tclements

using BenchmarkTools. LinearAlgebra
function naive_mul!(C,A,B)
    C[1,1] = A[1,1] * B[1,1] + A[1,2] * B[2,1]
    C[1,2] = A[1,1] * B[1,2] + A[1,2] * B[2,2]
    C[2,1] = A[2,1] * B[1,1] + A[2,2] * B[2,1]
    C[2,2] = A[2,1] * B[1,2] + A[2,2] * B[2,2]
    return nothing
end 

function strassen_mul!(C,A,B)

tclements

using GPUArrays, FFTW

"""
    hilbert(x)
Computes the analytic representation of x, ``x_a = x + j
\\hat{x}``, where ``\\hat{x}`` is the Hilbert transform of x,
along the first dimension of x.
"""
function hilbert(x::GPUArray{T}) where T<:Real
    N = size(x, 1)

tclements

# Create a function to reshape a 1d array using a sliding window with a step.
# NOTE: The function uses numpy's internat as_strided function because looping in python is slow in comparison.

# Adopted from http://www.rigtorp.se/2011/01/01/rolling-statistics-numpy.html and 
# https://gist.github.com/codehacken/708f19ae746784cef6e68b037af65788
import numpy as np

# Reshape a numpy array 'a' of shape (x) to form shape((n - window_size) // step + 1, window_size))
def rolling_window(a, window, step):
    shape = a.shape[:-1] + ((a.shape[-1] - window + 1)//step, window)

tclements

using GPUArrays
using CuArrays
import Base.sin, Base.cos, Base.exp

function sin(A::GPUArray{ComplexF64})
      return sin.(real(A)) .* cosh.(imag(A))  .+ im .* cos.(real(A)) .* sinh.(imag(A))
end

function cos(A::GPUArray{ComplexF64})
      return cos.(real(A)) .* cosh.(imag(A)) .- im .* sin.(real(A)) .* sinh.(imag(A))