Mercurial > lasercutter

     1 ;; Test routines for complex-numbers.clj

     2 

     3 ;; by Konrad Hinsen

     4 ;; last updated April 2, 2009

     5 

     6 ;; Copyright (c) Konrad Hinsen, 2008. All rights reserved.  The use

     7 ;; and distribution terms for this software are covered by the Eclipse

     8 ;; Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php)

     9 ;; which can be found in the file epl-v10.html at the root of this

    10 ;; distribution.  By using this software in any fashion, you are

    11 ;; agreeing to be bound by the terms of this license.  You must not

    12 ;; remove this notice, or any other, from this software.

    13 

    14 (ns clojure.contrib.test-complex-numbers

    15   (:refer-clojure :exclude [+ - * / = < > <= >=])

    16   (:use [clojure.test

    17 	 :only (deftest is are run-tests)]

    18 	[clojure.contrib.generic.arithmetic

    19 	 :only (+ - * /)]

    20 	[clojure.contrib.generic.comparison

    21 	 :only (= < > <= >=)]

    22 	[clojure.contrib.generic.math-functions

    23 	 :only (abs approx= conjugate exp sqr sqrt)]

    24 	[clojure.contrib.complex-numbers

    25 	 :only (complex imaginary real imag)]))

    26 

    27 (deftest complex-addition

    28   (is (= (+ (complex 1 2) (complex 1 2)) (complex 2 4)))

    29   (is (= (+ (complex 1 2) (complex -3 -7)) (complex -2 -5)))

    30   (is (= (+ (complex -3 -7) (complex 1 2)) (complex -2 -5)))

    31   (is (= (+ (complex 1 2) 3) (complex 4 2)))

    32   (is (= (+ 3 (complex 1 2)) (complex 4 2)))

    33   (is (= (+ (complex 1 2) -1) (imaginary 2)))

    34   (is (= (+ -1 (complex 1 2)) (imaginary 2)))

    35   (is (= (+ (complex 1 2) (imaginary -2)) 1))

    36   (is (= (+ (imaginary -2) (complex 1 2)) 1))

    37   (is (= (+ (complex 1 2) (imaginary 5)) (complex 1 7)))

    38   (is (= (+ (imaginary 5) (complex 1 2)) (complex 1 7)))

    39   (is (= (+ (complex -3 -7) (complex 1 2)) (complex -2 -5)))

    40   (is (= (+ (complex 1 2) (complex -3 -7)) (complex -2 -5)))

    41   (is (= (+ (complex -3 -7) (complex -3 -7)) (complex -6 -14)))

    42   (is (= (+ (complex -3 -7) 3) (imaginary -7)))

    43   (is (= (+ 3 (complex -3 -7)) (imaginary -7)))

    44   (is (= (+ (complex -3 -7) -1) (complex -4 -7)))

    45   (is (= (+ -1 (complex -3 -7)) (complex -4 -7)))

    46   (is (= (+ (complex -3 -7) (imaginary -2)) (complex -3 -9)))

    47   (is (= (+ (imaginary -2) (complex -3 -7)) (complex -3 -9)))

    48   (is (= (+ (complex -3 -7) (imaginary 5)) (complex -3 -2)))

    49   (is (= (+ (imaginary 5) (complex -3 -7)) (complex -3 -2)))

    50   (is (= (+ 3 (complex 1 2)) (complex 4 2)))

    51   (is (= (+ (complex 1 2) 3) (complex 4 2)))

    52   (is (= (+ 3 (complex -3 -7)) (imaginary -7)))

    53   (is (= (+ (complex -3 -7) 3) (imaginary -7)))

    54   (is (= (+ 3 (imaginary -2)) (complex 3 -2)))

    55   (is (= (+ (imaginary -2) 3) (complex 3 -2)))

    56   (is (= (+ 3 (imaginary 5)) (complex 3 5)))

    57   (is (= (+ (imaginary 5) 3) (complex 3 5)))

    58   (is (= (+ -1 (complex 1 2)) (imaginary 2)))

    59   (is (= (+ (complex 1 2) -1) (imaginary 2)))

    60   (is (= (+ -1 (complex -3 -7)) (complex -4 -7)))

    61   (is (= (+ (complex -3 -7) -1) (complex -4 -7)))

    62   (is (= (+ -1 (imaginary -2)) (complex -1 -2)))

    63   (is (= (+ (imaginary -2) -1) (complex -1 -2)))

    64   (is (= (+ -1 (imaginary 5)) (complex -1 5)))

    65   (is (= (+ (imaginary 5) -1) (complex -1 5)))

    66   (is (= (+ (imaginary -2) (complex 1 2)) 1))

    67   (is (= (+ (complex 1 2) (imaginary -2)) 1))

    68   (is (= (+ (imaginary -2) (complex -3 -7)) (complex -3 -9)))

    69   (is (= (+ (complex -3 -7) (imaginary -2)) (complex -3 -9)))

    70   (is (= (+ (imaginary -2) 3) (complex 3 -2)))

    71   (is (= (+ 3 (imaginary -2)) (complex 3 -2)))

    72   (is (= (+ (imaginary -2) -1) (complex -1 -2)))

    73   (is (= (+ -1 (imaginary -2)) (complex -1 -2)))

    74   (is (= (+ (imaginary -2) (imaginary -2)) (imaginary -4)))

    75   (is (= (+ (imaginary -2) (imaginary 5)) (imaginary 3)))

    76   (is (= (+ (imaginary 5) (imaginary -2)) (imaginary 3)))

    77   (is (= (+ (imaginary 5) (complex 1 2)) (complex 1 7)))

    78   (is (= (+ (complex 1 2) (imaginary 5)) (complex 1 7)))

    79   (is (= (+ (imaginary 5) (complex -3 -7)) (complex -3 -2)))

    80   (is (= (+ (complex -3 -7) (imaginary 5)) (complex -3 -2)))

    81   (is (= (+ (imaginary 5) 3) (complex 3 5)))

    82   (is (= (+ 3 (imaginary 5)) (complex 3 5)))

    83   (is (= (+ (imaginary 5) -1) (complex -1 5)))

    84   (is (= (+ -1 (imaginary 5)) (complex -1 5)))

    85   (is (= (+ (imaginary 5) (imaginary -2)) (imaginary 3)))

    86   (is (= (+ (imaginary -2) (imaginary 5)) (imaginary 3)))

    87   (is (= (+ (imaginary 5) (imaginary 5)) (imaginary 10))))

    88 

    89 (deftest complex-subtraction

    90   (is (= (- (complex 1 2) (complex 1 2)) 0))

    91   (is (= (- (complex 1 2) (complex -3 -7)) (complex 4 9)))

    92   (is (= (- (complex -3 -7) (complex 1 2)) (complex -4 -9)))

    93   (is (= (- (complex 1 2) 3) (complex -2 2)))

    94   (is (= (- 3 (complex 1 2)) (complex 2 -2)))

    95   (is (= (- (complex 1 2) -1) (complex 2 2)))

    96   (is (= (- -1 (complex 1 2)) (complex -2 -2)))

    97   (is (= (- (complex 1 2) (imaginary -2)) (complex 1 4)))

    98   (is (= (- (imaginary -2) (complex 1 2)) (complex -1 -4)))

    99   (is (= (- (complex 1 2) (imaginary 5)) (complex 1 -3)))

   100   (is (= (- (imaginary 5) (complex 1 2)) (complex -1 3)))

   101   (is (= (- (complex -3 -7) (complex 1 2)) (complex -4 -9)))

   102   (is (= (- (complex 1 2) (complex -3 -7)) (complex 4 9)))

   103   (is (= (- (complex -3 -7) (complex -3 -7)) 0))

   104   (is (= (- (complex -3 -7) 3) (complex -6 -7)))

   105   (is (= (- 3 (complex -3 -7)) (complex 6 7)))

   106   (is (= (- (complex -3 -7) -1) (complex -2 -7)))

   107   (is (= (- -1 (complex -3 -7)) (complex 2 7)))

   108   (is (= (- (complex -3 -7) (imaginary -2)) (complex -3 -5)))

   109   (is (= (- (imaginary -2) (complex -3 -7)) (complex 3 5)))

   110   (is (= (- (complex -3 -7) (imaginary 5)) (complex -3 -12)))

   111   (is (= (- (imaginary 5) (complex -3 -7)) (complex 3 12)))

   112   (is (= (- 3 (complex 1 2)) (complex 2 -2)))

   113   (is (= (- (complex 1 2) 3) (complex -2 2)))

   114   (is (= (- 3 (complex -3 -7)) (complex 6 7)))

   115   (is (= (- (complex -3 -7) 3) (complex -6 -7)))

   116   (is (= (- 3 (imaginary -2)) (complex 3 2)))

   117   (is (= (- (imaginary -2) 3) (complex -3 -2)))

   118   (is (= (- 3 (imaginary 5)) (complex 3 -5)))

   119   (is (= (- (imaginary 5) 3) (complex -3 5)))

   120   (is (= (- -1 (complex 1 2)) (complex -2 -2)))

   121   (is (= (- (complex 1 2) -1) (complex 2 2)))

   122   (is (= (- -1 (complex -3 -7)) (complex 2 7)))

   123   (is (= (- (complex -3 -7) -1) (complex -2 -7)))

   124   (is (= (- -1 (imaginary -2)) (complex -1 2)))

   125   (is (= (- (imaginary -2) -1) (complex 1 -2)))

   126   (is (= (- -1 (imaginary 5)) (complex -1 -5)))

   127   (is (= (- (imaginary 5) -1) (complex 1 5)))

   128   (is (= (- (imaginary -2) (complex 1 2)) (complex -1 -4)))

   129   (is (= (- (complex 1 2) (imaginary -2)) (complex 1 4)))

   130   (is (= (- (imaginary -2) (complex -3 -7)) (complex 3 5)))

   131   (is (= (- (complex -3 -7) (imaginary -2)) (complex -3 -5)))

   132   (is (= (- (imaginary -2) 3) (complex -3 -2)))

   133   (is (= (- 3 (imaginary -2)) (complex 3 2)))

   134   (is (= (- (imaginary -2) -1) (complex 1 -2)))

   135   (is (= (- -1 (imaginary -2)) (complex -1 2)))

   136   (is (= (- (imaginary -2) (imaginary -2)) 0))

   137   (is (= (- (imaginary -2) (imaginary 5)) (imaginary -7)))

   138   (is (= (- (imaginary 5) (imaginary -2)) (imaginary 7)))

   139   (is (= (- (imaginary 5) (complex 1 2)) (complex -1 3)))

   140   (is (= (- (complex 1 2) (imaginary 5)) (complex 1 -3)))

   141   (is (= (- (imaginary 5) (complex -3 -7)) (complex 3 12)))

   142   (is (= (- (complex -3 -7) (imaginary 5)) (complex -3 -12)))

   143   (is (= (- (imaginary 5) 3) (complex -3 5)))

   144   (is (= (- 3 (imaginary 5)) (complex 3 -5)))

   145   (is (= (- (imaginary 5) -1) (complex 1 5)))

   146   (is (= (- -1 (imaginary 5)) (complex -1 -5)))

   147   (is (= (- (imaginary 5) (imaginary -2)) (imaginary 7)))

   148   (is (= (- (imaginary -2) (imaginary 5)) (imaginary -7)))

   149   (is (= (- (imaginary 5) (imaginary 5)) 0)))

   150 

   151 (deftest complex-multiplication

   152   (is (= (* (complex 1 2) (complex 1 2)) (complex -3 4)))

   153   (is (= (* (complex 1 2) (complex -3 -7)) (complex 11 -13)))

   154   (is (= (* (complex -3 -7) (complex 1 2)) (complex 11 -13)))

   155   (is (= (* (complex 1 2) 3) (complex 3 6)))

   156   (is (= (* 3 (complex 1 2)) (complex 3 6)))

   157   (is (= (* (complex 1 2) -1) (complex -1 -2)))

   158   (is (= (* -1 (complex 1 2)) (complex -1 -2)))

   159   (is (= (* (complex 1 2) (imaginary -2)) (complex 4 -2)))

   160   (is (= (* (imaginary -2) (complex 1 2)) (complex 4 -2)))

   161   (is (= (* (complex 1 2) (imaginary 5)) (complex -10 5)))

   162   (is (= (* (imaginary 5) (complex 1 2)) (complex -10 5)))

   163   (is (= (* (complex -3 -7) (complex 1 2)) (complex 11 -13)))

   164   (is (= (* (complex 1 2) (complex -3 -7)) (complex 11 -13)))

   165   (is (= (* (complex -3 -7) (complex -3 -7)) (complex -40 42)))

   166   (is (= (* (complex -3 -7) 3) (complex -9 -21)))

   167   (is (= (* 3 (complex -3 -7)) (complex -9 -21)))

   168   (is (= (* (complex -3 -7) -1) (complex 3 7)))

   169   (is (= (* -1 (complex -3 -7)) (complex 3 7)))

   170   (is (= (* (complex -3 -7) (imaginary -2)) (complex -14 6)))

   171   (is (= (* (imaginary -2) (complex -3 -7)) (complex -14 6)))

   172   (is (= (* (complex -3 -7) (imaginary 5)) (complex 35 -15)))

   173   (is (= (* (imaginary 5) (complex -3 -7)) (complex 35 -15)))

   174   (is (= (* 3 (complex 1 2)) (complex 3 6)))

   175   (is (= (* (complex 1 2) 3) (complex 3 6)))

   176   (is (= (* 3 (complex -3 -7)) (complex -9 -21)))

   177   (is (= (* (complex -3 -7) 3) (complex -9 -21)))

   178   (is (= (* 3 (imaginary -2)) (imaginary -6)))

   179   (is (= (* (imaginary -2) 3) (imaginary -6)))

   180   (is (= (* 3 (imaginary 5)) (imaginary 15)))

   181   (is (= (* (imaginary 5) 3) (imaginary 15)))

   182   (is (= (* -1 (complex 1 2)) (complex -1 -2)))

   183   (is (= (* (complex 1 2) -1) (complex -1 -2)))

   184   (is (= (* -1 (complex -3 -7)) (complex 3 7)))

   185   (is (= (* (complex -3 -7) -1) (complex 3 7)))

   186   (is (= (* -1 (imaginary -2)) (imaginary 2)))

   187   (is (= (* (imaginary -2) -1) (imaginary 2)))

   188   (is (= (* -1 (imaginary 5)) (imaginary -5)))

   189   (is (= (* (imaginary 5) -1) (imaginary -5)))

   190   (is (= (* (imaginary -2) (complex 1 2)) (complex 4 -2)))

   191   (is (= (* (complex 1 2) (imaginary -2)) (complex 4 -2)))

   192   (is (= (* (imaginary -2) (complex -3 -7)) (complex -14 6)))

   193   (is (= (* (complex -3 -7) (imaginary -2)) (complex -14 6)))

   194   (is (= (* (imaginary -2) 3) (imaginary -6)))

   195   (is (= (* 3 (imaginary -2)) (imaginary -6)))

   196   (is (= (* (imaginary -2) -1) (imaginary 2)))

   197   (is (= (* -1 (imaginary -2)) (imaginary 2)))

   198   (is (= (* (imaginary -2) (imaginary -2)) -4))

   199   (is (= (* (imaginary -2) (imaginary 5)) 10))

   200   (is (= (* (imaginary 5) (imaginary -2)) 10))

   201   (is (= (* (imaginary 5) (complex 1 2)) (complex -10 5)))

   202   (is (= (* (complex 1 2) (imaginary 5)) (complex -10 5)))

   203   (is (= (* (imaginary 5) (complex -3 -7)) (complex 35 -15)))

   204   (is (= (* (complex -3 -7) (imaginary 5)) (complex 35 -15)))

   205   (is (= (* (imaginary 5) 3) (imaginary 15)))

   206   (is (= (* 3 (imaginary 5)) (imaginary 15)))

   207   (is (= (* (imaginary 5) -1) (imaginary -5)))

   208   (is (= (* -1 (imaginary 5)) (imaginary -5)))

   209   (is (= (* (imaginary 5) (imaginary -2)) 10))

   210   (is (= (* (imaginary -2) (imaginary 5)) 10))

   211   (is (= (* (imaginary 5) (imaginary 5)) -25)))

   212 

   213 (deftest complex-division

   214   (is (= (/ (complex 1 2) (complex 1 2)) 1))

   215   (is (= (/ (complex 1 2) (complex -3 -7)) (complex -17/58 1/58)))

   216   (is (= (/ (complex -3 -7) (complex 1 2)) (complex -17/5 -1/5)))

   217   (is (= (/ (complex 1 2) 3) (complex 1/3 2/3)))

   218   (is (= (/ 3 (complex 1 2)) (complex 3/5 -6/5)))

   219   (is (= (/ (complex 1 2) -1) (complex -1 -2)))

   220   (is (= (/ -1 (complex 1 2)) (complex -1/5 2/5)))

   221   (is (= (/ (complex 1 2) (imaginary -2)) (complex -1 1/2)))

   222   (is (= (/ (imaginary -2) (complex 1 2)) (complex -4/5 -2/5)))

   223   (is (= (/ (complex 1 2) (imaginary 5)) (complex 2/5 -1/5)))

   224   (is (= (/ (imaginary 5) (complex 1 2)) (complex 2 1)))

   225   (is (= (/ (complex -3 -7) (complex 1 2)) (complex -17/5 -1/5)))

   226   (is (= (/ (complex 1 2) (complex -3 -7)) (complex -17/58 1/58)))

   227   (is (= (/ (complex -3 -7) (complex -3 -7)) 1))

   228   (is (= (/ (complex -3 -7) 3) (complex -1 -7/3)))

   229   (is (= (/ 3 (complex -3 -7)) (complex -9/58 21/58)))

   230   (is (= (/ (complex -3 -7) -1) (complex 3 7)))

   231   (is (= (/ -1 (complex -3 -7)) (complex 3/58 -7/58)))

   232   (is (= (/ (complex -3 -7) (imaginary -2)) (complex 7/2 -3/2)))

   233   (is (= (/ (imaginary -2) (complex -3 -7)) (complex 7/29 3/29)))

   234   (is (= (/ (complex -3 -7) (imaginary 5)) (complex -7/5 3/5)))

   235   (is (= (/ (imaginary 5) (complex -3 -7)) (complex -35/58 -15/58)))

   236   (is (= (/ 3 (complex 1 2)) (complex 3/5 -6/5)))

   237   (is (= (/ (complex 1 2) 3) (complex 1/3 2/3)))

   238   (is (= (/ 3 (complex -3 -7)) (complex -9/58 21/58)))

   239   (is (= (/ (complex -3 -7) 3) (complex -1 -7/3)))

   240   #_(is (= (/ 3 (imaginary -2)) (imaginary 1.5)))

   241   (is (= (/ (imaginary -2) 3) (imaginary -2/3)))

   242   (is (= (/ 3 (imaginary 5)) (imaginary -3/5)))

   243   (is (= (/ (imaginary 5) 3) (imaginary 5/3)))

   244   (is (= (/ -1 (complex 1 2)) (complex -1/5 2/5)))

   245   (is (= (/ (complex 1 2) -1) (complex -1 -2)))

   246   (is (= (/ -1 (complex -3 -7)) (complex 3/58 -7/58)))

   247   (is (= (/ (complex -3 -7) -1) (complex 3 7)))

   248   (is (= (/ -1 (imaginary -2)) (imaginary -1/2)))

   249   (is (= (/ (imaginary -2) -1) (imaginary 2)))

   250   (is (= (/ -1 (imaginary 5)) (imaginary 1/5)))

   251   (is (= (/ (imaginary 5) -1) (imaginary -5)))

   252   (is (= (/ (imaginary -2) (complex 1 2)) (complex -4/5 -2/5)))

   253   (is (= (/ (complex 1 2) (imaginary -2)) (complex -1 1/2)))

   254   (is (= (/ (imaginary -2) (complex -3 -7)) (complex 7/29 3/29)))

   255   (is (= (/ (complex -3 -7) (imaginary -2)) (complex 7/2 -3/2)))

   256   (is (= (/ (imaginary -2) 3) (imaginary -2/3)))

   257   (is (= (/ 3 (imaginary -2)) (imaginary 3/2)))

   258   (is (= (/ (imaginary -2) -1) (imaginary 2)))

   259   (is (= (/ -1 (imaginary -2)) (imaginary -1/2)))

   260   (is (= (/ (imaginary -2) (imaginary -2)) 1))

   261   (is (= (/ (imaginary -2) (imaginary 5)) -2/5))

   262   (is (= (/ (imaginary 5) (imaginary -2)) -5/2))

   263   (is (= (/ (imaginary 5) (complex 1 2)) (complex 2 1)))

   264   (is (= (/ (complex 1 2) (imaginary 5)) (complex 2/5 -1/5)))

   265   (is (= (/ (imaginary 5) (complex -3 -7)) (complex -35/58 -15/58)))

   266   (is (= (/ (complex -3 -7) (imaginary 5)) (complex -7/5 3/5)))

   267   (is (= (/ (imaginary 5) 3) (imaginary 5/3)))

   268   (is (= (/ 3 (imaginary 5)) (imaginary -3/5)))

   269   (is (= (/ (imaginary 5) -1) (imaginary -5)))

   270   (is (= (/ -1 (imaginary 5)) (imaginary 1/5)))

   271   (is (= (/ (imaginary 5) (imaginary -2)) -5/2))

   272   (is (= (/ (imaginary -2) (imaginary 5)) -2/5))

   273   (is (= (/ (imaginary 5) (imaginary 5)) 1)))

   274 

   275 (deftest complex-conjugate

   276   (is (= (conjugate (complex 1 2)) (complex 1 -2)))

   277   (is (= (conjugate (complex -3 -7)) (complex -3 7)))

   278   (is (= (conjugate (imaginary -2)) (imaginary 2)))

   279   (is (= (conjugate (imaginary 5)) (imaginary -5))))

   280 

   281 (deftest complex-abs

   282   (doseq [c [(complex 1 2) (complex -2 3) (complex 4 -2)

   283 	     (complex -3 -7) (imaginary -2) (imaginary 5)]]

   284     (is (approx= (* c (conjugate c))

   285 		 (sqr (abs c))

   286 		 1e-14))))

   287 

   288 (deftest complex-sqrt

   289   (doseq [c [(complex 1 2) (complex -2 3) (complex 4 -2)

   290 	     (complex -3 -7) (imaginary -2) (imaginary 5)]]

   291     (let [r (sqrt c)]

   292       (is (approx= c (sqr r) 1e-14))

   293       (is (>= (real r) 0)))))

   294 

   295 (deftest complex-exp

   296   (is (approx= (exp (complex 1 2))

   297 	       (complex -1.1312043837568135 2.4717266720048188)

   298 	       1e-14))

   299   (is (approx= (exp (complex 2 3))

   300 	       (complex -7.3151100949011028 1.0427436562359045)

   301 	       1e-14))

   302   (is (approx= (exp (complex 4 -2))

   303 	       (complex -22.720847417619233 -49.645957334580565)

   304 	       1e-14))

   305   (is (approx= (exp (complex 3 -7))

   306 	       (complex 15.142531566086868 -13.195928586605717)

   307 	       1e-14))

   308   (is (approx= (exp (imaginary -2))

   309 	       (complex -0.41614683654714241 -0.90929742682568171)

   310 	       1e-14))

   311   (is (approx= (exp (imaginary 5))

   312 	       (complex 0.2836621854632263 -0.95892427466313845)

   313 	       1e-14)))
author	Robert McIntyre <rlm@mit.edu>
date	Sat, 21 Aug 2010 06:25:44 -0400
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