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author | james <james@8a072113-8704-0410-8d35-dd094bca7971> | 2011-12-08 23:55:05 +0000 |
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committer | james <james@8a072113-8704-0410-8d35-dd094bca7971> | 2011-12-08 23:55:05 +0000 |
commit | 2a41d09a428b2b1c77650a636ca7dffae6127b43 (patch) | |
tree | 6aff2da2a20c611f40eca256185ab8d2f6f6aaf6 /SRC/dtzrzf.f | |
parent | 5517e6dae18bc1db1454ede87e50ddfce4ee5e5b (diff) |
corrected documentation
Diffstat (limited to 'SRC/dtzrzf.f')
-rw-r--r-- | SRC/dtzrzf.f | 27 |
1 files changed, 9 insertions, 18 deletions
diff --git a/SRC/dtzrzf.f b/SRC/dtzrzf.f index 7177de09..520a60bd 100644 --- a/SRC/dtzrzf.f +++ b/SRC/dtzrzf.f @@ -130,31 +130,22 @@ *> *> \verbatim *> -*> 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 +*> The N-by-N matrix Z can be computed by *> -*> Z( k ) = ( I 0 ), -*> ( 0 T( k ) ) +*> Z = Z(1)*Z(2)* ... *Z(M) *> -*> where +*> where each N-by-N Z(k) is given by *> -*> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), -*> ( 0 ) -*> ( z( k ) ) +*> Z(k) = I - tau(k)*v(k)*v(k)**T *> -*> tau is a scalar and z( k ) is an ( n - m ) element vector. -*> tau and z( k ) are chosen to annihilate the elements of the kth row -*> of X. +*> with v(k) is the kth row vector of the M-by-N matrix *> -*> The scalar tau is returned in the kth element of TAU and the vector -*> 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. +*> V = ( I A(:,M+1:N) ) *> -*> 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 *> * ===================================================================== |