LAPACK: SRC/sormlq.f Source File

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00001       SUBROUTINE SORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00002      $                   WORK, LWORK, INFO )
00003 *
00004 *  -- LAPACK routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          SIDE, TRANS
00011       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
00015      $                   WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  SORMLQ overwrites the general real M-by-N matrix C with
00022 *
00023 *                  SIDE = 'L'     SIDE = 'R'
00024 *  TRANS = 'N':      Q * C          C * Q
00025 *  TRANS = 'T':      Q**T * C       C * Q**T
00026 *
00027 *  where Q is a real orthogonal matrix defined as the product of k
00028 *  elementary reflectors
00029 *
00030 *        Q = H(k) . . . H(2) H(1)
00031 *
00032 *  as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N
00033 *  if SIDE = 'R'.
00034 *
00035 *  Arguments
00036 *  =========
00037 *
00038 *  SIDE    (input) CHARACTER*1
00039 *          = 'L': apply Q or Q**T from the Left;
00040 *          = 'R': apply Q or Q**T from the Right.
00041 *
00042 *  TRANS   (input) CHARACTER*1
00043 *          = 'N':  No transpose, apply Q;
00044 *          = 'T':  Transpose, apply Q**T.
00045 *
00046 *  M       (input) INTEGER
00047 *          The number of rows of the matrix C. M >= 0.
00048 *
00049 *  N       (input) INTEGER
00050 *          The number of columns of the matrix C. N >= 0.
00051 *
00052 *  K       (input) INTEGER
00053 *          The number of elementary reflectors whose product defines
00054 *          the matrix Q.
00055 *          If SIDE = 'L', M >= K >= 0;
00056 *          if SIDE = 'R', N >= K >= 0.
00057 *
00058 *  A       (input) REAL array, dimension
00059 *                               (LDA,M) if SIDE = 'L',
00060 *                               (LDA,N) if SIDE = 'R'
00061 *          The i-th row must contain the vector which defines the
00062 *          elementary reflector H(i), for i = 1,2,...,k, as returned by
00063 *          SGELQF in the first k rows of its array argument A.
00064 *          A is modified by the routine but restored on exit.
00065 *
00066 *  LDA     (input) INTEGER
00067 *          The leading dimension of the array A. LDA >= max(1,K).
00068 *
00069 *  TAU     (input) REAL array, dimension (K)
00070 *          TAU(i) must contain the scalar factor of the elementary
00071 *          reflector H(i), as returned by SGELQF.
00072 *
00073 *  C       (input/output) REAL array, dimension (LDC,N)
00074 *          On entry, the M-by-N matrix C.
00075 *          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
00076 *
00077 *  LDC     (input) INTEGER
00078 *          The leading dimension of the array C. LDC >= max(1,M).
00079 *
00080 *  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
00081 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00082 *
00083 *  LWORK   (input) INTEGER
00084 *          The dimension of the array WORK.
00085 *          If SIDE = 'L', LWORK >= max(1,N);
00086 *          if SIDE = 'R', LWORK >= max(1,M).
00087 *          For optimum performance LWORK >= N*NB if SIDE = 'L', and
00088 *          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
00089 *          blocksize.
00090 *
00091 *          If LWORK = -1, then a workspace query is assumed; the routine
00092 *          only calculates the optimal size of the WORK array, returns
00093 *          this value as the first entry of the WORK array, and no error
00094 *          message related to LWORK is issued by XERBLA.
00095 *
00096 *  INFO    (output) INTEGER
00097 *          = 0:  successful exit
00098 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00099 *
00100 *  =====================================================================
00101 *
00102 *     .. Parameters ..
00103       INTEGER            NBMAX, LDT
00104       PARAMETER          ( NBMAX = 64, LDT = NBMAX+1 )
00105 *     ..
00106 *     .. Local Scalars ..
00107       LOGICAL            LEFT, LQUERY, NOTRAN
00108       CHARACTER          TRANST
00109       INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
00110      $                   LWKOPT, MI, NB, NBMIN, NI, NQ, NW
00111 *     ..
00112 *     .. Local Arrays ..
00113       REAL               T( LDT, NBMAX )
00114 *     ..
00115 *     .. External Functions ..
00116       LOGICAL            LSAME
00117       INTEGER            ILAENV
00118       EXTERNAL           LSAME, ILAENV
00119 *     ..
00120 *     .. External Subroutines ..
00121       EXTERNAL           SLARFB, SLARFT, SORML2, XERBLA
00122 *     ..
00123 *     .. Intrinsic Functions ..
00124       INTRINSIC          MAX, MIN
00125 *     ..
00126 *     .. Executable Statements ..
00127 *
00128 *     Test the input arguments
00129 *
00130       INFO = 0
00131       LEFT = LSAME( SIDE, 'L' )
00132       NOTRAN = LSAME( TRANS, 'N' )
00133       LQUERY = ( LWORK.EQ.-1 )
00134 *
00135 *     NQ is the order of Q and NW is the minimum dimension of WORK
00136 *
00137       IF( LEFT ) THEN
00138          NQ = M
00139          NW = N
00140       ELSE
00141          NQ = N
00142          NW = M
00143       END IF
00144       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00145          INFO = -1
00146       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
00147          INFO = -2
00148       ELSE IF( M.LT.0 ) THEN
00149          INFO = -3
00150       ELSE IF( N.LT.0 ) THEN
00151          INFO = -4
00152       ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
00153          INFO = -5
00154       ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
00155          INFO = -7
00156       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00157          INFO = -10
00158       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00159          INFO = -12
00160       END IF
00161 *
00162       IF( INFO.EQ.0 ) THEN
00163 *
00164 *        Determine the block size.  NB may be at most NBMAX, where NBMAX
00165 *        is used to define the local array T.
00166 *
00167          NB = MIN( NBMAX, ILAENV( 1, 'SORMLQ', SIDE // TRANS, M, N, K,
00168      $             -1 ) )
00169          LWKOPT = MAX( 1, NW )*NB
00170          WORK( 1 ) = LWKOPT
00171       END IF 
00172 *
00173       IF( INFO.NE.0 ) THEN
00174          CALL XERBLA( 'SORMLQ', -INFO )
00175          RETURN
00176       ELSE IF( LQUERY ) THEN
00177          RETURN
00178       END IF
00179 *
00180 *     Quick return if possible
00181 *
00182       IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
00183          WORK( 1 ) = 1
00184          RETURN
00185       END IF
00186 *
00187       NBMIN = 2
00188       LDWORK = NW
00189       IF( NB.GT.1 .AND. NB.LT.K ) THEN
00190          IWS = NW*NB
00191          IF( LWORK.LT.IWS ) THEN
00192             NB = LWORK / LDWORK
00193             NBMIN = MAX( 2, ILAENV( 2, 'SORMLQ', SIDE // TRANS, M, N, K,
00194      $              -1 ) )
00195          END IF
00196       ELSE
00197          IWS = NW
00198       END IF
00199 *
00200       IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
00201 *
00202 *        Use unblocked code
00203 *
00204          CALL SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
00205      $                IINFO )
00206       ELSE
00207 *
00208 *        Use blocked code
00209 *
00210          IF( ( LEFT .AND. NOTRAN ) .OR.
00211      $       ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
00212             I1 = 1
00213             I2 = K
00214             I3 = NB
00215          ELSE
00216             I1 = ( ( K-1 ) / NB )*NB + 1
00217             I2 = 1
00218             I3 = -NB
00219          END IF
00220 *
00221          IF( LEFT ) THEN
00222             NI = N
00223             JC = 1
00224          ELSE
00225             MI = M
00226             IC = 1
00227          END IF
00228 *
00229          IF( NOTRAN ) THEN
00230             TRANST = 'T'
00231          ELSE
00232             TRANST = 'N'
00233          END IF
00234 *
00235          DO 10 I = I1, I2, I3
00236             IB = MIN( NB, K-I+1 )
00237 *
00238 *           Form the triangular factor of the block reflector
00239 *           H = H(i) H(i+1) . . . H(i+ib-1)
00240 *
00241             CALL SLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ),
00242      $                   LDA, TAU( I ), T, LDT )
00243             IF( LEFT ) THEN
00244 *
00245 *              H or H' is applied to C(i:m,1:n)
00246 *
00247                MI = M - I + 1
00248                IC = I
00249             ELSE
00250 *
00251 *              H or H' is applied to C(1:m,i:n)
00252 *
00253                NI = N - I + 1
00254                JC = I
00255             END IF
00256 *
00257 *           Apply H or H'
00258 *
00259             CALL SLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
00260      $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
00261      $                   LDWORK )
00262    10    CONTINUE
00263       END IF
00264       WORK( 1 ) = LWKOPT
00265       RETURN
00266 *
00267 *     End of SORMLQ
00268 *
00269       END