| 1 | /*************************************************************************
|
|---|
| 2 | Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
|
|---|
| 3 |
|
|---|
| 4 | Contributors:
|
|---|
| 5 | * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
|
|---|
| 6 | pseudocode.
|
|---|
| 7 |
|
|---|
| 8 | See subroutines comments for additional copyrights.
|
|---|
| 9 |
|
|---|
| 10 | >>> SOURCE LICENSE >>>
|
|---|
| 11 | This program is free software; you can redistribute it and/or modify
|
|---|
| 12 | it under the terms of the GNU General Public License as published by
|
|---|
| 13 | the Free Software Foundation (www.fsf.org); either version 2 of the
|
|---|
| 14 | License, or (at your option) any later version.
|
|---|
| 15 |
|
|---|
| 16 | This program is distributed in the hope that it will be useful,
|
|---|
| 17 | but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|---|
| 18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|---|
| 19 | GNU General Public License for more details.
|
|---|
| 20 |
|
|---|
| 21 | A copy of the GNU General Public License is available at
|
|---|
| 22 | http://www.fsf.org/licensing/licenses
|
|---|
| 23 |
|
|---|
| 24 | >>> END OF LICENSE >>>
|
|---|
| 25 | *************************************************************************/
|
|---|
| 26 |
|
|---|
| 27 | using System;
|
|---|
| 28 |
|
|---|
| 29 | namespace alglib
|
|---|
| 30 | {
|
|---|
| 31 | public class tdbisinv
|
|---|
| 32 | {
|
|---|
| 33 | /*************************************************************************
|
|---|
| 34 | Subroutine for finding the tridiagonal matrix eigenvalues/vectors in a
|
|---|
| 35 | given half-interval (A, B] by using bisection and inverse iteration.
|
|---|
| 36 |
|
|---|
| 37 | Input parameters:
|
|---|
| 38 | D - the main diagonal of a tridiagonal matrix.
|
|---|
| 39 | Array whose index ranges within [0..N-1].
|
|---|
| 40 | E - the secondary diagonal of a tridiagonal matrix.
|
|---|
| 41 | Array whose index ranges within [0..N-2].
|
|---|
| 42 | N - size of matrix, N>=0.
|
|---|
| 43 | ZNeeded - flag controlling whether the eigenvectors are needed or not.
|
|---|
| 44 | If ZNeeded is equal to:
|
|---|
| 45 | * 0, the eigenvectors are not needed;
|
|---|
| 46 | * 1, the eigenvectors of a tridiagonal matrix are multiplied
|
|---|
| 47 | by the square matrix Z. It is used if the tridiagonal
|
|---|
| 48 | matrix is obtained by the similarity transformation
|
|---|
| 49 | of a symmetric matrix.
|
|---|
| 50 | * 2, the eigenvectors of a tridiagonal matrix replace matrix Z.
|
|---|
| 51 | A, B - half-interval (A, B] to search eigenvalues in.
|
|---|
| 52 | Z - if ZNeeded is equal to:
|
|---|
| 53 | * 0, Z isn't used and remains unchanged;
|
|---|
| 54 | * 1, Z contains the square matrix (array whose indexes range
|
|---|
| 55 | within [0..N-1, 0..N-1]) which reduces the given symmetric
|
|---|
| 56 | matrix to tridiagonal form;
|
|---|
| 57 | * 2, Z isn't used (but changed on the exit).
|
|---|
| 58 |
|
|---|
| 59 | Output parameters:
|
|---|
| 60 | D - array of the eigenvalues found.
|
|---|
| 61 | Array whose index ranges within [0..M-1].
|
|---|
| 62 | M - number of eigenvalues found in the given half-interval (M>=0).
|
|---|
| 63 | Z - if ZNeeded is equal to:
|
|---|
| 64 | * 0, doesn't contain any information;
|
|---|
| 65 | * 1, contains the product of a given NxN matrix Z (from the
|
|---|
| 66 | left) and NxM matrix of the eigenvectors found (from the
|
|---|
| 67 | right). Array whose indexes range within [0..N-1, 0..M-1].
|
|---|
| 68 | * 2, contains the matrix of the eigenvectors found.
|
|---|
| 69 | Array whose indexes range within [0..N-1, 0..M-1].
|
|---|
| 70 |
|
|---|
| 71 | Result:
|
|---|
| 72 |
|
|---|
| 73 | True, if successful. In that case, M contains the number of eigenvalues
|
|---|
| 74 | in the given half-interval (could be equal to 0), D contains the eigenvalues,
|
|---|
| 75 | Z contains the eigenvectors (if needed).
|
|---|
| 76 | It should be noted that the subroutine changes the size of arrays D and Z.
|
|---|
| 77 |
|
|---|
| 78 | False, if the bisection method subroutine wasn't able to find the
|
|---|
| 79 | eigenvalues in the given interval or if the inverse iteration subroutine
|
|---|
| 80 | wasn't able to find all the corresponding eigenvectors. In that case,
|
|---|
| 81 | the eigenvalues and eigenvectors are not returned, M is equal to 0.
|
|---|
| 82 |
|
|---|
| 83 | -- ALGLIB --
|
|---|
| 84 | Copyright 31.03.2008 by Bochkanov Sergey
|
|---|
| 85 | *************************************************************************/
|
|---|
| 86 | public static bool smatrixtdevdr(ref double[] d,
|
|---|
| 87 | ref double[] e,
|
|---|
| 88 | int n,
|
|---|
| 89 | int zneeded,
|
|---|
| 90 | double a,
|
|---|
| 91 | double b,
|
|---|
| 92 | ref int m,
|
|---|
| 93 | ref double[,] z)
|
|---|
| 94 | {
|
|---|
| 95 | bool result = new bool();
|
|---|
| 96 | int errorcode = 0;
|
|---|
| 97 | int nsplit = 0;
|
|---|
| 98 | int i = 0;
|
|---|
| 99 | int j = 0;
|
|---|
| 100 | int k = 0;
|
|---|
| 101 | int cr = 0;
|
|---|
| 102 | int[] iblock = new int[0];
|
|---|
| 103 | int[] isplit = new int[0];
|
|---|
| 104 | int[] ifail = new int[0];
|
|---|
| 105 | double[] d1 = new double[0];
|
|---|
| 106 | double[] e1 = new double[0];
|
|---|
| 107 | double[] w = new double[0];
|
|---|
| 108 | double[,] z2 = new double[0,0];
|
|---|
| 109 | double[,] z3 = new double[0,0];
|
|---|
| 110 | double v = 0;
|
|---|
| 111 | int i_ = 0;
|
|---|
| 112 | int i1_ = 0;
|
|---|
| 113 |
|
|---|
| 114 | System.Diagnostics.Debug.Assert(zneeded>=0 & zneeded<=2, "SMatrixTDEVDR: incorrect ZNeeded!");
|
|---|
| 115 |
|
|---|
| 116 | //
|
|---|
| 117 | // Special cases
|
|---|
| 118 | //
|
|---|
| 119 | if( (double)(b)<=(double)(a) )
|
|---|
| 120 | {
|
|---|
| 121 | m = 0;
|
|---|
| 122 | result = true;
|
|---|
| 123 | return result;
|
|---|
| 124 | }
|
|---|
| 125 | if( n<=0 )
|
|---|
| 126 | {
|
|---|
| 127 | m = 0;
|
|---|
| 128 | result = true;
|
|---|
| 129 | return result;
|
|---|
| 130 | }
|
|---|
| 131 |
|
|---|
| 132 | //
|
|---|
| 133 | // Copy D,E to D1, E1
|
|---|
| 134 | //
|
|---|
| 135 | d1 = new double[n+1];
|
|---|
| 136 | i1_ = (0) - (1);
|
|---|
| 137 | for(i_=1; i_<=n;i_++)
|
|---|
| 138 | {
|
|---|
| 139 | d1[i_] = d[i_+i1_];
|
|---|
| 140 | }
|
|---|
| 141 | if( n>1 )
|
|---|
| 142 | {
|
|---|
| 143 | e1 = new double[n-1+1];
|
|---|
| 144 | i1_ = (0) - (1);
|
|---|
| 145 | for(i_=1; i_<=n-1;i_++)
|
|---|
| 146 | {
|
|---|
| 147 | e1[i_] = e[i_+i1_];
|
|---|
| 148 | }
|
|---|
| 149 | }
|
|---|
| 150 |
|
|---|
| 151 | //
|
|---|
| 152 | // No eigen vectors
|
|---|
| 153 | //
|
|---|
| 154 | if( zneeded==0 )
|
|---|
| 155 | {
|
|---|
| 156 | result = internalbisectioneigenvalues(d1, e1, n, 2, 1, a, b, 0, 0, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 157 | if( !result | m==0 )
|
|---|
| 158 | {
|
|---|
| 159 | m = 0;
|
|---|
| 160 | return result;
|
|---|
| 161 | }
|
|---|
| 162 | d = new double[m-1+1];
|
|---|
| 163 | i1_ = (1) - (0);
|
|---|
| 164 | for(i_=0; i_<=m-1;i_++)
|
|---|
| 165 | {
|
|---|
| 166 | d[i_] = w[i_+i1_];
|
|---|
| 167 | }
|
|---|
| 168 | return result;
|
|---|
| 169 | }
|
|---|
| 170 |
|
|---|
| 171 | //
|
|---|
| 172 | // Eigen vectors are multiplied by Z
|
|---|
| 173 | //
|
|---|
| 174 | if( zneeded==1 )
|
|---|
| 175 | {
|
|---|
| 176 |
|
|---|
| 177 | //
|
|---|
| 178 | // Find eigen pairs
|
|---|
| 179 | //
|
|---|
| 180 | result = internalbisectioneigenvalues(d1, e1, n, 2, 2, a, b, 0, 0, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 181 | if( !result | m==0 )
|
|---|
| 182 | {
|
|---|
| 183 | m = 0;
|
|---|
| 184 | return result;
|
|---|
| 185 | }
|
|---|
| 186 | internaldstein(n, ref d1, e1, m, w, ref iblock, ref isplit, ref z2, ref ifail, ref cr);
|
|---|
| 187 | if( cr!=0 )
|
|---|
| 188 | {
|
|---|
| 189 | m = 0;
|
|---|
| 190 | result = false;
|
|---|
| 191 | return result;
|
|---|
| 192 | }
|
|---|
| 193 |
|
|---|
| 194 | //
|
|---|
| 195 | // Sort eigen values and vectors
|
|---|
| 196 | //
|
|---|
| 197 | for(i=1; i<=m; i++)
|
|---|
| 198 | {
|
|---|
| 199 | k = i;
|
|---|
| 200 | for(j=i; j<=m; j++)
|
|---|
| 201 | {
|
|---|
| 202 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 203 | {
|
|---|
| 204 | k = j;
|
|---|
| 205 | }
|
|---|
| 206 | }
|
|---|
| 207 | v = w[i];
|
|---|
| 208 | w[i] = w[k];
|
|---|
| 209 | w[k] = v;
|
|---|
| 210 | for(j=1; j<=n; j++)
|
|---|
| 211 | {
|
|---|
| 212 | v = z2[j,i];
|
|---|
| 213 | z2[j,i] = z2[j,k];
|
|---|
| 214 | z2[j,k] = v;
|
|---|
| 215 | }
|
|---|
| 216 | }
|
|---|
| 217 |
|
|---|
| 218 | //
|
|---|
| 219 | // Transform Z2 and overwrite Z
|
|---|
| 220 | //
|
|---|
| 221 | z3 = new double[m+1, n+1];
|
|---|
| 222 | for(i=1; i<=m; i++)
|
|---|
| 223 | {
|
|---|
| 224 | for(i_=1; i_<=n;i_++)
|
|---|
| 225 | {
|
|---|
| 226 | z3[i,i_] = z2[i_,i];
|
|---|
| 227 | }
|
|---|
| 228 | }
|
|---|
| 229 | for(i=1; i<=n; i++)
|
|---|
| 230 | {
|
|---|
| 231 | for(j=1; j<=m; j++)
|
|---|
| 232 | {
|
|---|
| 233 | i1_ = (1)-(0);
|
|---|
| 234 | v = 0.0;
|
|---|
| 235 | for(i_=0; i_<=n-1;i_++)
|
|---|
| 236 | {
|
|---|
| 237 | v += z[i-1,i_]*z3[j,i_+i1_];
|
|---|
| 238 | }
|
|---|
| 239 | z2[i,j] = v;
|
|---|
| 240 | }
|
|---|
| 241 | }
|
|---|
| 242 | z = new double[n-1+1, m-1+1];
|
|---|
| 243 | for(i=1; i<=m; i++)
|
|---|
| 244 | {
|
|---|
| 245 | i1_ = (1) - (0);
|
|---|
| 246 | for(i_=0; i_<=n-1;i_++)
|
|---|
| 247 | {
|
|---|
| 248 | z[i_,i-1] = z2[i_+i1_,i];
|
|---|
| 249 | }
|
|---|
| 250 | }
|
|---|
| 251 |
|
|---|
| 252 | //
|
|---|
| 253 | // Store W
|
|---|
| 254 | //
|
|---|
| 255 | d = new double[m-1+1];
|
|---|
| 256 | for(i=1; i<=m; i++)
|
|---|
| 257 | {
|
|---|
| 258 | d[i-1] = w[i];
|
|---|
| 259 | }
|
|---|
| 260 | return result;
|
|---|
| 261 | }
|
|---|
| 262 |
|
|---|
| 263 | //
|
|---|
| 264 | // Eigen vectors are stored in Z
|
|---|
| 265 | //
|
|---|
| 266 | if( zneeded==2 )
|
|---|
| 267 | {
|
|---|
| 268 |
|
|---|
| 269 | //
|
|---|
| 270 | // Find eigen pairs
|
|---|
| 271 | //
|
|---|
| 272 | result = internalbisectioneigenvalues(d1, e1, n, 2, 2, a, b, 0, 0, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 273 | if( !result | m==0 )
|
|---|
| 274 | {
|
|---|
| 275 | m = 0;
|
|---|
| 276 | return result;
|
|---|
| 277 | }
|
|---|
| 278 | internaldstein(n, ref d1, e1, m, w, ref iblock, ref isplit, ref z2, ref ifail, ref cr);
|
|---|
| 279 | if( cr!=0 )
|
|---|
| 280 | {
|
|---|
| 281 | m = 0;
|
|---|
| 282 | result = false;
|
|---|
| 283 | return result;
|
|---|
| 284 | }
|
|---|
| 285 |
|
|---|
| 286 | //
|
|---|
| 287 | // Sort eigen values and vectors
|
|---|
| 288 | //
|
|---|
| 289 | for(i=1; i<=m; i++)
|
|---|
| 290 | {
|
|---|
| 291 | k = i;
|
|---|
| 292 | for(j=i; j<=m; j++)
|
|---|
| 293 | {
|
|---|
| 294 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 295 | {
|
|---|
| 296 | k = j;
|
|---|
| 297 | }
|
|---|
| 298 | }
|
|---|
| 299 | v = w[i];
|
|---|
| 300 | w[i] = w[k];
|
|---|
| 301 | w[k] = v;
|
|---|
| 302 | for(j=1; j<=n; j++)
|
|---|
| 303 | {
|
|---|
| 304 | v = z2[j,i];
|
|---|
| 305 | z2[j,i] = z2[j,k];
|
|---|
| 306 | z2[j,k] = v;
|
|---|
| 307 | }
|
|---|
| 308 | }
|
|---|
| 309 |
|
|---|
| 310 | //
|
|---|
| 311 | // Store W
|
|---|
| 312 | //
|
|---|
| 313 | d = new double[m-1+1];
|
|---|
| 314 | for(i=1; i<=m; i++)
|
|---|
| 315 | {
|
|---|
| 316 | d[i-1] = w[i];
|
|---|
| 317 | }
|
|---|
| 318 | z = new double[n-1+1, m-1+1];
|
|---|
| 319 | for(i=1; i<=m; i++)
|
|---|
| 320 | {
|
|---|
| 321 | i1_ = (1) - (0);
|
|---|
| 322 | for(i_=0; i_<=n-1;i_++)
|
|---|
| 323 | {
|
|---|
| 324 | z[i_,i-1] = z2[i_+i1_,i];
|
|---|
| 325 | }
|
|---|
| 326 | }
|
|---|
| 327 | return result;
|
|---|
| 328 | }
|
|---|
| 329 | result = false;
|
|---|
| 330 | return result;
|
|---|
| 331 | }
|
|---|
| 332 |
|
|---|
| 333 |
|
|---|
| 334 | /*************************************************************************
|
|---|
| 335 | Subroutine for finding tridiagonal matrix eigenvalues/vectors with given
|
|---|
| 336 | indexes (in ascending order) by using the bisection and inverse iteraion.
|
|---|
| 337 |
|
|---|
| 338 | Input parameters:
|
|---|
| 339 | D - the main diagonal of a tridiagonal matrix.
|
|---|
| 340 | Array whose index ranges within [0..N-1].
|
|---|
| 341 | E - the secondary diagonal of a tridiagonal matrix.
|
|---|
| 342 | Array whose index ranges within [0..N-2].
|
|---|
| 343 | N - size of matrix. N>=0.
|
|---|
| 344 | ZNeeded - flag controlling whether the eigenvectors are needed or not.
|
|---|
| 345 | If ZNeeded is equal to:
|
|---|
| 346 | * 0, the eigenvectors are not needed;
|
|---|
| 347 | * 1, the eigenvectors of a tridiagonal matrix are multiplied
|
|---|
| 348 | by the square matrix Z. It is used if the
|
|---|
| 349 | tridiagonal matrix is obtained by the similarity transformation
|
|---|
| 350 | of a symmetric matrix.
|
|---|
| 351 | * 2, the eigenvectors of a tridiagonal matrix replace
|
|---|
| 352 | matrix Z.
|
|---|
| 353 | I1, I2 - index interval for searching (from I1 to I2).
|
|---|
| 354 | 0 <= I1 <= I2 <= N-1.
|
|---|
| 355 | Z - if ZNeeded is equal to:
|
|---|
| 356 | * 0, Z isn't used and remains unchanged;
|
|---|
| 357 | * 1, Z contains the square matrix (array whose indexes range within [0..N-1, 0..N-1])
|
|---|
| 358 | which reduces the given symmetric matrix to tridiagonal form;
|
|---|
| 359 | * 2, Z isn't used (but changed on the exit).
|
|---|
| 360 |
|
|---|
| 361 | Output parameters:
|
|---|
| 362 | D - array of the eigenvalues found.
|
|---|
| 363 | Array whose index ranges within [0..I2-I1].
|
|---|
| 364 | Z - if ZNeeded is equal to:
|
|---|
| 365 | * 0, doesn't contain any information;
|
|---|
| 366 | * 1, contains the product of a given NxN matrix Z (from the left) and
|
|---|
| 367 | Nx(I2-I1) matrix of the eigenvectors found (from the right).
|
|---|
| 368 | Array whose indexes range within [0..N-1, 0..I2-I1].
|
|---|
| 369 | * 2, contains the matrix of the eigenvalues found.
|
|---|
| 370 | Array whose indexes range within [0..N-1, 0..I2-I1].
|
|---|
| 371 |
|
|---|
| 372 |
|
|---|
| 373 | Result:
|
|---|
| 374 |
|
|---|
| 375 | True, if successful. In that case, D contains the eigenvalues,
|
|---|
| 376 | Z contains the eigenvectors (if needed).
|
|---|
| 377 | It should be noted that the subroutine changes the size of arrays D and Z.
|
|---|
| 378 |
|
|---|
| 379 | False, if the bisection method subroutine wasn't able to find the eigenvalues
|
|---|
| 380 | in the given interval or if the inverse iteration subroutine wasn't able
|
|---|
| 381 | to find all the corresponding eigenvectors. In that case, the eigenvalues
|
|---|
| 382 | and eigenvectors are not returned.
|
|---|
| 383 |
|
|---|
| 384 | -- ALGLIB --
|
|---|
| 385 | Copyright 25.12.2005 by Bochkanov Sergey
|
|---|
| 386 | *************************************************************************/
|
|---|
| 387 | public static bool smatrixtdevdi(ref double[] d,
|
|---|
| 388 | ref double[] e,
|
|---|
| 389 | int n,
|
|---|
| 390 | int zneeded,
|
|---|
| 391 | int i1,
|
|---|
| 392 | int i2,
|
|---|
| 393 | ref double[,] z)
|
|---|
| 394 | {
|
|---|
| 395 | bool result = new bool();
|
|---|
| 396 | int errorcode = 0;
|
|---|
| 397 | int nsplit = 0;
|
|---|
| 398 | int i = 0;
|
|---|
| 399 | int j = 0;
|
|---|
| 400 | int k = 0;
|
|---|
| 401 | int m = 0;
|
|---|
| 402 | int cr = 0;
|
|---|
| 403 | int[] iblock = new int[0];
|
|---|
| 404 | int[] isplit = new int[0];
|
|---|
| 405 | int[] ifail = new int[0];
|
|---|
| 406 | double[] w = new double[0];
|
|---|
| 407 | double[] d1 = new double[0];
|
|---|
| 408 | double[] e1 = new double[0];
|
|---|
| 409 | double[,] z2 = new double[0,0];
|
|---|
| 410 | double[,] z3 = new double[0,0];
|
|---|
| 411 | double v = 0;
|
|---|
| 412 | int i_ = 0;
|
|---|
| 413 | int i1_ = 0;
|
|---|
| 414 |
|
|---|
| 415 | System.Diagnostics.Debug.Assert(0<=i1 & i1<=i2 & i2<n, "SMatrixTDEVDI: incorrect I1/I2!");
|
|---|
| 416 |
|
|---|
| 417 | //
|
|---|
| 418 | // Copy D,E to D1, E1
|
|---|
| 419 | //
|
|---|
| 420 | d1 = new double[n+1];
|
|---|
| 421 | i1_ = (0) - (1);
|
|---|
| 422 | for(i_=1; i_<=n;i_++)
|
|---|
| 423 | {
|
|---|
| 424 | d1[i_] = d[i_+i1_];
|
|---|
| 425 | }
|
|---|
| 426 | if( n>1 )
|
|---|
| 427 | {
|
|---|
| 428 | e1 = new double[n-1+1];
|
|---|
| 429 | i1_ = (0) - (1);
|
|---|
| 430 | for(i_=1; i_<=n-1;i_++)
|
|---|
| 431 | {
|
|---|
| 432 | e1[i_] = e[i_+i1_];
|
|---|
| 433 | }
|
|---|
| 434 | }
|
|---|
| 435 |
|
|---|
| 436 | //
|
|---|
| 437 | // No eigen vectors
|
|---|
| 438 | //
|
|---|
| 439 | if( zneeded==0 )
|
|---|
| 440 | {
|
|---|
| 441 | result = internalbisectioneigenvalues(d1, e1, n, 3, 1, 0, 0, i1+1, i2+1, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 442 | if( !result )
|
|---|
| 443 | {
|
|---|
| 444 | return result;
|
|---|
| 445 | }
|
|---|
| 446 | if( m!=i2-i1+1 )
|
|---|
| 447 | {
|
|---|
| 448 | result = false;
|
|---|
| 449 | return result;
|
|---|
| 450 | }
|
|---|
| 451 | d = new double[m-1+1];
|
|---|
| 452 | for(i=1; i<=m; i++)
|
|---|
| 453 | {
|
|---|
| 454 | d[i-1] = w[i];
|
|---|
| 455 | }
|
|---|
| 456 | return result;
|
|---|
| 457 | }
|
|---|
| 458 |
|
|---|
| 459 | //
|
|---|
| 460 | // Eigen vectors are multiplied by Z
|
|---|
| 461 | //
|
|---|
| 462 | if( zneeded==1 )
|
|---|
| 463 | {
|
|---|
| 464 |
|
|---|
| 465 | //
|
|---|
| 466 | // Find eigen pairs
|
|---|
| 467 | //
|
|---|
| 468 | result = internalbisectioneigenvalues(d1, e1, n, 3, 2, 0, 0, i1+1, i2+1, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 469 | if( !result )
|
|---|
| 470 | {
|
|---|
| 471 | return result;
|
|---|
| 472 | }
|
|---|
| 473 | if( m!=i2-i1+1 )
|
|---|
| 474 | {
|
|---|
| 475 | result = false;
|
|---|
| 476 | return result;
|
|---|
| 477 | }
|
|---|
| 478 | internaldstein(n, ref d1, e1, m, w, ref iblock, ref isplit, ref z2, ref ifail, ref cr);
|
|---|
| 479 | if( cr!=0 )
|
|---|
| 480 | {
|
|---|
| 481 | result = false;
|
|---|
| 482 | return result;
|
|---|
| 483 | }
|
|---|
| 484 |
|
|---|
| 485 | //
|
|---|
| 486 | // Sort eigen values and vectors
|
|---|
| 487 | //
|
|---|
| 488 | for(i=1; i<=m; i++)
|
|---|
| 489 | {
|
|---|
| 490 | k = i;
|
|---|
| 491 | for(j=i; j<=m; j++)
|
|---|
| 492 | {
|
|---|
| 493 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 494 | {
|
|---|
| 495 | k = j;
|
|---|
| 496 | }
|
|---|
| 497 | }
|
|---|
| 498 | v = w[i];
|
|---|
| 499 | w[i] = w[k];
|
|---|
| 500 | w[k] = v;
|
|---|
| 501 | for(j=1; j<=n; j++)
|
|---|
| 502 | {
|
|---|
| 503 | v = z2[j,i];
|
|---|
| 504 | z2[j,i] = z2[j,k];
|
|---|
| 505 | z2[j,k] = v;
|
|---|
| 506 | }
|
|---|
| 507 | }
|
|---|
| 508 |
|
|---|
| 509 | //
|
|---|
| 510 | // Transform Z2 and overwrite Z
|
|---|
| 511 | //
|
|---|
| 512 | z3 = new double[m+1, n+1];
|
|---|
| 513 | for(i=1; i<=m; i++)
|
|---|
| 514 | {
|
|---|
| 515 | for(i_=1; i_<=n;i_++)
|
|---|
| 516 | {
|
|---|
| 517 | z3[i,i_] = z2[i_,i];
|
|---|
| 518 | }
|
|---|
| 519 | }
|
|---|
| 520 | for(i=1; i<=n; i++)
|
|---|
| 521 | {
|
|---|
| 522 | for(j=1; j<=m; j++)
|
|---|
| 523 | {
|
|---|
| 524 | i1_ = (1)-(0);
|
|---|
| 525 | v = 0.0;
|
|---|
| 526 | for(i_=0; i_<=n-1;i_++)
|
|---|
| 527 | {
|
|---|
| 528 | v += z[i-1,i_]*z3[j,i_+i1_];
|
|---|
| 529 | }
|
|---|
| 530 | z2[i,j] = v;
|
|---|
| 531 | }
|
|---|
| 532 | }
|
|---|
| 533 | z = new double[n-1+1, m-1+1];
|
|---|
| 534 | for(i=1; i<=m; i++)
|
|---|
| 535 | {
|
|---|
| 536 | i1_ = (1) - (0);
|
|---|
| 537 | for(i_=0; i_<=n-1;i_++)
|
|---|
| 538 | {
|
|---|
| 539 | z[i_,i-1] = z2[i_+i1_,i];
|
|---|
| 540 | }
|
|---|
| 541 | }
|
|---|
| 542 |
|
|---|
| 543 | //
|
|---|
| 544 | // Store W
|
|---|
| 545 | //
|
|---|
| 546 | d = new double[m-1+1];
|
|---|
| 547 | for(i=1; i<=m; i++)
|
|---|
| 548 | {
|
|---|
| 549 | d[i-1] = w[i];
|
|---|
| 550 | }
|
|---|
| 551 | return result;
|
|---|
| 552 | }
|
|---|
| 553 |
|
|---|
| 554 | //
|
|---|
| 555 | // Eigen vectors are stored in Z
|
|---|
| 556 | //
|
|---|
| 557 | if( zneeded==2 )
|
|---|
| 558 | {
|
|---|
| 559 |
|
|---|
| 560 | //
|
|---|
| 561 | // Find eigen pairs
|
|---|
| 562 | //
|
|---|
| 563 | result = internalbisectioneigenvalues(d1, e1, n, 3, 2, 0, 0, i1+1, i2+1, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 564 | if( !result )
|
|---|
| 565 | {
|
|---|
| 566 | return result;
|
|---|
| 567 | }
|
|---|
| 568 | if( m!=i2-i1+1 )
|
|---|
| 569 | {
|
|---|
| 570 | result = false;
|
|---|
| 571 | return result;
|
|---|
| 572 | }
|
|---|
| 573 | internaldstein(n, ref d1, e1, m, w, ref iblock, ref isplit, ref z2, ref ifail, ref cr);
|
|---|
| 574 | if( cr!=0 )
|
|---|
| 575 | {
|
|---|
| 576 | result = false;
|
|---|
| 577 | return result;
|
|---|
| 578 | }
|
|---|
| 579 |
|
|---|
| 580 | //
|
|---|
| 581 | // Sort eigen values and vectors
|
|---|
| 582 | //
|
|---|
| 583 | for(i=1; i<=m; i++)
|
|---|
| 584 | {
|
|---|
| 585 | k = i;
|
|---|
| 586 | for(j=i; j<=m; j++)
|
|---|
| 587 | {
|
|---|
| 588 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 589 | {
|
|---|
| 590 | k = j;
|
|---|
| 591 | }
|
|---|
| 592 | }
|
|---|
| 593 | v = w[i];
|
|---|
| 594 | w[i] = w[k];
|
|---|
| 595 | w[k] = v;
|
|---|
| 596 | for(j=1; j<=n; j++)
|
|---|
| 597 | {
|
|---|
| 598 | v = z2[j,i];
|
|---|
| 599 | z2[j,i] = z2[j,k];
|
|---|
| 600 | z2[j,k] = v;
|
|---|
| 601 | }
|
|---|
| 602 | }
|
|---|
| 603 |
|
|---|
| 604 | //
|
|---|
| 605 | // Store Z
|
|---|
| 606 | //
|
|---|
| 607 | z = new double[n-1+1, m-1+1];
|
|---|
| 608 | for(i=1; i<=m; i++)
|
|---|
| 609 | {
|
|---|
| 610 | i1_ = (1) - (0);
|
|---|
| 611 | for(i_=0; i_<=n-1;i_++)
|
|---|
| 612 | {
|
|---|
| 613 | z[i_,i-1] = z2[i_+i1_,i];
|
|---|
| 614 | }
|
|---|
| 615 | }
|
|---|
| 616 |
|
|---|
| 617 | //
|
|---|
| 618 | // Store W
|
|---|
| 619 | //
|
|---|
| 620 | d = new double[m-1+1];
|
|---|
| 621 | for(i=1; i<=m; i++)
|
|---|
| 622 | {
|
|---|
| 623 | d[i-1] = w[i];
|
|---|
| 624 | }
|
|---|
| 625 | return result;
|
|---|
| 626 | }
|
|---|
| 627 | result = false;
|
|---|
| 628 | return result;
|
|---|
| 629 | }
|
|---|
| 630 |
|
|---|
| 631 |
|
|---|
| 632 | public static bool tridiagonaleigenvaluesandvectorsininterval(ref double[] d,
|
|---|
| 633 | ref double[] e,
|
|---|
| 634 | int n,
|
|---|
| 635 | int zneeded,
|
|---|
| 636 | double a,
|
|---|
| 637 | double b,
|
|---|
| 638 | ref int m,
|
|---|
| 639 | ref double[,] z)
|
|---|
| 640 | {
|
|---|
| 641 | bool result = new bool();
|
|---|
| 642 | int errorcode = 0;
|
|---|
| 643 | int nsplit = 0;
|
|---|
| 644 | int i = 0;
|
|---|
| 645 | int j = 0;
|
|---|
| 646 | int k = 0;
|
|---|
| 647 | int cr = 0;
|
|---|
| 648 | int[] iblock = new int[0];
|
|---|
| 649 | int[] isplit = new int[0];
|
|---|
| 650 | int[] ifail = new int[0];
|
|---|
| 651 | double[] w = new double[0];
|
|---|
| 652 | double[,] z2 = new double[0,0];
|
|---|
| 653 | double[,] z3 = new double[0,0];
|
|---|
| 654 | double v = 0;
|
|---|
| 655 | int i_ = 0;
|
|---|
| 656 |
|
|---|
| 657 |
|
|---|
| 658 | //
|
|---|
| 659 | // No eigen vectors
|
|---|
| 660 | //
|
|---|
| 661 | if( zneeded==0 )
|
|---|
| 662 | {
|
|---|
| 663 | result = internalbisectioneigenvalues(d, e, n, 2, 1, a, b, 0, 0, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 664 | if( !result | m==0 )
|
|---|
| 665 | {
|
|---|
| 666 | m = 0;
|
|---|
| 667 | return result;
|
|---|
| 668 | }
|
|---|
| 669 | d = new double[m+1];
|
|---|
| 670 | for(i=1; i<=m; i++)
|
|---|
| 671 | {
|
|---|
| 672 | d[i] = w[i];
|
|---|
| 673 | }
|
|---|
| 674 | return result;
|
|---|
| 675 | }
|
|---|
| 676 |
|
|---|
| 677 | //
|
|---|
| 678 | // Eigen vectors are multiplied by Z
|
|---|
| 679 | //
|
|---|
| 680 | if( zneeded==1 )
|
|---|
| 681 | {
|
|---|
| 682 |
|
|---|
| 683 | //
|
|---|
| 684 | // Find eigen pairs
|
|---|
| 685 | //
|
|---|
| 686 | result = internalbisectioneigenvalues(d, e, n, 2, 2, a, b, 0, 0, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 687 | if( !result | m==0 )
|
|---|
| 688 | {
|
|---|
| 689 | m = 0;
|
|---|
| 690 | return result;
|
|---|
| 691 | }
|
|---|
| 692 | internaldstein(n, ref d, e, m, w, ref iblock, ref isplit, ref z2, ref ifail, ref cr);
|
|---|
| 693 | if( cr!=0 )
|
|---|
| 694 | {
|
|---|
| 695 | m = 0;
|
|---|
| 696 | result = false;
|
|---|
| 697 | return result;
|
|---|
| 698 | }
|
|---|
| 699 |
|
|---|
| 700 | //
|
|---|
| 701 | // Sort eigen values and vectors
|
|---|
| 702 | //
|
|---|
| 703 | for(i=1; i<=m; i++)
|
|---|
| 704 | {
|
|---|
| 705 | k = i;
|
|---|
| 706 | for(j=i; j<=m; j++)
|
|---|
| 707 | {
|
|---|
| 708 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 709 | {
|
|---|
| 710 | k = j;
|
|---|
| 711 | }
|
|---|
| 712 | }
|
|---|
| 713 | v = w[i];
|
|---|
| 714 | w[i] = w[k];
|
|---|
| 715 | w[k] = v;
|
|---|
| 716 | for(j=1; j<=n; j++)
|
|---|
| 717 | {
|
|---|
| 718 | v = z2[j,i];
|
|---|
| 719 | z2[j,i] = z2[j,k];
|
|---|
| 720 | z2[j,k] = v;
|
|---|
| 721 | }
|
|---|
| 722 | }
|
|---|
| 723 |
|
|---|
| 724 | //
|
|---|
| 725 | // Transform Z2 and overwrite Z
|
|---|
| 726 | //
|
|---|
| 727 | z3 = new double[m+1, n+1];
|
|---|
| 728 | for(i=1; i<=m; i++)
|
|---|
| 729 | {
|
|---|
| 730 | for(i_=1; i_<=n;i_++)
|
|---|
| 731 | {
|
|---|
| 732 | z3[i,i_] = z2[i_,i];
|
|---|
| 733 | }
|
|---|
| 734 | }
|
|---|
| 735 | for(i=1; i<=n; i++)
|
|---|
| 736 | {
|
|---|
| 737 | for(j=1; j<=m; j++)
|
|---|
| 738 | {
|
|---|
| 739 | v = 0.0;
|
|---|
| 740 | for(i_=1; i_<=n;i_++)
|
|---|
| 741 | {
|
|---|
| 742 | v += z[i,i_]*z3[j,i_];
|
|---|
| 743 | }
|
|---|
| 744 | z2[i,j] = v;
|
|---|
| 745 | }
|
|---|
| 746 | }
|
|---|
| 747 | z = new double[n+1, m+1];
|
|---|
| 748 | for(i=1; i<=m; i++)
|
|---|
| 749 | {
|
|---|
| 750 | for(i_=1; i_<=n;i_++)
|
|---|
| 751 | {
|
|---|
| 752 | z[i_,i] = z2[i_,i];
|
|---|
| 753 | }
|
|---|
| 754 | }
|
|---|
| 755 |
|
|---|
| 756 | //
|
|---|
| 757 | // Store W
|
|---|
| 758 | //
|
|---|
| 759 | d = new double[m+1];
|
|---|
| 760 | for(i=1; i<=m; i++)
|
|---|
| 761 | {
|
|---|
| 762 | d[i] = w[i];
|
|---|
| 763 | }
|
|---|
| 764 | return result;
|
|---|
| 765 | }
|
|---|
| 766 |
|
|---|
| 767 | //
|
|---|
| 768 | // Eigen vectors are stored in Z
|
|---|
| 769 | //
|
|---|
| 770 | if( zneeded==2 )
|
|---|
| 771 | {
|
|---|
| 772 |
|
|---|
| 773 | //
|
|---|
| 774 | // Find eigen pairs
|
|---|
| 775 | //
|
|---|
| 776 | result = internalbisectioneigenvalues(d, e, n, 2, 2, a, b, 0, 0, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 777 | if( !result | m==0 )
|
|---|
| 778 | {
|
|---|
| 779 | m = 0;
|
|---|
| 780 | return result;
|
|---|
| 781 | }
|
|---|
| 782 | internaldstein(n, ref d, e, m, w, ref iblock, ref isplit, ref z, ref ifail, ref cr);
|
|---|
| 783 | if( cr!=0 )
|
|---|
| 784 | {
|
|---|
| 785 | m = 0;
|
|---|
| 786 | result = false;
|
|---|
| 787 | return result;
|
|---|
| 788 | }
|
|---|
| 789 |
|
|---|
| 790 | //
|
|---|
| 791 | // Sort eigen values and vectors
|
|---|
| 792 | //
|
|---|
| 793 | for(i=1; i<=m; i++)
|
|---|
| 794 | {
|
|---|
| 795 | k = i;
|
|---|
| 796 | for(j=i; j<=m; j++)
|
|---|
| 797 | {
|
|---|
| 798 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 799 | {
|
|---|
| 800 | k = j;
|
|---|
| 801 | }
|
|---|
| 802 | }
|
|---|
| 803 | v = w[i];
|
|---|
| 804 | w[i] = w[k];
|
|---|
| 805 | w[k] = v;
|
|---|
| 806 | for(j=1; j<=n; j++)
|
|---|
| 807 | {
|
|---|
| 808 | v = z[j,i];
|
|---|
| 809 | z[j,i] = z[j,k];
|
|---|
| 810 | z[j,k] = v;
|
|---|
| 811 | }
|
|---|
| 812 | }
|
|---|
| 813 |
|
|---|
| 814 | //
|
|---|
| 815 | // Store W
|
|---|
| 816 | //
|
|---|
| 817 | d = new double[m+1];
|
|---|
| 818 | for(i=1; i<=m; i++)
|
|---|
| 819 | {
|
|---|
| 820 | d[i] = w[i];
|
|---|
| 821 | }
|
|---|
| 822 | return result;
|
|---|
| 823 | }
|
|---|
| 824 | result = false;
|
|---|
| 825 | return result;
|
|---|
| 826 | }
|
|---|
| 827 |
|
|---|
| 828 |
|
|---|
| 829 | public static bool tridiagonaleigenvaluesandvectorsbyindexes(ref double[] d,
|
|---|
| 830 | ref double[] e,
|
|---|
| 831 | int n,
|
|---|
| 832 | int zneeded,
|
|---|
| 833 | int i1,
|
|---|
| 834 | int i2,
|
|---|
| 835 | ref double[,] z)
|
|---|
| 836 | {
|
|---|
| 837 | bool result = new bool();
|
|---|
| 838 | int errorcode = 0;
|
|---|
| 839 | int nsplit = 0;
|
|---|
| 840 | int i = 0;
|
|---|
| 841 | int j = 0;
|
|---|
| 842 | int k = 0;
|
|---|
| 843 | int m = 0;
|
|---|
| 844 | int cr = 0;
|
|---|
| 845 | int[] iblock = new int[0];
|
|---|
| 846 | int[] isplit = new int[0];
|
|---|
| 847 | int[] ifail = new int[0];
|
|---|
| 848 | double[] w = new double[0];
|
|---|
| 849 | double[,] z2 = new double[0,0];
|
|---|
| 850 | double[,] z3 = new double[0,0];
|
|---|
| 851 | double v = 0;
|
|---|
| 852 | int i_ = 0;
|
|---|
| 853 |
|
|---|
| 854 |
|
|---|
| 855 | //
|
|---|
| 856 | // No eigen vectors
|
|---|
| 857 | //
|
|---|
| 858 | if( zneeded==0 )
|
|---|
| 859 | {
|
|---|
| 860 | result = internalbisectioneigenvalues(d, e, n, 3, 1, 0, 0, i1, i2, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 861 | if( !result )
|
|---|
| 862 | {
|
|---|
| 863 | return result;
|
|---|
| 864 | }
|
|---|
| 865 | d = new double[m+1];
|
|---|
| 866 | for(i=1; i<=m; i++)
|
|---|
| 867 | {
|
|---|
| 868 | d[i] = w[i];
|
|---|
| 869 | }
|
|---|
| 870 | return result;
|
|---|
| 871 | }
|
|---|
| 872 |
|
|---|
| 873 | //
|
|---|
| 874 | // Eigen vectors are multiplied by Z
|
|---|
| 875 | //
|
|---|
| 876 | if( zneeded==1 )
|
|---|
| 877 | {
|
|---|
| 878 |
|
|---|
| 879 | //
|
|---|
| 880 | // Find eigen pairs
|
|---|
| 881 | //
|
|---|
| 882 | result = internalbisectioneigenvalues(d, e, n, 3, 2, 0, 0, i1, i2, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 883 | if( !result )
|
|---|
| 884 | {
|
|---|
| 885 | return result;
|
|---|
| 886 | }
|
|---|
| 887 | internaldstein(n, ref d, e, m, w, ref iblock, ref isplit, ref z2, ref ifail, ref cr);
|
|---|
| 888 | if( cr!=0 )
|
|---|
| 889 | {
|
|---|
| 890 | result = false;
|
|---|
| 891 | return result;
|
|---|
| 892 | }
|
|---|
| 893 |
|
|---|
| 894 | //
|
|---|
| 895 | // Sort eigen values and vectors
|
|---|
| 896 | //
|
|---|
| 897 | for(i=1; i<=m; i++)
|
|---|
| 898 | {
|
|---|
| 899 | k = i;
|
|---|
| 900 | for(j=i; j<=m; j++)
|
|---|
| 901 | {
|
|---|
| 902 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 903 | {
|
|---|
| 904 | k = j;
|
|---|
| 905 | }
|
|---|
| 906 | }
|
|---|
| 907 | v = w[i];
|
|---|
| 908 | w[i] = w[k];
|
|---|
| 909 | w[k] = v;
|
|---|
| 910 | for(j=1; j<=n; j++)
|
|---|
| 911 | {
|
|---|
| 912 | v = z2[j,i];
|
|---|
| 913 | z2[j,i] = z2[j,k];
|
|---|
| 914 | z2[j,k] = v;
|
|---|
| 915 | }
|
|---|
| 916 | }
|
|---|
| 917 |
|
|---|
| 918 | //
|
|---|
| 919 | // Transform Z2 and overwrite Z
|
|---|
| 920 | //
|
|---|
| 921 | z3 = new double[m+1, n+1];
|
|---|
| 922 | for(i=1; i<=m; i++)
|
|---|
| 923 | {
|
|---|
| 924 | for(i_=1; i_<=n;i_++)
|
|---|
| 925 | {
|
|---|
| 926 | z3[i,i_] = z2[i_,i];
|
|---|
| 927 | }
|
|---|
| 928 | }
|
|---|
| 929 | for(i=1; i<=n; i++)
|
|---|
| 930 | {
|
|---|
| 931 | for(j=1; j<=m; j++)
|
|---|
| 932 | {
|
|---|
| 933 | v = 0.0;
|
|---|
| 934 | for(i_=1; i_<=n;i_++)
|
|---|
| 935 | {
|
|---|
| 936 | v += z[i,i_]*z3[j,i_];
|
|---|
| 937 | }
|
|---|
| 938 | z2[i,j] = v;
|
|---|
| 939 | }
|
|---|
| 940 | }
|
|---|
| 941 | z = new double[n+1, m+1];
|
|---|
| 942 | for(i=1; i<=m; i++)
|
|---|
| 943 | {
|
|---|
| 944 | for(i_=1; i_<=n;i_++)
|
|---|
| 945 | {
|
|---|
| 946 | z[i_,i] = z2[i_,i];
|
|---|
| 947 | }
|
|---|
| 948 | }
|
|---|
| 949 |
|
|---|
| 950 | //
|
|---|
| 951 | // Store W
|
|---|
| 952 | //
|
|---|
| 953 | d = new double[m+1];
|
|---|
| 954 | for(i=1; i<=m; i++)
|
|---|
| 955 | {
|
|---|
| 956 | d[i] = w[i];
|
|---|
| 957 | }
|
|---|
| 958 | return result;
|
|---|
| 959 | }
|
|---|
| 960 |
|
|---|
| 961 | //
|
|---|
| 962 | // Eigen vectors are stored in Z
|
|---|
| 963 | //
|
|---|
| 964 | if( zneeded==2 )
|
|---|
| 965 | {
|
|---|
| 966 |
|
|---|
| 967 | //
|
|---|
| 968 | // Find eigen pairs
|
|---|
| 969 | //
|
|---|
| 970 | result = internalbisectioneigenvalues(d, e, n, 3, 2, 0, 0, i1, i2, -1, ref w, ref m, ref nsplit, ref iblock, ref isplit, ref errorcode);
|
|---|
| 971 | if( !result )
|
|---|
| 972 | {
|
|---|
| 973 | return result;
|
|---|
| 974 | }
|
|---|
| 975 | internaldstein(n, ref d, e, m, w, ref iblock, ref isplit, ref z, ref ifail, ref cr);
|
|---|
| 976 | if( cr!=0 )
|
|---|
| 977 | {
|
|---|
| 978 | result = false;
|
|---|
| 979 | return result;
|
|---|
| 980 | }
|
|---|
| 981 |
|
|---|
| 982 | //
|
|---|
| 983 | // Sort eigen values and vectors
|
|---|
| 984 | //
|
|---|
| 985 | for(i=1; i<=m; i++)
|
|---|
| 986 | {
|
|---|
| 987 | k = i;
|
|---|
| 988 | for(j=i; j<=m; j++)
|
|---|
| 989 | {
|
|---|
| 990 | if( (double)(w[j])<(double)(w[k]) )
|
|---|
| 991 | {
|
|---|
| 992 | k = j;
|
|---|
| 993 | }
|
|---|
| 994 | }
|
|---|
| 995 | v = w[i];
|
|---|
| 996 | w[i] = w[k];
|
|---|
| 997 | w[k] = v;
|
|---|
| 998 | for(j=1; j<=n; j++)
|
|---|
| 999 | {
|
|---|
| 1000 | v = z[j,i];
|
|---|
| 1001 | z[j,i] = z[j,k];
|
|---|
| 1002 | z[j,k] = v;
|
|---|
| 1003 | }
|
|---|
| 1004 | }
|
|---|
| 1005 |
|
|---|
| 1006 | //
|
|---|
| 1007 | // Store W
|
|---|
| 1008 | //
|
|---|
| 1009 | d = new double[m+1];
|
|---|
| 1010 | for(i=1; i<=m; i++)
|
|---|
| 1011 | {
|
|---|
| 1012 | d[i] = w[i];
|
|---|
| 1013 | }
|
|---|
| 1014 | return result;
|
|---|
| 1015 | }
|
|---|
| 1016 | result = false;
|
|---|
| 1017 | return result;
|
|---|
| 1018 | }
|
|---|
| 1019 |
|
|---|
| 1020 |
|
|---|
| 1021 | public static bool internalbisectioneigenvalues(double[] d,
|
|---|
| 1022 | double[] e,
|
|---|
| 1023 | int n,
|
|---|
| 1024 | int irange,
|
|---|
| 1025 | int iorder,
|
|---|
| 1026 | double vl,
|
|---|
| 1027 | double vu,
|
|---|
| 1028 | int il,
|
|---|
| 1029 | int iu,
|
|---|
| 1030 | double abstol,
|
|---|
| 1031 | ref double[] w,
|
|---|
| 1032 | ref int m,
|
|---|
| 1033 | ref int nsplit,
|
|---|
| 1034 | ref int[] iblock,
|
|---|
| 1035 | ref int[] isplit,
|
|---|
| 1036 | ref int errorcode)
|
|---|
| 1037 | {
|
|---|
| 1038 | bool result = new bool();
|
|---|
| 1039 | double fudge = 0;
|
|---|
| 1040 | double relfac = 0;
|
|---|
| 1041 | bool ncnvrg = new bool();
|
|---|
| 1042 | bool toofew = new bool();
|
|---|
| 1043 | int ib = 0;
|
|---|
| 1044 | int ibegin = 0;
|
|---|
| 1045 | int idiscl = 0;
|
|---|
| 1046 | int idiscu = 0;
|
|---|
| 1047 | int ie = 0;
|
|---|
| 1048 | int iend = 0;
|
|---|
| 1049 | int iinfo = 0;
|
|---|
| 1050 | int im = 0;
|
|---|
| 1051 | int iin = 0;
|
|---|
| 1052 | int ioff = 0;
|
|---|
| 1053 | int iout = 0;
|
|---|
| 1054 | int itmax = 0;
|
|---|
| 1055 | int iw = 0;
|
|---|
| 1056 | int iwoff = 0;
|
|---|
| 1057 | int j = 0;
|
|---|
| 1058 | int itmp1 = 0;
|
|---|
| 1059 | int jb = 0;
|
|---|
| 1060 | int jdisc = 0;
|
|---|
| 1061 | int je = 0;
|
|---|
| 1062 | int nwl = 0;
|
|---|
| 1063 | int nwu = 0;
|
|---|
| 1064 | double atoli = 0;
|
|---|
| 1065 | double bnorm = 0;
|
|---|
| 1066 | double gl = 0;
|
|---|
| 1067 | double gu = 0;
|
|---|
| 1068 | double pivmin = 0;
|
|---|
| 1069 | double rtoli = 0;
|
|---|
| 1070 | double safemn = 0;
|
|---|
| 1071 | double tmp1 = 0;
|
|---|
| 1072 | double tmp2 = 0;
|
|---|
| 1073 | double tnorm = 0;
|
|---|
| 1074 | double ulp = 0;
|
|---|
| 1075 | double wkill = 0;
|
|---|
| 1076 | double wl = 0;
|
|---|
| 1077 | double wlu = 0;
|
|---|
| 1078 | double wu = 0;
|
|---|
| 1079 | double wul = 0;
|
|---|
| 1080 | double scalefactor = 0;
|
|---|
| 1081 | double t = 0;
|
|---|
| 1082 | int[] idumma = new int[0];
|
|---|
| 1083 | double[] work = new double[0];
|
|---|
| 1084 | int[] iwork = new int[0];
|
|---|
| 1085 | int[] ia1s2 = new int[0];
|
|---|
| 1086 | double[] ra1s2 = new double[0];
|
|---|
| 1087 | double[,] ra1s2x2 = new double[0,0];
|
|---|
| 1088 | int[,] ia1s2x2 = new int[0,0];
|
|---|
| 1089 | double[] ra1siin = new double[0];
|
|---|
| 1090 | double[] ra2siin = new double[0];
|
|---|
| 1091 | double[] ra3siin = new double[0];
|
|---|
| 1092 | double[] ra4siin = new double[0];
|
|---|
| 1093 | double[,] ra1siinx2 = new double[0,0];
|
|---|
| 1094 | int[,] ia1siinx2 = new int[0,0];
|
|---|
| 1095 | int[] iworkspace = new int[0];
|
|---|
| 1096 | double[] rworkspace = new double[0];
|
|---|
| 1097 | int tmpi = 0;
|
|---|
| 1098 |
|
|---|
| 1099 | d = (double[])d.Clone();
|
|---|
| 1100 | e = (double[])e.Clone();
|
|---|
| 1101 |
|
|---|
| 1102 |
|
|---|
| 1103 | //
|
|---|
| 1104 | // Quick return if possible
|
|---|
| 1105 | //
|
|---|
| 1106 | m = 0;
|
|---|
| 1107 | if( n==0 )
|
|---|
| 1108 | {
|
|---|
| 1109 | result = true;
|
|---|
| 1110 | return result;
|
|---|
| 1111 | }
|
|---|
| 1112 |
|
|---|
| 1113 | //
|
|---|
| 1114 | // Get machine constants
|
|---|
| 1115 | // NB is the minimum vector length for vector bisection, or 0
|
|---|
| 1116 | // if only scalar is to be done.
|
|---|
| 1117 | //
|
|---|
| 1118 | fudge = 2;
|
|---|
| 1119 | relfac = 2;
|
|---|
| 1120 | safemn = AP.Math.MinRealNumber;
|
|---|
| 1121 | ulp = 2*AP.Math.MachineEpsilon;
|
|---|
| 1122 | rtoli = ulp*relfac;
|
|---|
| 1123 | idumma = new int[1+1];
|
|---|
| 1124 | work = new double[4*n+1];
|
|---|
| 1125 | iwork = new int[3*n+1];
|
|---|
| 1126 | w = new double[n+1];
|
|---|
| 1127 | iblock = new int[n+1];
|
|---|
| 1128 | isplit = new int[n+1];
|
|---|
| 1129 | ia1s2 = new int[2+1];
|
|---|
| 1130 | ra1s2 = new double[2+1];
|
|---|
| 1131 | ra1s2x2 = new double[2+1, 2+1];
|
|---|
| 1132 | ia1s2x2 = new int[2+1, 2+1];
|
|---|
| 1133 | ra1siin = new double[n+1];
|
|---|
| 1134 | ra2siin = new double[n+1];
|
|---|
| 1135 | ra3siin = new double[n+1];
|
|---|
| 1136 | ra4siin = new double[n+1];
|
|---|
| 1137 | ra1siinx2 = new double[n+1, 2+1];
|
|---|
| 1138 | ia1siinx2 = new int[n+1, 2+1];
|
|---|
| 1139 | iworkspace = new int[n+1];
|
|---|
| 1140 | rworkspace = new double[n+1];
|
|---|
| 1141 |
|
|---|
| 1142 | //
|
|---|
| 1143 | // Check for Errors
|
|---|
| 1144 | //
|
|---|
| 1145 | result = false;
|
|---|
| 1146 | errorcode = 0;
|
|---|
| 1147 | if( irange<=0 | irange>=4 )
|
|---|
| 1148 | {
|
|---|
| 1149 | errorcode = -4;
|
|---|
| 1150 | }
|
|---|
| 1151 | if( iorder<=0 | iorder>=3 )
|
|---|
| 1152 | {
|
|---|
| 1153 | errorcode = -5;
|
|---|
| 1154 | }
|
|---|
| 1155 | if( n<0 )
|
|---|
| 1156 | {
|
|---|
| 1157 | errorcode = -3;
|
|---|
| 1158 | }
|
|---|
| 1159 | if( irange==2 & (double)(vl)>=(double)(vu) )
|
|---|
| 1160 | {
|
|---|
| 1161 | errorcode = -6;
|
|---|
| 1162 | }
|
|---|
| 1163 | if( irange==3 & (il<1 | il>Math.Max(1, n)) )
|
|---|
| 1164 | {
|
|---|
| 1165 | errorcode = -8;
|
|---|
| 1166 | }
|
|---|
| 1167 | if( irange==3 & (iu<Math.Min(n, il) | iu>n) )
|
|---|
| 1168 | {
|
|---|
| 1169 | errorcode = -9;
|
|---|
| 1170 | }
|
|---|
| 1171 | if( errorcode!=0 )
|
|---|
| 1172 | {
|
|---|
| 1173 | return result;
|
|---|
| 1174 | }
|
|---|
| 1175 |
|
|---|
| 1176 | //
|
|---|
| 1177 | // Initialize error flags
|
|---|
| 1178 | //
|
|---|
| 1179 | ncnvrg = false;
|
|---|
| 1180 | toofew = false;
|
|---|
| 1181 |
|
|---|
| 1182 | //
|
|---|
| 1183 | // Simplifications:
|
|---|
| 1184 | //
|
|---|
| 1185 | if( irange==3 & il==1 & iu==n )
|
|---|
| 1186 | {
|
|---|
| 1187 | irange = 1;
|
|---|
| 1188 | }
|
|---|
| 1189 |
|
|---|
| 1190 | //
|
|---|
| 1191 | // Special Case when N=1
|
|---|
| 1192 | //
|
|---|
| 1193 | if( n==1 )
|
|---|
| 1194 | {
|
|---|
| 1195 | nsplit = 1;
|
|---|
| 1196 | isplit[1] = 1;
|
|---|
| 1197 | if( irange==2 & ((double)(vl)>=(double)(d[1]) | (double)(vu)<(double)(d[1])) )
|
|---|
| 1198 | {
|
|---|
| 1199 | m = 0;
|
|---|
| 1200 | }
|
|---|
| 1201 | else
|
|---|
| 1202 | {
|
|---|
| 1203 | w[1] = d[1];
|
|---|
| 1204 | iblock[1] = 1;
|
|---|
| 1205 | m = 1;
|
|---|
| 1206 | }
|
|---|
| 1207 | result = true;
|
|---|
| 1208 | return result;
|
|---|
| 1209 | }
|
|---|
| 1210 |
|
|---|
| 1211 | //
|
|---|
| 1212 | // Scaling
|
|---|
| 1213 | //
|
|---|
| 1214 | t = Math.Abs(d[n]);
|
|---|
| 1215 | for(j=1; j<=n-1; j++)
|
|---|
| 1216 | {
|
|---|
| 1217 | t = Math.Max(t, Math.Abs(d[j]));
|
|---|
| 1218 | t = Math.Max(t, Math.Abs(e[j]));
|
|---|
| 1219 | }
|
|---|
| 1220 | scalefactor = 1;
|
|---|
| 1221 | if( (double)(t)!=(double)(0) )
|
|---|
| 1222 | {
|
|---|
| 1223 | if( (double)(t)>(double)(Math.Sqrt(Math.Sqrt(AP.Math.MinRealNumber))*Math.Sqrt(AP.Math.MaxRealNumber)) )
|
|---|
| 1224 | {
|
|---|
| 1225 | scalefactor = t;
|
|---|
| 1226 | }
|
|---|
| 1227 | if( (double)(t)<(double)(Math.Sqrt(Math.Sqrt(AP.Math.MaxRealNumber))*Math.Sqrt(AP.Math.MinRealNumber)) )
|
|---|
| 1228 | {
|
|---|
| 1229 | scalefactor = t;
|
|---|
| 1230 | }
|
|---|
| 1231 | for(j=1; j<=n-1; j++)
|
|---|
| 1232 | {
|
|---|
| 1233 | d[j] = d[j]/scalefactor;
|
|---|
| 1234 | e[j] = e[j]/scalefactor;
|
|---|
| 1235 | }
|
|---|
| 1236 | d[n] = d[n]/scalefactor;
|
|---|
| 1237 | }
|
|---|
| 1238 |
|
|---|
| 1239 | //
|
|---|
| 1240 | // Compute Splitting Points
|
|---|
| 1241 | //
|
|---|
| 1242 | nsplit = 1;
|
|---|
| 1243 | work[n] = 0;
|
|---|
| 1244 | pivmin = 1;
|
|---|
| 1245 | for(j=2; j<=n; j++)
|
|---|
| 1246 | {
|
|---|
| 1247 | tmp1 = AP.Math.Sqr(e[j-1]);
|
|---|
| 1248 | if( (double)(Math.Abs(d[j]*d[j-1])*AP.Math.Sqr(ulp)+safemn)>(double)(tmp1) )
|
|---|
| 1249 | {
|
|---|
| 1250 | isplit[nsplit] = j-1;
|
|---|
| 1251 | nsplit = nsplit+1;
|
|---|
| 1252 | work[j-1] = 0;
|
|---|
| 1253 | }
|
|---|
| 1254 | else
|
|---|
| 1255 | {
|
|---|
| 1256 | work[j-1] = tmp1;
|
|---|
| 1257 | pivmin = Math.Max(pivmin, tmp1);
|
|---|
| 1258 | }
|
|---|
| 1259 | }
|
|---|
| 1260 | isplit[nsplit] = n;
|
|---|
| 1261 | pivmin = pivmin*safemn;
|
|---|
| 1262 |
|
|---|
| 1263 | //
|
|---|
| 1264 | // Compute Interval and ATOLI
|
|---|
| 1265 | //
|
|---|
| 1266 | if( irange==3 )
|
|---|
| 1267 | {
|
|---|
| 1268 |
|
|---|
| 1269 | //
|
|---|
| 1270 | // RANGE='I': Compute the interval containing eigenvalues
|
|---|
| 1271 | // IL through IU.
|
|---|
| 1272 | //
|
|---|
| 1273 | // Compute Gershgorin interval for entire (split) matrix
|
|---|
| 1274 | // and use it as the initial interval
|
|---|
| 1275 | //
|
|---|
| 1276 | gu = d[1];
|
|---|
| 1277 | gl = d[1];
|
|---|
| 1278 | tmp1 = 0;
|
|---|
| 1279 | for(j=1; j<=n-1; j++)
|
|---|
| 1280 | {
|
|---|
| 1281 | tmp2 = Math.Sqrt(work[j]);
|
|---|
| 1282 | gu = Math.Max(gu, d[j]+tmp1+tmp2);
|
|---|
| 1283 | gl = Math.Min(gl, d[j]-tmp1-tmp2);
|
|---|
| 1284 | tmp1 = tmp2;
|
|---|
| 1285 | }
|
|---|
| 1286 | gu = Math.Max(gu, d[n]+tmp1);
|
|---|
| 1287 | gl = Math.Min(gl, d[n]-tmp1);
|
|---|
| 1288 | tnorm = Math.Max(Math.Abs(gl), Math.Abs(gu));
|
|---|
| 1289 | gl = gl-fudge*tnorm*ulp*n-fudge*2*pivmin;
|
|---|
| 1290 | gu = gu+fudge*tnorm*ulp*n+fudge*pivmin;
|
|---|
| 1291 |
|
|---|
| 1292 | //
|
|---|
| 1293 | // Compute Iteration parameters
|
|---|
| 1294 | //
|
|---|
| 1295 | itmax = (int)Math.Ceiling((Math.Log(tnorm+pivmin)-Math.Log(pivmin))/Math.Log(2))+2;
|
|---|
| 1296 | if( (double)(abstol)<=(double)(0) )
|
|---|
| 1297 | {
|
|---|
| 1298 | atoli = ulp*tnorm;
|
|---|
| 1299 | }
|
|---|
| 1300 | else
|
|---|
| 1301 | {
|
|---|
| 1302 | atoli = abstol;
|
|---|
| 1303 | }
|
|---|
| 1304 | work[n+1] = gl;
|
|---|
| 1305 | work[n+2] = gl;
|
|---|
| 1306 | work[n+3] = gu;
|
|---|
| 1307 | work[n+4] = gu;
|
|---|
| 1308 | work[n+5] = gl;
|
|---|
| 1309 | work[n+6] = gu;
|
|---|
| 1310 | iwork[1] = -1;
|
|---|
| 1311 | iwork[2] = -1;
|
|---|
| 1312 | iwork[3] = n+1;
|
|---|
| 1313 | iwork[4] = n+1;
|
|---|
| 1314 | iwork[5] = il-1;
|
|---|
| 1315 | iwork[6] = iu;
|
|---|
| 1316 |
|
|---|
| 1317 | //
|
|---|
| 1318 | // Calling DLAEBZ
|
|---|
| 1319 | //
|
|---|
| 1320 | // DLAEBZ( 3, ITMAX, N, 2, 2, NB, ATOLI, RTOLI, PIVMIN, D, E,
|
|---|
| 1321 | // WORK, IWORK( 5 ), WORK( N+1 ), WORK( N+5 ), IOUT,
|
|---|
| 1322 | // IWORK, W, IBLOCK, IINFO )
|
|---|
| 1323 | //
|
|---|
| 1324 | ia1s2[1] = iwork[5];
|
|---|
| 1325 | ia1s2[2] = iwork[6];
|
|---|
| 1326 | ra1s2[1] = work[n+5];
|
|---|
| 1327 | ra1s2[2] = work[n+6];
|
|---|
| 1328 | ra1s2x2[1,1] = work[n+1];
|
|---|
| 1329 | ra1s2x2[2,1] = work[n+2];
|
|---|
| 1330 | ra1s2x2[1,2] = work[n+3];
|
|---|
| 1331 | ra1s2x2[2,2] = work[n+4];
|
|---|
| 1332 | ia1s2x2[1,1] = iwork[1];
|
|---|
| 1333 | ia1s2x2[2,1] = iwork[2];
|
|---|
| 1334 | ia1s2x2[1,2] = iwork[3];
|
|---|
| 1335 | ia1s2x2[2,2] = iwork[4];
|
|---|
| 1336 | internaldlaebz(3, itmax, n, 2, 2, atoli, rtoli, pivmin, ref d, ref e, ref work, ref ia1s2, ref ra1s2x2, ref ra1s2, ref iout, ref ia1s2x2, ref w, ref iblock, ref iinfo);
|
|---|
| 1337 | iwork[5] = ia1s2[1];
|
|---|
| 1338 | iwork[6] = ia1s2[2];
|
|---|
| 1339 | work[n+5] = ra1s2[1];
|
|---|
| 1340 | work[n+6] = ra1s2[2];
|
|---|
| 1341 | work[n+1] = ra1s2x2[1,1];
|
|---|
| 1342 | work[n+2] = ra1s2x2[2,1];
|
|---|
| 1343 | work[n+3] = ra1s2x2[1,2];
|
|---|
| 1344 | work[n+4] = ra1s2x2[2,2];
|
|---|
| 1345 | iwork[1] = ia1s2x2[1,1];
|
|---|
| 1346 | iwork[2] = ia1s2x2[2,1];
|
|---|
| 1347 | iwork[3] = ia1s2x2[1,2];
|
|---|
| 1348 | iwork[4] = ia1s2x2[2,2];
|
|---|
| 1349 | if( iwork[6]==iu )
|
|---|
| 1350 | {
|
|---|
| 1351 | wl = work[n+1];
|
|---|
| 1352 | wlu = work[n+3];
|
|---|
| 1353 | nwl = iwork[1];
|
|---|
| 1354 | wu = work[n+4];
|
|---|
| 1355 | wul = work[n+2];
|
|---|
| 1356 | nwu = iwork[4];
|
|---|
| 1357 | }
|
|---|
| 1358 | else
|
|---|
| 1359 | {
|
|---|
| 1360 | wl = work[n+2];
|
|---|
| 1361 | wlu = work[n+4];
|
|---|
| 1362 | nwl = iwork[2];
|
|---|
| 1363 | wu = work[n+3];
|
|---|
| 1364 | wul = work[n+1];
|
|---|
| 1365 | nwu = iwork[3];
|
|---|
| 1366 | }
|
|---|
| 1367 | if( nwl<0 | nwl>=n | nwu<1 | nwu>n )
|
|---|
| 1368 | {
|
|---|
| 1369 | errorcode = 4;
|
|---|
| 1370 | result = false;
|
|---|
| 1371 | return result;
|
|---|
| 1372 | }
|
|---|
| 1373 | }
|
|---|
| 1374 | else
|
|---|
| 1375 | {
|
|---|
| 1376 |
|
|---|
| 1377 | //
|
|---|
| 1378 | // RANGE='A' or 'V' -- Set ATOLI
|
|---|
| 1379 | //
|
|---|
| 1380 | tnorm = Math.Max(Math.Abs(d[1])+Math.Abs(e[1]), Math.Abs(d[n])+Math.Abs(e[n-1]));
|
|---|
| 1381 | for(j=2; j<=n-1; j++)
|
|---|
| 1382 | {
|
|---|
| 1383 | tnorm = Math.Max(tnorm, Math.Abs(d[j])+Math.Abs(e[j-1])+Math.Abs(e[j]));
|
|---|
| 1384 | }
|
|---|
| 1385 | if( (double)(abstol)<=(double)(0) )
|
|---|
| 1386 | {
|
|---|
| 1387 | atoli = ulp*tnorm;
|
|---|
| 1388 | }
|
|---|
| 1389 | else
|
|---|
| 1390 | {
|
|---|
| 1391 | atoli = abstol;
|
|---|
| 1392 | }
|
|---|
| 1393 | if( irange==2 )
|
|---|
| 1394 | {
|
|---|
| 1395 | wl = vl;
|
|---|
| 1396 | wu = vu;
|
|---|
| 1397 | }
|
|---|
| 1398 | else
|
|---|
| 1399 | {
|
|---|
| 1400 | wl = 0;
|
|---|
| 1401 | wu = 0;
|
|---|
| 1402 | }
|
|---|
| 1403 | }
|
|---|
| 1404 |
|
|---|
| 1405 | //
|
|---|
| 1406 | // Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU.
|
|---|
| 1407 | // NWL accumulates the number of eigenvalues .le. WL,
|
|---|
| 1408 | // NWU accumulates the number of eigenvalues .le. WU
|
|---|
| 1409 | //
|
|---|
| 1410 | m = 0;
|
|---|
| 1411 | iend = 0;
|
|---|
| 1412 | errorcode = 0;
|
|---|
| 1413 | nwl = 0;
|
|---|
| 1414 | nwu = 0;
|
|---|
| 1415 | for(jb=1; jb<=nsplit; jb++)
|
|---|
| 1416 | {
|
|---|
| 1417 | ioff = iend;
|
|---|
| 1418 | ibegin = ioff+1;
|
|---|
| 1419 | iend = isplit[jb];
|
|---|
| 1420 | iin = iend-ioff;
|
|---|
| 1421 | if( iin==1 )
|
|---|
| 1422 | {
|
|---|
| 1423 |
|
|---|
| 1424 | //
|
|---|
| 1425 | // Special Case -- IIN=1
|
|---|
| 1426 | //
|
|---|
| 1427 | if( irange==1 | (double)(wl)>=(double)(d[ibegin]-pivmin) )
|
|---|
| 1428 | {
|
|---|
| 1429 | nwl = nwl+1;
|
|---|
| 1430 | }
|
|---|
| 1431 | if( irange==1 | (double)(wu)>=(double)(d[ibegin]-pivmin) )
|
|---|
| 1432 | {
|
|---|
| 1433 | nwu = nwu+1;
|
|---|
| 1434 | }
|
|---|
| 1435 | if( irange==1 | (double)(wl)<(double)(d[ibegin]-pivmin) & (double)(wu)>=(double)(d[ibegin]-pivmin) )
|
|---|
| 1436 | {
|
|---|
| 1437 | m = m+1;
|
|---|
| 1438 | w[m] = d[ibegin];
|
|---|
| 1439 | iblock[m] = jb;
|
|---|
| 1440 | }
|
|---|
| 1441 | }
|
|---|
| 1442 | else
|
|---|
| 1443 | {
|
|---|
| 1444 |
|
|---|
| 1445 | //
|
|---|
| 1446 | // General Case -- IIN > 1
|
|---|
| 1447 | //
|
|---|
| 1448 | // Compute Gershgorin Interval
|
|---|
| 1449 | // and use it as the initial interval
|
|---|
| 1450 | //
|
|---|
| 1451 | gu = d[ibegin];
|
|---|
| 1452 | gl = d[ibegin];
|
|---|
| 1453 | tmp1 = 0;
|
|---|
| 1454 | for(j=ibegin; j<=iend-1; j++)
|
|---|
| 1455 | {
|
|---|
| 1456 | tmp2 = Math.Abs(e[j]);
|
|---|
| 1457 | gu = Math.Max(gu, d[j]+tmp1+tmp2);
|
|---|
| 1458 | gl = Math.Min(gl, d[j]-tmp1-tmp2);
|
|---|
| 1459 | tmp1 = tmp2;
|
|---|
| 1460 | }
|
|---|
| 1461 | gu = Math.Max(gu, d[iend]+tmp1);
|
|---|
| 1462 | gl = Math.Min(gl, d[iend]-tmp1);
|
|---|
| 1463 | bnorm = Math.Max(Math.Abs(gl), Math.Abs(gu));
|
|---|
| 1464 | gl = gl-fudge*bnorm*ulp*iin-fudge*pivmin;
|
|---|
| 1465 | gu = gu+fudge*bnorm*ulp*iin+fudge*pivmin;
|
|---|
| 1466 |
|
|---|
| 1467 | //
|
|---|
| 1468 | // Compute ATOLI for the current submatrix
|
|---|
| 1469 | //
|
|---|
| 1470 | if( (double)(abstol)<=(double)(0) )
|
|---|
| 1471 | {
|
|---|
| 1472 | atoli = ulp*Math.Max(Math.Abs(gl), Math.Abs(gu));
|
|---|
| 1473 | }
|
|---|
| 1474 | else
|
|---|
| 1475 | {
|
|---|
| 1476 | atoli = abstol;
|
|---|
| 1477 | }
|
|---|
| 1478 | if( irange>1 )
|
|---|
| 1479 | {
|
|---|
| 1480 | if( (double)(gu)<(double)(wl) )
|
|---|
| 1481 | {
|
|---|
| 1482 | nwl = nwl+iin;
|
|---|
| 1483 | nwu = nwu+iin;
|
|---|
| 1484 | continue;
|
|---|
| 1485 | }
|
|---|
| 1486 | gl = Math.Max(gl, wl);
|
|---|
| 1487 | gu = Math.Min(gu, wu);
|
|---|
| 1488 | if( (double)(gl)>=(double)(gu) )
|
|---|
| 1489 | {
|
|---|
| 1490 | continue;
|
|---|
| 1491 | }
|
|---|
| 1492 | }
|
|---|
| 1493 |
|
|---|
| 1494 | //
|
|---|
| 1495 | // Set Up Initial Interval
|
|---|
| 1496 | //
|
|---|
| 1497 | work[n+1] = gl;
|
|---|
| 1498 | work[n+iin+1] = gu;
|
|---|
| 1499 |
|
|---|
| 1500 | //
|
|---|
| 1501 | // Calling DLAEBZ
|
|---|
| 1502 | //
|
|---|
| 1503 | // CALL DLAEBZ( 1, 0, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN,
|
|---|
| 1504 | // D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ),
|
|---|
| 1505 | // IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IM,
|
|---|
| 1506 | // IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
|
|---|
| 1507 | //
|
|---|
| 1508 | for(tmpi=1; tmpi<=iin; tmpi++)
|
|---|
| 1509 | {
|
|---|
| 1510 | ra1siin[tmpi] = d[ibegin-1+tmpi];
|
|---|
| 1511 | if( ibegin-1+tmpi<n )
|
|---|
| 1512 | {
|
|---|
| 1513 | ra2siin[tmpi] = e[ibegin-1+tmpi];
|
|---|
| 1514 | }
|
|---|
| 1515 | ra3siin[tmpi] = work[ibegin-1+tmpi];
|
|---|
| 1516 | ra1siinx2[tmpi,1] = work[n+tmpi];
|
|---|
| 1517 | ra1siinx2[tmpi,2] = work[n+tmpi+iin];
|
|---|
| 1518 | ra4siin[tmpi] = work[n+2*iin+tmpi];
|
|---|
| 1519 | rworkspace[tmpi] = w[m+tmpi];
|
|---|
| 1520 | iworkspace[tmpi] = iblock[m+tmpi];
|
|---|
| 1521 | ia1siinx2[tmpi,1] = iwork[tmpi];
|
|---|
| 1522 | ia1siinx2[tmpi,2] = iwork[tmpi+iin];
|
|---|
| 1523 | }
|
|---|
| 1524 | internaldlaebz(1, 0, iin, iin, 1, atoli, rtoli, pivmin, ref ra1siin, ref ra2siin, ref ra3siin, ref idumma, ref ra1siinx2, ref ra4siin, ref im, ref ia1siinx2, ref rworkspace, ref iworkspace, ref iinfo);
|
|---|
| 1525 | for(tmpi=1; tmpi<=iin; tmpi++)
|
|---|
| 1526 | {
|
|---|
| 1527 | work[n+tmpi] = ra1siinx2[tmpi,1];
|
|---|
| 1528 | work[n+tmpi+iin] = ra1siinx2[tmpi,2];
|
|---|
| 1529 | work[n+2*iin+tmpi] = ra4siin[tmpi];
|
|---|
| 1530 | w[m+tmpi] = rworkspace[tmpi];
|
|---|
| 1531 | iblock[m+tmpi] = iworkspace[tmpi];
|
|---|
| 1532 | iwork[tmpi] = ia1siinx2[tmpi,1];
|
|---|
| 1533 | iwork[tmpi+iin] = ia1siinx2[tmpi,2];
|
|---|
| 1534 | }
|
|---|
| 1535 | nwl = nwl+iwork[1];
|
|---|
| 1536 | nwu = nwu+iwork[iin+1];
|
|---|
| 1537 | iwoff = m-iwork[1];
|
|---|
| 1538 |
|
|---|
| 1539 | //
|
|---|
| 1540 | // Compute Eigenvalues
|
|---|
| 1541 | //
|
|---|
| 1542 | itmax = (int)Math.Ceiling((Math.Log(gu-gl+pivmin)-Math.Log(pivmin))/Math.Log(2))+2;
|
|---|
| 1543 |
|
|---|
| 1544 | //
|
|---|
| 1545 | // Calling DLAEBZ
|
|---|
| 1546 | //
|
|---|
| 1547 | //CALL DLAEBZ( 2, ITMAX, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN,
|
|---|
| 1548 | // D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ),
|
|---|
| 1549 | // IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IOUT,
|
|---|
| 1550 | // IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
|
|---|
| 1551 | //
|
|---|
| 1552 | for(tmpi=1; tmpi<=iin; tmpi++)
|
|---|
| 1553 | {
|
|---|
| 1554 | ra1siin[tmpi] = d[ibegin-1+tmpi];
|
|---|
| 1555 | if( ibegin-1+tmpi<n )
|
|---|
| 1556 | {
|
|---|
| 1557 | ra2siin[tmpi] = e[ibegin-1+tmpi];
|
|---|
| 1558 | }
|
|---|
| 1559 | ra3siin[tmpi] = work[ibegin-1+tmpi];
|
|---|
| 1560 | ra1siinx2[tmpi,1] = work[n+tmpi];
|
|---|
| 1561 | ra1siinx2[tmpi,2] = work[n+tmpi+iin];
|
|---|
| 1562 | ra4siin[tmpi] = work[n+2*iin+tmpi];
|
|---|
| 1563 | rworkspace[tmpi] = w[m+tmpi];
|
|---|
| 1564 | iworkspace[tmpi] = iblock[m+tmpi];
|
|---|
| 1565 | ia1siinx2[tmpi,1] = iwork[tmpi];
|
|---|
| 1566 | ia1siinx2[tmpi,2] = iwork[tmpi+iin];
|
|---|
| 1567 | }
|
|---|
| 1568 | internaldlaebz(2, itmax, iin, iin, 1, atoli, rtoli, pivmin, ref ra1siin, ref ra2siin, ref ra3siin, ref idumma, ref ra1siinx2, ref ra4siin, ref iout, ref ia1siinx2, ref rworkspace, ref iworkspace, ref iinfo);
|
|---|
| 1569 | for(tmpi=1; tmpi<=iin; tmpi++)
|
|---|
| 1570 | {
|
|---|
| 1571 | work[n+tmpi] = ra1siinx2[tmpi,1];
|
|---|
| 1572 | work[n+tmpi+iin] = ra1siinx2[tmpi,2];
|
|---|
| 1573 | work[n+2*iin+tmpi] = ra4siin[tmpi];
|
|---|
| 1574 | w[m+tmpi] = rworkspace[tmpi];
|
|---|
| 1575 | iblock[m+tmpi] = iworkspace[tmpi];
|
|---|
| 1576 | iwork[tmpi] = ia1siinx2[tmpi,1];
|
|---|
| 1577 | iwork[tmpi+iin] = ia1siinx2[tmpi,2];
|
|---|
| 1578 | }
|
|---|
| 1579 |
|
|---|
| 1580 | //
|
|---|
| 1581 | // Copy Eigenvalues Into W and IBLOCK
|
|---|
| 1582 | // Use -JB for block number for unconverged eigenvalues.
|
|---|
| 1583 | //
|
|---|
| 1584 | for(j=1; j<=iout; j++)
|
|---|
| 1585 | {
|
|---|
| 1586 | tmp1 = 0.5*(work[j+n]+work[j+iin+n]);
|
|---|
| 1587 |
|
|---|
| 1588 | //
|
|---|
| 1589 | // Flag non-convergence.
|
|---|
| 1590 | //
|
|---|
| 1591 | if( j>iout-iinfo )
|
|---|
| 1592 | {
|
|---|
| 1593 | ncnvrg = true;
|
|---|
| 1594 | ib = -jb;
|
|---|
| 1595 | }
|
|---|
| 1596 | else
|
|---|
| 1597 | {
|
|---|
| 1598 | ib = jb;
|
|---|
| 1599 | }
|
|---|
| 1600 | for(je=iwork[j]+1+iwoff; je<=iwork[j+iin]+iwoff; je++)
|
|---|
| 1601 | {
|
|---|
| 1602 | w[je] = tmp1;
|
|---|
| 1603 | iblock[je] = ib;
|
|---|
| 1604 | }
|
|---|
| 1605 | }
|
|---|
| 1606 | m = m+im;
|
|---|
| 1607 | }
|
|---|
| 1608 | }
|
|---|
| 1609 |
|
|---|
| 1610 | //
|
|---|
| 1611 | // If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU
|
|---|
| 1612 | // If NWL+1 < IL or NWU > IU, discard extra eigenvalues.
|
|---|
| 1613 | //
|
|---|
| 1614 | if( irange==3 )
|
|---|
| 1615 | {
|
|---|
| 1616 | im = 0;
|
|---|
| 1617 | idiscl = il-1-nwl;
|
|---|
| 1618 | idiscu = nwu-iu;
|
|---|
| 1619 | if( idiscl>0 | idiscu>0 )
|
|---|
| 1620 | {
|
|---|
| 1621 | for(je=1; je<=m; je++)
|
|---|
| 1622 | {
|
|---|
| 1623 | if( (double)(w[je])<=(double)(wlu) & idiscl>0 )
|
|---|
| 1624 | {
|
|---|
| 1625 | idiscl = idiscl-1;
|
|---|
| 1626 | }
|
|---|
| 1627 | else
|
|---|
| 1628 | {
|
|---|
| 1629 | if( (double)(w[je])>=(double)(wul) & idiscu>0 )
|
|---|
| 1630 | {
|
|---|
| 1631 | idiscu = idiscu-1;
|
|---|
| 1632 | }
|
|---|
| 1633 | else
|
|---|
| 1634 | {
|
|---|
| 1635 | im = im+1;
|
|---|
| 1636 | w[im] = w[je];
|
|---|
| 1637 | iblock[im] = iblock[je];
|
|---|
| 1638 | }
|
|---|
| 1639 | }
|
|---|
| 1640 | }
|
|---|
| 1641 | m = im;
|
|---|
| 1642 | }
|
|---|
| 1643 | if( idiscl>0 | idiscu>0 )
|
|---|
| 1644 | {
|
|---|
| 1645 |
|
|---|
| 1646 | //
|
|---|
| 1647 | // Code to deal with effects of bad arithmetic:
|
|---|
| 1648 | // Some low eigenvalues to be discarded are not in (WL,WLU],
|
|---|
| 1649 | // or high eigenvalues to be discarded are not in (WUL,WU]
|
|---|
| 1650 | // so just kill off the smallest IDISCL/largest IDISCU
|
|---|
| 1651 | // eigenvalues, by simply finding the smallest/largest
|
|---|
| 1652 | // eigenvalue(s).
|
|---|
| 1653 | //
|
|---|
| 1654 | // (If N(w) is monotone non-decreasing, this should never
|
|---|
| 1655 | // happen.)
|
|---|
| 1656 | //
|
|---|
| 1657 | if( idiscl>0 )
|
|---|
| 1658 | {
|
|---|
| 1659 | wkill = wu;
|
|---|
| 1660 | for(jdisc=1; jdisc<=idiscl; jdisc++)
|
|---|
| 1661 | {
|
|---|
| 1662 | iw = 0;
|
|---|
| 1663 | for(je=1; je<=m; je++)
|
|---|
| 1664 | {
|
|---|
| 1665 | if( iblock[je]!=0 & ((double)(w[je])<(double)(wkill) | iw==0) )
|
|---|
| 1666 | {
|
|---|
| 1667 | iw = je;
|
|---|
| 1668 | wkill = w[je];
|
|---|
| 1669 | }
|
|---|
| 1670 | }
|
|---|
| 1671 | iblock[iw] = 0;
|
|---|
| 1672 | }
|
|---|
| 1673 | }
|
|---|
| 1674 | if( idiscu>0 )
|
|---|
| 1675 | {
|
|---|
| 1676 | wkill = wl;
|
|---|
| 1677 | for(jdisc=1; jdisc<=idiscu; jdisc++)
|
|---|
| 1678 | {
|
|---|
| 1679 | iw = 0;
|
|---|
| 1680 | for(je=1; je<=m; je++)
|
|---|
| 1681 | {
|
|---|
| 1682 | if( iblock[je]!=0 & ((double)(w[je])>(double)(wkill) | iw==0) )
|
|---|
| 1683 | {
|
|---|
| 1684 | iw = je;
|
|---|
| 1685 | wkill = w[je];
|
|---|
| 1686 | }
|
|---|
| 1687 | }
|
|---|
| 1688 | iblock[iw] = 0;
|
|---|
| 1689 | }
|
|---|
| 1690 | }
|
|---|
| 1691 | im = 0;
|
|---|
| 1692 | for(je=1; je<=m; je++)
|
|---|
| 1693 | {
|
|---|
| 1694 | if( iblock[je]!=0 )
|
|---|
| 1695 | {
|
|---|
| 1696 | im = im+1;
|
|---|
| 1697 | w[im] = w[je];
|
|---|
| 1698 | iblock[im] = iblock[je];
|
|---|
| 1699 | }
|
|---|
| 1700 | }
|
|---|
| 1701 | m = im;
|
|---|
| 1702 | }
|
|---|
| 1703 | if( idiscl<0 | idiscu<0 )
|
|---|
| 1704 | {
|
|---|
| 1705 | toofew = true;
|
|---|
| 1706 | }
|
|---|
| 1707 | }
|
|---|
| 1708 |
|
|---|
| 1709 | //
|
|---|
| 1710 | // If ORDER='B', do nothing -- the eigenvalues are already sorted
|
|---|
| 1711 | // by block.
|
|---|
| 1712 | // If ORDER='E', sort the eigenvalues from smallest to largest
|
|---|
| 1713 | //
|
|---|
| 1714 | if( iorder==1 & nsplit>1 )
|
|---|
| 1715 | {
|
|---|
| 1716 | for(je=1; je<=m-1; je++)
|
|---|
| 1717 | {
|
|---|
| 1718 | ie = 0;
|
|---|
| 1719 | tmp1 = w[je];
|
|---|
| 1720 | for(j=je+1; j<=m; j++)
|
|---|
| 1721 | {
|
|---|
| 1722 | if( (double)(w[j])<(double)(tmp1) )
|
|---|
| 1723 | {
|
|---|
| 1724 | ie = j;
|
|---|
| 1725 | tmp1 = w[j];
|
|---|
| 1726 | }
|
|---|
| 1727 | }
|
|---|
| 1728 | if( ie!=0 )
|
|---|
| 1729 | {
|
|---|
| 1730 | itmp1 = iblock[ie];
|
|---|
| 1731 | w[ie] = w[je];
|
|---|
| 1732 | iblock[ie] = iblock[je];
|
|---|
| 1733 | w[je] = tmp1;
|
|---|
| 1734 | iblock[je] = itmp1;
|
|---|
| 1735 | }
|
|---|
| 1736 | }
|
|---|
| 1737 | }
|
|---|
| 1738 | for(j=1; j<=m; j++)
|
|---|
| 1739 | {
|
|---|
| 1740 | w[j] = w[j]*scalefactor;
|
|---|
| 1741 | }
|
|---|
| 1742 | errorcode = 0;
|
|---|
| 1743 | if( ncnvrg )
|
|---|
| 1744 | {
|
|---|
| 1745 | errorcode = errorcode+1;
|
|---|
| 1746 | }
|
|---|
| 1747 | if( toofew )
|
|---|
| 1748 | {
|
|---|
| 1749 | errorcode = errorcode+2;
|
|---|
| 1750 | }
|
|---|
| 1751 | result = errorcode==0;
|
|---|
| 1752 | return result;
|
|---|
| 1753 | }
|
|---|
| 1754 |
|
|---|
| 1755 |
|
|---|
| 1756 | public static void internaldstein(int n,
|
|---|
| 1757 | ref double[] d,
|
|---|
| 1758 | double[] e,
|
|---|
| 1759 | int m,
|
|---|
| 1760 | double[] w,
|
|---|
| 1761 | ref int[] iblock,
|
|---|
| 1762 | ref int[] isplit,
|
|---|
| 1763 | ref double[,] z,
|
|---|
| 1764 | ref int[] ifail,
|
|---|
| 1765 | ref int info)
|
|---|
| 1766 | {
|
|---|
| 1767 | int maxits = 0;
|
|---|
| 1768 | int extra = 0;
|
|---|
| 1769 | int b1 = 0;
|
|---|
| 1770 | int blksiz = 0;
|
|---|
| 1771 | int bn = 0;
|
|---|
| 1772 | int gpind = 0;
|
|---|
| 1773 | int i = 0;
|
|---|
| 1774 | int iinfo = 0;
|
|---|
| 1775 | int its = 0;
|
|---|
| 1776 | int j = 0;
|
|---|
| 1777 | int j1 = 0;
|
|---|
| 1778 | int jblk = 0;
|
|---|
| 1779 | int jmax = 0;
|
|---|
| 1780 | int nblk = 0;
|
|---|
| 1781 | int nrmchk = 0;
|
|---|
| 1782 | double dtpcrt = 0;
|
|---|
| 1783 | double eps = 0;
|
|---|
| 1784 | double eps1 = 0;
|
|---|
| 1785 | double nrm = 0;
|
|---|
| 1786 | double onenrm = 0;
|
|---|
| 1787 | double ortol = 0;
|
|---|
| 1788 | double pertol = 0;
|
|---|
| 1789 | double scl = 0;
|
|---|
| 1790 | double sep = 0;
|
|---|
| 1791 | double tol = 0;
|
|---|
| 1792 | double xj = 0;
|
|---|
| 1793 | double xjm = 0;
|
|---|
| 1794 | double ztr = 0;
|
|---|
| 1795 | double[] work1 = new double[0];
|
|---|
| 1796 | double[] work2 = new double[0];
|
|---|
| 1797 | double[] work3 = new double[0];
|
|---|
| 1798 | double[] work4 = new double[0];
|
|---|
| 1799 | double[] work5 = new double[0];
|
|---|
| 1800 | int[] iwork = new int[0];
|
|---|
| 1801 | bool tmpcriterion = new bool();
|
|---|
| 1802 | int ti = 0;
|
|---|
| 1803 | int i1 = 0;
|
|---|
| 1804 | int i2 = 0;
|
|---|
| 1805 | double v = 0;
|
|---|
| 1806 | int i_ = 0;
|
|---|
| 1807 | int i1_ = 0;
|
|---|
| 1808 |
|
|---|
| 1809 | e = (double[])e.Clone();
|
|---|
| 1810 | w = (double[])w.Clone();
|
|---|
| 1811 |
|
|---|
| 1812 | maxits = 5;
|
|---|
| 1813 | extra = 2;
|
|---|
| 1814 | work1 = new double[Math.Max(n, 1)+1];
|
|---|
| 1815 | work2 = new double[Math.Max(n-1, 1)+1];
|
|---|
| 1816 | work3 = new double[Math.Max(n, 1)+1];
|
|---|
| 1817 | work4 = new double[Math.Max(n, 1)+1];
|
|---|
| 1818 | work5 = new double[Math.Max(n, 1)+1];
|
|---|
| 1819 | iwork = new int[Math.Max(n, 1)+1];
|
|---|
| 1820 | ifail = new int[Math.Max(m, 1)+1];
|
|---|
| 1821 | z = new double[Math.Max(n, 1)+1, Math.Max(m, 1)+1];
|
|---|
| 1822 |
|
|---|
| 1823 | //
|
|---|
| 1824 | // Test the input parameters.
|
|---|
| 1825 | //
|
|---|
| 1826 | info = 0;
|
|---|
| 1827 | for(i=1; i<=m; i++)
|
|---|
| 1828 | {
|
|---|
| 1829 | ifail[i] = 0;
|
|---|
| 1830 | }
|
|---|
| 1831 | if( n<0 )
|
|---|
| 1832 | {
|
|---|
| 1833 | info = -1;
|
|---|
| 1834 | return;
|
|---|
| 1835 | }
|
|---|
| 1836 | if( m<0 | m>n )
|
|---|
| 1837 | {
|
|---|
| 1838 | info = -4;
|
|---|
| 1839 | return;
|
|---|
| 1840 | }
|
|---|
| 1841 | for(j=2; j<=m; j++)
|
|---|
| 1842 | {
|
|---|
| 1843 | if( iblock[j]<iblock[j-1] )
|
|---|
| 1844 | {
|
|---|
| 1845 | info = -6;
|
|---|
| 1846 | break;
|
|---|
| 1847 | }
|
|---|
| 1848 | if( iblock[j]==iblock[j-1] & (double)(w[j])<(double)(w[j-1]) )
|
|---|
| 1849 | {
|
|---|
| 1850 | info = -5;
|
|---|
| 1851 | break;
|
|---|
| 1852 | }
|
|---|
| 1853 | }
|
|---|
| 1854 | if( info!=0 )
|
|---|
| 1855 | {
|
|---|
| 1856 | return;
|
|---|
| 1857 | }
|
|---|
| 1858 |
|
|---|
| 1859 | //
|
|---|
| 1860 | // Quick return if possible
|
|---|
| 1861 | //
|
|---|
| 1862 | if( n==0 | m==0 )
|
|---|
| 1863 | {
|
|---|
| 1864 | return;
|
|---|
| 1865 | }
|
|---|
| 1866 | if( n==1 )
|
|---|
| 1867 | {
|
|---|
| 1868 | z[1,1] = 1;
|
|---|
| 1869 | return;
|
|---|
| 1870 | }
|
|---|
| 1871 |
|
|---|
| 1872 | //
|
|---|
| 1873 | // Some preparations
|
|---|
| 1874 | //
|
|---|
| 1875 | ti = n-1;
|
|---|
| 1876 | for(i_=1; i_<=ti;i_++)
|
|---|
| 1877 | {
|
|---|
| 1878 | work1[i_] = e[i_];
|
|---|
| 1879 | }
|
|---|
| 1880 | e = new double[n+1];
|
|---|
| 1881 | for(i_=1; i_<=ti;i_++)
|
|---|
| 1882 | {
|
|---|
| 1883 | e[i_] = work1[i_];
|
|---|
| 1884 | }
|
|---|
| 1885 | for(i_=1; i_<=m;i_++)
|
|---|
| 1886 | {
|
|---|
| 1887 | work1[i_] = w[i_];
|
|---|
| 1888 | }
|
|---|
| 1889 | w = new double[n+1];
|
|---|
| 1890 | for(i_=1; i_<=m;i_++)
|
|---|
| 1891 | {
|
|---|
| 1892 | w[i_] = work1[i_];
|
|---|
| 1893 | }
|
|---|
| 1894 |
|
|---|
| 1895 | //
|
|---|
| 1896 | // Get machine constants.
|
|---|
| 1897 | //
|
|---|
| 1898 | eps = AP.Math.MachineEpsilon;
|
|---|
| 1899 |
|
|---|
| 1900 | //
|
|---|
| 1901 | // Compute eigenvectors of matrix blocks.
|
|---|
| 1902 | //
|
|---|
| 1903 | j1 = 1;
|
|---|
| 1904 | for(nblk=1; nblk<=iblock[m]; nblk++)
|
|---|
| 1905 | {
|
|---|
| 1906 |
|
|---|
| 1907 | //
|
|---|
| 1908 | // Find starting and ending indices of block nblk.
|
|---|
| 1909 | //
|
|---|
| 1910 | if( nblk==1 )
|
|---|
| 1911 | {
|
|---|
| 1912 | b1 = 1;
|
|---|
| 1913 | }
|
|---|
| 1914 | else
|
|---|
| 1915 | {
|
|---|
| 1916 | b1 = isplit[nblk-1]+1;
|
|---|
| 1917 | }
|
|---|
| 1918 | bn = isplit[nblk];
|
|---|
| 1919 | blksiz = bn-b1+1;
|
|---|
| 1920 | if( blksiz!=1 )
|
|---|
| 1921 | {
|
|---|
| 1922 |
|
|---|
| 1923 | //
|
|---|
| 1924 | // Compute reorthogonalization criterion and stopping criterion.
|
|---|
| 1925 | //
|
|---|
| 1926 | gpind = b1;
|
|---|
| 1927 | onenrm = Math.Abs(d[b1])+Math.Abs(e[b1]);
|
|---|
| 1928 | onenrm = Math.Max(onenrm, Math.Abs(d[bn])+Math.Abs(e[bn-1]));
|
|---|
| 1929 | for(i=b1+1; i<=bn-1; i++)
|
|---|
| 1930 | {
|
|---|
| 1931 | onenrm = Math.Max(onenrm, Math.Abs(d[i])+Math.Abs(e[i-1])+Math.Abs(e[i]));
|
|---|
| 1932 | }
|
|---|
| 1933 | ortol = 0.001*onenrm;
|
|---|
| 1934 | dtpcrt = Math.Sqrt(0.1/blksiz);
|
|---|
| 1935 | }
|
|---|
| 1936 |
|
|---|
| 1937 | //
|
|---|
| 1938 | // Loop through eigenvalues of block nblk.
|
|---|
| 1939 | //
|
|---|
| 1940 | jblk = 0;
|
|---|
| 1941 | for(j=j1; j<=m; j++)
|
|---|
| 1942 | {
|
|---|
| 1943 | if( iblock[j]!=nblk )
|
|---|
| 1944 | {
|
|---|
| 1945 | j1 = j;
|
|---|
| 1946 | break;
|
|---|
| 1947 | }
|
|---|
| 1948 | jblk = jblk+1;
|
|---|
| 1949 | xj = w[j];
|
|---|
| 1950 | if( blksiz==1 )
|
|---|
| 1951 | {
|
|---|
| 1952 |
|
|---|
| 1953 | //
|
|---|
| 1954 | // Skip all the work if the block size is one.
|
|---|
| 1955 | //
|
|---|
| 1956 | work1[1] = 1;
|
|---|
| 1957 | }
|
|---|
| 1958 | else
|
|---|
| 1959 | {
|
|---|
| 1960 |
|
|---|
| 1961 | //
|
|---|
| 1962 | // If eigenvalues j and j-1 are too close, add a relatively
|
|---|
| 1963 | // small perturbation.
|
|---|
| 1964 | //
|
|---|
| 1965 | if( jblk>1 )
|
|---|
| 1966 | {
|
|---|
| 1967 | eps1 = Math.Abs(eps*xj);
|
|---|
| 1968 | pertol = 10*eps1;
|
|---|
| 1969 | sep = xj-xjm;
|
|---|
| 1970 | if( (double)(sep)<(double)(pertol) )
|
|---|
| 1971 | {
|
|---|
| 1972 | xj = xjm+pertol;
|
|---|
| 1973 | }
|
|---|
| 1974 | }
|
|---|
| 1975 | its = 0;
|
|---|
| 1976 | nrmchk = 0;
|
|---|
| 1977 |
|
|---|
| 1978 | //
|
|---|
| 1979 | // Get random starting vector.
|
|---|
| 1980 | //
|
|---|
| 1981 | for(ti=1; ti<=blksiz; ti++)
|
|---|
| 1982 | {
|
|---|
| 1983 | work1[ti] = 2*AP.Math.RandomReal()-1;
|
|---|
| 1984 | }
|
|---|
| 1985 |
|
|---|
| 1986 | //
|
|---|
| 1987 | // Copy the matrix T so it won't be destroyed in factorization.
|
|---|
| 1988 | //
|
|---|
| 1989 | for(ti=1; ti<=blksiz-1; ti++)
|
|---|
| 1990 | {
|
|---|
| 1991 | work2[ti] = e[b1+ti-1];
|
|---|
| 1992 | work3[ti] = e[b1+ti-1];
|
|---|
| 1993 | work4[ti] = d[b1+ti-1];
|
|---|
| 1994 | }
|
|---|
| 1995 | work4[blksiz] = d[b1+blksiz-1];
|
|---|
| 1996 |
|
|---|
| 1997 | //
|
|---|
| 1998 | // Compute LU factors with partial pivoting ( PT = LU )
|
|---|
| 1999 | //
|
|---|
| 2000 | tol = 0;
|
|---|
| 2001 | tdininternaldlagtf(blksiz, ref work4, xj, ref work2, ref work3, tol, ref work5, ref iwork, ref iinfo);
|
|---|
| 2002 |
|
|---|
| 2003 | //
|
|---|
| 2004 | // Update iteration count.
|
|---|
| 2005 | //
|
|---|
| 2006 | do
|
|---|
| 2007 | {
|
|---|
| 2008 | its = its+1;
|
|---|
| 2009 | if( its>maxits )
|
|---|
| 2010 | {
|
|---|
| 2011 |
|
|---|
| 2012 | //
|
|---|
| 2013 | // If stopping criterion was not satisfied, update info and
|
|---|
| 2014 | // store eigenvector number in array ifail.
|
|---|
| 2015 | //
|
|---|
| 2016 | info = info+1;
|
|---|
| 2017 | ifail[info] = j;
|
|---|
| 2018 | break;
|
|---|
| 2019 | }
|
|---|
| 2020 |
|
|---|
| 2021 | //
|
|---|
| 2022 | // Normalize and scale the righthand side vector Pb.
|
|---|
| 2023 | //
|
|---|
| 2024 | v = 0;
|
|---|
| 2025 | for(ti=1; ti<=blksiz; ti++)
|
|---|
| 2026 | {
|
|---|
| 2027 | v = v+Math.Abs(work1[ti]);
|
|---|
| 2028 | }
|
|---|
| 2029 | scl = blksiz*onenrm*Math.Max(eps, Math.Abs(work4[blksiz]))/v;
|
|---|
| 2030 | for(i_=1; i_<=blksiz;i_++)
|
|---|
| 2031 | {
|
|---|
| 2032 | work1[i_] = scl*work1[i_];
|
|---|
| 2033 | }
|
|---|
| 2034 |
|
|---|
| 2035 | //
|
|---|
| 2036 | // Solve the system LU = Pb.
|
|---|
| 2037 | //
|
|---|
| 2038 | tdininternaldlagts(blksiz, ref work4, ref work2, ref work3, ref work5, ref iwork, ref work1, ref tol, ref iinfo);
|
|---|
| 2039 |
|
|---|
| 2040 | //
|
|---|
| 2041 | // Reorthogonalize by modified Gram-Schmidt if eigenvalues are
|
|---|
| 2042 | // close enough.
|
|---|
| 2043 | //
|
|---|
| 2044 | if( jblk!=1 )
|
|---|
| 2045 | {
|
|---|
| 2046 | if( (double)(Math.Abs(xj-xjm))>(double)(ortol) )
|
|---|
| 2047 | {
|
|---|
| 2048 | gpind = j;
|
|---|
| 2049 | }
|
|---|
| 2050 | if( gpind!=j )
|
|---|
| 2051 | {
|
|---|
| 2052 | for(i=gpind; i<=j-1; i++)
|
|---|
| 2053 | {
|
|---|
| 2054 | i1 = b1;
|
|---|
| 2055 | i2 = b1+blksiz-1;
|
|---|
| 2056 | i1_ = (i1)-(1);
|
|---|
| 2057 | ztr = 0.0;
|
|---|
| 2058 | for(i_=1; i_<=blksiz;i_++)
|
|---|
| 2059 | {
|
|---|
| 2060 | ztr += work1[i_]*z[i_+i1_,i];
|
|---|
| 2061 | }
|
|---|
| 2062 | i1_ = (i1) - (1);
|
|---|
| 2063 | for(i_=1; i_<=blksiz;i_++)
|
|---|
| 2064 | {
|
|---|
| 2065 | work1[i_] = work1[i_] - ztr*z[i_+i1_,i];
|
|---|
| 2066 | }
|
|---|
| 2067 | }
|
|---|
| 2068 | }
|
|---|
| 2069 | }
|
|---|
| 2070 |
|
|---|
| 2071 | //
|
|---|
| 2072 | // Check the infinity norm of the iterate.
|
|---|
| 2073 | //
|
|---|
| 2074 | jmax = blas.vectoridxabsmax(ref work1, 1, blksiz);
|
|---|
| 2075 | nrm = Math.Abs(work1[jmax]);
|
|---|
| 2076 |
|
|---|
| 2077 | //
|
|---|
| 2078 | // Continue for additional iterations after norm reaches
|
|---|
| 2079 | // stopping criterion.
|
|---|
| 2080 | //
|
|---|
| 2081 | tmpcriterion = false;
|
|---|
| 2082 | if( (double)(nrm)<(double)(dtpcrt) )
|
|---|
| 2083 | {
|
|---|
| 2084 | tmpcriterion = true;
|
|---|
| 2085 | }
|
|---|
| 2086 | else
|
|---|
| 2087 | {
|
|---|
| 2088 | nrmchk = nrmchk+1;
|
|---|
| 2089 | if( nrmchk<extra+1 )
|
|---|
| 2090 | {
|
|---|
| 2091 | tmpcriterion = true;
|
|---|
| 2092 | }
|
|---|
| 2093 | }
|
|---|
| 2094 | }
|
|---|
| 2095 | while( tmpcriterion );
|
|---|
| 2096 |
|
|---|
| 2097 | //
|
|---|
| 2098 | // Accept iterate as jth eigenvector.
|
|---|
| 2099 | //
|
|---|
| 2100 | scl = 1/blas.vectornorm2(ref work1, 1, blksiz);
|
|---|
| 2101 | jmax = blas.vectoridxabsmax(ref work1, 1, blksiz);
|
|---|
| 2102 | if( (double)(work1[jmax])<(double)(0) )
|
|---|
| 2103 | {
|
|---|
| 2104 | scl = -scl;
|
|---|
| 2105 | }
|
|---|
| 2106 | for(i_=1; i_<=blksiz;i_++)
|
|---|
| 2107 | {
|
|---|
| 2108 | work1[i_] = scl*work1[i_];
|
|---|
| 2109 | }
|
|---|
| 2110 | }
|
|---|
| 2111 | for(i=1; i<=n; i++)
|
|---|
| 2112 | {
|
|---|
| 2113 | z[i,j] = 0;
|
|---|
| 2114 | }
|
|---|
| 2115 | for(i=1; i<=blksiz; i++)
|
|---|
| 2116 | {
|
|---|
| 2117 | z[b1+i-1,j] = work1[i];
|
|---|
| 2118 | }
|
|---|
| 2119 |
|
|---|
| 2120 | //
|
|---|
| 2121 | // Save the shift to check eigenvalue spacing at next
|
|---|
| 2122 | // iteration.
|
|---|
| 2123 | //
|
|---|
| 2124 | xjm = xj;
|
|---|
| 2125 | }
|
|---|
| 2126 | }
|
|---|
| 2127 | }
|
|---|
| 2128 |
|
|---|
| 2129 |
|
|---|
| 2130 | private static void tdininternaldlagtf(int n,
|
|---|
| 2131 | ref double[] a,
|
|---|
| 2132 | double lambda,
|
|---|
| 2133 | ref double[] b,
|
|---|
| 2134 | ref double[] c,
|
|---|
| 2135 | double tol,
|
|---|
| 2136 | ref double[] d,
|
|---|
| 2137 | ref int[] iin,
|
|---|
| 2138 | ref int info)
|
|---|
| 2139 | {
|
|---|
| 2140 | int k = 0;
|
|---|
| 2141 | double eps = 0;
|
|---|
| 2142 | double mult = 0;
|
|---|
| 2143 | double piv1 = 0;
|
|---|
| 2144 | double piv2 = 0;
|
|---|
| 2145 | double scale1 = 0;
|
|---|
| 2146 | double scale2 = 0;
|
|---|
| 2147 | double temp = 0;
|
|---|
| 2148 | double tl = 0;
|
|---|
| 2149 |
|
|---|
| 2150 | info = 0;
|
|---|
| 2151 | if( n<0 )
|
|---|
| 2152 | {
|
|---|
| 2153 | info = -1;
|
|---|
| 2154 | return;
|
|---|
| 2155 | }
|
|---|
| 2156 | if( n==0 )
|
|---|
| 2157 | {
|
|---|
| 2158 | return;
|
|---|
| 2159 | }
|
|---|
| 2160 | a[1] = a[1]-lambda;
|
|---|
| 2161 | iin[n] = 0;
|
|---|
| 2162 | if( n==1 )
|
|---|
| 2163 | {
|
|---|
| 2164 | if( (double)(a[1])==(double)(0) )
|
|---|
| 2165 | {
|
|---|
| 2166 | iin[1] = 1;
|
|---|
| 2167 | }
|
|---|
| 2168 | return;
|
|---|
| 2169 | }
|
|---|
| 2170 | eps = AP.Math.MachineEpsilon;
|
|---|
| 2171 | tl = Math.Max(tol, eps);
|
|---|
| 2172 | scale1 = Math.Abs(a[1])+Math.Abs(b[1]);
|
|---|
| 2173 | for(k=1; k<=n-1; k++)
|
|---|
| 2174 | {
|
|---|
| 2175 | a[k+1] = a[k+1]-lambda;
|
|---|
| 2176 | scale2 = Math.Abs(c[k])+Math.Abs(a[k+1]);
|
|---|
| 2177 | if( k<n-1 )
|
|---|
| 2178 | {
|
|---|
| 2179 | scale2 = scale2+Math.Abs(b[k+1]);
|
|---|
| 2180 | }
|
|---|
| 2181 | if( (double)(a[k])==(double)(0) )
|
|---|
| 2182 | {
|
|---|
| 2183 | piv1 = 0;
|
|---|
| 2184 | }
|
|---|
| 2185 | else
|
|---|
| 2186 | {
|
|---|
| 2187 | piv1 = Math.Abs(a[k])/scale1;
|
|---|
| 2188 | }
|
|---|
| 2189 | if( (double)(c[k])==(double)(0) )
|
|---|
| 2190 | {
|
|---|
| 2191 | iin[k] = 0;
|
|---|
| 2192 | piv2 = 0;
|
|---|
| 2193 | scale1 = scale2;
|
|---|
| 2194 | if( k<n-1 )
|
|---|
| 2195 | {
|
|---|
| 2196 | d[k] = 0;
|
|---|
| 2197 | }
|
|---|
| 2198 | }
|
|---|
| 2199 | else
|
|---|
| 2200 | {
|
|---|
| 2201 | piv2 = Math.Abs(c[k])/scale2;
|
|---|
| 2202 | if( (double)(piv2)<=(double)(piv1) )
|
|---|
| 2203 | {
|
|---|
| 2204 | iin[k] = 0;
|
|---|
| 2205 | scale1 = scale2;
|
|---|
| 2206 | c[k] = c[k]/a[k];
|
|---|
| 2207 | a[k+1] = a[k+1]-c[k]*b[k];
|
|---|
| 2208 | if( k<n-1 )
|
|---|
| 2209 | {
|
|---|
| 2210 | d[k] = 0;
|
|---|
| 2211 | }
|
|---|
| 2212 | }
|
|---|
| 2213 | else
|
|---|
| 2214 | {
|
|---|
| 2215 | iin[k] = 1;
|
|---|
| 2216 | mult = a[k]/c[k];
|
|---|
| 2217 | a[k] = c[k];
|
|---|
| 2218 | temp = a[k+1];
|
|---|
| 2219 | a[k+1] = b[k]-mult*temp;
|
|---|
| 2220 | if( k<n-1 )
|
|---|
| 2221 | {
|
|---|
| 2222 | d[k] = b[k+1];
|
|---|
| 2223 | b[k+1] = -(mult*d[k]);
|
|---|
| 2224 | }
|
|---|
| 2225 | b[k] = temp;
|
|---|
| 2226 | c[k] = mult;
|
|---|
| 2227 | }
|
|---|
| 2228 | }
|
|---|
| 2229 | if( (double)(Math.Max(piv1, piv2))<=(double)(tl) & iin[n]==0 )
|
|---|
| 2230 | {
|
|---|
| 2231 | iin[n] = k;
|
|---|
| 2232 | }
|
|---|
| 2233 | }
|
|---|
| 2234 | if( (double)(Math.Abs(a[n]))<=(double)(scale1*tl) & iin[n]==0 )
|
|---|
| 2235 | {
|
|---|
| 2236 | iin[n] = n;
|
|---|
| 2237 | }
|
|---|
| 2238 | }
|
|---|
| 2239 |
|
|---|
| 2240 |
|
|---|
| 2241 | private static void tdininternaldlagts(int n,
|
|---|
| 2242 | ref double[] a,
|
|---|
| 2243 | ref double[] b,
|
|---|
| 2244 | ref double[] c,
|
|---|
| 2245 | ref double[] d,
|
|---|
| 2246 | ref int[] iin,
|
|---|
| 2247 | ref double[] y,
|
|---|
| 2248 | ref double tol,
|
|---|
| 2249 | ref int info)
|
|---|
| 2250 | {
|
|---|
| 2251 | int k = 0;
|
|---|
| 2252 | double absak = 0;
|
|---|
| 2253 | double ak = 0;
|
|---|
| 2254 | double bignum = 0;
|
|---|
| 2255 | double eps = 0;
|
|---|
| 2256 | double pert = 0;
|
|---|
| 2257 | double sfmin = 0;
|
|---|
| 2258 | double temp = 0;
|
|---|
| 2259 |
|
|---|
| 2260 | info = 0;
|
|---|
| 2261 | if( n<0 )
|
|---|
| 2262 | {
|
|---|
| 2263 | info = -1;
|
|---|
| 2264 | return;
|
|---|
| 2265 | }
|
|---|
| 2266 | if( n==0 )
|
|---|
| 2267 | {
|
|---|
| 2268 | return;
|
|---|
| 2269 | }
|
|---|
| 2270 | eps = AP.Math.MachineEpsilon;
|
|---|
| 2271 | sfmin = AP.Math.MinRealNumber;
|
|---|
| 2272 | bignum = 1/sfmin;
|
|---|
| 2273 | if( (double)(tol)<=(double)(0) )
|
|---|
| 2274 | {
|
|---|
| 2275 | tol = Math.Abs(a[1]);
|
|---|
| 2276 | if( n>1 )
|
|---|
| 2277 | {
|
|---|
| 2278 | tol = Math.Max(tol, Math.Max(Math.Abs(a[2]), Math.Abs(b[1])));
|
|---|
| 2279 | }
|
|---|
| 2280 | for(k=3; k<=n; k++)
|
|---|
| 2281 | {
|
|---|
| 2282 | tol = Math.Max(tol, Math.Max(Math.Abs(a[k]), Math.Max(Math.Abs(b[k-1]), Math.Abs(d[k-2]))));
|
|---|
| 2283 | }
|
|---|
| 2284 | tol = tol*eps;
|
|---|
| 2285 | if( (double)(tol)==(double)(0) )
|
|---|
| 2286 | {
|
|---|
| 2287 | tol = eps;
|
|---|
| 2288 | }
|
|---|
| 2289 | }
|
|---|
| 2290 | for(k=2; k<=n; k++)
|
|---|
| 2291 | {
|
|---|
| 2292 | if( iin[k-1]==0 )
|
|---|
| 2293 | {
|
|---|
| 2294 | y[k] = y[k]-c[k-1]*y[k-1];
|
|---|
| 2295 | }
|
|---|
| 2296 | else
|
|---|
| 2297 | {
|
|---|
| 2298 | temp = y[k-1];
|
|---|
| 2299 | y[k-1] = y[k];
|
|---|
| 2300 | y[k] = temp-c[k-1]*y[k];
|
|---|
| 2301 | }
|
|---|
| 2302 | }
|
|---|
| 2303 | for(k=n; k>=1; k--)
|
|---|
| 2304 | {
|
|---|
| 2305 | if( k<=n-2 )
|
|---|
| 2306 | {
|
|---|
| 2307 | temp = y[k]-b[k]*y[k+1]-d[k]*y[k+2];
|
|---|
| 2308 | }
|
|---|
| 2309 | else
|
|---|
| 2310 | {
|
|---|
| 2311 | if( k==n-1 )
|
|---|
| 2312 | {
|
|---|
| 2313 | temp = y[k]-b[k]*y[k+1];
|
|---|
| 2314 | }
|
|---|
| 2315 | else
|
|---|
| 2316 | {
|
|---|
| 2317 | temp = y[k];
|
|---|
| 2318 | }
|
|---|
| 2319 | }
|
|---|
| 2320 | ak = a[k];
|
|---|
| 2321 | pert = Math.Abs(tol);
|
|---|
| 2322 | if( (double)(ak)<(double)(0) )
|
|---|
| 2323 | {
|
|---|
| 2324 | pert = -pert;
|
|---|
| 2325 | }
|
|---|
| 2326 | while( true )
|
|---|
| 2327 | {
|
|---|
| 2328 | absak = Math.Abs(ak);
|
|---|
| 2329 | if( (double)(absak)<(double)(1) )
|
|---|
| 2330 | {
|
|---|
| 2331 | if( (double)(absak)<(double)(sfmin) )
|
|---|
| 2332 | {
|
|---|
| 2333 | if( (double)(absak)==(double)(0) | (double)(Math.Abs(temp)*sfmin)>(double)(absak) )
|
|---|
| 2334 | {
|
|---|
| 2335 | ak = ak+pert;
|
|---|
| 2336 | pert = 2*pert;
|
|---|
| 2337 | continue;
|
|---|
| 2338 | }
|
|---|
| 2339 | else
|
|---|
| 2340 | {
|
|---|
| 2341 | temp = temp*bignum;
|
|---|
| 2342 | ak = ak*bignum;
|
|---|
| 2343 | }
|
|---|
| 2344 | }
|
|---|
| 2345 | else
|
|---|
| 2346 | {
|
|---|
| 2347 | if( (double)(Math.Abs(temp))>(double)(absak*bignum) )
|
|---|
| 2348 | {
|
|---|
| 2349 | ak = ak+pert;
|
|---|
| 2350 | pert = 2*pert;
|
|---|
| 2351 | continue;
|
|---|
| 2352 | }
|
|---|
| 2353 | }
|
|---|
| 2354 | }
|
|---|
| 2355 | break;
|
|---|
| 2356 | }
|
|---|
| 2357 | y[k] = temp/ak;
|
|---|
| 2358 | }
|
|---|
| 2359 | }
|
|---|
| 2360 |
|
|---|
| 2361 |
|
|---|
| 2362 | private static void internaldlaebz(int ijob,
|
|---|
| 2363 | int nitmax,
|
|---|
| 2364 | int n,
|
|---|
| 2365 | int mmax,
|
|---|
| 2366 | int minp,
|
|---|
| 2367 | double abstol,
|
|---|
| 2368 | double reltol,
|
|---|
| 2369 | double pivmin,
|
|---|
| 2370 | ref double[] d,
|
|---|
| 2371 | ref double[] e,
|
|---|
| 2372 | ref double[] e2,
|
|---|
| 2373 | ref int[] nval,
|
|---|
| 2374 | ref double[,] ab,
|
|---|
| 2375 | ref double[] c,
|
|---|
| 2376 | ref int mout,
|
|---|
| 2377 | ref int[,] nab,
|
|---|
| 2378 | ref double[] work,
|
|---|
| 2379 | ref int[] iwork,
|
|---|
| 2380 | ref int info)
|
|---|
| 2381 | {
|
|---|
| 2382 | int itmp1 = 0;
|
|---|
| 2383 | int itmp2 = 0;
|
|---|
| 2384 | int j = 0;
|
|---|
| 2385 | int ji = 0;
|
|---|
| 2386 | int jit = 0;
|
|---|
| 2387 | int jp = 0;
|
|---|
| 2388 | int kf = 0;
|
|---|
| 2389 | int kfnew = 0;
|
|---|
| 2390 | int kl = 0;
|
|---|
| 2391 | int klnew = 0;
|
|---|
| 2392 | double tmp1 = 0;
|
|---|
| 2393 | double tmp2 = 0;
|
|---|
| 2394 |
|
|---|
| 2395 | info = 0;
|
|---|
| 2396 | if( ijob<1 | ijob>3 )
|
|---|
| 2397 | {
|
|---|
| 2398 | info = -1;
|
|---|
| 2399 | return;
|
|---|
| 2400 | }
|
|---|
| 2401 |
|
|---|
| 2402 | //
|
|---|
| 2403 | // Initialize NAB
|
|---|
| 2404 | //
|
|---|
| 2405 | if( ijob==1 )
|
|---|
| 2406 | {
|
|---|
| 2407 |
|
|---|
| 2408 | //
|
|---|
| 2409 | // Compute the number of eigenvalues in the initial intervals.
|
|---|
| 2410 | //
|
|---|
| 2411 | mout = 0;
|
|---|
| 2412 |
|
|---|
| 2413 | //
|
|---|
| 2414 | //DIR$ NOVECTOR
|
|---|
| 2415 | //
|
|---|
| 2416 | for(ji=1; ji<=minp; ji++)
|
|---|
| 2417 | {
|
|---|
| 2418 | for(jp=1; jp<=2; jp++)
|
|---|
| 2419 | {
|
|---|
| 2420 | tmp1 = d[1]-ab[ji,jp];
|
|---|
| 2421 | if( (double)(Math.Abs(tmp1))<(double)(pivmin) )
|
|---|
| 2422 | {
|
|---|
| 2423 | tmp1 = -pivmin;
|
|---|
| 2424 | }
|
|---|
| 2425 | nab[ji,jp] = 0;
|
|---|
| 2426 | if( (double)(tmp1)<=(double)(0) )
|
|---|
| 2427 | {
|
|---|
| 2428 | nab[ji,jp] = 1;
|
|---|
| 2429 | }
|
|---|
| 2430 | for(j=2; j<=n; j++)
|
|---|
| 2431 | {
|
|---|
| 2432 | tmp1 = d[j]-e2[j-1]/tmp1-ab[ji,jp];
|
|---|
| 2433 | if( (double)(Math.Abs(tmp1))<(double)(pivmin) )
|
|---|
| 2434 | {
|
|---|
| 2435 | tmp1 = -pivmin;
|
|---|
| 2436 | }
|
|---|
| 2437 | if( (double)(tmp1)<=(double)(0) )
|
|---|
| 2438 | {
|
|---|
| 2439 | nab[ji,jp] = nab[ji,jp]+1;
|
|---|
| 2440 | }
|
|---|
| 2441 | }
|
|---|
| 2442 | }
|
|---|
| 2443 | mout = mout+nab[ji,2]-nab[ji,1];
|
|---|
| 2444 | }
|
|---|
| 2445 | return;
|
|---|
| 2446 | }
|
|---|
| 2447 |
|
|---|
| 2448 | //
|
|---|
| 2449 | // Initialize for loop
|
|---|
| 2450 | //
|
|---|
| 2451 | // KF and KL have the following meaning:
|
|---|
| 2452 | // Intervals 1,...,KF-1 have converged.
|
|---|
| 2453 | // Intervals KF,...,KL still need to be refined.
|
|---|
| 2454 | //
|
|---|
| 2455 | kf = 1;
|
|---|
| 2456 | kl = minp;
|
|---|
| 2457 |
|
|---|
| 2458 | //
|
|---|
| 2459 | // If IJOB=2, initialize C.
|
|---|
| 2460 | // If IJOB=3, use the user-supplied starting point.
|
|---|
| 2461 | //
|
|---|
| 2462 | if( ijob==2 )
|
|---|
| 2463 | {
|
|---|
| 2464 | for(ji=1; ji<=minp; ji++)
|
|---|
| 2465 | {
|
|---|
| 2466 | c[ji] = 0.5*(ab[ji,1]+ab[ji,2]);
|
|---|
| 2467 | }
|
|---|
| 2468 | }
|
|---|
| 2469 |
|
|---|
| 2470 | //
|
|---|
| 2471 | // Iteration loop
|
|---|
| 2472 | //
|
|---|
| 2473 | for(jit=1; jit<=nitmax; jit++)
|
|---|
| 2474 | {
|
|---|
| 2475 |
|
|---|
| 2476 | //
|
|---|
| 2477 | // Loop over intervals
|
|---|
| 2478 | //
|
|---|
| 2479 | //
|
|---|
| 2480 | // Serial Version of the loop
|
|---|
| 2481 | //
|
|---|
| 2482 | klnew = kl;
|
|---|
| 2483 | for(ji=kf; ji<=kl; ji++)
|
|---|
| 2484 | {
|
|---|
| 2485 |
|
|---|
| 2486 | //
|
|---|
| 2487 | // Compute N(w), the number of eigenvalues less than w
|
|---|
| 2488 | //
|
|---|
| 2489 | tmp1 = c[ji];
|
|---|
| 2490 | tmp2 = d[1]-tmp1;
|
|---|
| 2491 | itmp1 = 0;
|
|---|
| 2492 | if( (double)(tmp2)<=(double)(pivmin) )
|
|---|
| 2493 | {
|
|---|
| 2494 | itmp1 = 1;
|
|---|
| 2495 | tmp2 = Math.Min(tmp2, -pivmin);
|
|---|
| 2496 | }
|
|---|
| 2497 |
|
|---|
| 2498 | //
|
|---|
| 2499 | // A series of compiler directives to defeat vectorization
|
|---|
| 2500 | // for the next loop
|
|---|
| 2501 | //
|
|---|
| 2502 | //*$PL$ CMCHAR=' '
|
|---|
| 2503 | //CDIR$ NEXTSCALAR
|
|---|
| 2504 | //C$DIR SCALAR
|
|---|
| 2505 | //CDIR$ NEXT SCALAR
|
|---|
| 2506 | //CVD$L NOVECTOR
|
|---|
| 2507 | //CDEC$ NOVECTOR
|
|---|
| 2508 | //CVD$ NOVECTOR
|
|---|
| 2509 | //*VDIR NOVECTOR
|
|---|
| 2510 | //*VOCL LOOP,SCALAR
|
|---|
| 2511 | //CIBM PREFER SCALAR
|
|---|
| 2512 | //*$PL$ CMCHAR='*'
|
|---|
| 2513 | //
|
|---|
| 2514 | for(j=2; j<=n; j++)
|
|---|
| 2515 | {
|
|---|
| 2516 | tmp2 = d[j]-e2[j-1]/tmp2-tmp1;
|
|---|
| 2517 | if( (double)(tmp2)<=(double)(pivmin) )
|
|---|
| 2518 | {
|
|---|
| 2519 | itmp1 = itmp1+1;
|
|---|
| 2520 | tmp2 = Math.Min(tmp2, -pivmin);
|
|---|
| 2521 | }
|
|---|
| 2522 | }
|
|---|
| 2523 | if( ijob<=2 )
|
|---|
| 2524 | {
|
|---|
| 2525 |
|
|---|
| 2526 | //
|
|---|
| 2527 | // IJOB=2: Choose all intervals containing eigenvalues.
|
|---|
| 2528 | //
|
|---|
| 2529 | // Insure that N(w) is monotone
|
|---|
| 2530 | //
|
|---|
| 2531 | itmp1 = Math.Min(nab[ji,2], Math.Max(nab[ji,1], itmp1));
|
|---|
| 2532 |
|
|---|
| 2533 | //
|
|---|
| 2534 | // Update the Queue -- add intervals if both halves
|
|---|
| 2535 | // contain eigenvalues.
|
|---|
| 2536 | //
|
|---|
| 2537 | if( itmp1==nab[ji,2] )
|
|---|
| 2538 | {
|
|---|
| 2539 |
|
|---|
| 2540 | //
|
|---|
| 2541 | // No eigenvalue in the upper interval:
|
|---|
| 2542 | // just use the lower interval.
|
|---|
| 2543 | //
|
|---|
| 2544 | ab[ji,2] = tmp1;
|
|---|
| 2545 | }
|
|---|
| 2546 | else
|
|---|
| 2547 | {
|
|---|
| 2548 | if( itmp1==nab[ji,1] )
|
|---|
| 2549 | {
|
|---|
| 2550 |
|
|---|
| 2551 | //
|
|---|
| 2552 | // No eigenvalue in the lower interval:
|
|---|
| 2553 | // just use the upper interval.
|
|---|
| 2554 | //
|
|---|
| 2555 | ab[ji,1] = tmp1;
|
|---|
| 2556 | }
|
|---|
| 2557 | else
|
|---|
| 2558 | {
|
|---|
| 2559 | if( klnew<mmax )
|
|---|
| 2560 | {
|
|---|
| 2561 |
|
|---|
| 2562 | //
|
|---|
| 2563 | // Eigenvalue in both intervals -- add upper to queue.
|
|---|
| 2564 | //
|
|---|
| 2565 | klnew = klnew+1;
|
|---|
| 2566 | ab[klnew,2] = ab[ji,2];
|
|---|
| 2567 | nab[klnew,2] = nab[ji,2];
|
|---|
| 2568 | ab[klnew,1] = tmp1;
|
|---|
| 2569 | nab[klnew,1] = itmp1;
|
|---|
| 2570 | ab[ji,2] = tmp1;
|
|---|
| 2571 | nab[ji,2] = itmp1;
|
|---|
| 2572 | }
|
|---|
| 2573 | else
|
|---|
| 2574 | {
|
|---|
| 2575 | info = mmax+1;
|
|---|
| 2576 | return;
|
|---|
| 2577 | }
|
|---|
| 2578 | }
|
|---|
| 2579 | }
|
|---|
| 2580 | }
|
|---|
| 2581 | else
|
|---|
| 2582 | {
|
|---|
| 2583 |
|
|---|
| 2584 | //
|
|---|
| 2585 | // IJOB=3: Binary search. Keep only the interval
|
|---|
| 2586 | // containing w s.t. N(w) = NVAL
|
|---|
| 2587 | //
|
|---|
| 2588 | if( itmp1<=nval[ji] )
|
|---|
| 2589 | {
|
|---|
| 2590 | ab[ji,1] = tmp1;
|
|---|
| 2591 | nab[ji,1] = itmp1;
|
|---|
| 2592 | }
|
|---|
| 2593 | if( itmp1>=nval[ji] )
|
|---|
| 2594 | {
|
|---|
| 2595 | ab[ji,2] = tmp1;
|
|---|
| 2596 | nab[ji,2] = itmp1;
|
|---|
| 2597 | }
|
|---|
| 2598 | }
|
|---|
| 2599 | }
|
|---|
| 2600 | kl = klnew;
|
|---|
| 2601 |
|
|---|
| 2602 | //
|
|---|
| 2603 | // Check for convergence
|
|---|
| 2604 | //
|
|---|
| 2605 | kfnew = kf;
|
|---|
| 2606 | for(ji=kf; ji<=kl; ji++)
|
|---|
| 2607 | {
|
|---|
| 2608 | tmp1 = Math.Abs(ab[ji,2]-ab[ji,1]);
|
|---|
| 2609 | tmp2 = Math.Max(Math.Abs(ab[ji,2]), Math.Abs(ab[ji,1]));
|
|---|
| 2610 | if( (double)(tmp1)<(double)(Math.Max(abstol, Math.Max(pivmin, reltol*tmp2))) | nab[ji,1]>=nab[ji,2] )
|
|---|
| 2611 | {
|
|---|
| 2612 |
|
|---|
| 2613 | //
|
|---|
| 2614 | // Converged -- Swap with position KFNEW,
|
|---|
| 2615 | // then increment KFNEW
|
|---|
| 2616 | //
|
|---|
| 2617 | if( ji>kfnew )
|
|---|
| 2618 | {
|
|---|
| 2619 | tmp1 = ab[ji,1];
|
|---|
| 2620 | tmp2 = ab[ji,2];
|
|---|
| 2621 | itmp1 = nab[ji,1];
|
|---|
| 2622 | itmp2 = nab[ji,2];
|
|---|
| 2623 | ab[ji,1] = ab[kfnew,1];
|
|---|
| 2624 | ab[ji,2] = ab[kfnew,2];
|
|---|
| 2625 | nab[ji,1] = nab[kfnew,1];
|
|---|
| 2626 | nab[ji,2] = nab[kfnew,2];
|
|---|
| 2627 | ab[kfnew,1] = tmp1;
|
|---|
| 2628 | ab[kfnew,2] = tmp2;
|
|---|
| 2629 | nab[kfnew,1] = itmp1;
|
|---|
| 2630 | nab[kfnew,2] = itmp2;
|
|---|
| 2631 | if( ijob==3 )
|
|---|
| 2632 | {
|
|---|
| 2633 | itmp1 = nval[ji];
|
|---|
| 2634 | nval[ji] = nval[kfnew];
|
|---|
| 2635 | nval[kfnew] = itmp1;
|
|---|
| 2636 | }
|
|---|
| 2637 | }
|
|---|
| 2638 | kfnew = kfnew+1;
|
|---|
| 2639 | }
|
|---|
| 2640 | }
|
|---|
| 2641 | kf = kfnew;
|
|---|
| 2642 |
|
|---|
| 2643 | //
|
|---|
| 2644 | // Choose Midpoints
|
|---|
| 2645 | //
|
|---|
| 2646 | for(ji=kf; ji<=kl; ji++)
|
|---|
| 2647 | {
|
|---|
| 2648 | c[ji] = 0.5*(ab[ji,1]+ab[ji,2]);
|
|---|
| 2649 | }
|
|---|
| 2650 |
|
|---|
| 2651 | //
|
|---|
| 2652 | // If no more intervals to refine, quit.
|
|---|
| 2653 | //
|
|---|
| 2654 | if( kf>kl )
|
|---|
| 2655 | {
|
|---|
| 2656 | break;
|
|---|
| 2657 | }
|
|---|
| 2658 | }
|
|---|
| 2659 |
|
|---|
| 2660 | //
|
|---|
| 2661 | // Converged
|
|---|
| 2662 | //
|
|---|
| 2663 | info = Math.Max(kl+1-kf, 0);
|
|---|
| 2664 | mout = kl;
|
|---|
| 2665 | }
|
|---|
| 2666 | }
|
|---|
| 2667 | }
|
|---|
