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    1: *> \brief \b DORGHR
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DORGHR + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorghr.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorghr.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorghr.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
   28: *       ..
   29: *  
   30: *
   31: *> \par Purpose:
   32: *  =============
   33: *>
   34: *> \verbatim
   35: *>
   36: *> DORGHR generates a real orthogonal matrix Q which is defined as the
   37: *> product of IHI-ILO elementary reflectors of order N, as returned by
   38: *> DGEHRD:
   39: *>
   40: *> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
   41: *> \endverbatim
   42: *
   43: *  Arguments:
   44: *  ==========
   45: *
   46: *> \param[in] N
   47: *> \verbatim
   48: *>          N is INTEGER
   49: *>          The order of the matrix Q. N >= 0.
   50: *> \endverbatim
   51: *>
   52: *> \param[in] ILO
   53: *> \verbatim
   54: *>          ILO is INTEGER
   55: *> \endverbatim
   56: *>
   57: *> \param[in] IHI
   58: *> \verbatim
   59: *>          IHI is INTEGER
   60: *>
   61: *>          ILO and IHI must have the same values as in the previous call
   62: *>          of DGEHRD. Q is equal to the unit matrix except in the
   63: *>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
   64: *>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
   65: *> \endverbatim
   66: *>
   67: *> \param[in,out] A
   68: *> \verbatim
   69: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   70: *>          On entry, the vectors which define the elementary reflectors,
   71: *>          as returned by DGEHRD.
   72: *>          On exit, the N-by-N orthogonal matrix Q.
   73: *> \endverbatim
   74: *>
   75: *> \param[in] LDA
   76: *> \verbatim
   77: *>          LDA is INTEGER
   78: *>          The leading dimension of the array A. LDA >= max(1,N).
   79: *> \endverbatim
   80: *>
   81: *> \param[in] TAU
   82: *> \verbatim
   83: *>          TAU is DOUBLE PRECISION array, dimension (N-1)
   84: *>          TAU(i) must contain the scalar factor of the elementary
   85: *>          reflector H(i), as returned by DGEHRD.
   86: *> \endverbatim
   87: *>
   88: *> \param[out] WORK
   89: *> \verbatim
   90: *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
   91: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   92: *> \endverbatim
   93: *>
   94: *> \param[in] LWORK
   95: *> \verbatim
   96: *>          LWORK is INTEGER
   97: *>          The dimension of the array WORK. LWORK >= IHI-ILO.
   98: *>          For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
   99: *>          the optimal blocksize.
  100: *>
  101: *>          If LWORK = -1, then a workspace query is assumed; the routine
  102: *>          only calculates the optimal size of the WORK array, returns
  103: *>          this value as the first entry of the WORK array, and no error
  104: *>          message related to LWORK is issued by XERBLA.
  105: *> \endverbatim
  106: *>
  107: *> \param[out] INFO
  108: *> \verbatim
  109: *>          INFO is INTEGER
  110: *>          = 0:  successful exit
  111: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  112: *> \endverbatim
  113: *
  114: *  Authors:
  115: *  ========
  116: *
  117: *> \author Univ. of Tennessee 
  118: *> \author Univ. of California Berkeley 
  119: *> \author Univ. of Colorado Denver 
  120: *> \author NAG Ltd. 
  121: *
  122: *> \date November 2011
  123: *
  124: *> \ingroup doubleOTHERcomputational
  125: *
  126: *  =====================================================================
  127:       SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
  128: *
  129: *  -- LAPACK computational routine (version 3.4.0) --
  130: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  131: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  132: *     November 2011
  133: *
  134: *     .. Scalar Arguments ..
  135:       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
  136: *     ..
  137: *     .. Array Arguments ..
  138:       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
  139: *     ..
  140: *
  141: *  =====================================================================
  142: *
  143: *     .. Parameters ..
  144:       DOUBLE PRECISION   ZERO, ONE
  145:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
  146: *     ..
  147: *     .. Local Scalars ..
  148:       LOGICAL            LQUERY
  149:       INTEGER            I, IINFO, J, LWKOPT, NB, NH
  150: *     ..
  151: *     .. External Subroutines ..
  152:       EXTERNAL           DORGQR, XERBLA
  153: *     ..
  154: *     .. External Functions ..
  155:       INTEGER            ILAENV
  156:       EXTERNAL           ILAENV
  157: *     ..
  158: *     .. Intrinsic Functions ..
  159:       INTRINSIC          MAX, MIN
  160: *     ..
  161: *     .. Executable Statements ..
  162: *
  163: *     Test the input arguments
  164: *
  165:       INFO = 0
  166:       NH = IHI - ILO
  167:       LQUERY = ( LWORK.EQ.-1 )
  168:       IF( N.LT.0 ) THEN
  169:          INFO = -1
  170:       ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
  171:          INFO = -2
  172:       ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
  173:          INFO = -3
  174:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  175:          INFO = -5
  176:       ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
  177:          INFO = -8
  178:       END IF
  179: *
  180:       IF( INFO.EQ.0 ) THEN
  181:          NB = ILAENV( 1, 'DORGQR', ' ', NH, NH, NH, -1 )
  182:          LWKOPT = MAX( 1, NH )*NB
  183:          WORK( 1 ) = LWKOPT
  184:       END IF
  185: *
  186:       IF( INFO.NE.0 ) THEN
  187:          CALL XERBLA( 'DORGHR', -INFO )
  188:          RETURN
  189:       ELSE IF( LQUERY ) THEN
  190:          RETURN
  191:       END IF
  192: *
  193: *     Quick return if possible
  194: *
  195:       IF( N.EQ.0 ) THEN
  196:          WORK( 1 ) = 1
  197:          RETURN
  198:       END IF
  199: *
  200: *     Shift the vectors which define the elementary reflectors one
  201: *     column to the right, and set the first ilo and the last n-ihi
  202: *     rows and columns to those of the unit matrix
  203: *
  204:       DO 40 J = IHI, ILO + 1, -1
  205:          DO 10 I = 1, J - 1
  206:             A( I, J ) = ZERO
  207:    10    CONTINUE
  208:          DO 20 I = J + 1, IHI
  209:             A( I, J ) = A( I, J-1 )
  210:    20    CONTINUE
  211:          DO 30 I = IHI + 1, N
  212:             A( I, J ) = ZERO
  213:    30    CONTINUE
  214:    40 CONTINUE
  215:       DO 60 J = 1, ILO
  216:          DO 50 I = 1, N
  217:             A( I, J ) = ZERO
  218:    50    CONTINUE
  219:          A( J, J ) = ONE
  220:    60 CONTINUE
  221:       DO 80 J = IHI + 1, N
  222:          DO 70 I = 1, N
  223:             A( I, J ) = ZERO
  224:    70    CONTINUE
  225:          A( J, J ) = ONE
  226:    80 CONTINUE
  227: *
  228:       IF( NH.GT.0 ) THEN
  229: *
  230: *        Generate Q(ilo+1:ihi,ilo+1:ihi)
  231: *
  232:          CALL DORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
  233:      $                WORK, LWORK, IINFO )
  234:       END IF
  235:       WORK( 1 ) = LWKOPT
  236:       RETURN
  237: *
  238: *     End of DORGHR
  239: *
  240:       END