00001 SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, 00002 $ LDC, 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, VECT 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 * If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C 00021 * with 00022 * SIDE = 'L' SIDE = 'R' 00023 * TRANS = 'N': Q * C C * Q 00024 * TRANS = 'T': Q**T * C C * Q**T 00025 * 00026 * If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C 00027 * with 00028 * SIDE = 'L' SIDE = 'R' 00029 * TRANS = 'N': P * C C * P 00030 * TRANS = 'T': P**T * C C * P**T 00031 * 00032 * Here Q and P**T are the orthogonal matrices determined by DGEBRD when 00033 * reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and 00034 * P**T are defined as products of elementary reflectors H(i) and G(i) 00035 * respectively. 00036 * 00037 * Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the 00038 * order of the orthogonal matrix Q or P**T that is applied. 00039 * 00040 * If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: 00041 * if nq >= k, Q = H(1) H(2) . . . H(k); 00042 * if nq < k, Q = H(1) H(2) . . . H(nq-1). 00043 * 00044 * If VECT = 'P', A is assumed to have been a K-by-NQ matrix: 00045 * if k < nq, P = G(1) G(2) . . . G(k); 00046 * if k >= nq, P = G(1) G(2) . . . G(nq-1). 00047 * 00048 * Arguments 00049 * ========= 00050 * 00051 * VECT (input) CHARACTER*1 00052 * = 'Q': apply Q or Q**T; 00053 * = 'P': apply P or P**T. 00054 * 00055 * SIDE (input) CHARACTER*1 00056 * = 'L': apply Q, Q**T, P or P**T from the Left; 00057 * = 'R': apply Q, Q**T, P or P**T from the Right. 00058 * 00059 * TRANS (input) CHARACTER*1 00060 * = 'N': No transpose, apply Q or P; 00061 * = 'T': Transpose, apply Q**T or P**T. 00062 * 00063 * M (input) INTEGER 00064 * The number of rows of the matrix C. M >= 0. 00065 * 00066 * N (input) INTEGER 00067 * The number of columns of the matrix C. N >= 0. 00068 * 00069 * K (input) INTEGER 00070 * If VECT = 'Q', the number of columns in the original 00071 * matrix reduced by DGEBRD. 00072 * If VECT = 'P', the number of rows in the original 00073 * matrix reduced by DGEBRD. 00074 * K >= 0. 00075 * 00076 * A (input) DOUBLE PRECISION array, dimension 00077 * (LDA,min(nq,K)) if VECT = 'Q' 00078 * (LDA,nq) if VECT = 'P' 00079 * The vectors which define the elementary reflectors H(i) and 00080 * G(i), whose products determine the matrices Q and P, as 00081 * returned by DGEBRD. 00082 * 00083 * LDA (input) INTEGER 00084 * The leading dimension of the array A. 00085 * If VECT = 'Q', LDA >= max(1,nq); 00086 * if VECT = 'P', LDA >= max(1,min(nq,K)). 00087 * 00088 * TAU (input) DOUBLE PRECISION array, dimension (min(nq,K)) 00089 * TAU(i) must contain the scalar factor of the elementary 00090 * reflector H(i) or G(i) which determines Q or P, as returned 00091 * by DGEBRD in the array argument TAUQ or TAUP. 00092 * 00093 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) 00094 * On entry, the M-by-N matrix C. 00095 * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q 00096 * or P*C or P**T*C or C*P or C*P**T. 00097 * 00098 * LDC (input) INTEGER 00099 * The leading dimension of the array C. LDC >= max(1,M). 00100 * 00101 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00102 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00103 * 00104 * LWORK (input) INTEGER 00105 * The dimension of the array WORK. 00106 * If SIDE = 'L', LWORK >= max(1,N); 00107 * if SIDE = 'R', LWORK >= max(1,M). 00108 * For optimum performance LWORK >= N*NB if SIDE = 'L', and 00109 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00110 * blocksize. 00111 * 00112 * If LWORK = -1, then a workspace query is assumed; the routine 00113 * only calculates the optimal size of the WORK array, returns 00114 * this value as the first entry of the WORK array, and no error 00115 * message related to LWORK is issued by XERBLA. 00116 * 00117 * INFO (output) INTEGER 00118 * = 0: successful exit 00119 * < 0: if INFO = -i, the i-th argument had an illegal value 00120 * 00121 * ===================================================================== 00122 * 00123 * .. Local Scalars .. 00124 LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN 00125 CHARACTER TRANST 00126 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW 00127 * .. 00128 * .. External Functions .. 00129 LOGICAL LSAME 00130 INTEGER ILAENV 00131 EXTERNAL LSAME, ILAENV 00132 * .. 00133 * .. External Subroutines .. 00134 EXTERNAL DORMLQ, DORMQR, XERBLA 00135 * .. 00136 * .. Intrinsic Functions .. 00137 INTRINSIC MAX, MIN 00138 * .. 00139 * .. Executable Statements .. 00140 * 00141 * Test the input arguments 00142 * 00143 INFO = 0 00144 APPLYQ = LSAME( VECT, 'Q' ) 00145 LEFT = LSAME( SIDE, 'L' ) 00146 NOTRAN = LSAME( TRANS, 'N' ) 00147 LQUERY = ( LWORK.EQ.-1 ) 00148 * 00149 * NQ is the order of Q or P and NW is the minimum dimension of WORK 00150 * 00151 IF( LEFT ) THEN 00152 NQ = M 00153 NW = N 00154 ELSE 00155 NQ = N 00156 NW = M 00157 END IF 00158 IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN 00159 INFO = -1 00160 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00161 INFO = -2 00162 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00163 INFO = -3 00164 ELSE IF( M.LT.0 ) THEN 00165 INFO = -4 00166 ELSE IF( N.LT.0 ) THEN 00167 INFO = -5 00168 ELSE IF( K.LT.0 ) THEN 00169 INFO = -6 00170 ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. 00171 $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) 00172 $ THEN 00173 INFO = -8 00174 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00175 INFO = -11 00176 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00177 INFO = -13 00178 END IF 00179 * 00180 IF( INFO.EQ.0 ) THEN 00181 IF( APPLYQ ) THEN 00182 IF( LEFT ) THEN 00183 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, 00184 $ -1 ) 00185 ELSE 00186 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, 00187 $ -1 ) 00188 END IF 00189 ELSE 00190 IF( LEFT ) THEN 00191 NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1, 00192 $ -1 ) 00193 ELSE 00194 NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1, 00195 $ -1 ) 00196 END IF 00197 END IF 00198 LWKOPT = MAX( 1, NW )*NB 00199 WORK( 1 ) = LWKOPT 00200 END IF 00201 * 00202 IF( INFO.NE.0 ) THEN 00203 CALL XERBLA( 'DORMBR', -INFO ) 00204 RETURN 00205 ELSE IF( LQUERY ) THEN 00206 RETURN 00207 END IF 00208 * 00209 * Quick return if possible 00210 * 00211 WORK( 1 ) = 1 00212 IF( M.EQ.0 .OR. N.EQ.0 ) 00213 $ RETURN 00214 * 00215 IF( APPLYQ ) THEN 00216 * 00217 * Apply Q 00218 * 00219 IF( NQ.GE.K ) THEN 00220 * 00221 * Q was determined by a call to DGEBRD with nq >= k 00222 * 00223 CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 00224 $ WORK, LWORK, IINFO ) 00225 ELSE IF( NQ.GT.1 ) THEN 00226 * 00227 * Q was determined by a call to DGEBRD with nq < k 00228 * 00229 IF( LEFT ) THEN 00230 MI = M - 1 00231 NI = N 00232 I1 = 2 00233 I2 = 1 00234 ELSE 00235 MI = M 00236 NI = N - 1 00237 I1 = 1 00238 I2 = 2 00239 END IF 00240 CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, 00241 $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00242 END IF 00243 ELSE 00244 * 00245 * Apply P 00246 * 00247 IF( NOTRAN ) THEN 00248 TRANST = 'T' 00249 ELSE 00250 TRANST = 'N' 00251 END IF 00252 IF( NQ.GT.K ) THEN 00253 * 00254 * P was determined by a call to DGEBRD with nq > k 00255 * 00256 CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, 00257 $ WORK, LWORK, IINFO ) 00258 ELSE IF( NQ.GT.1 ) THEN 00259 * 00260 * P was determined by a call to DGEBRD with nq <= k 00261 * 00262 IF( LEFT ) THEN 00263 MI = M - 1 00264 NI = N 00265 I1 = 2 00266 I2 = 1 00267 ELSE 00268 MI = M 00269 NI = N - 1 00270 I1 = 1 00271 I2 = 2 00272 END IF 00273 CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, 00274 $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00275 END IF 00276 END IF 00277 WORK( 1 ) = LWKOPT 00278 RETURN 00279 * 00280 * End of DORMBR 00281 * 00282 END
1.7.2