Purposes 1. compute basic values: area, perimeter, length of diagonal 2. compute standard deviations of the values in 1. Formulas: area = h * w perimeter = 2*h + 2*w diag_length = √( h^2 + w^2 ) Propagation of variances formula: ∑_Y = J * ∑_X * transpose_J where: X: [[h],[w]] Y: [[area],[perimeter],[diag_length]] Y = F(X) ∑_X: [[var_h, 0],[0, var_w]] J: Jacobean of Y by X J = [[∂ area / ∂ h, ∂ area / ∂ w], [∂ perimeter / ∂ h, ∂ perimeter / ∂ w], [∂ diag_length / ∂ h, ∂ diag_length / ∂ w]] J = [[w, h], [2, 2], [h/√(w^2+h^2), w/√(w^2+h^2)]] ∑_Y = J ∑_X transpose_J ∑_Y: [[var_area, _, _], [_, var_perimeter, _], [_, _, var_diag_length]] The results: (Must click `Execute` button to get them) Standard dev. of area = √( ∑_Y[0][0] ) Standard dev. of perimeter = √( ∑_Y[1][1] ) Standard dev. of diagonal_length = √( ∑_Y[2][2] )
