A Complex Number is able to be created using the ComplexNum struct, and is constructed as follows:
# ComplexNum(re: Float64, im: Float64)
var myComplex = ComplexNum()
Reading Values
You can read the real and imaginary values from the Complex Number as follows:
myComplex[0] # This returns the real value
myComplex[1] # This returns the imaginary value
Setting Values
You can set the real and imaginary values as follows:
myComplex[0] = 0.1 # Sets real
myComplex[1] = 0.2 # Sets imaginary
Printing
You can print the number as follows:
myComplex.print()
# Prints formatted number (0 + 2i, 5 - 3i)
Operating
You can add, subtract, and multiply Complex Numbers with the +, -, * operators respectively.
Conjugation
You can retrieve the conjugate of the number with the ComplexNum.conjugate() or ComplexNum.c() methods as follows:
var newComplex = myComplex.c()
Or, alternatively, with the __inverse__ dunder method, as follows:
var newComplex = ~myComplex()
These two work exactly the same.
Magnitude
You can retrieve the magnitude of the number with the ComplexNum.magnitude or ComplexNum.m methods as follows:
var magnitude = myComplex.m()
Complex Arrays are Arrays that store Complex Numbers (ComplexNums)
Constructing
It is constructed as follows:
# ComplexArray(length: Int, default_value: ComplexNum = ComplexNum(0,0))
var myArray = ComplexArray(3) # This creates a Complex Array of length 3 with 0 + 0i in every index.
var myArray = ComplexArray(5, ComplexNum(0,-2)) # This creates a Complex Array of length 5 with 0 - 2i in every index.
Getting and Setting
You can get and set the items with the __getitem__ and __setitem__ dunder methods, as follows:
myArray[0] = ComplexNum(0,1)
myArray[0].print()
# Prints 0 + 1i
Printing
You can also print the array’s contents with ComplexArray.print as follows:
myArray.print()
We step away from Arrays and move into Matrices. These form the basis for Qubits and Quantum Gates.
Constructing
You can construct one as follows:
# ComplexMatrix(rows: Int, cols: Int, default_value: ComplexNum = ComplexNum(0,0))
var myMatrix = ComplexMatrix(3, 3) # Creates a 3x3 Matrix with values set to 0 + 0i
var myMatrix = ComplexMatrix(3, 4, ComplexNum(1,2)) # Creates a 3x4 Matrix with values set to 1 + 2i
Getting and Setting
You can set and get values from the matrix with the following syntax:
# ComplexMatrix[row: Int, col: Int]
var value = myMatrix[0, 0]
myMatrix[0,1] = ComplexNum(1,2)
Operating
You can perform elementary operations with the +, - operators.
The * operator is overloaded:
ComplexMatrix * Float64: Every element of the matrix is multiplied by the Float valueComplexMatrix * ComplexArray: Every row of the matrix is multiplied element-wise with the ComplexArrayComplexMatrix * ComplexMatrix: The two matrices are multiplied element-wise.The @ operator achieves matrix multiplication.
var newMat = myMatrixOne @ myMatrixTwo
Transposing
You can transpose any Complex Matrix with the ComplexMatrix.transpose, which swaps the axes.
var transposed = myMatrix.transpose()
You can get the conjugate transpose of any Complex Matrix with the ComplexMatrix.conjugate_transpose method:
var conj_trans = myMatrix.conjugate_transpose()
Printing
And of course, you can print the contents with ComplexMatrix.print()