◆ cgelq2()

subroutine cgelq2	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( * )	WORK,
		integer	INFO
	)

CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Download CGELQ2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 CGELQ2 computes an LQ factorization of a complex m-by-n matrix A:

    A = ( L 0 ) *  Q

 where:

    Q is a n-by-n orthogonal matrix;
    L is an lower-triangular m-by-m matrix;
    0 is a m-by-(n-m) zero matrix, if m < n.

Parameters

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	A	A is COMPLEX 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).
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	TAU	TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	WORK	WORK is COMPLEX array, dimension (M)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date: November 2019

Further Details:

  The matrix Q is represented as a product of elementary reflectors

     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  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).

Definition at line 131 of file cgelq2.f.

 *
 *  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N
 *     ..
 *     .. Array Arguments ..
       COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
 *     ..
 *
 *  =====================================================================
 *
 *     .. Parameters ..
       COMPLEX            ONE
       parameter( one = ( 1.0e+0, 0.0e+0 ) )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, K
       COMPLEX            ALPHA
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           clacgv, clarf, clarfg, 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( 'CGELQ2', -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 clacgv( n-i+1, a( i, i ), lda )
          alpha = a( i, i )
          CALL clarfg( 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 clarf( '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 clacgv( n-i+1, a( i, i ), lda )
    10 CONTINUE
       RETURN
 *
 *     End of CGELQ2
 *

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