Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | |
| 18 | package org.apache.commons.math.linear; |
| 19 | import java.io.Serializable; |
| 20 | import java.math.BigDecimal; |
| 21 | |
| 22 | import org.apache.commons.math.MathRuntimeException; |
| 23 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 24 | |
| 25 | /** |
| 26 | * Implementation of {@link BigMatrix} using a BigDecimal[][] array to store entries |
| 27 | * and <a href="http://www.math.gatech.edu/~bourbaki/math2601/Web-notes/2num.pdf"> |
| 28 | * LU decompostion</a> to support linear system |
| 29 | * solution and inverse. |
| 30 | * <p> |
| 31 | * The LU decompostion is performed as needed, to support the following operations: <ul> |
| 32 | * <li>solve</li> |
| 33 | * <li>isSingular</li> |
| 34 | * <li>getDeterminant</li> |
| 35 | * <li>inverse</li> </ul></p> |
| 36 | * <p> |
| 37 | * <strong>Usage notes</strong>:<br> |
| 38 | * <ul><li> |
| 39 | * The LU decomposition is stored and reused on subsequent calls. If matrix |
| 40 | * data are modified using any of the public setXxx methods, the saved |
| 41 | * decomposition is discarded. If data are modified via references to the |
| 42 | * underlying array obtained using <code>getDataRef()</code>, then the stored |
| 43 | * LU decomposition will not be discarded. In this case, you need to |
| 44 | * explicitly invoke <code>LUDecompose()</code> to recompute the decomposition |
| 45 | * before using any of the methods above.</li> |
| 46 | * <li> |
| 47 | * As specified in the {@link BigMatrix} interface, matrix element indexing |
| 48 | * is 0-based -- e.g., <code>getEntry(0, 0)</code> |
| 49 | * returns the element in the first row, first column of the matrix.</li></ul></p> |
| 50 | * |
| 51 | * @deprecated as of 2.0, replaced by {@link Array2DRowFieldMatrix} with a {@link |
| 52 | * org.apache.commons.math.util.BigReal} parameter |
| 53 | * @version $Revision: 1042376 $ $Date: 2010-12-05 16:54:55 +0100 (dim. 05 déc. 2010) $ |
| 54 | */ |
| 55 | @Deprecated |
| 56 | public class BigMatrixImpl implements BigMatrix, Serializable { |
| 57 | |
| 58 | /** BigDecimal 0 */ |
| 59 | static final BigDecimal ZERO = new BigDecimal(0); |
| 60 | |
| 61 | /** BigDecimal 1 */ |
| 62 | static final BigDecimal ONE = new BigDecimal(1); |
| 63 | |
| 64 | /** Bound to determine effective singularity in LU decomposition */ |
| 65 | private static final BigDecimal TOO_SMALL = new BigDecimal(10E-12); |
| 66 | |
| 67 | /** Serialization id */ |
| 68 | private static final long serialVersionUID = -1011428905656140431L; |
| 69 | |
| 70 | /** Entries of the matrix */ |
| 71 | protected BigDecimal data[][] = null; |
| 72 | |
| 73 | /** Entries of cached LU decomposition. |
| 74 | * All updates to data (other than luDecompose()) *must* set this to null |
| 75 | */ |
| 76 | protected BigDecimal lu[][] = null; |
| 77 | |
| 78 | /** Permutation associated with LU decomposition */ |
| 79 | protected int[] permutation = null; |
| 80 | |
| 81 | /** Parity of the permutation associated with the LU decomposition */ |
| 82 | protected int parity = 1; |
| 83 | |
| 84 | /** Rounding mode for divisions **/ |
| 85 | private int roundingMode = BigDecimal.ROUND_HALF_UP; |
| 86 | |
| 87 | /*** BigDecimal scale ***/ |
| 88 | private int scale = 64; |
| 89 | |
| 90 | /** |
| 91 | * Creates a matrix with no data |
| 92 | */ |
| 93 | public BigMatrixImpl() { |
| 94 | } |
| 95 | |
| 96 | /** |
| 97 | * Create a new BigMatrix with the supplied row and column dimensions. |
| 98 | * |
| 99 | * @param rowDimension the number of rows in the new matrix |
| 100 | * @param columnDimension the number of columns in the new matrix |
| 101 | * @throws IllegalArgumentException if row or column dimension is not |
| 102 | * positive |
| 103 | */ |
| 104 | public BigMatrixImpl(int rowDimension, int columnDimension) { |
| 105 | if (rowDimension < 1 ) { |
| 106 | throw MathRuntimeException.createIllegalArgumentException( |
| 107 | LocalizedFormats.INSUFFICIENT_DIMENSION, rowDimension, 1); |
| 108 | } |
| 109 | if (columnDimension < 1) { |
| 110 | throw MathRuntimeException.createIllegalArgumentException( |
| 111 | LocalizedFormats.INSUFFICIENT_DIMENSION, columnDimension, 1); |
| 112 | } |
| 113 | data = new BigDecimal[rowDimension][columnDimension]; |
| 114 | lu = null; |
| 115 | } |
| 116 | |
| 117 | /** |
| 118 | * Create a new BigMatrix using <code>d</code> as the underlying |
| 119 | * data array. |
| 120 | * <p>The input array is copied, not referenced. This constructor has |
| 121 | * the same effect as calling {@link #BigMatrixImpl(BigDecimal[][], boolean)} |
| 122 | * with the second argument set to <code>true</code>.</p> |
| 123 | * |
| 124 | * @param d data for new matrix |
| 125 | * @throws IllegalArgumentException if <code>d</code> is not rectangular |
| 126 | * (not all rows have the same length) or empty |
| 127 | * @throws NullPointerException if <code>d</code> is null |
| 128 | */ |
| 129 | public BigMatrixImpl(BigDecimal[][] d) { |
| 130 | this.copyIn(d); |
| 131 | lu = null; |
| 132 | } |
| 133 | |
| 134 | /** |
| 135 | * Create a new BigMatrix using the input array as the underlying |
| 136 | * data array. |
| 137 | * <p>If an array is built specially in order to be embedded in a |
| 138 | * BigMatrix and not used directly, the <code>copyArray</code> may be |
| 139 | * set to <code>false</code. This will prevent the copying and improve |
| 140 | * performance as no new array will be built and no data will be copied.</p> |
| 141 | * @param d data for new matrix |
| 142 | * @param copyArray if true, the input array will be copied, otherwise |
| 143 | * it will be referenced |
| 144 | * @throws IllegalArgumentException if <code>d</code> is not rectangular |
| 145 | * (not all rows have the same length) or empty |
| 146 | * @throws NullPointerException if <code>d</code> is null |
| 147 | * @see #BigMatrixImpl(BigDecimal[][]) |
| 148 | */ |
| 149 | public BigMatrixImpl(BigDecimal[][] d, boolean copyArray) { |
| 150 | if (copyArray) { |
| 151 | copyIn(d); |
| 152 | } else { |
| 153 | if (d == null) { |
| 154 | throw new NullPointerException(); |
| 155 | } |
| 156 | final int nRows = d.length; |
| 157 | if (nRows == 0) { |
| 158 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW); |
| 159 | } |
| 160 | |
| 161 | final int nCols = d[0].length; |
| 162 | if (nCols == 0) { |
| 163 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN); |
| 164 | } |
| 165 | for (int r = 1; r < nRows; r++) { |
| 166 | if (d[r].length != nCols) { |
| 167 | throw MathRuntimeException.createIllegalArgumentException( |
| 168 | LocalizedFormats.DIFFERENT_ROWS_LENGTHS, |
| 169 | nCols, d[r].length); |
| 170 | } |
| 171 | } |
| 172 | data = d; |
| 173 | } |
| 174 | lu = null; |
| 175 | } |
| 176 | |
| 177 | /** |
| 178 | * Create a new BigMatrix using <code>d</code> as the underlying |
| 179 | * data array. |
| 180 | * <p>Since the underlying array will hold <code>BigDecimal</code> |
| 181 | * instances, it will be created.</p> |
| 182 | * |
| 183 | * @param d data for new matrix |
| 184 | * @throws IllegalArgumentException if <code>d</code> is not rectangular |
| 185 | * (not all rows have the same length) or empty |
| 186 | * @throws NullPointerException if <code>d</code> is null |
| 187 | */ |
| 188 | public BigMatrixImpl(double[][] d) { |
| 189 | final int nRows = d.length; |
| 190 | if (nRows == 0) { |
| 191 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW); |
| 192 | } |
| 193 | |
| 194 | final int nCols = d[0].length; |
| 195 | if (nCols == 0) { |
| 196 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN); |
| 197 | } |
| 198 | for (int row = 1; row < nRows; row++) { |
| 199 | if (d[row].length != nCols) { |
| 200 | throw MathRuntimeException.createIllegalArgumentException( |
| 201 | LocalizedFormats.DIFFERENT_ROWS_LENGTHS, |
| 202 | nCols, d[row].length); |
| 203 | } |
| 204 | } |
| 205 | this.copyIn(d); |
| 206 | lu = null; |
| 207 | } |
| 208 | |
| 209 | /** |
| 210 | * Create a new BigMatrix using the values represented by the strings in |
| 211 | * <code>d</code> as the underlying data array. |
| 212 | * |
| 213 | * @param d data for new matrix |
| 214 | * @throws IllegalArgumentException if <code>d</code> is not rectangular |
| 215 | * (not all rows have the same length) or empty |
| 216 | * @throws NullPointerException if <code>d</code> is null |
| 217 | */ |
| 218 | public BigMatrixImpl(String[][] d) { |
| 219 | final int nRows = d.length; |
| 220 | if (nRows == 0) { |
| 221 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW); |
| 222 | } |
| 223 | |
| 224 | final int nCols = d[0].length; |
| 225 | if (nCols == 0) { |
| 226 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN); |
| 227 | } |
| 228 | for (int row = 1; row < nRows; row++) { |
| 229 | if (d[row].length != nCols) { |
| 230 | throw MathRuntimeException.createIllegalArgumentException( |
| 231 | LocalizedFormats.DIFFERENT_ROWS_LENGTHS, |
| 232 | nCols, d[row].length); |
| 233 | } |
| 234 | } |
| 235 | this.copyIn(d); |
| 236 | lu = null; |
| 237 | } |
| 238 | |
| 239 | /** |
| 240 | * Create a new (column) BigMatrix using <code>v</code> as the |
| 241 | * data for the unique column of the <code>v.length x 1</code> matrix |
| 242 | * created. |
| 243 | * <p> |
| 244 | * The input array is copied, not referenced.</p> |
| 245 | * |
| 246 | * @param v column vector holding data for new matrix |
| 247 | */ |
| 248 | public BigMatrixImpl(BigDecimal[] v) { |
| 249 | final int nRows = v.length; |
| 250 | data = new BigDecimal[nRows][1]; |
| 251 | for (int row = 0; row < nRows; row++) { |
| 252 | data[row][0] = v[row]; |
| 253 | } |
| 254 | } |
| 255 | |
| 256 | /** |
| 257 | * Create a new BigMatrix which is a copy of this. |
| 258 | * |
| 259 | * @return the cloned matrix |
| 260 | */ |
| 261 | public BigMatrix copy() { |
| 262 | return new BigMatrixImpl(this.copyOut(), false); |
| 263 | } |
| 264 | |
| 265 | /** |
| 266 | * Compute the sum of this and <code>m</code>. |
| 267 | * |
| 268 | * @param m matrix to be added |
| 269 | * @return this + m |
| 270 | * @throws IllegalArgumentException if m is not the same size as this |
| 271 | */ |
| 272 | public BigMatrix add(BigMatrix m) throws IllegalArgumentException { |
| 273 | try { |
| 274 | return add((BigMatrixImpl) m); |
| 275 | } catch (ClassCastException cce) { |
| 276 | |
| 277 | // safety check |
| 278 | MatrixUtils.checkAdditionCompatible(this, m); |
| 279 | |
| 280 | final int rowCount = getRowDimension(); |
| 281 | final int columnCount = getColumnDimension(); |
| 282 | final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount]; |
| 283 | for (int row = 0; row < rowCount; row++) { |
| 284 | final BigDecimal[] dataRow = data[row]; |
| 285 | final BigDecimal[] outDataRow = outData[row]; |
| 286 | for (int col = 0; col < columnCount; col++) { |
| 287 | outDataRow[col] = dataRow[col].add(m.getEntry(row, col)); |
| 288 | } |
| 289 | } |
| 290 | return new BigMatrixImpl(outData, false); |
| 291 | } |
| 292 | } |
| 293 | |
| 294 | /** |
| 295 | * Compute the sum of this and <code>m</code>. |
| 296 | * |
| 297 | * @param m matrix to be added |
| 298 | * @return this + m |
| 299 | * @throws IllegalArgumentException if m is not the same size as this |
| 300 | */ |
| 301 | public BigMatrixImpl add(BigMatrixImpl m) throws IllegalArgumentException { |
| 302 | |
| 303 | // safety check |
| 304 | MatrixUtils.checkAdditionCompatible(this, m); |
| 305 | |
| 306 | final int rowCount = getRowDimension(); |
| 307 | final int columnCount = getColumnDimension(); |
| 308 | final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount]; |
| 309 | for (int row = 0; row < rowCount; row++) { |
| 310 | final BigDecimal[] dataRow = data[row]; |
| 311 | final BigDecimal[] mRow = m.data[row]; |
| 312 | final BigDecimal[] outDataRow = outData[row]; |
| 313 | for (int col = 0; col < columnCount; col++) { |
| 314 | outDataRow[col] = dataRow[col].add(mRow[col]); |
| 315 | } |
| 316 | } |
| 317 | return new BigMatrixImpl(outData, false); |
| 318 | } |
| 319 | |
| 320 | /** |
| 321 | * Compute this minus <code>m</code>. |
| 322 | * |
| 323 | * @param m matrix to be subtracted |
| 324 | * @return this + m |
| 325 | * @throws IllegalArgumentException if m is not the same size as this |
| 326 | */ |
| 327 | public BigMatrix subtract(BigMatrix m) throws IllegalArgumentException { |
| 328 | try { |
| 329 | return subtract((BigMatrixImpl) m); |
| 330 | } catch (ClassCastException cce) { |
| 331 | |
| 332 | // safety check |
| 333 | MatrixUtils.checkSubtractionCompatible(this, m); |
| 334 | |
| 335 | final int rowCount = getRowDimension(); |
| 336 | final int columnCount = getColumnDimension(); |
| 337 | final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount]; |
| 338 | for (int row = 0; row < rowCount; row++) { |
| 339 | final BigDecimal[] dataRow = data[row]; |
| 340 | final BigDecimal[] outDataRow = outData[row]; |
| 341 | for (int col = 0; col < columnCount; col++) { |
| 342 | outDataRow[col] = dataRow[col].subtract(getEntry(row, col)); |
| 343 | } |
| 344 | } |
| 345 | return new BigMatrixImpl(outData, false); |
| 346 | } |
| 347 | } |
| 348 | |
| 349 | /** |
| 350 | * Compute this minus <code>m</code>. |
| 351 | * |
| 352 | * @param m matrix to be subtracted |
| 353 | * @return this + m |
| 354 | * @throws IllegalArgumentException if m is not the same size as this |
| 355 | */ |
| 356 | public BigMatrixImpl subtract(BigMatrixImpl m) throws IllegalArgumentException { |
| 357 | |
| 358 | // safety check |
| 359 | MatrixUtils.checkSubtractionCompatible(this, m); |
| 360 | |
| 361 | final int rowCount = getRowDimension(); |
| 362 | final int columnCount = getColumnDimension(); |
| 363 | final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount]; |
| 364 | for (int row = 0; row < rowCount; row++) { |
| 365 | final BigDecimal[] dataRow = data[row]; |
| 366 | final BigDecimal[] mRow = m.data[row]; |
| 367 | final BigDecimal[] outDataRow = outData[row]; |
| 368 | for (int col = 0; col < columnCount; col++) { |
| 369 | outDataRow[col] = dataRow[col].subtract(mRow[col]); |
| 370 | } |
| 371 | } |
| 372 | return new BigMatrixImpl(outData, false); |
| 373 | } |
| 374 | |
| 375 | /** |
| 376 | * Returns the result of adding d to each entry of this. |
| 377 | * |
| 378 | * @param d value to be added to each entry |
| 379 | * @return d + this |
| 380 | */ |
| 381 | public BigMatrix scalarAdd(BigDecimal d) { |
| 382 | final int rowCount = getRowDimension(); |
| 383 | final int columnCount = getColumnDimension(); |
| 384 | final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount]; |
| 385 | for (int row = 0; row < rowCount; row++) { |
| 386 | final BigDecimal[] dataRow = data[row]; |
| 387 | final BigDecimal[] outDataRow = outData[row]; |
| 388 | for (int col = 0; col < columnCount; col++) { |
| 389 | outDataRow[col] = dataRow[col].add(d); |
| 390 | } |
| 391 | } |
| 392 | return new BigMatrixImpl(outData, false); |
| 393 | } |
| 394 | |
| 395 | /** |
| 396 | * Returns the result of multiplying each entry of this by <code>d</code> |
| 397 | * @param d value to multiply all entries by |
| 398 | * @return d * this |
| 399 | */ |
| 400 | public BigMatrix scalarMultiply(BigDecimal d) { |
| 401 | final int rowCount = getRowDimension(); |
| 402 | final int columnCount = getColumnDimension(); |
| 403 | final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount]; |
| 404 | for (int row = 0; row < rowCount; row++) { |
| 405 | final BigDecimal[] dataRow = data[row]; |
| 406 | final BigDecimal[] outDataRow = outData[row]; |
| 407 | for (int col = 0; col < columnCount; col++) { |
| 408 | outDataRow[col] = dataRow[col].multiply(d); |
| 409 | } |
| 410 | } |
| 411 | return new BigMatrixImpl(outData, false); |
| 412 | } |
| 413 | |
| 414 | /** |
| 415 | * Returns the result of postmultiplying this by <code>m</code>. |
| 416 | * @param m matrix to postmultiply by |
| 417 | * @return this*m |
| 418 | * @throws IllegalArgumentException |
| 419 | * if columnDimension(this) != rowDimension(m) |
| 420 | */ |
| 421 | public BigMatrix multiply(BigMatrix m) throws IllegalArgumentException { |
| 422 | try { |
| 423 | return multiply((BigMatrixImpl) m); |
| 424 | } catch (ClassCastException cce) { |
| 425 | |
| 426 | // safety check |
| 427 | MatrixUtils.checkMultiplicationCompatible(this, m); |
| 428 | |
| 429 | final int nRows = this.getRowDimension(); |
| 430 | final int nCols = m.getColumnDimension(); |
| 431 | final int nSum = this.getColumnDimension(); |
| 432 | final BigDecimal[][] outData = new BigDecimal[nRows][nCols]; |
| 433 | for (int row = 0; row < nRows; row++) { |
| 434 | final BigDecimal[] dataRow = data[row]; |
| 435 | final BigDecimal[] outDataRow = outData[row]; |
| 436 | for (int col = 0; col < nCols; col++) { |
| 437 | BigDecimal sum = ZERO; |
| 438 | for (int i = 0; i < nSum; i++) { |
| 439 | sum = sum.add(dataRow[i].multiply(m.getEntry(i, col))); |
| 440 | } |
| 441 | outDataRow[col] = sum; |
| 442 | } |
| 443 | } |
| 444 | return new BigMatrixImpl(outData, false); |
| 445 | } |
| 446 | } |
| 447 | |
| 448 | /** |
| 449 | * Returns the result of postmultiplying this by <code>m</code>. |
| 450 | * @param m matrix to postmultiply by |
| 451 | * @return this*m |
| 452 | * @throws IllegalArgumentException |
| 453 | * if columnDimension(this) != rowDimension(m) |
| 454 | */ |
| 455 | public BigMatrixImpl multiply(BigMatrixImpl m) throws IllegalArgumentException { |
| 456 | |
| 457 | // safety check |
| 458 | MatrixUtils.checkMultiplicationCompatible(this, m); |
| 459 | |
| 460 | final int nRows = this.getRowDimension(); |
| 461 | final int nCols = m.getColumnDimension(); |
| 462 | final int nSum = this.getColumnDimension(); |
| 463 | final BigDecimal[][] outData = new BigDecimal[nRows][nCols]; |
| 464 | for (int row = 0; row < nRows; row++) { |
| 465 | final BigDecimal[] dataRow = data[row]; |
| 466 | final BigDecimal[] outDataRow = outData[row]; |
| 467 | for (int col = 0; col < nCols; col++) { |
| 468 | BigDecimal sum = ZERO; |
| 469 | for (int i = 0; i < nSum; i++) { |
| 470 | sum = sum.add(dataRow[i].multiply(m.data[i][col])); |
| 471 | } |
| 472 | outDataRow[col] = sum; |
| 473 | } |
| 474 | } |
| 475 | return new BigMatrixImpl(outData, false); |
| 476 | } |
| 477 | |
| 478 | /** |
| 479 | * Returns the result premultiplying this by <code>m</code>. |
| 480 | * @param m matrix to premultiply by |
| 481 | * @return m * this |
| 482 | * @throws IllegalArgumentException |
| 483 | * if rowDimension(this) != columnDimension(m) |
| 484 | */ |
| 485 | public BigMatrix preMultiply(BigMatrix m) throws IllegalArgumentException { |
| 486 | return m.multiply(this); |
| 487 | } |
| 488 | |
| 489 | /** |
| 490 | * Returns matrix entries as a two-dimensional array. |
| 491 | * <p> |
| 492 | * Makes a fresh copy of the underlying data.</p> |
| 493 | * |
| 494 | * @return 2-dimensional array of entries |
| 495 | */ |
| 496 | public BigDecimal[][] getData() { |
| 497 | return copyOut(); |
| 498 | } |
| 499 | |
| 500 | /** |
| 501 | * Returns matrix entries as a two-dimensional array. |
| 502 | * <p> |
| 503 | * Makes a fresh copy of the underlying data converted to |
| 504 | * <code>double</code> values.</p> |
| 505 | * |
| 506 | * @return 2-dimensional array of entries |
| 507 | */ |
| 508 | public double[][] getDataAsDoubleArray() { |
| 509 | final int nRows = getRowDimension(); |
| 510 | final int nCols = getColumnDimension(); |
| 511 | final double d[][] = new double[nRows][nCols]; |
| 512 | for (int i = 0; i < nRows; i++) { |
| 513 | for (int j = 0; j < nCols; j++) { |
| 514 | d[i][j] = data[i][j].doubleValue(); |
| 515 | } |
| 516 | } |
| 517 | return d; |
| 518 | } |
| 519 | |
| 520 | /** |
| 521 | * Returns a reference to the underlying data array. |
| 522 | * <p> |
| 523 | * Does not make a fresh copy of the underlying data.</p> |
| 524 | * |
| 525 | * @return 2-dimensional array of entries |
| 526 | */ |
| 527 | public BigDecimal[][] getDataRef() { |
| 528 | return data; |
| 529 | } |
| 530 | |
| 531 | /*** |
| 532 | * Gets the rounding mode for division operations |
| 533 | * The default is {@link java.math.BigDecimal#ROUND_HALF_UP} |
| 534 | * @see BigDecimal |
| 535 | * @return the rounding mode. |
| 536 | */ |
| 537 | public int getRoundingMode() { |
| 538 | return roundingMode; |
| 539 | } |
| 540 | |
| 541 | /*** |
| 542 | * Sets the rounding mode for decimal divisions. |
| 543 | * @see BigDecimal |
| 544 | * @param roundingMode rounding mode for decimal divisions |
| 545 | */ |
| 546 | public void setRoundingMode(int roundingMode) { |
| 547 | this.roundingMode = roundingMode; |
| 548 | } |
| 549 | |
| 550 | /*** |
| 551 | * Sets the scale for division operations. |
| 552 | * The default is 64 |
| 553 | * @see BigDecimal |
| 554 | * @return the scale |
| 555 | */ |
| 556 | public int getScale() { |
| 557 | return scale; |
| 558 | } |
| 559 | |
| 560 | /*** |
| 561 | * Sets the scale for division operations. |
| 562 | * @see BigDecimal |
| 563 | * @param scale scale for division operations |
| 564 | */ |
| 565 | public void setScale(int scale) { |
| 566 | this.scale = scale; |
| 567 | } |
| 568 | |
| 569 | /** |
| 570 | * Returns the <a href="http://mathworld.wolfram.com/MaximumAbsoluteRowSumNorm.html"> |
| 571 | * maximum absolute row sum norm</a> of the matrix. |
| 572 | * |
| 573 | * @return norm |
| 574 | */ |
| 575 | public BigDecimal getNorm() { |
| 576 | BigDecimal maxColSum = ZERO; |
| 577 | for (int col = 0; col < this.getColumnDimension(); col++) { |
| 578 | BigDecimal sum = ZERO; |
| 579 | for (int row = 0; row < this.getRowDimension(); row++) { |
| 580 | sum = sum.add(data[row][col].abs()); |
| 581 | } |
| 582 | maxColSum = maxColSum.max(sum); |
| 583 | } |
| 584 | return maxColSum; |
| 585 | } |
| 586 | |
| 587 | /** |
| 588 | * Gets a submatrix. Rows and columns are indicated |
| 589 | * counting from 0 to n-1. |
| 590 | * |
| 591 | * @param startRow Initial row index |
| 592 | * @param endRow Final row index |
| 593 | * @param startColumn Initial column index |
| 594 | * @param endColumn Final column index |
| 595 | * @return The subMatrix containing the data of the |
| 596 | * specified rows and columns |
| 597 | * @exception MatrixIndexException if row or column selections are not valid |
| 598 | */ |
| 599 | public BigMatrix getSubMatrix(int startRow, int endRow, |
| 600 | int startColumn, int endColumn) |
| 601 | throws MatrixIndexException { |
| 602 | |
| 603 | MatrixUtils.checkRowIndex(this, startRow); |
| 604 | MatrixUtils.checkRowIndex(this, endRow); |
| 605 | if (startRow > endRow) { |
| 606 | throw new MatrixIndexException(LocalizedFormats.INITIAL_ROW_AFTER_FINAL_ROW, |
| 607 | startRow, endRow); |
| 608 | } |
| 609 | |
| 610 | MatrixUtils.checkColumnIndex(this, startColumn); |
| 611 | MatrixUtils.checkColumnIndex(this, endColumn); |
| 612 | if (startColumn > endColumn) { |
| 613 | throw new MatrixIndexException(LocalizedFormats.INITIAL_COLUMN_AFTER_FINAL_COLUMN, |
| 614 | startColumn, endColumn); |
| 615 | } |
| 616 | |
| 617 | final BigDecimal[][] subMatrixData = |
| 618 | new BigDecimal[endRow - startRow + 1][endColumn - startColumn + 1]; |
| 619 | for (int i = startRow; i <= endRow; i++) { |
| 620 | System.arraycopy(data[i], startColumn, |
| 621 | subMatrixData[i - startRow], 0, |
| 622 | endColumn - startColumn + 1); |
| 623 | } |
| 624 | |
| 625 | return new BigMatrixImpl(subMatrixData, false); |
| 626 | |
| 627 | } |
| 628 | |
| 629 | /** |
| 630 | * Gets a submatrix. Rows and columns are indicated |
| 631 | * counting from 0 to n-1. |
| 632 | * |
| 633 | * @param selectedRows Array of row indices must be non-empty |
| 634 | * @param selectedColumns Array of column indices must be non-empty |
| 635 | * @return The subMatrix containing the data in the |
| 636 | * specified rows and columns |
| 637 | * @exception MatrixIndexException if supplied row or column index arrays |
| 638 | * are not valid |
| 639 | */ |
| 640 | public BigMatrix getSubMatrix(int[] selectedRows, int[] selectedColumns) |
| 641 | throws MatrixIndexException { |
| 642 | |
| 643 | if (selectedRows.length * selectedColumns.length == 0) { |
| 644 | if (selectedRows.length == 0) { |
| 645 | throw new MatrixIndexException(LocalizedFormats.EMPTY_SELECTED_ROW_INDEX_ARRAY); |
| 646 | } |
| 647 | throw new MatrixIndexException(LocalizedFormats.EMPTY_SELECTED_COLUMN_INDEX_ARRAY); |
| 648 | } |
| 649 | |
| 650 | final BigDecimal[][] subMatrixData = |
| 651 | new BigDecimal[selectedRows.length][selectedColumns.length]; |
| 652 | try { |
| 653 | for (int i = 0; i < selectedRows.length; i++) { |
| 654 | final BigDecimal[] subI = subMatrixData[i]; |
| 655 | final BigDecimal[] dataSelectedI = data[selectedRows[i]]; |
| 656 | for (int j = 0; j < selectedColumns.length; j++) { |
| 657 | subI[j] = dataSelectedI[selectedColumns[j]]; |
| 658 | } |
| 659 | } |
| 660 | } catch (ArrayIndexOutOfBoundsException e) { |
| 661 | // we redo the loop with checks enabled |
| 662 | // in order to generate an appropriate message |
| 663 | for (final int row : selectedRows) { |
| 664 | MatrixUtils.checkRowIndex(this, row); |
| 665 | } |
| 666 | for (final int column : selectedColumns) { |
| 667 | MatrixUtils.checkColumnIndex(this, column); |
| 668 | } |
| 669 | } |
| 670 | return new BigMatrixImpl(subMatrixData, false); |
| 671 | } |
| 672 | |
| 673 | /** |
| 674 | * Replace the submatrix starting at <code>row, column</code> using data in |
| 675 | * the input <code>subMatrix</code> array. Indexes are 0-based. |
| 676 | * <p> |
| 677 | * Example:<br> |
| 678 | * Starting with <pre> |
| 679 | * 1 2 3 4 |
| 680 | * 5 6 7 8 |
| 681 | * 9 0 1 2 |
| 682 | * </pre> |
| 683 | * and <code>subMatrix = {{3, 4} {5,6}}</code>, invoking |
| 684 | * <code>setSubMatrix(subMatrix,1,1))</code> will result in <pre> |
| 685 | * 1 2 3 4 |
| 686 | * 5 3 4 8 |
| 687 | * 9 5 6 2 |
| 688 | * </pre></p> |
| 689 | * |
| 690 | * @param subMatrix array containing the submatrix replacement data |
| 691 | * @param row row coordinate of the top, left element to be replaced |
| 692 | * @param column column coordinate of the top, left element to be replaced |
| 693 | * @throws MatrixIndexException if subMatrix does not fit into this |
| 694 | * matrix from element in (row, column) |
| 695 | * @throws IllegalArgumentException if <code>subMatrix</code> is not rectangular |
| 696 | * (not all rows have the same length) or empty |
| 697 | * @throws NullPointerException if <code>subMatrix</code> is null |
| 698 | * @since 1.1 |
| 699 | */ |
| 700 | public void setSubMatrix(BigDecimal[][] subMatrix, int row, int column) |
| 701 | throws MatrixIndexException { |
| 702 | |
| 703 | final int nRows = subMatrix.length; |
| 704 | if (nRows == 0) { |
| 705 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW); |
| 706 | } |
| 707 | |
| 708 | final int nCols = subMatrix[0].length; |
| 709 | if (nCols == 0) { |
| 710 | throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN); |
| 711 | } |
| 712 | |
| 713 | for (int r = 1; r < nRows; r++) { |
| 714 | if (subMatrix[r].length != nCols) { |
| 715 | throw MathRuntimeException.createIllegalArgumentException( |
| 716 | LocalizedFormats.DIFFERENT_ROWS_LENGTHS, |
| 717 | nCols, subMatrix[r].length); |
| 718 | } |
| 719 | } |
| 720 | |
| 721 | if (data == null) { |
| 722 | if (row > 0) { |
| 723 | throw MathRuntimeException.createIllegalStateException( |
| 724 | LocalizedFormats.FIRST_ROWS_NOT_INITIALIZED_YET, |
| 725 | row); |
| 726 | } |
| 727 | if (column > 0) { |
| 728 | throw MathRuntimeException.createIllegalStateException( |
| 729 | LocalizedFormats.FIRST_COLUMNS_NOT_INITIALIZED_YET, |
| 730 | column); |
| 731 | } |
| 732 | data = new BigDecimal[nRows][nCols]; |
| 733 | System.arraycopy(subMatrix, 0, data, 0, subMatrix.length); |
| 734 | } else { |
| 735 | MatrixUtils.checkRowIndex(this, row); |
| 736 | MatrixUtils.checkColumnIndex(this, column); |
| 737 | MatrixUtils.checkRowIndex(this, nRows + row - 1); |
| 738 | MatrixUtils.checkColumnIndex(this, nCols + column - 1); |
| 739 | } |
| 740 | for (int i = 0; i < nRows; i++) { |
| 741 | System.arraycopy(subMatrix[i], 0, data[row + i], column, nCols); |
| 742 | } |
| 743 | |
| 744 | lu = null; |
| 745 | |
| 746 | } |
| 747 | |
| 748 | /** |
| 749 | * Returns the entries in row number <code>row</code> |
| 750 | * as a row matrix. Row indices start at 0. |
| 751 | * |
| 752 | * @param row the row to be fetched |
| 753 | * @return row matrix |
| 754 | * @throws MatrixIndexException if the specified row index is invalid |
| 755 | */ |
| 756 | public BigMatrix getRowMatrix(int row) throws MatrixIndexException { |
| 757 | MatrixUtils.checkRowIndex(this, row); |
| 758 | final int ncols = this.getColumnDimension(); |
| 759 | final BigDecimal[][] out = new BigDecimal[1][ncols]; |
| 760 | System.arraycopy(data[row], 0, out[0], 0, ncols); |
| 761 | return new BigMatrixImpl(out, false); |
| 762 | } |
| 763 | |
| 764 | /** |
| 765 | * Returns the entries in column number <code>column</code> |
| 766 | * as a column matrix. Column indices start at 0. |
| 767 | * |
| 768 | * @param column the column to be fetched |
| 769 | * @return column matrix |
| 770 | * @throws MatrixIndexException if the specified column index is invalid |
| 771 | */ |
| 772 | public BigMatrix getColumnMatrix(int column) throws MatrixIndexException { |
| 773 | MatrixUtils.checkColumnIndex(this, column); |
| 774 | final int nRows = this.getRowDimension(); |
| 775 | final BigDecimal[][] out = new BigDecimal[nRows][1]; |
| 776 | for (int row = 0; row < nRows; row++) { |
| 777 | out[row][0] = data[row][column]; |
| 778 | } |
| 779 | return new BigMatrixImpl(out, false); |
| 780 | } |
| 781 | |
| 782 | /** |
| 783 | * Returns the entries in row number <code>row</code> as an array. |
| 784 | * <p> |
| 785 | * Row indices start at 0. A <code>MatrixIndexException</code> is thrown |
| 786 | * unless <code>0 <= row < rowDimension.</code></p> |
| 787 | * |
| 788 | * @param row the row to be fetched |
| 789 | * @return array of entries in the row |
| 790 | * @throws MatrixIndexException if the specified row index is not valid |
| 791 | */ |
| 792 | public BigDecimal[] getRow(int row) throws MatrixIndexException { |
| 793 | MatrixUtils.checkRowIndex(this, row); |
| 794 | final int ncols = this.getColumnDimension(); |
| 795 | final BigDecimal[] out = new BigDecimal[ncols]; |
| 796 | System.arraycopy(data[row], 0, out, 0, ncols); |
| 797 | return out; |
| 798 | } |
| 799 | |
| 800 | /** |
| 801 | * Returns the entries in row number <code>row</code> as an array |
| 802 | * of double values. |
| 803 | * <p> |
| 804 | * Row indices start at 0. A <code>MatrixIndexException</code> is thrown |
| 805 | * unless <code>0 <= row < rowDimension.</code></p> |
| 806 | * |
| 807 | * @param row the row to be fetched |
| 808 | * @return array of entries in the row |
| 809 | * @throws MatrixIndexException if the specified row index is not valid |
| 810 | */ |
| 811 | public double[] getRowAsDoubleArray(int row) throws MatrixIndexException { |
| 812 | MatrixUtils.checkRowIndex(this, row); |
| 813 | final int ncols = this.getColumnDimension(); |
| 814 | final double[] out = new double[ncols]; |
| 815 | for (int i=0;i<ncols;i++) { |
| 816 | out[i] = data[row][i].doubleValue(); |
| 817 | } |
| 818 | return out; |
| 819 | } |
| 820 | |
| 821 | /** |
| 822 | * Returns the entries in column number <code>col</code> as an array. |
| 823 | * <p> |
| 824 | * Column indices start at 0. A <code>MatrixIndexException</code> is thrown |
| 825 | * unless <code>0 <= column < columnDimension.</code></p> |
| 826 | * |
| 827 | * @param col the column to be fetched |
| 828 | * @return array of entries in the column |
| 829 | * @throws MatrixIndexException if the specified column index is not valid |
| 830 | */ |
| 831 | public BigDecimal[] getColumn(int col) throws MatrixIndexException { |
| 832 | MatrixUtils.checkColumnIndex(this, col); |
| 833 | final int nRows = this.getRowDimension(); |
| 834 | final BigDecimal[] out = new BigDecimal[nRows]; |
| 835 | for (int i = 0; i < nRows; i++) { |
| 836 | out[i] = data[i][col]; |
| 837 | } |
| 838 | return out; |
| 839 | } |
| 840 | |
| 841 | /** |
| 842 | * Returns the entries in column number <code>col</code> as an array |
| 843 | * of double values. |
| 844 | * <p> |
| 845 | * Column indices start at 0. A <code>MatrixIndexException</code> is thrown |
| 846 | * unless <code>0 <= column < columnDimension.</code></p> |
| 847 | * |
| 848 | * @param col the column to be fetched |
| 849 | * @return array of entries in the column |
| 850 | * @throws MatrixIndexException if the specified column index is not valid |
| 851 | */ |
| 852 | public double[] getColumnAsDoubleArray(int col) throws MatrixIndexException { |
| 853 | MatrixUtils.checkColumnIndex(this, col); |
| 854 | final int nrows = this.getRowDimension(); |
| 855 | final double[] out = new double[nrows]; |
| 856 | for (int i=0;i<nrows;i++) { |
| 857 | out[i] = data[i][col].doubleValue(); |
| 858 | } |
| 859 | return out; |
| 860 | } |
| 861 | |
| 862 | /** |
| 863 | * Returns the entry in the specified row and column. |
| 864 | * <p> |
| 865 | * Row and column indices start at 0 and must satisfy |
| 866 | * <ul> |
| 867 | * <li><code>0 <= row < rowDimension</code></li> |
| 868 | * <li><code> 0 <= column < columnDimension</code></li> |
| 869 | * </ul> |
| 870 | * otherwise a <code>MatrixIndexException</code> is thrown.</p> |
| 871 | * |
| 872 | * @param row row location of entry to be fetched |
| 873 | * @param column column location of entry to be fetched |
| 874 | * @return matrix entry in row,column |
| 875 | * @throws MatrixIndexException if the row or column index is not valid |
| 876 | */ |
| 877 | public BigDecimal getEntry(int row, int column) |
| 878 | throws MatrixIndexException { |
| 879 | try { |
| 880 | return data[row][column]; |
| 881 | } catch (ArrayIndexOutOfBoundsException e) { |
| 882 | throw new MatrixIndexException( |
| 883 | LocalizedFormats.NO_SUCH_MATRIX_ENTRY, |
| 884 | row, column, getRowDimension(), getColumnDimension()); |
| 885 | } |
| 886 | } |
| 887 | |
| 888 | /** |
| 889 | * Returns the entry in the specified row and column as a double. |
| 890 | * <p> |
| 891 | * Row and column indices start at 0 and must satisfy |
| 892 | * <ul> |
| 893 | * <li><code>0 <= row < rowDimension</code></li> |
| 894 | * <li><code> 0 <= column < columnDimension</code></li> |
| 895 | * </ul> |
| 896 | * otherwise a <code>MatrixIndexException</code> is thrown.</p> |
| 897 | * |
| 898 | * @param row row location of entry to be fetched |
| 899 | * @param column column location of entry to be fetched |
| 900 | * @return matrix entry in row,column |
| 901 | * @throws MatrixIndexException if the row |
| 902 | * or column index is not valid |
| 903 | */ |
| 904 | public double getEntryAsDouble(int row, int column) throws MatrixIndexException { |
| 905 | return getEntry(row,column).doubleValue(); |
| 906 | } |
| 907 | |
| 908 | /** |
| 909 | * Returns the transpose matrix. |
| 910 | * |
| 911 | * @return transpose matrix |
| 912 | */ |
| 913 | public BigMatrix transpose() { |
| 914 | final int nRows = this.getRowDimension(); |
| 915 | final int nCols = this.getColumnDimension(); |
| 916 | final BigDecimal[][] outData = new BigDecimal[nCols][nRows]; |
| 917 | for (int row = 0; row < nRows; row++) { |
| 918 | final BigDecimal[] dataRow = data[row]; |
| 919 | for (int col = 0; col < nCols; col++) { |
| 920 | outData[col][row] = dataRow[col]; |
| 921 | } |
| 922 | } |
| 923 | return new BigMatrixImpl(outData, false); |
| 924 | } |
| 925 | |
| 926 | /** |
| 927 | * Returns the inverse matrix if this matrix is invertible. |
| 928 | * |
| 929 | * @return inverse matrix |
| 930 | * @throws InvalidMatrixException if this is not invertible |
| 931 | */ |
| 932 | public BigMatrix inverse() throws InvalidMatrixException { |
| 933 | return solve(MatrixUtils.createBigIdentityMatrix(getRowDimension())); |
| 934 | } |
| 935 | |
| 936 | /** |
| 937 | * Returns the determinant of this matrix. |
| 938 | * |
| 939 | * @return determinant |
| 940 | * @throws InvalidMatrixException if matrix is not square |
| 941 | */ |
| 942 | public BigDecimal getDeterminant() throws InvalidMatrixException { |
| 943 | if (!isSquare()) { |
| 944 | throw new NonSquareMatrixException(getRowDimension(), getColumnDimension()); |
| 945 | } |
| 946 | if (isSingular()) { // note: this has side effect of attempting LU decomp if lu == null |
| 947 | return ZERO; |
| 948 | } else { |
| 949 | BigDecimal det = (parity == 1) ? ONE : ONE.negate(); |
| 950 | for (int i = 0; i < getRowDimension(); i++) { |
| 951 | det = det.multiply(lu[i][i]); |
| 952 | } |
| 953 | return det; |
| 954 | } |
| 955 | } |
| 956 | |
| 957 | /** |
| 958 | * Is this a square matrix? |
| 959 | * @return true if the matrix is square (rowDimension = columnDimension) |
| 960 | */ |
| 961 | public boolean isSquare() { |
| 962 | return getColumnDimension() == getRowDimension(); |
| 963 | } |
| 964 | |
| 965 | /** |
| 966 | * Is this a singular matrix? |
| 967 | * @return true if the matrix is singular |
| 968 | */ |
| 969 | public boolean isSingular() { |
| 970 | if (lu == null) { |
| 971 | try { |
| 972 | luDecompose(); |
| 973 | return false; |
| 974 | } catch (InvalidMatrixException ex) { |
| 975 | return true; |
| 976 | } |
| 977 | } else { // LU decomp must have been successfully performed |
| 978 | return false; // so the matrix is not singular |
| 979 | } |
| 980 | } |
| 981 | |
| 982 | /** |
| 983 | * Returns the number of rows in the matrix. |
| 984 | * |
| 985 | * @return rowDimension |
| 986 | */ |
| 987 | public int getRowDimension() { |
| 988 | return data.length; |
| 989 | } |
| 990 | |
| 991 | /** |
| 992 | * Returns the number of columns in the matrix. |
| 993 | * |
| 994 | * @return columnDimension |
| 995 | */ |
| 996 | public int getColumnDimension() { |
| 997 | return data[0].length; |
| 998 | } |
| 999 | |
| 1000 | /** |
| 1001 | * Returns the <a href="http://mathworld.wolfram.com/MatrixTrace.html"> |
| 1002 | * trace</a> of the matrix (the sum of the elements on the main diagonal). |
| 1003 | * |
| 1004 | * @return trace |
| 1005 | * |
| 1006 | * @throws IllegalArgumentException if this matrix is not square. |
| 1007 | */ |
| 1008 | public BigDecimal getTrace() throws IllegalArgumentException { |
| 1009 | if (!isSquare()) { |
| 1010 | throw new NonSquareMatrixException(getRowDimension(), getColumnDimension()); |
| 1011 | } |
| 1012 | BigDecimal trace = data[0][0]; |
| 1013 | for (int i = 1; i < this.getRowDimension(); i++) { |
| 1014 | trace = trace.add(data[i][i]); |
| 1015 | } |
| 1016 | return trace; |
| 1017 | } |
| 1018 | |
| 1019 | /** |
| 1020 | * Returns the result of multiplying this by the vector <code>v</code>. |
| 1021 | * |
| 1022 | * @param v the vector to operate on |
| 1023 | * @return this*v |
| 1024 | * @throws IllegalArgumentException if columnDimension != v.size() |
| 1025 | */ |
| 1026 | public BigDecimal[] operate(BigDecimal[] v) throws IllegalArgumentException { |
| 1027 | if (v.length != getColumnDimension()) { |
| 1028 | throw MathRuntimeException.createIllegalArgumentException( |
| 1029 | LocalizedFormats.VECTOR_LENGTH_MISMATCH, |
| 1030 | v.length, getColumnDimension() ); |
| 1031 | } |
| 1032 | final int nRows = this.getRowDimension(); |
| 1033 | final int nCols = this.getColumnDimension(); |
| 1034 | final BigDecimal[] out = new BigDecimal[nRows]; |
| 1035 | for (int row = 0; row < nRows; row++) { |
| 1036 | BigDecimal sum = ZERO; |
| 1037 | for (int i = 0; i < nCols; i++) { |
| 1038 | sum = sum.add(data[row][i].multiply(v[i])); |
| 1039 | } |
| 1040 | out[row] = sum; |
| 1041 | } |
| 1042 | return out; |
| 1043 | } |
| 1044 | |
| 1045 | /** |
| 1046 | * Returns the result of multiplying this by the vector <code>v</code>. |
| 1047 | * |
| 1048 | * @param v the vector to operate on |
| 1049 | * @return this*v |
| 1050 | * @throws IllegalArgumentException if columnDimension != v.size() |
| 1051 | */ |
| 1052 | public BigDecimal[] operate(double[] v) throws IllegalArgumentException { |
| 1053 | final BigDecimal bd[] = new BigDecimal[v.length]; |
| 1054 | for (int i = 0; i < bd.length; i++) { |
| 1055 | bd[i] = new BigDecimal(v[i]); |
| 1056 | } |
| 1057 | return operate(bd); |
| 1058 | } |
| 1059 | |
| 1060 | /** |
| 1061 | * Returns the (row) vector result of premultiplying this by the vector <code>v</code>. |
| 1062 | * |
| 1063 | * @param v the row vector to premultiply by |
| 1064 | * @return v*this |
| 1065 | * @throws IllegalArgumentException if rowDimension != v.size() |
| 1066 | */ |
| 1067 | public BigDecimal[] preMultiply(BigDecimal[] v) throws IllegalArgumentException { |
| 1068 | final int nRows = this.getRowDimension(); |
| 1069 | if (v.length != nRows) { |
| 1070 | throw MathRuntimeException.createIllegalArgumentException( |
| 1071 | LocalizedFormats.VECTOR_LENGTH_MISMATCH, |
| 1072 | v.length, nRows ); |
| 1073 | } |
| 1074 | final int nCols = this.getColumnDimension(); |
| 1075 | final BigDecimal[] out = new BigDecimal[nCols]; |
| 1076 | for (int col = 0; col < nCols; col++) { |
| 1077 | BigDecimal sum = ZERO; |
| 1078 | for (int i = 0; i < nRows; i++) { |
| 1079 | sum = sum.add(data[i][col].multiply(v[i])); |
| 1080 | } |
| 1081 | out[col] = sum; |
| 1082 | } |
| 1083 | return out; |
| 1084 | } |
| 1085 | |
| 1086 | /** |
| 1087 | * Returns a matrix of (column) solution vectors for linear systems with |
| 1088 | * coefficient matrix = this and constant vectors = columns of |
| 1089 | * <code>b</code>. |
| 1090 | * |
| 1091 | * @param b array of constants forming RHS of linear systems to |
| 1092 | * to solve |
| 1093 | * @return solution array |
| 1094 | * @throws IllegalArgumentException if this.rowDimension != row dimension |
| 1095 | * @throws InvalidMatrixException if this matrix is not square or is singular |
| 1096 | */ |
| 1097 | public BigDecimal[] solve(BigDecimal[] b) throws IllegalArgumentException, InvalidMatrixException { |
| 1098 | final int nRows = this.getRowDimension(); |
| 1099 | if (b.length != nRows) { |
| 1100 | throw MathRuntimeException.createIllegalArgumentException( |
| 1101 | LocalizedFormats.VECTOR_LENGTH_MISMATCH, |
| 1102 | b.length, nRows); |
| 1103 | } |
| 1104 | final BigMatrix bMatrix = new BigMatrixImpl(b); |
| 1105 | final BigDecimal[][] solution = ((BigMatrixImpl) (solve(bMatrix))).getDataRef(); |
| 1106 | final BigDecimal[] out = new BigDecimal[nRows]; |
| 1107 | for (int row = 0; row < nRows; row++) { |
| 1108 | out[row] = solution[row][0]; |
| 1109 | } |
| 1110 | return out; |
| 1111 | } |
| 1112 | |
| 1113 | /** |
| 1114 | * Returns a matrix of (column) solution vectors for linear systems with |
| 1115 | * coefficient matrix = this and constant vectors = columns of |
| 1116 | * <code>b</code>. |
| 1117 | * |
| 1118 | * @param b array of constants forming RHS of linear systems to |
| 1119 | * to solve |
| 1120 | * @return solution array |
| 1121 | * @throws IllegalArgumentException if this.rowDimension != row dimension |
| 1122 | * @throws InvalidMatrixException if this matrix is not square or is singular |
| 1123 | */ |
| 1124 | public BigDecimal[] solve(double[] b) throws IllegalArgumentException, InvalidMatrixException { |
| 1125 | final BigDecimal bd[] = new BigDecimal[b.length]; |
| 1126 | for (int i = 0; i < bd.length; i++) { |
| 1127 | bd[i] = new BigDecimal(b[i]); |
| 1128 | } |
| 1129 | return solve(bd); |
| 1130 | } |
| 1131 | |
| 1132 | /** |
| 1133 | * Returns a matrix of (column) solution vectors for linear systems with |
| 1134 | * coefficient matrix = this and constant vectors = columns of |
| 1135 | * <code>b</code>. |
| 1136 | * |
| 1137 | * @param b matrix of constant vectors forming RHS of linear systems to |
| 1138 | * to solve |
| 1139 | * @return matrix of solution vectors |
| 1140 | * @throws IllegalArgumentException if this.rowDimension != row dimension |
| 1141 | * @throws InvalidMatrixException if this matrix is not square or is singular |
| 1142 | */ |
| 1143 | public BigMatrix solve(BigMatrix b) throws IllegalArgumentException, InvalidMatrixException { |
| 1144 | if (b.getRowDimension() != getRowDimension()) { |
| 1145 | throw MathRuntimeException.createIllegalArgumentException( |
| 1146 | LocalizedFormats.DIMENSIONS_MISMATCH_2x2, |
| 1147 | b.getRowDimension(), b.getColumnDimension(), getRowDimension(), "n"); |
| 1148 | } |
| 1149 | if (!isSquare()) { |
| 1150 | throw new NonSquareMatrixException(getRowDimension(), getColumnDimension()); |
| 1151 | } |
| 1152 | if (this.isSingular()) { // side effect: compute LU decomp |
| 1153 | throw new SingularMatrixException(); |
| 1154 | } |
| 1155 | |
| 1156 | final int nCol = this.getColumnDimension(); |
| 1157 | final int nColB = b.getColumnDimension(); |
| 1158 | final int nRowB = b.getRowDimension(); |
| 1159 | |
| 1160 | // Apply permutations to b |
| 1161 | final BigDecimal[][] bp = new BigDecimal[nRowB][nColB]; |
| 1162 | for (int row = 0; row < nRowB; row++) { |
| 1163 | final BigDecimal[] bpRow = bp[row]; |
| 1164 | for (int col = 0; col < nColB; col++) { |
| 1165 | bpRow[col] = b.getEntry(permutation[row], col); |
| 1166 | } |
| 1167 | } |
| 1168 | |
| 1169 | // Solve LY = b |
| 1170 | for (int col = 0; col < nCol; col++) { |
| 1171 | for (int i = col + 1; i < nCol; i++) { |
| 1172 | final BigDecimal[] bpI = bp[i]; |
| 1173 | final BigDecimal[] luI = lu[i]; |
| 1174 | for (int j = 0; j < nColB; j++) { |
| 1175 | bpI[j] = bpI[j].subtract(bp[col][j].multiply(luI[col])); |
| 1176 | } |
| 1177 | } |
| 1178 | } |
| 1179 | |
| 1180 | // Solve UX = Y |
| 1181 | for (int col = nCol - 1; col >= 0; col--) { |
| 1182 | final BigDecimal[] bpCol = bp[col]; |
| 1183 | final BigDecimal luDiag = lu[col][col]; |
| 1184 | for (int j = 0; j < nColB; j++) { |
| 1185 | bpCol[j] = bpCol[j].divide(luDiag, scale, roundingMode); |
| 1186 | } |
| 1187 | for (int i = 0; i < col; i++) { |
| 1188 | final BigDecimal[] bpI = bp[i]; |
| 1189 | final BigDecimal[] luI = lu[i]; |
| 1190 | for (int j = 0; j < nColB; j++) { |
| 1191 | bpI[j] = bpI[j].subtract(bp[col][j].multiply(luI[col])); |
| 1192 | } |
| 1193 | } |
| 1194 | } |
| 1195 | |
| 1196 | return new BigMatrixImpl(bp, false); |
| 1197 | |
| 1198 | } |
| 1199 | |
| 1200 | /** |
| 1201 | * Computes a new |
| 1202 | * <a href="http://www.math.gatech.edu/~bourbaki/math2601/Web-notes/2num.pdf"> |
| 1203 | * LU decompostion</a> for this matrix, storing the result for use by other methods. |
| 1204 | * <p> |
| 1205 | * <strong>Implementation Note</strong>:<br> |
| 1206 | * Uses <a href="http://www.damtp.cam.ac.uk/user/fdl/people/sd/lectures/nummeth98/linear.htm"> |
| 1207 | * Crout's algortithm</a>, with partial pivoting.</p> |
| 1208 | * <p> |
| 1209 | * <strong>Usage Note</strong>:<br> |
| 1210 | * This method should rarely be invoked directly. Its only use is |
| 1211 | * to force recomputation of the LU decomposition when changes have been |
| 1212 | * made to the underlying data using direct array references. Changes |
| 1213 | * made using setXxx methods will trigger recomputation when needed |
| 1214 | * automatically.</p> |
| 1215 | * |
| 1216 | * @throws InvalidMatrixException if the matrix is non-square or singular. |
| 1217 | */ |
| 1218 | public void luDecompose() throws InvalidMatrixException { |
| 1219 | |
| 1220 | final int nRows = this.getRowDimension(); |
| 1221 | final int nCols = this.getColumnDimension(); |
| 1222 | if (nRows != nCols) { |
| 1223 | throw new NonSquareMatrixException(getRowDimension(), getColumnDimension()); |
| 1224 | } |
| 1225 | lu = this.getData(); |
| 1226 | |
| 1227 | // Initialize permutation array and parity |
| 1228 | permutation = new int[nRows]; |
| 1229 | for (int row = 0; row < nRows; row++) { |
| 1230 | permutation[row] = row; |
| 1231 | } |
| 1232 | parity = 1; |
| 1233 | |
| 1234 | // Loop over columns |
| 1235 | for (int col = 0; col < nCols; col++) { |
| 1236 | |
| 1237 | BigDecimal sum = ZERO; |
| 1238 | |
| 1239 | // upper |
| 1240 | for (int row = 0; row < col; row++) { |
| 1241 | final BigDecimal[] luRow = lu[row]; |
| 1242 | sum = luRow[col]; |
| 1243 | for (int i = 0; i < row; i++) { |
| 1244 | sum = sum.subtract(luRow[i].multiply(lu[i][col])); |
| 1245 | } |
| 1246 | luRow[col] = sum; |
| 1247 | } |
| 1248 | |
| 1249 | // lower |
| 1250 | int max = col; // permutation row |
| 1251 | BigDecimal largest = ZERO; |
| 1252 | for (int row = col; row < nRows; row++) { |
| 1253 | final BigDecimal[] luRow = lu[row]; |
| 1254 | sum = luRow[col]; |
| 1255 | for (int i = 0; i < col; i++) { |
| 1256 | sum = sum.subtract(luRow[i].multiply(lu[i][col])); |
| 1257 | } |
| 1258 | luRow[col] = sum; |
| 1259 | |
| 1260 | // maintain best permutation choice |
| 1261 | if (sum.abs().compareTo(largest) == 1) { |
| 1262 | largest = sum.abs(); |
| 1263 | max = row; |
| 1264 | } |
| 1265 | } |
| 1266 | |
| 1267 | // Singularity check |
| 1268 | if (lu[max][col].abs().compareTo(TOO_SMALL) <= 0) { |
| 1269 | lu = null; |
| 1270 | throw new SingularMatrixException(); |
| 1271 | } |
| 1272 | |
| 1273 | // Pivot if necessary |
| 1274 | if (max != col) { |
| 1275 | BigDecimal tmp = ZERO; |
| 1276 | for (int i = 0; i < nCols; i++) { |
| 1277 | tmp = lu[max][i]; |
| 1278 | lu[max][i] = lu[col][i]; |
| 1279 | lu[col][i] = tmp; |
| 1280 | } |
| 1281 | int temp = permutation[max]; |
| 1282 | permutation[max] = permutation[col]; |
| 1283 | permutation[col] = temp; |
| 1284 | parity = -parity; |
| 1285 | } |
| 1286 | |
| 1287 | // Divide the lower elements by the "winning" diagonal elt. |
| 1288 | final BigDecimal luDiag = lu[col][col]; |
| 1289 | for (int row = col + 1; row < nRows; row++) { |
| 1290 | final BigDecimal[] luRow = lu[row]; |
| 1291 | luRow[col] = luRow[col].divide(luDiag, scale, roundingMode); |
| 1292 | } |
| 1293 | |
| 1294 | } |
| 1295 | |
| 1296 | } |
| 1297 | |
| 1298 | /** |
| 1299 | * Get a string representation for this matrix. |
| 1300 | * @return a string representation for this matrix |
| 1301 | */ |
| 1302 | @Override |
| 1303 | public String toString() { |
| 1304 | StringBuilder res = new StringBuilder(); |
| 1305 | res.append("BigMatrixImpl{"); |
| 1306 | if (data != null) { |
| 1307 | for (int i = 0; i < data.length; i++) { |
| 1308 | if (i > 0) { |
| 1309 | res.append(","); |
| 1310 | } |
| 1311 | res.append("{"); |
| 1312 | for (int j = 0; j < data[0].length; j++) { |
| 1313 | if (j > 0) { |
| 1314 | res.append(","); |
| 1315 | } |
| 1316 | res.append(data[i][j]); |
| 1317 | } |
| 1318 | res.append("}"); |
| 1319 | } |
| 1320 | } |
| 1321 | res.append("}"); |
| 1322 | return res.toString(); |
| 1323 | } |
| 1324 | |
| 1325 | /** |
| 1326 | * Returns true iff <code>object</code> is a |
| 1327 | * <code>BigMatrixImpl</code> instance with the same dimensions as this |
| 1328 | * and all corresponding matrix entries are equal. BigDecimal.equals |
| 1329 | * is used to compare corresponding entries. |
| 1330 | * |
| 1331 | * @param object the object to test equality against. |
| 1332 | * @return true if object equals this |
| 1333 | */ |
| 1334 | @Override |
| 1335 | public boolean equals(Object object) { |
| 1336 | if (object == this ) { |
| 1337 | return true; |
| 1338 | } |
| 1339 | if (object instanceof BigMatrixImpl == false) { |
| 1340 | return false; |
| 1341 | } |
| 1342 | final BigMatrix m = (BigMatrix) object; |
| 1343 | final int nRows = getRowDimension(); |
| 1344 | final int nCols = getColumnDimension(); |
| 1345 | if (m.getColumnDimension() != nCols || m.getRowDimension() != nRows) { |
| 1346 | return false; |
| 1347 | } |
| 1348 | for (int row = 0; row < nRows; row++) { |
| 1349 | final BigDecimal[] dataRow = data[row]; |
| 1350 | for (int col = 0; col < nCols; col++) { |
| 1351 | if (!dataRow[col].equals(m.getEntry(row, col))) { |
| 1352 | return false; |
| 1353 | } |
| 1354 | } |
| 1355 | } |
| 1356 | return true; |
| 1357 | } |
| 1358 | |
| 1359 | /** |
| 1360 | * Computes a hashcode for the matrix. |
| 1361 | * |
| 1362 | * @return hashcode for matrix |
| 1363 | */ |
| 1364 | @Override |
| 1365 | public int hashCode() { |
| 1366 | int ret = 7; |
| 1367 | final int nRows = getRowDimension(); |
| 1368 | final int nCols = getColumnDimension(); |
| 1369 | ret = ret * 31 + nRows; |
| 1370 | ret = ret * 31 + nCols; |
| 1371 | for (int row = 0; row < nRows; row++) { |
| 1372 | final BigDecimal[] dataRow = data[row]; |
| 1373 | for (int col = 0; col < nCols; col++) { |
| 1374 | ret = ret * 31 + (11 * (row+1) + 17 * (col+1)) * |
| 1375 | dataRow[col].hashCode(); |
| 1376 | } |
| 1377 | } |
| 1378 | return ret; |
| 1379 | } |
| 1380 | |
| 1381 | //------------------------ Protected methods |
| 1382 | |
| 1383 | /** |
| 1384 | * Returns the LU decomposition as a BigMatrix. |
| 1385 | * Returns a fresh copy of the cached LU matrix if this has been computed; |
| 1386 | * otherwise the composition is computed and cached for use by other methods. |
| 1387 | * Since a copy is returned in either case, changes to the returned matrix do not |
| 1388 | * affect the LU decomposition property. |
| 1389 | * <p> |
| 1390 | * The matrix returned is a compact representation of the LU decomposition. |
| 1391 | * Elements below the main diagonal correspond to entries of the "L" matrix; |
| 1392 | * elements on and above the main diagonal correspond to entries of the "U" |
| 1393 | * matrix.</p> |
| 1394 | * <p> |
| 1395 | * Example: <pre> |
| 1396 | * |
| 1397 | * Returned matrix L U |
| 1398 | * 2 3 1 1 0 0 2 3 1 |
| 1399 | * 5 4 6 5 1 0 0 4 6 |
| 1400 | * 1 7 8 1 7 1 0 0 8 |
| 1401 | * </pre> |
| 1402 | * |
| 1403 | * The L and U matrices satisfy the matrix equation LU = permuteRows(this), <br> |
| 1404 | * where permuteRows reorders the rows of the matrix to follow the order determined |
| 1405 | * by the <a href=#getPermutation()>permutation</a> property.</p> |
| 1406 | * |
| 1407 | * @return LU decomposition matrix |
| 1408 | * @throws InvalidMatrixException if the matrix is non-square or singular. |
| 1409 | */ |
| 1410 | protected BigMatrix getLUMatrix() throws InvalidMatrixException { |
| 1411 | if (lu == null) { |
| 1412 | luDecompose(); |
| 1413 | } |
| 1414 | return new BigMatrixImpl(lu); |
| 1415 | } |
| 1416 | |
| 1417 | /** |
| 1418 | * Returns the permutation associated with the lu decomposition. |
| 1419 | * The entries of the array represent a permutation of the numbers 0, ... , nRows - 1. |
| 1420 | * <p> |
| 1421 | * Example: |
| 1422 | * permutation = [1, 2, 0] means current 2nd row is first, current third row is second |
| 1423 | * and current first row is last.</p> |
| 1424 | * <p> |
| 1425 | * Returns a fresh copy of the array.</p> |
| 1426 | * |
| 1427 | * @return the permutation |
| 1428 | */ |
| 1429 | protected int[] getPermutation() { |
| 1430 | final int[] out = new int[permutation.length]; |
| 1431 | System.arraycopy(permutation, 0, out, 0, permutation.length); |
| 1432 | return out; |
| 1433 | } |
| 1434 | |
| 1435 | //------------------------ Private methods |
| 1436 | |
| 1437 | /** |
| 1438 | * Returns a fresh copy of the underlying data array. |
| 1439 | * |
| 1440 | * @return a copy of the underlying data array. |
| 1441 | */ |
| 1442 | private BigDecimal[][] copyOut() { |
| 1443 | final int nRows = this.getRowDimension(); |
| 1444 | final BigDecimal[][] out = new BigDecimal[nRows][this.getColumnDimension()]; |
| 1445 | // can't copy 2-d array in one shot, otherwise get row references |
| 1446 | for (int i = 0; i < nRows; i++) { |
| 1447 | System.arraycopy(data[i], 0, out[i], 0, data[i].length); |
| 1448 | } |
| 1449 | return out; |
| 1450 | } |
| 1451 | |
| 1452 | /** |
| 1453 | * Replaces data with a fresh copy of the input array. |
| 1454 | * <p> |
| 1455 | * Verifies that the input array is rectangular and non-empty.</p> |
| 1456 | * |
| 1457 | * @param in data to copy in |
| 1458 | * @throws IllegalArgumentException if input array is emtpy or not |
| 1459 | * rectangular |
| 1460 | * @throws NullPointerException if input array is null |
| 1461 | */ |
| 1462 | private void copyIn(BigDecimal[][] in) { |
| 1463 | setSubMatrix(in,0,0); |
| 1464 | } |
| 1465 | |
| 1466 | /** |
| 1467 | * Replaces data with a fresh copy of the input array. |
| 1468 | * |
| 1469 | * @param in data to copy in |
| 1470 | */ |
| 1471 | private void copyIn(double[][] in) { |
| 1472 | final int nRows = in.length; |
| 1473 | final int nCols = in[0].length; |
| 1474 | data = new BigDecimal[nRows][nCols]; |
| 1475 | for (int i = 0; i < nRows; i++) { |
| 1476 | final BigDecimal[] dataI = data[i]; |
| 1477 | final double[] inI = in[i]; |
| 1478 | for (int j = 0; j < nCols; j++) { |
| 1479 | dataI[j] = new BigDecimal(inI[j]); |
| 1480 | } |
| 1481 | } |
| 1482 | lu = null; |
| 1483 | } |
| 1484 | |
| 1485 | /** |
| 1486 | * Replaces data with BigDecimals represented by the strings in the input |
| 1487 | * array. |
| 1488 | * |
| 1489 | * @param in data to copy in |
| 1490 | */ |
| 1491 | private void copyIn(String[][] in) { |
| 1492 | final int nRows = in.length; |
| 1493 | final int nCols = in[0].length; |
| 1494 | data = new BigDecimal[nRows][nCols]; |
| 1495 | for (int i = 0; i < nRows; i++) { |
| 1496 | final BigDecimal[] dataI = data[i]; |
| 1497 | final String[] inI = in[i]; |
| 1498 | for (int j = 0; j < nCols; j++) { |
| 1499 | dataI[j] = new BigDecimal(inI[j]); |
| 1500 | } |
| 1501 | } |
| 1502 | lu = null; |
| 1503 | } |
| 1504 | |
| 1505 | } |