numpy.sqrt

Eigenvalues with numpy.linalg: normal modes of coupled oscillators

• print(f"one glider on one spring: sqrt(k/m) = {np.sqrt(k / m):.3f} rad/s")
• omega = np.sqrt(w2) # rad/s
• f_exact = np.sqrt(k / m * np.array([2 - np.sqrt(2), 2, 2 + np.sqrt(2)])) / (2 * np.pi)
• D = K1 / np.sqrt(np.outer(m_co2, m_co2)) # K_ij / sqrt(m_i m_j)
• X = Q / np.sqrt(m_co2)[:, None] # back from q to displacements x
• D = stiffness([0, k_bond, k_bond, 0]) / np.sqrt(np.outer(mass, mass))

and 2 more lines in this tutorial

Filtering with scipy.signal: mains hum and noise out of an ECG

• return np.sqrt(np.mean(d ** 2))
• predicted = 0.05 * np.sqrt(40 / (fs / 2))

Numerical integration with scipy.integrate: the area under a measured peak

• counts = (AREA / (WIDTH * np.sqrt(2 * np.pi)) * np.exp(-0.5 * ((lam - CENTER) / WIDTH) ** 2)
• d_slope, d_intercept = np.sqrt(np.diag(C))
• sigma = fwhm / (2 * np.sqrt(2 * np.log(2)))
• I, err, info = quad(lambda theta: 1 / np.sqrt(np.cos(theta) - np.cos(theta0)), 0, theta0, full_output=1)
• T = 4 * np.sqrt(L / (2 * g)) * I
• T0 = 2 * np.pi * np.sqrt(L / g)

and 7 more lines in this tutorial

Random numbers with numpy.random: ten thousand reproducible random walks

• rel_se = x2.std(ddof=1) / np.sqrt(W) / msd
• rel_se_theory = np.sqrt(2 / W)
• x_uniform = rng.uniform(-np.sqrt(3), np.sqrt(3), size=(W, N)).sum(axis=1)
• band = 1.96 * np.sqrt(2 * (n**2 - n) / W) # 95 % band of the theory, from Step 3
• top.plot(n, sign * np.sqrt(msd_n), color=ACCENT)
• top.plot(n, sign * np.sqrt(n), color=INK, lw=1.2)

and 2 more lines in this tutorial

scipy.stats from the ground up: is the difference between two samples real?

• print(f"{name}: mean {d.mean:5.2f} mg variance {d.variance:4.2f} mg² sd {np.sqrt(d.variance):4.2f} mg "
• se_diff = np.sqrt(stats.sem(a)**2 + stats.sem(b)**2)

solve_ivp from the ground up: the pendulum beyond small angles

• T0 = 2 * np.pi * np.sqrt(L / g)
• T_exact = 4 * np.sqrt(L / g) * ellipk(np.sin(theta0 / 2) ** 2)
• T_exact = 4 * np.sqrt(L / g) * ellipk(np.sin(np.radians(a_fine) / 2) ** 2)