@@ -19,7 +19,6 @@ synonyms are listed.
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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 )
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# Gaussian matrix ensembles
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@@ -44,7 +43,6 @@ The hierarchy of dense matrices provided are
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- Circular symplectic ensemble (CSE, ` beta=4 ` )
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- Laguerre matrices = white Wishart matrices
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- Jacobi matrices = MANOVA matrices
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- - Unitary invariant ensembles
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Unless otherwise specified, ` beta=1,2,4 ` are supported. For the symplectic matrices ` beta=4 ` ,
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the 2x2 outer block-diagonal complex representation ` USp(2N) ` is used.
@@ -89,11 +87,6 @@ Hermite, Laguerre(m) and Jacobi(m1, m2) ensembles.
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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.
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- Only available if ApproxFun package is installed.
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-
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The parameters ` m ` , ` m1 ` , ` m2 ` refer to the number to independent "data" degrees of freedom.
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For the dense samples these must be ` Integer ` s but can be ` Real ` s for the rest.
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@@ -168,21 +161,7 @@ The available `StochasticProcess`es are
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# Invariant ensembles
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` InvariantEnsemble(str,n) ` supports n x n unitary invariant ensemble
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- with distribution
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-
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- ` exp(- Tr Q(M)) dM `
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-
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- ` str ` specifies an ensemble with precomputed recurrence coefficients.
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- The currently include ensembles are
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-
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- | | Q(M) |
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- | ----------------- | ----- |
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- | ` Quartic ` | n M^4 |
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- | ` Eighth ` | n M^8 |
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- | ` HODecay ` | n (M^4/20 - 4/15M^3 +M^2/5 + 8/5M) |
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- | ` CoshUnscaled ` | cosh(M) |
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- | ` QuarticUnscaled ` | M^4 |
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- | ` EightUnscaled ` | M^8 |
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+ with distribution. This has been moved to separate package [ InvariantEnsembles.jl] ( https://github.com/dlfivefifty/InvariantEnsembles.jl )
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# References
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- James Albrecht, Cy Chan, and Alan Edelman,
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