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Diffstat (limited to 'src/clojure/contrib/complex_numbers.clj')
-rw-r--r-- | src/clojure/contrib/complex_numbers.clj | 293 |
1 files changed, 0 insertions, 293 deletions
diff --git a/src/clojure/contrib/complex_numbers.clj b/src/clojure/contrib/complex_numbers.clj deleted file mode 100644 index 01f90b9c..00000000 --- a/src/clojure/contrib/complex_numbers.clj +++ /dev/null @@ -1,293 +0,0 @@ -;; Complex numbers - -;; by Konrad Hinsen -;; last updated May 4, 2009 - -;; Copyright (c) Konrad Hinsen, 2009. 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 - #^{:author "Konrad Hinsen" - :doc "Complex numbers - NOTE: This library is in evolution. Most math functions are - not implemented yet."} - clojure.contrib.complex-numbers - (:refer-clojure :exclude (deftype)) - (:use [clojure.contrib.types :only (deftype)] - [clojure.contrib.generic :only (root-type)]) - (:require [clojure.contrib.generic.arithmetic :as ga] - [clojure.contrib.generic.comparison :as gc] - [clojure.contrib.generic.math-functions :as gm])) - -; -; Complex numbers are represented as struct maps. The real and imaginary -; parts can be of any type for which arithmetic and maths functions -; are defined. -; -(defstruct complex-struct :real :imag) - -; -; The general complex number type -; -(deftype ::complex complex - (fn [real imag] (struct complex-struct real imag)) - (fn [c] (vals c))) - -(derive ::complex root-type) - -; -; A specialized subtype for pure imaginary numbers. Introducing this type -; reduces the number of operations by eliminating additions with and -; multiplications by zero. -; -(deftype ::pure-imaginary imaginary - (fn [imag] (struct complex-struct 0 imag)) - (fn [c] (list (:imag c)))) - -(derive ::pure-imaginary ::complex) - -; -; Extraction of real and imaginary parts -; -(def real (accessor complex-struct :real)) -(def imag (accessor complex-struct :imag)) - -; -; Equality and zero test -; -(defmethod gc/zero? ::complex - [x] - (let [[rx ix] (vals x)] - (and (zero? rx) (zero? ix)))) - -(defmethod gc/= [::complex ::complex] - [x y] - (let [[rx ix] (vals x) - [ry iy] (vals y)] - (and (gc/= rx ry) (gc/= ix iy)))) - -(defmethod gc/= [::pure-imaginary ::pure-imaginary] - [x y] - (gc/= (imag x) (imag y))) - -(defmethod gc/= [::complex ::pure-imaginary] - [x y] - (let [[rx ix] (vals x)] - (and (gc/zero? rx) (gc/= ix (imag y))))) - -(defmethod gc/= [::pure-imaginary ::complex] - [x y] - (let [[ry iy] (vals y)] - (and (gc/zero? ry) (gc/= (imag x) iy)))) - -(defmethod gc/= [::complex root-type] - [x y] - (let [[rx ix] (vals x)] - (and (gc/zero? ix) (gc/= rx y)))) - -(defmethod gc/= [root-type ::complex] - [x y] - (let [[ry iy] (vals y)] - (and (gc/zero? iy) (gc/= x ry)))) - -(defmethod gc/= [::pure-imaginary root-type] - [x y] - (and (gc/zero? (imag x)) (gc/zero? y))) - -(defmethod gc/= [root-type ::pure-imaginary] - [x y] - (and (gc/zero? x) (gc/zero? (imag y)))) - -; -; Addition -; -(defmethod ga/+ [::complex ::complex] - [x y] - (let [[rx ix] (vals x) - [ry iy] (vals y)] - (complex (ga/+ rx ry) (ga/+ ix iy)))) - -(defmethod ga/+ [::pure-imaginary ::pure-imaginary] - [x y] - (imaginary (ga/+ (imag x) (imag y)))) - -(defmethod ga/+ [::complex ::pure-imaginary] - [x y] - (let [[rx ix] (vals x)] - (complex rx (ga/+ ix (imag y))))) - -(defmethod ga/+ [::pure-imaginary ::complex] - [x y] - (let [[ry iy] (vals y)] - (complex ry (ga/+ (imag x) iy)))) - -(defmethod ga/+ [::complex root-type] - [x y] - (let [[rx ix] (vals x)] - (complex (ga/+ rx y) ix))) - -(defmethod ga/+ [root-type ::complex] - [x y] - (let [[ry iy] (vals y)] - (complex (ga/+ x ry) iy))) - -(defmethod ga/+ [::pure-imaginary root-type] - [x y] - (complex y (imag x))) - -(defmethod ga/+ [root-type ::pure-imaginary] - [x y] - (complex x (imag y))) - -; -; Negation -; -(defmethod ga/- ::complex - [x] - (let [[rx ix] (vals x)] - (complex (ga/- rx) (ga/- ix)))) - -(defmethod ga/- ::pure-imaginary - [x] - (imaginary (ga/- (imag x)))) - -; -; Subtraction is automatically supplied by ga/-, optimized implementations -; can be added later... -; - -; -; Multiplication -; -(defmethod ga/* [::complex ::complex] - [x y] - (let [[rx ix] (vals x) - [ry iy] (vals y)] - (complex (ga/- (ga/* rx ry) (ga/* ix iy)) - (ga/+ (ga/* rx iy) (ga/* ix ry))))) - -(defmethod ga/* [::pure-imaginary ::pure-imaginary] - [x y] - (ga/- (ga/* (imag x) (imag y)))) - -(defmethod ga/* [::complex ::pure-imaginary] - [x y] - (let [[rx ix] (vals x) - iy (imag y)] - (complex (ga/- (ga/* ix iy)) - (ga/* rx iy)))) - -(defmethod ga/* [::pure-imaginary ::complex] - [x y] - (let [ix (imag x) - [ry iy] (vals y)] - (complex (ga/- (ga/* ix iy)) - (ga/* ix ry)))) - -(defmethod ga/* [::complex root-type] - [x y] - (let [[rx ix] (vals x)] - (complex (ga/* rx y) (ga/* ix y)))) - -(defmethod ga/* [root-type ::complex] - [x y] - (let [[ry iy] (vals y)] - (complex (ga/* x ry) (ga/* x iy)))) - -(defmethod ga/* [::pure-imaginary root-type] - [x y] - (imaginary (ga/* (imag x) y))) - -(defmethod ga/* [root-type ::pure-imaginary] - [x y] - (imaginary (ga/* x (imag y)))) - -; -; Inversion -; -(ga/defmethod* ga / ::complex - [x] - (let [[rx ix] (vals x) - den ((ga/qsym ga /) (ga/+ (ga/* rx rx) (ga/* ix ix)))] - (complex (ga/* rx den) (ga/- (ga/* ix den))))) - -(ga/defmethod* ga / ::pure-imaginary - [x] - (imaginary (ga/- ((ga/qsym ga /) (imag x))))) - -; -; Division is automatically supplied by ga//, optimized implementations -; can be added later... -; - -; -; Conjugation -; -(defmethod gm/conjugate ::complex - [x] - (let [[r i] (vals x)] - (complex r (ga/- i)))) - -(defmethod gm/conjugate ::pure-imaginary - [x] - (imaginary (ga/- (imag x)))) - -; -; Absolute value -; -(defmethod gm/abs ::complex - [x] - (let [[r i] (vals x)] - (gm/sqrt (ga/+ (ga/* r r) (ga/* i i))))) - -(defmethod gm/abs ::pure-imaginary - [x] - (gm/abs (imag x))) - -; -; Square root -; -(let [one-half (/ 1 2) - one-eighth (/ 1 8)] - (defmethod gm/sqrt ::complex - [x] - (let [[r i] (vals x)] - (if (and (gc/zero? r) (gc/zero? i)) - 0 - (let [; The basic formula would say - ; abs (gm/sqrt (ga/+ (ga/* r r) (ga/* i i))) - ; p (gm/sqrt (ga/* one-half (ga/+ abs r))) - ; but the slightly more complicated one below - ; avoids overflow for large r or i. - ar (gm/abs r) - ai (gm/abs i) - r8 (ga/* one-eighth ar) - i8 (ga/* one-eighth ai) - abs (gm/sqrt (ga/+ (ga/* r8 r8) (ga/* i8 i8))) - p (ga/* 2 (gm/sqrt (ga/+ abs r8))) - q ((ga/qsym ga /) ai (ga/* 2 p)) - s (gm/sgn i)] - (if (gc/< r 0) - (complex q (ga/* s p)) - (complex p (ga/* s q)))))))) - -; -; Exponential function -; -(defmethod gm/exp ::complex - [x] - (let [[r i] (vals x) - exp-r (gm/exp r) - cos-i (gm/cos i) - sin-i (gm/sin i)] - (complex (ga/* exp-r cos-i) (ga/* exp-r sin-i)))) - -(defmethod gm/exp ::pure-imaginary - [x] - (let [i (imag x)] - (complex (gm/cos i) (gm/sin i)))) |