tablepress / libraries / vendor / Complex / Functions.php

Functions.php in TablePress – Tables in WordPress made easy 2.2.1, at libraries/vendor/Complex/Functions.php

824 lines 28.0 KB

Raw Download Zip

1	<?php
2
3	namespace TablePress\Complex;
4
5	use InvalidArgumentException;
6
7	class Functions
8	{
9	/**
10	* Returns the absolute value (modulus) of a complex number.
11	* Also known as the rho of the complex number, i.e. the distance/radius
12	* from the centrepoint to the representation of the number in polar coordinates.
13	*
14	* This function is a synonym for rho()
15	*
16	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
17	* @return float The absolute (or rho) value of the complex argument.
18	* @throws Exception If argument isn't a valid real or complex number.
19	*
20	* @see rho
21	*
22	*/
23	public static function abs($complex): float
24	{
25	return self::rho($complex);
26	}
27
28	/**
29	* Returns the inverse cosine of a complex number.
30	*
31	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
32	* @return TablePress\Complex The inverse cosine of the complex argument.
33	* @throws Exception If argument isn't a valid real or complex number.
34	*/
35	public static function acos($complex): TablePress\Complex
36	{
37	$complex = Complex::validateComplexArgument($complex);
38
39	$invsqrt = self::sqrt(Operations::subtract(1, Operations::multiply($complex, $complex)));
40	$adjust = new Complex(
41	$complex->getReal() - $invsqrt->getImaginary(),
42	$complex->getImaginary() + $invsqrt->getReal()
43	);
44	$log = self::ln($adjust);
45
46	return new Complex(
47	$log->getImaginary(),
48	-1 * $log->getReal()
49	);
50	}
51
52	/**
53	* Returns the inverse hyperbolic cosine of a complex number.
54	*
55	* Formula from Wolfram Alpha:
56	* cosh^(-1)z = ln(z + sqrt(z + 1) sqrt(z - 1)).
57	*
58	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
59	* @return TablePress\Complex The inverse hyperbolic cosine of the complex argument.
60	* @throws Exception If argument isn't a valid real or complex number.
61	*/
62	public static function acosh($complex): TablePress\Complex
63	{
64	$complex = Complex::validateComplexArgument($complex);
65
66	if ($complex->isReal() && ($complex->getReal() > 1)) {
67	return new Complex(\acosh($complex->getReal()));
68	}
69
70	$acosh = self::ln(
71	Operations::add(
72	$complex,
73	Operations::multiply(
74	self::sqrt(Operations::add($complex, 1)),
75	self::sqrt(Operations::subtract($complex, 1))
76	)
77	)
78	);
79
80	return $acosh;
81	}
82
83	/**
84	* Returns the inverse cotangent of a complex number.
85	*
86	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
87	* @return TablePress\Complex The inverse cotangent of the complex argument.
88	* @throws Exception If argument isn't a valid real or complex number.
89	* @throws \InvalidArgumentException If function would result in a division by zero
90	*/
91	public static function acot($complex): TablePress\Complex
92	{
93	$complex = Complex::validateComplexArgument($complex);
94
95	return self::atan(self::inverse($complex));
96	}
97
98	/**
99	* Returns the inverse hyperbolic cotangent of a complex number.
100	*
101	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
102	* @return TablePress\Complex The inverse hyperbolic cotangent of the complex argument.
103	* @throws Exception If argument isn't a valid real or complex number.
104	* @throws \InvalidArgumentException If function would result in a division by zero
105	*/
106	public static function acoth($complex): TablePress\Complex
107	{
108	$complex = Complex::validateComplexArgument($complex);
109
110	return self::atanh(self::inverse($complex));
111	}
112
113	/**
114	* Returns the inverse cosecant of a complex number.
115	*
116	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
117	* @return TablePress\Complex The inverse cosecant of the complex argument.
118	* @throws Exception If argument isn't a valid real or complex number.
119	* @throws \InvalidArgumentException If function would result in a division by zero
120	*/
121	public static function acsc($complex): TablePress\Complex
122	{
123	$complex = Complex::validateComplexArgument($complex);
124
125	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
126	return new Complex(INF);
127	}
128
129	return self::asin(self::inverse($complex));
130	}
131
132	/**
133	* Returns the inverse hyperbolic cosecant of a complex number.
134	*
135	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
136	* @return TablePress\Complex The inverse hyperbolic cosecant of the complex argument.
137	* @throws Exception If argument isn't a valid real or complex number.
138	* @throws \InvalidArgumentException If function would result in a division by zero
139	*/
140	public static function acsch($complex): TablePress\Complex
141	{
142	$complex = Complex::validateComplexArgument($complex);
143
144	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
145	return new Complex(INF);
146	}
147
148	return self::asinh(self::inverse($complex));
149	}
150
151	/**
152	* Returns the argument of a complex number.
153	* Also known as the theta of the complex number, i.e. the angle in radians
154	* from the real axis to the representation of the number in polar coordinates.
155	*
156	* This function is a synonym for theta()
157	*
158	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
159	* @return float The argument (or theta) value of the complex argument.
160	* @throws Exception If argument isn't a valid real or complex number.
161	*
162	* @see theta
163	*/
164	public static function argument($complex): float
165	{
166	return self::theta($complex);
167	}
168
169	/**
170	* Returns the inverse secant of a complex number.
171	*
172	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
173	* @return TablePress\Complex The inverse secant of the complex argument.
174	* @throws Exception If argument isn't a valid real or complex number.
175	* @throws \InvalidArgumentException If function would result in a division by zero
176	*/
177	public static function asec($complex): TablePress\Complex
178	{
179	$complex = Complex::validateComplexArgument($complex);
180
181	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
182	return new Complex(INF);
183	}
184
185	return self::acos(self::inverse($complex));
186	}
187
188	/**
189	* Returns the inverse hyperbolic secant of a complex number.
190	*
191	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
192	* @return TablePress\Complex The inverse hyperbolic secant of the complex argument.
193	* @throws Exception If argument isn't a valid real or complex number.
194	* @throws \InvalidArgumentException If function would result in a division by zero
195	*/
196	public static function asech($complex): TablePress\Complex
197	{
198	$complex = Complex::validateComplexArgument($complex);
199
200	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
201	return new Complex(INF);
202	}
203
204	return self::acosh(self::inverse($complex));
205	}
206
207	/**
208	* Returns the inverse sine of a complex number.
209	*
210	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
211	* @return TablePress\Complex The inverse sine of the complex argument.
212	* @throws Exception If argument isn't a valid real or complex number.
213	*/
214	public static function asin($complex): TablePress\Complex
215	{
216	$complex = Complex::validateComplexArgument($complex);
217
218	$invsqrt = self::sqrt(Operations::subtract(1, Operations::multiply($complex, $complex)));
219	$adjust = new Complex(
220	$invsqrt->getReal() - $complex->getImaginary(),
221	$invsqrt->getImaginary() + $complex->getReal()
222	);
223	$log = self::ln($adjust);
224
225	return new Complex(
226	$log->getImaginary(),
227	-1 * $log->getReal()
228	);
229	}
230
231	/**
232	* Returns the inverse hyperbolic sine of a complex number.
233	*
234	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
235	* @return TablePress\Complex The inverse hyperbolic sine of the complex argument.
236	* @throws Exception If argument isn't a valid real or complex number.
237	*/
238	public static function asinh($complex): TablePress\Complex
239	{
240	$complex = Complex::validateComplexArgument($complex);
241
242	if ($complex->isReal() && ($complex->getReal() > 1)) {
243	return new Complex(\asinh($complex->getReal()));
244	}
245
246	$asinh = clone $complex;
247	$asinh = $asinh->reverse()
248	->invertReal();
249	$asinh = self::asin($asinh);
250
251	return $asinh->reverse()
252	->invertImaginary();
253	}
254
255	/**
256	* Returns the inverse tangent of a complex number.
257	*
258	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
259	* @return TablePress\Complex The inverse tangent of the complex argument.
260	* @throws Exception If argument isn't a valid real or complex number.
261	* @throws \InvalidArgumentException If function would result in a division by zero
262	*/
263	public static function atan($complex): TablePress\Complex
264	{
265	$complex = Complex::validateComplexArgument($complex);
266
267	if ($complex->isReal()) {
268	return new Complex(\atan($complex->getReal()));
269	}
270
271	$t1Value = new Complex(-1 * $complex->getImaginary(), $complex->getReal());
272	$uValue = new Complex(1, 0);
273
274	$d1Value = clone $uValue;
275	$d1Value = Operations::subtract($d1Value, $t1Value);
276	$d2Value = Operations::add($t1Value, $uValue);
277	$uResult = $d1Value->divideBy($d2Value);
278	$uResult = self::ln($uResult);
279
280	$realMultiplier = -0.5;
281	$imaginaryMultiplier = 0.5;
282
283	if (abs($uResult->getImaginary()) === M_PI) {
284	// If we have an imaginary value at the max or min (PI or -PI), then we need to ensure
285	// that the primary is assigned for the correct quadrant.
286	$realMultiplier = (
287	($uResult->getImaginary() === M_PI && $uResult->getReal() > 0.0) \|\|
288	($uResult->getImaginary() === -M_PI && $uResult->getReal() < 0.0)
289	) ? 0.5 : -0.5;
290	}
291
292	return new Complex(
293	$uResult->getImaginary() * $realMultiplier,
294	$uResult->getReal() * $imaginaryMultiplier,
295	$complex->getSuffix()
296	);
297	}
298
299	/**
300	* Returns the inverse hyperbolic tangent of a complex number.
301	*
302	* Formula from Wolfram Alpha:
303	* tanh^(-1)z = 1/2 [ln(1 + z) - ln(1 - z)].
304	*
305	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
306	* @return TablePress\Complex The inverse hyperbolic tangent of the complex argument.
307	* @throws Exception If argument isn't a valid real or complex number.
308	*/
309	public static function atanh($complex): TablePress\Complex
310	{
311	$complex = Complex::validateComplexArgument($complex);
312
313	if ($complex->isReal()) {
314	$real = $complex->getReal();
315	if ($real >= -1.0 && $real <= 1.0) {
316	return new Complex(\atanh($real));
317	} else {
318	return new Complex(\atanh(1 / $real), (($real < 0.0) ? M_PI_2 : -1 * M_PI_2));
319	}
320	}
321
322	$atanh = Operations::multiply(
323	Operations::subtract(
324	self::ln(Operations::add(1.0, $complex)),
325	self::ln(Operations::subtract(1.0, $complex))
326	),
327	0.5
328	);
329
330	return $atanh;
331	}
332
333	/**
334	* Returns the complex conjugate of a complex number
335	*
336	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
337	* @return TablePress\Complex The conjugate of the complex argument.
338	* @throws Exception If argument isn't a valid real or complex number.
339	*/
340	public static function conjugate($complex): TablePress\Complex
341	{
342	$complex = Complex::validateComplexArgument($complex);
343
344	return new Complex(
345	$complex->getReal(),
346	-1 * $complex->getImaginary(),
347	$complex->getSuffix()
348	);
349	}
350
351	/**
352	* Returns the cosine of a complex number.
353	*
354	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
355	* @return TablePress\Complex The cosine of the complex argument.
356	* @throws Exception If argument isn't a valid real or complex number.
357	*/
358	public static function cos($complex): TablePress\Complex
359	{
360	$complex = Complex::validateComplexArgument($complex);
361
362	if ($complex->isReal()) {
363	return new Complex(\cos($complex->getReal()));
364	}
365
366	return self::conjugate(
367	new Complex(
368	\cos($complex->getReal()) * \cosh($complex->getImaginary()),
369	\sin($complex->getReal()) * \sinh($complex->getImaginary()),
370	$complex->getSuffix()
371	)
372	);
373	}
374
375	/**
376	* Returns the hyperbolic cosine of a complex number.
377	*
378	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
379	* @return TablePress\Complex The hyperbolic cosine of the complex argument.
380	* @throws Exception If argument isn't a valid real or complex number.
381	*/
382	public static function cosh($complex): TablePress\Complex
383	{
384	$complex = Complex::validateComplexArgument($complex);
385
386	if ($complex->isReal()) {
387	return new Complex(\cosh($complex->getReal()));
388	}
389
390	return new Complex(
391	\cosh($complex->getReal()) * \cos($complex->getImaginary()),
392	\sinh($complex->getReal()) * \sin($complex->getImaginary()),
393	$complex->getSuffix()
394	);
395	}
396
397	/**
398	* Returns the cotangent of a complex number.
399	*
400	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
401	* @return TablePress\Complex The cotangent of the complex argument.
402	* @throws Exception If argument isn't a valid real or complex number.
403	* @throws \InvalidArgumentException If function would result in a division by zero
404	*/
405	public static function cot($complex): TablePress\Complex
406	{
407	$complex = Complex::validateComplexArgument($complex);
408
409	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
410	return new Complex(INF);
411	}
412
413	return self::inverse(self::tan($complex));
414	}
415
416	/**
417	* Returns the hyperbolic cotangent of a complex number.
418	*
419	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
420	* @return TablePress\Complex The hyperbolic cotangent of the complex argument.
421	* @throws Exception If argument isn't a valid real or complex number.
422	* @throws \InvalidArgumentException If function would result in a division by zero
423	*/
424	public static function coth($complex): TablePress\Complex
425	{
426	$complex = Complex::validateComplexArgument($complex);
427
428	return self::inverse(self::tanh($complex));
429	}
430
431	/**
432	* Returns the cosecant of a complex number.
433	*
434	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
435	* @return TablePress\Complex The cosecant of the complex argument.
436	* @throws Exception If argument isn't a valid real or complex number.
437	* @throws \InvalidArgumentException If function would result in a division by zero
438	*/
439	public static function csc($complex): TablePress\Complex
440	{
441	$complex = Complex::validateComplexArgument($complex);
442
443	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
444	return new Complex(INF);
445	}
446
447	return self::inverse(self::sin($complex));
448	}
449
450	/**
451	* Returns the hyperbolic cosecant of a complex number.
452	*
453	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
454	* @return TablePress\Complex The hyperbolic cosecant of the complex argument.
455	* @throws Exception If argument isn't a valid real or complex number.
456	* @throws \InvalidArgumentException If function would result in a division by zero
457	*/
458	public static function csch($complex): TablePress\Complex
459	{
460	$complex = Complex::validateComplexArgument($complex);
461
462	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
463	return new Complex(INF);
464	}
465
466	return self::inverse(self::sinh($complex));
467	}
468
469	/**
470	* Returns the exponential of a complex number.
471	*
472	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
473	* @return TablePress\Complex The exponential of the complex argument.
474	* @throws Exception If argument isn't a valid real or complex number.
475	*/
476	public static function exp($complex): TablePress\Complex
477	{
478	$complex = Complex::validateComplexArgument($complex);
479
480	if (($complex->getReal() == 0.0) && (\abs($complex->getImaginary()) == M_PI)) {
481	return new Complex(-1.0, 0.0);
482	}
483
484	$rho = \exp($complex->getReal());
485
486	return new Complex(
487	$rho * \cos($complex->getImaginary()),
488	$rho * \sin($complex->getImaginary()),
489	$complex->getSuffix()
490	);
491	}
492
493	/**
494	* Returns the inverse of a complex number.
495	*
496	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
497	* @return TablePress\Complex The inverse of the complex argument.
498	* @throws Exception If argument isn't a valid real or complex number.
499	* @throws InvalidArgumentException If function would result in a division by zero
500	*/
501	public static function inverse($complex): TablePress\Complex
502	{
503	$complex = clone Complex::validateComplexArgument($complex);
504
505	if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
506	throw new InvalidArgumentException('Division by zero');
507	}
508
509	return $complex->divideInto(1.0);
510	}
511
512	/**
513	* Returns the natural logarithm of a complex number.
514	*
515	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
516	* @return TablePress\Complex The natural logarithm of the complex argument.
517	* @throws Exception If argument isn't a valid real or complex number.
518	* @throws InvalidArgumentException If the real and the imaginary parts are both zero
519	*/
520	public static function ln($complex): TablePress\Complex
521	{
522	$complex = Complex::validateComplexArgument($complex);
523
524	if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
525	throw new InvalidArgumentException();
526	}
527
528	return new Complex(
529	\log(self::rho($complex)),
530	self::theta($complex),
531	$complex->getSuffix()
532	);
533	}
534
535	/**
536	* Returns the base-2 logarithm of a complex number.
537	*
538	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
539	* @return TablePress\Complex The base-2 logarithm of the complex argument.
540	* @throws Exception If argument isn't a valid real or complex number.
541	* @throws InvalidArgumentException If the real and the imaginary parts are both zero
542	*/
543	public static function log2($complex): TablePress\Complex
544	{
545	$complex = Complex::validateComplexArgument($complex);
546
547	if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
548	throw new InvalidArgumentException();
549	} elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
550	return new Complex(\log($complex->getReal(), 2), 0.0, $complex->getSuffix());
551	}
552
553	return self::ln($complex)
554	->multiply(\log(Complex::EULER, 2));
555	}
556
557	/**
558	* Returns the common logarithm (base 10) of a complex number.
559	*
560	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
561	* @return TablePress\Complex The common logarithm (base 10) of the complex argument.
562	* @throws Exception If argument isn't a valid real or complex number.
563	* @throws InvalidArgumentException If the real and the imaginary parts are both zero
564	*/
565	public static function log10($complex): TablePress\Complex
566	{
567	$complex = Complex::validateComplexArgument($complex);
568
569	if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
570	throw new InvalidArgumentException();
571	} elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
572	return new Complex(\log10($complex->getReal()), 0.0, $complex->getSuffix());
573	}
574
575	return self::ln($complex)
576	->multiply(\log10(Complex::EULER));
577	}
578
579	/**
580	* Returns the negative of a complex number.
581	*
582	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
583	* @return TablePress\Complex The negative value of the complex argument.
584	* @throws Exception If argument isn't a valid real or complex number.
585	*
586	* @see rho
587	*
588	*/
589	public static function negative($complex): TablePress\Complex
590	{
591	$complex = Complex::validateComplexArgument($complex);
592
593	return new Complex(
594	-1 * $complex->getReal(),
595	-1 * $complex->getImaginary(),
596	$complex->getSuffix()
597	);
598	}
599
600	/**
601	* Returns a complex number raised to a power.
602	*
603	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
604	* @param float\|integer $power The power to raise this value to
605	* @return TablePress\Complex The complex argument raised to the real power.
606	* @throws Exception If the power argument isn't a valid real
607	*/
608	public static function pow($complex, $power): TablePress\Complex
609	{
610	$complex = Complex::validateComplexArgument($complex);
611
612	if (!is_numeric($power)) {
613	throw new Exception('Power argument must be a real number');
614	}
615
616	if ($complex->getImaginary() == 0.0 && $complex->getReal() >= 0.0) {
617	return new Complex(\pow($complex->getReal(), $power));
618	}
619
620	$rValue = \sqrt(($complex->getReal() * $complex->getReal()) + ($complex->getImaginary() * $complex->getImaginary()));
621	$rPower = \pow($rValue, $power);
622	$theta = $complex->argument() * $power;
623	if ($theta == 0) {
624	return new Complex(1);
625	}
626
627	return new Complex($rPower * \cos($theta), $rPower * \sin($theta), $complex->getSuffix());
628	}
629
630	/**
631	* Returns the rho of a complex number.
632	* This is the distance/radius from the centrepoint to the representation of the number in polar coordinates.
633	*
634	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
635	* @return float The rho value of the complex argument.
636	* @throws Exception If argument isn't a valid real or complex number.
637	*/
638	public static function rho($complex): float
639	{
640	$complex = Complex::validateComplexArgument($complex);
641
642	return \sqrt(
643	($complex->getReal() * $complex->getReal()) +
644	($complex->getImaginary() * $complex->getImaginary())
645	);
646	}
647
648	/**
649	* Returns the secant of a complex number.
650	*
651	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
652	* @return TablePress\Complex The secant of the complex argument.
653	* @throws Exception If argument isn't a valid real or complex number.
654	* @throws \InvalidArgumentException If function would result in a division by zero
655	*/
656	public static function sec($complex): TablePress\Complex
657	{
658	$complex = Complex::validateComplexArgument($complex);
659
660	return self::inverse(self::cos($complex));
661	}
662
663	/**
664	* Returns the hyperbolic secant of a complex number.
665	*
666	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
667	* @return TablePress\Complex The hyperbolic secant of the complex argument.
668	* @throws Exception If argument isn't a valid real or complex number.
669	* @throws \InvalidArgumentException If function would result in a division by zero
670	*/
671	public static function sech($complex): TablePress\Complex
672	{
673	$complex = Complex::validateComplexArgument($complex);
674
675	return self::inverse(self::cosh($complex));
676	}
677
678	/**
679	* Returns the sine of a complex number.
680	*
681	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
682	* @return TablePress\Complex The sine of the complex argument.
683	* @throws Exception If argument isn't a valid real or complex number.
684	*/
685	public static function sin($complex): TablePress\Complex
686	{
687	$complex = Complex::validateComplexArgument($complex);
688
689	if ($complex->isReal()) {
690	return new Complex(\sin($complex->getReal()));
691	}
692
693	return new Complex(
694	\sin($complex->getReal()) * \cosh($complex->getImaginary()),
695	\cos($complex->getReal()) * \sinh($complex->getImaginary()),
696	$complex->getSuffix()
697	);
698	}
699
700	/**
701	* Returns the hyperbolic sine of a complex number.
702	*
703	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
704	* @return TablePress\Complex The hyperbolic sine of the complex argument.
705	* @throws Exception If argument isn't a valid real or complex number.
706	*/
707	public static function sinh($complex): TablePress\Complex
708	{
709	$complex = Complex::validateComplexArgument($complex);
710
711	if ($complex->isReal()) {
712	return new Complex(\sinh($complex->getReal()));
713	}
714
715	return new Complex(
716	\sinh($complex->getReal()) * \cos($complex->getImaginary()),
717	\cosh($complex->getReal()) * \sin($complex->getImaginary()),
718	$complex->getSuffix()
719	);
720	}
721
722	/**
723	* Returns the square root of a complex number.
724	*
725	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
726	* @return TablePress\Complex The Square root of the complex argument.
727	* @throws Exception If argument isn't a valid real or complex number.
728	*/
729	public static function sqrt($complex): TablePress\Complex
730	{
731	$complex = Complex::validateComplexArgument($complex);
732
733	$theta = self::theta($complex);
734	$delta1 = \cos($theta / 2);
735	$delta2 = \sin($theta / 2);
736	$rho = \sqrt(self::rho($complex));
737
738	return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix());
739	}
740
741	/**
742	* Returns the tangent of a complex number.
743	*
744	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
745	* @return TablePress\Complex The tangent of the complex argument.
746	* @throws Exception If argument isn't a valid real or complex number.
747	* @throws InvalidArgumentException If function would result in a division by zero
748	*/
749	public static function tan($complex): TablePress\Complex
750	{
751	$complex = Complex::validateComplexArgument($complex);
752
753	if ($complex->isReal()) {
754	return new Complex(\tan($complex->getReal()));
755	}
756
757	$real = $complex->getReal();
758	$imaginary = $complex->getImaginary();
759	$divisor = 1 + \pow(\tan($real), 2) * \pow(\tanh($imaginary), 2);
760	if ($divisor == 0.0) {
761	throw new InvalidArgumentException('Division by zero');
762	}
763
764	return new Complex(
765	\pow(self::sech($imaginary)->getReal(), 2) * \tan($real) / $divisor,
766	\pow(self::sec($real)->getReal(), 2) * \tanh($imaginary) / $divisor,
767	$complex->getSuffix()
768	);
769	}
770
771	/**
772	* Returns the hyperbolic tangent of a complex number.
773	*
774	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
775	* @return TablePress\Complex The hyperbolic tangent of the complex argument.
776	* @throws Exception If argument isn't a valid real or complex number.
777	* @throws \InvalidArgumentException If function would result in a division by zero
778	*/
779	public static function tanh($complex): TablePress\Complex
780	{
781	$complex = Complex::validateComplexArgument($complex);
782	$real = $complex->getReal();
783	$imaginary = $complex->getImaginary();
784	$divisor = \cos($imaginary) * \cos($imaginary) + \sinh($real) * \sinh($real);
785	if ($divisor == 0.0) {
786	throw new InvalidArgumentException('Division by zero');
787	}
788
789	return new Complex(
790	\sinh($real) * \cosh($real) / $divisor,
791	0.5 * \sin(2 * $imaginary) / $divisor,
792	$complex->getSuffix()
793	);
794	}
795
796	/**
797	* Returns the theta of a complex number.
798	* This is the angle in radians from the real axis to the representation of the number in polar coordinates.
799	*
800	* @param TablePress\Complex\|mixed $complex TablePress\Complex number or a numeric value.
801	* @return float The theta value of the complex argument.
802	* @throws Exception If argument isn't a valid real or complex number.
803	*/
804	public static function theta($complex): float
805	{
806	$complex = Complex::validateComplexArgument($complex);
807
808	if ($complex->getReal() == 0.0) {
809	if ($complex->isReal()) {
810	return 0.0;
811	} elseif ($complex->getImaginary() < 0.0) {
812	return M_PI / -2;
813	}
814	return M_PI / 2;
815	} elseif ($complex->getReal() > 0.0) {
816	return \atan($complex->getImaginary() / $complex->getReal());
817	} elseif ($complex->getImaginary() < 0.0) {
818	return -(M_PI - \atan(\abs($complex->getImaginary()) / \abs($complex->getReal())));
819	}
820
821	return M_PI - \atan($complex->getImaginary() / \abs($complex->getReal()));
822	}
823	}
824