LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sormbr.f
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00001 *> \brief \b SORMBR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SORMBR + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormbr.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormbr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
00022 *                          LDC, WORK, LWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          SIDE, TRANS, VECT
00026 *       INTEGER            INFO, K, 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 *> If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C
00040 *> with
00041 *>                 SIDE = 'L'     SIDE = 'R'
00042 *> TRANS = 'N':      Q * C          C * Q
00043 *> TRANS = 'T':      Q**T * C       C * Q**T
00044 *>
00045 *> If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C
00046 *> with
00047 *>                 SIDE = 'L'     SIDE = 'R'
00048 *> TRANS = 'N':      P * C          C * P
00049 *> TRANS = 'T':      P**T * C       C * P**T
00050 *>
00051 *> Here Q and P**T are the orthogonal matrices determined by SGEBRD when
00052 *> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
00053 *> P**T are defined as products of elementary reflectors H(i) and G(i)
00054 *> respectively.
00055 *>
00056 *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
00057 *> order of the orthogonal matrix Q or P**T that is applied.
00058 *>
00059 *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
00060 *> if nq >= k, Q = H(1) H(2) . . . H(k);
00061 *> if nq < k, Q = H(1) H(2) . . . H(nq-1).
00062 *>
00063 *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
00064 *> if k < nq, P = G(1) G(2) . . . G(k);
00065 *> if k >= nq, P = G(1) G(2) . . . G(nq-1).
00066 *> \endverbatim
00067 *
00068 *  Arguments:
00069 *  ==========
00070 *
00071 *> \param[in] VECT
00072 *> \verbatim
00073 *>          VECT is CHARACTER*1
00074 *>          = 'Q': apply Q or Q**T;
00075 *>          = 'P': apply P or P**T.
00076 *> \endverbatim
00077 *>
00078 *> \param[in] SIDE
00079 *> \verbatim
00080 *>          SIDE is CHARACTER*1
00081 *>          = 'L': apply Q, Q**T, P or P**T from the Left;
00082 *>          = 'R': apply Q, Q**T, P or P**T from the Right.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] TRANS
00086 *> \verbatim
00087 *>          TRANS is CHARACTER*1
00088 *>          = 'N':  No transpose, apply Q  or P;
00089 *>          = 'T':  Transpose, apply Q**T or P**T.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] M
00093 *> \verbatim
00094 *>          M is INTEGER
00095 *>          The number of rows of the matrix C. M >= 0.
00096 *> \endverbatim
00097 *>
00098 *> \param[in] N
00099 *> \verbatim
00100 *>          N is INTEGER
00101 *>          The number of columns of the matrix C. N >= 0.
00102 *> \endverbatim
00103 *>
00104 *> \param[in] K
00105 *> \verbatim
00106 *>          K is INTEGER
00107 *>          If VECT = 'Q', the number of columns in the original
00108 *>          matrix reduced by SGEBRD.
00109 *>          If VECT = 'P', the number of rows in the original
00110 *>          matrix reduced by SGEBRD.
00111 *>          K >= 0.
00112 *> \endverbatim
00113 *>
00114 *> \param[in] A
00115 *> \verbatim
00116 *>          A is REAL array, dimension
00117 *>                                (LDA,min(nq,K)) if VECT = 'Q'
00118 *>                                (LDA,nq)        if VECT = 'P'
00119 *>          The vectors which define the elementary reflectors H(i) and
00120 *>          G(i), whose products determine the matrices Q and P, as
00121 *>          returned by SGEBRD.
00122 *> \endverbatim
00123 *>
00124 *> \param[in] LDA
00125 *> \verbatim
00126 *>          LDA is INTEGER
00127 *>          The leading dimension of the array A.
00128 *>          If VECT = 'Q', LDA >= max(1,nq);
00129 *>          if VECT = 'P', LDA >= max(1,min(nq,K)).
00130 *> \endverbatim
00131 *>
00132 *> \param[in] TAU
00133 *> \verbatim
00134 *>          TAU is REAL array, dimension (min(nq,K))
00135 *>          TAU(i) must contain the scalar factor of the elementary
00136 *>          reflector H(i) or G(i) which determines Q or P, as returned
00137 *>          by SGEBRD in the array argument TAUQ or TAUP.
00138 *> \endverbatim
00139 *>
00140 *> \param[in,out] C
00141 *> \verbatim
00142 *>          C is REAL array, dimension (LDC,N)
00143 *>          On entry, the M-by-N matrix C.
00144 *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
00145 *>          or P*C or P**T*C or C*P or C*P**T.
00146 *> \endverbatim
00147 *>
00148 *> \param[in] LDC
00149 *> \verbatim
00150 *>          LDC is INTEGER
00151 *>          The leading dimension of the array C. LDC >= max(1,M).
00152 *> \endverbatim
00153 *>
00154 *> \param[out] WORK
00155 *> \verbatim
00156 *>          WORK is REAL array, dimension (MAX(1,LWORK))
00157 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00158 *> \endverbatim
00159 *>
00160 *> \param[in] LWORK
00161 *> \verbatim
00162 *>          LWORK is INTEGER
00163 *>          The dimension of the array WORK.
00164 *>          If SIDE = 'L', LWORK >= max(1,N);
00165 *>          if SIDE = 'R', LWORK >= max(1,M).
00166 *>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
00167 *>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
00168 *>          blocksize.
00169 *>
00170 *>          If LWORK = -1, then a workspace query is assumed; the routine
00171 *>          only calculates the optimal size of the WORK array, returns
00172 *>          this value as the first entry of the WORK array, and no error
00173 *>          message related to LWORK is issued by XERBLA.
00174 *> \endverbatim
00175 *>
00176 *> \param[out] INFO
00177 *> \verbatim
00178 *>          INFO is INTEGER
00179 *>          = 0:  successful exit
00180 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00181 *> \endverbatim
00182 *
00183 *  Authors:
00184 *  ========
00185 *
00186 *> \author Univ. of Tennessee 
00187 *> \author Univ. of California Berkeley 
00188 *> \author Univ. of Colorado Denver 
00189 *> \author NAG Ltd. 
00190 *
00191 *> \date November 2011
00192 *
00193 *> \ingroup realOTHERcomputational
00194 *
00195 *  =====================================================================
00196       SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
00197      $                   LDC, WORK, LWORK, INFO )
00198 *
00199 *  -- LAPACK computational routine (version 3.4.0) --
00200 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00201 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00202 *     November 2011
00203 *
00204 *     .. Scalar Arguments ..
00205       CHARACTER          SIDE, TRANS, VECT
00206       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00207 *     ..
00208 *     .. Array Arguments ..
00209       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
00210      $                   WORK( * )
00211 *     ..
00212 *
00213 *  =====================================================================
00214 *
00215 *     .. Local Scalars ..
00216       LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
00217       CHARACTER          TRANST
00218       INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
00219 *     ..
00220 *     .. External Functions ..
00221       LOGICAL            LSAME
00222       INTEGER            ILAENV
00223       EXTERNAL           ILAENV, LSAME
00224 *     ..
00225 *     .. External Subroutines ..
00226       EXTERNAL           SORMLQ, SORMQR, XERBLA
00227 *     ..
00228 *     .. Intrinsic Functions ..
00229       INTRINSIC          MAX, MIN
00230 *     ..
00231 *     .. Executable Statements ..
00232 *
00233 *     Test the input arguments
00234 *
00235       INFO = 0
00236       APPLYQ = LSAME( VECT, 'Q' )
00237       LEFT = LSAME( SIDE, 'L' )
00238       NOTRAN = LSAME( TRANS, 'N' )
00239       LQUERY = ( LWORK.EQ.-1 )
00240 *
00241 *     NQ is the order of Q or P and NW is the minimum dimension of WORK
00242 *
00243       IF( LEFT ) THEN
00244          NQ = M
00245          NW = N
00246       ELSE
00247          NQ = N
00248          NW = M
00249       END IF
00250       IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
00251          INFO = -1
00252       ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00253          INFO = -2
00254       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
00255          INFO = -3
00256       ELSE IF( M.LT.0 ) THEN
00257          INFO = -4
00258       ELSE IF( N.LT.0 ) THEN
00259          INFO = -5
00260       ELSE IF( K.LT.0 ) THEN
00261          INFO = -6
00262       ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
00263      $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
00264      $          THEN
00265          INFO = -8
00266       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00267          INFO = -11
00268       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00269          INFO = -13
00270       END IF
00271 *
00272       IF( INFO.EQ.0 ) THEN
00273          IF( APPLYQ ) THEN
00274             IF( LEFT ) THEN
00275                NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M-1, N, M-1,
00276      $                      -1 )
00277             ELSE
00278                NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, N-1, N-1,
00279      $                      -1 )
00280             END IF   
00281          ELSE
00282             IF( LEFT ) THEN
00283                NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M-1, N, M-1,
00284      $                      -1 ) 
00285             ELSE
00286                NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M, N-1, N-1,
00287      $                      -1 )
00288             END IF
00289          END IF
00290          LWKOPT = MAX( 1, NW )*NB
00291          WORK( 1 ) = LWKOPT 
00292       END IF
00293 *
00294       IF( INFO.NE.0 ) THEN
00295          CALL XERBLA( 'SORMBR', -INFO )
00296          RETURN
00297       ELSE IF( LQUERY ) THEN
00298          RETURN
00299       END IF
00300 *
00301 *     Quick return if possible
00302 *
00303       WORK( 1 ) = 1
00304       IF( M.EQ.0 .OR. N.EQ.0 )
00305      $   RETURN
00306 *
00307       IF( APPLYQ ) THEN
00308 *
00309 *        Apply Q
00310 *
00311          IF( NQ.GE.K ) THEN
00312 *
00313 *           Q was determined by a call to SGEBRD with nq >= k
00314 *
00315             CALL SORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00316      $                   WORK, LWORK, IINFO )
00317          ELSE IF( NQ.GT.1 ) THEN
00318 *
00319 *           Q was determined by a call to SGEBRD with nq < k
00320 *
00321             IF( LEFT ) THEN
00322                MI = M - 1
00323                NI = N
00324                I1 = 2
00325                I2 = 1
00326             ELSE
00327                MI = M
00328                NI = N - 1
00329                I1 = 1
00330                I2 = 2
00331             END IF
00332             CALL SORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
00333      $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00334          END IF
00335       ELSE
00336 *
00337 *        Apply P
00338 *
00339          IF( NOTRAN ) THEN
00340             TRANST = 'T'
00341          ELSE
00342             TRANST = 'N'
00343          END IF
00344          IF( NQ.GT.K ) THEN
00345 *
00346 *           P was determined by a call to SGEBRD with nq > k
00347 *
00348             CALL SORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
00349      $                   WORK, LWORK, IINFO )
00350          ELSE IF( NQ.GT.1 ) THEN
00351 *
00352 *           P was determined by a call to SGEBRD with nq <= k
00353 *
00354             IF( LEFT ) THEN
00355                MI = M - 1
00356                NI = N
00357                I1 = 2
00358                I2 = 1
00359             ELSE
00360                MI = M
00361                NI = N - 1
00362                I1 = 1
00363                I2 = 2
00364             END IF
00365             CALL SORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
00366      $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00367          END IF
00368       END IF
00369       WORK( 1 ) = LWKOPT
00370       RETURN
00371 *
00372 *     End of SORMBR
00373 *
00374       END
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