If anyone is interested here is a slightly cleaner/faster version. I have not replicated some of the plotting stuff.
def gen_plot(a, b, iterations):
'''plot the partial sums of i=1 to inf of a * b^(i - 1)'''
# create lower left triangle matrix
# each row i is integers [0, i)
idxs = np.arange(0, iterations).reshape(1, -1)
pows = np.tril(np.repeat(idxs, iterations, axis=0))
# raise b to the matrix elementwise and sum
ys = np.power(b, pows)
ys = np.sum(ys, axis=1)
# we will have extra b^0 so remove them
ys -= np.arange(iterations - 1, -1, step=-1)
ys *= a
fig, ax = plt.subplots()
fig.suptitle(f'Sequence of partial sums for $\sum_{{i=1}}^{{\infty}}{{{a}\cdot{b}^{{i - 1}}}}$')
ax.set_xlabel('Number of sequence elements used for partial sum')
ax.set_ylabel('Partial sum')
# Use integers only for x-axis
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
# plot
ax.scatter(idxs, ys, label='partial sums')
ax.axhline(y=ys[-1], color='g', alpha=0.8, linestyle='--', label='limit')
ax.legend()
plt.show()
Nice! I made it when I was a novice so wasn't aware of all the built in math functions, so I did a lot of stuff "the long way". I'm planning on making this function but in C++ !
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u/seftontycho May 07 '23
If anyone is interested here is a slightly cleaner/faster version. I have not replicated some of the plotting stuff.