You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
157 lines
4.4 KiB
Markdown
157 lines
4.4 KiB
Markdown
PHPComplex
|
|
==========
|
|
|
|
---
|
|
|
|
PHP Class for handling Complex numbers
|
|
|
|
Master: [](http://travis-ci.org/MarkBaker/PHPComplex)
|
|
|
|
Develop: [](http://travis-ci.org/MarkBaker/PHPComplex)
|
|
|
|
[](https://xkcd.com/2028/)
|
|
|
|
---
|
|
|
|
The library currently provides the following operations:
|
|
|
|
- addition
|
|
- subtraction
|
|
- multiplication
|
|
- division
|
|
- division by
|
|
- division into
|
|
|
|
together with functions for
|
|
|
|
- theta (polar theta angle)
|
|
- rho (polar distance/radius)
|
|
- conjugate
|
|
* negative
|
|
- inverse (1 / complex)
|
|
- cos (cosine)
|
|
- acos (inverse cosine)
|
|
- cosh (hyperbolic cosine)
|
|
- acosh (inverse hyperbolic cosine)
|
|
- sin (sine)
|
|
- asin (inverse sine)
|
|
- sinh (hyperbolic sine)
|
|
- asinh (inverse hyperbolic sine)
|
|
- sec (secant)
|
|
- asec (inverse secant)
|
|
- sech (hyperbolic secant)
|
|
- asech (inverse hyperbolic secant)
|
|
- csc (cosecant)
|
|
- acsc (inverse cosecant)
|
|
- csch (hyperbolic secant)
|
|
- acsch (inverse hyperbolic secant)
|
|
- tan (tangent)
|
|
- atan (inverse tangent)
|
|
- tanh (hyperbolic tangent)
|
|
- atanh (inverse hyperbolic tangent)
|
|
- cot (cotangent)
|
|
- acot (inverse cotangent)
|
|
- coth (hyperbolic cotangent)
|
|
- acoth (inverse hyperbolic cotangent)
|
|
- sqrt (square root)
|
|
- exp (exponential)
|
|
- ln (natural log)
|
|
- log10 (base-10 log)
|
|
- log2 (base-2 log)
|
|
- pow (raised to the power of a real number)
|
|
|
|
|
|
---
|
|
|
|
# Usage
|
|
|
|
To create a new complex object, you can provide either the real, imaginary and suffix parts as individual values, or as an array of values passed passed to the constructor; or a string representing the value. e.g
|
|
|
|
```
|
|
$real = 1.23;
|
|
$imaginary = -4.56;
|
|
$suffix = 'i';
|
|
|
|
$complexObject = new Complex\Complex($real, $imaginary, $suffix);
|
|
```
|
|
or
|
|
```
|
|
$real = 1.23;
|
|
$imaginary = -4.56;
|
|
$suffix = 'i';
|
|
|
|
$arguments = [$real, $imaginary, $suffix];
|
|
|
|
$complexObject = new Complex\Complex($arguments);
|
|
```
|
|
or
|
|
```
|
|
$complexString = '1.23-4.56i';
|
|
|
|
$complexObject = new Complex\Complex($complexString);
|
|
```
|
|
|
|
Complex objects are immutable: whenever you call a method or pass a complex value to a function that returns a complex value, a new Complex object will be returned, and the original will remain unchanged.
|
|
This also allows you to chain multiple methods as you would for a fluent interface (as long as they are methods that will return a Complex result).
|
|
|
|
## Performing Mathematical Operations
|
|
|
|
To perform mathematical operations with Complex values, you can call the appropriate method against a complex value, passing other values as arguments
|
|
|
|
```
|
|
$complexString1 = '1.23-4.56i';
|
|
$complexString2 = '2.34+5.67i';
|
|
|
|
$complexObject = new Complex\Complex($complexString1);
|
|
echo $complexObject->add($complexString2);
|
|
```
|
|
or pass all values to the appropriate function
|
|
```
|
|
$complexString1 = '1.23-4.56i';
|
|
$complexString2 = '2.34+5.67i';
|
|
|
|
echo Complex\add($complexString1, $complexString2);
|
|
```
|
|
If you want to perform the same operation against multiple values (e.g. to add three or more complex numbers), then you can pass multiple arguments to any of the operations.
|
|
|
|
You can pass these arguments as Complex objects, or as an array or string that will parse to a complex object.
|
|
|
|
## Using functions
|
|
|
|
When calling any of the available functions for a complex value, you can either call the relevant method for the Complex object
|
|
```
|
|
$complexString = '1.23-4.56i';
|
|
|
|
$complexObject = new Complex\Complex($complexString);
|
|
echo $complexObject->sinh();
|
|
```
|
|
or you can call the function as you would in procedural code, passing the Complex object as an argument
|
|
```
|
|
$complexString = '1.23-4.56i';
|
|
|
|
$complexObject = new Complex\Complex($complexString);
|
|
echo Complex\sinh($complexObject);
|
|
```
|
|
When called procedurally using the function, you can pass in the argument as a Complex object, or as an array or string that will parse to a complex object.
|
|
```
|
|
$complexString = '1.23-4.56i';
|
|
|
|
echo Complex\sinh($complexString);
|
|
```
|
|
|
|
In the case of the `pow()` function (the only implemented function that requires an additional argument) you need to pass both arguments when calling the function procedurally
|
|
|
|
```
|
|
$complexString = '1.23-4.56i';
|
|
|
|
$complexObject = new Complex\Complex($complexString);
|
|
echo Complex\pow($complexObject, 2);
|
|
```
|
|
or pass the additional argument when calling the method
|
|
```
|
|
$complexString = '1.23-4.56i';
|
|
|
|
$complexObject = new Complex\Complex($complexString);
|
|
echo $complexObject->pow(2);
|
|
```
|