Implemented minimization of 1-norm for ar arx

src/PCA.jl

-""" Performs PCA   PCA(W,doplot=false)"""
-function PCA(W,doplot=false)
+""" Performs PCA   PCA(W)"""
+function PCA(W)
     W0 = mean(W,1);
     W = W-repmat(W0,size(W,1),1);
     (score,latent,C) = svd(W)
     score = score*diagm(latent)
-    if doplot
-        newplot(cumsum(latent)./sum(latent),"o")
-        title("Fraction of variance explained")
-        ylim([0,1])
-    end
     C,score,latent,W0
 end

src/armax.jl

+using Convex
+using SCS
 """`ar(y, na; λ = 0)`"""
-function ar(y::Vector{Float64}, na; λ = 0)
+function ar(y::Vector{Float64}, na; λ = 0, normtype=2, verbose=false)
     y_train, A = getARregressor(y,na)
     n_points = size(A,1)
+    if normtype == 2
         if λ == 0
             w = A\y_train
         else
             w = (A'A + λ*eye(size(A,2)))\A'y_train
         end
+    elseif normtype == 1
+        w = Variable(size(A,2),1)
+        problem = minimize(sum(abs(A*w-y_train )) + λ*norm(w))
+        solve!(problem, SCSSolver(verbose=Int(verbose)))
+        w = w.value[:]
+    end
     prediction = A*w
     error = y_train - prediction
     model = AR(w,na)
@@ -16,14 +25,21 @@ end
 ar(iddata::IdData, na; λ = 0) = ar(iddata.y, na; λ = 0)
 
 """arx(y, u, na, nb; λ = 0)"""
-function arx(y::Vector{Float64}, u::VecOrMat{Float64}, na, nb; λ = 0)
+function arx(y::Vector{Float64}, u::VecOrMat{Float64}, na, nb; λ = 0, normtype=2, verbose=false)
     y_train, A = getARXregressor(y,u, na, nb)
     n_points = size(A,1)
+    if normtype == 2
         if λ == 0
             w = A\y_train
         else
             w = (A'A + λ*eye(size(A,2)))\A'y_train
         end
+    elseif normtype == 1
+        w = Variable(size(A,2),1)
+        problem = minimize(sum(abs(A*w-y_train )) + λ*norm(w))
+        solve!(problem, SCSSolver(verbose=Int(verbose)))
+        w = w.value[:]
+    end
     prediction = A*w
     error = y_train - prediction