| 1 | package de.uka.ipd.sdq.probfunction.math.util; |
| 2 | |
| 3 | import java.math.BigDecimal; |
| 4 | import java.math.BigInteger; |
| 5 | import java.util.ArrayList; |
| 6 | import java.util.Comparator; |
| 7 | import java.util.HashMap; |
| 8 | import java.util.List; |
| 9 | |
| 10 | import de.uka.ipd.sdq.probfunction.BoxedPDF; |
| 11 | import de.uka.ipd.sdq.probfunction.ContinuousSample; |
| 12 | import de.uka.ipd.sdq.probfunction.math.IBoxedPDF; |
| 13 | import de.uka.ipd.sdq.probfunction.math.IContinuousSample; |
| 14 | import de.uka.ipd.sdq.probfunction.math.ISample; |
| 15 | import flanagan.complex.Complex; |
| 16 | |
| 17 | /** |
| 18 | * MathTools contains a set of commonly used mathematical functions, that are |
| 19 | * not provided by the Java libraries. |
| 20 | * |
| 21 | * @author ihssane, jens |
| 22 | * |
| 23 | */ |
| 24 | public class MathTools { |
| 25 | |
| 26 | /** |
| 27 | * Difference up to which two values are considered as equal. |
| 28 | */ |
| 29 | public static final double EPSILON_ERROR = 1e-5; |
| 30 | |
| 31 | /** |
| 32 | * Computes the greatest common divisor (GDC) of a set of numbers. |
| 33 | * |
| 34 | * @param numbers |
| 35 | * List of numbers for which the GDC shall be computed. |
| 36 | * @return Returns the greatest common divisor of all numbers |
| 37 | */ |
| 38 | public static double gcd(List<Double> numbers) { |
| 39 | if (numbers.size() < 1) |
| 40 | throw new IllegalArgumentException( |
| 41 | "number of digit must be greater than 0"); |
| 42 | if(numbers.size() < 2) |
| 43 | return numbers.get(0); |
| 44 | |
| 45 | double gcd = gcd(numbers.get(0), numbers.get(1)); |
| 46 | for (int i = 2; i < numbers.size(); i++) |
| 47 | gcd = gcd(gcd, numbers.get(i)); |
| 48 | return gcd; |
| 49 | } |
| 50 | |
| 51 | /** |
| 52 | * Computes something similar to the greatest common |
| 53 | * divisor (GCD) of two numbers. |
| 54 | * Note that the GCD for two doubles is calculates, which is |
| 55 | * different to the standard definition of GCD. |
| 56 | * |
| 57 | * @param x |
| 58 | * first number |
| 59 | * @param y |
| 60 | * second number |
| 61 | * @return Returns the GDC of y and x. |
| 62 | */ |
| 63 | public static double gcd(double x, double y) { |
| 64 | |
| 65 | if (x == 0.0) |
| 66 | return y; |
| 67 | if (y == 0.0) |
| 68 | return x; |
| 69 | |
| 70 | //if one already divides the other almost without remainder, return the smaller one |
| 71 | if (Math.abs(x%y) < EPSILON_ERROR) return y; |
| 72 | if (Math.abs(y%x) < EPSILON_ERROR) return x; |
| 73 | |
| 74 | while (Math.abs(x - y) > EPSILON_ERROR) { |
| 75 | if (x > y) { |
| 76 | x -= y; |
| 77 | } else { |
| 78 | y -= x; |
| 79 | } |
| 80 | } |
| 81 | return x; |
| 82 | } |
| 83 | |
| 84 | /** |
| 85 | * Transforms a list of complex values to a list of double values by |
| 86 | * throwing away the imaginary part. |
| 87 | * |
| 88 | * @param values |
| 89 | * List of complex values to transform. |
| 90 | * @return The real part of the value list as doubles. |
| 91 | */ |
| 92 | public static List<Double> transformComplexToDouble(List<Complex> values) { |
| 93 | List<Double> resultList = new ArrayList<Double>(); |
| 94 | for (Complex complex : values) { |
| 95 | resultList.add(complex.getReal()); |
| 96 | } |
| 97 | return resultList; |
| 98 | } |
| 99 | |
| 100 | /** |
| 101 | * Transforms a list of double values to a list of complex values. The real |
| 102 | * parts are set to the values in the list, the imaginary part is set to |
| 103 | * zero. |
| 104 | * |
| 105 | * @param values |
| 106 | * List of double values to transform. |
| 107 | * @return A list of complex values equivalent to the doubles. |
| 108 | */ |
| 109 | public static List<Complex> transformDoubleToComplex(List<Double> values) { |
| 110 | List<Complex> resultList = new ArrayList<Complex>(); |
| 111 | for (Double d : values) { |
| 112 | resultList.add(new Complex(d)); |
| 113 | } |
| 114 | return resultList; |
| 115 | } |
| 116 | |
| 117 | /** |
| 118 | * Compares two doubles. |
| 119 | * |
| 120 | * @param d1 |
| 121 | * @param d2 |
| 122 | * @return True, if the difference between both values is lower than |
| 123 | * EPSILON_ERROR; false otherwise. |
| 124 | */ |
| 125 | public static boolean equalsDouble(double d1, double d2) { |
| 126 | boolean result = false; |
| 127 | if (d1 == Double.NaN && d2 == Double.NaN) { |
| 128 | result = true; |
| 129 | } else { |
| 130 | result = (Math.abs(d1 - d2) < EPSILON_ERROR); |
| 131 | } |
| 132 | return result; |
| 133 | } |
| 134 | |
| 135 | public static boolean equalsComplex(Complex z1, Complex z2) { |
| 136 | boolean result = false; |
| 137 | if (z1.isNaN() && z2.isNaN()) { |
| 138 | result = true; |
| 139 | } else { |
| 140 | result = equalsDouble(z1.getReal(), z2.getReal()) |
| 141 | && equalsDouble(z1.getImag(), z2.getImag()); |
| 142 | } |
| 143 | return result; |
| 144 | |
| 145 | } |
| 146 | |
| 147 | /** |
| 148 | * Compute the sum of probabilities associated with a set of |
| 149 | * IContinuousSamples. |
| 150 | * |
| 151 | * @param list |
| 152 | * @return the computed value. |
| 153 | */ |
| 154 | public static double sumOfCountinuousSamples(List<IContinuousSample> list) { |
| 155 | double sum = 0.0; |
| 156 | for (IContinuousSample s : list) |
| 157 | sum += s.getProbability(); |
| 158 | return sum; |
| 159 | } |
| 160 | |
| 161 | /** |
| 162 | * Compute the sum of probabilities associated with a set of ISamples. |
| 163 | * |
| 164 | * @param list |
| 165 | * @return the computed value. |
| 166 | */ |
| 167 | public static double sumOfSamples(List<ISample> list) { |
| 168 | double sum = 0.0; |
| 169 | for (ISample s : list) { |
| 170 | sum += s.getProbability(); |
| 171 | System.out.println(sum); |
| 172 | } |
| 173 | return sum; |
| 174 | } |
| 175 | |
| 176 | /** |
| 177 | * Compute the sum of a set Doubles. |
| 178 | * |
| 179 | * @param list |
| 180 | * @return the computed value. |
| 181 | */ |
| 182 | public static double sumOfDoubles(List<Double> list) { |
| 183 | double sum = 0.0; |
| 184 | for (Double d : list) |
| 185 | sum += d; |
| 186 | return sum; |
| 187 | } |
| 188 | |
| 189 | /** |
| 190 | * Returns the cumulative probabilities of the list of input probabilities. |
| 191 | * The size of the result list might be smaller than the size of the input list, |
| 192 | * since the function terminates when it reaches 1.0. |
| 193 | * |
| 194 | * @param probabilityList |
| 195 | * @return |
| 196 | */ |
| 197 | public static List<Double> computeCumulativeProbabilities(List<Double> probabilityList) { |
| 198 | List<Double> resultList = new ArrayList<Double>(probabilityList.size()); |
| 199 | if (probabilityList == null || probabilityList.size() == 0) |
| 200 | throw new IllegalArgumentException("ProbabilityList is empty or null!"); |
| 201 | double prob = 0; |
| 202 | for(Double d : probabilityList){ |
| 203 | prob += d; |
| 204 | resultList.add(prob); |
| 205 | } |
| 206 | return resultList; |
| 207 | } |
| 208 | |
| 209 | /** |
| 210 | * @param samples |
| 211 | * @param prob |
| 212 | * @return |
| 213 | */ |
| 214 | public static HashMap<Double, Line> computeLines( |
| 215 | List<IContinuousSample> samples, List<Double> intervals) { |
| 216 | HashMap<Double, Line> lines = new HashMap<Double, Line>(); |
| 217 | lines.put(intervals.get(0), new Line(0, 0, samples.get(0).getValue(), |
| 218 | samples.get(0).getProbability())); |
| 219 | |
| 220 | for (int i = 1; i < intervals.size(); i++) { |
| 221 | double x1 = samples.get(i - 1).getValue(); |
| 222 | double y1 = intervals.get(i - 1); |
| 223 | double x2 = samples.get(i).getValue(); |
| 224 | double y2 = intervals.get(i); |
| 225 | if (y1 != y2) |
| 226 | lines.put(intervals.get(i), new Line(x1, y1, x2, y2)); |
| 227 | } |
| 228 | |
| 229 | return lines; |
| 230 | } |
| 231 | |
| 232 | public static Comparator<IContinuousSample> getContinuousSampleComparator() { |
| 233 | Comparator<IContinuousSample> comp = new Comparator<IContinuousSample>() { |
| 234 | @SuppressWarnings("unchecked") |
| 235 | public int compare(IContinuousSample o1, IContinuousSample o2) { |
| 236 | return ((Comparable) o1.getValue()).compareTo(o2.getValue()); |
| 237 | } |
| 238 | |
| 239 | }; |
| 240 | return comp; |
| 241 | } |
| 242 | |
| 243 | public static Comparator<ISample> getSampleComparator() { |
| 244 | Comparator<ISample> sComparator = new Comparator<ISample>() { |
| 245 | |
| 246 | @SuppressWarnings("unchecked") |
| 247 | public int compare(ISample o1, ISample o2) { |
| 248 | return ((Comparable) o1.getValue()).compareTo(o2.getValue()); |
| 249 | } |
| 250 | }; |
| 251 | return sComparator; |
| 252 | } |
| 253 | |
| 254 | public static String asString(double val) { |
| 255 | double rVal = ((double) Math.round(val * 10000.0)) / 10000.0; |
| 256 | return Double.toString(rVal); |
| 257 | } |
| 258 | |
| 259 | public static BigDecimal over(int n, int k) { |
| 260 | return factorial(n).divide(factorial(k).multiply(factorial(n - k))); |
| 261 | } |
| 262 | |
| 263 | public static BigDecimal over(int n, int[] nList){ |
| 264 | BigDecimal numerator = factorial(n); |
| 265 | BigDecimal denominator = BigDecimal.ONE; |
| 266 | for (int ni : nList) { |
| 267 | denominator = denominator.multiply(factorial(ni)); |
| 268 | } |
| 269 | return numerator.divide(denominator); |
| 270 | } |
| 271 | |
| 272 | |
| 273 | public static BigDecimal computeJointProbability(BigDecimal[] probList, int[] nList){ |
| 274 | assert(nList.length == probList.length); |
| 275 | BigDecimal result = BigDecimal.ONE; |
| 276 | for (int i = 0; i < nList.length; i++) { |
| 277 | result = result.multiply(probList[i].pow(nList[i])); |
| 278 | } |
| 279 | return result; |
| 280 | } |
| 281 | |
| 282 | |
| 283 | public static BigDecimal factorial(long n) { |
| 284 | if (n < 0) |
| 285 | return null; |
| 286 | if (n == 0) |
| 287 | return BigDecimal.ONE; |
| 288 | BigDecimal fac = BigDecimal.ONE; |
| 289 | for (long i = 1; i <= n; i++) { |
| 290 | fac = fac.multiply(new BigDecimal(i)); |
| 291 | } |
| 292 | return fac; |
| 293 | } |
| 294 | |
| 295 | public static boolean isNumeric(Object value) { |
| 296 | if ((value instanceof Double) || (value instanceof Integer) |
| 297 | || (value instanceof Long) || (value instanceof Float)) |
| 298 | return true; |
| 299 | return false; |
| 300 | } |
| 301 | |
| 302 | public static List<Complex> transformSampleToComplex(List<ISample> samples) { |
| 303 | List<Complex> resultList = new ArrayList<Complex>(); |
| 304 | for (ISample s : samples) { |
| 305 | resultList.add(new Complex(s.getProbability(), convertToDouble(s |
| 306 | .getValue()))); |
| 307 | } |
| 308 | return resultList; |
| 309 | } |
| 310 | |
| 311 | public static double convertToDouble(Object value) { |
| 312 | double r = 0.0; |
| 313 | if (value instanceof Double) { |
| 314 | r = (Double) value; |
| 315 | } else if (value instanceof Integer) { |
| 316 | r = ((Integer) value).doubleValue(); |
| 317 | } else if (value instanceof Boolean) { |
| 318 | r = ((Boolean) value).booleanValue() ? 1.0 : 0.0; |
| 319 | } else if (value instanceof Float) |
| 320 | r = ((Float) value).doubleValue(); |
| 321 | return r; |
| 322 | } |
| 323 | |
| 324 | public static double round(double value,double precision){ |
| 325 | long factor = (long)(1 / precision); |
| 326 | value *= factor; |
| 327 | long temp = Math.round(value); |
| 328 | return (double)temp / (double)factor; |
| 329 | } |
| 330 | |
| 331 | public static boolean lessOrEqual(double d1, double d2) { |
| 332 | return d1 <= d2 + EPSILON_ERROR; |
| 333 | } |
| 334 | |
| 335 | public static boolean less(double d1, double d2) { |
| 336 | return d1 < d2 && !equalsDouble(d1, d2); |
| 337 | } |
| 338 | } |