"""
function rmse, ypred = calculateRMSE(X, y, beta)

Regner ut RMSE for lineær regresjonsmodell med eller uten konstantledd.
(Konstantledd må være første element i beta hvis med)    
"""

function calculateRMSE(X, y, beta)

if length(beta) == size(X,2)
    ypred = X * beta;
elseif length(beta) == (size(X,2) +  1)
    ypred = beta[1] .+ X * beta[2:end]
end

rmsep = sqrt(mean(y - ypred).^2)

return rmse, ypred
end




"""
    function oldRegCoeffs(X, y, cvfolds, ncomps, regFunction=PLS)

Calculates "old" regression coefficients using CV and the 1 S.E. rule.
regFunction = PLS or PCR
"""
function oldRegCoeffs(X, y, cvfolds, ncomps, regFunction=PLS)
    cverror = zeros(ncomps,1);

    # Iterating through each cv segment
    for i=1:length(unique(cvfolds))
        Xtrain = X[vec(i .!= cvfolds), :];
        ytrain = y[vec(i .!= cvfolds), :];
        Xtest  = X[vec(i .== cvfolds), :];
        ytest  = y[vec(i .== cvfolds), :];

        betas, _ = regFunction(Xtrain, ytrain, ncomps)
        cverror += sum((ytest .- Xtest*betas[2:end,:] .- betas[1,:]').^2, dims=1)';
    end

    # Select components using 1 S.E. rule
    cverror       = cverror ./ size(X,1);
    regCoeffsInds = findfirst(cverror .< (minimum(cverror) + std(cverror)/sqrt(length(unique(cvfolds)))))[1]
    
    # Find model for whole dataset with selected number of components
    betas, _ = regFunction(X, y, ncomps)
    bold = betas[:, regCoeffsInds]
    
    return bold, regCoeffsInds, cverror
end

"""
    function PCR(X, y, kmax)

Principal Component Regression (PCR).
B, \\_ = PCR(X, y, 10);
"""
function PCR(X, y, kmax)

stdX = std(X, dims=1);
mX   = mean(X, dims=1);
my   = mean(y, dims=1);
y    = y .- my;

if centre
    X = X .- mX;
end

#if standardize
#    X = X ./ stdX;
#end

U, s, V = svd(X, full=false);

q  = s[1:kmax].^(-1) .*(U[:,1:kmax]'y);
B  = cumsum(V[:,1:kmax] .* q', dims=2);
    
if centre
    b0 = my .- mX * B
    B  = [b0; B];
end
        
return B, U, s, V
end





"""
    PLS(X, y, A)
    
Julia version of the bidiag2 MATLAB function in Björck and Indahl (2017)
    
### Arguments
    - 'X' - Data matrix of predictors
    - 'y' - Vector of responses
    - 'A' - Number of components

### Returns:
    - beta    - Matrix with regression coefficients (including constant term if centre==true)
    - W, B, T - Matrices such that X \approx T*B*W'.
"""
function PLS(X, y, A, centre=true)

n, p = size(X);

w    = zeros(p, 1);
W    = zeros(p, A);
t    = zeros(n, 1);
T    = zeros(n, A);
P    = zeros(p, A);
beta = zeros(p, A);
B    = zeros(A,2);

mX   = mean(X, dims=1);
my   = mean(y, dims=1);
y    = y .- my;

if centre
    X = X .- mX;
end

w      = X'y;
w      = w / norm(w);
W[:,1] = w;
t      = X*w;
rho    = norm(t);
t      = t / rho;
T[:,1] = t;

B[1,1]    = rho;
d         = w / rho;
beta[:,1] = (t'y) .* d;

for a in 2:A
    w         = X'*t - rho * w;
    w         = w - W*(W'*w);
    theta     = norm(w);
    w         = w / theta;
    W[:,a]    = w;
    t         = X * w - theta * t;
    t         = t - T*(T'*t);
    rho       = norm(t);
    t         = t / rho;
    T[:,a]    = t;
    B[a-1, 2] = theta;
    B[a, 1]   = rho;
    d         = (w - theta*d) / rho;
    beta[:,a] = beta[:,a-1] + (t'y) .* d;
end
    
if centre
    b0 = my .- mX * beta
    beta  = [b0; beta];
end

B = Bidiagonal(B[:,1], B[1:end-1,2], :U);
  
returnvals = beta, W, B, T
return returnvals
end