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SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DGEQL2 computes a QL factorization of a real m by n matrix A:
* A = Q * L.
*
* 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, if m >= n, the lower triangle of the subarray
* A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
* if m <= n, the elements on and below the (n-m)-th
* superdiagonal contain the m by n lower trapezoidal matrix L;
* the remaining elements, 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) DOUBLE PRECISION array, dimension (N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal 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**T
*
* where tau is a real scalar, and v is a real vector with
* v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
* A(1:m-k+i-1,n-k+i), and tau in TAU(i).
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, K
DOUBLE PRECISION AII
* ..
* .. External Subroutines ..
EXTERNAL DLARF, DLARFG, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGEQL2', -INFO )
RETURN
END IF
*
K = MIN( M, N )
*
DO 10 I = K, 1, -1
*
* Generate elementary reflector H(i) to annihilate
* A(1:m-k+i-1,n-k+i)
*
CALL DLARFG( M-K+I, A( M-K+I, N-K+I ), A( 1, N-K+I ), 1,
$ TAU( I ) )
*
* Apply H(i) to A(1:m-k+i,1:n-k+i-1) from the left
*
AII = A( M-K+I, N-K+I )
A( M-K+I, N-K+I ) = ONE
CALL DLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, TAU( I ),
$ A, LDA, WORK )
A( M-K+I, N-K+I ) = AII
10 CONTINUE
RETURN
*
* End of DGEQL2
*
END
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