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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORGBR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORGBR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgbr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgbr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgbr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER VECT 00025 * INTEGER INFO, K, LDA, LWORK, M, N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DORGBR generates one of the real orthogonal matrices Q or P**T 00038 *> determined by DGEBRD when reducing a real matrix A to bidiagonal 00039 *> form: A = Q * B * P**T. Q and P**T are defined as products of 00040 *> elementary reflectors H(i) or G(i) respectively. 00041 *> 00042 *> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q 00043 *> is of order M: 00044 *> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n 00045 *> columns of Q, where m >= n >= k; 00046 *> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an 00047 *> M-by-M matrix. 00048 *> 00049 *> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T 00050 *> is of order N: 00051 *> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m 00052 *> rows of P**T, where n >= m >= k; 00053 *> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as 00054 *> an N-by-N matrix. 00055 *> \endverbatim 00056 * 00057 * Arguments: 00058 * ========== 00059 * 00060 *> \param[in] VECT 00061 *> \verbatim 00062 *> VECT is CHARACTER*1 00063 *> Specifies whether the matrix Q or the matrix P**T is 00064 *> required, as defined in the transformation applied by DGEBRD: 00065 *> = 'Q': generate Q; 00066 *> = 'P': generate P**T. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] M 00070 *> \verbatim 00071 *> M is INTEGER 00072 *> The number of rows of the matrix Q or P**T to be returned. 00073 *> M >= 0. 00074 *> \endverbatim 00075 *> 00076 *> \param[in] N 00077 *> \verbatim 00078 *> N is INTEGER 00079 *> The number of columns of the matrix Q or P**T to be returned. 00080 *> N >= 0. 00081 *> If VECT = 'Q', M >= N >= min(M,K); 00082 *> if VECT = 'P', N >= M >= min(N,K). 00083 *> \endverbatim 00084 *> 00085 *> \param[in] K 00086 *> \verbatim 00087 *> K is INTEGER 00088 *> If VECT = 'Q', the number of columns in the original M-by-K 00089 *> matrix reduced by DGEBRD. 00090 *> If VECT = 'P', the number of rows in the original K-by-N 00091 *> matrix reduced by DGEBRD. 00092 *> K >= 0. 00093 *> \endverbatim 00094 *> 00095 *> \param[in,out] A 00096 *> \verbatim 00097 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00098 *> On entry, the vectors which define the elementary reflectors, 00099 *> as returned by DGEBRD. 00100 *> On exit, the M-by-N matrix Q or P**T. 00101 *> \endverbatim 00102 *> 00103 *> \param[in] LDA 00104 *> \verbatim 00105 *> LDA is INTEGER 00106 *> The leading dimension of the array A. LDA >= max(1,M). 00107 *> \endverbatim 00108 *> 00109 *> \param[in] TAU 00110 *> \verbatim 00111 *> TAU is DOUBLE PRECISION array, dimension 00112 *> (min(M,K)) if VECT = 'Q' 00113 *> (min(N,K)) if VECT = 'P' 00114 *> TAU(i) must contain the scalar factor of the elementary 00115 *> reflector H(i) or G(i), which determines Q or P**T, as 00116 *> returned by DGEBRD in its array argument TAUQ or TAUP. 00117 *> \endverbatim 00118 *> 00119 *> \param[out] WORK 00120 *> \verbatim 00121 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00122 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00123 *> \endverbatim 00124 *> 00125 *> \param[in] LWORK 00126 *> \verbatim 00127 *> LWORK is INTEGER 00128 *> The dimension of the array WORK. LWORK >= max(1,min(M,N)). 00129 *> For optimum performance LWORK >= min(M,N)*NB, where NB 00130 *> is the optimal blocksize. 00131 *> 00132 *> If LWORK = -1, then a workspace query is assumed; the routine 00133 *> only calculates the optimal size of the WORK array, returns 00134 *> this value as the first entry of the WORK array, and no error 00135 *> message related to LWORK is issued by XERBLA. 00136 *> \endverbatim 00137 *> 00138 *> \param[out] INFO 00139 *> \verbatim 00140 *> INFO is INTEGER 00141 *> = 0: successful exit 00142 *> < 0: if INFO = -i, the i-th argument had an illegal value 00143 *> \endverbatim 00144 * 00145 * Authors: 00146 * ======== 00147 * 00148 *> \author Univ. of Tennessee 00149 *> \author Univ. of California Berkeley 00150 *> \author Univ. of Colorado Denver 00151 *> \author NAG Ltd. 00152 * 00153 *> \date April 2012 00154 * 00155 *> \ingroup doubleGBcomputational 00156 * 00157 * ===================================================================== 00158 SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) 00159 * 00160 * -- LAPACK computational routine (version 3.4.1) -- 00161 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00163 * April 2012 00164 * 00165 * .. Scalar Arguments .. 00166 CHARACTER VECT 00167 INTEGER INFO, K, LDA, LWORK, M, N 00168 * .. 00169 * .. Array Arguments .. 00170 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00171 * .. 00172 * 00173 * ===================================================================== 00174 * 00175 * .. Parameters .. 00176 DOUBLE PRECISION ZERO, ONE 00177 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00178 * .. 00179 * .. Local Scalars .. 00180 LOGICAL LQUERY, WANTQ 00181 INTEGER I, IINFO, J, LWKOPT, MN 00182 * .. 00183 * .. External Functions .. 00184 LOGICAL LSAME 00185 INTEGER ILAENV 00186 EXTERNAL LSAME, ILAENV 00187 * .. 00188 * .. External Subroutines .. 00189 EXTERNAL DORGLQ, DORGQR, XERBLA 00190 * .. 00191 * .. Intrinsic Functions .. 00192 INTRINSIC MAX, MIN 00193 * .. 00194 * .. Executable Statements .. 00195 * 00196 * Test the input arguments 00197 * 00198 INFO = 0 00199 WANTQ = LSAME( VECT, 'Q' ) 00200 MN = MIN( M, N ) 00201 LQUERY = ( LWORK.EQ.-1 ) 00202 IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN 00203 INFO = -1 00204 ELSE IF( M.LT.0 ) THEN 00205 INFO = -2 00206 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M, 00207 $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT. 00208 $ MIN( N, K ) ) ) ) THEN 00209 INFO = -3 00210 ELSE IF( K.LT.0 ) THEN 00211 INFO = -4 00212 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00213 INFO = -6 00214 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN 00215 INFO = -9 00216 END IF 00217 * 00218 IF( INFO.EQ.0 ) THEN 00219 WORK( 1 ) = 1 00220 IF( WANTQ ) THEN 00221 IF( M.GE.K ) THEN 00222 CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) 00223 ELSE 00224 IF( M.GT.1 ) THEN 00225 CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, 00226 $ -1, IINFO ) 00227 END IF 00228 END IF 00229 ELSE 00230 IF( K.LT.N ) THEN 00231 CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) 00232 ELSE 00233 IF( N.GT.1 ) THEN 00234 CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, 00235 $ -1, IINFO ) 00236 END IF 00237 END IF 00238 END IF 00239 LWKOPT = WORK( 1 ) 00240 LWKOPT = MAX (LWKOPT, MN) 00241 END IF 00242 * 00243 IF( INFO.NE.0 ) THEN 00244 CALL XERBLA( 'DORGBR', -INFO ) 00245 RETURN 00246 ELSE IF( LQUERY ) THEN 00247 WORK( 1 ) = LWKOPT 00248 RETURN 00249 END IF 00250 * 00251 * Quick return if possible 00252 * 00253 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00254 WORK( 1 ) = 1 00255 RETURN 00256 END IF 00257 * 00258 IF( WANTQ ) THEN 00259 * 00260 * Form Q, determined by a call to DGEBRD to reduce an m-by-k 00261 * matrix 00262 * 00263 IF( M.GE.K ) THEN 00264 * 00265 * If m >= k, assume m >= n >= k 00266 * 00267 CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) 00268 * 00269 ELSE 00270 * 00271 * If m < k, assume m = n 00272 * 00273 * Shift the vectors which define the elementary reflectors one 00274 * column to the right, and set the first row and column of Q 00275 * to those of the unit matrix 00276 * 00277 DO 20 J = M, 2, -1 00278 A( 1, J ) = ZERO 00279 DO 10 I = J + 1, M 00280 A( I, J ) = A( I, J-1 ) 00281 10 CONTINUE 00282 20 CONTINUE 00283 A( 1, 1 ) = ONE 00284 DO 30 I = 2, M 00285 A( I, 1 ) = ZERO 00286 30 CONTINUE 00287 IF( M.GT.1 ) THEN 00288 * 00289 * Form Q(2:m,2:m) 00290 * 00291 CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, 00292 $ LWORK, IINFO ) 00293 END IF 00294 END IF 00295 ELSE 00296 * 00297 * Form P**T, determined by a call to DGEBRD to reduce a k-by-n 00298 * matrix 00299 * 00300 IF( K.LT.N ) THEN 00301 * 00302 * If k < n, assume k <= m <= n 00303 * 00304 CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) 00305 * 00306 ELSE 00307 * 00308 * If k >= n, assume m = n 00309 * 00310 * Shift the vectors which define the elementary reflectors one 00311 * row downward, and set the first row and column of P**T to 00312 * those of the unit matrix 00313 * 00314 A( 1, 1 ) = ONE 00315 DO 40 I = 2, N 00316 A( I, 1 ) = ZERO 00317 40 CONTINUE 00318 DO 60 J = 2, N 00319 DO 50 I = J - 1, 2, -1 00320 A( I, J ) = A( I-1, J ) 00321 50 CONTINUE 00322 A( 1, J ) = ZERO 00323 60 CONTINUE 00324 IF( N.GT.1 ) THEN 00325 * 00326 * Form P**T(2:n,2:n) 00327 * 00328 CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, 00329 $ LWORK, IINFO ) 00330 END IF 00331 END IF 00332 END IF 00333 WORK( 1 ) = LWKOPT 00334 RETURN 00335 * 00336 * End of DORGBR 00337 * 00338 END