plotDecisionBoundary <- function (theta, X, y) {
  
  #   Plots the data points X and y into a new figure with
  #   the decision boundary defined by theta
  #
  #   plotDecisionBoundary(theta, X,y) plots the data points with + for the
  #   positive examples and o for the negative examples. X is assumed to be
  #   a either
  #   1) Mx3 matrix, where the first column is an all-ones column for the
  #      intercept.
  #   2) MxN, N>3 matrix, where the first column is all-ones

  plot(X[,2:3], xlab = "", ylab = "",
       col = ifelse(y == 1, "gold", "black"),
       pch = ifelse(y == 1, 3, 1))

  if(ncol(X) <= 3){
    # Only need 2 points to define a line, so choose two endpoints
    plot_x = c(min(X[,2])-2,  max(X[,2]+2))
    # Calculate the decision boundary line
    plot_y = (-1/theta[3])*(theta[2]*plot_x + theta[1])
    # Plot boundary
    lines(plot_x, plot_y, col = "red")
    # Axes & legend, specific for the exercise
    title(xlab = "Biomarker 1", ylab = "Biomarker 2")
    legend("topright", c("Malaria", "No"),
           col = c("gold", "black"),
           pch = c(3, 1))
  } else {
    # Here is the grid range
    u <- v <- seq(-1, 1.5, 0.05)
    z <- matrix(0, nrow = length(u), ncol = length(v))
    for (i in 1:length(u)){
      for (j in 1:length(v)){
        z[i,j] <- mapFeature(u[i], v[j])%*%theta
      }
    }
    contour(u, v, z, levels = 0, lwd = 2,
            add = TRUE, drawlabels = FALSE, col = "green")

    # Axis and legend, specific for the exercise
    title(main = paste("lambda = ",lambda),
          xlab = "Test 1", ylab = "Test 2")
    legend("topright", c("Affected", "No"),
           col = c("gold", "black"),
           pch = c(3, 1))
  }
}