The OpenNET Project / Index page

[ новости /+++ | форум | теги | ]

Интерактивная система просмотра системных руководств (man-ов)

 ТемаНаборКатегория 
 
 [Cписок руководств | Печать]

sgebd2 (3)
  • >> sgebd2 (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sgebd2 - reduce a real general m by n matrix A to  upper  or
         lower bidiagonal form B by an orthogonal transformation
    
    SYNOPSIS
         SUBROUTINE SGEBD2( M, N, A, LDA, D,  E,  TAUQ,  TAUP,  WORK,
                   INFO )
    
         INTEGER INFO, LDA, M, N
    
         REAL A( LDA, * ), D( * ), E( * ), TAUP(  *  ),  TAUQ(  *  ),
                   WORK( * )
    
    
    
         #include <sunperf.h>
    
         void sgebd2(int m, int n, float  *sa,  int  lda,  float  *d,
                   float *e, float *tauq, float *taup, int *info) ;
    
    PURPOSE
         SGEBD2 reduces a real general m by n matrix A  to  upper  or
         lower  bidiagonal form B by an orthogonal transformation: Q'
         * A * P = B.
    
         If m >= n, B is upper bidiagonal; if m < n, B is lower bidi-
         agonal.
    
    
    ARGUMENTS
         M         (input) INTEGER
                   The number of rows in the matrix A.  M >= 0.
    
         N         (input) INTEGER
                   The number of columns in the matrix A.  N >= 0.
    
         A         (input/output) REAL array, dimension (LDA,N)
                   On entry, the m by n general matrix to be reduced.
                   On  exit,  if  m  >= n, the diagonal and the first
                   superdiagonal are overwritten with the upper bidi-
                   agonal  matrix B; the elements below the diagonal,
                   with the  array  TAUQ,  represent  the  orthogonal
                   matrix  Q  as  a product of elementary reflectors,
                   and the elements above  the  first  superdiagonal,
                   with  the  array  TAUP,  represent  the orthogonal
                   matrix P as a product of elementary reflectors; if
                   m  < n, the diagonal and the first subdiagonal are
                   overwritten with the lower  bidiagonal  matrix  B;
                   the elements below the first subdiagonal, with the
                   array TAUQ, represent the orthogonal matrix Q as a
                   product of elementary reflectors, and the elements
                   above the diagonal, with the array TAUP, represent
                   the orthogonal matrix P as a product of elementary
                   reflectors.  See Further Details.  LDA     (input)
                   INTEGER The leading dimension of the array A.  LDA
                   >= max(1,M).
    
         D         (output) REAL array, dimension (min(M,N))
                   The diagonal elements of the bidiagonal matrix  B:
                   D(i) = A(i,i).
    
         E         (output) REAL array, dimension (min(M,N)-1)
                   The off-diagonal elements of the bidiagonal matrix
                   B:   if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-
                   1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
    
         TAUQ      (output) REAL array dimension (min(M,N))
                   The scalar factors of  the  elementary  reflectors
                   which  represent  the  orthogonal  matrix  Q.  See
                   Further Details.   TAUP     (output)  REAL  array,
                   dimension  (min(M,N))  The  scalar  factors of the
                   elementary reflectors which represent the orthogo-
                   nal   matrix   P.   See   Further  Details.   WORK
                   (workspace) REAL array, dimension (max(M,N))
    
         INFO      (output) INTEGER
                   = 0: successful exit.
                   < 0: if INFO = -i, the i-th argument had an  ille-
                   gal value.
    
    FURTHER DETAILS
         The matrices Q and P are represented as products of  elemen-
         tary reflectors:
    
         If m >= n,
    
            Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
    
         Each H(i) and G(i) has the form:
    
            H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
    
         where tauq and taup are real scalars, and v and u  are  real
         vectors;  v(1:i-1)  = 0, v(i) = 1, and v(i+1:m) is stored on
         exit in A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n)  is
         stored  on exit in A(i,i+2:n); tauq is stored in TAUQ(i) and
         taup in TAUP(i).
    
         If m < n,
    
            Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
    
         Each H(i) and G(i) has the form:
    
            H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
    
         where tauq and taup are real scalars, and v and u  are  real
         vectors;  v(1:i)  = 0, v(i+1) = 1, and v(i+2:m) is stored on
         exit in A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n)  is
         stored  on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and
         taup in TAUP(i).
    
         The contents of A on exit are illustrated by  the  following
         examples:
    
         m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
    
           (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
           (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
           (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
           (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
           (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
           (  v1  v2  v3  v4  v5 )
    
         where d and e denote diagonal and off-diagonal  elements  of
         B, vi denotes an element of the vector defining H(i), and ui
         an element of the vector defining G(i).
    
    
    
    


    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