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    1: *> \brief \b ZUPGTR
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZUPGTR + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zupgtr.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zupgtr.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zupgtr.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          UPLO
   25: *       INTEGER            INFO, LDQ, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       COMPLEX*16         AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> ZUPGTR generates a complex unitary matrix Q which is defined as the
   38: *> product of n-1 elementary reflectors H(i) of order n, as returned by
   39: *> ZHPTRD using packed storage:
   40: *>
   41: *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
   42: *>
   43: *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
   44: *> \endverbatim
   45: *
   46: *  Arguments:
   47: *  ==========
   48: *
   49: *> \param[in] UPLO
   50: *> \verbatim
   51: *>          UPLO is CHARACTER*1
   52: *>          = 'U': Upper triangular packed storage used in previous
   53: *>                 call to ZHPTRD;
   54: *>          = 'L': Lower triangular packed storage used in previous
   55: *>                 call to ZHPTRD.
   56: *> \endverbatim
   57: *>
   58: *> \param[in] N
   59: *> \verbatim
   60: *>          N is INTEGER
   61: *>          The order of the matrix Q. N >= 0.
   62: *> \endverbatim
   63: *>
   64: *> \param[in] AP
   65: *> \verbatim
   66: *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
   67: *>          The vectors which define the elementary reflectors, as
   68: *>          returned by ZHPTRD.
   69: *> \endverbatim
   70: *>
   71: *> \param[in] TAU
   72: *> \verbatim
   73: *>          TAU is COMPLEX*16 array, dimension (N-1)
   74: *>          TAU(i) must contain the scalar factor of the elementary
   75: *>          reflector H(i), as returned by ZHPTRD.
   76: *> \endverbatim
   77: *>
   78: *> \param[out] Q
   79: *> \verbatim
   80: *>          Q is COMPLEX*16 array, dimension (LDQ,N)
   81: *>          The N-by-N unitary matrix Q.
   82: *> \endverbatim
   83: *>
   84: *> \param[in] LDQ
   85: *> \verbatim
   86: *>          LDQ is INTEGER
   87: *>          The leading dimension of the array Q. LDQ >= max(1,N).
   88: *> \endverbatim
   89: *>
   90: *> \param[out] WORK
   91: *> \verbatim
   92: *>          WORK is COMPLEX*16 array, dimension (N-1)
   93: *> \endverbatim
   94: *>
   95: *> \param[out] INFO
   96: *> \verbatim
   97: *>          INFO is INTEGER
   98: *>          = 0:  successful exit
   99: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  100: *> \endverbatim
  101: *
  102: *  Authors:
  103: *  ========
  104: *
  105: *> \author Univ. of Tennessee
  106: *> \author Univ. of California Berkeley
  107: *> \author Univ. of Colorado Denver
  108: *> \author NAG Ltd.
  109: *
  110: *> \ingroup complex16OTHERcomputational
  111: *
  112: *  =====================================================================
  113:       SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
  114: *
  115: *  -- LAPACK computational routine --
  116: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  117: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  118: *
  119: *     .. Scalar Arguments ..
  120:       CHARACTER          UPLO
  121:       INTEGER            INFO, LDQ, N
  122: *     ..
  123: *     .. Array Arguments ..
  124:       COMPLEX*16         AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
  125: *     ..
  126: *
  127: *  =====================================================================
  128: *
  129: *     .. Parameters ..
  130:       COMPLEX*16         CZERO, CONE
  131:       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
  132:      $                   CONE = ( 1.0D+0, 0.0D+0 ) )
  133: *     ..
  134: *     .. Local Scalars ..
  135:       LOGICAL            UPPER
  136:       INTEGER            I, IINFO, IJ, J
  137: *     ..
  138: *     .. External Functions ..
  139:       LOGICAL            LSAME
  140:       EXTERNAL           LSAME
  141: *     ..
  142: *     .. External Subroutines ..
  143:       EXTERNAL           XERBLA, ZUNG2L, ZUNG2R
  144: *     ..
  145: *     .. Intrinsic Functions ..
  146:       INTRINSIC          MAX
  147: *     ..
  148: *     .. Executable Statements ..
  149: *
  150: *     Test the input arguments
  151: *
  152:       INFO = 0
  153:       UPPER = LSAME( UPLO, 'U' )
  154:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  155:          INFO = -1
  156:       ELSE IF( N.LT.0 ) THEN
  157:          INFO = -2
  158:       ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
  159:          INFO = -6
  160:       END IF
  161:       IF( INFO.NE.0 ) THEN
  162:          CALL XERBLA( 'ZUPGTR', -INFO )
  163:          RETURN
  164:       END IF
  165: *
  166: *     Quick return if possible
  167: *
  168:       IF( N.EQ.0 )
  169:      $   RETURN
  170: *
  171:       IF( UPPER ) THEN
  172: *
  173: *        Q was determined by a call to ZHPTRD with UPLO = 'U'
  174: *
  175: *        Unpack the vectors which define the elementary reflectors and
  176: *        set the last row and column of Q equal to those of the unit
  177: *        matrix
  178: *
  179:          IJ = 2
  180:          DO 20 J = 1, N - 1
  181:             DO 10 I = 1, J - 1
  182:                Q( I, J ) = AP( IJ )
  183:                IJ = IJ + 1
  184:    10       CONTINUE
  185:             IJ = IJ + 2
  186:             Q( N, J ) = CZERO
  187:    20    CONTINUE
  188:          DO 30 I = 1, N - 1
  189:             Q( I, N ) = CZERO
  190:    30    CONTINUE
  191:          Q( N, N ) = CONE
  192: *
  193: *        Generate Q(1:n-1,1:n-1)
  194: *
  195:          CALL ZUNG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
  196: *
  197:       ELSE
  198: *
  199: *        Q was determined by a call to ZHPTRD with UPLO = 'L'.
  200: *
  201: *        Unpack the vectors which define the elementary reflectors and
  202: *        set the first row and column of Q equal to those of the unit
  203: *        matrix
  204: *
  205:          Q( 1, 1 ) = CONE
  206:          DO 40 I = 2, N
  207:             Q( I, 1 ) = CZERO
  208:    40    CONTINUE
  209:          IJ = 3
  210:          DO 60 J = 2, N
  211:             Q( 1, J ) = CZERO
  212:             DO 50 I = J + 1, N
  213:                Q( I, J ) = AP( IJ )
  214:                IJ = IJ + 1
  215:    50       CONTINUE
  216:             IJ = IJ + 2
  217:    60    CONTINUE
  218:          IF( N.GT.1 ) THEN
  219: *
  220: *           Generate Q(2:n,2:n)
  221: *
  222:             CALL ZUNG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
  223:      $                   IINFO )
  224:          END IF
  225:       END IF
  226:       RETURN
  227: *
  228: *     End of ZUPGTR
  229: *
  230:       END