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    1:       SUBROUTINE ZUNGR2( M, N, K, A, LDA, TAU, WORK, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       INTEGER            INFO, K, LDA, M, N
   10: *     ..
   11: *     .. Array Arguments ..
   12:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   13: *     ..
   14: *
   15: *  Purpose
   16: *  =======
   17: *
   18: *  ZUNGR2 generates an m by n complex matrix Q with orthonormal rows,
   19: *  which is defined as the last m rows of a product of k elementary
   20: *  reflectors of order n
   21: *
   22: *        Q  =  H(1)' H(2)' . . . H(k)'
   23: *
   24: *  as returned by ZGERQF.
   25: *
   26: *  Arguments
   27: *  =========
   28: *
   29: *  M       (input) INTEGER
   30: *          The number of rows of the matrix Q. M >= 0.
   31: *
   32: *  N       (input) INTEGER
   33: *          The number of columns of the matrix Q. N >= M.
   34: *
   35: *  K       (input) INTEGER
   36: *          The number of elementary reflectors whose product defines the
   37: *          matrix Q. M >= K >= 0.
   38: *
   39: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
   40: *          On entry, the (m-k+i)-th row must contain the vector which
   41: *          defines the elementary reflector H(i), for i = 1,2,...,k, as
   42: *          returned by ZGERQF in the last k rows of its array argument
   43: *          A.
   44: *          On exit, the m-by-n matrix Q.
   45: *
   46: *  LDA     (input) INTEGER
   47: *          The first dimension of the array A. LDA >= max(1,M).
   48: *
   49: *  TAU     (input) COMPLEX*16 array, dimension (K)
   50: *          TAU(i) must contain the scalar factor of the elementary
   51: *          reflector H(i), as returned by ZGERQF.
   52: *
   53: *  WORK    (workspace) COMPLEX*16 array, dimension (M)
   54: *
   55: *  INFO    (output) INTEGER
   56: *          = 0: successful exit
   57: *          < 0: if INFO = -i, the i-th argument has an illegal value
   58: *
   59: *  =====================================================================
   60: *
   61: *     .. Parameters ..
   62:       COMPLEX*16         ONE, ZERO
   63:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
   64:      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
   65: *     ..
   66: *     .. Local Scalars ..
   67:       INTEGER            I, II, J, L
   68: *     ..
   69: *     .. External Subroutines ..
   70:       EXTERNAL           XERBLA, ZLACGV, ZLARF, ZSCAL
   71: *     ..
   72: *     .. Intrinsic Functions ..
   73:       INTRINSIC          DCONJG, MAX
   74: *     ..
   75: *     .. Executable Statements ..
   76: *
   77: *     Test the input arguments
   78: *
   79:       INFO = 0
   80:       IF( M.LT.0 ) THEN
   81:          INFO = -1
   82:       ELSE IF( N.LT.M ) THEN
   83:          INFO = -2
   84:       ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
   85:          INFO = -3
   86:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
   87:          INFO = -5
   88:       END IF
   89:       IF( INFO.NE.0 ) THEN
   90:          CALL XERBLA( 'ZUNGR2', -INFO )
   91:          RETURN
   92:       END IF
   93: *
   94: *     Quick return if possible
   95: *
   96:       IF( M.LE.0 )
   97:      $   RETURN
   98: *
   99:       IF( K.LT.M ) THEN
  100: *
  101: *        Initialise rows 1:m-k to rows of the unit matrix
  102: *
  103:          DO 20 J = 1, N
  104:             DO 10 L = 1, M - K
  105:                A( L, J ) = ZERO
  106:    10       CONTINUE
  107:             IF( J.GT.N-M .AND. J.LE.N-K )
  108:      $         A( M-N+J, J ) = ONE
  109:    20    CONTINUE
  110:       END IF
  111: *
  112:       DO 40 I = 1, K
  113:          II = M - K + I
  114: *
  115: *        Apply H(i)' to A(1:m-k+i,1:n-k+i) from the right
  116: *
  117:          CALL ZLACGV( N-M+II-1, A( II, 1 ), LDA )
  118:          A( II, N-M+II ) = ONE
  119:          CALL ZLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA,
  120:      $               DCONJG( TAU( I ) ), A, LDA, WORK )
  121:          CALL ZSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
  122:          CALL ZLACGV( N-M+II-1, A( II, 1 ), LDA )
  123:          A( II, N-M+II ) = ONE - DCONJG( TAU( I ) )
  124: *
  125: *        Set A(m-k+i,n-k+i+1:n) to zero
  126: *
  127:          DO 30 L = N - M + II + 1, N
  128:             A( II, L ) = ZERO
  129:    30    CONTINUE
  130:    40 CONTINUE
  131:       RETURN
  132: *
  133: *     End of ZUNGR2
  134: *
  135:       END