LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sorml2.f
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00001 *> \brief \b SORML2
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SORML2 + 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/sorml2.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00022 *                          WORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          SIDE, TRANS
00026 *       INTEGER            INFO, K, 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 *> SORML2 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 = 'T', or
00043 *>
00044 *>       C * Q  if SIDE = 'R' and TRANS = 'N', or
00045 *>
00046 *>       C * Q**T if SIDE = 'R' and TRANS = 'T',
00047 *>
00048 *> where Q is a real orthogonal matrix defined as the product of k
00049 *> elementary reflectors
00050 *>
00051 *>       Q = H(k) . . . H(2) H(1)
00052 *>
00053 *> as returned by SGELQF. 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] A
00096 *> \verbatim
00097 *>          A is REAL array, dimension
00098 *>                               (LDA,M) if SIDE = 'L',
00099 *>                               (LDA,N) if SIDE = 'R'
00100 *>          The i-th row must contain the vector which defines the
00101 *>          elementary reflector H(i), for i = 1,2,...,k, as returned by
00102 *>          SGELQF in the first k rows of its array argument A.
00103 *>          A is modified by the routine but restored on exit.
00104 *> \endverbatim
00105 *>
00106 *> \param[in] LDA
00107 *> \verbatim
00108 *>          LDA is INTEGER
00109 *>          The leading dimension of the array A. LDA >= max(1,K).
00110 *> \endverbatim
00111 *>
00112 *> \param[in] TAU
00113 *> \verbatim
00114 *>          TAU is REAL array, dimension (K)
00115 *>          TAU(i) must contain the scalar factor of the elementary
00116 *>          reflector H(i), as returned by SGELQF.
00117 *> \endverbatim
00118 *>
00119 *> \param[in,out] C
00120 *> \verbatim
00121 *>          C is REAL array, dimension (LDC,N)
00122 *>          On entry, the m by n matrix C.
00123 *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
00124 *> \endverbatim
00125 *>
00126 *> \param[in] LDC
00127 *> \verbatim
00128 *>          LDC is INTEGER
00129 *>          The leading dimension of the array C. LDC >= max(1,M).
00130 *> \endverbatim
00131 *>
00132 *> \param[out] WORK
00133 *> \verbatim
00134 *>          WORK is REAL array, dimension
00135 *>                                   (N) if SIDE = 'L',
00136 *>                                   (M) if SIDE = 'R'
00137 *> \endverbatim
00138 *>
00139 *> \param[out] INFO
00140 *> \verbatim
00141 *>          INFO is INTEGER
00142 *>          = 0: successful exit
00143 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00144 *> \endverbatim
00145 *
00146 *  Authors:
00147 *  ========
00148 *
00149 *> \author Univ. of Tennessee 
00150 *> \author Univ. of California Berkeley 
00151 *> \author Univ. of Colorado Denver 
00152 *> \author NAG Ltd. 
00153 *
00154 *> \date November 2011
00155 *
00156 *> \ingroup realOTHERcomputational
00157 *
00158 *  =====================================================================
00159       SUBROUTINE SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00160      $                   WORK, INFO )
00161 *
00162 *  -- LAPACK computational routine (version 3.4.0) --
00163 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00164 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00165 *     November 2011
00166 *
00167 *     .. Scalar Arguments ..
00168       CHARACTER          SIDE, TRANS
00169       INTEGER            INFO, K, LDA, LDC, M, N
00170 *     ..
00171 *     .. Array Arguments ..
00172       REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00173 *     ..
00174 *
00175 *  =====================================================================
00176 *
00177 *     .. Parameters ..
00178       REAL               ONE
00179       PARAMETER          ( ONE = 1.0E+0 )
00180 *     ..
00181 *     .. Local Scalars ..
00182       LOGICAL            LEFT, NOTRAN
00183       INTEGER            I, I1, I2, I3, IC, JC, MI, NI, NQ
00184       REAL               AII
00185 *     ..
00186 *     .. External Functions ..
00187       LOGICAL            LSAME
00188       EXTERNAL           LSAME
00189 *     ..
00190 *     .. External Subroutines ..
00191       EXTERNAL           SLARF, XERBLA
00192 *     ..
00193 *     .. Intrinsic Functions ..
00194       INTRINSIC          MAX
00195 *     ..
00196 *     .. Executable Statements ..
00197 *
00198 *     Test the input arguments
00199 *
00200       INFO = 0
00201       LEFT = LSAME( SIDE, 'L' )
00202       NOTRAN = LSAME( TRANS, 'N' )
00203 *
00204 *     NQ is the order of Q
00205 *
00206       IF( LEFT ) THEN
00207          NQ = M
00208       ELSE
00209          NQ = N
00210       END IF
00211       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00212          INFO = -1
00213       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
00214          INFO = -2
00215       ELSE IF( M.LT.0 ) THEN
00216          INFO = -3
00217       ELSE IF( N.LT.0 ) THEN
00218          INFO = -4
00219       ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
00220          INFO = -5
00221       ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
00222          INFO = -7
00223       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00224          INFO = -10
00225       END IF
00226       IF( INFO.NE.0 ) THEN
00227          CALL XERBLA( 'SORML2', -INFO )
00228          RETURN
00229       END IF
00230 *
00231 *     Quick return if possible
00232 *
00233       IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
00234      $   RETURN
00235 *
00236       IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) )
00237      $     THEN
00238          I1 = 1
00239          I2 = K
00240          I3 = 1
00241       ELSE
00242          I1 = K
00243          I2 = 1
00244          I3 = -1
00245       END IF
00246 *
00247       IF( LEFT ) THEN
00248          NI = N
00249          JC = 1
00250       ELSE
00251          MI = M
00252          IC = 1
00253       END IF
00254 *
00255       DO 10 I = I1, I2, I3
00256          IF( LEFT ) THEN
00257 *
00258 *           H(i) is applied to C(i:m,1:n)
00259 *
00260             MI = M - I + 1
00261             IC = I
00262          ELSE
00263 *
00264 *           H(i) is applied to C(1:m,i:n)
00265 *
00266             NI = N - I + 1
00267             JC = I
00268          END IF
00269 *
00270 *        Apply H(i)
00271 *
00272          AII = A( I, I )
00273          A( I, I ) = ONE
00274          CALL SLARF( SIDE, MI, NI, A( I, I ), LDA, TAU( I ),
00275      $               C( IC, JC ), LDC, WORK )
00276          A( I, I ) = AII
00277    10 CONTINUE
00278       RETURN
00279 *
00280 *     End of SORML2
00281 *
00282       END
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