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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DORMQR( 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 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * DORMQR 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 DGEQRF. 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 (LDA,K) 00058 * The i-th column must contain the vector which defines the 00059 * elementary reflector H(i), for i = 1,2,...,k, as returned by 00060 * DGEQRF in the first k columns of its array argument A. 00061 * A is modified by the routine but restored on exit. 00062 * 00063 * LDA (input) INTEGER 00064 * The leading dimension of the array A. 00065 * If SIDE = 'L', LDA >= max(1,M); 00066 * if SIDE = 'R', LDA >= max(1,N). 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 DGEQRF. 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 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, 00108 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW 00109 * .. 00110 * .. Local Arrays .. 00111 DOUBLE PRECISION T( LDT, NBMAX ) 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 INTEGER ILAENV 00116 EXTERNAL LSAME, ILAENV 00117 * .. 00118 * .. External Subroutines .. 00119 EXTERNAL DLARFB, DLARFT, DORM2R, XERBLA 00120 * .. 00121 * .. Intrinsic Functions .. 00122 INTRINSIC MAX, MIN 00123 * .. 00124 * .. Executable Statements .. 00125 * 00126 * Test the input arguments 00127 * 00128 INFO = 0 00129 LEFT = LSAME( SIDE, 'L' ) 00130 NOTRAN = LSAME( TRANS, 'N' ) 00131 LQUERY = ( LWORK.EQ.-1 ) 00132 * 00133 * NQ is the order of Q and NW is the minimum dimension of WORK 00134 * 00135 IF( LEFT ) THEN 00136 NQ = M 00137 NW = N 00138 ELSE 00139 NQ = N 00140 NW = M 00141 END IF 00142 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00143 INFO = -1 00144 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00145 INFO = -2 00146 ELSE IF( M.LT.0 ) THEN 00147 INFO = -3 00148 ELSE IF( N.LT.0 ) THEN 00149 INFO = -4 00150 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00151 INFO = -5 00152 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00153 INFO = -7 00154 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00155 INFO = -10 00156 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00157 INFO = -12 00158 END IF 00159 * 00160 IF( INFO.EQ.0 ) THEN 00161 * 00162 * Determine the block size. NB may be at most NBMAX, where NBMAX 00163 * is used to define the local array T. 00164 * 00165 NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K, 00166 $ -1 ) ) 00167 LWKOPT = MAX( 1, NW )*NB 00168 WORK( 1 ) = LWKOPT 00169 END IF 00170 * 00171 IF( INFO.NE.0 ) THEN 00172 CALL XERBLA( 'DORMQR', -INFO ) 00173 RETURN 00174 ELSE IF( LQUERY ) THEN 00175 RETURN 00176 END IF 00177 * 00178 * Quick return if possible 00179 * 00180 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN 00181 WORK( 1 ) = 1 00182 RETURN 00183 END IF 00184 * 00185 NBMIN = 2 00186 LDWORK = NW 00187 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00188 IWS = NW*NB 00189 IF( LWORK.LT.IWS ) THEN 00190 NB = LWORK / LDWORK 00191 NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K, 00192 $ -1 ) ) 00193 END IF 00194 ELSE 00195 IWS = NW 00196 END IF 00197 * 00198 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00199 * 00200 * Use unblocked code 00201 * 00202 CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, 00203 $ IINFO ) 00204 ELSE 00205 * 00206 * Use blocked code 00207 * 00208 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. 00209 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN 00210 I1 = 1 00211 I2 = K 00212 I3 = NB 00213 ELSE 00214 I1 = ( ( K-1 ) / NB )*NB + 1 00215 I2 = 1 00216 I3 = -NB 00217 END IF 00218 * 00219 IF( LEFT ) THEN 00220 NI = N 00221 JC = 1 00222 ELSE 00223 MI = M 00224 IC = 1 00225 END IF 00226 * 00227 DO 10 I = I1, I2, I3 00228 IB = MIN( NB, K-I+1 ) 00229 * 00230 * Form the triangular factor of the block reflector 00231 * H = H(i) H(i+1) . . . H(i+ib-1) 00232 * 00233 CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), 00234 $ LDA, TAU( I ), T, LDT ) 00235 IF( LEFT ) THEN 00236 * 00237 * H or H' is applied to C(i:m,1:n) 00238 * 00239 MI = M - I + 1 00240 IC = I 00241 ELSE 00242 * 00243 * H or H' is applied to C(1:m,i:n) 00244 * 00245 NI = N - I + 1 00246 JC = I 00247 END IF 00248 * 00249 * Apply H or H' 00250 * 00251 CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, 00252 $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, 00253 $ WORK, LDWORK ) 00254 10 CONTINUE 00255 END IF 00256 WORK( 1 ) = LWKOPT 00257 RETURN 00258 * 00259 * End of DORMQR 00260 * 00261 END
1.7.3 
