source("./complex-numbers.R") library(testthat) # Real part test_that("Real part of a purely real number", { z <- create(1.0, 0.0) expect_equal(real(z), 1.0) }) test_that("Real part of a purely imaginary number", { z <- create(0.0, 1.0) expect_equal(real(z), 0.0) }) test_that("Real part of a number with real and imaginary part", { z <- create(1.0, 2.0) expect_equal(real(z), 1.0) }) # Imaginary part test_that("Imaginary part of a purely real number", { z <- create(1.0, 0.0) expect_equal(imag(z), 0.0) }) test_that("Imaginary part of a purely imaginary number", { z <- create(0.0, 1.0) expect_equal(imag(z), 1.0) }) test_that("Imaginary part of a number with real and imaginary part", { z <- create(1.0, 2.0) expect_equal(imag(z), 2.0) }) test_that("Imaginary unit", { z1 <- create(0, 1.0) z2 <- create(0, 1.0) expect_equal(multiply(z1, z2), create(-1.0, 0.0)) }) # Arithmetic # Addition test_that("Add purely real numbers", { z1 <- create(1.0, 0.0) z2 <- create(2.0, 0.0) expect_equal(add(z1, z2), create(3.0, 0.0)) }) test_that("Add purely imaginary numbers", { z1 <- create(0.0, 1.0) z2 <- create(0.0, 2.0) expect_equal(add(z1, z2), create(0.0, 3.0)) }) test_that("Add numbers with real and imaginary part", { z1 <- create(1.0, 2.0) z2 <- create(3.0, 4.0) expect_equal(add(z1, z2), create(4.0, 6.0)) }) # Subtraction test_that("Subtract purely real numbers", { z1 <- create(1.0, 0.0) z2 <- create(2.0, 0.0) expect_equal(subtract(z1, z2), create(-1.0, 0.0)) }) test_that("Subtract purely imaginary numbers", { z1 <- create(0.0, 1.0) z2 <- create(0.0, 2.0) expect_equal(subtract(z1, z2), create(0.0, -1.0)) }) test_that("Subtract numbers with real and imaginary part", { z1 <- create(1.0, 2.0) z2 <- create(3.0, 4.0) expect_equal(subtract(z1, z2), create(-2.0, -2.0)) }) # Multiplication test_that("Multiply purely real numbers", { z1 <- create(1.0, 0.0) z2 <- create(2.0, 0.0) expect_equal(multiply(z1, z2), create(2.0, 0.0), tolerance = 1e-4) }) test_that("Multiply purely imaginary numbers", { z1 <- create(0.0, 1.0) z2 <- create(0.0, 2.0) expect_equal(multiply(z1, z2), create(-2.0, 0.0), tolerance = 1e-4) }) test_that("Multiply numbers with real and imaginary part", { z1 <- create(1.0, 2.0) z2 <- create(3.0, 4.0) expect_equal(multiply(z1, z2), create(-5.0, 10.0), tolerance = 1e-4) }) # Division test_that("Divide purely real numbers", { z1 <- create(1.0, 0.0) z2 <- create(2.0, 0.0) expect_equal(divide(z1, z2), create(0.5, 0.0), tolerance = 1e-4) }) test_that("Divide purely imaginary numbers", { z1 <- create(0.0, 1.0) z2 <- create(0.0, 2.0) expect_equal(divide(z1, z2), create(0.5, 0.0), tolerance = 1e-4) }) test_that("Divide numbers with real and imaginary part", { z1 <- create(1.0, 2.0) z2 <- create(3.0, 4.0) expect_equal(divide(z1, z2), create(0.44, 0.08), tolerance = 1e-4) }) # Absolute value test_that("Absolute value of a positive purely real number", { z <- create(5.0, 0.0) expect_equal(absolute(z), 5.0, tolerance = 1e-4) }) test_that("Absolute value of a negative purely real number", { z <- create(-5.0, 0.0) expect_equal(absolute(z), 5.0, tolerance = 1e-4) }) test_that("Absolute value of a purely imag number with positive imag part", { z <- create(0.0, 5.0) expect_equal(absolute(z), 5.0, tolerance = 1e-4) }) test_that("Absolute value of a purely imag number with negative imag part", { z <- create(0.0, -5.0) expect_equal(absolute(z), 5.0, tolerance = 1e-4) }) test_that("Absolute value of a number with real and imaginary part", { z <- create(3.0, 4.0) expect_equal(absolute(z), 5.0, tolerance = 1e-4) }) # Complex conjugate test_that("Conjugate a purely real number", { z <- create(5.0, 0.0) expect_equal(conjugate(z), create(5.0, 0.0), tolerance = 1e-4) }) test_that("Conjugate a purely imaginary number", { z <- create(0.0, 5.0) expect_equal(conjugate(z), create(0.0, -5.0), tolerance = 1e-4) }) test_that("Conjugate a number with real and imaginary part", { z <- create(1.0, 1.0) expect_equal(conjugate(z), create(1.0, -1.0), tolerance = 1e-4) }) # Exponential test_that("Euler's identity/formula", { z <- create(0.0, pi) expect_equal(exponential(z), create(-1.0, 0.0), tolerance = 1e-4) }) test_that("Exponential of 0", { z <- create(0.0, 0.0) expect_equal(exponential(z), create(1.0, 0.0), tolerance = 1e-4) }) test_that("Exponential of a purely real number", { z <- create(1.0, 0.0) expect_equal(exponential(z), create(exp(1), 0.0), tolerance = 1e-4) }) test_that("Exponential of a number with real and imaginary part", { z <- create(log(2), pi) expect_equal(exponential(z), create(-2.0, 0.0), tolerance = 1e-4) }) test_that("Exponential resulting in a number with real and imaginary part", { z <- create(log(2) / 2, pi / 4) expect_equal(exponential(z), create(1.0, 1.0), tolerance = 1e-4) }) # Operations between real numbers and complex numbers test_that("Add real number to complex number", { z1 <- create(1.0, 2.0) z2 <- 5.0 expect_equal(add(z1, z2), create(6.0, 2.0), tolerance = 1e-4) }) test_that("Add complex number to real number", { z1 <- 5.0 z2 <- create(1.0, 2.0) expect_equal(add(z1, z2), create(6.0, 2.0), tolerance = 1e-4) }) test_that("Subtract real number from complex number", { z1 <- create(5.0, 7.0) z2 <- 4.0 expect_equal(subtract(z1, z2), create(1.0, 7.0), tolerance = 1e-4) }) test_that("Subtract complex number from real number", { z1 <- 4.0 z2 <- create(5.0, 7.0) expect_equal(subtract(z1, z2), create(-1.0, -7.0), tolerance = 1e-4) }) test_that("Multiply complex number by real number", { z1 <- create(2.0, 5.0) z2 <- 5.0 expect_equal(multiply(z1, z2), create(10.0, 25.0), tolerance = 1e-4) }) test_that("Multiply real number by complex number", { z1 <- 5.0 z2 <- create(2.0, 5.0) expect_equal(multiply(z1, z2), create(10.0, 25.0), tolerance = 1e-4) }) test_that("Divide complex number by real number", { z1 <- create(10.0, 100.0) z2 <- 10.0 expect_equal(divide(z1, z2), create(1.0, 10.0)) }) test_that("Divide real number by complex number", { z1 <- 5.0 z2 <- create(1.0, 1.0) expect_equal(divide(z1, z2), create(2.5, -2.5), tolerance = 1e-4) }) message("All tests passed for exercise: complex-numbers")