Finished exercise 4.

Made all matrices have delimiters `[]`.

Co-authored-by: Ricardo-Rodrigues <R1cardu7@users.noreply.github.com>

code/4-matrix.R

@@ -30,4 +30,6 @@ while (steps < 100) {
 
 cat(sprintf("Took %d steps\n", steps))
 cat(sprintf("Final matrix:\n"))
+step_matrix <- apply(step_matrix, 1, function(cell) round(cell, 4))
 print(step_matrix)
+write.table(step_matrix, "output/4-matrix.csv", sep = "\t", col.names = FALSE, row.names = FALSE)

code/4-sim.R

@@ -25,8 +25,7 @@ for (round_idx in 1:rounds) {
   cur_state <- next_state
 }
 
-for (state in 1:3) {
-  state_count <- length(states[states == state])
-  state_prob <- state_count / rounds
-  cat(sprintf("State %d prob: %f\n", state, state_prob))
-}
+probs <- sapply(1:3, function(state) length(states[states == state]) / length(states))
+probs <- sapply(probs, function(x) round(x, 4))
+print(probs)
+write.table(probs, "output/4-sim.csv", sep = "\t", col.names = FALSE, row.names = FALSE)

code/4-solve.R

@@ -11,16 +11,7 @@ prob_matrix <- matrix(
 )
 
 # Build the coefficient matrix and constants
-coef_matrix <- matrix(
-  c(
-    c(-prob_matrix[1, 2] - prob_matrix[1, 3], prob_matrix[2, 1], prob_matrix[3, 1]),
-    c(prob_matrix[1, 2], -prob_matrix[2, 1] - prob_matrix[2, 3], prob_matrix[3, 2]),
-    c(prob_matrix[1, 3], prob_matrix[2, 3], -prob_matrix[3, 1] - prob_matrix[3, 2])
-  ),
-  nrow = 3,
-  ncol = 3,
-  byrow = TRUE
-)
+coef_matrix <- t(prob_matrix) - diag(rowSums(prob_matrix))
 consts <- c(0, 0, 0)
 
 # Substitute one of the rows by the final `pi0 + pi1 + pi2 = 1` equation.
@@ -29,4 +20,6 @@ coef_matrix[subst_idx, ] <- c(1, 1, 1)
 consts[subst_idx] <- 1
 
 solution <- solve(coef_matrix, consts)
+solution <- sapply(solution, function(x) round(x, 4))
 print(solution)
+write.table(solution, "output/4-solve.csv", sep = "\t", col.names = FALSE, row.names = FALSE)