# I use the function knn.reg to evaluate the numerical solution at a fixed grid of points
#
if( !require('FNN') ){ 
    install.packages('FNN', dependencies=TRUE, repos='http://cran.rstudio.com/')
}
library(FNN)

source('vector_predictor_corrector.R')

t0 = 0.0
xy0 = c(1, 0)
t1 = 0.4

# Where do we want to evaluate the solution:
#
t_grid = c( t1 )
vector_f = function(t, x, y){
    f = rep(NA, 2)
    f[1] = x - 4*y
    f[2] = -x + y
    return(f)
}

# The vector predictor corrector method:
#
h=0.0001
res = vector_predictor_corrector(vector_f, h=h, start=t0, xy0=xy0, end=t1)
pc_xhat = knn.reg( as.matrix( res$ts ), y=res$xys[1, ], test=as.matrix( t_grid ), k=1, algorithm='brute')
pc_yhat = knn.reg( as.matrix( res$ts ), y=res$xys[2, ], test=as.matrix( t_grid ), k=1 , algorithm='brute')
print(sprintf('x_hat(%.3f)= %f; y_hat(%.3f)= %f', t1, pc_xhat$pred, t1, pc_yhat$pred))