@@ -3,6 +3,11 @@ RandomMatrices.jl
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Random matrix package for [ Julia] ( http://julialang.org ) .
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+ [ ![ RandomMatrices on Julia release] ( http://pkg.julialang.org/badges/RandomMatrices_release.svg )] ( http://pkg.julialang.org/?pkg=RandomMatrices&ver=release )
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+ [ ![ RandomMatrices on Julia nightly] ( http://pkg.julialang.org/badges/RandomMatrices_nightly.svg )] ( http://pkg.julialang.org/?pkg=RandomMatrices&ver=nightly )
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+ [ ![ Build Status] ( https://travis-ci.org/jiahao/RandomMatrices.jl.png?branch=master )] ( https://travis-ci.org/jiahao/RandomMatrices.jl )
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+ [ ![ Coverage Status] ( https://coveralls.io/repos/jiahao/RandomMatrices.jl/badge.svg?branch=master )] ( https://coveralls.io/r/jiahao/RandomMatrices.jl?branch=master )
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This extends the [ Distributions] ( https://github.com/JuliaStats/Distributions.jl )
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package to provide methods for working with matrix-valued random variables,
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a.k.a. random matrices. State of the art methods for computing random matrix
@@ -11,11 +16,6 @@ samples and their associated distributions are provided.
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The names of the various ensembles can vary widely across disciplines. Where possible,
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synonyms are listed.
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- [ ![ Build Status] ( https://travis-ci.org/jiahao/RandomMatrices.jl.png?branch=master )] ( https://travis-ci.org/jiahao/RandomMatrices.jl )
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- [ ![ RandomMatrices] ( http://pkg.julialang.org/badges/RandomMatrices_release.svg )] ( http://pkg.julialang.org/?pkg=RandomMatrices&ver=release )
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- [ ![ RandomMatrices] ( http://pkg.julialang.org/badges/RandomMatrices_nightly.svg )] ( http://pkg.julialang.org/?pkg=RandomMatrices&ver=nightly )
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- [ ![ Coverage Status] ( https://img.shields.io/coveralls/jiahao/RandomMatrices.jl.svg )] ( https://img.shields.io/coveralls/jiahao/RandomMatrices.jl.svg )
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-
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Additional functionality is provided when these optional packages are installed:
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- Symbolic manipulation of Haar matrices with [ GSL.jl] ( https://github.com/jiahao/GSL.jl )
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- Invariant ensembles with [ ApproxFun.jl] ( https://github.com/dlfivefifty/ApproxFun.jl )
@@ -71,7 +71,7 @@ Hermite, Laguerre(m) and Jacobi(m1, m2) ensembles.
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` GaussianLaguerreTridiagonalMatrix(n, m, beta) ` ,
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` GaussianJacobiSparseMatrix(n, m1, m2, beta) `
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each construct a sparse ` n ` x` n ` matrix for the corresponding matrix ensemble
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- for arbitrary positive finite ` beta ` .
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+ for arbitrary positive finite ` beta ` .
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` GaussianHermiteTridiagonalMatrix(n, Inf) ` is also allowed.
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These sampled matrices have the same eigenvalues as above but are much faster
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to diagonalize oweing to their sparsity. They also extend Dyson's threefold
@@ -87,7 +87,7 @@ Hermite, Laguerre(m) and Jacobi(m1, m2) ensembles.
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is applied to the raw QR decomposition. By default, ` correction=1 ` (Edelman's correction) is
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used. Other valid values are ` 0 ` (no correction) and ` 2 ` (Mezzadri's correction).
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- ` NeedsPiecewiseCorrection() ` implements a simple test to see if a correction is necessary.
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- ` InvariantEnsemble(str,n) `
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Generates a unitary invariant ensemble, where str determines the
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potential of the ensemble, see below.
@@ -151,15 +151,15 @@ Provides finite-dimensional matrix representations of stochastic operators.
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In the following, ` dt ` is the time interval being discretized over and ` t_end ` is the final time.
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- ` BrownianProcess(dt, t_end) ` generates a vector corresponding to a Brownian random walk starting
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- from time ` t=0 ` and position ` x=0 `
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+ from time ` t=0 ` and position ` x=0 `
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- ` WhiteNoiseProcess(dt, t_end) ` generates a vector corresponding to white noise.
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- ` StochasticAiryProcess(dt, t_end, beta) ` generates the largest eigenvalue corresponding to the
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stochastic Airy process with real positive ` beta ` . This is known to be distributed in the ` t_end -> Inf `
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limit to the ` beta ` -Tracy-Widom law.
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# Invariant ensembles
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- ` InvariantEnsemble(str,n) ` supports n x n unitary invariant ensemble
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+ ` InvariantEnsemble(str,n) ` supports n x n unitary invariant ensemble
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with distribution
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` exp(- Tr Q(M)) dM `
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