---
title: "comparison_one_state_01"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{comparison_one_state_01}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(SmoothPLS)
#library(ggplot2)
```

This vignette show the comparison for a one state Categorical Functional Data 
(CFD) between the naive PLS, Functional PLS and Smooth PLS.

# Parameters
```{r}
nind = 100 # number of individuals (train set)
start = 0 # First time
end = 100 # end time

lambda_0 = 0.2 # Exponential law parameter for state 0 
lambda_1 = 0.1 # Exponential law parameter for state 1
prob_start = 0.5 # Probability of starting with state 1

curve_type = 'cat'

TTRatio = 0.2 # Train Test Ratio means we have floor(nind*TTRatio/(1-TTRatio))
# individuals in the test set
NotS_ratio = 0.2 # noise variance over total variance for Y
beta_0_real=5.4321 # Intercept value for the link between X(t) and Y

nbasis = 10 # number of basis functions
norder = 4 # 4 for cubic splines basis

beta_real_func = beta_1_real_func # link between X(t) and Y

regul_time = seq(start, end, 5) # regularisation time sequence
regul_time_0 = seq(start, end, 1)

int_mode = 1 # in case of integration errors.
```

```{r}
plot(regul_time, beta_real_func(regul_time))
lines(regul_time, beta_real_func(regul_time))
```

# Data creation
## df & df_test
Here we create some data to work with :
```{r df}
df = generate_X_df(nind = nind, start = start, end = end, curve_type = 'cat',
                   lambda_0 = lambda_0, lambda_1 = lambda_1, 
                   prob_start = prob_start)

head(df)
```

```{r df_test}
nind_test = number_of_test_id(TTRatio = TTRatio, nind = nind)

df_test = generate_X_df(nind = nind_test, start = start, end = end, 
                        curve_type = 'cat', lambda_0 = lambda_0, lambda_1 = lambda_1,
                        prob_start = prob_start)
```

```{r}
names(df)
print(paste0("We have ", length(unique(df_test$id)), " id on test set."))
```

```{r plot df individuals}
plot_CFD_individuals(df)
```

```{r}
plot_CFD_individuals(df,by_cfda = TRUE)
```

## Y_df & Y_df_test
```{r Y_df & Y_df_test}
Y_df = generate_Y_df(df, curve_type = 'cat',
                     beta_real_func_or_list = beta_real_func, 
                     beta_0_real, NotS_ratio, id_col = 'id', time_col = 'time')

Y_df_test = generate_Y_df(df_test, curve_type = 'cat', 
                          beta_real_func_or_list =  beta_real_func, 
                          beta_0_real, NotS_ratio, 
                          id_col = 'id', time_col = 'time')
Y = Y_df$Y_noised
names(Y_df)
```

```{r hist Y noised}
oldpar <- par(mfrow=c(1, 2))
hist(Y_df$Y_real)
hist(Y_df$Y_noised)
par(oldpar)
```

## Data manipulation
The following manipulation will be required form some of the following chunks.
```{r}
length(regul_time)
```

```{r}
df_regul = regularize_time_series(df, time_seq = regul_time, 
                                  curve_type = curve_type)
df_wide = convert_to_wide_format(df_regul)

df_test_regul = regularize_time_series(df_test, time_seq = regul_time,
                                       curve_type = curve_type)
df_test_wide = convert_to_wide_format(df_test_regul)
```

# Basis creation 
```{r basis creation}
basis = create_bspline_basis(start, end, nbasis, norder)
# ORTHOGONAL
#basis = fda::create.fourier.basis(rangeval=c(start, end), nbasis=(nbasis)) 
plot(basis, main=paste0(nbasis, " Function basis")) # note cubic or Fourier
```

# Naive PLS
## Model
Here we perform the naive PLS on the data.
```{r}
naive_pls_obj = naivePLS(df_list = df, Y = Y, curve_type_obj = 'cat',
                         regul_time_obj = regul_time, 
                         id_col_obj = 'id', time_col_obj = 'time', 
                         print_steps = TRUE, plot_rmsep = TRUE,
                         print_nbComp = TRUE, plot_reg_curves = TRUE)
names(naive_pls_obj)
```
## Regression coefficients
We can plot the coefficients : 
```{r}
plot(x = regul_time, y = naive_pls_obj$opti_reg_coef, 
     xlab='regul_time', ylab='beta coefficient value', 
     main="naive pls regression coefficients")
lines(x = regul_time, y = naive_pls_obj$opti_reg_coef, col='blue')
lines(x=start:end, y=beta_real_func(start:end, end), col='red')
```
## Results
On train set : 
```{r}
Y_hat = predict(naive_pls_obj$plsr_model, 
                ncomp = naive_pls_obj$nbCP_opti, 
                newdata = as.matrix(df_wide[, -c(1)]))

cat("R^2 \n")
r_squared_values(Y, Y_hat)
r_squared_values(Y_df$Y_real, Y_hat)
cat("Press \n")
press_values(Y, Y_hat)
cat("RMSEP \n")
sqrt(press_values(Y, Y_hat)/nind)
```
On test set : 
```{r}
Y_hat_test = predict(naive_pls_obj$plsr_model,
                     ncomp = naive_pls_obj$nbCP_opti, 
                     newdata = as.matrix(df_test_wide[, -c(1)]))

cat("R^2 \n")
print(paste0("There is ", 100*NotS_ratio, "% of noised in Y"))
cat("R^2 on Y_df_test$Y_noised \n")
r_squared_values(Y_df_test$Y_noised, Y_hat_test)
cat("R^2 on Y_df_test$Y_real \n")
r_squared_values(Y_df_test$Y_real, Y_hat_test)
cat("Press \n")
press_values(Y_df_test$Y_real, Y_hat_test)
cat("RMSEP \n")
sqrt(press_values(Y_df_test$Y_real, Y_hat_test)/length(Y_hat_test))
```
# FPLS
```{r}
fpls_obj = funcPLS(df_list = list(df), Y = Y, basis_obj = basis, 
                     regul_time_obj = regul_time, curve_type_obj = 'cat',
                     plot_rmsep = TRUE, plot_reg_curves = TRUE, 
                     print_steps =TRUE)
```

```{r}
y_lim = eval_max_min_y(f_list = list(beta_real_func, 
                                     fpls_obj$reg_obj$CatFD), 
                       regul_time = regul_time_0)

plot(regul_time_0, beta_real_func(regul_time_0), type='l', xlab="Beta_t",
     ylim = c(-2, 3.5))
plot(fpls_obj$reg_obj$CatFD, add=TRUE, col='red')
legend("topleft",
         legend = c("delta_FPLS"),
         col = c("red"),
         lty = 1,
         lwd = 1)
```


## Result
```{r}
Y_hat_fpls = (predict(fpls_obj$plsr_model, ncomp = fpls_obj$nbCP_opti,
                newdata = fpls_obj$trans_alphas) 
              + fpls_obj$reg_obj$Intercept
              + mean(Y))

sqrt(press_values(Y_df$Y_real, Y_hat_fpls)/length(Y_hat_fpls))
sqrt(press_values(Y_df$Y_noised, Y_hat_fpls)/length(Y_hat_fpls))

cat("NotS_ratio \n")
print(paste0("There is ", 100*NotS_ratio, "% of noise in Y"))
cat("R^2 on Y_df_test$Y_noised \n")
r_squared_values(Y_df$Y_noised, Y_hat_fpls)
cat("R^2 on Y_df_test$Y_real \n")
r_squared_values(Y_df$Y_real, Y_hat_fpls)
```

```{r}
Y_hat_fpls_test = smoothPLS_predict(df_predict = df_test, 
                                    delta_list = fpls_obj$reg_obj,
                                    curve_type = curve_type,
                                    regul_time_obj = regul_time) 

sqrt(press_values(Y_df_test$Y_real, Y_hat_fpls_test)/length(Y_hat_fpls_test))
sqrt(press_values(Y_df_test$Y_noised, Y_hat_fpls_test)/length(Y_hat_fpls_test))

cat("R^2 \n")
print(paste0("There is ", 100*NotS_ratio, "% of noise in Y"))
cat("R^2 on Y_df_test$Y_noised \n")
r_squared_values(Y_df_test$Y_noised, Y_hat_fpls_test)
cat("R^2 on Y_df_test$Y_real \n")
r_squared_values(Y_df_test$Y_real, Y_hat_fpls_test)
```
# Smooth PLS
```{r}
spls_obj = smoothPLS(df_list = df, Y = Y, basis_obj = basis,
                     curve_type_obj = 'cat', orth_obj = TRUE, int_mode = 1,
                     print_steps = TRUE, print_nbComp = TRUE, 
                     plot_rmsep = TRUE, plot_reg_curves = TRUE,
                     id_col_obj = 'id',time_col_obj = 'time',
                     jackknife = TRUE, validation = 'LOO',
                     parallel=FALSE)
```
## delta
Delta Smooth_PLS
```{r}
delta_0 = spls_obj$reg_obj$Intercept
delta_0

delta = spls_obj$reg_obj$CatFD_1_state_1
plot(delta)
```

```{r}
y_lim = eval_max_min_y(f_list = list(beta_real_func, 
                                     delta), 
                       regul_time = regul_time_0)

plot(regul_time_0, beta_real_func(regul_time_0), type='l', xlab="Beta_t",
     ylim = c(-2, 3.5))
plot(delta, add=TRUE, col='blue')
legend("topleft",
         legend = c("delta_SmoothPLS"),
         col = c("blue"),
         lty = 1,
         lwd = 1)
```


## Results
```{r}
#delta_0_spls
Y_hat_spls = smoothPLS_predict(df_predict = df, 
                               delta_list = list(delta_0, delta), 
                               curve_type = 'cat', regul_time_obj = regul_time,
                               int_mode = int_mode)


sqrt(press_values(Y_df$Y_real, Y_hat_spls)/length(Y_hat_spls))
sqrt(press_values(Y_df$Y_noised, Y_hat_spls)/length(Y_hat_spls))

cat("R^2 \n")
print(paste0("There is ", 100*NotS_ratio, "% of noise in Y"))
cat("R^2 on Y_df_test$Y_noised \n")
r_squared_values(Y_df$Y_noised, Y_hat_spls)
cat("R^2 on Y_df_test$Y_real \n")
r_squared_values(Y_df$Y_real, Y_hat_spls)
```

```{r}
Y_hat_spls_test = smoothPLS_predict(df_predict = df_test,
                                    delta_list = list(delta_0, delta),
                                    curve_type = curve_type,
                                    regul_time_obj = regul_time,
                                    int_mode = int_mode)


sqrt(press_values(Y_df_test$Y_real, Y_hat_spls)/length(Y_hat_spls_test))
sqrt(press_values(Y_df_test$Y_noised, Y_hat_spls)/length(Y_hat_spls_test))

cat("R^2 \n")
print(paste0("There is ", 100*NotS_ratio, "% of noise in Y"))
cat("R^2 on Y_df_test$Y_noised \n")
r_squared_values(Y_df_test$Y_noised, Y_hat_spls_test)
cat("R^2 on Y_df_test$Y_real \n")
r_squared_values(Y_df_test$Y_real, Y_hat_spls_test)
```

# Curve comparison
```{r}
cat("curve_1 : smooth PLS regression curve.\n")
cat("curve_2 : functional PLS regression curve.\n")
cat("curve_3 : naive PLS regression coefficients\n")

evaluate_curves_distances(real_f = beta_real_func,
                          regul_time = regul_time, 
                          fun_fd_list = list(
                            delta, 
                            fpls_obj$reg_obj$CatFD,
                            approxfun(x = regul_time,
                                      y = naive_pls_obj$opti_reg_coef)
                            )
                          )
```

```{r}
y_lim = eval_max_min_y(f_list = list(spls_obj$reg_obj$CatFD_1_state_1,
                                     fpls_obj$reg_obj$CatFD_1_state_1,
                                     approxfun(x = regul_time,
                                               y = naive_pls_obj$opti_reg_coef),
                                     beta_real_func ), 
                         regul_time = regul_time_0)
  
plot(regul_time_0, beta_real_func(regul_time_0), col = 'black', 
     ylim = y_lim, xlab = 'Time', ylab = 'Value', type = 'l')
lines(regul_time_0, approxfun(x = regul_time, 
                              y = naive_pls_obj$opti_reg_coef)(regul_time_0), 
      col = 'green')
title(paste0(names(spls_obj$reg_obj)[2], " regression curves"))
plot(spls_obj$reg_obj$CatFD_1_state_1, col = 'blue', add = TRUE)
plot(fpls_obj$reg_obj$CatFD_1_state_1, col = 'red', add = TRUE)
legend("topleft",
       legend = c("Real curve", "NaivePLS coef", 
                  "SmoothPLS reg curve", "FunctionalPLS reg curve"),
       col = c("black", "green", "blue", "red"),
       lty = 1,
       lwd = 1)
```

```{r}
y_lim = eval_max_min_y(f_list = list(spls_obj$reg_obj$CatFD_1_state_1,
                                     fpls_obj$reg_obj$CatFD_1_state_1,
                                     beta_real_func ), 
                         regul_time = regul_time_0)

plot(regul_time_0, beta_real_func(regul_time_0), type='l', ylab="Values",
     xlab = 'Time', ylim = y_lim, col = 'black')
title(paste0(names(spls_obj$reg_obj)[2], " regression curves"))
plot(spls_obj$reg_obj$CatFD_1_state_1, add=TRUE, col='blue')
plot(fpls_obj$reg_obj$CatFD_1_state_1, add=TRUE, col='red')
legend("topleft",
         legend = c("Real curve", "SmoothPLS", "FuncPLS"),
         col = c("black", "blue", "red"),
         lty = 1,
         lwd = 1)
```

Plot the second derivatives for the smoothness :
```{r}
plot(fda::deriv.fd(expr = delta, Lfdobj = 2), col='blue')
plot(fda::deriv.fd(expr = fpls_obj$reg_obj$CatFD, Lfdobj = 2),
     add=TRUE, col='red')
title("Second derivatives")
legend("bottomleft",
         legend = c("delta_SmoothPLS''", "delta_FPLS''"),
         col = c("blue", "red"),
         lty = 1,
         lwd = 1)
```

# Results
```{r}
train_results = data.frame(matrix(ncol = 5, nrow = 3))
colnames(train_results) = c("PRESS", "RMSE", "MAE", "R2", "var_Y")
rownames(train_results) = c("NaivePLS", "FPLS", "SmoothPLS")

test_results = train_results
```

```{r}
print(paste0("There is ", 100*NotS_ratio, "% of noised in Y"))
```

## Train set
```{r}

Y_train = Y_df$Y_noised

# Naive
Y_hat = predict(naive_pls_obj$plsr_model, 
                ncomp = naive_pls_obj$nbCP_opti, 
                newdata = as.matrix(df_wide[, -c(1)]))
train_results["NaivePLS", ] = evaluate_results(Y_train, Y_hat)


# FPLS
Y_hat_fpls = (predict(fpls_obj$plsr_model, ncomp = fpls_obj$nbCP_opti,
                newdata = fpls_obj$trans_alphas) 
              + fpls_obj$reg_obj$Intercept
              + mean(Y))

Y_hat_fpls = smoothPLS_predict(df_predict = df,
                               delta_list = fpls_obj$reg_obj,
                               curve_type = curve_type,
                               regul_time_obj = regul_time, 
                               int_mode = int_mode) 

train_results["FPLS", ] = evaluate_results(Y_train, Y_hat_fpls)

# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict = df, 
                               delta_list = list(delta_0, delta), 
                               curve_type = 'cat',
                               regul_time_obj = regul_time, 
                               int_mode = int_mode)

train_results["SmoothPLS", ] = evaluate_results(Y_train, Y_hat_spls)

train_results["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
train_results["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
train_results["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti

```

```{r}
train_results
```

```{r}
oldpar <- par(mfrow=c(1,2))
hist(Y_train - Y_hat_fpls)
hist(Y_train - Y_hat_spls)
par(oldpar)
```


## Test set
```{r}

Y_test = Y_df_test$Y_noised

# Naive
Y_hat = naivePLS_predict(naive_pls_obj = naive_pls_obj,
                         df_predict_list = df_test,
                         regul_time_obj = regul_time,
                         curve_type_obj = 'cat')
test_results["NaivePLS", ] = evaluate_results(Y_test, Y_hat)

# FPLS
Y_hat_fpls = smoothPLS_predict(df_predict = df_test,
                               delta_list = fpls_obj$reg_obj,
                               curve_type = curve_type,
                               regul_time_obj = regul_time, 
                               int_mode = int_mode) 

test_results["FPLS", ] = evaluate_results(Y_test, Y_hat_fpls)

# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict = df_test,
                               delta_list = list(delta_0, delta),
                               curve_type = curve_type,
                               regul_time_obj = regul_time, 
                               int_mode = int_mode)

test_results["SmoothPLS", ] = evaluate_results(Y_test, Y_hat_spls)

test_results["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
test_results["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
test_results["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti
```

```{r}
Y_hat_naivePLS = naivePLS_predict(naive_pls_obj = naive_pls_obj,
                                  df_predict_list = df_test,
                                  regul_time_obj = regul_time,
                                  curve_type_obj = 'cat')
```

```{r}
test_results
```

```{r}
oldpar <- par(mfrow=c(1,2))
hist(Y_test - Y_hat_fpls)
hist(Y_test - Y_hat_spls)
par(oldpar)
```

## Results plots
### All
```{r}
plot_model_metrics_base(train_results, test_results)
```

### FPLS & SmoothPLS
```{r}
plot_model_metrics_base(train_results, test_results,
                        models_to_plot = c('FPLS', 'SmoothPLS'))
```


# Fourier basis test
```{r basis creation Fourier}
basis_f = fda::create.fourier.basis(rangeval=c(start, end), nbasis=(nbasis)) 
plot(basis_f, main=paste0(nbasis, " Function basis")) # note cubic or Fourier
```

## FPLS
```{r}
fpls_obj_2 = funcPLS(df_list = df, Y = Y, basis_obj = basis_f,
                     regul_time_obj = regul_time, curve_type_obj = curve_type,
                     print_steps = TRUE, plot_rmsep = TRUE, 
                     print_nbComp = TRUE, plot_reg_curves = TRUE)
```

## Smooth PLS 
```{r}
spls_obj_2 = smoothPLS(df_list = df, Y = Y, basis_obj = basis_f,
                       orth_obj = FALSE, curve_type_obj = curve_type,
                       print_steps = TRUE, plot_rmsep = TRUE, 
                       print_nbComp = TRUE, plot_reg_curves = TRUE)
```

```{r}
delta_0_2 = spls_obj_2$reg_obj$Intercept

delta_2 = spls_obj_2$reg_obj$CatFD_1_state_1
plot(delta_2)
```

## Curve comparison
```{r}
plot(regul_time_0, beta_real_func(regul_time_0), type='l', xlab="Beta_t",
     ylim = c(-2, 3.5))
plot(delta_2, add=TRUE, col='blue')
plot(fpls_obj_2$reg_obj$CatFD, add=TRUE, col='red')
legend("topleft",
         legend = c("delta_SmoothPLS", "delta_FPLS"),
         col = c("blue", "red"),
         lty = 1,
         lwd = 1)
```

```{r}
evaluate_curves_distances(real_f = beta_real_func,
                          regul_time = regul_time, 
                          fun_fd_list = list(delta_2, 
                                             fpls_obj_2$reg_obj$CatFD))
```

```{r}
cat("curve_1 : smooth PLS regression curve.\n")
cat("curve_2 : functional PLS regression curve.\n")
cat("curve_3 : naive PLS regression coefficients\n")

evaluate_curves_distances(real_f = beta_real_func,
                          regul_time = regul_time, 
                          fun_fd_list = list(
                            spls_obj_2$reg_obj$CatFD_1_state_1, 
                            fpls_obj_2$reg_obj$CatFD_1_state_1,
                            approxfun(x = regul_time,
                                      y = naive_pls_obj$opti_reg_coef)
                            )
                          )
```

```{r}
y_lim = eval_max_min_y(f_list = list(spls_obj_2$reg_obj$CatFD_1_state_1,
                                     fpls_obj_2$reg_obj$CatFD_1_state_1,
                                     approxfun(x = regul_time,
                                               y = naive_pls_obj$opti_reg_coef),
                                     beta_real_func ), 
                         regul_time = regul_time_0)
  
plot(regul_time_0, beta_real_func(regul_time_0), col = 'black', 
     ylim = y_lim, xlab = 'Time', ylab = 'Value', type = 'l')
lines(regul_time_0, approxfun(x = regul_time, 
                              y = naive_pls_obj$opti_reg_coef)(regul_time_0), 
      col = 'green')
title(paste0(names(spls_obj_2$reg_obj)[2], " regression curves"))
plot(spls_obj_2$reg_obj$CatFD_1_state_1, col = 'blue', add = TRUE)
plot(fpls_obj_2$reg_obj$CatFD_1_state_1, col = 'red', add = TRUE)
legend("topleft",
       legend = c("Real curve", "NaivePLS coef", 
                  "SmoothPLS reg curve", "FunctionalPLS reg curve"),
       col = c("black", "green", "blue", "red"),
       lty = 1,
       lwd = 1)
```

```{r}
y_lim = eval_max_min_y(f_list = list(spls_obj_2$reg_obj$CatFD_1_state_1,
                                     fpls_obj_2$reg_obj$CatFD_1_state_1,
                                     beta_real_func), 
                         regul_time = regul_time_0)

plot(regul_time_0, beta_real_func(regul_time_0), type='l', ylab="Values",
     xlab = 'Time', ylim = y_lim, col = 'black')
title(paste0(names(spls_obj_2$reg_obj)[2], " regression curves"))
plot(spls_obj_2$reg_obj$CatFD_1_state_1, add=TRUE, col='blue')
plot(fpls_obj_2$reg_obj$CatFD_1_state_1, add=TRUE, col='red')
legend("topleft",
         legend = c("Real curve", "SmoothPLS", "FuncPLS"),
         col = c("black", "blue", "red"),
         lty = 1,
         lwd = 1)
```

# Results
```{r}
train_results_f = data.frame(matrix(ncol = 5, nrow = 3))
colnames(train_results_f) = c("PRESS", "RMSE", "MAE", "R2", "var_Y")
rownames(train_results_f) = c("NaivePLS", "FPLS", "SmoothPLS")

test_results_f = train_results_f
```

```{r}
print(paste0("There is ", 100*NotS_ratio, "% of noised in Y"))
```

## Train set
```{r}

Y_train = Y_df$Y_noised

# Naive
Y_hat = predict(naive_pls_obj$plsr_model, 
                ncomp = naive_pls_obj$nbCP_opti, 
                newdata = as.matrix(df_wide[, -c(1)]))
train_results_f["NaivePLS", ] = evaluate_results(Y_train, Y_hat)


# FPLS
Y_hat_fpls = (predict(fpls_obj_2$plsr_model, ncomp = fpls_obj_2$nbCP_opti,
                newdata = fpls_obj_2$trans_alphas) 
              + fpls_obj_2$reg_obj$Intercept
              + mean(Y))

train_results_f["FPLS", ] = evaluate_results(Y_train, Y_hat_fpls)

# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict_list = df, 
                               delta_list = list(delta_0_2, delta_2), 
                               curve_type = 'cat',
                               int_mode = int_mode)

train_results_f["SmoothPLS", ] = evaluate_results(Y_train, Y_hat_spls)

train_results_f["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
train_results_f["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
train_results_f["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti

```

```{r}
train_results_f
```

## Test set
```{r}

Y_test = Y_df_test$Y_noised

# Naive
Y_hat = predict(naive_pls_obj$plsr_model,
                ncomp = naive_pls_obj$nbCP_opti, 
                newdata = as.matrix(df_test_wide[, -c(1)]))
test_results_f["NaivePLS", ] = evaluate_results(Y_test, Y_hat)

# FPLS
Y_hat_fpls = smoothPLS_predict(df_predict = df_test,
                               delta_list = fpls_obj_2$reg_obj,
                               curve_type = curve_type) 

test_results_f["FPLS", ] = evaluate_results(Y_test, Y_hat_fpls)

# Smooth PLS
Y_hat_spls_f = smoothPLS_predict(df_predict = df_test,
                               delta_list = list(delta_0_2, delta_2),
                               curve_type = curve_type,
                               int_mode = int_mode)

test_results_f["SmoothPLS", ] = evaluate_results(Y_test, Y_hat_spls_f)

test_results_f["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
test_results_f["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
test_results_f["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti
```

```{r}
test_results_f
```
## Plot Fourier Results
```{r}
plot_model_metrics_base(train_results_f, test_results_f)
```

```{r}
plot_model_metrics_base(train_results_f, test_results_f,
                        models_to_plot = c('FPLS', 'SmoothPLS'))
```