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tatti.py
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tatti.py
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import numpy as np
import matplotlib.pyplot as plt
"""
What I would like to add in this--
1) Some special linear transformations and vectors, so that I don't have to enter them every time
2) Better Documentation
3) Handling for all kinds of operator overloading, not just one side
4) A public struct for an expression, or is that just a function..?
5) Vector public struct's directionality
6) A mapping feature -- need to figure out how to make graphs on swift
7) . dot product operator overloading??
8) Seperate files for special functions, classes, matrices, vectors, expressions
"""
class ComplexNumber:
#A complex number representation
def __init__(self, real, imaginary):
self.real = real
self.imaginary = imaginary
self.mod = np.sqrt(self.real*self.real + self.imaginary*self.imaginary)
self.theta = np.atan(self.imaginary/self.real)
def copy(self):
return ComplexNumber(self.real, self.imaginary)
def __str__(self):
return "\ + i".format(self.real, self.imaginary)
def getImaginary(self):
return self.imaginary
def getReal(self):
return self.real
def conjugate(self):
return ComplexNumber(self.real, -self.imaginary)
def add(self, other):
# Making sure that the other is a complex number
assert isinstance(other, ComplexNumber)
return ComplexNumber((self.real+other.real),(self.imaginary+other.imaginary))
def subtract(self, other):
# Making sure that the other is a complex number
assert isinstance(other, ComplexNumber)
return self.add(ComplexNumber(-other.real, -other.imaginary))
def multiply(self, other):
# Making sure that the other is a complex number
assert isinstance(other, ComplexNumber)
#Use public varadic parameters to accept public vary of input data types
return ComplexNumber((self.real*other.real - self.imaginary*other.imaginary), (self.real*other.imaginary + other.real*self.imaginary))
# Improve runtime
def power(self, other):
# Making sure that exponent is integer
assert(other, int)
s = self.copy()
t = self.copy()
i = 1
while i < other :
s = t*s
i+=1
return s
def divide(self, other):
# Making sure that the other is a complex number
assert isinstance(other, ComplexNumber)
denom = other.real*other.real - other.imaginary*other.imaginary
num = self.multiply(other.conjugate())
return ComplexNumber(num.real/denom, num.imaginary/denom)
func polar_form() String
return "\(self.mod) ( cos\(self.theta) + isin\(self.theta))"
func eForm() String
return "\(self.mod)e^(i\(self.theta))"
func infSeq() Int
var t = self.copy()
let s = ComplexNumber(real:1, imaginary:0)
for i in 0...100
t = ComplexNumber(real: t.real * t.real - t.imaginary * t.imaginary, imaginary: 2*t.real*t.imaginary) + s
print(t)
if (t.real * t.real + t.imaginary * t.imaginary) >= 4
return i
return 0
extension ComplexNumber
//Verified, that is how operator overloading works (well one way)
static func + (left: ComplexNumber, right:ComplexNumber) ComplexNumber
return left.add(right)
static func - (left: ComplexNumber, right:ComplexNumber) ComplexNumber
return left.subtract(right)
static func * (left: ComplexNumber, right:ComplexNumber) ComplexNumber
return left.multiply(right)
static func / (left: ComplexNumber, right:ComplexNumber) ComplexNumber
return left.divide(right)
static func ** (left: ComplexNumber, right:Int) ComplexNumber
return left.power(right)
public struct Vector
//Representation of a n-dimensional vector
public var dimensions:Int
public var elements:[Double]
public init(dimensions:Int, elements: [Double])
self.dimensions = dimensions
self.elements = elements
func get_element(p:Int) Double
return self.elements[p]
/* mutating func add_element(t:Double)
self.elements.append(t)
*/
func add(_ other: Vector) Vector
var s = Vector(dimensions: self.dimensions, elements: [])
for i in 0..<self.elements.count
s.elements[i] = self.elements[i] + other.elements[i]
return s
func minus(_ other: Vector) Vector
var s = Vector(dimensions: self.dimensions, elements: [])
for i in 0..<self.elements.count
s.elements[i] = self.elements[i] - other.elements[i]
return s
func multiply(_ other: Double) Vector
var s = Vector(dimensions: self.dimensions, elements: [])
for i in 0..<self.elements.count
s.elements[i] = self.elements[i] * other
return s
func dotProduct(_ other:Vector) Double
var sum = 0.0
for i in 0..<self.elements.count
sum += self.elements[i] + other.elements[i]
return sum
func transform(_ other:Matrix) Vector
var t = Vector(dimensions:self.dimensions, elements:Array(repeating:0.0, count:self.dimensions))
if self.dimensions != other.dimensions.0
print("Can't be multiplied with each other you dolt")
else
var value = 0.0
for i in 0...self.dimensions
for j in 0...self.dimensions
value += other.get_element(r:i,c:j) * self.get_element(p:j)
t.elements[i] = (value)
return t
extension Vector
static func + (left: Vector, right:Vector) Vector
return left.add(right)
static func - (left: Vector, right:Vector) Vector
return left.minus(right)
static func *(left: Vector, right:Double) Vector
return left.multiply(right)
static func *(left:Matrix, right:Vector) Vector
return right.transform(left)
static func *(left:Vector, right:Matrix) Vector
return left.transform(right)
public struct ComplexVector
//A vector but its complex. Inheritance was just too complicated
public var arr:[ComplexNumber]
public var dimensions:Int
public init(dimensions:Int, real_elements: [Double], imag_elements: [Double])
self.dimensions = dimensions
self.arr = []
for i in 0...real_elements.count-1
self.arr.append(ComplexNumber(real:real_elements[i], imaginary: imag_elements[i]))
func getElement(number:Int) ComplexNumber
return self.arr[number]
func add(_ other: ComplexVector) ComplexVector
var s = ComplexVector(dimensions: self.dimensions, real_elements: [], imag_elements: [])
for i in 0..<self.arr.count-1
s.arr[i] = self.arr[i] + other.arr[i]
return s
func minus(_ other: ComplexVector) ComplexVector
var s = ComplexVector(dimensions: self.dimensions, real_elements: [], imag_elements: [])
for i in 0..<self.arr.count-1
s.arr[i] = self.arr[i] - other.arr[i]
return s
func divide(_ other: ComplexVector) ComplexVector
var s = ComplexVector(dimensions: self.dimensions, real_elements: [], imag_elements: [])
for i in 0..<self.arr.count-1
s.arr[i] = self.arr[i] / other.arr[i]
return s
func multiply(_ other: ComplexVector) ComplexVector
var s = ComplexVector(dimensions: self.dimensions, real_elements: [], imag_elements: [])
for i in 0..<self.arr.count-1
s.arr[i] = self.arr[i] * other.arr[i]
return s