Added TRSVD first draft

src/MinPakke.jl

@@ -35,10 +35,21 @@ export calculateRMSECV
 export PCR
 export bidiag2
 
+export regularizationMatrix
+export TRSVDDecomp
+export TRRegCoeffs
+export TRPress
+export TRGCV
+export TRLooCV
+export PlotTRLooCV
+export TRLooCVNum
+export TRGCVNum
+
 
 include("preprocessing.jl")
 include("convenience.jl")
 include("conveniencePlots.jl")
 include("variousRegressionFunctions.jl")
+include("TR.jl")
 
 end

src/TR.jl

@@ -0,0 +1,56 @@
+
+
+
+
+
+
+using Optimization
+using OptimizationOptimJL
+
+
+"""
+### TO DO: ADD FRACTIONAL DERIVATIVE REGULARIZATION ###
+
+    regularizationMatrix(X; regType="legendre", regParam1=0, regParam2=1e-14)
+    regularizationMatrix(p::Int64; regType="legendre", regParam1=0, regParam2=1e-14)
+
+Calculates and returns square regularization matrix.
+
+Inputs:
+    - X/p       : Size of regularization matrix or data matrix (size of reg. mat. will then be size(X,2)
+    - regType   : "L2" (returns identity matrix)
+                  "bc" (boundary condition, forces zero on right endpoint for derivative regularization) or
+                  "legendre" (no boundary condition, but fills out reg. mat. with lower order polynomial trends to get square matrix)
+                  "std" (standardization, FILL OUT WHEN DONE)
+    - regParam1 : Int64, Indicates degree of derivative regularization (0 gives L\\_2)
+    - regParam2 : For regType=="plegendre" added polynomials are multiplied by sqrt(regParam2)
+
+Output: Square regularization matrix
+"""
+function regularizationMatrix(X; regType="L2", regParam1=0, regParam2=1e-14)
+
+if regType == "std"
+    regParam2 = Diagonal(vec(std(X, dims=1)));
+end
+
+regMat = regularizationMatrix(size(X,2); regType, regParam1, regParam2)
+
+return regMat
+end
+
+function regularizationMatrix(p::Int64; regType="L2", regParam1=0, regParam2=1e-14)
+    
+if regType == "bc"
+    regMat  = [I(p); zeros(regParam1,p)]; for i = 1:regParam1 regMat = diff(regMat, dims = 1); end
+elseif regType == "legendre"
+    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(size(X,2));
+elseif regType == "std"
+    regMat = regParam2;
+end
+
+return regMat
+end