API reference

Data

vp.features Features on event tables

Per-entity features with state, called on a pandas DataFrame. vipyr

delinquency

Days past due, worst in 12 months, ever cured after 60+ (catalog/delinquency.viv).

ewma

Gap-aware EWMA with resets (catalog/ewma.viv).

sessions

Gap-based sessions per user (catalog/sessions.viv).

since_last

Seconds since the last event of a kind, and of any kind (catalog/since_last.viv).

streaks

Consecutive active days (catalog/streaks.viv).

velocity

Trailing-window counts, sum and distinct count (catalog/velocity.viv).

Statistics

vp.stats Statistics

Probability distributions, the special functions under them, descriptive statistics, least squares with inference, and generalized linear models. vipyr

describe

The mean, variance, skewness and kurtosis of a sample, with sums that keep their digits.

glm

Generalized linear models by R's IRLS: binomial, Poisson, Gamma and Gaussian, with R's warnings.

ols

Least squares with statsmodels' inference table, by pivoted QR, checked against NIST's certified results.

quantile

Sample quantiles of Hyndman and Fan's nine types, as R's quantile() computes them.

Machine learning

vp.gpt Language models

A small GPT (nanoGPT's shape, the speedrun's Muon and Adam) trained on text, sampled, and returned as named arrays. vipyr

attention

The attention weights of every head of a GPT for one prompt.

generate

Continue a prompt with a trained GPT, one sampled token at a time.

loss

The mean next-token cross-entropy of a GPT on a text.

train

Train a small GPT on a text, character by character, and get the model back as named arrays.

Finance

vp.finance Option pricing

Black-Scholes, binomial trees, Heston by Fourier-cosine series, finite differences. vipyr

bs_greeks

Black-Scholes delta, gamma and vega of one option.

bs_price

The Black-Scholes price of a European option on a stock with continuous dividend yield q.

cn_american_put

The American put by Crank-Nicolson on M space intervals over [0, Smax] and Nt time steps, of which the first `implicit` are fully implicit (two half-size steps each).

crr_price

The CRR value with N steps: u = exp(sigma sqrt(dt)), d = 1/u, the risk-neutral up probability p = (exp((r - q) dt) - d) / (u - d), values rolled back from maturity; an American option takes the larger of continuing and exercising at every node.

heston_cos

Heston prices of European options on one stock for an array of strikes, with N cosine terms and the truncation half-width L standard deviations.

implied_vol

The implied volatility of one quote, or NaN when the price is outside the no-arbitrage bounds.

Science

vp.scf Quantum chemistry

Hartree-Fock for molecules in Gaussian basis sets. vipyr-chem

run

Restricted or unrestricted Hartree-Fock for a molecule in a Gaussian basis set, with PySCF's names, shapes and units.

vp.dft Electronic structure of solids

Plane-wave density-functional theory of crystals. vipyr-chem

pw

The iterative engine: the same Kohn-Sham calculation as dft/pwdft.viv, without ever forming the Hamiltonian as a matrix.

vp.nuclear Nuclear structure

Mean-field and shell-model calculations of nuclei. vipyr-nuclear

shell_model

The lowest states of a nucleus in the nuclear shell model: Z valence protons and N valence neutrons outside a closed core, in one of the shipped spaces (the sd shell with USDB, the p shell with Cohen-Kurath), or in a .sps and .int pair read from disk.

skyrme_hf

The Skyrme-Hartree-Fock ground state of a spherical closed-shell nucleus: binding energy, radii, single-particle levels and densities, with the forces SLy4, SLy5, SIII or SkM*.

vp.plasma Plasma physics

Kinetic simulations of a collisionless plasma. vipyr-plasma

landau

Landau damping of a Langmuir wave, computed from the Vlasov-Poisson equations and checked against the exact root of the dispersion relation.

vp.statmech Statistical mechanics

Lattice models sampled by Monte Carlo, checked against exact solutions. vipyr

ising

The two-dimensional Ising model on an L by L square lattice with periodic edges, sampled by Metropolis (checkerboard order) or Wolff clusters at temperature T, coupling J and field h.

Math

vp.special Special functions

Functions with no closed form that physics codes call in their inner loops. vipyr

boys

The Boys functions F_0(T) ..

faddeeva_w

The Faddeeva function w(z) = exp(-z^2) erfc(-i z).

plasma_z

The plasma dispersion function Z(zeta) = i sqrt(pi) w(zeta) and its derivative Z'(zeta) = -2 (1 + zeta Z(zeta)), anywhere in the plane.

vp.linalg Linear algebra

The Euclidean norm, and SciPy-named aliases of vp.control's solvers. vipyr

enorm

The Euclidean norm of x, with no overflow or underflow in the sum of squares (MINPACK enorm).

lqr

Alias of vp.control.lqr .

schur

Alias of vp.control.schur .

solve_care

Alias of vp.control.care .

solve_lyapunov

Alias of vp.control.lyapunov .

vp.ode Differential equations

Stiff and non-stiff initial value problems: Dormand-Prince, Radau IIA and BDF, with events, exact Jacobians and batches. vipyr

batch

Solve one initial value problem for many parameter sets and initial states in one call.

solve

Solve an initial value problem y' = f(t, y, p), stiff or not, with the right-hand side in Viv.

vp.optimize Fitting and optimization

Nonlinear least squares, curve fitting with parameter covariances and root finding by MINPACK's Levenberg-Marquardt, the residuals compiled with it. vipyr

curve_fit

Fit a model's parameters to data by least squares and estimate their covariance, as SciPy's curve_fit.

least_squares

Minimize a sum of squares of nonlinear residuals by MINPACK's Levenberg-Marquardt, with the residuals in Viv.

root

Solve a square nonlinear system F(x) = 0 by Levenberg-Marquardt, as SciPy's root(method='lm').

vp.gguf Model files

GGUF files, the format of ggml and llama.cpp: metadata, the tensor table, and tensors dequantized from ggml's number formats. vipyr

read

Read a GGUF file's metadata and tensor table.

tensor

One tensor of a GGUF file, dequantized to float32.

vp.randla Randomized linear algebra

Low-rank approximations and trace estimates from random sketches. vipyr

rp_cholesky

Randomly pivoted Cholesky: F with A ~ F F^T.

trace_hutchpp

Hutch++'s trace estimate from m products.

vp.liquids Simulation of liquids

Molecular dynamics and Monte Carlo of the Lennard-Jones liquid, from Allen and Tildesley's examples, with g(r), diffusion and the equation of state they are tested against. vipyr-liquids

diffusion

Time correlation functions of a trajectory and the diffusion coefficient they give: the velocity autocorrelation function <v(0) .

eos

The Lennard-Jones equation of state at one state point, from the fits of Thol et al.: pressure, energy, heat capacities, chemical potential and activity for the full potential, the same moved to the potential cut (not shifted) at 2.5 sigma by the long-range and delta corrections, and for the potential cut and shifted at 2.5 sigma, with the residual free energy and its derivatives behind each.

error_calc

How correlation between successive values changes the error of a time average, shown on a series whose correlation time is known exactly.

mc_npt

Metropolis Monte Carlo of Lennard-Jones atoms at constant N, P and T, the potential cut (not shifted) at r_cut.

mc_nvt

Metropolis Monte Carlo of Lennard-Jones atoms at constant N, V and T, the potential cut (not shifted) at r_cut.

md_nve

Molecular dynamics of Lennard-Jones atoms at constant N, V and E: velocity Verlet in a periodic cubic box, the potential cut and shifted at r_cut.

md_nvt

Molecular dynamics of Lennard-Jones atoms at constant N, V and T, the temperature held by a Nose-Hoover chain of three thermostats, integrated by the time-reversible splitting of Martyna, Tuckerman, Tobias and Klein (1996): velocity Verlet for the atoms, wrapped in quarter and half steps of the chain.

pair_distribution

The pair distribution function g(r) of a set of configurations of N atoms in a periodic cubic box: a histogram of every pair's separation (nearest image) out to half the box, divided by what an ideal gas of the same density would give in each spherical shell.

Dynamics and control

vp.control Control

LQR gains, Riccati and Lyapunov solvers, and closed-loop simulation of a cart-pole. vipyr

care

The stabilizing solution X of A^T X + X A - X B R^-1 B^T X + Q = 0, as scipy.linalg.solve_continuous_are(A, B, Q, R).

cartpole_model

The cart-pole linearized about the upright: A = df/ds (4 by 4) and B = df/du (4 by 1), by central differences of step h on the nonlinear dynamics, so the linear model is the one the simulation runs.

lqr

The linear-quadratic regulator for xdot = A x + B u with cost int x^T Q x + u^T R u: the gain K = R^-1 B^T P, m by n, with u = -K x, and the Riccati solution P.

lyapunov

The X with A X + X A^T = Q, as scipy.linalg.solve_continuous_lyapunov(A, Q).

schur

The real Schur decomposition A = Z T Z^T: T quasi-triangular, Z orthogonal.

simulate

The nonlinear cart-pole under the state feedback u = -K s, from the state s0 for `steps` steps of dt (fourth-order Runge-Kutta, the force held over each step).

Power systems

vp.power Power systems

AC and DC power flow on MATPOWER cases: Newton-Raphson, fast-decoupled and DC. vipyr

contingency

N-1 contingency analysis: every branch and generator outage solved by AC power flow, with DC PTDF/LODF screening.

cpf

The continuation power flow: the PV curve of a transfer into one bus, through the nose.

interconnect

A generator-interconnection study: violations before and after the project, distribution factors, and the transfer limit.

read_raw

Read a PSS/E RAW file (revisions 32 to 34) into MATPOWER's arrays.

runpf

Solve the AC or DC power flow of a MATPOWER case: bus voltages, generator outputs and branch flows.

short_circuit

Three-phase short-circuit currents by IEC 60909 at the buses of a case.