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dgelqf (3)
  • >> dgelqf (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dgelqf - compute an LQ factorization of a real M-by-N matrix
         A
    
    SYNOPSIS
         SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
    
         INTEGER INFO, LDA, LWORK, M, N
    
         DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
    
    
    
         #include <sunperf.h>
    
         void dgelqf(int m, int n, double *da, int lda, double  *tau,
                   int *info) ;
    
    PURPOSE
         DGELQF computes an LQ factorization of a real M-by-N  matrix
         A:  A = L * Q.
    
    
    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 >= 0.
    
         A         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDA,N)
                   On entry, the M-by-N matrix A.  On exit, the  ele-
                   ments  on and below the diagonal of the array con-
                   tain the m-by-min(m,n) lower trapezoidal matrix  L
                   (L  is  lower  triangular if m <= n); the elements
                   above the diagonal, with the array TAU,  represent
                   the orthogonal matrix Q as a product of elementary
                   reflectors (see Further Details).  LDA     (input)
                   INTEGER The leading dimension of the array A.  LDA
                   >= max(1,M).
    
         TAU       (output)   DOUBLE   PRECISION   array,   dimension
                   (min(M,N))
                   The scalar factors of  the  elementary  reflectors
                   (see Further Details).
    
         WORK      (workspace/output) DOUBLE PRECISION array,  dimen-
                   sion (LWORK)
                   On exit, if INFO = 0, WORK(1) returns the  optimal
                   LWORK.
    
         LWORK     (input) INTEGER
                   The  dimension  of  the  array  WORK.   LWORK   >=
                   max(1,M).   For optimum performance LWORK >= M*NB,
                   where NB is the optimal blocksize.
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
    
    FURTHER DETAILS
         The matrix Q is  represented  as  a  product  of  elementary
         reflectors
    
            Q = H(k) . . . H(2) H(1), where k = min(m,n).
    
         Each H(i) has the form
    
            H(i) = I - tau * v * v'
    
         where tau is a real scalar, and v is a real vector with
         v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is  stored  on  exit  in
         A(i,i+1:n), and tau in TAU(i).
    
    
    
    


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