diff --git a/scripts/symbolic_calculations.jl b/scripts/symbolic_calculations.jl index 2b98fc48c18145c24f8c96e16dad58aadc71cc1f..a4cc08f498a877598111da90e83ea65f3c6ee8b2 100644 --- a/scripts/symbolic_calculations.jl +++ b/scripts/symbolic_calculations.jl @@ -17,3 +17,21 @@ function l1triangle() return result end + +function norm_grad() + function ref_int(f) + inty_f = Algebra.int(f, :y, 0, :(1 - x)) + return Algebra.int(inty_f, :x, 0, 1) + end + + # \|f\| + f = :(a * x + b * y + c * (1 - x - y)) + n2_f = ref_int(:(($f)^2)) + + # \|grad f\| + dx_f = Algebra.df(f, :x) + dy_f = Algebra.df(f, :y) + n2_gradf = ref_int(:(($dx_f)^2 + ($dy_f)^2)) + + return :($n2_gradf / $n2_f) +end