version 1.9, 2011/11/21 20:43:23
|
version 1.16, 2017/06/17 10:54:32
|
Line 2
|
Line 2
|
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download ZTZRZF + dependencies |
*> Download ZTZRZF + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztzrzf.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztzrzf.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztzrzf.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztzrzf.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztzrzf.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztzrzf.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
* SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER INFO, LDA, LWORK, M, N |
* INTEGER INFO, LDA, LWORK, M, N |
* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
Line 111
|
Line 111
|
* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date November 2011 |
*> \date April 2012 |
* |
* |
*> \ingroup complex16OTHERcomputational |
*> \ingroup complex16OTHERcomputational |
* |
* |
Line 130
|
Line 130
|
*> |
*> |
*> \verbatim |
*> \verbatim |
*> |
*> |
*> The factorization is obtained by Householder's method. The kth |
*> The N-by-N matrix Z can be computed by |
*> transformation matrix, Z( k ), which is used to introduce zeros into |
|
*> the ( m - k + 1 )th row of A, is given in the form |
|
*> |
*> |
*> Z( k ) = ( I 0 ), |
*> Z = Z(1)*Z(2)* ... *Z(M) |
*> ( 0 T( k ) ) |
|
*> |
*> |
*> where |
*> where each N-by-N Z(k) is given by |
*> |
*> |
*> T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), |
*> Z(k) = I - tau(k)*v(k)*v(k)**H |
*> ( 0 ) |
|
*> ( z( k ) ) |
|
*> |
*> |
*> tau is a scalar and z( k ) is an ( n - m ) element vector. |
*> with v(k) is the kth row vector of the M-by-N matrix |
*> tau and z( k ) are chosen to annihilate the elements of the kth row |
|
*> of X. |
|
*> |
*> |
*> The scalar tau is returned in the kth element of TAU and the vector |
*> V = ( I A(:,M+1:N) ) |
*> u( k ) in the kth row of A, such that the elements of z( k ) are |
|
*> in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in |
|
*> the upper triangular part of A. |
|
*> |
*> |
*> Z is given by |
*> I is the M-by-M identity matrix, A(:,M+1:N) |
|
*> is the output stored in A on exit from DTZRZF, |
|
*> and tau(k) is the kth element of the array TAU. |
*> |
*> |
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). |
|
*> \endverbatim |
*> \endverbatim |
*> |
*> |
* ===================================================================== |
* ===================================================================== |
SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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..-- |
* November 2011 |
* April 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, LWORK, M, N |
INTEGER INFO, LDA, LWORK, M, N |