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1 package JSci.maths.analysis;
2
3 import JSci.maths.Complex;
4 import JSci.maths.ComplexMapping;
5 import JSci.maths.groups.AbelianGroup;
6 import JSci.maths.fields.Ring;
7 import JSci.maths.polynomials.ComplexPolynomial;
8
9
14 public abstract class ComplexFunction implements ComplexMapping, Ring.Member {
15
18 public final int dimension() {
19 return 1;
20 }
21 public Object  getSet() {
22 throw new RuntimeException ("Not implemented: please file bug report");
23 }
24
25 public ComplexFunction compose(ComplexFunction f) {
26 return new Composition(this, f);
27 }
28 private static class Composition extends ComplexFunction {
29 private final ComplexFunction f1, f2;
30 public Composition(ComplexFunction f1, ComplexFunction f2) {
31 this.f1 = f1;
32 this.f2 = f2;
33 }
34 public Complex map(double x, double y) {
35 return f1.map(f2.map(x, y));
36 }
37 public Complex map(Complex z) {
38 return f1.map(f2.map(z));
39 }
40
43 public ComplexFunction differentiate() {
44 return new Product(new Composition(f1.differentiate(), f2), f2.differentiate());
45 }
46 }
47
48
51 public AbelianGroup.Member negate() {
52 return new Negation(this);
53 }
54 private static class Negation extends ComplexFunction {
55 private final ComplexFunction f;
56 public Negation(ComplexFunction f) {
57 this.f = f;
58 }
59 public Complex map(double x, double y) {
60 return (Complex) f.map(x, y).negate();
61 }
62 public Complex map(Complex z) {
63 return (Complex) f.map(z).negate();
64 }
65 public ComplexFunction differentiate() {
66 return new Negation(f.differentiate());
67 }
68 }
69
70
73 public AbelianGroup.Member add(final AbelianGroup.Member f) {
74 if(f instanceof ComplexFunction)
75 return add((ComplexFunction)f);
76 else
77 throw new IllegalArgumentException ("Member class not recognised by this method.");
78 }
79 public ComplexFunction add(ComplexFunction f) {
80 return new Sum(this, f);
81 }
82 private static class Sum extends ComplexFunction {
83 private final ComplexFunction f1, f2;
84 public Sum(ComplexFunction f1, ComplexFunction f2) {
85 this.f1 = f1;
86 this.f2 = f2;
87 }
88 public Complex map(double x, double y) {
89 return f1.map(x, y).add(f2.map(x, y));
90 }
91 public Complex map(Complex z) {
92 return f1.map(z).add(f2.map(z));
93 }
94 public ComplexFunction differentiate() {
95 return new Sum(f1.differentiate(), f2.differentiate());
96 }
97 }
98
99
102 public AbelianGroup.Member subtract(final AbelianGroup.Member f) {
103 if(f instanceof ComplexFunction)
104 return subtract((ComplexFunction)f);
105 else
106 throw new IllegalArgumentException ("Member class not recognised by this method.");
107 }
108 public ComplexFunction subtract(ComplexFunction f) {
109 return new Difference(this, f);
110 }
111 private static class Difference extends ComplexFunction {
112 private final ComplexFunction f1, f2;
113 public Difference(ComplexFunction f1, ComplexFunction f2) {
114 this.f1 = f1;
115 this.f2 = f2;
116 }
117 public Complex map(double x, double y) {
118 return f1.map(x, y).subtract(f2.map(x, y));
119 }
120 public Complex map(Complex z) {
121 return f1.map(z).subtract(f2.map(z));
122 }
123 public ComplexFunction differentiate() {
124 return new Difference(f1.differentiate(), f2.differentiate());
125 }
126 }
127
128
131 public Ring.Member multiply(Ring.Member f) {
132 if(f instanceof ComplexFunction)
133 return multiply((ComplexFunction)f);
134 else
135 throw new IllegalArgumentException ("Member class not recognised by this method.");
136 }
137 public ComplexFunction multiply(ComplexFunction f) {
138 return new Product(this, f);
139 }
140 private static class Product extends ComplexFunction {
141 private final ComplexFunction f1, f2;
142 public Product(ComplexFunction f1, ComplexFunction f2) {
143 this.f1 = f1;
144 this.f2 = f2;
145 }
146 public Complex map(double x, double y) {
147 return f1.map(x, y).multiply(f2.map(x, y));
148 }
149 public Complex map(Complex z) {
150 return f1.map(z).multiply(f2.map(z));
151 }
152
155 public ComplexFunction differentiate() {
156 return new Sum(new Product(f1.differentiate(), f2), new Product(f1, f2.differentiate()));
157 }
158 }
159
160
163 public Ring.Member inverse() {
164 return new Reciprocal(this);
165 }
166 private static class Reciprocal extends ComplexFunction {
167 private final ComplexFunction f;
168 public Reciprocal(ComplexFunction f) {
169 this.f = f;
170 }
171 public Complex map(double x, double y) {
172 return Complex.ONE.divide(f.map(x, y));
173 }
174 public Complex map(Complex z) {
175 return Complex.ONE.divide(f.map(z));
176 }
177 public ComplexFunction differentiate() {
178 return new Quotient(new Negation(f.differentiate()), new Product(f, f));
179 }
180 }
181
182
185 public Ring.Member divide(Ring.Member f) {
186 if(f instanceof ComplexFunction)
187 return divide((ComplexFunction)f);
188 else
189 throw new IllegalArgumentException ("Member class not recognised by this method.");
190 }
191 public ComplexFunction divide(ComplexFunction f) {
192 return new Quotient(this, f);
193 }
194 private static class Quotient extends ComplexFunction {
195 private final ComplexFunction f1, f2;
196 public Quotient(ComplexFunction f1, ComplexFunction f2) {
197 this.f1 = f1;
198 this.f2 = f2;
199 }
200 public Complex map(double x, double y) {
201 return f1.map(x, y).divide(f2.map(x, y));
202 }
203 public Complex map(Complex z) {
204 return f1.map(z).divide(f2.map(z));
205 }
206
209 public ComplexFunction differentiate() {
210 return new Quotient(new Difference(new Product(f1.differentiate(), f2), new Product(f1, f2.differentiate())), new Product(f2, f2));
211 }
212 }
213
214
217 public abstract ComplexFunction differentiate();
218
219 public static ComplexFunction constant(Complex k) {
220 return new Constant(k);
221 }
222 private static final ComplexFunction ZERO = constant(Complex.ZERO);
223 private static class Constant extends ComplexFunction {
224 private final Complex A;
225 public Constant(Complex A) {
226 this.A = A;
227 }
228 public Complex map(double x, double y) {
229 return A;
230 }
231 public Complex map(Complex z) {
232 return A;
233 }
234 public ComplexFunction differentiate() {
235 return ZERO;
236 }
237 }
238 }
239 |
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