First edition - Numerical Methods in Physics with Python

Codes (first edition)

Here are all the code listings from the book, bundled together into a zipped directory. Alternatively, you can clone the git repo.

Below, you can browse through the same codes, chapter by chapter. These programs are discussed in detail in the main text so, to avoid duplication, they don’t contain comments.

Chapter 1: Idiomatic Python

forelse.py	Illustration of the for-else idiom
plotex.py	Basic example of Matplotlib use
vectorfield.py	Visualizing a vector field via Matplotlib's streamplot()

Chapter 2: Numbers

kahansum.py	Compensated summation
naiveval.py	Naive evaluation of a mathematically tricky function
compexp.py	Computing the exponential function
recforw.py	Forward recursion
recback.py	Backward recursion
cancel.py	Example where rounding errors cancel
chargearray.py	Constructing an array of electrical charges
legendre.py	Evaluating Legendre polynomials and their derivatives
multipole.py	Multipole expansion for point charges

Chapter 3: Derivatives

finitediff.py	Finite-difference approximations to the first derivative
richardsondiff.py	Richardson extrapolation for finite differences
psis.py	Computing the wave function for two physical scenarios
kinetic.py	Evaluating the local kinetic energy

Chapter 4: Matrices

triang.py	Infrastructure for triangular matrices and testing
gauelim.py	Gaussian elimination
ludec.py	LU decomposition
gauelim_pivot.py	Gaussian elimination with partial pivoting
jacobi.py	Jacobi iterative method for linear systems
power.py	Power method for eigenvalue/eigenvector evaluation
invpowershift.py	Inverse-power method with shifting
qrdec.py	QR decomposition
qrmet.py	QR method for eigenvalues
eig.py	All eigenvalues and eigenvectors
kron.py	Kronecker product of two matrices
twospins.py	Two interacting spin-half particles
threespins.py	Three interacting spin-half particles

Chapter 5: Roots

fixedpoint.py	Fixed-point iteration
bisection.py	Bisection method
secant.py	Secant method
legroots.py	Zeros of Legendre polynomials using Newton's method
multi_newton.py	Newton's method for multidimensional problems
descent.py	Minimization via the gradient descent method
action.py	Discrete Newton method for extremizing the action

Chapter 6: Approximation

barycentric.py	Lagrange interpolation using the barycentric formula
splines.py	Cubic-spline interpolation
triginterp.py	Trigonometric interpolation using sines and cosines
fft.py	Fast Fourier transform
linefit.py	Least-squares straight-line fit
normalfit.py	Least-squares fitting using the normal equations
blackbody.py	Non-linear fitting for the Stefan-Boltzmann law

Chapter 7: Integrals

newtoncotes.py	Newton-Cotes quadrature
adaptive.py	Adaptive integration
romberg.py	Romberg integration
gauleg.py	Gauss-Legendre quadrature
montecarlo.py	Monte Carlo quadrature with importance sampling
eloc.py	Many-particle wave function and local energy
vmc.py	Variational Monte Carlo via the Metropolis algorithm

Chapter 8: Differential Equations

ivp_one.py	Initial-value problem solvers
ivp_two.py	Runge-Kutta for simultaneous differential equations
bvp_shoot.py	Boundary-value problem via the shooting method
bvp_matrix.py	Boundary-value problem via the matrix approach
evp_shoot.py	Mathieu equation via the shooting method
evp_matrix.py	Mathieu equation via the matrix approach
poisson.py	Poisson's equation in two dimensions via the FFT

Errata (first edition)

p. 124 For elimination (third bullet point) not to impact the determinant, this should refer (not to a linear combination, but) to “the sum of that row/equation with a multiple of any other row/equation”.
p. 306 Problem 11 should say “Taylor expand $f(x^{(k-1)})$ and $f(x^{(k-2)})$ “. Then, it should say “Plug these relations”.
p. 363 “Observe that in $\partial p(x)$ ” –> “Observe that in $\partial p(x_j)$ “
p. 390 Problem 29 should be referring to polynomials with 2, 3, and 4 parameters (and “third degree” –> “three-parameter case” and “fourth-degree” –> “four-parameter case”)
p. 436 In Eq. (7.120), there should be no product symbol
p. 437 In Eq. (7.128), the sum should be over k
p. 459 In fn 42, the integrand should be using x’
p. 490 In problem 26, it would be more appropriate to say that $I_4$ can be given in terms of the first and second complete elliptic integrals
p. 491 In problem 31, $Y_0 = (X_0 - \mu)/\sigma^2$ –> $Y_0 = (X_0 - \mu)/\sigma$
p. 491 In problem 34, you’re supposed to use Gauss-Legendre for “ $n = 5-30$ “
p. 493 Problem 43: “the fact that $H_1(x) = 2x$ ” –> “the needed Hermite polynomials”
p. 556 Problem 25, $w(0)=1$ –> $w(0)=0$

Numerical Methods in Physics with Python

ALEX GEZERLIS

Codes (first edition)

Errata (first edition)