# richhickey/clojure-contrib

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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)))