Clean up

src/MCMC/testStan.jl

-######### Stan program example  ###########
-
-# module Tmp
-const σw0 = 1.0
-const σw = 1
-const σv = 1.0
-const theta0 = [0.5, 25, 8]
-s2piσv = log(sqrt(2*pi) * σv)
-ProjDir = pwd()
-
-function f_sample(x::Vector, t::Int64)
-    c = 8*cos(1.2*(t-1))
-    @inbounds for i = 1:length(x)
-        x[i] =  0.5*x[i] + 25*x[i]./(1+x[i]^2) + c + σw*randn()
-    end
-    return x
-end
-f_sample(x::Float64, t::Int64) = 0.5*x + 25*x/(1+x^2) + 8*cos(1.2*(t-1)) + σw*randn()
-
-
-
-T = 100
-M = 1
-x = Array(Float64,T)
-y = Array(Float64,T)
-x0 = 0
-
-x[1] = σw*randn()
-y[1] = σv*randn()
-for t = 1:T-1
-    x[t+1] = f_sample(x[t],t)
-    y[t+1] = 0.05x[t+1]^2  + σv*randn()
-end # t
-
-
-
-
-using Stan, Mamba
-
-
-odemodel ="
-data {
-  int<lower=1> T;
-  real y[T];
-}
-
-parameters {
-  real theta[3];
-  real sigma[2];
-  real x[T];
-}
-
-model {
-  sigma[1] ~ cauchy(1,1);
-  sigma[2] ~ cauchy(1,1);
-  theta[1] ~ cauchy(0.5,0.5);
-  theta[2] ~ cauchy(25,25);
-  theta[3] ~ cauchy(8,8);
-  x[1] ~ normal(0,1);
-  y[1] ~ normal(0.05*x[1]*x[1], sigma);
-  for (t in 1:(T-1)){
-   x[t+1] ~ normal(theta[1]*x[t] + theta[2]*x[t]/(1+x[t]*x[t]) + theta[3]*cos(1.2*(t-1)),sigma[1]);
-   y[t+1] ~ normal(0.05*x[t+1]*x[t+1], sigma[2]);
-  }
-}
-"
-
-odedict =
-  Dict(
-    "T" => T,
-    "y" => y)
-
-stanmodel = Stanmodel(name="ode", model=odemodel, nchains=4, update=10000)
-@time sim1 = stan(stanmodel, [odedict], ProjDir, diagnostics=false, CmdStanDir=CMDSTAN_HOME)
-
-## Subset Sampler Output to variables suitable for describe().
-monitor = ["lp__", "accept_stat__"]
-sim = sim1[1:size(sim1, 1), monitor, 1:size(sim1, 3)]
-
-describe(sim)
-println()
-
-p = plot(sim, [:trace, :mean, :density, :autocor], legend=true)
-draw(p, ncol=4, filename="$(stanmodel.name)-infoplot", fmt=:pdf)
-
-
-
-## Subset Sampler Output to variables suitable for describe().
-monitor = ["theta.1","theta.2","theta.3"]
-sim = sim1[1:size(sim1, 1), monitor, 1:size(sim1, 3)]
-
-describe(sim)
-println()
-
-p = plot(sim, [:trace, :mean, :density, :autocor], legend=true)
-draw(p, ncol=4, filename="$(stanmodel.name)-thetaplot", fmt=:pdf)
-
-
-
-## Subset Sampler Output to variables suitable for describe().
-monitor = ["sigma.1", "sigma.2"]
-sim = sim1[:, monitor, :]
-describe(sim)
-println()
-
-p = plot(sim, [:trace, :mean, :density, :autocor], legend=true)
-draw(p, nrow=4, ncol=4, filename="$(stanmodel.name)-sigmaplot", fmt=:pdf)
-
-

src/PCA.jl

@@ -6,3 +6,17 @@ function PCA(W)
     score = score*diagm(latent)
     C,score,latent,W0
 end
+
+
+using MLKernels
+function kernelPCA(X; α=1.0)
+    κ = GaussianKernel(α)
+    K = kernelmatrix(κ,X)
+    N = size(K)[1]
+    In = fill(1/N,(N,N))
+    K = K-In*K - K*In + In*K*In # Make sure mean is zero
+
+    (D,V) = eig(K)
+    Kpc = K*V
+    Kpc,D,V
+end

src/SystemIdentification.jl

@@ -13,7 +13,7 @@ FitResult,
 IdData,
 # Functions
 ar,arx,getARregressor,getARXregressor,find_na,
-toeplitz, kalman, kalman_smoother, forward_kalman, PCA
+toeplitz, kalman, kalman_smoother, forward_kalman, PCA, plotmodel
 
 ## Fit Methods =================
 :LS

src/armax.jl

@@ -93,7 +93,7 @@ getARXregressor(iddata::IdData, na, nb) = getARXregressor(iddata.y,iddata.u, na,
 
 
 """Plots the RMSE and AIC for model orders up to `n`. Useful for model selection"""
-function find_na(y::Vector{Float64},n::Int)
+function find_na(y::Vector,n::Int)
     error = zeros(n,2)
     for i = 1:n
         w,e = ar(y,i)
@@ -102,18 +102,21 @@ function find_na(y::Vector{Float64},n::Int)
         print(i,", ")
     end
     println("Done")
-    plotsub(error,"-o")
-    show()
+    scatter(error, show=true)
 end
 
-import PyPlot
-function PyPlot.plot(y,m::AR)
+"""
+    plotmodel(y,m::AR)
+
+Plots a signal `y` and the output of the model `m`
+"""
+function plotmodel(y,m::AR)
     na = length(m.a)
     y,A = getARregressor(y,na)
     yh = A*m.a
     error = y-yh
-    newplot(y,"k")
-    plot(yh,"b")
-    plot(error,"r")
-    title("Fitresult, AR, n_a: $na, RMSE = $(rms(error)) Fit = $(fit(y,yh))")
+    plot(y,c=:black)
+    plot(yh,c=:b)
+    plot(error,c=:r, title="Fitresult, AR, n_a: $na, RMSE = $(rms(error)) Fit = $(fit(y,yh))")
+
 end

src/cuckooSearch.jl

 using Devectorize
 """
 `cuckoo_search(f,X0;Lb=-convert(Float64,Inf),Ub=convert(Float64,Inf),n=25,pa=0.25, Tol=1.0e-5, max_iter = 1e5, timeout = Inf)`\n
+
 `n` = Number of nests (or different solutions)
 `pa=0.25` Discovery rate of alien eggs/solutions
 Change this if you want to get better results

src/idinput.jl

+"""
+    idinput(N, class = "prbs"; band = 1)
+
+Create a input signal for a sys.id. experiment, currently only supports prbs signals.
+"""
 function idinput(N, class = "prbs"; band = 1)
     output = zeros(N)
     if lowercase(class) == "prbs"
@@ -18,4 +23,3 @@ function idinput(N, class = "prbs"; band = 1)
 
     return output
 end
-

src/kernelPCA.jl

-using MLKernels
-function kernelPCA(X; α=1.0)
-    κ = GaussianKernel(α)
-    K = kernelmatrix(κ,X)
-    N = size(K)[1]
-    In = fill(1/N,(N,N))
-    K = K-In*K - K*In + In*K*In # Make sure mean is zero
-
-    (D,V) = eig(K)
-    Kpc = K*V
-    Kpc,D,V
-end

src/least_squares.jl

@@ -36,9 +36,13 @@ function dsvd(A,b,λ)
     dsvd(A,U,S,V,b,λ)
 end
 
+"""
+    Lcurve(normE, normX, λ)
+
+Plots the L-curve. normE and normX are obtained from, e.g., `dsvd`
+"""
 function Lcurve(normE, normX, λ)
-    plot(normE,normX,xscale=:log10,yscale=:log10,m=:o)
+    plot(normE,normX,xscale=:log10,yscale=:log10,m=:o, xlabel="RMSE", ylabel="||k||", title="L-curve")
     annotations = [(normE[i],normX[i],"λ=$(round(λ[i],8))") for i in 1:length(λ)]
     annotate!(annotations)
-    xlabel!("RMSE"); ylabel!("||k||"); title!("L-curve")
 end

src/sobol.jl

@@ -194,21 +194,18 @@ function InitSobol(dim::Int64)
 end
 
 """
-`using Winston`
 Plots the first 4 outputs of sobel(2,512)
 """
 function test_sobol()
     X, nextseed, MeM = sobol(2,512)
-    figure(); pp = plot(X[:,1],X[:,2],".b"); hold(true)
+    plot(X[:,1],X[:,2],c=:b)
 
     X, nextseed, MeM = sobol(X, nextseed, MeM )
-    plot(X[:,1],X[:,2],".g")
+    plot(X[:,1],X[:,2],c=:g)
 
     X, nextseed, MeM = sobol(X, nextseed, MeM )
-    plot(X[:,1],X[:,2],".r")
+    plot(X[:,1],X[:,2],c=:r)
 
     X, nextseed, MeM = sobol(X, nextseed, MeM )
-    plot(X[:,1],X[:,2],".m")
-
-    display(pp)
+    plot(X[:,1],X[:,2],c=:m)
 end

src/toeplitz.jl

-function toeplitz{T}(c::Array{T},r::Array{T})
-    nc = length(c)
-    nr = length(r)
-    A = zeros(T, nc, nr)
-    A[:,1] = c
-    A[1,:] = r
-    for i in 2:nr
-        A[2:end,i] = A[1:end-1,i-1]
-    end
-    A
-end

src/transfer_functions.jl

 using DSP
 
+"""
+    tfest(y,u)
+
+Estimate a transfer function model using the Correlogram approach
+H = Syu/Suu
+"""
 function tfest(y,u)
     Cyu = xcorr(y,u)
     Cuu = xcorr(u,u)
@@ -9,11 +15,3 @@ function tfest(y,u)
 end
 
 tfest(iddata::IdData) = tfest(iddata.y,iddata.u)
-
-
-N = 200000;
-u = randn(N);
-y = filt(ones(5),5,u);
-
-H = tfest(y,u);
-semilogy(H.F,abs(H.P))