguments |
|
* ========= |
|
* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= M. |
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* |
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* A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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* On entry, the leading M-by-N upper trapezoidal part of the |
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* array A must contain the matrix to be factorized. |
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* On exit, the leading M-by-M upper triangular part of A |
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* contains the upper triangular matrix R, and elements M+1 to |
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* N of the first M rows of A, with the array TAU, represent the |
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* unitary matrix Z as a product of M elementary reflectors. |
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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,M). |
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* |
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* TAU (output) COMPLEX*16 array, dimension (M) |
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* The scalar factors of the elementary reflectors. |
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* |
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* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. LWORK >= max(1,M). |
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* For optimum performance LWORK >= M*NB, where NB is |
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* the optimal blocksize. |
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* |
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* If LWORK = -1, then a workspace query is assumed; the routine |
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* only calculates the optimal size of the WORK array, returns |
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* this value as the first entry of the WORK array, and no error |
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* message related to LWORK is issued by XERBLA. |
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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 = -i, the i-th argument had an illegal value |
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* |
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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
|
* |
|
* The factorization is obtained by Householder's method. The kth |
|
* transformation matrix, Z( k ), which is used to introduce zeros into |
|
* the ( m - k + 1 )th row of A, is given in the form |
|
* |
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* Z( k ) = ( I 0 ), |
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* ( 0 T( k ) ) |
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* |
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* where |
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* |
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* T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), |
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* ( 0 ) |
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* ( z( k ) ) |
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* |
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* tau is a scalar and z( k ) is an ( n - m ) element vector. |
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* tau and z( k ) are chosen to annihilate the elements of the kth row |
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* of X. |
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* |
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* The scalar tau is returned in the kth element of TAU and the vector |
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* u( k ) in the kth row of A, such that the elements of z( k ) are |
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* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in |
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* the upper triangular part of A. |
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* |
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* Z is given by |
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* |
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* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |