Updates

I plan to add more methods along the way

The trigonometric interpolation is yet to be updates and configured the below code presents the current problems being faced any help would be much appreciated

import numpy as np
import plotly.graph_objs as go
from plotly.subplots import make_subplots
import sys
import math
import matplotlib.pyplot as plt
## will be updated later in development

def plot_trigonometric_interpolation(x_points, y_points, x_new, y_new):

    fig = make_subplots(rows=1, cols=1)

    # Scatter plot of original data points
    fig.add_trace(
        go.Scatter(x=x_points, y=y_points, mode='markers', name='Data Points', marker=dict(color='black')),
        row=1, col=1
    )

    # Line plot of interpolated values
    fig.add_trace(
        go.Scatter(x=x_new, y=y_new, mode='lines', name='Trigonometric Interpolation', line=dict(color='red')),
        row=1, col=1
    )

    # Update layout
    fig.update_layout(
        title='Trigonometric Interpolation',
        xaxis_title='x',
        yaxis_title='y',
        showlegend=True,
        legend=dict(x=0.7, y=1.1),
        template='plotly_white'
    )

    # Show plot
    fig.show()

def trigonometric_interpolation(x, y, x_new):

    N = len(x)
    if N % 2 == 0:
        k = np.arange(-N//2, N//2)
    else:
        k = np.arange(-(N-1)//2, (N+1)//2)

    Y_k = np.fft.fftshift(np.fft.fft(y)) / N
    y_new = np.zeros_like(x_new, dtype=np.complex128)

    for i, k_val in enumerate(k):
        y_new += Y_k[i] * np.exp(2j * np.pi * k_val * x_new / N)

    return y_new.real
def trigonometric_interpolation(x, y, x_new):
    N = len(x)
    if N % 2 == 0:
        k = np.arange(-N//2, N//2)  # Use a symmetric range of k values for even N
    else:
        k = np.arange(-(N-1)//2, (N+1)//2)  # Use a symmetric range of k values for odd N 

    Y_k = np.fft.fftshift(np.fft.fft(y)) / N
    y_new = np.zeros_like(x_new, dtype=np.complex128)

    for i, k_val in enumerate(k):
        y_new += Y_k[i] * np.exp(2j * np.pi * k_val * x_new / (x[-1] - x[0])) # Scale x_new by the range of original x

    return y_new.real
def e_complex_pow(power):
    return complex(np.cos(power), np.sin(power))

def get_complex_representation(points):
    N = len(points)
    xs = np.array([(2*np.pi * i) / N for i in range(N)])
    ys = np.array(points, dtype=np.complex_)

    w = e_complex_pow(2*np.pi / N)

    # Fourier-Matrix
    F_N = np.array([ [w ** (j * k) for j in range(N)] for k in range(-(N-1)//2, (N-1)//2 + 1) ])

    Ck_s = (1 / N) * (np.conj(F_N) @ ys)  # Fourier-Coefficients    
    return Ck_s


def get_sin_cos_representation(points):
    Ck_s = get_complex_representation(points)
    Ck_zero_idx = (len(Ck_s)-1) // 2

    Ak_s = [2 * Ck_s[Ck_zero_idx]] + [Ck_s[Ck_zero_idx + n] + Ck_s[Ck_zero_idx - n] for n in range(1, Ck_zero_idx+1)]  # cosine coefficients
    Bk_s = [0] + [complex(0, Ck_s[Ck_zero_idx + n] - Ck_s[Ck_zero_idx - n]) for n in range(1, Ck_zero_idx+1)]  # sine coefficients

    for n in range(len(Ak_s)):
        if Ak_s[n].imag < 1e-3:
            Ak_s[n] = Ak_s[n].real

        if Bk_s[n].imag < 1e-3:
            Bk_s[n] = Bk_s[n].real

    return np.array(Ak_s), np.array(Bk_s)


def eval_sin_cos_representation(t, A, B):
    return A[0]/2 + sum(A[n] * np.cos(n * t) + B[n] * np.sin(n * t) for n in range(1, len(A)))


def plot_sin_cos_representation(A, B, y_points, start=-10, end=10):
    Xs = np.linspace(start, end, 5000)
    Ys = [eval_sin_cos_representation(t, A, B) for t in Xs]

    N = len(points)
    x_points = np.array([(2*np.pi * i) / N for i in range(N)])

    plt.figure(figsize=(14,7))
    plt.plot(Xs, Ys)
    plt.scatter(x_points, y_points, c='black')
    plt.show()