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;; Test routines for complex-numbers.clj
;; by Konrad Hinsen
;; last updated April 2, 2009
;; Copyright (c) Konrad Hinsen, 2008. All rights reserved. The use
;; and distribution terms for this software are covered by the Eclipse
;; Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php)
;; which can be found in the file epl-v10.html at the root of this
;; distribution. By using this software in any fashion, you are
;; agreeing to be bound by the terms of this license. You must not
;; remove this notice, or any other, from this software.
(ns clojure.contrib.test-complex-numbers
(:refer-clojure :exclude [+ - * / = < > <= >=])
(:use [clojure.test
:only (deftest is are run-tests)]
[clojure.contrib.generic.arithmetic
:only (+ - * /)]
[clojure.contrib.generic.comparison
:only (= < > <= >=)]
[clojure.contrib.generic.math-functions
:only (abs approx= conjugate exp sqr sqrt)]
[clojure.contrib.complex-numbers
:only (complex imaginary real imag)]))
(deftest complex-addition
(is (= (+ (complex 1 2) (complex 1 2)) (complex 2 4)))
(is (= (+ (complex 1 2) (complex -3 -7)) (complex -2 -5)))
(is (= (+ (complex -3 -7) (complex 1 2)) (complex -2 -5)))
(is (= (+ (complex 1 2) 3) (complex 4 2)))
(is (= (+ 3 (complex 1 2)) (complex 4 2)))
(is (= (+ (complex 1 2) -1) (imaginary 2)))
(is (= (+ -1 (complex 1 2)) (imaginary 2)))
(is (= (+ (complex 1 2) (imaginary -2)) 1))
(is (= (+ (imaginary -2) (complex 1 2)) 1))
(is (= (+ (complex 1 2) (imaginary 5)) (complex 1 7)))
(is (= (+ (imaginary 5) (complex 1 2)) (complex 1 7)))
(is (= (+ (complex -3 -7) (complex 1 2)) (complex -2 -5)))
(is (= (+ (complex 1 2) (complex -3 -7)) (complex -2 -5)))
(is (= (+ (complex -3 -7) (complex -3 -7)) (complex -6 -14)))
(is (= (+ (complex -3 -7) 3) (imaginary -7)))
(is (= (+ 3 (complex -3 -7)) (imaginary -7)))
(is (= (+ (complex -3 -7) -1) (complex -4 -7)))
(is (= (+ -1 (complex -3 -7)) (complex -4 -7)))
(is (= (+ (complex -3 -7) (imaginary -2)) (complex -3 -9)))
(is (= (+ (imaginary -2) (complex -3 -7)) (complex -3 -9)))
(is (= (+ (complex -3 -7) (imaginary 5)) (complex -3 -2)))
(is (= (+ (imaginary 5) (complex -3 -7)) (complex -3 -2)))
(is (= (+ 3 (complex 1 2)) (complex 4 2)))
(is (= (+ (complex 1 2) 3) (complex 4 2)))
(is (= (+ 3 (complex -3 -7)) (imaginary -7)))
(is (= (+ (complex -3 -7) 3) (imaginary -7)))
(is (= (+ 3 (imaginary -2)) (complex 3 -2)))
(is (= (+ (imaginary -2) 3) (complex 3 -2)))
(is (= (+ 3 (imaginary 5)) (complex 3 5)))
(is (= (+ (imaginary 5) 3) (complex 3 5)))
(is (= (+ -1 (complex 1 2)) (imaginary 2)))
(is (= (+ (complex 1 2) -1) (imaginary 2)))
(is (= (+ -1 (complex -3 -7)) (complex -4 -7)))
(is (= (+ (complex -3 -7) -1) (complex -4 -7)))
(is (= (+ -1 (imaginary -2)) (complex -1 -2)))
(is (= (+ (imaginary -2) -1) (complex -1 -2)))
(is (= (+ -1 (imaginary 5)) (complex -1 5)))
(is (= (+ (imaginary 5) -1) (complex -1 5)))
(is (= (+ (imaginary -2) (complex 1 2)) 1))
(is (= (+ (complex 1 2) (imaginary -2)) 1))
(is (= (+ (imaginary -2) (complex -3 -7)) (complex -3 -9)))
(is (= (+ (complex -3 -7) (imaginary -2)) (complex -3 -9)))
(is (= (+ (imaginary -2) 3) (complex 3 -2)))
(is (= (+ 3 (imaginary -2)) (complex 3 -2)))
(is (= (+ (imaginary -2) -1) (complex -1 -2)))
(is (= (+ -1 (imaginary -2)) (complex -1 -2)))
(is (= (+ (imaginary -2) (imaginary -2)) (imaginary -4)))
(is (= (+ (imaginary -2) (imaginary 5)) (imaginary 3)))
(is (= (+ (imaginary 5) (imaginary -2)) (imaginary 3)))
(is (= (+ (imaginary 5) (complex 1 2)) (complex 1 7)))
(is (= (+ (complex 1 2) (imaginary 5)) (complex 1 7)))
(is (= (+ (imaginary 5) (complex -3 -7)) (complex -3 -2)))
(is (= (+ (complex -3 -7) (imaginary 5)) (complex -3 -2)))
(is (= (+ (imaginary 5) 3) (complex 3 5)))
(is (= (+ 3 (imaginary 5)) (complex 3 5)))
(is (= (+ (imaginary 5) -1) (complex -1 5)))
(is (= (+ -1 (imaginary 5)) (complex -1 5)))
(is (= (+ (imaginary 5) (imaginary -2)) (imaginary 3)))
(is (= (+ (imaginary -2) (imaginary 5)) (imaginary 3)))
(is (= (+ (imaginary 5) (imaginary 5)) (imaginary 10))))
(deftest complex-subtraction
(is (= (- (complex 1 2) (complex 1 2)) 0))
(is (= (- (complex 1 2) (complex -3 -7)) (complex 4 9)))
(is (= (- (complex -3 -7) (complex 1 2)) (complex -4 -9)))
(is (= (- (complex 1 2) 3) (complex -2 2)))
(is (= (- 3 (complex 1 2)) (complex 2 -2)))
(is (= (- (complex 1 2) -1) (complex 2 2)))
(is (= (- -1 (complex 1 2)) (complex -2 -2)))
(is (= (- (complex 1 2) (imaginary -2)) (complex 1 4)))
(is (= (- (imaginary -2) (complex 1 2)) (complex -1 -4)))
(is (= (- (complex 1 2) (imaginary 5)) (complex 1 -3)))
(is (= (- (imaginary 5) (complex 1 2)) (complex -1 3)))
(is (= (- (complex -3 -7) (complex 1 2)) (complex -4 -9)))
(is (= (- (complex 1 2) (complex -3 -7)) (complex 4 9)))
(is (= (- (complex -3 -7) (complex -3 -7)) 0))
(is (= (- (complex -3 -7) 3) (complex -6 -7)))
(is (= (- 3 (complex -3 -7)) (complex 6 7)))
(is (= (- (complex -3 -7) -1) (complex -2 -7)))
(is (= (- -1 (complex -3 -7)) (complex 2 7)))
(is (= (- (complex -3 -7) (imaginary -2)) (complex -3 -5)))
(is (= (- (imaginary -2) (complex -3 -7)) (complex 3 5)))
(is (= (- (complex -3 -7) (imaginary 5)) (complex -3 -12)))
(is (= (- (imaginary 5) (complex -3 -7)) (complex 3 12)))
(is (= (- 3 (complex 1 2)) (complex 2 -2)))
(is (= (- (complex 1 2) 3) (complex -2 2)))
(is (= (- 3 (complex -3 -7)) (complex 6 7)))
(is (= (- (complex -3 -7) 3) (complex -6 -7)))
(is (= (- 3 (imaginary -2)) (complex 3 2)))
(is (= (- (imaginary -2) 3) (complex -3 -2)))
(is (= (- 3 (imaginary 5)) (complex 3 -5)))
(is (= (- (imaginary 5) 3) (complex -3 5)))
(is (= (- -1 (complex 1 2)) (complex -2 -2)))
(is (= (- (complex 1 2) -1) (complex 2 2)))
(is (= (- -1 (complex -3 -7)) (complex 2 7)))
(is (= (- (complex -3 -7) -1) (complex -2 -7)))
(is (= (- -1 (imaginary -2)) (complex -1 2)))
(is (= (- (imaginary -2) -1) (complex 1 -2)))
(is (= (- -1 (imaginary 5)) (complex -1 -5)))
(is (= (- (imaginary 5) -1) (complex 1 5)))
(is (= (- (imaginary -2) (complex 1 2)) (complex -1 -4)))
(is (= (- (complex 1 2) (imaginary -2)) (complex 1 4)))
(is (= (- (imaginary -2) (complex -3 -7)) (complex 3 5)))
(is (= (- (complex -3 -7) (imaginary -2)) (complex -3 -5)))
(is (= (- (imaginary -2) 3) (complex -3 -2)))
(is (= (- 3 (imaginary -2)) (complex 3 2)))
(is (= (- (imaginary -2) -1) (complex 1 -2)))
(is (= (- -1 (imaginary -2)) (complex -1 2)))
(is (= (- (imaginary -2) (imaginary -2)) 0))
(is (= (- (imaginary -2) (imaginary 5)) (imaginary -7)))
(is (= (- (imaginary 5) (imaginary -2)) (imaginary 7)))
(is (= (- (imaginary 5) (complex 1 2)) (complex -1 3)))
(is (= (- (complex 1 2) (imaginary 5)) (complex 1 -3)))
(is (= (- (imaginary 5) (complex -3 -7)) (complex 3 12)))
(is (= (- (complex -3 -7) (imaginary 5)) (complex -3 -12)))
(is (= (- (imaginary 5) 3) (complex -3 5)))
(is (= (- 3 (imaginary 5)) (complex 3 -5)))
(is (= (- (imaginary 5) -1) (complex 1 5)))
(is (= (- -1 (imaginary 5)) (complex -1 -5)))
(is (= (- (imaginary 5) (imaginary -2)) (imaginary 7)))
(is (= (- (imaginary -2) (imaginary 5)) (imaginary -7)))
(is (= (- (imaginary 5) (imaginary 5)) 0)))
(deftest complex-multiplication
(is (= (* (complex 1 2) (complex 1 2)) (complex -3 4)))
(is (= (* (complex 1 2) (complex -3 -7)) (complex 11 -13)))
(is (= (* (complex -3 -7) (complex 1 2)) (complex 11 -13)))
(is (= (* (complex 1 2) 3) (complex 3 6)))
(is (= (* 3 (complex 1 2)) (complex 3 6)))
(is (= (* (complex 1 2) -1) (complex -1 -2)))
(is (= (* -1 (complex 1 2)) (complex -1 -2)))
(is (= (* (complex 1 2) (imaginary -2)) (complex 4 -2)))
(is (= (* (imaginary -2) (complex 1 2)) (complex 4 -2)))
(is (= (* (complex 1 2) (imaginary 5)) (complex -10 5)))
(is (= (* (imaginary 5) (complex 1 2)) (complex -10 5)))
(is (= (* (complex -3 -7) (complex 1 2)) (complex 11 -13)))
(is (= (* (complex 1 2) (complex -3 -7)) (complex 11 -13)))
(is (= (* (complex -3 -7) (complex -3 -7)) (complex -40 42)))
(is (= (* (complex -3 -7) 3) (complex -9 -21)))
(is (= (* 3 (complex -3 -7)) (complex -9 -21)))
(is (= (* (complex -3 -7) -1) (complex 3 7)))
(is (= (* -1 (complex -3 -7)) (complex 3 7)))
(is (= (* (complex -3 -7) (imaginary -2)) (complex -14 6)))
(is (= (* (imaginary -2) (complex -3 -7)) (complex -14 6)))
(is (= (* (complex -3 -7) (imaginary 5)) (complex 35 -15)))
(is (= (* (imaginary 5) (complex -3 -7)) (complex 35 -15)))
(is (= (* 3 (complex 1 2)) (complex 3 6)))
(is (= (* (complex 1 2) 3) (complex 3 6)))
(is (= (* 3 (complex -3 -7)) (complex -9 -21)))
(is (= (* (complex -3 -7) 3) (complex -9 -21)))
(is (= (* 3 (imaginary -2)) (imaginary -6)))
(is (= (* (imaginary -2) 3) (imaginary -6)))
(is (= (* 3 (imaginary 5)) (imaginary 15)))
(is (= (* (imaginary 5) 3) (imaginary 15)))
(is (= (* -1 (complex 1 2)) (complex -1 -2)))
(is (= (* (complex 1 2) -1) (complex -1 -2)))
(is (= (* -1 (complex -3 -7)) (complex 3 7)))
(is (= (* (complex -3 -7) -1) (complex 3 7)))
(is (= (* -1 (imaginary -2)) (imaginary 2)))
(is (= (* (imaginary -2) -1) (imaginary 2)))
(is (= (* -1 (imaginary 5)) (imaginary -5)))
(is (= (* (imaginary 5) -1) (imaginary -5)))
(is (= (* (imaginary -2) (complex 1 2)) (complex 4 -2)))
(is (= (* (complex 1 2) (imaginary -2)) (complex 4 -2)))
(is (= (* (imaginary -2) (complex -3 -7)) (complex -14 6)))
(is (= (* (complex -3 -7) (imaginary -2)) (complex -14 6)))
(is (= (* (imaginary -2) 3) (imaginary -6)))
(is (= (* 3 (imaginary -2)) (imaginary -6)))
(is (= (* (imaginary -2) -1) (imaginary 2)))
(is (= (* -1 (imaginary -2)) (imaginary 2)))
(is (= (* (imaginary -2) (imaginary -2)) -4))
(is (= (* (imaginary -2) (imaginary 5)) 10))
(is (= (* (imaginary 5) (imaginary -2)) 10))
(is (= (* (imaginary 5) (complex 1 2)) (complex -10 5)))
(is (= (* (complex 1 2) (imaginary 5)) (complex -10 5)))
(is (= (* (imaginary 5) (complex -3 -7)) (complex 35 -15)))
(is (= (* (complex -3 -7) (imaginary 5)) (complex 35 -15)))
(is (= (* (imaginary 5) 3) (imaginary 15)))
(is (= (* 3 (imaginary 5)) (imaginary 15)))
(is (= (* (imaginary 5) -1) (imaginary -5)))
(is (= (* -1 (imaginary 5)) (imaginary -5)))
(is (= (* (imaginary 5) (imaginary -2)) 10))
(is (= (* (imaginary -2) (imaginary 5)) 10))
(is (= (* (imaginary 5) (imaginary 5)) -25)))
(deftest complex-division
(is (= (/ (complex 1 2) (complex 1 2)) 1))
(is (= (/ (complex 1 2) (complex -3 -7)) (complex -17/58 1/58)))
(is (= (/ (complex -3 -7) (complex 1 2)) (complex -17/5 -1/5)))
(is (= (/ (complex 1 2) 3) (complex 1/3 2/3)))
(is (= (/ 3 (complex 1 2)) (complex 3/5 -6/5)))
(is (= (/ (complex 1 2) -1) (complex -1 -2)))
(is (= (/ -1 (complex 1 2)) (complex -1/5 2/5)))
(is (= (/ (complex 1 2) (imaginary -2)) (complex -1 1/2)))
(is (= (/ (imaginary -2) (complex 1 2)) (complex -4/5 -2/5)))
(is (= (/ (complex 1 2) (imaginary 5)) (complex 2/5 -1/5)))
(is (= (/ (imaginary 5) (complex 1 2)) (complex 2 1)))
(is (= (/ (complex -3 -7) (complex 1 2)) (complex -17/5 -1/5)))
(is (= (/ (complex 1 2) (complex -3 -7)) (complex -17/58 1/58)))
(is (= (/ (complex -3 -7) (complex -3 -7)) 1))
(is (= (/ (complex -3 -7) 3) (complex -1 -7/3)))
(is (= (/ 3 (complex -3 -7)) (complex -9/58 21/58)))
(is (= (/ (complex -3 -7) -1) (complex 3 7)))
(is (= (/ -1 (complex -3 -7)) (complex 3/58 -7/58)))
(is (= (/ (complex -3 -7) (imaginary -2)) (complex 7/2 -3/2)))
(is (= (/ (imaginary -2) (complex -3 -7)) (complex 7/29 3/29)))
(is (= (/ (complex -3 -7) (imaginary 5)) (complex -7/5 3/5)))
(is (= (/ (imaginary 5) (complex -3 -7)) (complex -35/58 -15/58)))
(is (= (/ 3 (complex 1 2)) (complex 3/5 -6/5)))
(is (= (/ (complex 1 2) 3) (complex 1/3 2/3)))
(is (= (/ 3 (complex -3 -7)) (complex -9/58 21/58)))
(is (= (/ (complex -3 -7) 3) (complex -1 -7/3)))
#_(is (= (/ 3 (imaginary -2)) (imaginary 1.5)))
(is (= (/ (imaginary -2) 3) (imaginary -2/3)))
(is (= (/ 3 (imaginary 5)) (imaginary -3/5)))
(is (= (/ (imaginary 5) 3) (imaginary 5/3)))
(is (= (/ -1 (complex 1 2)) (complex -1/5 2/5)))
(is (= (/ (complex 1 2) -1) (complex -1 -2)))
(is (= (/ -1 (complex -3 -7)) (complex 3/58 -7/58)))
(is (= (/ (complex -3 -7) -1) (complex 3 7)))
(is (= (/ -1 (imaginary -2)) (imaginary -1/2)))
(is (= (/ (imaginary -2) -1) (imaginary 2)))
(is (= (/ -1 (imaginary 5)) (imaginary 1/5)))
(is (= (/ (imaginary 5) -1) (imaginary -5)))
(is (= (/ (imaginary -2) (complex 1 2)) (complex -4/5 -2/5)))
(is (= (/ (complex 1 2) (imaginary -2)) (complex -1 1/2)))
(is (= (/ (imaginary -2) (complex -3 -7)) (complex 7/29 3/29)))
(is (= (/ (complex -3 -7) (imaginary -2)) (complex 7/2 -3/2)))
(is (= (/ (imaginary -2) 3) (imaginary -2/3)))
(is (= (/ 3 (imaginary -2)) (imaginary 3/2)))
(is (= (/ (imaginary -2) -1) (imaginary 2)))
(is (= (/ -1 (imaginary -2)) (imaginary -1/2)))
(is (= (/ (imaginary -2) (imaginary -2)) 1))
(is (= (/ (imaginary -2) (imaginary 5)) -2/5))
(is (= (/ (imaginary 5) (imaginary -2)) -5/2))
(is (= (/ (imaginary 5) (complex 1 2)) (complex 2 1)))
(is (= (/ (complex 1 2) (imaginary 5)) (complex 2/5 -1/5)))
(is (= (/ (imaginary 5) (complex -3 -7)) (complex -35/58 -15/58)))
(is (= (/ (complex -3 -7) (imaginary 5)) (complex -7/5 3/5)))
(is (= (/ (imaginary 5) 3) (imaginary 5/3)))
(is (= (/ 3 (imaginary 5)) (imaginary -3/5)))
(is (= (/ (imaginary 5) -1) (imaginary -5)))
(is (= (/ -1 (imaginary 5)) (imaginary 1/5)))
(is (= (/ (imaginary 5) (imaginary -2)) -5/2))
(is (= (/ (imaginary -2) (imaginary 5)) -2/5))
(is (= (/ (imaginary 5) (imaginary 5)) 1)))
(deftest complex-conjugate
(is (= (conjugate (complex 1 2)) (complex 1 -2)))
(is (= (conjugate (complex -3 -7)) (complex -3 7)))
(is (= (conjugate (imaginary -2)) (imaginary 2)))
(is (= (conjugate (imaginary 5)) (imaginary -5))))
(deftest complex-abs
(doseq [c [(complex 1 2) (complex -2 3) (complex 4 -2)
(complex -3 -7) (imaginary -2) (imaginary 5)]]
(is (approx= (* c (conjugate c))
(sqr (abs c))
1e-14))))
(deftest complex-sqrt
(doseq [c [(complex 1 2) (complex -2 3) (complex 4 -2)
(complex -3 -7) (imaginary -2) (imaginary 5)]]
(let [r (sqrt c)]
(is (approx= c (sqr r) 1e-14))
(is (>= (real r) 0)))))
(deftest complex-exp
(is (approx= (exp (complex 1 2))
(complex -1.1312043837568135 2.4717266720048188)
1e-14))
(is (approx= (exp (complex 2 3))
(complex -7.3151100949011028 1.0427436562359045)
1e-14))
(is (approx= (exp (complex 4 -2))
(complex -22.720847417619233 -49.645957334580565)
1e-14))
(is (approx= (exp (complex 3 -7))
(complex 15.142531566086868 -13.195928586605717)
1e-14))
(is (approx= (exp (imaginary -2))
(complex -0.41614683654714241 -0.90929742682568171)
1e-14))
(is (approx= (exp (imaginary 5))
(complex 0.2836621854632263 -0.95892427466313845)
1e-14)))