1SGEQRF(1)                LAPACK routine (version 3.2)                SGEQRF(1)
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NAME

6       SGEQRF - computes a QR factorization of a real M-by-N matrix A
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SYNOPSIS

9       SUBROUTINE SGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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11           INTEGER        INFO, LDA, LWORK, M, N
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13           REAL           A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       SGEQRF  computes  a QR factorization of a real M-by-N matrix A: A = Q *
17       R.
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ARGUMENTS

20       M       (input) INTEGER
21               The number of rows of the matrix A.  M >= 0.
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23       N       (input) INTEGER
24               The number of columns of the matrix A.  N >= 0.
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26       A       (input/output) REAL array, dimension (LDA,N)
27               On entry, the M-by-N matrix A.  On exit, the  elements  on  and
28               above the diagonal of the array contain the min(M,N)-by-N upper
29               trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
30               elements  below the diagonal, with the array TAU, represent the
31               orthogonal matrix Q as a product of min(m,n) elementary reflec‐
32               tors (see Further Details).
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34       LDA     (input) INTEGER
35               The leading dimension of the array A.  LDA >= max(1,M).
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37       TAU     (output) REAL array, dimension (min(M,N))
38               The  scalar  factors  of the elementary reflectors (see Further
39               Details).
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41       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
42               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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44       LWORK   (input) INTEGER
45               The dimension of the array WORK.  LWORK >= max(1,N).  For opti‐
46               mum  performance  LWORK >= N*NB, where NB is the optimal block‐
47               size.  If LWORK = -1, then a workspace query  is  assumed;  the
48               routine  only  calculates  the  optimal size of the WORK array,
49               returns this value as the first entry of the WORK array, and no
50               error message related to LWORK is issued by XERBLA.
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52       INFO    (output) INTEGER
53               = 0:  successful exit
54               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

57       The matrix Q is represented as a product of elementary reflectors
58          Q = H(1) H(2) . . . H(k), where k = min(m,n).
59       Each H(i) has the form
60          H(i) = I - tau * v * v'
61       where tau is a real scalar, and v is a real vector with
62       v(1:i-1)  =  0  and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
63       and tau in TAU(i).
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67 LAPACK routine (version 3.2)    November 2008                       SGEQRF(1)