added chp 1

chapter_1.R

@@ -0,0 +1,45 @@
+# CHAPTER 1
+
+# Figure 1.1
+p <- 1/2
+n <- seq(0, 9)
+# In Python, the np.arange(start, stop) function will not include
+# the end of the interval. Thus, seq is (0,9).
+X <- `^`(p,n)
+barplot(X)
+
+# Binomial Theorem
+n <- 10
+k <- 2
+choose(n,k)
+factorial(k)
+
+# R code to perform an inner product
+x <- c(1,0,-1)
+y <- c(3,2,0)
+z <- t(x) %*% y
+print(z)
+
+# R code to compute the norm
+x <- c(1,0,-1)
+x_norm <- norm(x, type = "2")
+# "2" specifies the “spectral” or 2-norm, which is the largest singular value of x
+print(x_norm)
+
+# R code to compute the weighted norm
+W <- matrix(1:9, ncol = 3, nrow = 3)
+x <- matrix(c(2,-1,1))
+z <- t(x) %*% (W %*% x)
+print(z)
+
+# R code to compute a matrix inverse
+X <- matrix(c(1,-2,0,3,7,1), nrow = 3, ncol = 2)
+XtX <- t(X) %*% X
+Xtxinv <- solve(XtX)
+print(Xtxinv)
+
+# R code to solve X beta = y
+X <- matrix(c(1,-2,0,3,7,1), nrow = 3, ncol = 2)
+y <- matrix(c(2,1,0))
+beta <- solve(qr(X), y)
+print(beta)