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    1: *> \brief \b ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZGEQR2 + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqr2.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqr2.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqr2.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INFO, LDA, M, N
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   28: *       ..
   29: *
   30: *
   31: *> \par Purpose:
   32: *  =============
   33: *>
   34: *> \verbatim
   35: *>
   36: *> ZGEQR2 computes a QR factorization of a complex m-by-n matrix A:
   37: *>
   38: *>    A = Q * ( R ),
   39: *>            ( 0 )
   40: *>
   41: *> where:
   42: *>
   43: *>    Q is a m-by-m orthogonal matrix;
   44: *>    R is an upper-triangular n-by-n matrix;
   45: *>    0 is a (m-n)-by-n zero matrix, if m > n.
   46: *>
   47: *> \endverbatim
   48: *
   49: *  Arguments:
   50: *  ==========
   51: *
   52: *> \param[in] M
   53: *> \verbatim
   54: *>          M is INTEGER
   55: *>          The number of rows of the matrix A.  M >= 0.
   56: *> \endverbatim
   57: *>
   58: *> \param[in] N
   59: *> \verbatim
   60: *>          N is INTEGER
   61: *>          The number of columns of the matrix A.  N >= 0.
   62: *> \endverbatim
   63: *>
   64: *> \param[in,out] A
   65: *> \verbatim
   66: *>          A is COMPLEX*16 array, dimension (LDA,N)
   67: *>          On entry, the m by n matrix A.
   68: *>          On exit, the elements on and above the diagonal of the array
   69: *>          contain the min(m,n) by n upper trapezoidal matrix R (R is
   70: *>          upper triangular if m >= n); the elements below the diagonal,
   71: *>          with the array TAU, represent the unitary matrix Q as a
   72: *>          product of elementary reflectors (see Further Details).
   73: *> \endverbatim
   74: *>
   75: *> \param[in] LDA
   76: *> \verbatim
   77: *>          LDA is INTEGER
   78: *>          The leading dimension of the array A.  LDA >= max(1,M).
   79: *> \endverbatim
   80: *>
   81: *> \param[out] TAU
   82: *> \verbatim
   83: *>          TAU is COMPLEX*16 array, dimension (min(M,N))
   84: *>          The scalar factors of the elementary reflectors (see Further
   85: *>          Details).
   86: *> \endverbatim
   87: *>
   88: *> \param[out] WORK
   89: *> \verbatim
   90: *>          WORK is COMPLEX*16 array, dimension (N)
   91: *> \endverbatim
   92: *>
   93: *> \param[out] INFO
   94: *> \verbatim
   95: *>          INFO is INTEGER
   96: *>          = 0: successful exit
   97: *>          < 0: if INFO = -i, the i-th argument had an illegal value
   98: *> \endverbatim
   99: *
  100: *  Authors:
  101: *  ========
  102: *
  103: *> \author Univ. of Tennessee
  104: *> \author Univ. of California Berkeley
  105: *> \author Univ. of Colorado Denver
  106: *> \author NAG Ltd.
  107: *
  108: *> \ingroup complex16GEcomputational
  109: *
  110: *> \par Further Details:
  111: *  =====================
  112: *>
  113: *> \verbatim
  114: *>
  115: *>  The matrix Q is represented as a product of elementary reflectors
  116: *>
  117: *>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
  118: *>
  119: *>  Each H(i) has the form
  120: *>
  121: *>     H(i) = I - tau * v * v**H
  122: *>
  123: *>  where tau is a complex scalar, and v is a complex vector with
  124: *>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
  125: *>  and tau in TAU(i).
  126: *> \endverbatim
  127: *>
  128: *  =====================================================================
  129:       SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
  130: *
  131: *  -- LAPACK computational routine --
  132: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  133: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  134: *
  135: *     .. Scalar Arguments ..
  136:       INTEGER            INFO, LDA, M, N
  137: *     ..
  138: *     .. Array Arguments ..
  139:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
  140: *     ..
  141: *
  142: *  =====================================================================
  143: *
  144: *     .. Parameters ..
  145:       COMPLEX*16         ONE
  146:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
  147: *     ..
  148: *     .. Local Scalars ..
  149:       INTEGER            I, K
  150:       COMPLEX*16         ALPHA
  151: *     ..
  152: *     .. External Subroutines ..
  153:       EXTERNAL           XERBLA, ZLARF, ZLARFG
  154: *     ..
  155: *     .. Intrinsic Functions ..
  156:       INTRINSIC          DCONJG, MAX, MIN
  157: *     ..
  158: *     .. Executable Statements ..
  159: *
  160: *     Test the input arguments
  161: *
  162:       INFO = 0
  163:       IF( M.LT.0 ) THEN
  164:          INFO = -1
  165:       ELSE IF( N.LT.0 ) THEN
  166:          INFO = -2
  167:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
  168:          INFO = -4
  169:       END IF
  170:       IF( INFO.NE.0 ) THEN
  171:          CALL XERBLA( 'ZGEQR2', -INFO )
  172:          RETURN
  173:       END IF
  174: *
  175:       K = MIN( M, N )
  176: *
  177:       DO 10 I = 1, K
  178: *
  179: *        Generate elementary reflector H(i) to annihilate A(i+1:m,i)
  180: *
  181:          CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
  182:      $                TAU( I ) )
  183:          IF( I.LT.N ) THEN
  184: *
  185: *           Apply H(i)**H to A(i:m,i+1:n) from the left
  186: *
  187:             ALPHA = A( I, I )
  188:             A( I, I ) = ONE
  189:             CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
  190:      $                  DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
  191:             A( I, I ) = ALPHA
  192:          END IF
  193:    10 CONTINUE
  194:       RETURN
  195: *
  196: *     End of ZGEQR2
  197: *
  198:       END