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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 00002 $ WORK, LWORK, INFO ) 00003 * 00004 * -- LAPACK routine (version 3.3.1) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * -- April 2011 -- 00008 * 00009 * .. Scalar Arguments .. 00010 CHARACTER SIDE, TRANS 00011 INTEGER INFO, K, L, LDA, LDC, LWORK, M, N 00012 * .. 00013 * .. Array Arguments .. 00014 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * SORMRZ overwrites the general real M-by-N matrix C with 00021 * 00022 * SIDE = 'L' SIDE = 'R' 00023 * TRANS = 'N': Q * C C * Q 00024 * TRANS = 'T': Q**T * C C * Q**T 00025 * 00026 * where Q is a real orthogonal matrix defined as the product of k 00027 * elementary reflectors 00028 * 00029 * Q = H(1) H(2) . . . H(k) 00030 * 00031 * as returned by STZRZF. Q is of order M if SIDE = 'L' and of order N 00032 * if SIDE = 'R'. 00033 * 00034 * Arguments 00035 * ========= 00036 * 00037 * SIDE (input) CHARACTER*1 00038 * = 'L': apply Q or Q**T from the Left; 00039 * = 'R': apply Q or Q**T from the Right. 00040 * 00041 * TRANS (input) CHARACTER*1 00042 * = 'N': No transpose, apply Q; 00043 * = 'T': Transpose, apply Q**T. 00044 * 00045 * M (input) INTEGER 00046 * The number of rows of the matrix C. M >= 0. 00047 * 00048 * N (input) INTEGER 00049 * The number of columns of the matrix C. N >= 0. 00050 * 00051 * K (input) INTEGER 00052 * The number of elementary reflectors whose product defines 00053 * the matrix Q. 00054 * If SIDE = 'L', M >= K >= 0; 00055 * if SIDE = 'R', N >= K >= 0. 00056 * 00057 * L (input) INTEGER 00058 * The number of columns of the matrix A containing 00059 * the meaningful part of the Householder reflectors. 00060 * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. 00061 * 00062 * A (input) REAL array, dimension 00063 * (LDA,M) if SIDE = 'L', 00064 * (LDA,N) if SIDE = 'R' 00065 * The i-th row must contain the vector which defines the 00066 * elementary reflector H(i), for i = 1,2,...,k, as returned by 00067 * STZRZF in the last k rows of its array argument A. 00068 * A is modified by the routine but restored on exit. 00069 * 00070 * LDA (input) INTEGER 00071 * The leading dimension of the array A. LDA >= max(1,K). 00072 * 00073 * TAU (input) REAL array, dimension (K) 00074 * TAU(i) must contain the scalar factor of the elementary 00075 * reflector H(i), as returned by STZRZF. 00076 * 00077 * C (input/output) REAL array, dimension (LDC,N) 00078 * On entry, the M-by-N matrix C. 00079 * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. 00080 * 00081 * LDC (input) INTEGER 00082 * The leading dimension of the array C. LDC >= max(1,M). 00083 * 00084 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) 00085 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00086 * 00087 * LWORK (input) INTEGER 00088 * The dimension of the array WORK. 00089 * If SIDE = 'L', LWORK >= max(1,N); 00090 * if SIDE = 'R', LWORK >= max(1,M). 00091 * For optimum performance LWORK >= N*NB if SIDE = 'L', and 00092 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00093 * blocksize. 00094 * 00095 * If LWORK = -1, then a workspace query is assumed; the routine 00096 * only calculates the optimal size of the WORK array, returns 00097 * this value as the first entry of the WORK array, and no error 00098 * message related to LWORK is issued by XERBLA. 00099 * 00100 * INFO (output) INTEGER 00101 * = 0: successful exit 00102 * < 0: if INFO = -i, the i-th argument had an illegal value 00103 * 00104 * Further Details 00105 * =============== 00106 * 00107 * Based on contributions by 00108 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 00109 * 00110 * ===================================================================== 00111 * 00112 * .. Parameters .. 00113 INTEGER NBMAX, LDT 00114 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) 00115 * .. 00116 * .. Local Scalars .. 00117 LOGICAL LEFT, LQUERY, NOTRAN 00118 CHARACTER TRANST 00119 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC, 00120 $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW 00121 * .. 00122 * .. Local Arrays .. 00123 REAL T( LDT, NBMAX ) 00124 * .. 00125 * .. External Functions .. 00126 LOGICAL LSAME 00127 INTEGER ILAENV 00128 EXTERNAL LSAME, ILAENV 00129 * .. 00130 * .. External Subroutines .. 00131 EXTERNAL SLARZB, SLARZT, SORMR3, XERBLA 00132 * .. 00133 * .. Intrinsic Functions .. 00134 INTRINSIC MAX, MIN 00135 * .. 00136 * .. Executable Statements .. 00137 * 00138 * Test the input arguments 00139 * 00140 INFO = 0 00141 LEFT = LSAME( SIDE, 'L' ) 00142 NOTRAN = LSAME( TRANS, 'N' ) 00143 LQUERY = ( LWORK.EQ.-1 ) 00144 * 00145 * NQ is the order of Q and NW is the minimum dimension of WORK 00146 * 00147 IF( LEFT ) THEN 00148 NQ = M 00149 NW = MAX( 1, N ) 00150 ELSE 00151 NQ = N 00152 NW = MAX( 1, M ) 00153 END IF 00154 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00155 INFO = -1 00156 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00157 INFO = -2 00158 ELSE IF( M.LT.0 ) THEN 00159 INFO = -3 00160 ELSE IF( N.LT.0 ) THEN 00161 INFO = -4 00162 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00163 INFO = -5 00164 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR. 00165 $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN 00166 INFO = -6 00167 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN 00168 INFO = -8 00169 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00170 INFO = -11 00171 END IF 00172 * 00173 IF( INFO.EQ.0 ) THEN 00174 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00175 LWKOPT = 1 00176 ELSE 00177 * 00178 * Determine the block size. NB may be at most NBMAX, where 00179 * NBMAX is used to define the local array T. 00180 * 00181 NB = MIN( NBMAX, ILAENV( 1, 'SORMRQ', SIDE // TRANS, M, N, 00182 $ K, -1 ) ) 00183 LWKOPT = NW*NB 00184 END IF 00185 WORK( 1 ) = LWKOPT 00186 * 00187 IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00188 INFO = -13 00189 END IF 00190 END IF 00191 * 00192 IF( INFO.NE.0 ) THEN 00193 CALL XERBLA( 'SORMRZ', -INFO ) 00194 RETURN 00195 ELSE IF( LQUERY ) THEN 00196 RETURN 00197 END IF 00198 * 00199 * Quick return if possible 00200 * 00201 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00202 RETURN 00203 END IF 00204 * 00205 NBMIN = 2 00206 LDWORK = NW 00207 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00208 IWS = NW*NB 00209 IF( LWORK.LT.IWS ) THEN 00210 NB = LWORK / LDWORK 00211 NBMIN = MAX( 2, ILAENV( 2, 'SORMRQ', SIDE // TRANS, M, N, K, 00212 $ -1 ) ) 00213 END IF 00214 ELSE 00215 IWS = NW 00216 END IF 00217 * 00218 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00219 * 00220 * Use unblocked code 00221 * 00222 CALL SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 00223 $ WORK, IINFO ) 00224 ELSE 00225 * 00226 * Use blocked code 00227 * 00228 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. 00229 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN 00230 I1 = 1 00231 I2 = K 00232 I3 = NB 00233 ELSE 00234 I1 = ( ( K-1 ) / NB )*NB + 1 00235 I2 = 1 00236 I3 = -NB 00237 END IF 00238 * 00239 IF( LEFT ) THEN 00240 NI = N 00241 JC = 1 00242 JA = M - L + 1 00243 ELSE 00244 MI = M 00245 IC = 1 00246 JA = N - L + 1 00247 END IF 00248 * 00249 IF( NOTRAN ) THEN 00250 TRANST = 'T' 00251 ELSE 00252 TRANST = 'N' 00253 END IF 00254 * 00255 DO 10 I = I1, I2, I3 00256 IB = MIN( NB, K-I+1 ) 00257 * 00258 * Form the triangular factor of the block reflector 00259 * H = H(i+ib-1) . . . H(i+1) H(i) 00260 * 00261 CALL SLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA, 00262 $ TAU( I ), T, LDT ) 00263 * 00264 IF( LEFT ) THEN 00265 * 00266 * H or H**T is applied to C(i:m,1:n) 00267 * 00268 MI = M - I + 1 00269 IC = I 00270 ELSE 00271 * 00272 * H or H**T is applied to C(1:m,i:n) 00273 * 00274 NI = N - I + 1 00275 JC = I 00276 END IF 00277 * 00278 * Apply H or H**T 00279 * 00280 CALL SLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, 00281 $ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ), 00282 $ LDC, WORK, LDWORK ) 00283 10 CONTINUE 00284 * 00285 END IF 00286 * 00287 WORK( 1 ) = LWKOPT 00288 * 00289 RETURN 00290 * 00291 * End of SORMRZ 00292 * 00293 END
1.7.3 
