The OpenNET Project / Index page

[ новости /+++ | форум | теги | ]

Интерактивная система просмотра системных руководств (man-ов)

 ТемаНаборКатегория 
 
 [Cписок руководств | Печать]

dtzrqf (3)
  • >> dtzrqf (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dtzrqf - reduce the M-by-N ( M<=N ) real  upper  trapezoidal
         matrix  A  to  upper  triangular form by means of orthogonal
         transformations
    
    SYNOPSIS
         SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO )
    
         INTEGER INFO, LDA, M, N
    
         DOUBLE PRECISION A( LDA, * ), TAU( * )
    
    
    
         #include <sunperf.h>
    
         void dtzrqf(int m, int n, double *da, int lda, double  *tau,
                   int *info) ;
    
    PURPOSE
         DTZRQF reduces the M-by-N ( M<=N )  real  upper  trapezoidal
         matrix  A  to  upper  triangular form by means of orthogonal
         transformations.
    
         The upper trapezoidal matrix A is factored as
    
            A = ( R  0 ) * Z,
    
         where Z is an N-by-N orthogonal matrix and R  is  an  M-by-M
         upper triangular matrix.
    
    
    ARGUMENTS
         M         (input) INTEGER
                   The number of rows of the matrix A.  M >= 0.
    
         N         (input) INTEGER
                   The number of columns of the matrix A.  N >= M.
    
         A         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDA,N)
                   On entry, the  leading  M-by-N  upper  trapezoidal
                   part  of the array A must contain the matrix to be
                   factorized.  On exit,  the  leading  M-by-M  upper
                   triangular part of A contains the upper triangular
                   matrix R, and elements M+1 to N  of  the  first  M
                   rows  of  A,  with  the  array  TAU, represent the
                   orthogonal matrix Z as a product of  M  elementary
                   reflectors.
    
         LDA       (input) INTEGER
                   The leading dimension of  the  array  A.   LDA  >=
                   max(1,M).
    
         TAU       (output) DOUBLE PRECISION array, dimension (M)
                   The scalar factors of the elementary reflectors.
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
    
    FURTHER DETAILS
         The factorization is obtained by Householder's method.   The
         kth  transformation  matrix, Z( k ), which is used to intro-
         duce zeros into the ( m - k + 1 )th row of A,  is  given  in
         the form
    
            Z( k ) = ( I     0   ),
                     ( 0  T( k ) )
    
         where
    
            T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
                                                        (   0    )
                                                        ( z( k ) )
    
         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.
    
         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.
    
         Z is given by
    
            Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
    
    
    
    


    Поиск по тексту MAN-ов: 




    Партнёры:
    PostgresPro
    Inferno Solutions
    Hosting by Hoster.ru
    Хостинг:

    Закладки на сайте
    Проследить за страницей
    Created 1996-2024 by Maxim Chirkov
    Добавить, Поддержать, Вебмастеру