#!/usr/bin/env octave
% Exercise I.1.1
x = 1 : 5
printf ("x (3) + x (2) = %f\n", x (3) + x (2));

% Exercise I.1.2
x = x'

% Exercise I.2.1
A = zeros (3, 3)
A += eye (3)
A += [0 0 0; 2 0 0; 3 4 0]
B = A'
A + B
A - B
A * B  % matmul
A .* B % element-wise mul
A(1:2, 1:2)
A(1:3)
A(1:3, 1) % col
A(:, 1) % col

% Exercise I.3
function avg = mean (v)
  avg = sum (v) / numel (v);
end
mean (x)

% Exercise I.4
function price = ebill (kwh)
  l = [50 50 100 100 100 Inf];
  p = [1.484 1.533 1.786 2.242 2.503 2.587];
  for i = 1 : 6
    if (kwh > l(i))
      kwh -= l(i);
    else
      l(i) = kwh;
      kwh = 0;
    end
  end
  price = sum (l .* p);
end

% Exercise I.5.1
a = (@(x) x*x') (1 : 1000)
b = sum (arrayfun (@(x) (-1)^x / (1 + x*2), [0 : 501]))
c = sum (arrayfun (@(x) 1 / (1 + x*2)^2 / (3 + x*2)^2, [0 : 420])) - (pi^2 - 8)/16

% Exercise I.5.2
function p = permutations (n, k)
  p = factorial (n) / factorial (n - k);
end
function c = combinations (n, k)
  c = permutations (n, k) / factorial (k);
end

% Exercise I.6
log (2) / log (1.1)

% Exercise I.7
x = linspace(-5, 5);
plot (x, x + 1, 'color', 'green');