DAY 1
Been chatting with chatGpt4, hoping for the inside track on smooth curves. Ended
up asking for an example problem which - in desperation - I asked DeepSeek to solve.
They did an appreciable job, with a quadratic.Then went back to ChatGpt and asked for the
expected solution!! Had to giggle, ChatGpt had python code do the job.Below:
DeepSeek:
Python Code:
import numpy as np
import matplotlib.pyplot as plt
def f(x):
return 0.5*x**2 - 0.5*x + 2
def fp(x):
return x - 0.5
def fpp(x):
return 1.0
x = np.linspace(0.5, 3.5, 400)
plt.figure(figsize=(9,7))
# Position
plt.subplot(3,1,1)
plt.plot(x, f(x), 'b', label='Quadratic interpolant')
plt.scatter([1,2,3],[2,3,5], color='k', zorder=5, label='Data points')
plt.ylabel('f(x)')
plt.legend(loc='upper left')
plt.grid(True, alpha=0.3)
# First derivative (slope)
plt.subplot(3,1,2)
plt.plot(x, fp(x), 'g', label="f'(x)")
plt.axhline(0, color='k', lw=0.7)
plt.ylabel("f'(x)")
plt.legend(loc='upper left')
plt.grid(True, alpha=0.3)
# Second derivative (curvature)
plt.subplot(3,1,3)
plt.plot(x, fpp(x)*np.ones_like(x), 'r', label="f''(x)=1")
plt.ylabel("f''(x)")
plt.xlabel('x')
plt.legend(loc='upper left')
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
* * *
ChatGpt:
Python Code:
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import CubicSpline
# Given data points
x = np.array([1, 2, 3])
y = np.array([2, 3, 5])
# Create a cubic spline interpolation of the data
cs = CubicSpline(x, y, bc_type='natural')
# Generate points for plotting
x_new = np.linspace(1, 3, 100)
y_new = cs(x_new)
# Plotting
plt.figure(figsize=(8, 5))
plt.plot(x, y, 'o', label='Data Points', color='red') # original data points
plt.plot(x_new, y_new, label='Cubic Spline', color='blue') # spline curve
plt.title('Cubic Spline Interpolation')
plt.xlabel('X-axis')
plt.ylabel('Y-axis')
plt.grid()
plt.legend()
plt.show()
* * *
In DeepSeek's defense, I just asked for a smooth curve...
DAY 2
Decided I needed to learn some math!!
Copilot:
* * *
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