version 1.9, 2011/11/21 20:43:23
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version 1.11, 2012/07/31 11:06:40
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*> \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 |
* |
* |
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*> |
*> |
*> \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 |
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*> the ( m - k + 1 )th row of A, is given in the form |
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*> |
*> |
*> Z( k ) = ( I 0 ), |
*> Z = Z(1)*Z(2)* ... *Z(M) |
*> ( 0 T( k ) ) |
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*> |
*> |
*> 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 ) |
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*> ( z( k ) ) |
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*> |
*> |
*> 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 |
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*> of X. |
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*> |
*> |
*> 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 |
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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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*> |
*> |
*> Z is given by |
*> I is the M-by-M identity matrix, A(:,M+1:N) |
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*> is the output stored in A on exit from DTZRZF, |
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*> and tau(k) is the kth element of the array TAU. |
*> |
*> |
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). |
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*> \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 3.4.1) -- |
* -- 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 |