QMCPy Documentation

Contents

• About Our QMC Software Community
  • Quasi-Monte Carlo Community Software
    • Installation
    • The QMCPy Framework
    • Quickstart
    • Developers
    • Collaborators
    • Contributors
    • Citation
    • References
    • Sponsors
• License
• QMCPy Documentation
  • Discrete Distribution Class
    • Abstract Discrete Distribution Class
    • Digital Net Base 2
    • Lattice
    • Halton
    • IID Standard Uniform
  • True Measure Class
    • Abstract Measure Class
    • Uniform
    • Gaussian
    • Brownian Motion
    • Lebesgue
    • Continuous Bernoulli
    • Johnson’s SU
    • Kumaraswamy
    • SciPy Wrapper
  • Integrand Class
    • Abstract Integrand Class
    • Custom Function
    • Keister Function
    • Box Integral
    • European Option
    • Asian Option
    • Multilevel Call Options with Milstein Discretization
    • Linear Function
    • Sobol’ Indices
  • Stopping Criterion Algorithms
    • Abstract Stopping Criterion Class
    • Guaranteed Digital Net Cubature (QMC)
    • Guaranteed Lattice Cubature (QMC)
    • Bayesian Lattice Cubature (QMC)
    • Bayesian Digital Net Cubature (QMC)
    • CLT QMC Cubature (with Replications)
    • Guaranteed MC Cubature
    • CLT MC Cubature
    • Continuation Multilevel QMC Cubature
    • Multilevel QMC Cubature
    • Continuation Multilevel MC Cubature
    • Multilevel MC Cubature
  • Utilities
• Demos
  • A QMCPy Quick Start
    • References
  • Welcome to QMCPy
    • Importing QMCPy
    • Important Notes
  • Integration Examples using QMCPy package
    • Keister Example
    • Arithmetic-Mean Asian Put Option: Single Level
    • Arithmetic-Mean Asian Put Option: Multi-Level
    • Keister Example using Bayesian Cubature
  • QMCPy for Lebesgue Integration
    • Sample Problem 1
    • Sample Problem 2
    • Sample Problem 3
    • Sample Problem 4
  • Scatter Plots of Samples
    • IID Samples
    • LD Samples
    • Transform to the True Distribution
    • Shift and Stretch the True Distribution
    • Plots samples on a 2D Keister function
  • Quasi-Random Sequence Generator Comparison
    • General Usage
    • QMCPy Generator Times Comparison
  • Importance Sampling Examples
    • Game Example
    • Asian Call Option Example
    • Importance Sampling MC vs QMC
  • NEI (Noisy Expected Improvement) Demo
    • Goal
    • Computation of the QEI quantity using qmcpy
  • QEI (Q-Noisy Expected Improvement) Demo for Blog
    • Problem setup
    • Computation of the qEI quantity using qmcpy
    • GP model definition (kernel information) and qEI definition
    • Demonstrate the concept of qEI on 2 points
    • Choose some set of next points against which to test the computation
  • Basic Ray Tracing
  • A closer look at QMCPy’s Sobol’ generator
    • Basic usage
    • Randomize with digital shift / linear matrix scramble
    • Support for graycode and natural ordering
  • Custom Dimensions
    • Custom generating matricies
    • Skipping points vs randomization
  • LatNetBuilder
    • Ordinary Lattice
    • Polynomial Lattice
    • Sobol’
    • Output Directories
  • Some True Measures
    • Mathematics
    • Imports
    • 1D Density Plot
    • 2D Density Plot
    • 1D Expected Values
    • Importance Samling with a Single Kumaraswamy
    • Importance Sampling with 2 (Composed) Kumaraswamys
    • Can we Improve the Keister function?
  • Comparison of multilevel (Quasi-)Monte Carlo for an Asian option problem
  • Control Variates in QMCPy
    • Setup
    • Problem 1: Polynomial Function
    • Problem 2: Keister Function
    • Problem 3: Option Pricing
  • Elliptic PDE
    • 1. Problem definition
    • 2. Single-level methods
    • 3. Multilevel methods
    • 4. Convergence tests
  • Gaussian Diagnostics
    • Example 1: Exponential of Cosine
    • Example 2: Random function
    • Example 3a: Keister integrand: npts = 64
    • Example 3b: Keister integrand: npts = 1024

Indices and tables

• Index

• Module Index

• Search Page

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