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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 DORMLQ( 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 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * DORMLQ 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(k) . . . H(2) H(1) 00030 * 00031 * as returned by DGELQF. 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 * A (input) DOUBLE PRECISION array, dimension 00058 * (LDA,M) if SIDE = 'L', 00059 * (LDA,N) if SIDE = 'R' 00060 * The i-th row must contain the vector which defines the 00061 * elementary reflector H(i), for i = 1,2,...,k, as returned by 00062 * DGELQF in the first k rows of its array argument A. 00063 * A is modified by the routine but restored on exit. 00064 * 00065 * LDA (input) INTEGER 00066 * The leading dimension of the array A. LDA >= max(1,K). 00067 * 00068 * TAU (input) DOUBLE PRECISION array, dimension (K) 00069 * TAU(i) must contain the scalar factor of the elementary 00070 * reflector H(i), as returned by DGELQF. 00071 * 00072 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) 00073 * On entry, the M-by-N matrix C. 00074 * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. 00075 * 00076 * LDC (input) INTEGER 00077 * The leading dimension of the array C. LDC >= max(1,M). 00078 * 00079 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00080 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00081 * 00082 * LWORK (input) INTEGER 00083 * The dimension of the array WORK. 00084 * If SIDE = 'L', LWORK >= max(1,N); 00085 * if SIDE = 'R', LWORK >= max(1,M). 00086 * For optimum performance LWORK >= N*NB if SIDE = 'L', and 00087 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00088 * blocksize. 00089 * 00090 * If LWORK = -1, then a workspace query is assumed; the routine 00091 * only calculates the optimal size of the WORK array, returns 00092 * this value as the first entry of the WORK array, and no error 00093 * message related to LWORK is issued by XERBLA. 00094 * 00095 * INFO (output) INTEGER 00096 * = 0: successful exit 00097 * < 0: if INFO = -i, the i-th argument had an illegal value 00098 * 00099 * ===================================================================== 00100 * 00101 * .. Parameters .. 00102 INTEGER NBMAX, LDT 00103 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) 00104 * .. 00105 * .. Local Scalars .. 00106 LOGICAL LEFT, LQUERY, NOTRAN 00107 CHARACTER TRANST 00108 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, 00109 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW 00110 * .. 00111 * .. Local Arrays .. 00112 DOUBLE PRECISION T( LDT, NBMAX ) 00113 * .. 00114 * .. External Functions .. 00115 LOGICAL LSAME 00116 INTEGER ILAENV 00117 EXTERNAL LSAME, ILAENV 00118 * .. 00119 * .. External Subroutines .. 00120 EXTERNAL DLARFB, DLARFT, DORML2, 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 = N 00139 ELSE 00140 NQ = N 00141 NW = 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, K ) ) THEN 00154 INFO = -7 00155 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00156 INFO = -10 00157 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00158 INFO = -12 00159 END IF 00160 * 00161 IF( INFO.EQ.0 ) THEN 00162 * 00163 * Determine the block size. NB may be at most NBMAX, where NBMAX 00164 * is used to define the local array T. 00165 * 00166 NB = MIN( NBMAX, ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N, K, 00167 $ -1 ) ) 00168 LWKOPT = MAX( 1, NW )*NB 00169 WORK( 1 ) = LWKOPT 00170 END IF 00171 * 00172 IF( INFO.NE.0 ) THEN 00173 CALL XERBLA( 'DORMLQ', -INFO ) 00174 RETURN 00175 ELSE IF( LQUERY ) THEN 00176 RETURN 00177 END IF 00178 * 00179 * Quick return if possible 00180 * 00181 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN 00182 WORK( 1 ) = 1 00183 RETURN 00184 END IF 00185 * 00186 NBMIN = 2 00187 LDWORK = NW 00188 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00189 IWS = NW*NB 00190 IF( LWORK.LT.IWS ) THEN 00191 NB = LWORK / LDWORK 00192 NBMIN = MAX( 2, ILAENV( 2, 'DORMLQ', SIDE // TRANS, M, N, K, 00193 $ -1 ) ) 00194 END IF 00195 ELSE 00196 IWS = NW 00197 END IF 00198 * 00199 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00200 * 00201 * Use unblocked code 00202 * 00203 CALL DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, 00204 $ IINFO ) 00205 ELSE 00206 * 00207 * Use blocked code 00208 * 00209 IF( ( LEFT .AND. NOTRAN ) .OR. 00210 $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN 00211 I1 = 1 00212 I2 = K 00213 I3 = NB 00214 ELSE 00215 I1 = ( ( K-1 ) / NB )*NB + 1 00216 I2 = 1 00217 I3 = -NB 00218 END IF 00219 * 00220 IF( LEFT ) THEN 00221 NI = N 00222 JC = 1 00223 ELSE 00224 MI = M 00225 IC = 1 00226 END IF 00227 * 00228 IF( NOTRAN ) THEN 00229 TRANST = 'T' 00230 ELSE 00231 TRANST = 'N' 00232 END IF 00233 * 00234 DO 10 I = I1, I2, I3 00235 IB = MIN( NB, K-I+1 ) 00236 * 00237 * Form the triangular factor of the block reflector 00238 * H = H(i) H(i+1) . . . H(i+ib-1) 00239 * 00240 CALL DLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ), 00241 $ LDA, TAU( I ), T, LDT ) 00242 IF( LEFT ) THEN 00243 * 00244 * H or H**T is applied to C(i:m,1:n) 00245 * 00246 MI = M - I + 1 00247 IC = I 00248 ELSE 00249 * 00250 * H or H**T is applied to C(1:m,i:n) 00251 * 00252 NI = N - I + 1 00253 JC = I 00254 END IF 00255 * 00256 * Apply H or H**T 00257 * 00258 CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, 00259 $ A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK, 00260 $ LDWORK ) 00261 10 CONTINUE 00262 END IF 00263 WORK( 1 ) = LWKOPT 00264 RETURN 00265 * 00266 * End of DORMLQ 00267 * 00268 END
1.7.3 
