LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sormr3.f
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00001 *> \brief \b SORMR3
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SORMR3 + 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/sormr3.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
00022 *                          WORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          SIDE, TRANS
00026 *       INTEGER            INFO, K, L, LDA, LDC, M, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> SORMR3 overwrites the general real m by n matrix C with
00039 *>
00040 *>       Q * C  if SIDE = 'L' and TRANS = 'N', or
00041 *>
00042 *>       Q**T* C  if SIDE = 'L' and TRANS = 'C', or
00043 *>
00044 *>       C * Q  if SIDE = 'R' and TRANS = 'N', or
00045 *>
00046 *>       C * Q**T if SIDE = 'R' and TRANS = 'C',
00047 *>
00048 *> where Q is a real orthogonal matrix defined as the product of k
00049 *> elementary reflectors
00050 *>
00051 *>       Q = H(1) H(2) . . . H(k)
00052 *>
00053 *> as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n
00054 *> if SIDE = 'R'.
00055 *> \endverbatim
00056 *
00057 *  Arguments:
00058 *  ==========
00059 *
00060 *> \param[in] SIDE
00061 *> \verbatim
00062 *>          SIDE is CHARACTER*1
00063 *>          = 'L': apply Q or Q**T from the Left
00064 *>          = 'R': apply Q or Q**T from the Right
00065 *> \endverbatim
00066 *>
00067 *> \param[in] TRANS
00068 *> \verbatim
00069 *>          TRANS is CHARACTER*1
00070 *>          = 'N': apply Q  (No transpose)
00071 *>          = 'T': apply Q**T (Transpose)
00072 *> \endverbatim
00073 *>
00074 *> \param[in] M
00075 *> \verbatim
00076 *>          M is INTEGER
00077 *>          The number of rows of the matrix C. M >= 0.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] N
00081 *> \verbatim
00082 *>          N is INTEGER
00083 *>          The number of columns of the matrix C. N >= 0.
00084 *> \endverbatim
00085 *>
00086 *> \param[in] K
00087 *> \verbatim
00088 *>          K is INTEGER
00089 *>          The number of elementary reflectors whose product defines
00090 *>          the matrix Q.
00091 *>          If SIDE = 'L', M >= K >= 0;
00092 *>          if SIDE = 'R', N >= K >= 0.
00093 *> \endverbatim
00094 *>
00095 *> \param[in] L
00096 *> \verbatim
00097 *>          L is INTEGER
00098 *>          The number of columns of the matrix A containing
00099 *>          the meaningful part of the Householder reflectors.
00100 *>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
00101 *> \endverbatim
00102 *>
00103 *> \param[in] A
00104 *> \verbatim
00105 *>          A is REAL array, dimension
00106 *>                               (LDA,M) if SIDE = 'L',
00107 *>                               (LDA,N) if SIDE = 'R'
00108 *>          The i-th row must contain the vector which defines the
00109 *>          elementary reflector H(i), for i = 1,2,...,k, as returned by
00110 *>          STZRZF in the last k rows of its array argument A.
00111 *>          A is modified by the routine but restored on exit.
00112 *> \endverbatim
00113 *>
00114 *> \param[in] LDA
00115 *> \verbatim
00116 *>          LDA is INTEGER
00117 *>          The leading dimension of the array A. LDA >= max(1,K).
00118 *> \endverbatim
00119 *>
00120 *> \param[in] TAU
00121 *> \verbatim
00122 *>          TAU is REAL array, dimension (K)
00123 *>          TAU(i) must contain the scalar factor of the elementary
00124 *>          reflector H(i), as returned by STZRZF.
00125 *> \endverbatim
00126 *>
00127 *> \param[in,out] C
00128 *> \verbatim
00129 *>          C is REAL array, dimension (LDC,N)
00130 *>          On entry, the m-by-n matrix C.
00131 *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
00132 *> \endverbatim
00133 *>
00134 *> \param[in] LDC
00135 *> \verbatim
00136 *>          LDC is INTEGER
00137 *>          The leading dimension of the array C. LDC >= max(1,M).
00138 *> \endverbatim
00139 *>
00140 *> \param[out] WORK
00141 *> \verbatim
00142 *>          WORK is REAL array, dimension
00143 *>                                   (N) if SIDE = 'L',
00144 *>                                   (M) if SIDE = 'R'
00145 *> \endverbatim
00146 *>
00147 *> \param[out] INFO
00148 *> \verbatim
00149 *>          INFO is INTEGER
00150 *>          = 0: successful exit
00151 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00152 *> \endverbatim
00153 *
00154 *  Authors:
00155 *  ========
00156 *
00157 *> \author Univ. of Tennessee 
00158 *> \author Univ. of California Berkeley 
00159 *> \author Univ. of Colorado Denver 
00160 *> \author NAG Ltd. 
00161 *
00162 *> \date November 2011
00163 *
00164 *> \ingroup realOTHERcomputational
00165 *
00166 *> \par Contributors:
00167 *  ==================
00168 *>
00169 *>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
00170 *
00171 *> \par Further Details:
00172 *  =====================
00173 *>
00174 *> \verbatim
00175 *> \endverbatim
00176 *>
00177 *  =====================================================================
00178       SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
00179      $                   WORK, INFO )
00180 *
00181 *  -- LAPACK computational routine (version 3.4.0) --
00182 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00183 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00184 *     November 2011
00185 *
00186 *     .. Scalar Arguments ..
00187       CHARACTER          SIDE, TRANS
00188       INTEGER            INFO, K, L, LDA, LDC, M, N
00189 *     ..
00190 *     .. Array Arguments ..
00191       REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00192 *     ..
00193 *
00194 *  =====================================================================
00195 *
00196 *     .. Local Scalars ..
00197       LOGICAL            LEFT, NOTRAN
00198       INTEGER            I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
00199 *     ..
00200 *     .. External Functions ..
00201       LOGICAL            LSAME
00202       EXTERNAL           LSAME
00203 *     ..
00204 *     .. External Subroutines ..
00205       EXTERNAL           SLARZ, XERBLA
00206 *     ..
00207 *     .. Intrinsic Functions ..
00208       INTRINSIC          MAX
00209 *     ..
00210 *     .. Executable Statements ..
00211 *
00212 *     Test the input arguments
00213 *
00214       INFO = 0
00215       LEFT = LSAME( SIDE, 'L' )
00216       NOTRAN = LSAME( TRANS, 'N' )
00217 *
00218 *     NQ is the order of Q
00219 *
00220       IF( LEFT ) THEN
00221          NQ = M
00222       ELSE
00223          NQ = N
00224       END IF
00225       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00226          INFO = -1
00227       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
00228          INFO = -2
00229       ELSE IF( M.LT.0 ) THEN
00230          INFO = -3
00231       ELSE IF( N.LT.0 ) THEN
00232          INFO = -4
00233       ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
00234          INFO = -5
00235       ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
00236      $         ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
00237          INFO = -6
00238       ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
00239          INFO = -8
00240       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00241          INFO = -11
00242       END IF
00243       IF( INFO.NE.0 ) THEN
00244          CALL XERBLA( 'SORMR3', -INFO )
00245          RETURN
00246       END IF
00247 *
00248 *     Quick return if possible
00249 *
00250       IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
00251      $   RETURN
00252 *
00253       IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN
00254          I1 = 1
00255          I2 = K
00256          I3 = 1
00257       ELSE
00258          I1 = K
00259          I2 = 1
00260          I3 = -1
00261       END IF
00262 *
00263       IF( LEFT ) THEN
00264          NI = N
00265          JA = M - L + 1
00266          JC = 1
00267       ELSE
00268          MI = M
00269          JA = N - L + 1
00270          IC = 1
00271       END IF
00272 *
00273       DO 10 I = I1, I2, I3
00274          IF( LEFT ) THEN
00275 *
00276 *           H(i) or H(i)**T is applied to C(i:m,1:n)
00277 *
00278             MI = M - I + 1
00279             IC = I
00280          ELSE
00281 *
00282 *           H(i) or H(i)**T is applied to C(1:m,i:n)
00283 *
00284             NI = N - I + 1
00285             JC = I
00286          END IF
00287 *
00288 *        Apply H(i) or H(i)**T
00289 *
00290          CALL SLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ),
00291      $               C( IC, JC ), LDC, WORK )
00292 *
00293    10 CONTINUE
00294 *
00295       RETURN
00296 *
00297 *     End of SORMR3
00298 *
00299       END
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