LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sormhr.f
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00001 *> \brief \b SORMHR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SORMHR + 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/sormhr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
00022 *                          LDC, WORK, LWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          SIDE, TRANS
00026 *       INTEGER            IHI, ILO, INFO, LDA, LDC, LWORK, M, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
00030 *      $                   WORK( * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> SORMHR overwrites the general real M-by-N matrix C with
00040 *>
00041 *>                 SIDE = 'L'     SIDE = 'R'
00042 *> TRANS = 'N':      Q * C          C * Q
00043 *> TRANS = 'T':      Q**T * C       C * Q**T
00044 *>
00045 *> where Q is a real orthogonal matrix of order nq, with nq = m if
00046 *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
00047 *> IHI-ILO elementary reflectors, as returned by SGEHRD:
00048 *>
00049 *> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
00050 *> \endverbatim
00051 *
00052 *  Arguments:
00053 *  ==========
00054 *
00055 *> \param[in] SIDE
00056 *> \verbatim
00057 *>          SIDE is CHARACTER*1
00058 *>          = 'L': apply Q or Q**T from the Left;
00059 *>          = 'R': apply Q or Q**T from the Right.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] TRANS
00063 *> \verbatim
00064 *>          TRANS is CHARACTER*1
00065 *>          = 'N':  No transpose, apply Q;
00066 *>          = 'T':  Transpose, apply Q**T.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] M
00070 *> \verbatim
00071 *>          M is INTEGER
00072 *>          The number of rows of the matrix C. M >= 0.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] N
00076 *> \verbatim
00077 *>          N is INTEGER
00078 *>          The number of columns of the matrix C. N >= 0.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] ILO
00082 *> \verbatim
00083 *>          ILO is INTEGER
00084 *> \endverbatim
00085 *>
00086 *> \param[in] IHI
00087 *> \verbatim
00088 *>          IHI is INTEGER
00089 *>
00090 *>          ILO and IHI must have the same values as in the previous call
00091 *>          of SGEHRD. Q is equal to the unit matrix except in the
00092 *>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
00093 *>          If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
00094 *>          ILO = 1 and IHI = 0, if M = 0;
00095 *>          if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
00096 *>          ILO = 1 and IHI = 0, if N = 0.
00097 *> \endverbatim
00098 *>
00099 *> \param[in] A
00100 *> \verbatim
00101 *>          A is REAL array, dimension
00102 *>                               (LDA,M) if SIDE = 'L'
00103 *>                               (LDA,N) if SIDE = 'R'
00104 *>          The vectors which define the elementary reflectors, as
00105 *>          returned by SGEHRD.
00106 *> \endverbatim
00107 *>
00108 *> \param[in] LDA
00109 *> \verbatim
00110 *>          LDA is INTEGER
00111 *>          The leading dimension of the array A.
00112 *>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
00113 *> \endverbatim
00114 *>
00115 *> \param[in] TAU
00116 *> \verbatim
00117 *>          TAU is REAL array, dimension
00118 *>                               (M-1) if SIDE = 'L'
00119 *>                               (N-1) if SIDE = 'R'
00120 *>          TAU(i) must contain the scalar factor of the elementary
00121 *>          reflector H(i), as returned by SGEHRD.
00122 *> \endverbatim
00123 *>
00124 *> \param[in,out] C
00125 *> \verbatim
00126 *>          C is REAL array, dimension (LDC,N)
00127 *>          On entry, the M-by-N matrix C.
00128 *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
00129 *> \endverbatim
00130 *>
00131 *> \param[in] LDC
00132 *> \verbatim
00133 *>          LDC is INTEGER
00134 *>          The leading dimension of the array C. LDC >= max(1,M).
00135 *> \endverbatim
00136 *>
00137 *> \param[out] WORK
00138 *> \verbatim
00139 *>          WORK is REAL array, dimension (MAX(1,LWORK))
00140 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00141 *> \endverbatim
00142 *>
00143 *> \param[in] LWORK
00144 *> \verbatim
00145 *>          LWORK is INTEGER
00146 *>          The dimension of the array WORK.
00147 *>          If SIDE = 'L', LWORK >= max(1,N);
00148 *>          if SIDE = 'R', LWORK >= max(1,M).
00149 *>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
00150 *>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
00151 *>          blocksize.
00152 *>
00153 *>          If LWORK = -1, then a workspace query is assumed; the routine
00154 *>          only calculates the optimal size of the WORK array, returns
00155 *>          this value as the first entry of the WORK array, and no error
00156 *>          message related to LWORK is issued by XERBLA.
00157 *> \endverbatim
00158 *>
00159 *> \param[out] INFO
00160 *> \verbatim
00161 *>          INFO is INTEGER
00162 *>          = 0:  successful exit
00163 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00164 *> \endverbatim
00165 *
00166 *  Authors:
00167 *  ========
00168 *
00169 *> \author Univ. of Tennessee 
00170 *> \author Univ. of California Berkeley 
00171 *> \author Univ. of Colorado Denver 
00172 *> \author NAG Ltd. 
00173 *
00174 *> \date November 2011
00175 *
00176 *> \ingroup realOTHERcomputational
00177 *
00178 *  =====================================================================
00179       SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
00180      $                   LDC, WORK, LWORK, INFO )
00181 *
00182 *  -- LAPACK computational routine (version 3.4.0) --
00183 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00184 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00185 *     November 2011
00186 *
00187 *     .. Scalar Arguments ..
00188       CHARACTER          SIDE, TRANS
00189       INTEGER            IHI, ILO, INFO, LDA, LDC, LWORK, M, N
00190 *     ..
00191 *     .. Array Arguments ..
00192       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
00193      $                   WORK( * )
00194 *     ..
00195 *
00196 *  =====================================================================
00197 *
00198 *     .. Local Scalars ..
00199       LOGICAL            LEFT, LQUERY
00200       INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW
00201 *     ..
00202 *     .. External Functions ..
00203       LOGICAL            LSAME
00204       INTEGER            ILAENV
00205       EXTERNAL           ILAENV, LSAME
00206 *     ..
00207 *     .. External Subroutines ..
00208       EXTERNAL           SORMQR, XERBLA
00209 *     ..
00210 *     .. Intrinsic Functions ..
00211       INTRINSIC          MAX, MIN
00212 *     ..
00213 *     .. Executable Statements ..
00214 *
00215 *     Test the input arguments
00216 *
00217       INFO = 0
00218       NH = IHI - ILO
00219       LEFT = LSAME( SIDE, 'L' )
00220       LQUERY = ( LWORK.EQ.-1 )
00221 *
00222 *     NQ is the order of Q and NW is the minimum dimension of WORK
00223 *
00224       IF( LEFT ) THEN
00225          NQ = M
00226          NW = N
00227       ELSE
00228          NQ = N
00229          NW = M
00230       END IF
00231       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00232          INFO = -1
00233       ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) )
00234      $          THEN
00235          INFO = -2
00236       ELSE IF( M.LT.0 ) THEN
00237          INFO = -3
00238       ELSE IF( N.LT.0 ) THEN
00239          INFO = -4
00240       ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN
00241          INFO = -5
00242       ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN
00243          INFO = -6
00244       ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
00245          INFO = -8
00246       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00247          INFO = -11
00248       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00249          INFO = -13
00250       END IF
00251 *
00252       IF( INFO.EQ.0 ) THEN
00253          IF( LEFT ) THEN
00254             NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, NH, N, NH, -1 )
00255          ELSE
00256             NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, NH, NH, -1 ) 
00257          END IF
00258          LWKOPT = MAX( 1, NW )*NB
00259          WORK( 1 ) = LWKOPT
00260       END IF
00261 *
00262       IF( INFO.NE.0 ) THEN
00263          CALL XERBLA( 'SORMHR', -INFO )
00264          RETURN
00265       ELSE IF( LQUERY ) THEN
00266          RETURN
00267       END IF
00268 *
00269 *     Quick return if possible
00270 *
00271       IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN
00272          WORK( 1 ) = 1
00273          RETURN
00274       END IF
00275 *
00276       IF( LEFT ) THEN
00277          MI = NH
00278          NI = N
00279          I1 = ILO + 1
00280          I2 = 1
00281       ELSE
00282          MI = M
00283          NI = NH
00284          I1 = 1
00285          I2 = ILO + 1
00286       END IF
00287 *
00288       CALL SORMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA,
00289      $             TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00290 *
00291       WORK( 1 ) = LWKOPT
00292       RETURN
00293 *
00294 *     End of SORMHR
00295 *
00296       END
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