The cl-random Reference Manual

Table of Contents

The cl-random Reference Manual

This is the cl-random Reference Manual, version 0.0.1, generated automatically by Declt version 3.0 "Montgomery Scott" on Mon Apr 19 15:13:54 2021 GMT+0.

1 Introduction

This library is unsupported.

Introduction

cl-random is a library for (1) generating random draws from various commonly used distributions, and (2) calculating statistical functions, such as density, distribution and quantiles for these distributions.

In the implementation and the interface, our primary considerations were

1. Correctness. Above everything, all calculations should be correct. Correctness shall not be sacrificed for speed or implementational simplicity. Consequently, everything should be unit-tested all the time.

2. Simple and unified interface. Random variables are instances which can be used for calculations and random draws, for example,

(let ((rv (r-normal 13 2)))
  (pdf rv 15d0)             ; density
  (cdf rv 13d0)             ; CDF
  (draw rv))                ; a random draw

1. Speed and exposed building blocks on demand. You can obtain the generator function for random draws as a closure using the accessor "generator" from an rv. In addition, the package exports independent building blocks such as draw-standard-normal, which can be inlined into your code if absolutely necessary.

Implementation note: Subclasses are allowed to calculate intermediate values (eg to speed up computation) any time, eg right after the initialization of the instance, or on demand. The consequences or changing the slots of RV classes are UNDEFINED, but probably quite nasty. Don't do it. Note: lazy slots are currently not used, will be reintroduced in the future after some serious profiling/benchmarking.

To do list

Roadmap

1. Sketch the interface.

2. Some basic functionality. We are currently here, eg exponential, normal and gamma distributions are partially implemented.

3. Keep extending the library based on user demand.

4. Optimize things on demand, see where the bottlenecks are.

Specific planned improvements, roughly in order of priority

• more serious testing. I like the approach in Cook (2006): we should transform empirical quantiles to z-statistics and calculate the p-value using chi-square tests

• (mm rv x) and similar methods for multivariate normal (and maybe T)

Coding guidelines

Always try to implement state-of-the-art generation and calculation methods. If you need something, read up on the literature, the field has developed a lot in the last decades, and most older books present obsolete methods. Good starting points are Gentle (2005) and Press et al (2007), though you should use the latter one with care and don't copy algorithms without reading a few recent articles, they are not always the best ones (the authors admit this, but they claim that some algorithms are there for pedagogical purposes).

Always document the references in the docstring, and include the full citation in doc/references.bib (BibTeX format).

Do at least basic optimization with declarations (eg until SBCL doesn't give a notes any more, notes about return values are OK). Benchmarks are always welcome, and should be documented.

Document doubts and suggestions for improvements, use !! and ??, more marks mean higher priority.

The naming convention for building blocks is something like (draw|cdf|pdf|quantile|...)-(standard-)?distribution-name(possible-suffix)?, eg pdf-standard-normal or draw-standard-gamma1

2 Systems

The main system appears first, followed by any subsystem dependency.

2.1 cl-random

Author

Tamas K Papp

License

MIT

Description

Random numbers and distributions.

Version

0.0.1

Dependencies

• alexandria
• anaphora
• array-operations
• cl-num-utils
• cl-rmath
• cl-slice
• gsll
• let-plus
• lla

Source

cl-random.asd (file)

Components

• internals.lisp (file)
• package.lisp (file)
• generator.lisp (file)
• simple-multiplicative-congruential-generators.lisp (file)
• random.lisp (file)
• discrete.lisp (file)
• univariate.lisp (file)
• continuous-time.lisp (file)

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

3.1 Lisp

3.1.1 cl-random.asd

Location

/home/quickref/quicklisp/dists/quicklisp/software/cl-random-20180328-git/cl-random.asd

Systems

cl-random (system)

3.1.2 cl-random/internals.lisp

Parent

cl-random (system)

Location

internals.lisp

Packages

cl-random.internals

Exported Definitions

• as-float (function)
• as-float-probabilities (function)
• as-float-vector (function)
• float-vector (type)
• internal-float (type)
• maybe-ignore-constant (macro)
• try (macro)
• with-floats (macro)

3.1.3 cl-random/package.lisp

Dependency

internals.lisp (file)

Parent

cl-random (system)

Location

package.lisp

Packages

cl-random

3.1.4 cl-random/generator.lisp

Dependency

package.lisp (file)

Parent

cl-random (system)

Location

generator.lisp

Exported Definitions

• generator (class)
• make-generator (function)
• next (function)

Internal Definitions

• %next-double-float (function)
• %next-integer (function)
• %next-single-float (function)
• *default-generator-type* (special variable)
• chunk-length (method)
• default-seed (method)
• generate-seed (function)
• generate-state (generic function)
• generate-state (method)
• state (method)
• (setf state) (method)

3.1.5 cl-random/simple-multiplicative-congruential-generators.lisp

Dependency

generator.lisp (file)

Parent

cl-random (system)

Location

simple-multiplicative-congruential-generators.lisp

Exported Definitions

• borosh13 (class)
• randu (class)
• transputer (class)
• waterman14 (class)

Internal Definitions

• a (method)
• clone (method)
• generate-state (method)
• m (method)
• next-chunk (method)
• next-real (method)
• simple-multiplicative-congruential (class)

3.1.6 cl-random/random.lisp

Dependency

simple-multiplicative-congruential-generators.lisp (file)

Parent

cl-random (system)

Location

random.lisp

Exported Definitions

• cdf (generic function)
• draw (generic function)
• draw (method)
• generator (generic function)
• generator (method)
• log-pdf (generic function)
• mean (generic function)
• pdf (function)
• variance (generic function)

Internal Definitions

• check-probability (function)
• define-rv (macro)

3.1.7 cl-random/discrete.lisp

Dependency

random.lisp (file)

Parent

cl-random (system)

Location

discrete.lisp

Exported Definitions

• distinct-random-integers (function)
• distinct-random-integers-dense (function)

3.1.8 cl-random/univariate.lisp

Dependency

discrete.lisp (file)

Parent

cl-random (system)

Location

univariate.lisp

Exported Definitions

• alpha (method)
• alpha (method)
• alpha (method)
• beta (method)
• beta (method)
• beta (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw-bernoulli (function)
• draw-binomial (function)
• draw-exponential (function)
• draw-geometric (function)
• draw-poisson (function)
• draw-rayleigh (function)
• draw-standard-exponential (function)
• draw-standard-normal (function)
• draw-standard-t (function)
• draw-uniform (function)
• from-standard-normal (function)
• left (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• nu (generic function)
• nu (method)
• nu (method)
• nu (method)
• probabilities (method)
• quantile (generic function)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• r-bernoulli (function)
• r-bernoulli (structure)
• r-beta (function)
• r-beta (structure)
• r-binomial (function)
• r-binomial (structure)
• r-chi-square (function)
• r-discrete (function)
• r-discrete (structure)
• r-exponential (function)
• r-exponential (structure)
• r-gamma (function)
• r-gamma (structure)
• r-geometric (function)
• r-geometric (structure)
• r-inverse-chi-square (function)
• r-inverse-gamma (function)
• r-inverse-gamma (structure)
• r-log-normal (function)
• r-log-normal (structure)
• r-normal (function)
• r-normal (structure)
• r-rayleigh (function)
• r-rayleigh (structure)
• r-t (function)
• r-t (structure)
• r-truncated-normal (function)
• r-uniform (function)
• r-uniform (structure)
• rate (method)
• right (method)
• scale (method)
• scale (method)
• standard-deviation (generic function)
• standard-deviation (method)
• t-scale-to-variance-coefficient (function)
• to-standard-normal (function)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)

Internal Definitions

• +normal-log-pdf-constant+ (constant)
• cdf-normal% (function)
• copy-left-truncated-normal (function)
• copy-r-bernoulli (function)
• copy-r-beta (function)
• copy-r-binomial (function)
• copy-r-discrete (function)
• copy-r-exponential (function)
• copy-r-gamma (function)
• copy-r-geometric (function)
• copy-r-inverse-gamma (function)
• copy-r-log-normal (function)
• copy-r-normal (function)
• copy-r-rayleigh (function)
• copy-r-t (function)
• copy-r-uniform (function)
• copy-r-univariate (function)
• draw-bernoulli-bit (function)
• draw-left-truncated-standard-normal (function)
• draw-standard-gamma1 (function)
• left-truncated-normal (function)
• left-truncated-normal (structure)
• left-truncated-normal-alpha (function)
• (setf left-truncated-normal-alpha) (function)
• left-truncated-normal-left (function)
• (setf left-truncated-normal-left) (function)
• left-truncated-normal-left-standardized (function)
• (setf left-truncated-normal-left-standardized) (function)
• left-truncated-normal-m0 (function)
• (setf left-truncated-normal-m0) (function)
• left-truncated-normal-mu (function)
• (setf left-truncated-normal-mu) (function)
• left-truncated-normal-p (function)
• left-truncated-normal-sigma (function)
• (setf left-truncated-normal-sigma) (function)
• log-gamma (function)
• make-left-truncated-normal (function)
• make-r-bernoulli (function)
• make-r-beta (function)
• make-r-binomial (function)
• make-r-discrete (function)
• make-r-exponential (function)
• make-r-gamma (function)
• make-r-geometric (function)
• make-r-inverse-gamma (function)
• make-r-log-normal (function)
• make-r-normal (function)
• make-r-rayleigh (function)
• make-r-t (function)
• make-r-uniform (function)
• make-r-univariate (function)
• n (method)
• pr (method)
• pr (method)
• pr (method)
• quantile-normal% (function)
• r-bernoulli-p (function)
• r-bernoulli-pr (function)
• (setf r-bernoulli-pr) (function)
• r-beta-alpha (function)
• (setf r-beta-alpha) (function)
• r-beta-beta (function)
• (setf r-beta-beta) (function)
• r-beta-p (function)
• r-binomial-n (function)
• (setf r-binomial-n) (function)
• r-binomial-p (function)
• r-binomial-pr (function)
• (setf r-binomial-pr) (function)
• r-discrete-alias (function)
• (setf r-discrete-alias) (function)
• r-discrete-n-float (function)
• (setf r-discrete-n-float) (function)
• r-discrete-p (function)
• r-discrete-prob (function)
• (setf r-discrete-prob) (function)
• r-discrete-probabilities (function)
• (setf r-discrete-probabilities) (function)
• r-exponential-p (function)
• r-exponential-rate (function)
• (setf r-exponential-rate) (function)
• r-gamma-alpha (function)
• (setf r-gamma-alpha) (function)
• r-gamma-beta (function)
• (setf r-gamma-beta) (function)
• r-gamma-p (function)
• r-geometric-p (function)
• r-geometric-pr (function)
• (setf r-geometric-pr) (function)
• r-inverse-gamma-alpha (function)
• (setf r-inverse-gamma-alpha) (function)
• r-inverse-gamma-beta (function)
• (setf r-inverse-gamma-beta) (function)
• r-inverse-gamma-p (function)
• r-log-normal-log-mean (function)
• (setf r-log-normal-log-mean) (function)
• r-log-normal-log-sd (function)
• (setf r-log-normal-log-sd) (function)
• r-log-normal-p (function)
• r-normal-mean (function)
• (setf r-normal-mean) (function)
• r-normal-p (function)
• r-normal-sd (function)
• (setf r-normal-sd) (function)
• r-rayleigh-p (function)
• r-rayleigh-scale (function)
• (setf r-rayleigh-scale) (function)
• r-t-mean (function)
• (setf r-t-mean) (function)
• r-t-nu (function)
• (setf r-t-nu) (function)
• r-t-p (function)
• r-t-scale (function)
• (setf r-t-scale) (function)
• r-uniform-left (function)
• (setf r-uniform-left) (function)
• r-uniform-p (function)
• r-uniform-right (function)
• (setf r-uniform-right) (function)
• r-uniform-width (function)
• (setf r-uniform-width) (function)
• r-univariate (structure)
• r-univariate-p (function)
• s^2 (generic function)
• s^2 (method)
• sd (method)
• standard-gamma1-d-c (function)
• truncated-normal-moments% (function)
• truncated-normal-optimal-alpha (function)

3.1.9 cl-random/continuous-time.lisp

Dependency

univariate.lisp (file)

Parent

cl-random (system)

Location

continuous-time.lisp

Exported Definitions

• draw (method)
• r-uniformized-markov-jump (function)
• r-uniformized-markov-jump (structure)

Internal Definitions

• copy-r-uniformized-markov-jump (function)
• duration (method)
• jump (method)
• make-r-uniformized-markov-jump (function)
• r-uniformized-markov-jump-duration (function)
• (setf r-uniformized-markov-jump-duration) (function)
• r-uniformized-markov-jump-jump (function)
• (setf r-uniformized-markov-jump-jump) (function)
• r-uniformized-markov-jump-keys (function)
• (setf r-uniformized-markov-jump-keys) (function)
• r-uniformized-markov-jump-n (function)
• (setf r-uniformized-markov-jump-n) (function)
• r-uniformized-markov-jump-no-change (function)
• (setf r-uniformized-markov-jump-no-change) (function)
• r-uniformized-markov-jump-p (function)

4 Packages

Packages are listed by definition order.

4.1 cl-random.internals

Source

internals.lisp (file)

Use List

• let-plus
• alexandria
• common-lisp

Used By List

cl-random

Exported Definitions

• as-float (function)
• as-float-probabilities (function)
• as-float-vector (function)
• float-vector (type)
• internal-float (type)
• maybe-ignore-constant (macro)
• try (macro)
• with-floats (macro)

4.2 cl-random

Source

package.lisp (file)

Nickname

rv

Use List

• lla
• let-plus
• cl-slice
• cl-random.internals
• cl-num-utils.num=
• cl-num-utils.matrix
• cl-num-utils.elementwise
• anaphora
• alexandria
• common-lisp

Exported Definitions

• alpha (generic function)
• alpha (method)
• alpha (method)
• alpha (method)
• beta (generic function)
• beta (method)
• beta (method)
• beta (method)
• borosh13 (class)
• cdf (generic function)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• cdf (method)
• distinct-random-integers (function)
• distinct-random-integers-dense (function)
• draw (generic function)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw (method)
• draw-bernoulli (function)
• draw-binomial (function)
• draw-exponential (function)
• draw-geometric (function)
• draw-poisson (function)
• draw-rayleigh (function)
• draw-standard-exponential (function)
• draw-standard-normal (function)
• draw-standard-t (function)
• draw-uniform (function)
• from-standard-normal (function)
• generator (generic function)
• generator (method)
• generator (class)
• left (generic function)
• left (method)
• log-pdf (generic function)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• log-pdf (method)
• make-generator (function)
• mean (generic function)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• mean (method)
• next (function)
• nu (generic function)
• nu (method)
• nu (method)
• nu (method)
• pdf (function)
• probabilities (generic function)
• probabilities (method)
• quantile (generic function)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• quantile (method)
• r-bernoulli (function)
• r-bernoulli (structure)
• r-beta (function)
• r-beta (structure)
• r-binomial (function)
• r-binomial (structure)
• r-chi-square (function)
• r-discrete (function)
• r-discrete (structure)
• r-exponential (function)
• r-exponential (structure)
• r-gamma (function)
• r-gamma (structure)
• r-geometric (function)
• r-geometric (structure)
• r-inverse-chi-square (function)
• r-inverse-gamma (function)
• r-inverse-gamma (structure)
• r-log-normal (function)
• r-log-normal (structure)
• r-normal (function)
• r-normal (structure)
• r-rayleigh (function)
• r-rayleigh (structure)
• r-t (function)
• r-t (structure)
• r-truncated-normal (function)
• r-uniform (function)
• r-uniform (structure)
• r-uniformized-markov-jump (function)
• r-uniformized-markov-jump (structure)
• randu (class)
• rate (generic function)
• rate (method)
• right (generic function)
• right (method)
• scale (generic function)
• scale (method)
• scale (method)
• standard-deviation (generic function)
• standard-deviation (method)
• t-scale-to-variance-coefficient (function)
• to-standard-normal (function)
• transputer (class)
• variance (generic function)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• variance (method)
• waterman14 (class)

Internal Definitions

• %next-double-float (function)
• %next-integer (function)
• %next-single-float (function)
• *default-generator-type* (special variable)
• +normal-log-pdf-constant+ (constant)
• a (generic function)
• a (method)
• cdf-normal% (function)
• check-probability (function)
• chunk-length (generic function)
• chunk-length (method)
• clone (generic function)
• clone (method)
• copy-left-truncated-normal (function)
• copy-r-bernoulli (function)
• copy-r-beta (function)
• copy-r-binomial (function)
• copy-r-discrete (function)
• copy-r-exponential (function)
• copy-r-gamma (function)
• copy-r-geometric (function)
• copy-r-inverse-gamma (function)
• copy-r-log-normal (function)
• copy-r-normal (function)
• copy-r-rayleigh (function)
• copy-r-t (function)
• copy-r-uniform (function)
• copy-r-uniformized-markov-jump (function)
• copy-r-univariate (function)
• default-seed (generic function)
• default-seed (method)
• define-rv (macro)
• draw-bernoulli-bit (function)
• draw-left-truncated-standard-normal (function)
• draw-standard-gamma1 (function)
• duration (generic function)
• duration (method)
• generate-seed (function)
• generate-state (generic function)
• generate-state (method)
• generate-state (method)
• jump (generic function)
• jump (method)
• left-truncated-normal (function)
• left-truncated-normal (structure)
• left-truncated-normal-alpha (function)
• (setf left-truncated-normal-alpha) (function)
• left-truncated-normal-left (function)
• (setf left-truncated-normal-left) (function)
• left-truncated-normal-left-standardized (function)
• (setf left-truncated-normal-left-standardized) (function)
• left-truncated-normal-m0 (function)
• (setf left-truncated-normal-m0) (function)
• left-truncated-normal-mu (function)
• (setf left-truncated-normal-mu) (function)
• left-truncated-normal-p (function)
• left-truncated-normal-sigma (function)
• (setf left-truncated-normal-sigma) (function)
• log-gamma (function)
• m (generic function)
• m (method)
• make-left-truncated-normal (function)
• make-r-bernoulli (function)
• make-r-beta (function)
• make-r-binomial (function)
• make-r-discrete (function)
• make-r-exponential (function)
• make-r-gamma (function)
• make-r-geometric (function)
• make-r-inverse-gamma (function)
• make-r-log-normal (function)
• make-r-normal (function)
• make-r-rayleigh (function)
• make-r-t (function)
• make-r-uniform (function)
• make-r-uniformized-markov-jump (function)
• make-r-univariate (function)
• n (generic function)
• n (method)
• next-chunk (generic function)
• next-chunk (method)
• next-real (generic function)
• next-real (method)
• pr (generic function)
• pr (method)
• pr (method)
• pr (method)
• quantile-normal% (function)
• r-bernoulli-p (function)
• r-bernoulli-pr (function)
• (setf r-bernoulli-pr) (function)
• r-beta-alpha (function)
• (setf r-beta-alpha) (function)
• r-beta-beta (function)
• (setf r-beta-beta) (function)
• r-beta-p (function)
• r-binomial-n (function)
• (setf r-binomial-n) (function)
• r-binomial-p (function)
• r-binomial-pr (function)
• (setf r-binomial-pr) (function)
• r-discrete-alias (function)
• (setf r-discrete-alias) (function)
• r-discrete-n-float (function)
• (setf r-discrete-n-float) (function)
• r-discrete-p (function)
• r-discrete-prob (function)
• (setf r-discrete-prob) (function)
• r-discrete-probabilities (function)
• (setf r-discrete-probabilities) (function)
• r-exponential-p (function)
• r-exponential-rate (function)
• (setf r-exponential-rate) (function)
• r-gamma-alpha (function)
• (setf r-gamma-alpha) (function)
• r-gamma-beta (function)
• (setf r-gamma-beta) (function)
• r-gamma-p (function)
• r-geometric-p (function)
• r-geometric-pr (function)
• (setf r-geometric-pr) (function)
• r-inverse-gamma-alpha (function)
• (setf r-inverse-gamma-alpha) (function)
• r-inverse-gamma-beta (function)
• (setf r-inverse-gamma-beta) (function)
• r-inverse-gamma-p (function)
• r-log-normal-log-mean (function)
• (setf r-log-normal-log-mean) (function)
• r-log-normal-log-sd (function)
• (setf r-log-normal-log-sd) (function)
• r-log-normal-p (function)
• r-normal-mean (function)
• (setf r-normal-mean) (function)
• r-normal-p (function)
• r-normal-sd (function)
• (setf r-normal-sd) (function)
• r-rayleigh-p (function)
• r-rayleigh-scale (function)
• (setf r-rayleigh-scale) (function)
• r-t-mean (function)
• (setf r-t-mean) (function)
• r-t-nu (function)
• (setf r-t-nu) (function)
• r-t-p (function)
• r-t-scale (function)
• (setf r-t-scale) (function)
• r-uniform-left (function)
• (setf r-uniform-left) (function)
• r-uniform-p (function)
• r-uniform-right (function)
• (setf r-uniform-right) (function)
• r-uniform-width (function)
• (setf r-uniform-width) (function)
• r-uniformized-markov-jump-duration (function)
• (setf r-uniformized-markov-jump-duration) (function)
• r-uniformized-markov-jump-jump (function)
• (setf r-uniformized-markov-jump-jump) (function)
• r-uniformized-markov-jump-keys (function)
• (setf r-uniformized-markov-jump-keys) (function)
• r-uniformized-markov-jump-n (function)
• (setf r-uniformized-markov-jump-n) (function)
• r-uniformized-markov-jump-no-change (function)
• (setf r-uniformized-markov-jump-no-change) (function)
• r-uniformized-markov-jump-p (function)
• r-univariate (structure)
• r-univariate-p (function)
• s^2 (generic function)
• s^2 (method)
• sd (generic function)
• sd (method)
• simple-multiplicative-congruential (class)
• standard-gamma1-d-c (function)
• state (generic function)
• state (method)
• (setf state) (method)
• (setf state) (generic function)
• truncated-normal-moments% (function)
• truncated-normal-optimal-alpha (function)

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

5.1 Exported definitions

5.1.1 Macros

Macro: maybe-ignore-constant IGNORE-CONSTANT? VALUE CONSTANT

Handle a constant that is calculated only when IGNORE-CONSTANT? is NIL and VALUE is not negative infinity (represented by NIL).

Package

cl-random.internals

Source

internals.lisp (file)

Macro: try (&rest BINDINGS) CONDITION VALUE

Evaluate bindings (expanding into LET+, so all features can be used) until condition is satisfied, then return value.

Package

cl-random.internals

Source

internals.lisp (file)

Macro: with-floats (&rest VARIABLES) &body BODY

Rebind each variable, coerced to a the internal float type used by CL-RANDOM.

Package

cl-random.internals

Source

internals.lisp (file)

5.1.2 Functions

Function: as-float X

Return the argument coerced to the CL-RANDOM library’s internal float type.

Package

cl-random.internals

Source

internals.lisp (file)

Function: as-float-probabilities VECTOR

Normalize vector as probabilities, assert that all are positive, return them as a VECTOR-DOUBLE-FLOAT. Vector is always copied.

Package

cl-random.internals

Source

internals.lisp (file)

Function: as-float-vector VECTOR &key COPY?

Return VECTOR converted to another vector with elements converted to INTERNAL-FLOAT if necessary. When COPY?, the vector is always copied.

Package

cl-random.internals

Source

internals.lisp (file)

Function: distinct-random-integers COUNT LIMIT &key RNG

Return a vector of COUNT distinct random integers, in increasing order, drawn from the uniform discrete distribution on {0 , ..., limit-1}.

Package

cl-random

Source

discrete.lisp (file)

Function: distinct-random-integers-dense COUNT LIMIT &key RNG

Implementation of DISTINCT-RANDOM-INTEGERS when count/limit is (relatively) high. Implements algorithm S from @cite{taocp3}, p 142.

Package

cl-random

Source

discrete.lisp (file)

Function: draw-bernoulli P &key RNG

Return T with probability p, otherwise NIL. Rationals are handled exactly.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-binomial P N &key RNG

Return the number of successes out of N Bernoulli trials with probability of success P.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-exponential RATE &key RNG

Return a random variable from the Exponential(rate) distribution which has density rate*exp(-rate*x) for x>=0 and 0 for x<0. rate > 0.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-geometric P &key RNG

Return the number of Bernoulli trials, with probability of success P, that were needed to reach the first success. This is >= 1.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-poisson LAMDA &key RNG

Return the number of events that occur with probability LAMDA. The algorithm is from Donald E. Knuth (1969). Seminumerical Algorithms. The Art of Computer Programming, Volume 2. Addison Wesley. WARNING: It’s simple but only linear in the return value K and is numerically unstable for large LAMDA.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-rayleigh SCALE &key RNG

Return a random variable from the Rayleigh(scale) distribution, where scale > 0 and density x * exp(-x^2 / (2 scale^2)) / scale^2 for x>=0 and 0 for x<0.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-standard-exponential &key RNG

Return a random variable from the Exponential(1) distribution, which has density exp(-x) for x>=0 and 0 for x<0.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-standard-normal &key RNG

Draw a random number from N(0,1).

Package

cl-random

Source

univariate.lisp (file)

Function: draw-standard-t NU &key RNG

Draw a standard T random variate, with NU degrees of freedom.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-uniform LEFT RIGHT &key RNG

Return a random variable from the uniform distribution between LEFT and RIGHT. It’s type is the same as that of (- LEFT RIGHT).

Package

cl-random

Source

univariate.lisp (file)

Function: from-standard-normal X MU SIGMA

Scale x from standard normal.

Package

cl-random

Source

univariate.lisp (file)

Function: make-generator &key SEED TYPE

Make a random number generator object. SEED can be any of NIL, T, an other generator, an integer, or any type of seed that a generator of type TYPE supports:
- NIL: the generator’s STD-SEED is used;
- T: a random seed is used;
- a generator: a clone is returned;
- otherwise: SEED is used as depends on the generator.

Package

cl-random

Source

generator.lisp (file)

Function: next LIMIT &optional RNG

Generates a uniformly distributed pseudo-random number greater than or equal to zero and less than LIMIT. RNG, if supplied, is the random generator to use.

Package

cl-random

Source

generator.lisp (file)

Function: pdf RV X &optional IGNORE-CONSTANT?

Probability distribution function of RANDOM-VARIABLE at X. See LOG-PDF for the semantics of IGNORE-CONSTANT?.

Package

cl-random

Source

random.lisp (file)

Function: r-bernoulli PR

Package

cl-random

Source

univariate.lisp (file)

Function: r-beta ALPHA BETA

Package

cl-random

Source

univariate.lisp (file)

Function: r-binomial PR N

Package

cl-random

Source

univariate.lisp (file)

Function: r-chi-square NU

Chi-square distribution with NU degrees of freedom.

Package

cl-random

Source

univariate.lisp (file)

Function: r-discrete PROBABILITIES

Package

cl-random

Source

univariate.lisp (file)

Function: r-exponential RATE

Package

cl-random

Source

univariate.lisp (file)

Function: r-gamma ALPHA BETA

Package

cl-random

Source

univariate.lisp (file)

Function: r-geometric PR

Package

cl-random

Source

univariate.lisp (file)

Function: r-inverse-chi-square NU &optional S^2

Generalized inverse chi-square distribution. Reparametrized to INVERSE-GAMMA.

Package

cl-random

Source

univariate.lisp (file)

Function: r-inverse-gamma ALPHA BETA

Package

cl-random

Source

univariate.lisp (file)

Function: r-log-normal LOG-MEAN LOG-SD

Package

cl-random

Source

univariate.lisp (file)

Function: r-normal &optional MEAN VARIANCE

Package

cl-random

Source

univariate.lisp (file)

Function: r-rayleigh SCALE

Package

cl-random

Source

univariate.lisp (file)

Function: r-t MEAN SCALE NU

Package

cl-random

Source

univariate.lisp (file)

Function: r-truncated-normal LEFT RIGHT &optional MU SIGMA

Truncated normal distribution. If LEFT or RIGHT is NIL, it corresponds to -/+ infinity.

Package

cl-random

Source

univariate.lisp (file)

Function: r-uniform LEFT RIGHT

Package

cl-random

Source

univariate.lisp (file)

Function: r-uniformized-markov-jump RATES &key TRANSITION-RATE KEYS NO-CHANGE

Package

cl-random

Source

continuous-time.lisp (file)

Function: t-scale-to-variance-coefficient NU

Return the coefficient that multiplies the Sigma matrix or the squared scale to get the variance of a (multivariate) Student-T distribution. Also checks that nu > 2, ie the variance is defined.

Package

cl-random

Source

univariate.lisp (file)

Function: to-standard-normal X MU SIGMA

Scale x to standard normal.

Package

cl-random

Source

univariate.lisp (file)

5.1.3 Generic functions

Generic Function: alpha R-GAMMA0

Package

cl-random

Methods

Method: alpha (R-BETA0 r-beta)

Source

univariate.lisp (file)

Method: alpha (R-INVERSE-GAMMA0 r-inverse-gamma)

Source

univariate.lisp (file)

Method: alpha (R-GAMMA0 r-gamma)

Source

univariate.lisp (file)

Generic Function: beta R-GAMMA0

Package

cl-random

Methods

Method: beta (R-BETA0 r-beta)

Source

univariate.lisp (file)

Method: beta (R-INVERSE-GAMMA0 r-inverse-gamma)

Source

univariate.lisp (file)

Method: beta (R-GAMMA0 r-gamma)

Source

univariate.lisp (file)

Generic Function: cdf RANDOM-VARIABLE X

Cumulative distribution function of RANDOM-VARIABLE at X.

Package

cl-random

Source

random.lisp (file)

Methods

Method: cdf (R-BERNOULLI0 r-bernoulli) X

Source

univariate.lisp (file)

Method: cdf (INSTANCE r-discrete) I

Source

univariate.lisp (file)

Method: cdf (R-RAYLEIGH0 r-rayleigh) X

Source

univariate.lisp (file)

Method: cdf (R-GAMMA0 r-gamma) X

Source

univariate.lisp (file)

Method: cdf (R-LOG-NORMAL0 r-log-normal) X

Source

univariate.lisp (file)

Method: cdf (LEFT-TRUNCATED-NORMAL0 left-truncated-normal) X

Source

univariate.lisp (file)

Method: cdf (R-NORMAL0 r-normal) X

Source

univariate.lisp (file)

Method: cdf (R-EXPONENTIAL0 r-exponential) X

Source

univariate.lisp (file)

Method: cdf (R-UNIFORM0 r-uniform) X

Source

univariate.lisp (file)

Generic Function: draw RANDOM-VARIABLE &key RNG &allow-other-keys

Draw random variates. Can also be used on generators.

Package

cl-random

Source

random.lisp (file)

Methods

Method: draw (R-UNIFORMIZED-MARKOV-JUMP0 r-uniformized-markov-jump) &key

Source

continuous-time.lisp (file)

Method: draw (R-GEOMETRIC0 r-geometric) &key RNG

Source

univariate.lisp (file)

Method: draw (R-BINOMIAL0 r-binomial) &key RNG

Source

univariate.lisp (file)

Method: draw (R-BERNOULLI0 r-bernoulli) &key RNG

Source

univariate.lisp (file)

Method: draw (INSTANCE r-discrete) &key RNG

Source

univariate.lisp (file)

Method: draw (R-RAYLEIGH0 r-rayleigh) &key RNG

Source

univariate.lisp (file)

Method: draw (R-BETA0 r-beta) &key RNG

Source

univariate.lisp (file)

Method: draw (R-INVERSE-GAMMA0 r-inverse-gamma) &key RNG

Source

univariate.lisp (file)

Method: draw (R-GAMMA0 r-gamma) &key RNG

Source

univariate.lisp (file)

Method: draw (R-T0 r-t) &key RNG

Source

univariate.lisp (file)

Method: draw (R-LOG-NORMAL0 r-log-normal) &key RNG

Source

univariate.lisp (file)

Method: draw (LEFT-TRUNCATED-NORMAL0 left-truncated-normal) &key RNG

Source

univariate.lisp (file)

Method: draw (R-NORMAL0 r-normal) &key RNG

Source

univariate.lisp (file)

Method: draw (R-EXPONENTIAL0 r-exponential) &key RNG

Source

univariate.lisp (file)

Method: draw (R-UNIFORM0 r-uniform) &key RNG

Source

univariate.lisp (file)

Method: draw (FUNCTION function) &key RNG

Generic Function: generator RANDOM-VARIABLE &key RNG

Return a closure that returns random draws.

Package

cl-random

Source

random.lisp (file)

Methods

Method: generator RANDOM-VARIABLE &key RNG

Generic Function: left R-UNIFORM0

Package

cl-random

Methods

Method: left (R-UNIFORM0 r-uniform)

Source

univariate.lisp (file)

Generic Function: log-pdf RANDOM-VARIABLE X &optional IGNORE-CONSTANT?

Log of probability distribution function of RANDOM-VARIABLE at X. NIL corresponds to log(-infinity). When IGNORE-CONSTANT?, the result may be shifted by an arbitrary real constant that does not change between calls of the same RANDOM-VARIABLE. This may save computation, and is useful for MCMC methods, etc.

Package

cl-random

Source

random.lisp (file)

Methods

Method: log-pdf (INSTANCE r-discrete) I &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Method: log-pdf (R-INVERSE-GAMMA0 r-inverse-gamma) X &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Method: log-pdf (R-GAMMA0 r-gamma) X &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Method: log-pdf (R-LOG-NORMAL0 r-log-normal) X &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Method: log-pdf (LEFT-TRUNCATED-NORMAL0 left-truncated-normal) X &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Method: log-pdf (R-NORMAL0 r-normal) X &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Method: log-pdf (R-EXPONENTIAL0 r-exponential) X &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Method: log-pdf (R-UNIFORM0 r-uniform) X &optional IGNORE-CONSTANT?

Source

univariate.lisp (file)

Generic Function: mean RANDOM-VARIABLE

Mean of random variable.

Package

cl-random

Source

random.lisp (file)

Methods

Method: mean (R-GEOMETRIC0 r-geometric)

Source

univariate.lisp (file)

Method: mean (R-BINOMIAL0 r-binomial)

Source

univariate.lisp (file)

Method: mean (R-BERNOULLI0 r-bernoulli)

Source

univariate.lisp (file)

Method: mean (INSTANCE r-discrete)

Source

univariate.lisp (file)

Method: mean (R-RAYLEIGH0 r-rayleigh)

Source

univariate.lisp (file)

Method: mean (R-BETA0 r-beta)

Source

univariate.lisp (file)

Method: mean (R-INVERSE-GAMMA0 r-inverse-gamma)

Source

univariate.lisp (file)

Method: mean (R-GAMMA0 r-gamma)

Source

univariate.lisp (file)

Method: mean (R-T0 r-t)

Source

univariate.lisp (file)

Method: mean (R-LOG-NORMAL0 r-log-normal)

Source

univariate.lisp (file)

Method: mean (LEFT-TRUNCATED-NORMAL0 left-truncated-normal)

Source

univariate.lisp (file)

Method: mean (R-NORMAL0 r-normal)

Source

univariate.lisp (file)

Method: mean (R-EXPONENTIAL0 r-exponential)

Source

univariate.lisp (file)

Method: mean (R-UNIFORM0 r-uniform)

Source

univariate.lisp (file)

Generic Function: nu DISTRIBUTION

Return the degrees of freedom when applicable.

Package

cl-random

Source

univariate.lisp (file)

Methods

Method: nu (R-INVERSE-GAMMA r-inverse-gamma)

Method: nu (R-GAMMA r-gamma)

Method: nu (R-T0 r-t)

Generic Function: probabilities INSTANCE

Package

cl-random

Methods

Method: probabilities (INSTANCE r-discrete)

Source

univariate.lisp (file)

Generic Function: quantile RANDOM-VARIABLE Q

Quantile of RANDOM-VARIABLE at Q.

Package

cl-random

Source

univariate.lisp (file)

Methods

Method: quantile (R-BETA0 r-beta) Q

Method: quantile (R-GAMMA0 r-gamma) Q

Method: quantile (R-LOG-NORMAL0 r-log-normal) Q

Method: quantile (LEFT-TRUNCATED-NORMAL0 left-truncated-normal) Q

Method: quantile (R-NORMAL0 r-normal) Q

Method: quantile (R-EXPONENTIAL0 r-exponential) P

Method: quantile (R-UNIFORM0 r-uniform) P

Generic Function: rate R-EXPONENTIAL0

Package

cl-random

Methods

Method: rate (R-EXPONENTIAL0 r-exponential)

Source

univariate.lisp (file)

Generic Function: right R-UNIFORM0

Package

cl-random

Methods

Method: right (R-UNIFORM0 r-uniform)

Source

univariate.lisp (file)

Generic Function: scale R-T0

Package

cl-random

Methods

Method: scale (R-RAYLEIGH0 r-rayleigh)

Source

univariate.lisp (file)

Method: scale (R-T0 r-t)

Source

univariate.lisp (file)

Generic Function: standard-deviation RANDOM-VARIABLE

Standard deviation of random variable.

Package

cl-random

Source

univariate.lisp (file)

Methods

Method: standard-deviation (RANDOM-VARIABLE r-univariate)

Generic Function: variance RANDOM-VARIABLE

Variance of random variable.

Package

cl-random

Source

random.lisp (file)

Methods

Method: variance (R-GEOMETRIC0 r-geometric)

Source

univariate.lisp (file)

Method: variance (R-BINOMIAL0 r-binomial)

Source

univariate.lisp (file)

Method: variance (R-BERNOULLI0 r-bernoulli)

Source

univariate.lisp (file)

Method: variance (INSTANCE r-discrete)

Source

univariate.lisp (file)

Method: variance (R-RAYLEIGH0 r-rayleigh)

Source

univariate.lisp (file)

Method: variance (R-BETA0 r-beta)

Source

univariate.lisp (file)

Method: variance (R-INVERSE-GAMMA0 r-inverse-gamma)

Source

univariate.lisp (file)

Method: variance (R-GAMMA0 r-gamma)

Source

univariate.lisp (file)

Method: variance (R-T0 r-t)

Source

univariate.lisp (file)

Method: variance (R-LOG-NORMAL0 r-log-normal)

Source

univariate.lisp (file)

Method: variance (LEFT-TRUNCATED-NORMAL0 left-truncated-normal)

Source

univariate.lisp (file)

Method: variance (R-NORMAL0 r-normal)

Source

univariate.lisp (file)

Method: variance (R-EXPONENTIAL0 r-exponential)

Source

univariate.lisp (file)

Method: variance (R-UNIFORM0 r-uniform)

Source

univariate.lisp (file)

5.1.4 Structures

Structure: r-bernoulli ()

Bernoulli(pr) distribution, with probability PR for success and 1-PR for failure.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• cdf (method)
• draw (method)
• variance (method)
• mean (method)
• pr (method)

Direct slots

Slot: pr

Type

cl-random.internals:internal-float

Readers

r-bernoulli-pr (function)

Writers

(setf r-bernoulli-pr) (function)

Structure: r-beta ()

Beta(alpha,beta) distribution, with density proportional to x^(alpha-1)*(1-x)^(beta-1).

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• quantile (method)
• draw (method)
• variance (method)
• mean (method)
• alpha (method)
• beta (method)

Direct slots

Slot: alpha

Type

cl-random.internals:internal-float

Readers

r-beta-alpha (function)

Writers

(setf r-beta-alpha) (function)

Slot: beta

Type

cl-random.internals:internal-float

Readers

r-beta-beta (function)

Writers

(setf r-beta-beta) (function)

Structure: r-binomial ()

Binomial(pr,n) distribution, with N Bernoulli trials with probability PR for success.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• variance (method)
• mean (method)
• pr (method)
• n (method)

Direct slots

Slot: pr

Type

cl-random.internals:internal-float

Readers

r-binomial-pr (function)

Writers

(setf r-binomial-pr) (function)

Slot: n

Type

integer

Readers

r-binomial-n (function)

Writers

(setf r-binomial-n) (function)

Structure: r-discrete ()

Discrete probabilities.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• cdf (method)
• log-pdf (method)
• variance (method)
• mean (method)
• probabilities (method)

Direct slots

Slot: probabilities

Type

cl-random.internals:float-vector

Readers

r-discrete-probabilities (function)

Writers

(setf r-discrete-probabilities) (function)

Slot: prob

Type

cl-random.internals:float-vector

Readers

r-discrete-prob (function)

Writers

(setf r-discrete-prob) (function)

Slot: alias

Type

(simple-array fixnum (*))

Readers

r-discrete-alias (function)

Writers

(setf r-discrete-alias) (function)

Slot: n-float

Type

cl-random.internals:internal-float

Readers

r-discrete-n-float (function)

Writers

(setf r-discrete-n-float) (function)

Structure: r-exponential ()

Exponential(rate) distribution, with density rate*exp(-rate*x) for x>=0 and 0 for x<0. rate > 0.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• quantile (method)
• cdf (method)
• log-pdf (method)
• variance (method)
• mean (method)
• rate (method)

Direct slots

Slot: rate

Type

cl-random.internals:internal-float

Readers

r-exponential-rate (function)

Writers

(setf r-exponential-rate) (function)

Structure: r-gamma ()

Gamma(alpha,beta) distribution, with density proportional to x^(alpha-1) exp(-x*beta). Alpha and beta are known as shape and inverse scale (or rate) parameters, respectively.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• nu (method)
• draw (method)
• quantile (method)
• cdf (method)
• log-pdf (method)
• variance (method)
• mean (method)
• alpha (method)
• beta (method)

Direct slots

Slot: alpha

Type

cl-random.internals:internal-float

Readers

r-gamma-alpha (function)

Writers

(setf r-gamma-alpha) (function)

Slot: beta

Type

cl-random.internals:internal-float

Readers

r-gamma-beta (function)

Writers

(setf r-gamma-beta) (function)

Structure: r-geometric ()

Geometric(pr) distribution.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• variance (method)
• mean (method)
• pr (method)

Direct slots

Slot: pr

Type

cl-random.internals:internal-float

Readers

r-geometric-pr (function)

Writers

(setf r-geometric-pr) (function)

Structure: r-inverse-gamma ()

Inverse-Gamma(alpha,beta) distribution, with density p(x) proportional to x^(-alpha+1) exp(-beta/x)

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• s^2 (method)
• nu (method)
• num= (method)
• draw (method)
• log-pdf (method)
• variance (method)
• mean (method)
• alpha (method)
• beta (method)

Direct slots

Slot: alpha

Type

cl-random.internals:internal-float

Readers

r-inverse-gamma-alpha (function)

Writers

(setf r-inverse-gamma-alpha) (function)

Slot: beta

Type

cl-random.internals:internal-float

Readers

r-inverse-gamma-beta (function)

Writers

(setf r-inverse-gamma-beta) (function)

Structure: r-log-normal ()

Log-normal distribution with location log-mean and scale log-sd.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• quantile (method)
• cdf (method)
• log-pdf (method)
• variance (method)
• mean (method)

Direct slots

Slot: log-mean

Type

cl-random.internals:internal-float

Readers

r-log-normal-log-mean (function)

Writers

(setf r-log-normal-log-mean) (function)

Slot: log-sd

Type

cl-random.internals:internal-float

Readers

r-log-normal-log-sd (function)

Writers

(setf r-log-normal-log-sd) (function)

Structure: r-normal ()

Normal(mean,variance) distribution.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• quantile (method)
• cdf (method)
• log-pdf (method)
• variance (method)
• mean (method)
• sd (method)

Direct slots

Slot: mean

Type

cl-random.internals:internal-float

Readers

r-normal-mean (function)

Writers

(setf r-normal-mean) (function)

Slot: sd

Type

cl-random.internals:internal-float

Readers

r-normal-sd (function)

Writers

(setf r-normal-sd) (function)

Structure: r-rayleigh ()

Rayleigh(scale) distribution with scale > 0 and density x * exp(-x^2 / (2 scale^2)) / scale^2 for x>=0 and 0 for x<0.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• cdf (method)
• draw (method)
• variance (method)
• mean (method)
• scale (method)

Direct slots

Slot: scale

Type

cl-random.internals:internal-float

Readers

r-rayleigh-scale (function)

Writers

(setf r-rayleigh-scale) (function)

Structure: r-t ()

T(mean,scale,nu) random variate.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• variance (method)
• mean (method)
• scale (method)
• nu (method)

Direct slots

Slot: mean

Type

cl-random.internals:internal-float

Readers

r-t-mean (function)

Writers

(setf r-t-mean) (function)

Slot: scale

Type

cl-random.internals:internal-float

Readers

r-t-scale (function)

Writers

(setf r-t-scale) (function)

Slot: nu

Type

cl-random.internals:internal-float

Readers

r-t-nu (function)

Writers

(setf r-t-nu) (function)

Structure: r-uniform ()

Uniform(left,right) distribution.

Package

cl-random

Source

univariate.lisp (file)

Direct superclasses

r-univariate (structure)

Direct methods

• draw (method)
• quantile (method)
• cdf (method)
• log-pdf (method)
• variance (method)
• mean (method)
• left (method)
• right (method)

Direct slots

Slot: left

Type

cl-random.internals:internal-float

Readers

r-uniform-left (function)

Writers

(setf r-uniform-left) (function)

Slot: right

Type

cl-random.internals:internal-float

Readers

r-uniform-right (function)

Writers

(setf r-uniform-right) (function)

Slot: width

Type

cl-random.internals:internal-float

Readers

r-uniform-width (function)

Writers

(setf r-uniform-width) (function)

Structure: r-uniformized-markov-jump ()

Define a random variable for uniformized markov jumps,
which returns two values: the time spent in the state, and the index of the next state (or the corresponding element in KEYS, which is a vector of the same length). TRANSITION-RATES defaults to the sum of keys, however, it can be specified to be larger, in which case the markov chain may remain in the same state and return NO-CHANGE as the second value. Defines features DURATION and JUMP, which return the two underlying random variables.

Package

cl-random

Source

continuous-time.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

• draw (method)
• duration (method)
• jump (method)

Direct slots

Slot: duration

Readers

r-uniformized-markov-jump-duration (function)

Writers

(setf r-uniformized-markov-jump-duration) (function)

Slot: jump

Readers

r-uniformized-markov-jump-jump (function)

Writers

(setf r-uniformized-markov-jump-jump) (function)

Slot: no-change

Readers

r-uniformized-markov-jump-no-change (function)

Writers

(setf r-uniformized-markov-jump-no-change) (function)

Slot: n

Type

fixnum

Readers

r-uniformized-markov-jump-n (function)

Writers

(setf r-uniformized-markov-jump-n) (function)

Slot: keys

Type

(or null vector)

Readers

r-uniformized-markov-jump-keys (function)

Writers

(setf r-uniformized-markov-jump-keys) (function)

5.1.5 Classes

Class: borosh13 ()

Donald E. Knuth’s Borosh-Niederreiter, The Art of Computer Programming, Volume 2, Third Edition, Addison-Wesley, pp 106-108.

Package

cl-random

Source

simple-multiplicative-congruential-generators.lisp (file)

Direct superclasses

simple-multiplicative-congruential (class)

Direct slots

Slot: a

Initform

1812433253

Slot: chunk-length

Initform

32

Class: generator ()

Base class for random number generators.

Package

cl-random

Source

generator.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses

simple-multiplicative-congruential (class)

Direct methods

• generate-state (method)
• initialize-instance (method)
• default-seed (method)
• chunk-length (method)
• state (method)
• state (method)

Direct slots

Slot: state

All information needed by the generator to create the next chunk
of random bits. This state is modified after each call to NEXT-CHUNK.

Initargs

:state

Readers

state (generic function)

Writers

(setf state) (generic function)

Slot: min

The minimum value return by NEXT-CHUNK.

Initargs

:min

Slot: max

The maximum value return by NEXT-CHUNK.

Initargs

:max

Slot: chunk-length

The length in bits of the integer returned by NEXT-CHUNK.

Readers

chunk-length (generic function)

Slot: default-seed

The seed used by default, when the seed is NIL.

Initform

0

Readers

default-seed (generic function)

Class: randu ()

The poor IBM randu generator. Park and Miller, Random Number
Generators: Good ones are hard to find, Communications of the ACM, October 1988, Volume 31, No 10, pp 1192-1201.

Package

cl-random

Source

simple-multiplicative-congruential-generators.lisp (file)

Direct superclasses

simple-multiplicative-congruential (class)

Direct slots

Slot: a

Initform

65539

Slot: chunk-length

Initform

31

Class: transputer ()

INMOS Transputer Development System generator.

Package

cl-random

Source

simple-multiplicative-congruential-generators.lisp (file)

Direct superclasses

simple-multiplicative-congruential (class)

Direct slots

Slot: a

Initform

1664525

Slot: chunk-length

Initform

32

Class: waterman14 ()

Donald E. Knuth’s Waterman, The Art of Computer Programming, Volume 2, Third Edition, Addison-Wesley, pp 106-108.

Package

cl-random

Source

simple-multiplicative-congruential-generators.lisp (file)

Direct superclasses

simple-multiplicative-congruential (class)

Direct slots

Slot: a

Initform

1566083941

Slot: chunk-length

Initform

32

5.1.6 Types

Type: float-vector &optional N

Package

cl-random.internals

Source

internals.lisp (file)

Type: internal-float &optional LOWER-LIMIT UPPER-LIMIT

Type used for internal representation of floats in the CL-RANDOM library.

Package

cl-random.internals

Source

internals.lisp (file)

5.2 Internal definitions

5.2.1 Constants

Constant: +normal-log-pdf-constant+

Normalizing constant for a standard normal PDF.

Package

cl-random

Source

univariate.lisp (file)

5.2.2 Special variables

Special Variable: *default-generator-type*

Package

cl-random

Source

generator.lisp (file)

5.2.3 Macros

Macro: define-rv NAME CONSTRUCTOR-LAMBDA-LIST OPTIONS SLOTS CONSTRUCTOR-FORM &rest METHODS

Define a random variable, abstracting from the representation. Syntax:

NAME is a symbol, and will name the class and the creation function.

CONSTRUCTOR-LAMBDA-LIST will be used to wrap the CONSTRUCTOR-FORM, which can use the locally define macro (MAKE :slot-name value1 ...) to initialize slots.

SLOTS is a list of (slot-name &key type read-only reader) slot specifications. When READER is T, SLOT-NAME is used instead, otherwise a method is defined using the given symbol.

OPTIONS is (&key documentation instance), the default instance is a gensym.

METHODS are (function-name lambda-list &body body), with (INSTANCE NAME) prepended to the lambda-list, ie the instance is accessible using INSTANCE. Also, within BODY, slots are accessible by their names.

Package

cl-random

Source

random.lisp (file)

5.2.4 Functions

Function: %next-double-float LIMIT RNG

Handle the single or double float case of RANDOM. We generate a float in [0d0, 1d0) by clobbering the mantissa of 1d0 with random bits (52 bits); this yields a number in [1d0, 2d0). Then 1d0 is subtracted.

Package

cl-random

Source

generator.lisp (file)

Function: %next-integer LIMIT RNG

Generates an integer greater than or equal to zero and less than LIMIT. Successive chunks are concatenated without overlap to construct integers larger than a single chunk. The return value has this property: If two integers are generated from the same RNG with LIMIT equal to 2^m and 2^n, respectively, then bit k is the same in both integers for 0 <= k < min(m,n). Each call to %NEXT-INTEGER consumes at least one chunk; bits left over from previous chunks are not re-used.

Package

cl-random

Source

generator.lisp (file)

Function: %next-single-float LIMIT RNG

Handle the single or double float case of RANDOM. We generate a float in [0f0, 1f0) by clobbering the mantissa of 1f0 with random bits (23 bits); this yields a number in [1f0, 2f0). Then 1f0 is subtracted.

Package

cl-random

Source

generator.lisp (file)

Function: cdf-normal% X MEAN SD

Internal function for normal CDF.

Package

cl-random

Source

univariate.lisp (file)

Function: check-probability P &optional OPEN

Assert that P is a probability (ie a real number between 0 and 1). When OPEN is given, it is checked that p is not 0 (:LEFT), 1 (:RIGHT), or 0/1 (:BOTH).

Package

cl-random

Source

random.lisp (file)

Function: copy-left-truncated-normal INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-bernoulli INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-beta INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-binomial INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-discrete INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-exponential INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-gamma INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-geometric INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-inverse-gamma INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-log-normal INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-normal INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-rayleigh INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-t INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-uniform INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: copy-r-uniformized-markov-jump INSTANCE

Package

cl-random

Source

continuous-time.lisp (file)

Function: copy-r-univariate INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: draw-bernoulli-bit P &key RNG

Package

cl-random

Source

univariate.lisp (file)

Function: draw-left-truncated-standard-normal LEFT ALPHA &key RNG

Draw a left truncated standard normal, using an Exp(alpha,left) distribution. LEFT is the standardized boundary, ALPHA should be calculated with TRUNCATED-NORMAL-OPTIMAL-ALPHA.

Package

cl-random

Source

univariate.lisp (file)

Function: draw-standard-gamma1 ALPHA D C &key RNG

Return a standard gamma variate (beta=1) with shape parameter alpha >= 1. See Marsaglia and Tsang (2004). You should precalculate d and c using the utility function above.

Package

cl-random

Source

univariate.lisp (file)

Function: generate-seed ()

Return a 64-bit random seed, based on current time.

Package

cl-random

Source

generator.lisp (file)

Function: left-truncated-normal MU SIGMA LEFT

Package

cl-random

Source

univariate.lisp (file)

Function: left-truncated-normal-alpha INSTANCE

Function: (setf left-truncated-normal-alpha) VALUE INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: left-truncated-normal-left INSTANCE

Function: (setf left-truncated-normal-left) VALUE INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: left-truncated-normal-left-standardized INSTANCE

Function: (setf left-truncated-normal-left-standardized) VALUE INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: left-truncated-normal-m0 INSTANCE

Function: (setf left-truncated-normal-m0) VALUE INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: left-truncated-normal-mu INSTANCE

Function: (setf left-truncated-normal-mu) VALUE INSTANCE

Package

cl-random

Source

univariate.lisp (file)

Function: left-truncated-normal-p OBJECT

Package

cl-random

Source

univariate.lisp (file)