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Cohérence Lapack.

    1: *> \brief \b ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (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 ZUNGL2 + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zungl2.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zungl2.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zungl2.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INFO, K, 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: *> ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
   37: *> which is defined as the first m rows of a product of k elementary
   38: *> reflectors of order n
   39: *>
   40: *>       Q  =  H(k)**H . . . H(2)**H H(1)**H
   41: *>
   42: *> as returned by ZGELQF.
   43: *> \endverbatim
   44: *
   45: *  Arguments:
   46: *  ==========
   47: *
   48: *> \param[in] M
   49: *> \verbatim
   50: *>          M is INTEGER
   51: *>          The number of rows of the matrix Q. M >= 0.
   52: *> \endverbatim
   53: *>
   54: *> \param[in] N
   55: *> \verbatim
   56: *>          N is INTEGER
   57: *>          The number of columns of the matrix Q. N >= M.
   58: *> \endverbatim
   59: *>
   60: *> \param[in] K
   61: *> \verbatim
   62: *>          K is INTEGER
   63: *>          The number of elementary reflectors whose product defines the
   64: *>          matrix Q. M >= K >= 0.
   65: *> \endverbatim
   66: *>
   67: *> \param[in,out] A
   68: *> \verbatim
   69: *>          A is COMPLEX*16 array, dimension (LDA,N)
   70: *>          On entry, the i-th row must contain the vector which defines
   71: *>          the elementary reflector H(i), for i = 1,2,...,k, as returned
   72: *>          by ZGELQF in the first k rows of its array argument A.
   73: *>          On exit, the m by n matrix Q.
   74: *> \endverbatim
   75: *>
   76: *> \param[in] LDA
   77: *> \verbatim
   78: *>          LDA is INTEGER
   79: *>          The first dimension of the array A. LDA >= max(1,M).
   80: *> \endverbatim
   81: *>
   82: *> \param[in] TAU
   83: *> \verbatim
   84: *>          TAU is COMPLEX*16 array, dimension (K)
   85: *>          TAU(i) must contain the scalar factor of the elementary
   86: *>          reflector H(i), as returned by ZGELQF.
   87: *> \endverbatim
   88: *>
   89: *> \param[out] WORK
   90: *> \verbatim
   91: *>          WORK is COMPLEX*16 array, dimension (M)
   92: *> \endverbatim
   93: *>
   94: *> \param[out] INFO
   95: *> \verbatim
   96: *>          INFO is INTEGER
   97: *>          = 0: successful exit
   98: *>          < 0: if INFO = -i, the i-th argument has an illegal value
   99: *> \endverbatim
  100: *
  101: *  Authors:
  102: *  ========
  103: *
  104: *> \author Univ. of Tennessee 
  105: *> \author Univ. of California Berkeley 
  106: *> \author Univ. of Colorado Denver 
  107: *> \author NAG Ltd. 
  108: *
  109: *> \date September 2012
  110: *
  111: *> \ingroup complex16OTHERcomputational
  112: *
  113: *  =====================================================================
  114:       SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
  115: *
  116: *  -- LAPACK computational routine (version 3.4.2) --
  117: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  118: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  119: *     September 2012
  120: *
  121: *     .. Scalar Arguments ..
  122:       INTEGER            INFO, K, LDA, M, N
  123: *     ..
  124: *     .. Array Arguments ..
  125:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
  126: *     ..
  127: *
  128: *  =====================================================================
  129: *
  130: *     .. Parameters ..
  131:       COMPLEX*16         ONE, ZERO
  132:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
  133:      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
  134: *     ..
  135: *     .. Local Scalars ..
  136:       INTEGER            I, J, L
  137: *     ..
  138: *     .. External Subroutines ..
  139:       EXTERNAL           XERBLA, ZLACGV, ZLARF, ZSCAL
  140: *     ..
  141: *     .. Intrinsic Functions ..
  142:       INTRINSIC          DCONJG, MAX
  143: *     ..
  144: *     .. Executable Statements ..
  145: *
  146: *     Test the input arguments
  147: *
  148:       INFO = 0
  149:       IF( M.LT.0 ) THEN
  150:          INFO = -1
  151:       ELSE IF( N.LT.M ) THEN
  152:          INFO = -2
  153:       ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
  154:          INFO = -3
  155:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
  156:          INFO = -5
  157:       END IF
  158:       IF( INFO.NE.0 ) THEN
  159:          CALL XERBLA( 'ZUNGL2', -INFO )
  160:          RETURN
  161:       END IF
  162: *
  163: *     Quick return if possible
  164: *
  165:       IF( M.LE.0 )
  166:      $   RETURN
  167: *
  168:       IF( K.LT.M ) THEN
  169: *
  170: *        Initialise rows k+1:m to rows of the unit matrix
  171: *
  172:          DO 20 J = 1, N
  173:             DO 10 L = K + 1, M
  174:                A( L, J ) = ZERO
  175:    10       CONTINUE
  176:             IF( J.GT.K .AND. J.LE.M )
  177:      $         A( J, J ) = ONE
  178:    20    CONTINUE
  179:       END IF
  180: *
  181:       DO 40 I = K, 1, -1
  182: *
  183: *        Apply H(i)**H to A(i:m,i:n) from the right
  184: *
  185:          IF( I.LT.N ) THEN
  186:             CALL ZLACGV( N-I, A( I, I+1 ), LDA )
  187:             IF( I.LT.M ) THEN
  188:                A( I, I ) = ONE
  189:                CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
  190:      $                     DCONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
  191:             END IF
  192:             CALL ZSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
  193:             CALL ZLACGV( N-I, A( I, I+1 ), LDA )
  194:          END IF
  195:          A( I, I ) = ONE - DCONJG( TAU( I ) )
  196: *
  197: *        Set A(i,1:i-1) to zero
  198: *
  199:          DO 30 L = 1, I - 1
  200:             A( I, L ) = ZERO
  201:    30    CONTINUE
  202:    40 CONTINUE
  203:       RETURN
  204: *
  205: *     End of ZUNGL2
  206: *
  207:       END