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    1:       SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, 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:       CHARACTER          UPLO
   10:       INTEGER            INFO, LDA, LWORK, N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  ZUNGTR generates a complex unitary matrix Q which is defined as the
   20: *  product of n-1 elementary reflectors of order N, as returned by
   21: *  ZHETRD:
   22: *
   23: *  if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
   24: *
   25: *  if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
   26: *
   27: *  Arguments
   28: *  =========
   29: *
   30: *  UPLO    (input) CHARACTER*1
   31: *          = 'U': Upper triangle of A contains elementary reflectors
   32: *                 from ZHETRD;
   33: *          = 'L': Lower triangle of A contains elementary reflectors
   34: *                 from ZHETRD.
   35: *
   36: *  N       (input) INTEGER
   37: *          The order of the matrix Q. N >= 0.
   38: *
   39: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
   40: *          On entry, the vectors which define the elementary reflectors,
   41: *          as returned by ZHETRD.
   42: *          On exit, the N-by-N unitary matrix Q.
   43: *
   44: *  LDA     (input) INTEGER
   45: *          The leading dimension of the array A. LDA >= N.
   46: *
   47: *  TAU     (input) COMPLEX*16 array, dimension (N-1)
   48: *          TAU(i) must contain the scalar factor of the elementary
   49: *          reflector H(i), as returned by ZHETRD.
   50: *
   51: *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
   52: *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   53: *
   54: *  LWORK   (input) INTEGER
   55: *          The dimension of the array WORK. LWORK >= N-1.
   56: *          For optimum performance LWORK >= (N-1)*NB, where NB is
   57: *          the optimal blocksize.
   58: *
   59: *          If LWORK = -1, then a workspace query is assumed; the routine
   60: *          only calculates the optimal size of the WORK array, returns
   61: *          this value as the first entry of the WORK array, and no error
   62: *          message related to LWORK is issued by XERBLA.
   63: *
   64: *  INFO    (output) INTEGER
   65: *          = 0:  successful exit
   66: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   67: *
   68: *  =====================================================================
   69: *
   70: *     .. Parameters ..
   71:       COMPLEX*16         ZERO, ONE
   72:       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
   73:      $                   ONE = ( 1.0D+0, 0.0D+0 ) )
   74: *     ..
   75: *     .. Local Scalars ..
   76:       LOGICAL            LQUERY, UPPER
   77:       INTEGER            I, IINFO, J, LWKOPT, NB
   78: *     ..
   79: *     .. External Functions ..
   80:       LOGICAL            LSAME
   81:       INTEGER            ILAENV
   82:       EXTERNAL           LSAME, ILAENV
   83: *     ..
   84: *     .. External Subroutines ..
   85:       EXTERNAL           XERBLA, ZUNGQL, ZUNGQR
   86: *     ..
   87: *     .. Intrinsic Functions ..
   88:       INTRINSIC          MAX
   89: *     ..
   90: *     .. Executable Statements ..
   91: *
   92: *     Test the input arguments
   93: *
   94:       INFO = 0
   95:       LQUERY = ( LWORK.EQ.-1 )
   96:       UPPER = LSAME( UPLO, 'U' )
   97:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
   98:          INFO = -1
   99:       ELSE IF( N.LT.0 ) THEN
  100:          INFO = -2
  101:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  102:          INFO = -4
  103:       ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
  104:          INFO = -7
  105:       END IF
  106: *
  107:       IF( INFO.EQ.0 ) THEN
  108:          IF( UPPER ) THEN
  109:             NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 )
  110:          ELSE
  111:             NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 )
  112:          END IF
  113:          LWKOPT = MAX( 1, N-1 )*NB
  114:          WORK( 1 ) = LWKOPT
  115:       END IF
  116: *
  117:       IF( INFO.NE.0 ) THEN
  118:          CALL XERBLA( 'ZUNGTR', -INFO )
  119:          RETURN
  120:       ELSE IF( LQUERY ) THEN
  121:          RETURN
  122:       END IF
  123: *
  124: *     Quick return if possible
  125: *
  126:       IF( N.EQ.0 ) THEN
  127:          WORK( 1 ) = 1
  128:          RETURN
  129:       END IF
  130: *
  131:       IF( UPPER ) THEN
  132: *
  133: *        Q was determined by a call to ZHETRD with UPLO = 'U'
  134: *
  135: *        Shift the vectors which define the elementary reflectors one
  136: *        column to the left, and set the last row and column of Q to
  137: *        those of the unit matrix
  138: *
  139:          DO 20 J = 1, N - 1
  140:             DO 10 I = 1, J - 1
  141:                A( I, J ) = A( I, J+1 )
  142:    10       CONTINUE
  143:             A( N, J ) = ZERO
  144:    20    CONTINUE
  145:          DO 30 I = 1, N - 1
  146:             A( I, N ) = ZERO
  147:    30    CONTINUE
  148:          A( N, N ) = ONE
  149: *
  150: *        Generate Q(1:n-1,1:n-1)
  151: *
  152:          CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
  153: *
  154:       ELSE
  155: *
  156: *        Q was determined by a call to ZHETRD with UPLO = 'L'.
  157: *
  158: *        Shift the vectors which define the elementary reflectors one
  159: *        column to the right, and set the first row and column of Q to
  160: *        those of the unit matrix
  161: *
  162:          DO 50 J = N, 2, -1
  163:             A( 1, J ) = ZERO
  164:             DO 40 I = J + 1, N
  165:                A( I, J ) = A( I, J-1 )
  166:    40       CONTINUE
  167:    50    CONTINUE
  168:          A( 1, 1 ) = ONE
  169:          DO 60 I = 2, N
  170:             A( I, 1 ) = ZERO
  171:    60    CONTINUE
  172:          IF( N.GT.1 ) THEN
  173: *
  174: *           Generate Q(2:n,2:n)
  175: *
  176:             CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
  177:      $                   LWORK, IINFO )
  178:          END IF
  179:       END IF
  180:       WORK( 1 ) = LWKOPT
  181:       RETURN
  182: *
  183: *     End of ZUNGTR
  184: *
  185:       END