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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 SORMQL( SIDE, TRANS, M, N, K, 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, 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 * SORMQL 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 SGEQLF. 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 (LDA,K) 00059 * The i-th column must contain the vector which defines the 00060 * elementary reflector H(i), for i = 1,2,...,k, as returned by 00061 * SGEQLF in the last k columns of its array argument A. 00062 * A is modified by the routine but restored on exit. 00063 * 00064 * LDA (input) INTEGER 00065 * The leading dimension of the array A. 00066 * If SIDE = 'L', LDA >= max(1,M); 00067 * if SIDE = 'R', LDA >= max(1,N). 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 SGEQLF. 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 INTEGER I, I1, I2, I3, IB, IINFO, IWS, LDWORK, LWKOPT, 00109 $ MI, NB, NBMIN, NI, NQ, NW 00110 * .. 00111 * .. Local Arrays .. 00112 REAL T( LDT, NBMAX ) 00113 * .. 00114 * .. External Functions .. 00115 LOGICAL LSAME 00116 INTEGER ILAENV 00117 EXTERNAL LSAME, ILAENV 00118 * .. 00119 * .. External Subroutines .. 00120 EXTERNAL SLARFB, SLARFT, SORM2L, XERBLA 00121 * .. 00122 * .. Intrinsic Functions .. 00123 INTRINSIC MAX, MIN 00124 * .. 00125 * .. Executable Statements .. 00126 * 00127 * Test the input arguments 00128 * 00129 INFO = 0 00130 LEFT = LSAME( SIDE, 'L' ) 00131 NOTRAN = LSAME( TRANS, 'N' ) 00132 LQUERY = ( LWORK.EQ.-1 ) 00133 * 00134 * NQ is the order of Q and NW is the minimum dimension of WORK 00135 * 00136 IF( LEFT ) THEN 00137 NQ = M 00138 NW = MAX( 1, N ) 00139 ELSE 00140 NQ = N 00141 NW = MAX( 1, M ) 00142 END IF 00143 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00144 INFO = -1 00145 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00146 INFO = -2 00147 ELSE IF( M.LT.0 ) THEN 00148 INFO = -3 00149 ELSE IF( N.LT.0 ) THEN 00150 INFO = -4 00151 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00152 INFO = -5 00153 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00154 INFO = -7 00155 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00156 INFO = -10 00157 END IF 00158 * 00159 IF( INFO.EQ.0 ) THEN 00160 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00161 LWKOPT = 1 00162 ELSE 00163 * 00164 * Determine the block size. NB may be at most NBMAX, where 00165 * NBMAX is used to define the local array T. 00166 * 00167 * 00168 NB = MIN( NBMAX, ILAENV( 1, 'SORMQL', SIDE // TRANS, M, N, 00169 $ K, -1 ) ) 00170 LWKOPT = NW*NB 00171 END IF 00172 WORK( 1 ) = LWKOPT 00173 * 00174 IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN 00175 INFO = -12 00176 END IF 00177 END IF 00178 * 00179 IF( INFO.NE.0 ) THEN 00180 CALL XERBLA( 'SORMQL', -INFO ) 00181 RETURN 00182 ELSE IF( LQUERY ) THEN 00183 RETURN 00184 END IF 00185 * 00186 * Quick return if possible 00187 * 00188 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00189 RETURN 00190 END IF 00191 * 00192 NBMIN = 2 00193 LDWORK = NW 00194 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00195 IWS = NW*NB 00196 IF( LWORK.LT.IWS ) THEN 00197 NB = LWORK / LDWORK 00198 NBMIN = MAX( 2, ILAENV( 2, 'SORMQL', SIDE // TRANS, M, N, K, 00199 $ -1 ) ) 00200 END IF 00201 ELSE 00202 IWS = NW 00203 END IF 00204 * 00205 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00206 * 00207 * Use unblocked code 00208 * 00209 CALL SORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, 00210 $ IINFO ) 00211 ELSE 00212 * 00213 * Use blocked code 00214 * 00215 IF( ( LEFT .AND. NOTRAN ) .OR. 00216 $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN 00217 I1 = 1 00218 I2 = K 00219 I3 = NB 00220 ELSE 00221 I1 = ( ( K-1 ) / NB )*NB + 1 00222 I2 = 1 00223 I3 = -NB 00224 END IF 00225 * 00226 IF( LEFT ) THEN 00227 NI = N 00228 ELSE 00229 MI = M 00230 END IF 00231 * 00232 DO 10 I = I1, I2, I3 00233 IB = MIN( NB, K-I+1 ) 00234 * 00235 * Form the triangular factor of the block reflector 00236 * H = H(i+ib-1) . . . H(i+1) H(i) 00237 * 00238 CALL SLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB, 00239 $ A( 1, I ), LDA, TAU( I ), T, LDT ) 00240 IF( LEFT ) THEN 00241 * 00242 * H or H**T is applied to C(1:m-k+i+ib-1,1:n) 00243 * 00244 MI = M - K + I + IB - 1 00245 ELSE 00246 * 00247 * H or H**T is applied to C(1:m,1:n-k+i+ib-1) 00248 * 00249 NI = N - K + I + IB - 1 00250 END IF 00251 * 00252 * Apply H or H**T 00253 * 00254 CALL SLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI, 00255 $ IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK, 00256 $ LDWORK ) 00257 10 CONTINUE 00258 END IF 00259 WORK( 1 ) = LWKOPT 00260 RETURN 00261 * 00262 * End of SORMQL 00263 * 00264 END
1.7.3 
