LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dopmtr.f
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00001 *> \brief \b DOPMTR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DOPMTR + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dopmtr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
00022 *                          INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          SIDE, TRANS, UPLO
00026 *       INTEGER            INFO, LDC, M, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       DOUBLE PRECISION   AP( * ), C( LDC, * ), TAU( * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> DOPMTR overwrites the general real M-by-N matrix C with
00039 *>
00040 *>                 SIDE = 'L'     SIDE = 'R'
00041 *> TRANS = 'N':      Q * C          C * Q
00042 *> TRANS = 'T':      Q**T * C       C * Q**T
00043 *>
00044 *> where Q is a real orthogonal matrix of order nq, with nq = m if
00045 *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
00046 *> nq-1 elementary reflectors, as returned by DSPTRD using packed
00047 *> storage:
00048 *>
00049 *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
00050 *>
00051 *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
00052 *> \endverbatim
00053 *
00054 *  Arguments:
00055 *  ==========
00056 *
00057 *> \param[in] SIDE
00058 *> \verbatim
00059 *>          SIDE is CHARACTER*1
00060 *>          = 'L': apply Q or Q**T from the Left;
00061 *>          = 'R': apply Q or Q**T from the Right.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] UPLO
00065 *> \verbatim
00066 *>          UPLO is CHARACTER*1
00067 *>          = 'U': Upper triangular packed storage used in previous
00068 *>                 call to DSPTRD;
00069 *>          = 'L': Lower triangular packed storage used in previous
00070 *>                 call to DSPTRD.
00071 *> \endverbatim
00072 *>
00073 *> \param[in] TRANS
00074 *> \verbatim
00075 *>          TRANS is CHARACTER*1
00076 *>          = 'N':  No transpose, apply Q;
00077 *>          = 'T':  Transpose, apply Q**T.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] M
00081 *> \verbatim
00082 *>          M is INTEGER
00083 *>          The number of rows of the matrix C. M >= 0.
00084 *> \endverbatim
00085 *>
00086 *> \param[in] N
00087 *> \verbatim
00088 *>          N is INTEGER
00089 *>          The number of columns of the matrix C. N >= 0.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] AP
00093 *> \verbatim
00094 *>          AP is DOUBLE PRECISION array, dimension
00095 *>                               (M*(M+1)/2) if SIDE = 'L'
00096 *>                               (N*(N+1)/2) if SIDE = 'R'
00097 *>          The vectors which define the elementary reflectors, as
00098 *>          returned by DSPTRD.  AP is modified by the routine but
00099 *>          restored on exit.
00100 *> \endverbatim
00101 *>
00102 *> \param[in] TAU
00103 *> \verbatim
00104 *>          TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
00105 *>                                     or (N-1) if SIDE = 'R'
00106 *>          TAU(i) must contain the scalar factor of the elementary
00107 *>          reflector H(i), as returned by DSPTRD.
00108 *> \endverbatim
00109 *>
00110 *> \param[in,out] C
00111 *> \verbatim
00112 *>          C is DOUBLE PRECISION array, dimension (LDC,N)
00113 *>          On entry, the M-by-N matrix C.
00114 *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
00115 *> \endverbatim
00116 *>
00117 *> \param[in] LDC
00118 *> \verbatim
00119 *>          LDC is INTEGER
00120 *>          The leading dimension of the array C. LDC >= max(1,M).
00121 *> \endverbatim
00122 *>
00123 *> \param[out] WORK
00124 *> \verbatim
00125 *>          WORK is DOUBLE PRECISION array, dimension
00126 *>                                   (N) if SIDE = 'L'
00127 *>                                   (M) if SIDE = 'R'
00128 *> \endverbatim
00129 *>
00130 *> \param[out] INFO
00131 *> \verbatim
00132 *>          INFO is INTEGER
00133 *>          = 0:  successful exit
00134 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00135 *> \endverbatim
00136 *
00137 *  Authors:
00138 *  ========
00139 *
00140 *> \author Univ. of Tennessee 
00141 *> \author Univ. of California Berkeley 
00142 *> \author Univ. of Colorado Denver 
00143 *> \author NAG Ltd. 
00144 *
00145 *> \date November 2011
00146 *
00147 *> \ingroup doubleOTHERcomputational
00148 *
00149 *  =====================================================================
00150       SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
00151      $                   INFO )
00152 *
00153 *  -- LAPACK computational routine (version 3.4.0) --
00154 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00155 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00156 *     November 2011
00157 *
00158 *     .. Scalar Arguments ..
00159       CHARACTER          SIDE, TRANS, UPLO
00160       INTEGER            INFO, LDC, M, N
00161 *     ..
00162 *     .. Array Arguments ..
00163       DOUBLE PRECISION   AP( * ), C( LDC, * ), TAU( * ), WORK( * )
00164 *     ..
00165 *
00166 *  =====================================================================
00167 *
00168 *     .. Parameters ..
00169       DOUBLE PRECISION   ONE
00170       PARAMETER          ( ONE = 1.0D+0 )
00171 *     ..
00172 *     .. Local Scalars ..
00173       LOGICAL            FORWRD, LEFT, NOTRAN, UPPER
00174       INTEGER            I, I1, I2, I3, IC, II, JC, MI, NI, NQ
00175       DOUBLE PRECISION   AII
00176 *     ..
00177 *     .. External Functions ..
00178       LOGICAL            LSAME
00179       EXTERNAL           LSAME
00180 *     ..
00181 *     .. External Subroutines ..
00182       EXTERNAL           DLARF, XERBLA
00183 *     ..
00184 *     .. Intrinsic Functions ..
00185       INTRINSIC          MAX
00186 *     ..
00187 *     .. Executable Statements ..
00188 *
00189 *     Test the input arguments
00190 *
00191       INFO = 0
00192       LEFT = LSAME( SIDE, 'L' )
00193       NOTRAN = LSAME( TRANS, 'N' )
00194       UPPER = LSAME( UPLO, 'U' )
00195 *
00196 *     NQ is the order of Q
00197 *
00198       IF( LEFT ) THEN
00199          NQ = M
00200       ELSE
00201          NQ = N
00202       END IF
00203       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00204          INFO = -1
00205       ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00206          INFO = -2
00207       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
00208          INFO = -3
00209       ELSE IF( M.LT.0 ) THEN
00210          INFO = -4
00211       ELSE IF( N.LT.0 ) THEN
00212          INFO = -5
00213       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00214          INFO = -9
00215       END IF
00216       IF( INFO.NE.0 ) THEN
00217          CALL XERBLA( 'DOPMTR', -INFO )
00218          RETURN
00219       END IF
00220 *
00221 *     Quick return if possible
00222 *
00223       IF( M.EQ.0 .OR. N.EQ.0 )
00224      $   RETURN
00225 *
00226       IF( UPPER ) THEN
00227 *
00228 *        Q was determined by a call to DSPTRD with UPLO = 'U'
00229 *
00230          FORWRD = ( LEFT .AND. NOTRAN ) .OR.
00231      $            ( .NOT.LEFT .AND. .NOT.NOTRAN )
00232 *
00233          IF( FORWRD ) THEN
00234             I1 = 1
00235             I2 = NQ - 1
00236             I3 = 1
00237             II = 2
00238          ELSE
00239             I1 = NQ - 1
00240             I2 = 1
00241             I3 = -1
00242             II = NQ*( NQ+1 ) / 2 - 1
00243          END IF
00244 *
00245          IF( LEFT ) THEN
00246             NI = N
00247          ELSE
00248             MI = M
00249          END IF
00250 *
00251          DO 10 I = I1, I2, I3
00252             IF( LEFT ) THEN
00253 *
00254 *              H(i) is applied to C(1:i,1:n)
00255 *
00256                MI = I
00257             ELSE
00258 *
00259 *              H(i) is applied to C(1:m,1:i)
00260 *
00261                NI = I
00262             END IF
00263 *
00264 *           Apply H(i)
00265 *
00266             AII = AP( II )
00267             AP( II ) = ONE
00268             CALL DLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
00269      $                  WORK )
00270             AP( II ) = AII
00271 *
00272             IF( FORWRD ) THEN
00273                II = II + I + 2
00274             ELSE
00275                II = II - I - 1
00276             END IF
00277    10    CONTINUE
00278       ELSE
00279 *
00280 *        Q was determined by a call to DSPTRD with UPLO = 'L'.
00281 *
00282          FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
00283      $            ( .NOT.LEFT .AND. NOTRAN )
00284 *
00285          IF( FORWRD ) THEN
00286             I1 = 1
00287             I2 = NQ - 1
00288             I3 = 1
00289             II = 2
00290          ELSE
00291             I1 = NQ - 1
00292             I2 = 1
00293             I3 = -1
00294             II = NQ*( NQ+1 ) / 2 - 1
00295          END IF
00296 *
00297          IF( LEFT ) THEN
00298             NI = N
00299             JC = 1
00300          ELSE
00301             MI = M
00302             IC = 1
00303          END IF
00304 *
00305          DO 20 I = I1, I2, I3
00306             AII = AP( II )
00307             AP( II ) = ONE
00308             IF( LEFT ) THEN
00309 *
00310 *              H(i) is applied to C(i+1:m,1:n)
00311 *
00312                MI = M - I
00313                IC = I + 1
00314             ELSE
00315 *
00316 *              H(i) is applied to C(1:m,i+1:n)
00317 *
00318                NI = N - I
00319                JC = I + 1
00320             END IF
00321 *
00322 *           Apply H(i)
00323 *
00324             CALL DLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
00325      $                  C( IC, JC ), LDC, WORK )
00326             AP( II ) = AII
00327 *
00328             IF( FORWRD ) THEN
00329                II = II + NQ - I + 1
00330             ELSE
00331                II = II - NQ + I - 2
00332             END IF
00333    20    CONTINUE
00334       END IF
00335       RETURN
00336 *
00337 *     End of DOPMTR
00338 *
00339       END
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