update Readme

README.md

@@ -8,3 +8,91 @@
 
 This repository is just for testing the spline implementation of compboost by providing the spline functions directly without any bloated code around it.
 
+## Installation
+
+Just install it using devtools:
+```r
+devtools::install_github("schalkdaniel/compboostSplines")
+```
+
+## How to Use
+
+This package can build spline bases for you. Ether as dense or sparse matrix. With that matrix it is possible to do e.g. spline regression or other cool stuff:
+```r
+library(compboostSpliens)
+
+nsim = 100
+
+# Sample data:
+x = sort(runif(nsim, 0, 10))
+y = 2 * sin(x) + rnorm(nsim, 0, 0.5)
+
+# Calculate knots of given x values:
+knots = createKnots(values = x, n_knots = 20, degree = 3)
+
+# Create basis using that knots:
+basis = createSplineBasis(values = x, degree = 3, knots = knots)
+basis[1:10, 1:10]
+##            [,1]     [,2]    [,3]     [,4]    [,5]     [,6] [,7] [,8] [,9] [,10]
+##  [1,] 0.1666667 0.666667 0.16667 0.000000 0.00000 0.000000    0    0    0     0
+##  [2,] 0.0508134 0.577242 0.36612 0.005825 0.00000 0.000000    0    0    0     0
+##  [3,] 0.0435305 0.559983 0.38866 0.007827 0.00000 0.000000    0    0    0     0
+##  [4,] 0.0016032 0.290810 0.62625 0.081341 0.00000 0.000000    0    0    0     0
+##  [5,] 0.0012435 0.279729 0.63221 0.086813 0.00000 0.000000    0    0    0     0
+##  [6,] 0.0002767 0.232053 0.65348 0.114195 0.00000 0.000000    0    0    0     0
+##  [7,] 0.0000000 0.016360 0.45463 0.502954 0.02606 0.000000    0    0    0     0
+##  [8,] 0.0000000 0.005581 0.36303 0.579521 0.05187 0.000000    0    0    0     0
+##  [9,] 0.0000000 0.000000 0.04624 0.566734 0.38002 0.007012    0    0    0     0
+## [10,] 0.0000000 0.000000 0.01405 0.439872 0.51657 0.029512    0    0    0     0
+
+
+
+# Check if row sums add up to 1:
+rowSums(basis)
+##  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+
+# Polynomial regression using b-splines:
+beta = solve(t(basis) %*% basis) %*% t(basis) %*% y
+
+# 20 knots may tend to overfit on the data, lets try p-splines with a penalty term of 4!
+penalty = 4
+
+# Get penalty matrix:
+K = penaltyMat(ncol(basis), differences = 2)
+K[1:6, 1:6]
+##      [,1] [,2] [,3] [,4] [,5] [,6]
+## [1,]    1   -2    1    0    0    0
+## [2,]   -2    5   -4    1    0    0
+## [3,]    1   -4    6   -4    1    0
+## [4,]    0    1   -4    6   -4    1
+## [5,]    0    0    1   -4    6   -4
+## [6,]    0    0    0    1   -4    6
+
+
+# Get new estimator:
+beta.pen = solve(t(basis) %*% basis + penalty * K) %*% t(basis) %*% y
+
+# Lets visualize the curves:
+
+library(ggplot2)
+library(ggthemes)
+
+plot.df = data.frame(
+	x = x,
+	y = y
+)
+spline.df = data.frame(
+	"Spline" = c(rep("B-Spline", nsim), rep("P-Spline", nsim)),
+	"x" = rep(x, 2),
+	"y" = c(basis %*% beta, basis %*% beta.pen)
+)
+
+ggplot() + geom_point(data = plot.df, mapping = aes(x = x, y = y)) +
+  geom_line(data = spline.df, mapping = aes(x = x, y = y, color = Spline)) +
+  theme_tufte() + 
+  scale_color_brewer(palette = "Set1")
+```
+![Spline Viz](other/spline.png?raw=true)