zgeqr2()

subroutine zgeqr2	(	integer	M,
		integer	N,
		complex*16, dimension( lda, * )	A,
		integer	LDA,
		complex*16, dimension( * )	TAU,
		complex*16, dimension( * )	WORK,
		integer	INFO
	)

ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Download ZGEQR2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 ZGEQR2 computes a QR factorization of a complex m-by-n matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a m-by-m orthogonal matrix;
    R is an upper-triangular n-by-n matrix;
    0 is a (m-n)-by-n 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*16 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 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*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	WORK	WORK is COMPLEX*16 array, dimension (N)
[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(1) H(2) . . . H(k), 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; v(i+1:m) is stored on exit in A(i+1:m,i),
  and tau in TAU(i).

Definition at line 132 of file zgeqr2.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*16         A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      parameter( one = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, K
      COMPLEX*16         ALPHA
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zlarf, zlarfg
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dconjg, 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( 'ZGEQR2', -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 zlarfg( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
     $                tau( i ) )
         IF( i.LT.n ) THEN
*
*           Apply H(i)**H to A(i:m,i+1:n) from the left
*
            alpha = a( i, i )
            a( i, i ) = one
            CALL zlarf( 'Left', m-i+1, n-i, a( i, i ), 1,
     $                  dconjg( tau( i ) ), a( i, i+1 ), lda, work )
            a( i, i ) = alpha
         END IF
   10 CONTINUE
      RETURN
*
*     End of ZGEQR2
*

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