#   Nested loops

n = 10
for (i in 1:n){                 # control statement for the outer loop
    cat("count to ", i, "\n")   # indent the statements of the outer loop 4 spaces
    for ( j in 1:i){            # control statement for the inner loop
         cat("  ", j)           # indent 4 more spaces for the inner loop
                                # no "\n" here so all these are on the same line.
      }                         # curley to end the inner loop, indented 4+2 spaces
    cat(" -- done!\n")          # statement in the body of the outer loop, indent 4
  }                             # close of the outer loop, indent 2
   

#   Create A, a specific 3 X 3 matrix

c1 = c(1, 2, 3)      # column 1
c2 = c(1, 1, 1)      # column 2
c3 = c(0, 1, 1)      # column 3

A = matrix( cbind( c1, c2, c3), nrow=3, ncol=3)

cat("\n Print A, row by row\n\n")

cat("Row 1 of A is ", A[1,1:3], "\n")
cat("Row 2 of A is ", A[2,1:3], "\n")
cat("Row 3 of A is ", A[3,1:3], "\n")




#        Create D, a diagonal n X n matrix with D[i,i] = i

n = 3                       # the size of the matrix

d_list = 1:(n^2)            # create a list of n^2 numbers, which will be the matrix entries
D      = matrix(d_list, n)  # re-arrange these numbers into an n X n matrix
                            # other languages (Matlab, Python) have easier ways to do this.

cat("\n Print D, row by row\n\n")

cat("Row 1 of D is ", D[1,1:3], "\n")
cat("Row 2 of D is ", D[2,1:3], "\n")
cat("Row 3 of D is ", D[3,1:3], "\n")

#   Zero out the entries of D, use a nested loop (also called double loop)

for ( i in 1:n){      #  start of the outer loop
    for ( j in 1:n){  #  start of the inner loop
        D[i,j] = 0
      }               #  end of the inner loop
  }                   #  end of the outer loop

cat("\n Print D, row by row\n\n")

cat("Row 1 of D is ", D[1,1:3], "\n")
cat("Row 2 of D is ", D[2,1:3], "\n")
cat("Row 3 of D is ", D[3,1:3], "\n")

#    Set the diagonal entries of D

for ( i in 1:n){
    D[i,i] = i
  }

cat("\n Print D, row by row\n\n")

cat("Row 1 of D is ", D[1,1:3], "\n")
cat("Row 2 of D is ", D[2,1:3], "\n")
cat("Row 3 of D is ", D[3,1:3], "\n")

x = c(4, 5, 6)

y = D %*% x

cat("\n y is",y, "\n")

for ( i in 1:n){
    sum = 0
    for ( j in 1:n){
        sum = sum + A[i,j]*x[j]
      }
    y[i] = sum
  }

cat("\n y is",y, "\n")