Python — SciPy

Install & relationship to NumPy

pip install scipy

SciPy builds ON NumPy: same arrays, plus a library of tested scientific algorithms. Rule of thumb — NumPy stores the numbers; SciPy computes the hard stuff.

import numpy as np
import scipy

Constants & special values

from scipy import constants

constants.speed_of_light     # 299792458.0
constants.g                  # 9.80665
constants.pi                 # (np.pi too)

Statistics — the most-used module

from scipy import stats

data = [22, 25, 21, 28, 90]     # 90 is an outlier

stats.describe(data)             # n, minmax, mean, variance, skew…
stats.mode(data)

# z-scores: how many standard deviations from the mean?
z = stats.zscore(data)           # 90 → ~2.1 → outlier flag

# distributions:
stats.norm.pdf(0)                # normal curve height at 0
stats.norm.cdf(1.96)             # area left of 1.96 ≈ 0.975

# statistical tests:
group_a = [20, 22, 19, 24]
group_b = [30, 28, 32, 27]
t, p = stats.ttest_ind(group_a, group_b)
p < 0.05        # is the difference statistically meaningful?

Optimization — finding minimums

from scipy.optimize import minimize

def cost(x):
    return (x - 3) ** 2 + 5       # parabola with minimum at x=3

result = minimize(cost, x0=0)      # start searching from 0
result.x                           # array([2.999…]) — found it!
result.fun                         # minimum value ≈ 5

Also minimize_scalar, linprog (linear programming), curve_fit (fit equations to data).

Interpolation — filling gaps

from scipy.interpolate import interp1d

x = [0, 10, 20]
y = [0, 100, 200]
f = interp1d(x, y)          # linear in-betweens

f(5)                        # 50.0 — estimated value between points
f_smooth = interp1d(x, y, kind="cubic")   # smooth curves through points

Signal & image quickies

from scipy import signal, ndimage

# smooth noisy data with a moving filter:
clean = signal.savgol_filter(noisy, window_length=11, polyorder=2)

# rotate/zoom/filter images as arrays:
rotated = ndimage.rotate(img_array, angle=45)
blurred = ndimage.gaussian_filter(img_array, sigma=2)

Sparse matrices (awareness)

Huge mostly-zero grids (graphs, recommender data) waste memory densely:

from scipy.sparse import csr_matrix

sparse = csr_matrix(big_and_mostly_zero_array)   # stores only nonzeros

When to reach for SciPy vs hand-rolling

Need	Module
Means/spreads/tests	scipy.stats
Find optimum of function	scipy.optimize
Estimate between samples	scipy.interpolate
Clean noisy signals	scipy.signal
Array math only	stay in NumPy

Gotcha: SciPy functions return NumPy arrays/objects with rich attributes (result.x, .pvalue) — print the result object first to see what you got.

Mini Practice

1. describe() + zscore on a list with one obvious outlier.
2. t-test two grade lists; interpret p-value.
3. minimize(x-5)²+sin(x); verify against graph.
4. Linear-interpolate temperature gaps in hourly readings.
5. Savgol-smooth random noise; plot raw vs clean.

Python track complete — every syllabus topic covered. 🐍✅