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+ SUBROUTINE DGEQR2( 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
+* =======
+*
+* DGEQR2 computes a QR factorization of a real m by n matrix A:
+* A = Q * R.
+*
+* 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, the elements on and above the diagonal of the array
+* contain the min(m,n) by n upper trapezoidal matrix R (R is
+* upper triangular if m >= n); the elements below the diagonal,
+* 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(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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,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( 'DGEQR2', -INFO )
+ RETURN
+ END IF
+*
+ K = MIN( M, N )
+*
+ DO 10 I = 1, K
+*
+* Generate elementary reflector H(i) to annihilate A(i+1:m,i)
+*
+ CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
+ $ TAU( I ) )
+ IF( I.LT.N ) THEN
+*
+* Apply H(i) to A(i:m,i+1:n) from the left
+*
+ AII = A( I, I )
+ A( I, I ) = ONE
+ CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
+ $ A( I, I+1 ), LDA, WORK )
+ A( I, I ) = AII
+ END IF
+ 10 CONTINUE
+ RETURN
+*
+* End of DGEQR2
+*
+ END