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.ode.nonstiff; 19 20 import org.apache.commons.math.exception.util.LocalizedFormats; 21 import org.apache.commons.math.ode.AbstractIntegrator; 22 import org.apache.commons.math.ode.DerivativeException; 23 import org.apache.commons.math.ode.ExtendedFirstOrderDifferentialEquations; 24 import org.apache.commons.math.ode.FirstOrderDifferentialEquations; 25 import org.apache.commons.math.ode.IntegratorException; 26 import org.apache.commons.math.util.FastMath; 27 28 /** 29 * This abstract class holds the common part of all adaptive 30 * stepsize integrators for Ordinary Differential Equations. 31 * 32 * <p>These algorithms perform integration with stepsize control, which 33 * means the user does not specify the integration step but rather a 34 * tolerance on error. The error threshold is computed as 35 * <pre> 36 * threshold_i = absTol_i + relTol_i * max (abs (ym), abs (ym+1)) 37 * </pre> 38 * where absTol_i is the absolute tolerance for component i of the 39 * state vector and relTol_i is the relative tolerance for the same 40 * component. The user can also use only two scalar values absTol and 41 * relTol which will be used for all components. 42 * </p> 43 * 44 * <p>If the Ordinary Differential Equations is an {@link ExtendedFirstOrderDifferentialEquations 45 * extended ODE} rather than a {@link FirstOrderDifferentialEquations basic ODE}, 46 * then <em>only</em> the {@link ExtendedFirstOrderDifferentialEquations#getMainSetDimension() 47 * main set} part of the state vector is used for stepsize control, not the complete 48 * state vector. 49 * </p> 50 * 51 * <p>If the estimated error for ym+1 is such that 52 * <pre> 53 * sqrt((sum (errEst_i / threshold_i)^2 ) / n) < 1 54 * </pre> 55 * 56 * (where n is the main set dimension) then the step is accepted, 57 * otherwise the step is rejected and a new attempt is made with a new 58 * stepsize.</p> 59 * 60 * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 fvr. 2011) $ 61 * @since 1.2 62 * 63 */ 64 65 public abstract class AdaptiveStepsizeIntegrator 66 extends AbstractIntegrator { 67 68 /** Allowed absolute scalar error. */ 69 protected final double scalAbsoluteTolerance; 70 71 /** Allowed relative scalar error. */ 72 protected final double scalRelativeTolerance; 73 74 /** Allowed absolute vectorial error. */ 75 protected final double[] vecAbsoluteTolerance; 76 77 /** Allowed relative vectorial error. */ 78 protected final double[] vecRelativeTolerance; 79 80 /** Main set dimension. */ 81 protected int mainSetDimension; 82 83 /** User supplied initial step. */ 84 private double initialStep; 85 86 /** Minimal step. */ 87 private final double minStep; 88 89 /** Maximal step. */ 90 private final double maxStep; 91 92 /** Build an integrator with the given stepsize bounds. 93 * The default step handler does nothing. 94 * @param name name of the method 95 * @param minStep minimal step (must be positive even for backward 96 * integration), the last step can be smaller than this 97 * @param maxStep maximal step (must be positive even for backward 98 * integration) 99 * @param scalAbsoluteTolerance allowed absolute error 100 * @param scalRelativeTolerance allowed relative error 101 */ 102 public AdaptiveStepsizeIntegrator(final String name, 103 final double minStep, final double maxStep, 104 final double scalAbsoluteTolerance, 105 final double scalRelativeTolerance) { 106 107 super(name); 108 109 this.minStep = FastMath.abs(minStep); 110 this.maxStep = FastMath.abs(maxStep); 111 this.initialStep = -1.0; 112 113 this.scalAbsoluteTolerance = scalAbsoluteTolerance; 114 this.scalRelativeTolerance = scalRelativeTolerance; 115 this.vecAbsoluteTolerance = null; 116 this.vecRelativeTolerance = null; 117 118 resetInternalState(); 119 120 } 121 122 /** Build an integrator with the given stepsize bounds. 123 * The default step handler does nothing. 124 * @param name name of the method 125 * @param minStep minimal step (must be positive even for backward 126 * integration), the last step can be smaller than this 127 * @param maxStep maximal step (must be positive even for backward 128 * integration) 129 * @param vecAbsoluteTolerance allowed absolute error 130 * @param vecRelativeTolerance allowed relative error 131 */ 132 public AdaptiveStepsizeIntegrator(final String name, 133 final double minStep, final double maxStep, 134 final double[] vecAbsoluteTolerance, 135 final double[] vecRelativeTolerance) { 136 137 super(name); 138 139 this.minStep = minStep; 140 this.maxStep = maxStep; 141 this.initialStep = -1.0; 142 143 this.scalAbsoluteTolerance = 0; 144 this.scalRelativeTolerance = 0; 145 this.vecAbsoluteTolerance = vecAbsoluteTolerance.clone(); 146 this.vecRelativeTolerance = vecRelativeTolerance.clone(); 147 148 resetInternalState(); 149 150 } 151 152 /** Set the initial step size. 153 * <p>This method allows the user to specify an initial positive 154 * step size instead of letting the integrator guess it by 155 * itself. If this method is not called before integration is 156 * started, the initial step size will be estimated by the 157 * integrator.</p> 158 * @param initialStepSize initial step size to use (must be positive even 159 * for backward integration ; providing a negative value or a value 160 * outside of the min/max step interval will lead the integrator to 161 * ignore the value and compute the initial step size by itself) 162 */ 163 public void setInitialStepSize(final double initialStepSize) { 164 if ((initialStepSize < minStep) || (initialStepSize > maxStep)) { 165 initialStep = -1.0; 166 } else { 167 initialStep = initialStepSize; 168 } 169 } 170 171 /** Perform some sanity checks on the integration parameters. 172 * @param equations differential equations set 173 * @param t0 start time 174 * @param y0 state vector at t0 175 * @param t target time for the integration 176 * @param y placeholder where to put the state vector 177 * @exception IntegratorException if some inconsistency is detected 178 */ 179 @Override 180 protected void sanityChecks(final FirstOrderDifferentialEquations equations, 181 final double t0, final double[] y0, 182 final double t, final double[] y) 183 throws IntegratorException { 184 185 super.sanityChecks(equations, t0, y0, t, y); 186 187 if (equations instanceof ExtendedFirstOrderDifferentialEquations) { 188 mainSetDimension = ((ExtendedFirstOrderDifferentialEquations) equations).getMainSetDimension(); 189 } else { 190 mainSetDimension = equations.getDimension(); 191 } 192 193 if ((vecAbsoluteTolerance != null) && (vecAbsoluteTolerance.length != mainSetDimension)) { 194 throw new IntegratorException( 195 LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, mainSetDimension, vecAbsoluteTolerance.length); 196 } 197 198 if ((vecRelativeTolerance != null) && (vecRelativeTolerance.length != mainSetDimension)) { 199 throw new IntegratorException( 200 LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, mainSetDimension, vecRelativeTolerance.length); 201 } 202 203 } 204 205 /** Initialize the integration step. 206 * @param equations differential equations set 207 * @param forward forward integration indicator 208 * @param order order of the method 209 * @param scale scaling vector for the state vector (can be shorter than state vector) 210 * @param t0 start time 211 * @param y0 state vector at t0 212 * @param yDot0 first time derivative of y0 213 * @param y1 work array for a state vector 214 * @param yDot1 work array for the first time derivative of y1 215 * @return first integration step 216 * @exception DerivativeException this exception is propagated to 217 * the caller if the underlying user function triggers one 218 */ 219 public double initializeStep(final FirstOrderDifferentialEquations equations, 220 final boolean forward, final int order, final double[] scale, 221 final double t0, final double[] y0, final double[] yDot0, 222 final double[] y1, final double[] yDot1) 223 throws DerivativeException { 224 225 if (initialStep > 0) { 226 // use the user provided value 227 return forward ? initialStep : -initialStep; 228 } 229 230 // very rough first guess : h = 0.01 * ||y/scale|| / ||y'/scale|| 231 // this guess will be used to perform an Euler step 232 double ratio; 233 double yOnScale2 = 0; 234 double yDotOnScale2 = 0; 235 for (int j = 0; j < scale.length; ++j) { 236 ratio = y0[j] / scale[j]; 237 yOnScale2 += ratio * ratio; 238 ratio = yDot0[j] / scale[j]; 239 yDotOnScale2 += ratio * ratio; 240 } 241 242 double h = ((yOnScale2 < 1.0e-10) || (yDotOnScale2 < 1.0e-10)) ? 243 1.0e-6 : (0.01 * FastMath.sqrt(yOnScale2 / yDotOnScale2)); 244 if (! forward) { 245 h = -h; 246 } 247 248 // perform an Euler step using the preceding rough guess 249 for (int j = 0; j < y0.length; ++j) { 250 y1[j] = y0[j] + h * yDot0[j]; 251 } 252 computeDerivatives(t0 + h, y1, yDot1); 253 254 // estimate the second derivative of the solution 255 double yDDotOnScale = 0; 256 for (int j = 0; j < scale.length; ++j) { 257 ratio = (yDot1[j] - yDot0[j]) / scale[j]; 258 yDDotOnScale += ratio * ratio; 259 } 260 yDDotOnScale = FastMath.sqrt(yDDotOnScale) / h; 261 262 // step size is computed such that 263 // h^order * max (||y'/tol||, ||y''/tol||) = 0.01 264 final double maxInv2 = FastMath.max(FastMath.sqrt(yDotOnScale2), yDDotOnScale); 265 final double h1 = (maxInv2 < 1.0e-15) ? 266 FastMath.max(1.0e-6, 0.001 * FastMath.abs(h)) : 267 FastMath.pow(0.01 / maxInv2, 1.0 / order); 268 h = FastMath.min(100.0 * FastMath.abs(h), h1); 269 h = FastMath.max(h, 1.0e-12 * FastMath.abs(t0)); // avoids cancellation when computing t1 - t0 270 if (h < getMinStep()) { 271 h = getMinStep(); 272 } 273 if (h > getMaxStep()) { 274 h = getMaxStep(); 275 } 276 if (! forward) { 277 h = -h; 278 } 279 280 return h; 281 282 } 283 284 /** Filter the integration step. 285 * @param h signed step 286 * @param forward forward integration indicator 287 * @param acceptSmall if true, steps smaller than the minimal value 288 * are silently increased up to this value, if false such small 289 * steps generate an exception 290 * @return a bounded integration step (h if no bound is reach, or a bounded value) 291 * @exception IntegratorException if the step is too small and acceptSmall is false 292 */ 293 protected double filterStep(final double h, final boolean forward, final boolean acceptSmall) 294 throws IntegratorException { 295 296 double filteredH = h; 297 if (FastMath.abs(h) < minStep) { 298 if (acceptSmall) { 299 filteredH = forward ? minStep : -minStep; 300 } else { 301 throw new IntegratorException( 302 LocalizedFormats.MINIMAL_STEPSIZE_REACHED_DURING_INTEGRATION, 303 minStep, FastMath.abs(h)); 304 } 305 } 306 307 if (filteredH > maxStep) { 308 filteredH = maxStep; 309 } else if (filteredH < -maxStep) { 310 filteredH = -maxStep; 311 } 312 313 return filteredH; 314 315 } 316 317 /** {@inheritDoc} */ 318 public abstract double integrate (FirstOrderDifferentialEquations equations, 319 double t0, double[] y0, 320 double t, double[] y) 321 throws DerivativeException, IntegratorException; 322 323 /** {@inheritDoc} */ 324 @Override 325 public double getCurrentStepStart() { 326 return stepStart; 327 } 328 329 /** Reset internal state to dummy values. */ 330 protected void resetInternalState() { 331 stepStart = Double.NaN; 332 stepSize = FastMath.sqrt(minStep * maxStep); 333 } 334 335 /** Get the minimal step. 336 * @return minimal step 337 */ 338 public double getMinStep() { 339 return minStep; 340 } 341 342 /** Get the maximal step. 343 * @return maximal step 344 */ 345 public double getMaxStep() { 346 return maxStep; 347 } 348 349 } 350
