Contents
1 Introduction
1.1 Routines Available in the Science Collection
1.2 The Science Collection is Free Software
1.3 Obtaining the Science Collection
1.4 No Warranty
2 Using the Science Collection
2.1 An Example
2.2 Loading Modules in the Science Collection
2.3 Graphics Modules
3 Error Handling
3.1 Contracts
3.1.1 Fixed Number of Arguments with a Single Result
3.1.2 Multiple Lambda Forms (case-lambda)
3.1.3 Interparameter Constraints
3.2 Infinities and Not-a-Number
3.3 Exceptions
4 Mathematical Functions
4.1 Mathematical Constants
4.2 Infinities and Not-a-Number
4.3 Elementary Functions
4.4 Testing the Sign of Numbers
4.5 Approximate Comparisons of Real Numbers
5 Special Functions
5.1 Error Functions
5.1.1 Error Function
5.1.2 Complementary Error Function
5.1.3 Hazard Function
5.2 Exponential Integral Functions
5.2.1 Exponential Integral
5.2.2 Ei(x)
5.3 Gamma and Beta Functions
5.3.1 Gamma Function
5.3.2 Regulated Gamma Function
5.3.3 Incomplete Gamma Function
5.3.4 Factorial Function
5.3.5 Double Factorial Function
5.3.6 Binomial Coefficient Function
5.3.7 Beta Functions
5.4 Psi Functions
5.4.1 Psi (Digamma) Functions
5.4.2 Psi-1 (Trigamma) Functions
5.4.3 Psi-n (Polygamma) Function
5.5 Zeta Functions
5.5.1 Riemann Zeta Functions
5.5.2 Riemann Zeta Functions Minus One
5.5.3 Hurwitz Zeta Function
5.5.4 Eta Functions
6 Random Number Generation
6.1 The SRFI 27 Specification
6.2 Additional Random Number Functionality
6.2.1 The current-random-source Parameter
6.2.2 Uniform Random Numbers
6.2.3 Miscellaneous Functions
6.2.4 Random Source Vectors
6.3 Examples
7 Random Number Distributions
7.1 The Beta Distribution
7.1.1 Random Variates from the Beta Distribution
7.1.2 Beta Distribution Density Functions
7.1.3 Beta Distribution Graphics
7.2 The Bivariate Gaussian Distribution
7.2.1 Random Variates from the Bivariate Gaussian Distribution
7.2.2 Bivariate Gaussian Distribution Density Functions
7.2.3 Bivariate Gaussian Distribution Graphics
7.3 The Chi-Squared Distribution
7.3.1 Random Variates from the Chi-Squared Distribution
7.3.2 Chi-Squared Distribution Density Functions
7.3.3 Chi-Squared Distribution Graphics
7.4 The Exponential Distribution
7.4.1 Random Variates from the Exponential Distribution
7.4.2 Exponential Distribution Density Functions
7.4.3 Exponential Distribution Graphics
7.5 The F-Distribution
7.5.1 Random Variates from the F-Distribution
7.5.2 F-Distribution Density Functions
7.5.3 F-Distribution Graphics
7.6 The Flat (Uniform) Distribution
7.6.1 Random Variates from the Flat Distribution
7.6.2 Flat Distribution Density Functions
7.6.3 Flat Distribution Graphics
7.7 The Gamma Distribution
7.7.1 Random Variates from the Gamma Distribution
7.7.2 Gamma Distribution Density Functions
7.7.3 Gamma Distribution Graphics
7.8 The Gaussian Distribution
7.8.1 Random Variates from the Gaussian Distribution
7.8.2 Gaussian Distribution Density Functions
7.8.3 Gaussian Distribution Graphics
7.9 The Gaussian Tail Distribution
7.9.1 Random Variates from the Gaussian Tail Distribution
7.9.2 Gaussian Tail Distribution Density Functions
7.9.3 Gaussian Tail Distribution Graphics
7.10 The Log Normal Distribution
7.10.1 Random Variates from the Log Normal Distribution
7.10.2 Log Normal Distribution Density Functions
7.10.3 Log Normal Distribution Graphics
7.11 The Pareto Distribution
7.11.1 Random Variates from the Pareto Distribution
7.11.2 Pareto Distribution Density Functions
7.11.3 Pareto Distribution Graphics
7.12 The T-Distribution
7.12.1 Random Variates from the T-Distribution
7.12.2 T-Distribution Density Functions
7.12.3 T-Distribution Graphics
7.13 The Triangular Distribution
7.13.1 Random Variates from the Triangular Distribution
7.13.2 Triangular Distribution Density Functions
7.13.3 Triangular Distribution Graphics
7.14 The Bernoulli Distribution
7.14.1 Random Variates from the Bernoulli Distribution
7.14.2 Bernoulli Distribution Density Functions
7.14.3 Bernoulli Distribution Graphics
7.15 The Binomial Distribution
7.15.1 Random Variates from the Binomial Distribution
7.15.2 Binomial Distribution Density Functions
7.15.3 Binomial Distribution Graphics
7.16 The Geometric Distribution
7.16.1 Random Variates from the Geometric Distribution
7.16.2 Geometric Distribution Density Functions
7.16.3 Geometric Distribution Graphics
7.17 The Logarithmic Distribution
7.17.1 Random Variates from the Logarithmic Distribution
7.17.2 Logarithmic Distribution Density Functions
7.17.3 Logarithmic Distribution Graphics
7.18 The Poisson Distribution
7.18.1 Random Variates from the Poisson Distribution
7.18.2 Poisson Distribution Density Functions
7.18.3 Poisson Distribution Graphics
7.19 The General Discrete Distribution
7.19.1 Creating Discrete Distributions
7.19.2 Random Variates from a Discrete Distribution
7.19.3 Discrete Distribution Density Functions
7.19.4 General Discrete Distribution Graphics
8 Statistics
8.1 Mean, Standard Deviation, and Variance
8.2 Absolute Deviation
8.3 Higher Moments (Skewness and Kurtosis)
8.4 Autocorrelation
8.5 Covariance
8.6 Weighted Samples
8.7 Maximum and Minimum
8.8 Median and Percentiles
8.9 Example
9 Histograms
9.1 1D Histograms
9.1.1 Creating 1D Histograms
9.1.2 Updating and Accessing 1D Histogram Elements
9.1.3 1D Histogram Statistics
9.1.4 1D Histogram Graphics
9.1.5 Examples
9.2 2D Histograms
9.2.1 Creating 2D Histograms
9.2.2 Updating and Accessing 2D Histogram Elements
9.2.3 2D Histogram Statistics
9.2.4 2D Histogram Graphics
9.2.5 Example
9.3 Discrete Histograms
9.3.1 Creating Discrete Histograms
9.3.2 Updating and Accessing Discrete Histogram Elements
9.3.3 Discrete Histogram Statistics
9.3.4 Discrete Histogram Graphics
9.3.5 Examples
10 Ordinary Differential Equations
10.1 Defining the ODE System
10.2 Stepping Functions
10.3 Adaptive Step-Size Control
10.4 Evolution
10.5 Examples
11 Chebyshev Approximations
11.1 The chebyshev-series Structure
11.2 Creation and Calculation of Chebyshev Series
11.3 Chebyshev Series Evaluation
11.4 Examples
A GNU Lesser General Public License (LGPL)