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+ SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
+*
+* -- LAPACK routine (version 3.1) --
+* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+* November 2006
+*
+* .. Scalar Arguments ..
+ INTEGER INFO, LDA, M, N
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+* Purpose
+* =======
+*
+* DGERQ2 computes an RQ factorization of a real m by n matrix A:
+* A = R * 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, if m <= n, the upper triangle of the subarray
+* A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
+* if m >= n, the elements on and above the (m-n)-th subdiagonal
+* contain the m by n upper trapezoidal matrix R; 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 (M)
+*
+* 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
+* A(m-k+i,1:n-k+i-1), 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( 'DGERQ2', -INFO )
+ RETURN
+ END IF
+*
+ K = MIN( M, N )
+*
+ DO 10 I = K, 1, -1
+*
+* Generate elementary reflector H(i) to annihilate
+* A(m-k+i,1:n-k+i-1)
+*
+ CALL DLARFG( N-K+I, A( M-K+I, N-K+I ), A( M-K+I, 1 ), LDA,
+ $ TAU( I ) )
+*
+* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
+*
+ AII = A( M-K+I, N-K+I )
+ A( M-K+I, N-K+I ) = ONE
+ CALL DLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
+ $ TAU( I ), A, LDA, WORK )
+ A( M-K+I, N-K+I ) = AII
+ 10 CONTINUE
+ RETURN
+*
+* End of DGERQ2
+*
+ END