---
title: "smoothPLS_multi_states_03"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{smoothPLS_multi_states_03}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup}
library(SmoothPLS)
library(pls)
```

This notebook show the Smooth PLS algorithm for a multi-states Categorical 
Functional Data (MS-CFD).

# Parameters
```{r}

N_states = 3

nind = 100 # number of individuals (train set)
start = 0 # First time
end = 100 # end time

curve_type = 'cat'

TTRatio = 0.2 # Train Test Ratio means we have floor(nind*TTRatio/(1-TTRatio))
NotS_ratio = 0.2 # noise variance over total variance for Y
beta_0_real=65.4321 # Intercept value for the link between X(t) and Y

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

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

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

# Data generation
## lambda_determination
```{r}
# Initialized the lambdas values
lambdas = lambda_determination(N_states)
lambdas
```

## tranfer_probabilities
```{r}
# Initialized the transition matrix
transition_df = transfer_probabilities(N_states)
transition_df
```


## df_cfd
```{r}
df_cfd = generate_X_df_multistates(nind = nind, N_states, start, end,
                              lambdas,  transition_df)
head(df_cfd)
```

```{r}
plot_CFD_individuals(df_cfd)
```

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

# Basis creation 
All the states will share the same basis.
```{r}
basis = create_bspline_basis(start, end, nbasis, norder)
#basis = fda::create.fourier.basis(c(start,end), nbasis = nbasis)

# All the states will share the same basis.
basis_list = obj_list_creation(N_rep = N_states, obj = basis)

plot(basis, main=paste0(nbasis, " ", basis$type," functions basis"))
```

# Data processing
We have to prepare the data before the FPLS method. For each state, we build its 
indicator function.

```{r}
names(df_cfd)
```

## cat_data_to_indicator
```{r}
df_processed = cat_data_to_indicator(df_cfd)

length(df_processed)
names(df_processed)
```

```{r}
head(df_processed$state_3, 20)
```

# beta list
```{r}
##### beta_real #####
###### beta_0_real ######
beta_0_real
```

```{r}
beta_func_list = beta_list_generation(N_states = N_states)
```


```{r}
for(i in 1:length(beta_func_list)){
  plot(0:end,  beta_func_list[[i]](0:end, end_time = end),
       ylab=paste0("Beta(t) n°=", i), type = 'l')
  title(paste0("Beta(t) n°=", i))
}
```

# Y evaluation
Y generation is based on the following equation : 
$Y = \beta_0 + \sum_{i=1}^K \int_0^T \beta_i(t) ind_i(t) dt $
with $ind_i(t) = \{0, 1\}_{t \in [0, T]}$ the indicator function of the state $i$.

We link $\beta_i$ with the $state_i$.

```{r}
Y_df = generate_Y_df(df = df_processed, curve_type = curve_type,
                     beta_real_func_or_list =  beta_func_list,
                     beta_0_real = beta_0_real,
                     NotS_ratio = NotS_ratio)
Y = Y_df$Y_noised
names(Y_df)
```

```{r}
head(Y_df)
```

# Test set

```{r df_test}
nind_test = floor(nind*TTRatio/(1-TTRatio))
df_test = generate_X_df_multistates(nind = nind_test, N_states, start, end,
                              lambdas,  transition_df)
```

```{r}
df_test_processed = cat_data_to_indicator(df_test)

Y_df_test = generate_Y_df(df_test_processed, curve_type = curve_type,
                          beta_real_func_or_list = beta_func_list,
                          beta_0_real = beta_0_real,
                          NotS_ratio= NotS_ratio)
```


# PLS functions

## Naive PLS
```{r}
naivePLS_obj = naivePLS(df_list = df_cfd, Y = Y, regul_time_obj = regul_time,
                        curve_type_obj = 'cat', 
                        id_col_obj = 'id', time_col_obj = 'time',
                        print_steps = TRUE, plot_rmsep = TRUE,
                        print_nbComp = TRUE,plot_reg_curves = TRUE)
```

## Functional PLS
```{r}
fpls_obj = funcPLS(df_list = df_cfd, Y = Y_df$Y_noised,
                   basis_obj = basis,
                   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)
```

## Smooth PLS
```{r}
spls_obj = smoothPLS(df_list = df_cfd, Y = Y_df$Y_noised, basis_obj = basis,
                     orth_obj = TRUE, curve_type_obj = 'cat',
                     int_mode = 1, 
                     id_col_obj ='id', time_col_obj = 'time',
                     print_steps = TRUE, plot_rmsep = TRUE,
                     print_nbComp = TRUE, plot_reg_curves = TRUE)
```

```{r}
names(spls_obj$reg_obj)
```

# Curves comparison
```{r}
# Warning ms_spls_obj$delta_ms_list[[1]] is the intercept!
cat("curve_1 : smooth PLS regression curve.\n")
cat("curve_2 : functional PLS regression curve.\n")
cat("curve_3 : naive PLS regression coefficients\n")

for(i in 1:N_states){
  start = 0
  print(paste0("State_", (i)))
  evaluate_curves_distances(real_f = beta_func_list[[i]],
                          regul_time = regul_time, 
                          fun_fd_list = list(spls_obj$reg_obj[[i+1]], 
                                             fpls_obj$reg_obj[[i+1]],
                                             approxfun(
                                               x = regul_time,
                                               y = naivePLS_obj$opti_reg_coef[
                                                 start:(start+length(regul_time)
                                                        )])
                                             )
                          )
  start = start + length(regul_time)
  
}


```

```{r}
for(i in 1:N_states){
  start = 0
  
  y_lim = eval_max_min_y(f_list = list(spls_obj$reg_ob[[i+1]],
                                       fpls_obj$reg_ob[[i+1]],
                                       approxfun(
                                         x = regul_time,
                                         y = naivePLS_obj$opti_reg_coef[
                                           start:(start+length(regul_time))]),
                                       beta_func_list[[i]]
                                       ), 
                         regul_time = regul_time_0)
  
  plot(regul_time_0, beta_func_list[[i]](regul_time_0), col = 'black', 
       ylim = y_lim, xlab = 'Time', ylab = 'Value', type = 'l')
  lines(regul_time_0, approxfun(x = regul_time,
                                y = naivePLS_obj$opti_reg_coef[
                                  start:(start+
                                           length(regul_time))])(regul_time_0), 
       col = 'green')
  title(paste0(names(spls_obj$reg_obj)[i+1], " regression curves"))
  plot(spls_obj$reg_obj[[i+1]], col = 'blue', add = TRUE)
  plot(fpls_obj$reg_obj[[i+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)
  
  start = start + length(regul_time)
}
```

# 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(naivePLS_obj$plsr_model, 
                ncomp = naivePLS_obj$nbCP_opti, 
                newdata = naivePLS_obj$plsr_model$model$`as.matrix(df_mod_wide)`)
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_list = df_cfd,
                               delta_list = fpls_obj$reg_obj, 
                               curve_type_obj = curve_type,
                               int_mode = int_mode,
                               regul_time_obj = regul_time)

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

# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict_list = df_cfd,
                               delta_list = spls_obj$reg_obj, 
                               curve_type_obj = curve_type,
                               int_mode = int_mode,
                               regul_time_obj = regul_time)

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

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

```

```{r}
train_results
```
## Test set 
```{r}
Y_test = Y_df_test$Y_noised

# Naive
df_test_wide = naivePLS_formatting(df_list = df_test,
                                  regul_time_obj = regul_time,
                                  curve_type_obj = curve_type, 
                                  id_col_obj = 'id', time_col_obj = 'time')

Y_hat = predict(naivePLS_obj$plsr_model,
                ncomp = naivePLS_obj$nbCP_opti, 
                newdata = as.matrix(df_test_wide))
test_results["NaivePLS", ] = evaluate_results(Y_test, Y_hat)

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

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

# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict_list = df_test,
                               delta_list = spls_obj$reg_obj,
                               curve_type_obj = curve_type,
                               int_mode = int_mode, 
                               regul_time_obj = regul_time)

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

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

```{r}
test_results
```

## Plot results
```{r}
train_results

test_results
```

```{r}
plot_model_metrics_base(train_results, test_results)
```

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