1SGEQR2(1)                LAPACK routine (version 3.1)                SGEQR2(1)
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NAME

6       SGEQR2 - a QR factorization of a real m by n matrix A
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SYNOPSIS

9       SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO )
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11           INTEGER        INFO, LDA, M, N
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13           REAL           A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       SGEQR2  computes  a QR factorization of a real m by n matrix A: A = Q *
17       R.
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ARGUMENTS

21       M       (input) INTEGER
22               The number of rows of the matrix A.  M >= 0.
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24       N       (input) INTEGER
25               The number of columns of the matrix A.  N >= 0.
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27       A       (input/output) REAL array, dimension (LDA,N)
28               On entry, the m by n matrix A.  On exit, the  elements  on  and
29               above the diagonal of the array contain the min(m,n) by n upper
30               trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
31               elements  below the diagonal, with the array TAU, represent the
32               orthogonal matrix Q as a product of elementary reflectors  (see
33               Further  Details).   LDA     (input) INTEGER The leading dimen‐
34               sion of the array A.  LDA >= max(1,M).
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36       TAU     (output) REAL array, dimension (min(M,N))
37               The scalar factors of the elementary  reflectors  (see  Further
38               Details).
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40       WORK    (workspace) REAL array, dimension (N)
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42       INFO    (output) INTEGER
43               = 0: successful exit
44               < 0: if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

47       The matrix Q is represented as a product of elementary reflectors
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49          Q = H(1) H(2) . . . H(k), where k = min(m,n).
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51       Each H(i) has the form
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53          H(i) = I - tau * v * v'
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55       where tau is a real scalar, and v is a real vector with
56       v(1:i-1)  =  0  and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
57       and tau in TAU(i).
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62 LAPACK routine (version 3.1)    November 2006                       SGEQR2(1)
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