1SGEQL2(1)                LAPACK routine (version 3.2)                SGEQL2(1)
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NAME

6       SGEQL2 - computes a QL factorization of a real m by n matrix A
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SYNOPSIS

9       SUBROUTINE SGEQL2( 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       SGEQL2  computes  a QL factorization of a real m by n matrix A: A = Q *
17       L.
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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, if m >= n,  the  lower
28               triangle  of  the  subarray  A(m-n+1:m,1:n) contains the n by n
29               lower triangular matrix L; if m <= n, the elements on and below
30               the (n-m)-th superdiagonal contain the m by n lower trapezoidal
31               matrix L; the remaining elements, with the array TAU, represent
32               the  orthogonal  matrix Q as a product of elementary reflectors
33               (see Further Details).  LDA      (input)  INTEGER  The  leading
34               dimension 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
48          Q = H(k) . . . H(2) H(1), where k = min(m,n).
49       Each H(i) has the form
50          H(i) = I - tau * v * v'
51       where tau is a real scalar, and v is a real vector with
52       v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored  on  exit  in
53       A(1:m-k+i-1,n-k+i), and tau in TAU(i).
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57 LAPACK routine (version 3.2)    November 2008                       SGEQL2(1)