solve polynomial with points via matrix

Schrick-Noah_Homework-5.R

@@ -12,16 +12,41 @@ x <- solve(A,b)
 x
 
 # b. Verify with matrix mult
-A%*%x == b
+all.equal(b, as.matrix(A %*% x))
 
 ## 2. Matrix from polynomial
-# a. Create vector  for x and y
+# a. Create vectors for x and y
+xvec <- c(-3,-1.5,0.5,2,5)
+yvec <- c(6.8,15.2,14.5,-21.2,10)
 
 # b. Create coefficient matrix
+A.2 <- matrix(ncol=length(xvec), nrow=length(xvec))
+for (i in 1:length(xvec)){
+  A.2[,i] = xvec^(i-1)
+}
+A.2
 
 # c. Solve 
+if (!require("matlib")) install.packages("matlib")
+library(matlib)
+
+# verify
+bvec <- solve(A.2, yvec)
+all.equal(as.matrix(yvec), A.2 %*% bvec) # use all.equal instead of == (tols and storage type)
+# EX: identical(as.double(8), as.integer(8)) returns FALSE
+
+
 
 # d. Plot
+poly_predict <- function(x){ 
+  # given input x, returns polynomial prediction 
+  sum(bvec*c(1,x,x^2,x^3,x^4))
+}
+
+xdomain <- seq(min(xvec),max(xvec),.2)    # predicted domain
+y.predict <- sapply(xdomain,poly_predict) # predicted range
+plot(xvec,yvec,ylim=c(-50,20))    # plot data
+lines(xdomain,y.predict,type="l") # overlay solid line
 
 ## 3. Kirchoff
 # a. Create vectors