module Tests exposing (tests) import ComplexNumbers as Complex exposing (Complex) import Expect exposing (Expectation, FloatingPointTolerance(..)) import Test exposing (Test, describe, skip, test) tolerance : FloatingPointTolerance tolerance = Absolute 0.00001 approximatelyEqual : Complex -> Complex -> Expectation approximatelyEqual z1 z2 = Complex.sub z1 z2 |> Expect.all [ Complex.real >> Expect.within tolerance 0 , Complex.imaginary >> Expect.within tolerance 0 ] tests : Test tests = describe "ComplexNumbers" [ describe "Real part" [ test "Real part of a purely real number" <| \() -> Complex.real (Complex.fromPair ( 1, 0 )) |> Expect.within tolerance 1 , skip <| test "Real part of a purely imaginary number" <| \() -> Complex.real (Complex.fromPair ( 0, 1 )) |> Expect.within tolerance 0 , skip <| test "Real part of a number with real and imaginary part" <| \() -> Complex.real (Complex.fromPair ( 1, 2 )) |> Expect.within tolerance 1 ] , describe "Imaginary part" [ skip <| test "Imaginary part of a purely real number" <| \() -> Complex.imaginary (Complex.fromPair ( 1, 0 )) |> Expect.within tolerance 0 , skip <| test "Imaginary part of a purely imaginary number" <| \() -> Complex.imaginary (Complex.fromPair ( 0, 1 )) |> Expect.within tolerance 1 , skip <| test "Imaginary part of a number with real and imaginary part" <| \() -> Complex.imaginary (Complex.fromPair ( 1, 2 )) |> Expect.within tolerance 2 ] , skip <| test "Imaginary unit" <| \() -> Complex.mul (Complex.fromPair ( 0, 1 )) (Complex.fromPair ( 0, 1 )) |> approximatelyEqual (Complex.fromPair ( -1, 0 )) , describe "Arithmetic" [ describe "Addition" [ skip <| test "Add purely real numbers" <| \() -> Complex.add (Complex.fromPair ( 1, 0 )) (Complex.fromPair ( 2, 0 )) |> approximatelyEqual (Complex.fromPair ( 3, 0 )) , skip <| test "Add purely imaginary numbers" <| \() -> Complex.add (Complex.fromPair ( 0, 1 )) (Complex.fromPair ( 0, 2 )) |> approximatelyEqual (Complex.fromPair ( 0, 3 )) , skip <| test "Add numbers with real and imaginary part" <| \() -> Complex.add (Complex.fromPair ( 1, 2 )) (Complex.fromPair ( 3, 4 )) |> approximatelyEqual (Complex.fromPair ( 4, 6 )) ] , describe "Subtraction" [ skip <| test "Subtract purely real numbers" <| \() -> Complex.sub (Complex.fromPair ( 1, 0 )) (Complex.fromPair ( 2, 0 )) |> approximatelyEqual (Complex.fromPair ( -1, 0 )) , skip <| test "Subtract purely imaginary numbers" <| \() -> Complex.sub (Complex.fromPair ( 0, 1 )) (Complex.fromPair ( 0, 2 )) |> approximatelyEqual (Complex.fromPair ( 0, -1 )) , skip <| test "Subtract numbers with real and imaginary part" <| \() -> Complex.sub (Complex.fromPair ( 1, 2 )) (Complex.fromPair ( 3, 4 )) |> approximatelyEqual (Complex.fromPair ( -2, -2 )) ] , describe "Multiplication" [ skip <| test "Multiply purely real numbers" <| \() -> Complex.mul (Complex.fromPair ( 1, 0 )) (Complex.fromPair ( 2, 0 )) |> approximatelyEqual (Complex.fromPair ( 2, 0 )) , skip <| test "Multiply purely imaginary numbers" <| \() -> Complex.mul (Complex.fromPair ( 0, 1 )) (Complex.fromPair ( 0, 2 )) |> approximatelyEqual (Complex.fromPair ( -2, 0 )) , skip <| test "Multiply numbers with real and imaginary part" <| \() -> Complex.mul (Complex.fromPair ( 1, 2 )) (Complex.fromPair ( 3, 4 )) |> approximatelyEqual (Complex.fromPair ( -5, 10 )) ] , describe "Division" [ skip <| test "Divide purely real numbers" <| \() -> Complex.div (Complex.fromPair ( 1, 0 )) (Complex.fromPair ( 2, 0 )) |> approximatelyEqual (Complex.fromPair ( 0.5, 0 )) , skip <| test "Divide purely imaginary numbers" <| \() -> Complex.div (Complex.fromPair ( 0, 1 )) (Complex.fromPair ( 0, 2 )) |> approximatelyEqual (Complex.fromPair ( 0.5, 0 )) , skip <| test "Divide numbers with real and imaginary part" <| \() -> Complex.div (Complex.fromPair ( 1, 2 )) (Complex.fromPair ( 3, 4 )) |> approximatelyEqual (Complex.fromPair ( 0.44, 0.08 )) ] ] , describe "Absolute value" [ skip <| test "Absolute value of a positive purely real number" <| \() -> Complex.abs (Complex.fromPair ( 5, 0 )) |> Expect.within tolerance 5 , skip <| test "Absolute value of a negative purely real number" <| \() -> Complex.abs (Complex.fromPair ( -5, 0 )) |> Expect.within tolerance 5 , skip <| test "Absolute value of a purely imaginary number with positive imaginary part" <| \() -> Complex.abs (Complex.fromPair ( 0, 5 )) |> Expect.within tolerance 5 , skip <| test "Absolute value of a purely imaginary number with negative imaginary part" <| \() -> Complex.abs (Complex.fromPair ( 0, -5 )) |> Expect.within tolerance 5 , skip <| test "Absolute value of a number with real and imaginary part" <| \() -> Complex.abs (Complex.fromPair ( 3, 4 )) |> Expect.within tolerance 5 ] , describe "Complex conjugate" [ skip <| test "Conjugate a purely real number" <| \() -> Complex.conjugate (Complex.fromPair ( 5, 0 )) |> approximatelyEqual (Complex.fromPair ( 5, 0 )) , skip <| test "Conjugate a purely imaginary number" <| \() -> Complex.conjugate (Complex.fromPair ( 0, 5 )) |> approximatelyEqual (Complex.fromPair ( 0, -5 )) , skip <| test "Conjugate a number with real and imaginary part" <| \() -> Complex.conjugate (Complex.fromPair ( 1, 1 )) |> approximatelyEqual (Complex.fromPair ( 1, -1 )) ] , describe "Complex exponential function" [ skip <| test "Euler's identity/formula" <| \() -> Complex.exp (Complex.fromPair ( 0, pi )) |> approximatelyEqual (Complex.fromPair ( -1, 0 )) , skip <| test "Exponential of 0" <| \() -> Complex.exp (Complex.fromPair ( 0, 0 )) |> approximatelyEqual (Complex.fromPair ( 1, 0 )) , skip <| test "Exponential of a purely real number" <| \() -> Complex.exp (Complex.fromPair ( 1, 0 )) |> approximatelyEqual (Complex.fromPair ( e, 0 )) , skip <| test "Exponential of a number with real and imaginary part" <| \() -> Complex.exp (Complex.fromPair ( logBase e 2, pi )) |> approximatelyEqual (Complex.fromPair ( -2, 0 )) , skip <| test "Exponential resulting in a number with real and imaginary part" <| \() -> Complex.exp (Complex.fromPair ( logBase e 2 / 2, pi / 4 )) |> approximatelyEqual (Complex.fromPair ( 1, 1 )) ] , describe "Operations between real numbers and complex numbers" [ skip <| test "Add real number to complex number" <| \() -> Complex.add (Complex.fromPair ( 1, 2 )) (Complex.fromReal 5) |> approximatelyEqual (Complex.fromPair ( 6, 2 )) , skip <| test "Add complex number to real number" <| \() -> Complex.add (Complex.fromReal 5) (Complex.fromPair ( 1, 2 )) |> approximatelyEqual (Complex.fromPair ( 6, 2 )) , skip <| test "Subtract real number from complex number" <| \() -> Complex.sub (Complex.fromPair ( 5, 7 )) (Complex.fromReal 4) |> approximatelyEqual (Complex.fromPair ( 1, 7 )) , skip <| test "Subtract complex number from real number" <| \() -> Complex.sub (Complex.fromReal 4) (Complex.fromPair ( 5, 7 )) |> approximatelyEqual (Complex.fromPair ( -1, -7 )) , skip <| test "Multiply complex number by real number" <| \() -> Complex.mul (Complex.fromPair ( 2, 5 )) (Complex.fromReal 5) |> approximatelyEqual (Complex.fromPair ( 10, 25 )) , skip <| test "Multiply real number by complex number" <| \() -> Complex.mul (Complex.fromReal 5) (Complex.fromPair ( 2, 5 )) |> approximatelyEqual (Complex.fromPair ( 10, 25 )) , skip <| test "Divide complex number by real number" <| \() -> Complex.div (Complex.fromPair ( 10, 100 )) (Complex.fromReal 10) |> approximatelyEqual (Complex.fromPair ( 1, 10 )) , skip <| test "Divide real number by complex number" <| \() -> Complex.div (Complex.fromReal 5) (Complex.fromPair ( 1, 1 )) |> approximatelyEqual (Complex.fromPair ( 2.5, -2.5 )) ] ]