Added basic simulation of spectroscopic data

src/MinPakke.jl

@@ -44,6 +44,11 @@ export TRLooCV
 export PlotTRLooCV
 export TRLooCVNum
 export TRGCVNum
+export TRSegCV
+export TRVirCV
+export TRBidiagDecomp
+
+export simulateSpectrum
 
 
 include("preprocessing.jl")
@@ -51,5 +56,6 @@ include("convenience.jl")
 include("conveniencePlots.jl")
 include("variousRegressionFunctions.jl")
 include("TR.jl")
+include("simulateSpectroscopicData.jl")
 
 end

src/TR.jl

@@ -1,13 +1,6 @@
 
-
+using Optimization        # For numerical minimization of PRESS statistic
-
+using OptimizationOptimJL # For numerical minimization of PRESS statistic
-
-
-
-using Optimization
-using OptimizationOptimJL
-
-
 
 struct TRSVD
     U::Matrix{Float64}
@@ -22,12 +15,26 @@ struct TRSVD
 end
 
 
+struct TRBidiag
+    W::Matrix{Float64}
+    B::Bidiagonal{Float64, Vector{Float64}}
+    T::Matrix{Float64}
+    y::Vector{Float64}
+    mX::Matrix{Float64}
+    my::Float64
+    regType::String
+    regParam1::Float64
+    regMat::Matrix{Float64}
+    n::Int64
+    p::Int64
+end
+
 
 """
 ### TO DO: ADD FRACTIONAL DERIVATIVE REGULARIZATION ###
 
-    regularizationMatrix(X; regType="legendre", regParam1=0, regParam2=1e-14)
+    regularizationMatrix(X; regType="L2", regParam1=0, regParam2=1e-14)
-    regularizationMatrix(p::Int64; regType="legendre", regParam1=0, regParam2=1e-14)
+    regularizationMatrix(p::Int64; regType="L2", regParam1=0, regParam2=1e-14)
 
 Calculates and returns square regularization matrix.
 
@@ -55,22 +62,56 @@ end
 
 function regularizationMatrix(p::Int64; regType="L2", regParam1=0, regParam2=1e-14)
     
-if regType == "bc"
+if regType == "bc" # Discrete derivative with boundary conditions
     regMat  = [I(p); zeros(regParam1,p)]; for i = 1:regParam1 regMat = diff(regMat, dims = 1); end
-elseif regType == "legendre"
+elseif regType == "legendre" # Fill in polynomials in bottom row(s) to get square matrix
     regMat  = [I(p); zeros(regParam1,p)]; for i = 1:regParam1 regMat = diff(regMat, dims = 1); end
     P, _    = plegendre(regParam1-1, p);   
     regMat[end-regParam1+1:end,:] = sqrt(regParam2) * P;
 elseif regType == "L2"
     regMat = I(p);
-elseif regType == "std"
+elseif regType == "std" # Standardization
     regMat = regParam2;
+elseif regType == "GL" # Grünwald-Letnikov fractional derivative regulariztion
+    # regParam1 is alpha (order of fractional derivative)
+    C = ones(p)*1.0;
+    for k in 2:p
+        C[k] = (1-(regParam1+1)/(k-1)) * C[k-1];
+    end
+
+    regMat = zeros(p,p);
+
+    for i in 1:p
+        regMat[i:end, i] = C[1:end-i+1];
+    end
 end
 
 return regMat
 end
 
 
+"""
+    function TRBidiagDecomp(X, y, A=(minimum(size(X))-1), regType="L2", regParam1=0, regParam2=1e-14)
+
+Calculates regularization matrix (using function "RegularizationMatrix"),
+and centres and transforms data matrix according to "X / regMat".
+Output is an object of type "TRBidiag" and is used as input to other TR functions.
+"""
+function TRBidiagDecomp(X, y, A=(minimum(size(X))-1), regType="L2", regParam1=0, regParam2=1e-14)
+
+n, p       = size(X);
+mX         = mean(X, dims=1);    
+X          = X .- mX;
+my         = mean(y);
+y          = vec(y .- my);
+regMat     = regularizationMatrix(X; regType, regParam1, regParam2);
+X          = X / regMat;
+_, W, B, T = bidiag2(X, y, A);
+TRObj      = TRBidiag(W, B, T, y, mX, my, regType, regParam1, regMat, n, p);
+    
+return TRObj
+end
+
 
 """
     function TRSVDDecomp(X, regType="L2", regParam1=0, regParam2=1e-14)
@@ -92,6 +133,112 @@ TRObj   = TRSVD(U, s, V, mX, regType, regParam1, regMat, n, p);
 return TRObj
 end
 
+function TRSegmentOrth(X, segments)
+
+n = size(X,1);
+n_segments = maximum(segments);
+
+U = zeros(n,n);
+
+for seg in 1:n_segments
+    inds = vec(seg .== segments)
+    U[inds, inds], _, _ = svd(X[inds,:], full=false);
+end
+
+return U
+end
+
+"""
+    function TRVirCV(X, y, segments, lambdas, regType="L2", regParam1=0, regParam2=1e-14)
+
+Segmented virtual cross-validation (VirCV) for TR models.
+Outputs: b, press, lambda_min, lambda_min_ind, GCV
+b are (virtual) press-minimal regression coefficients.
+"""
+function TRVirCV(X, y, segments, lambdas, regType="L2", regParam1=0, regParam2=1e-14)
+
+U_segments = TRSegmentOrth(X, segments);
+bs         = vec(sum(U_segments, dims=1).^2);
+
+n, p    = size(X);
+mX      = mean(X, dims=1);    
+X       = X .- mX;
+my      = mean(y);
+y       = vec(y .- my);
+X       = U_segments' * X;
+y       = U_segments' * y;
+regMat  = regularizationMatrix(p; regType, regParam1, regParam2);
+X       = X / regMat;
+U, s, V = svd(X, full=false);
+
+denom  = broadcast(.+, broadcast(./, lambdas, s'), s')';
+H      = broadcast(.+, U.^2 * broadcast(./, s, denom), bs./n);
+resid  = broadcast(.-, y, U * broadcast(./, s .* (U'*y), denom));
+rescv  = broadcast(./, resid, broadcast(.-, 1, H));
+press  = vec(sum(rescv.^2, dims=1));
+#rmsecv = sqrt.(1/n .* press);
+GCV    = vec(broadcast(./, sum(resid.^2, dims=1), mean(broadcast(.-, 1, H), dims=1).^2));
+
+lambda_min, lambda_min_ind = findmin(press);
+lambda_min_ind             = lambda_min_ind[1];
+
+denom2  = broadcast(.+, lambda_min ./ s', s')';
+b       = V * broadcast(./, (U' * y), denom2);
+b       = regMat \ b;
+b       = [my .- mX*b; b];
+
+return b, press, lambda_min, lambda_min_ind, GCV
+end
+
+
+
+"""
+    function TRSegCV(X, y, lambdas, cv, regType="L2", regParam1=0, regParam2=1e-14)
+
+Segmented cross-validation based on the Sherman-Morrison-Woodbury updating formula.
+Inputs:
+    - X : Data matrix
+    - y : Response vector
+    - lambdas : Vector of regularization parameter values
+    - cv : Vector of length n indicating segment membership for each sample
+    - regType, regParam1, regParam2 : Inputs to regularizationMatrix function
+
+Outputs: rmsecv, b, lambda_min, lambda_min_ind.
+b are regression coefficients corresponding to the lambda value minimising the CV-error.
+"""
+function TRSegCV(X, y, lambdas, cv, regType="L2", regParam1=0, regParam2=1e-14)
+
+TR        = TRSVDDecomp(X, regType, regParam1, regParam2);
+n_seg     = maximum(cv);
+n_lambdas = length(lambdas);
+my        = mean(y);
+y         = y .- my;
+
+denom  = broadcast(.+, broadcast(./, lambdas, TR.s'), TR.s')';
+resid  = broadcast(.-, y, TR.U * broadcast(./, TR.s .* (TR.U'*y), denom));
+rescv  = zeros(TR.n, n_lambdas);
+sdenom = sqrt.(broadcast(./, TR.s, denom))';
+
+for seg in 1:n_seg
+        
+    Useg = TR.U[vec(cv .== seg),:];
+    Id   = 1.0 * I(size(Useg,1)) .- 1/TR.n;
+        
+    for k in 1:n_lambdas
+        Uk                        = Useg .* sdenom[k,:]';
+        rescv[vec(cv .== seg), k] = (Id - Uk * Uk') \ resid[vec(cv .== seg), k];
+    end
+end
+
+press  = sum(rescv.^2, dims=1)';
+rmsecv = sqrt.(1/TR.n .* press);
+    
+lambda_min, lambda_min_ind = findmin(rmsecv)
+lambda_min_ind             = lambda_min_ind[1]
+b                          = TRRegCoeffs(TR, y, lambda_min, my)
+    
+return b, rmsecv, lambda_min, lambda_min_ind
+end
 
 
 """

src/simulateSpectroscopicData.jl

@@ -0,0 +1,43 @@
+Lk(waves, c, gamma) = @. gamma / (pi*(waves-c)^2+gamma^2);
+Gk(waves, c, gamma) = @. 1/(sqrt(2*pi)*gamma) * exp(-(waves-c)^2 / (2*gamma^2));
+
+function pseudoVoigtPeak(waves, c, gamma, eta, alpha)
+    
+fk = zeros(length(waves));
+
+for i in 1:length(c)
+        fk += alpha[i] .* pseudoVoigtPeak(waves, c[i], gamma[i], eta[i]);
+end
+    
+return fk
+end
+    
+function pseudoVoigtPeak(waves, c, gamma::Float64, eta::Float64)
+
+fk = eta * Lk(waves, c, gamma) + (1-eta) * Gk(waves, c, gamma);
+
+return fk
+end
+
+function simulateBaseline(waves, a)
+
+vm = zeros(length(waves), length(a));
+
+for i in 0:(length(a)-1)
+    vm[:, i+1] = waves.^i ./ norm(waves.^i);
+end
+
+b = vm * a;
+    
+return b
+end
+
+function simulateSpectrum(waves, c, gamma, eta, alpha, a, sigma=0.0)
+    
+pure_spec = pseudoVoigtPeak(waves, c, gamma, eta, alpha);
+b         = simulateBaseline(waves, a);
+noise     = randn(length(waves)) .* sigma;
+spec      = pure_spec + b + noise;
+return spec, pure_spec, b, noise
+end
+