# 1 a and b
errs = zeros(56)
errs2 = zeros(56)
lambda = [0 2.0^-1 2^0 2^1 2^2 2^3 2^4]
for i in 1:size(combs)[1]
    two = setdiff(collect(1:8), combs[i,:][1])
    testX = reshape(sets[combs[i,:][1],:,:], (6*16,9))
    testy = reshape(ys[combs[i,:][1],:], (6*16,1))

    y1 = ys[two[1],:]
    y2 = ys[two[2],:]

    #1 a
    U, S, V = svd(testX)
    diagS = Diagonal(S)
    err1 = zeros(9)
    w = zeros(9,9)
    err2 = zeros(9)
    for k in 1:9
        kS = copy(S)
        kS = kS.^-1
        kS = Diagonal(kS)
        for j in k:8
            kS[j+1,j+1] = 0
        end
        w[k,:] = V*kS*U'*testy
        #println(w[k,:])

        # predict
        preds1 = sets[two[1],:,:]*w[k,:]
        #println(sign(preds1))
        preds2 = sets[two[2],:,:]*w[k,:]

        # find errors
        err1[k] = error(preds1, y1)
        err2[k] = error(preds2, y2)
        #println("err1: $(err1[k]), err2: $(err2[k])")
    end
    minidx1 = indmin(err1)
    minidx2 = indmin(err2)
    #print(minidx1)
    #println(err1)

    preds1 = sets[two[2],:,:]*w[minidx1,:]
    preds2 = sets[two[1],:,:]*w[minidx2,:]

    errs[2*i-1] = error(preds1, y2)
    errs[2*i] = error(preds2, y1)
    #println("err1: $(errs[2*i-1]), err2: $(errs[2*i])")


    #1b

    err1 = zeros(length(lambda))
    w = zeros(length(lambda),9)
    err2 = zeros(length(lambda))
    for l in 1:length(lambda)
        w[l,:] = (V*diagS^2*V' + lambda[l]*eye(9, 9))^-1*V*diagS*U'*testy

        # predict
        preds1 = sets[two[1],:,:]*w[l,:]
        #println(sign(preds1))
        preds2 = sets[two[2],:,:]*w[l,:]

        # find errors
        err1[l] = error(preds1, y1)
        err2[l] = error(preds2, y2)
    end

    minidx1 = indmin(err1)
    minidx2 = indmin(err2)
    #print(minidx1)
    #println(err1)

    preds1 = sets[two[2],:,:]*w[minidx1,:]
    preds2 = sets[two[1],:,:]*w[minidx2,:]

    errs2[2*i-1] = error(preds1, y2)
    errs2[2*i] = error(preds2, y1)

end
avgErr = sum(errs)/56.0
avgErr2 = sum(errs2)/56.0
println("Average error 1a: $(avgErr)")
println("Average error 1b: $(avgErr2)")