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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DLAGGE 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE DLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) 00012 * 00013 * .. Scalar Arguments .. 00014 * INTEGER INFO, KL, KU, LDA, M, N 00015 * .. 00016 * .. Array Arguments .. 00017 * INTEGER ISEED( 4 ) 00018 * DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) 00019 * .. 00020 * 00021 * 00022 *> \par Purpose: 00023 * ============= 00024 *> 00025 *> \verbatim 00026 *> 00027 *> DLAGGE generates a real general m by n matrix A, by pre- and post- 00028 *> multiplying a real diagonal matrix D with random orthogonal matrices: 00029 *> A = U*D*V. The lower and upper bandwidths may then be reduced to 00030 *> kl and ku by additional orthogonal transformations. 00031 *> \endverbatim 00032 * 00033 * Arguments: 00034 * ========== 00035 * 00036 *> \param[in] M 00037 *> \verbatim 00038 *> M is INTEGER 00039 *> The number of rows of the matrix A. M >= 0. 00040 *> \endverbatim 00041 *> 00042 *> \param[in] N 00043 *> \verbatim 00044 *> N is INTEGER 00045 *> The number of columns of the matrix A. N >= 0. 00046 *> \endverbatim 00047 *> 00048 *> \param[in] KL 00049 *> \verbatim 00050 *> KL is INTEGER 00051 *> The number of nonzero subdiagonals within the band of A. 00052 *> 0 <= KL <= M-1. 00053 *> \endverbatim 00054 *> 00055 *> \param[in] KU 00056 *> \verbatim 00057 *> KU is INTEGER 00058 *> The number of nonzero superdiagonals within the band of A. 00059 *> 0 <= KU <= N-1. 00060 *> \endverbatim 00061 *> 00062 *> \param[in] D 00063 *> \verbatim 00064 *> D is DOUBLE PRECISION array, dimension (min(M,N)) 00065 *> The diagonal elements of the diagonal matrix D. 00066 *> \endverbatim 00067 *> 00068 *> \param[out] A 00069 *> \verbatim 00070 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00071 *> The generated m by n matrix A. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] LDA 00075 *> \verbatim 00076 *> LDA is INTEGER 00077 *> The leading dimension of the array A. LDA >= M. 00078 *> \endverbatim 00079 *> 00080 *> \param[in,out] ISEED 00081 *> \verbatim 00082 *> ISEED is INTEGER array, dimension (4) 00083 *> On entry, the seed of the random number generator; the array 00084 *> elements must be between 0 and 4095, and ISEED(4) must be 00085 *> odd. 00086 *> On exit, the seed is updated. 00087 *> \endverbatim 00088 *> 00089 *> \param[out] WORK 00090 *> \verbatim 00091 *> WORK is DOUBLE PRECISION array, dimension (M+N) 00092 *> \endverbatim 00093 *> 00094 *> \param[out] INFO 00095 *> \verbatim 00096 *> INFO is INTEGER 00097 *> = 0: successful exit 00098 *> < 0: if INFO = -i, the i-th argument had an illegal value 00099 *> \endverbatim 00100 * 00101 * Authors: 00102 * ======== 00103 * 00104 *> \author Univ. of Tennessee 00105 *> \author Univ. of California Berkeley 00106 *> \author Univ. of Colorado Denver 00107 *> \author NAG Ltd. 00108 * 00109 *> \date November 2011 00110 * 00111 *> \ingroup double_matgen 00112 * 00113 * ===================================================================== 00114 SUBROUTINE DLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) 00115 * 00116 * -- LAPACK auxiliary routine (version 3.4.0) -- 00117 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00119 * November 2011 00120 * 00121 * .. Scalar Arguments .. 00122 INTEGER INFO, KL, KU, LDA, M, N 00123 * .. 00124 * .. Array Arguments .. 00125 INTEGER ISEED( 4 ) 00126 DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) 00127 * .. 00128 * 00129 * ===================================================================== 00130 * 00131 * .. Parameters .. 00132 DOUBLE PRECISION ZERO, ONE 00133 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00134 * .. 00135 * .. Local Scalars .. 00136 INTEGER I, J 00137 DOUBLE PRECISION TAU, WA, WB, WN 00138 * .. 00139 * .. External Subroutines .. 00140 EXTERNAL DGEMV, DGER, DLARNV, DSCAL, XERBLA 00141 * .. 00142 * .. Intrinsic Functions .. 00143 INTRINSIC MAX, MIN, SIGN 00144 * .. 00145 * .. External Functions .. 00146 DOUBLE PRECISION DNRM2 00147 EXTERNAL DNRM2 00148 * .. 00149 * .. Executable Statements .. 00150 * 00151 * Test the input arguments 00152 * 00153 INFO = 0 00154 IF( M.LT.0 ) THEN 00155 INFO = -1 00156 ELSE IF( N.LT.0 ) THEN 00157 INFO = -2 00158 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN 00159 INFO = -3 00160 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN 00161 INFO = -4 00162 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00163 INFO = -7 00164 END IF 00165 IF( INFO.LT.0 ) THEN 00166 CALL XERBLA( 'DLAGGE', -INFO ) 00167 RETURN 00168 END IF 00169 * 00170 * initialize A to diagonal matrix 00171 * 00172 DO 20 J = 1, N 00173 DO 10 I = 1, M 00174 A( I, J ) = ZERO 00175 10 CONTINUE 00176 20 CONTINUE 00177 DO 30 I = 1, MIN( M, N ) 00178 A( I, I ) = D( I ) 00179 30 CONTINUE 00180 * 00181 * pre- and post-multiply A by random orthogonal matrices 00182 * 00183 DO 40 I = MIN( M, N ), 1, -1 00184 IF( I.LT.M ) THEN 00185 * 00186 * generate random reflection 00187 * 00188 CALL DLARNV( 3, ISEED, M-I+1, WORK ) 00189 WN = DNRM2( M-I+1, WORK, 1 ) 00190 WA = SIGN( WN, WORK( 1 ) ) 00191 IF( WN.EQ.ZERO ) THEN 00192 TAU = ZERO 00193 ELSE 00194 WB = WORK( 1 ) + WA 00195 CALL DSCAL( M-I, ONE / WB, WORK( 2 ), 1 ) 00196 WORK( 1 ) = ONE 00197 TAU = WB / WA 00198 END IF 00199 * 00200 * multiply A(i:m,i:n) by random reflection from the left 00201 * 00202 CALL DGEMV( 'Transpose', M-I+1, N-I+1, ONE, A( I, I ), LDA, 00203 $ WORK, 1, ZERO, WORK( M+1 ), 1 ) 00204 CALL DGER( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1, 00205 $ A( I, I ), LDA ) 00206 END IF 00207 IF( I.LT.N ) THEN 00208 * 00209 * generate random reflection 00210 * 00211 CALL DLARNV( 3, ISEED, N-I+1, WORK ) 00212 WN = DNRM2( N-I+1, WORK, 1 ) 00213 WA = SIGN( WN, WORK( 1 ) ) 00214 IF( WN.EQ.ZERO ) THEN 00215 TAU = ZERO 00216 ELSE 00217 WB = WORK( 1 ) + WA 00218 CALL DSCAL( N-I, ONE / WB, WORK( 2 ), 1 ) 00219 WORK( 1 ) = ONE 00220 TAU = WB / WA 00221 END IF 00222 * 00223 * multiply A(i:m,i:n) by random reflection from the right 00224 * 00225 CALL DGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ), 00226 $ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 ) 00227 CALL DGER( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, 00228 $ A( I, I ), LDA ) 00229 END IF 00230 40 CONTINUE 00231 * 00232 * Reduce number of subdiagonals to KL and number of superdiagonals 00233 * to KU 00234 * 00235 DO 70 I = 1, MAX( M-1-KL, N-1-KU ) 00236 IF( KL.LE.KU ) THEN 00237 * 00238 * annihilate subdiagonal elements first (necessary if KL = 0) 00239 * 00240 IF( I.LE.MIN( M-1-KL, N ) ) THEN 00241 * 00242 * generate reflection to annihilate A(kl+i+1:m,i) 00243 * 00244 WN = DNRM2( M-KL-I+1, A( KL+I, I ), 1 ) 00245 WA = SIGN( WN, A( KL+I, I ) ) 00246 IF( WN.EQ.ZERO ) THEN 00247 TAU = ZERO 00248 ELSE 00249 WB = A( KL+I, I ) + WA 00250 CALL DSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) 00251 A( KL+I, I ) = ONE 00252 TAU = WB / WA 00253 END IF 00254 * 00255 * apply reflection to A(kl+i:m,i+1:n) from the left 00256 * 00257 CALL DGEMV( 'Transpose', M-KL-I+1, N-I, ONE, 00258 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, 00259 $ WORK, 1 ) 00260 CALL DGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1, 00261 $ A( KL+I, I+1 ), LDA ) 00262 A( KL+I, I ) = -WA 00263 END IF 00264 * 00265 IF( I.LE.MIN( N-1-KU, M ) ) THEN 00266 * 00267 * generate reflection to annihilate A(i,ku+i+1:n) 00268 * 00269 WN = DNRM2( N-KU-I+1, A( I, KU+I ), LDA ) 00270 WA = SIGN( WN, A( I, KU+I ) ) 00271 IF( WN.EQ.ZERO ) THEN 00272 TAU = ZERO 00273 ELSE 00274 WB = A( I, KU+I ) + WA 00275 CALL DSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) 00276 A( I, KU+I ) = ONE 00277 TAU = WB / WA 00278 END IF 00279 * 00280 * apply reflection to A(i+1:m,ku+i:n) from the right 00281 * 00282 CALL DGEMV( 'No transpose', M-I, N-KU-I+1, ONE, 00283 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, 00284 $ WORK, 1 ) 00285 CALL DGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), 00286 $ LDA, A( I+1, KU+I ), LDA ) 00287 A( I, KU+I ) = -WA 00288 END IF 00289 ELSE 00290 * 00291 * annihilate superdiagonal elements first (necessary if 00292 * KU = 0) 00293 * 00294 IF( I.LE.MIN( N-1-KU, M ) ) THEN 00295 * 00296 * generate reflection to annihilate A(i,ku+i+1:n) 00297 * 00298 WN = DNRM2( N-KU-I+1, A( I, KU+I ), LDA ) 00299 WA = SIGN( WN, A( I, KU+I ) ) 00300 IF( WN.EQ.ZERO ) THEN 00301 TAU = ZERO 00302 ELSE 00303 WB = A( I, KU+I ) + WA 00304 CALL DSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) 00305 A( I, KU+I ) = ONE 00306 TAU = WB / WA 00307 END IF 00308 * 00309 * apply reflection to A(i+1:m,ku+i:n) from the right 00310 * 00311 CALL DGEMV( 'No transpose', M-I, N-KU-I+1, ONE, 00312 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, 00313 $ WORK, 1 ) 00314 CALL DGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), 00315 $ LDA, A( I+1, KU+I ), LDA ) 00316 A( I, KU+I ) = -WA 00317 END IF 00318 * 00319 IF( I.LE.MIN( M-1-KL, N ) ) THEN 00320 * 00321 * generate reflection to annihilate A(kl+i+1:m,i) 00322 * 00323 WN = DNRM2( M-KL-I+1, A( KL+I, I ), 1 ) 00324 WA = SIGN( WN, A( KL+I, I ) ) 00325 IF( WN.EQ.ZERO ) THEN 00326 TAU = ZERO 00327 ELSE 00328 WB = A( KL+I, I ) + WA 00329 CALL DSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) 00330 A( KL+I, I ) = ONE 00331 TAU = WB / WA 00332 END IF 00333 * 00334 * apply reflection to A(kl+i:m,i+1:n) from the left 00335 * 00336 CALL DGEMV( 'Transpose', M-KL-I+1, N-I, ONE, 00337 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, 00338 $ WORK, 1 ) 00339 CALL DGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1, 00340 $ A( KL+I, I+1 ), LDA ) 00341 A( KL+I, I ) = -WA 00342 END IF 00343 END IF 00344 * 00345 DO 50 J = KL + I + 1, M 00346 A( J, I ) = ZERO 00347 50 CONTINUE 00348 * 00349 DO 60 J = KU + I + 1, N 00350 A( I, J ) = ZERO 00351 60 CONTINUE 00352 70 CONTINUE 00353 RETURN 00354 * 00355 * End of DLAGGE 00356 * 00357 END