QMCPy Documentation

Contents

• About Our QMC Software Community
  • Quasi-Monte Carlo Community Software
    • Installation
    • The QMCPy Framework
    • Quickstart
    • Community
    • Citation
    • Video Tutorial
    • References
    • Sponsors
• Contributing to QMCSoftware
  • For Contributors
    • Installation
    • Visual Studio Code Tips and Tricks
• 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
    • Bayesian Logistic Regression
    • Genz Function
    • Ishigami Function
    • Sensitivity Indices
    • UM-Bridge Wrapper
    • Sin 1d
    • Multimodal 2d
    • Four Branch 2d
    • Hartmann 6d
  • 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
    • Probability of Failure with Guassian Processes
  • 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
  • A Monte Carlo vs Quasi-Monte Carlo Comparison
    • Vary Absolute Tolerance
    • Vary Dimension
  • 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 matrices
    • Skipping points vs. randomization
  • Some True Measures
    • Mathematics
    • Imports
    • 1D Density Plot
    • 2D Density Plot
    • 1D Expected Values
    • Importance Sampling 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
  • ML Sensitivity Indices
    • Load Data
    • Importance of Decision Tree Hyperparameters
    • Bayesian Optimization of Hyperparameters
    • Best Decision Tree Analysis
  • Vectorized QMC
    • LD Sequence
    • Simple Example
    • BO QEI
    • Bayesian Logistic Regression
    • Sensitivity Indices
  • Vectorized QMC (Bayesian)
    • LD Sequence
    • Simple Example
    • BO QEI
    • Bayesian Logistic Regression
    • Sensitivity Indices
  • UM-Bridge with QMCPy
    • Imports
    • Start Docker Container
    • Problem Setup
    • Model Evaluation
    • Automatically Approximate the Expectation
    • Parallel Evaluation
    • Shut Down Docker Image
  • Random Lattice Generators Are Not Bad
    • Lattice Declaration and the gen_samples function
    • Integration
  • Challenges in Developing Great QMC Software
    • Import the necessary packages and set up plotting routines
    • Here are some plots of Low Discrepancy (LD) Lattice Points
    • Beam Example Plots
    • Beam Example Computations
  • Purdue University Colloquium Talk
    • Import the necessary packages and set up plotting routines
    • Here are some plots of IID and Low Discrepancy (LD) Points
    • Beam Example Figures
    • Beam Example Computations
  • Genz Function in Dakota and QMCPy
  • Monte Carlo for Vector Functions of Integrals
    • Monte Carlo Problem
    • Python Setup
    • Discrete Distribution
    • True Measure
    • Integrand
    • Stopping Criterion
    • Vectorized Stopping Criterion
  • Probability of Failure Estimation with Gaussian Processes
    • Method Visual
    • Sin 1d Problem
    • Multimodal 2d Problem
    • Four Branch 2d Problem
    • Ishigami 3d Problem
    • Hartmann 6d Problem
    • Tsunami
  • Linear Matrix Scrambling and Digital Shift for Halton
    • Here we explain Linear Matrix Scrambling:
    • Here we explain Digital Shift:
    • Here we explain Linear Matrix Scrambling Combined with Digital Shift:
    • Here we set up the QMCPY environment:
    • Here we explain the parameters of the init function:
    • Here we explain the parameters of the gen_samples function:
    • Comparison between LMS, DS, and LMS_DS:
    • Examples of Linear Matrix Scrambling with plots:
    • Examples of Digital Shifts with plots:
    • Examples of Linear Matrix Scrambling Combined with Digital Shift with plots:
    • Speed Comparison Between Different Halton Randomize Options:
  • The QMCPY Plot Projection Function for Discrete Distribution and True Measure
    • Here we set up the QMCPY environment enabling us to utilize this function:
    • Here we explain the parameters of the plot_proj function:
    • The following examples show plotting of different Discrete Distribution Objects:
    • The following examples show plotting of different True Measure Objects:
  • Argonne Lab Talk
    • Import the necessary packages and set up plotting routines
    • Trapezoidal rule and its error
    • Plots of IID and Low Discrepancy (LD) Points
    • Beam Example Figures
    • Bayesian Logistic Regression
    • Asian Option
    • Beam Example Computations

Indices and tables

• Index

• Module Index

• Search Page

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