1 // ******************************************************************************
2 //
3 // Title: Force Field X.
4 // Description: Force Field X - Software for Molecular Biophysics.
5 // Copyright: Copyright (c) Michael J. Schnieders 2001-2024.
6 //
7 // This file is part of Force Field X.
8 //
9 // Force Field X is free software; you can redistribute it and/or modify it
10 // under the terms of the GNU General Public License version 3 as published by
11 // the Free Software Foundation.
12 //
13 // Force Field X is distributed in the hope that it will be useful, but WITHOUT
14 // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
15 // FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
16 // details.
17 //
18 // You should have received a copy of the GNU General Public License along with
19 // Force Field X; if not, write to the Free Software Foundation, Inc., 59 Temple
20 // Place, Suite 330, Boston, MA 02111-1307 USA
21 //
22 // Linking this library statically or dynamically with other modules is making a
23 // combined work based on this library. Thus, the terms and conditions of the
24 // GNU General Public License cover the whole combination.
25 //
26 // As a special exception, the copyright holders of this library give you
27 // permission to link this library with independent modules to produce an
28 // executable, regardless of the license terms of these independent modules, and
29 // to copy and distribute the resulting executable under terms of your choice,
30 // provided that you also meet, for each linked independent module, the terms
31 // and conditions of the license of that module. An independent module is a
32 // module which is not derived from or based on this library. If you modify this
33 // library, you may extend this exception to your version of the library, but
34 // you are not obligated to do so. If you do not wish to do so, delete this
35 // exception statement from your version.
36 //
37 // ******************************************************************************
38 package ffx.numerics.math;
39
40 import static org.apache.commons.math3.util.FastMath.atan2;
41 import static org.apache.commons.math3.util.FastMath.cosh;
42 import static org.apache.commons.math3.util.FastMath.hypot;
43 import static org.apache.commons.math3.util.FastMath.sinh;
44
45 import org.apache.commons.math3.util.FastMath;
46
47 /**
48 * ComplexNumber class.
49 *
50 * @author Timothy D. Fenn
51 * @since 1.0
52 */
53 public class ComplexNumber {
54
55 private double re;
56 private double im;
57
58 /**
59 * Constructor for ComplexNumber.
60 */
61 public ComplexNumber() {
62 }
63
64 /**
65 * Constructor for ComplexNumber.
66 *
67 * @param real a double.
68 * @param imag a double.
69 */
70 public ComplexNumber(double real, double imag) {
71 re = real;
72 im = imag;
73 }
74
75 /**
76 * Static version of phaseShift.
77 *
78 * @param a a {@link ComplexNumber} object.
79 * @param s a double.
80 * @return a {@link ComplexNumber} object.
81 */
82 public static ComplexNumber phaseShift(ComplexNumber a, double s) {
83 ComplexNumber sc = new ComplexNumber(FastMath.cos(s), FastMath.sin(s));
84 return a.times(sc);
85 }
86
87 /**
88 * abs
89 *
90 * @return a double.
91 */
92 public double abs() {
93 return hypot(re, im);
94 }
95
96 /**
97 * Return a new Complex object whose value is the conjugate of this.
98 *
99 * @return a {@link ComplexNumber} object.
100 */
101 public ComplexNumber conjugate() {
102 return new ComplexNumber(re, -im);
103 }
104
105 /**
106 * conjugateIP
107 */
108 public void conjugateIP() {
109 this.im = -this.im;
110 }
111
112 /**
113 * copy
114 *
115 * @param b a {@link ComplexNumber} object.
116 */
117 public void copy(ComplexNumber b) {
118 ComplexNumber a = this;
119 a.re = b.re;
120 a.im = b.im;
121 }
122
123 /**
124 * Return a new Complex object whose value is the complex cosine of this.
125 *
126 * @return a {@link ComplexNumber} object.
127 */
128 public ComplexNumber cos() {
129 return new ComplexNumber(FastMath.cos(re) * cosh(im), -FastMath.sin(re) * sinh(im));
130 }
131
132 /**
133 * Return a / b.
134 *
135 * @param b a {@link ComplexNumber} object.
136 * @return a {@link ComplexNumber} object.
137 */
138 public ComplexNumber divides(ComplexNumber b) {
139 ComplexNumber a = this;
140 return a.times(b.reciprocal());
141 }
142
143 /**
144 * Return a new Complex object whose value is the complex exponential of this.
145 *
146 * @return a {@link ComplexNumber} object.
147 */
148 public ComplexNumber exp() {
149 return new ComplexNumber(
150 FastMath.exp(re) * FastMath.cos(im), FastMath.exp(re) * FastMath.sin(im));
151 }
152
153 /**
154 * im
155 *
156 * @return a double.
157 */
158 public double im() {
159 return im;
160 }
161
162 /**
163 * im
164 *
165 * @param im a double.
166 */
167 public void im(double im) {
168 this.im = im;
169 }
170
171 /**
172 * Return a new Complex object whose value is (this - b).
173 *
174 * @param b a {@link ComplexNumber} object.
175 * @return a {@link ComplexNumber} object.
176 */
177 public ComplexNumber minus(ComplexNumber b) {
178 ComplexNumber a = this;
179 var real = a.re - b.re;
180 var imag = a.im - b.im;
181 return new ComplexNumber(real, imag);
182 }
183
184 /**
185 * minusIP
186 *
187 * @param b a {@link ComplexNumber} object.
188 */
189 public void minusIP(ComplexNumber b) {
190 ComplexNumber a = this;
191 a.re -= b.re;
192 a.im -= b.im;
193 }
194
195 /**
196 * phase
197 *
198 * @return a double.
199 */
200 public double phase() {
201 return atan2(im, re);
202 }
203
204 /**
205 * phaseShift
206 *
207 * @param s a double.
208 * @return a {@link ComplexNumber} object.
209 */
210 public ComplexNumber phaseShift(double s) {
211 ComplexNumber sc = new ComplexNumber(FastMath.cos(s), FastMath.sin(s));
212 return this.times(sc);
213 }
214
215 /**
216 * phaseShiftIP
217 *
218 * @param s a double.
219 */
220 public void phaseShiftIP(double s) {
221 ComplexNumber a = this;
222 var sr = FastMath.cos(s);
223 var si = FastMath.sin(s);
224 var real = a.re * sr - a.im * si;
225 var imag = a.re * si + a.im * sr;
226 a.re = real;
227 a.im = imag;
228 }
229
230 /**
231 * Return a new Complex object whose value is (this + b).
232 *
233 * @param b a {@link ComplexNumber} object.
234 * @return a {@link ComplexNumber} object.
235 */
236 public ComplexNumber plus(ComplexNumber b) {
237 ComplexNumber a = this;
238 var real = a.re + b.re;
239 var imag = a.im + b.im;
240 return new ComplexNumber(real, imag);
241 }
242
243 /**
244 * plusIP
245 *
246 * @param b a {@link ComplexNumber} object.
247 */
248 public void plusIP(ComplexNumber b) {
249 ComplexNumber a = this;
250 a.re += b.re;
251 a.im += b.im;
252 }
253
254 /**
255 * re
256 *
257 * @return a double.
258 */
259 public double re() {
260 return re;
261 }
262
263 /**
264 * re
265 *
266 * @param re a double.
267 */
268 public void re(double re) {
269 this.re = re;
270 }
271
272 /**
273 * Return a new Complex object whose value is the reciprocal of this.
274 *
275 * @return a {@link ComplexNumber} object.
276 */
277 public ComplexNumber reciprocal() {
278 var scale = re * re + im * im;
279 var iScale = 1.0 / scale;
280 return new ComplexNumber(re * iScale, -im * iScale);
281 }
282
283 /**
284 * reciprocalIP
285 */
286 public void reciprocalIP() {
287 var scale = re * re + im * im;
288 var iScale = 1.0 / scale;
289 re *= iScale;
290 im *= -iScale;
291 }
292
293 /**
294 * Return a new Complex object whose value is the complex sine of this.
295 *
296 * @return a {@link ComplexNumber} object.
297 */
298 public ComplexNumber sin() {
299 return new ComplexNumber(FastMath.sin(re) * cosh(im), FastMath.cos(re) * sinh(im));
300 }
301
302 /**
303 * Return a new Complex object whose value is the complex tangent of this.
304 *
305 * @return a {@link ComplexNumber} object.
306 */
307 public ComplexNumber tan() {
308 return sin().divides(cos());
309 }
310
311 /**
312 * Return a new Complex object whose value is (this * b).
313 *
314 * @param b a {@link ComplexNumber} object.
315 * @return a {@link ComplexNumber} object.
316 */
317 public ComplexNumber times(ComplexNumber b) {
318 ComplexNumber a = this;
319 var real = a.re * b.re - a.im * b.im;
320 var imag = a.re * b.im + a.im * b.re;
321 return new ComplexNumber(real, imag);
322 }
323
324 /**
325 * Return a new object whose value is (this * alpha).
326 *
327 * @param alpha a double.
328 * @return a {@link ComplexNumber} object.
329 */
330 public ComplexNumber times(double alpha) {
331 return new ComplexNumber(alpha * re, alpha * im);
332 }
333
334 /**
335 * timesIP
336 *
337 * @param b a {@link ComplexNumber} object.
338 */
339 public void timesIP(ComplexNumber b) {
340 ComplexNumber a = this;
341 var real = a.re * b.re - a.im * b.im;
342 var imag = a.re * b.im + a.im * b.re;
343 a.re = real;
344 a.im = imag;
345 }
346
347 /**
348 * timesIP
349 *
350 * @param alpha a double.
351 */
352 public void timesIP(double alpha) {
353 ComplexNumber a = this;
354 a.re *= alpha;
355 a.im *= alpha;
356 }
357
358 /**
359 * {@inheritDoc}
360 */
361 @Override
362 public String toString() {
363 if (im == 0) {
364 return re + "";
365 }
366 if (re == 0) {
367 return im + "i";
368 }
369 if (im < 0) {
370 return re + " - " + (-im) + "i";
371 }
372 return re + " + " + im + "i";
373 }
374 }