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SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* ZGELQ2 computes an LQ factorization of a complex m by n matrix A:
* A = L * 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) COMPLEX*16 array, dimension (LDA,N)
* On entry, the m by n matrix A.
* On exit, the elements on and below the diagonal of the array
* contain the m by min(m,n) lower trapezoidal matrix L (L is
* lower triangular if m <= n); the elements above the diagonal,
* with the array TAU, represent the unitary 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) COMPLEX*16 array, dimension (min(M,N))
* The scalar factors of the elementary reflectors (see Further
* Details).
*
* WORK (workspace) COMPLEX*16 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(k)' . . . H(2)' H(1)', where k = min(m,n).
*
* Each H(i) has the form
*
* H(i) = I - tau * v * v'
*
* where tau is a complex scalar, and v is a complex vector with
* v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
* A(i,i+1:n), and tau in TAU(i).
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, K
COMPLEX*16 ALPHA
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLACGV, ZLARF, ZLARFP
* ..
* .. 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( 'ZGELQ2', -INFO )
RETURN
END IF
*
K = MIN( M, N )
*
DO 10 I = 1, K
*
* Generate elementary reflector H(i) to annihilate A(i,i+1:n)
*
CALL ZLACGV( N-I+1, A( I, I ), LDA )
ALPHA = A( I, I )
CALL ZLARFP( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA,
$ TAU( I ) )
IF( I.LT.M ) THEN
*
* Apply H(i) to A(i+1:m,i:n) from the right
*
A( I, I ) = ONE
CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ),
$ A( I+1, I ), LDA, WORK )
END IF
A( I, I ) = ALPHA
CALL ZLACGV( N-I+1, A( I, I ), LDA )
10 CONTINUE
RETURN
*
* End of ZGELQ2
*
END
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