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1 package JSci.io;
2
3 import java.lang.Comparable  ;
4 import java.util.List ;
5 import java.util.Map ;
6 import java.util.ArrayList ;
7 import JSci.maths.*;
8 import JSci.maths.matrices.*;
9 import JSci.maths.vectors.*;
10 import JSci.maths.groups.AbelianGroup;
11 import JSci.maths.algebras.*;
12 import JSci.maths.fields.*;
13
14
20 public final class MathMLExpression extends Object {
21 private String operation;
22 private List args=new ArrayList ();
23
24
27 public MathMLExpression() {}
28
33 public void setOperation(String op) {
34 operation=op;
35 }
36
40 public String getOperation() {
41 return operation;
42 }
43
46 public void addArgument(Object obj) {
47 args.add(obj);
48 }
49
52 public Object getArgument(int n) {
53 return args.get(n);
54 }
55
58 public int length() {
59 return args.size();
60 }
61
67 public MathMLExpression substitute(String var,Object value) {
68 MathMLExpression subExpr=new MathMLExpression();
69 subExpr.operation=operation;
70 Object arg;
71 for(int i=0;i<length();i++) {
72 arg=getArgument(i);
73 if(arg instanceof MathMLExpression)
74 arg=((MathMLExpression)arg).substitute(var,value);
75 else if(arg.equals(var))
76 arg=value;
77 subExpr.addArgument(arg);
78 }
79 return subExpr;
80 }
81
86 public MathMLExpression substitute(Map vars) {
87 MathMLExpression subExpr=new MathMLExpression();
88 subExpr.operation=operation;
89 Object arg;
90 for(int i=0;i<length();i++) {
91 arg=getArgument(i);
92 if(arg instanceof MathMLExpression)
93 arg=((MathMLExpression)arg).substitute(vars);
94 else if(vars.containsKey(arg))
95 arg=vars.get(arg);
96 subExpr.addArgument(arg);
97 }
98 return subExpr;
99 }
100
103 public Object evaluate() {
104 if(length()==1)
105 return unaryEvaluate();
106 else if(length()==2)
107 return binaryEvaluate();
108 else
109 return nAryEvaluate();
110 }
111
114 private Object unaryEvaluate() {
115 Object value=getArgument(0);
116 if(value instanceof MathMLExpression)
117 value=((MathMLExpression)value).evaluate();
118 if(operation.equals("abs")) {
119 if(value instanceof MathDouble)
120 value=new MathDouble(Math.abs(((MathDouble)value).value()));
121 else if(value instanceof Complex)
122 value=new MathDouble(((Complex)value).mod());
123 } else if(operation.equals("arg")) {
124 if(value instanceof MathDouble) {
125 if(((MathDouble)value).value()>=0.0)
126 value=RealField.ZERO;
127 else
128 value=RealField.PI;
129 } else if(value instanceof Complex)
130 value=new MathDouble(((Complex)value).arg());
131 } else if(operation.equals("real")) {
132 if(value instanceof Complex)
133 value=new MathDouble(((Complex)value).real());
134 else if(value instanceof AbstractComplexVector)
135 value=((AbstractComplexVector)value).real();
136 else if(value instanceof AbstractComplexMatrix)
137 value=((AbstractComplexMatrix)value).real();
138 } else if(operation.equals("imaginary")) {
139 if(value instanceof Complex)
140 value=new MathDouble(((Complex)value).imag());
141 else if(value instanceof AbstractComplexVector)
142 value=((AbstractComplexVector)value).imag();
143 else if(value instanceof AbstractComplexMatrix)
144 value=((AbstractComplexMatrix)value).imag();
145 } else if(operation.equals("conjugate")) {
146 if(value instanceof Complex)
147 value=((Complex)value).conjugate();
148 else if(value instanceof AbstractComplexVector)
149 value=((AbstractComplexVector)value).conjugate();
150 else if(value instanceof AbstractComplexMatrix)
151 value=((AbstractComplexMatrix)value).conjugate();
152 } else if(operation.equals("transpose")) {
153 if(value instanceof Matrix)
154 value=((Matrix)value).transpose();
155 } else if(operation.equals("exp")) {
156 if(value instanceof MathDouble)
157 value=MathDouble.exp((MathDouble)value);
158 else if(value instanceof Complex)
159 value=Complex.exp((Complex)value);
160 } else if(operation.equals("ln")) {
161 if(value instanceof MathDouble)
162 value=MathDouble.log((MathDouble)value);
163 else if(value instanceof Complex)
164 value=Complex.log((Complex)value);
165 } else if(operation.equals("sin")) {
166 if(value instanceof MathDouble)
167 value=MathDouble.sin((MathDouble)value);
168 else if(value instanceof Complex)
169 value=Complex.sin((Complex)value);
170 } else if(operation.equals("cos")) {
171 if(value instanceof MathDouble)
172 value=MathDouble.cos((MathDouble)value);
173 else if(value instanceof Complex)
174 value=Complex.cos((Complex)value);
175 } else if(operation.equals("tan")) {
176 if(value instanceof MathDouble)
177 value=MathDouble.tan((MathDouble)value);
178 else if(value instanceof Complex)
179 value=Complex.tan((Complex)value);
180 } else if(operation.equals("arcsin")) {
181 if(value instanceof MathDouble)
182 value=MathDouble.asin((MathDouble)value);
183 else if(value instanceof Complex)
184 value=Complex.asin((Complex)value);
185 } else if(operation.equals("arccos")) {
186 if(value instanceof MathDouble)
187 value=MathDouble.acos((MathDouble)value);
188 else if(value instanceof Complex)
189 value=Complex.acos((Complex)value);
190 } else if(operation.equals("arctan")) {
191 if(value instanceof MathDouble)
192 value=MathDouble.atan((MathDouble)value);
193 else if(value instanceof Complex)
194 value=Complex.atan((Complex)value);
195 } else if(operation.equals("sinh")) {
196 if(value instanceof MathDouble)
197 value=MathDouble.sinh((MathDouble)value);
198 else if(value instanceof Complex)
199 value=Complex.sinh((Complex)value);
200 } else if(operation.equals("cosh")) {
201 if(value instanceof MathDouble)
202 value=MathDouble.cosh((MathDouble)value);
203 else if(value instanceof Complex)
204 value=Complex.cosh((Complex)value);
205 } else if(operation.equals("tanh")) {
206 if(value instanceof MathDouble)
207 value=MathDouble.tanh((MathDouble)value);
208 else if(value instanceof Complex)
209 value=Complex.tanh((Complex)value);
210 } else if(operation.equals("factorial")) {
211 if(value instanceof MathDouble)
212 value=new MathDouble(ExtraMath.factorial(((MathDouble)value).value()));
213 } else if(operation.equals("not")) {
214 if(value instanceof Boolean )
215 value=new Boolean (!((Boolean )value).booleanValue());
216 }
217 return value;
218 }
219
222 private Object binaryEvaluate() {
223 Object value=getArgument(0);
224 if(value instanceof MathMLExpression)
225 value=((MathMLExpression)value).evaluate();
226 Object next=getArgument(1);
227 if(next instanceof MathMLExpression)
228 next=((MathMLExpression)next).evaluate();
229 if(operation.equals("minus")) {
230 if(value instanceof AbelianGroup.Member)
231 value=((AbelianGroup.Member)value).subtract((AbelianGroup.Member)next);
232 } else if(operation.equals("divide")) {
233 if(next instanceof Field.Member) {
234 if(value instanceof Field.Member)
235 value=((Field.Member)value).divide((Field.Member)next);
236 else if(value instanceof VectorSpace.Member)
237 value=((VectorSpace.Member)value).scalarDivide((Field.Member)next);
238 }
239 } else if(operation.equals("scalarproduct")) {
240 if(value instanceof AbstractDoubleVector)
241 value=new MathDouble(((AbstractDoubleVector)value).scalarProduct((AbstractDoubleVector)next));
242 else if(value instanceof AbstractComplexVector)
243 value=((AbstractComplexVector)value).scalarProduct((AbstractComplexVector)next);
244 } else if(operation.equals("vectorproduct")) {
245 if(value instanceof Double3Vector)
246 value=((Double3Vector)value).multiply((Double3Vector)next);
247 else if(value instanceof Complex3Vector)
248 value=((Complex3Vector)value).multiply((Complex3Vector)next);
249 } else if(operation.equals("power")) {
250 if(value instanceof MathDouble)
251 value=new MathDouble(Math.pow(((MathDouble)value).value(),((MathDouble)next).value()));
252 } else if(operation.equals("neq")) {
253 value=new Boolean (!value.equals(next));
254 } else
255 return nAryEvaluate();
256 return value;
257 }
258
261 private Object nAryEvaluate() {
262 Object value=getArgument(0);
263 if(value instanceof MathMLExpression)
264 value=((MathMLExpression)value).evaluate();
265 if(operation.equals("plus")) {
266 if(value instanceof AbelianGroup.Member) {
267 AbelianGroup.Member ans=(AbelianGroup.Member)value;
268 for(int i=1;i<length();i++) {
269 Object next=getArgument(i);
270 if(next instanceof MathMLExpression)
271 next=((MathMLExpression)next).evaluate();
272 if(next instanceof AbelianGroup.Member)
273 ans=ans.add((AbelianGroup.Member)next);
274 }
275 value=ans;
276 }
277 } else if(operation.equals("times")) {
278 if(value instanceof Ring.Member) {
279 for(int i=1;i<length();i++) {
280 Object next=getArgument(i);
281 if(next instanceof MathMLExpression)
282 next=((MathMLExpression)next).evaluate();
283 if(next instanceof Ring.Member)
284 value=((Ring.Member)value).multiply((Ring.Member)next);
285 else if(next instanceof Module.Member)
286 value=((Module.Member)next).scalarMultiply((Ring.Member)value);
287 }
288 }
289 } else if(operation.equals("min")) {
290 Comparable ans=(Comparable )value;
291 for(int i=1;i<length();i++) {
292 Object next=getArgument(i);
293 if(next instanceof MathMLExpression)
294 next=((MathMLExpression)next).evaluate();
295 if(ans.compareTo(next)>0)
296 ans=(Comparable )next;
297 }
298 value=ans;
299 } else if(operation.equals("max")) {
300 Comparable ans=(Comparable )value;
301 for(int i=1;i<length();i++) {
302 Object next=getArgument(i);
303 if(next instanceof MathMLExpression)
304 next=((MathMLExpression)next).evaluate();
305 if(ans.compareTo(next)<0)
306 ans=(Comparable )next;
307 }
308 value=ans;
309 } else if(operation.equals("mean")) {
310 value=new MathDouble(mean());
311 } else if(operation.equals("sdev")) {
312 value=new MathDouble(Math.sqrt(variance()));
313 } else if(operation.equals("var")) {
314 value=new MathDouble(variance());
315 } else if(operation.equals("median")) {
316 double nums[]=new double[length()];
317 nums[0]=((MathDouble)value).value();
318 for(int i=1;i<nums.length;i++) {
319 Object next=getArgument(i);
320 if(next instanceof MathMLExpression)
321 next=((MathMLExpression)next).evaluate();
322 nums[i]=((MathDouble)next).value();
323 }
324 value=new MathDouble(ArrayMath.median(nums));
325 } else if(operation.equals("union")) {
326 if(value instanceof MathSet) {
327 MathSet ans=(MathSet)value;
328 for(int i=1;i<length();i++) {
329 Object next=getArgument(i);
330 if(next instanceof MathMLExpression)
331 next=((MathMLExpression)next).evaluate();
332 if(next instanceof MathSet)
333 ans=ans.union((MathSet)next);
334 }
335 value=ans;
336 }
337 } else if(operation.equals("intersect")) {
338 if(value instanceof MathSet) {
339 MathSet ans=(MathSet)value;
340 for(int i=1;i<length();i++) {
341 Object next=getArgument(i);
342 if(next instanceof MathMLExpression)
343 next=((MathMLExpression)next).evaluate();
344 if(next instanceof MathSet)
345 ans=ans.intersect((MathSet)next);
346 }
347 value=ans;
348 }
349 } else if(operation.equals("and")) {
350 if(value instanceof Boolean ) {
351 boolean ans=((Boolean )value).booleanValue();
352 for(int i=1;i<length();i++) {
353 Object next=getArgument(i);
354 if(next instanceof MathMLExpression)
355 next=((MathMLExpression)next).evaluate();
356 if(next instanceof Boolean )
357 ans&=((Boolean )next).booleanValue();
358 }
359 value=new Boolean (ans);
360 }
361 } else if(operation.equals("or")) {
362 if(value instanceof Boolean ) {
363 boolean ans=((Boolean )value).booleanValue();
364 for(int i=1;i<length();i++) {
365 Object next=getArgument(i);
366 if(next instanceof MathMLExpression)
367 next=((MathMLExpression)next).evaluate();
368 if(next instanceof Boolean )
369 ans|=((Boolean )next).booleanValue();
370 }
371 value=new Boolean (ans);
372 }
373 } else if(operation.equals("xor")) {
374 if(value instanceof Boolean ) {
375 boolean ans=((Boolean )value).booleanValue();
376 for(int i=1;i<length();i++) {
377 Object next=getArgument(i);
378 if(next instanceof MathMLExpression)
379 next=((MathMLExpression)next).evaluate();
380 if(next instanceof Boolean )
381 ans^=((Boolean )next).booleanValue();
382 }
383 value=new Boolean (ans);
384 }
385 } else if(operation.equals("eq")) {
386 Object arg1=value;
387 boolean ans=true;
388 for(int i=1;i<length();i++) {
389 Object arg2=getArgument(i);
390 if(arg2 instanceof MathMLExpression)
391 arg2=((MathMLExpression)arg2).evaluate();
392 ans&=arg1.equals(arg2);
393 arg1=arg2;
394 }
395 value=new Boolean (ans);
396 } else if(operation.equals("lt")) {
397 if(value instanceof Comparable ) {
398 Comparable arg1=(Comparable )value;
399 boolean ans=true;
400 for(int i=1;i<length();i++) {
401 Object arg2=getArgument(i);
402 if(arg2 instanceof MathMLExpression)
403 arg2=((MathMLExpression)arg2).evaluate();
404 ans&=arg1.compareTo(arg2)<0;
405 if(arg2 instanceof Comparable )
406 arg1=(Comparable )arg2;
407 }
408 value=new Boolean (ans);
409 }
410 } else if(operation.equals("leq")) {
411 if(value instanceof Comparable ) {
412 Comparable arg1=(Comparable )value;
413 boolean ans=true;
414 for(int i=1;i<length();i++) {
415 Object arg2=getArgument(i);
416 if(arg2 instanceof MathMLExpression)
417 arg2=((MathMLExpression)arg2).evaluate();
418 ans&=arg1.compareTo(arg2)<=0;
419 if(arg2 instanceof Comparable )
420 arg1=(Comparable )arg2;
421 }
422 value=new Boolean (ans);
423 }
424 } else if(operation.equals("gt")) {
425 if(value instanceof Comparable ) {
426 Comparable arg1=(Comparable )value;
427 boolean ans=true;
428 for(int i=1;i<length();i++) {
429 Object arg2=getArgument(i);
430 if(arg2 instanceof MathMLExpression)
431 arg2=((MathMLExpression)arg2).evaluate();
432 ans&=arg1.compareTo(arg2)>0;
433 if(arg2 instanceof Comparable )
434 arg1=(Comparable )arg2;
435 }
436 value=new Boolean (ans);
437 }
438 } else if(operation.equals("geq")) {
439 if(value instanceof Comparable ) {
440 Comparable arg1=(Comparable )value;
441 boolean ans=true;
442 for(int i=1;i<length();i++) {
443 Object arg2=getArgument(i);
444 if(arg2 instanceof MathMLExpression)
445 arg2=((MathMLExpression)arg2).evaluate();
446 ans&=arg1.compareTo(arg2)>=0;
447 if(arg2 instanceof Comparable )
448 arg1=(Comparable )arg2;
449 }
450 value=new Boolean (ans);
451 }
452 }
453 return value;
454 }
455
458 private double mean() {
459 double sum=((MathDouble)getArgument(0)).value();
460 for(int i=1;i<length();i++) {
461 Object next=getArgument(i);
462 if(next instanceof MathMLExpression)
463 next=((MathMLExpression)next).evaluate();
464 sum+=((MathDouble)next).value();
465 }
466 return sum/length();
467 }
468
471 private double variance() {
472 final double m=mean();
473 double num=((MathDouble)getArgument(0)).value();
474 double ans=(num-m)*(num-m);
475 for(int i=1;i<length();i++) {
476 Object next=getArgument(i);
477 if(next instanceof MathMLExpression)
478 next=((MathMLExpression)next).evaluate();
479 num=((MathDouble)next).value();
480 ans+=(num-m)*(num-m);
481 }
482 return ans/(length()-1);
483 }
484 }
485
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