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authorMarkSafronov <>2011-10-17 10:08:12 (GMT)
committerhdiff <hdiff@luite.com>2011-10-17 10:08:12 (GMT)
commit463ce8e06512065219ac67b188a254bf91ccc6da (patch)
tree2886a0a131634f7c284d5d736c4641babb669473
version 0.10.1
-rw-r--r--LICENSE34
-rw-r--r--Numeric/Functions/Theta.hs91
-rw-r--r--Setup.hs2
-rw-r--r--theta-functions.cabal62
4 files changed, 189 insertions, 0 deletions
diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
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diff --git a/Numeric/Functions/Theta.hs b/Numeric/Functions/Theta.hs
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index 0000000..b07e25e
--- /dev/null
+++ b/Numeric/Functions/Theta.hs
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+-- | Theta-functions implemented on top of trigonometric series.
+-- Theta-functions are special functions of several complex variables
+-- Their importance is that we can construct an elliptic functions from
+-- combination of theta-functions
+-- http://en.wikipedia.org/wiki/Theta_function
+-- Depend on parameter <tau>, which should be positive
+-- Call every function as thetaN <n> (qpar <tau>) <u>
+-- where <n> is a number of addends in series representing the function
+-- <tau> is a tau parameter defining the theta-function
+-- <u> is an argument, which is a complex number
+--
+-- WARNING: theta-functions are raising their values very quickly when arg is raising.
+-- This depends on behaviour of cos and sin of complex functions,
+-- which are very rapidly increasing their values.
+-- Call theta-functions with n < 20, q < 1, |u| < pi
+
+module Numeric.Functions.Theta (
+ qpar,
+ theta1,
+ theta2,
+ theta3,
+ theta4
+) where
+
+-- We do not use parallelism yet
+-- import Control.Parallel
+-- import Control.Parallel.Strategies
+
+-- We work with complex numbers only
+import Data.Complex
+-- And we have exceptional situations
+import Control.Exception
+
+-- | Theta-function depends on parameter q, which abs should be lower than 1
+-- Parameter q, however, depends on the main parameter tau,
+-- so we will make q dependent variable
+qpar :: RealFloat a => a -> Complex a
+qpar tau
+ | tau > 0 = exp $ (pi :+ 0) * (0 :+ tau) * (0 :+ 1)
+ | otherwise = throw $ ErrorCall "tau should be > 0 !"
+
+-- | This is an analogue to $ (-1)^n $
+signfun :: (RealFloat a) => Integer -> Complex a
+signfun nn
+ | odd nn = ((-1) :+ 0)
+ | otherwise = (1 :+ 0)
+
+-- | Function $ q^n^2 $
+qfun1 :: (RealFloat a) => Complex a -> Integer -> Complex a
+qfun1 q n = q ** (fromInteger n) ** 2
+
+-- | Function $ q^{n + 1/2}^2 $
+qfun2 :: (RealFloat a) => Complex a -> Integer -> Complex a
+qfun2 q n = q ** (0.5 + fromInteger n) ** 2
+
+-- | Cosine function tailored for our types
+cosfun :: (RealFloat a) => Complex a -> Integer -> Complex a
+cosfun u n = cos $ u * fromInteger n
+
+-- | Sine function tailored for our types
+sinfun :: (RealFloat a) => Complex a -> Integer -> Complex a
+sinfun u n = sin $ u * fromInteger n
+
+-- | \Theta_1
+theta1 :: (RealFloat a) => Integer -> Complex a -> Complex a -> Complex a
+theta1 n q u = (* 2) . sum $ map (theta1_arg q u) [0..n]
+
+theta1_arg :: (RealFloat a) => Complex a -> Complex a -> Integer -> Complex a
+theta1_arg q u nn = (signfun nn) * (qfun2 q nn) * (sinfun u (2 * nn + 1))
+
+-- | \Theta_2
+theta2 :: (RealFloat a) => Integer -> Complex a -> Complex a -> Complex a
+theta2 n q u = (* 2) . sum $ map (theta2_arg q u) [0..n]
+
+theta2_arg :: (RealFloat a) => Complex a -> Complex a -> Integer -> Complex a
+theta2_arg q u nn = (qfun2 q nn) * (cosfun u (2 * nn + 1))
+
+-- | \Theta_3
+theta3 :: (RealFloat a) => Integer -> Complex a -> Complex a -> Complex a
+theta3 n q u = (+ 1) . (* 2) . sum $ map (theta3_arg q u) [1..n]
+
+theta3_arg :: (RealFloat a) => Complex a -> Complex a -> Integer -> Complex a
+theta3_arg q u nn = (qfun1 q nn) * (cosfun u (2 * nn))
+
+-- | \Theta_4
+theta4 :: (RealFloat a) => Integer -> Complex a -> Complex a -> Complex a
+theta4 n q u = (+ 1) . (* 2) . sum $ map (theta4_arg q u) [1..n]
+
+theta4_arg :: (RealFloat a) => Complex a -> Complex a -> Integer -> Complex a
+theta4_arg q u nn = (signfun nn) * (qfun1 q nn) * (cosfun u (2 * nn))
+
diff --git a/Setup.hs b/Setup.hs
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+++ b/Setup.hs
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+import Distribution.Simple
+main = defaultMain
diff --git a/theta-functions.cabal b/theta-functions.cabal
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+++ b/theta-functions.cabal
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+-- theta-functions.cabal auto-generated by cabal init. For additional
+-- options, see
+-- http://www.haskell.org/cabal/release/cabal-latest/doc/users-guide/authors.html#pkg-descr.
+-- The name of the package.
+Name: theta-functions
+
+-- The package version. See the Haskell package versioning policy
+-- (http://www.haskell.org/haskellwiki/Package_versioning_policy) for
+-- standards guiding when and how versions should be incremented.
+Version: 0.1
+
+-- A short (one-line) description of the package.
+Synopsis: Theta-functions implemented as trigonometric series
+
+-- A longer description of the package.
+Description:
+ Small and simple library for computing values of Theta functions.
+ They're the special functions of two variables. Described very well at "http://en.wikipedia.org/wiki/Theta_function".
+ Library exports four theta-functions and a small helper to calculate their second parameter.
+ Theta functions are functions of Complex variables, FYI.
+
+-- The license under which the package is released.
+License: PublicDomain
+
+-- The file containing the license text.
+License-file: LICENSE
+
+-- The package author(s).
+Author: Mark Safronov a.k.a. hijarian
+
+-- An email address to which users can send suggestions, bug reports,
+-- and patches.
+Maintainer: hijarian@gmail.com
+
+-- A copyright notice.
+-- Copyright:
+
+Category: Math
+
+Build-type: Simple
+
+-- Extra files to be distributed with the package, such as examples or
+-- a README.
+-- Extra-source-files:
+
+-- Constraint on the version of Cabal needed to build this package.
+Cabal-version: >=1.2
+
+
+Library
+ -- Modules exported by the library.
+ Exposed-modules: Numeric.Functions.Theta
+
+ -- Packages needed in order to build this package.
+ Build-Depends: base >= 4.3 && < 5
+
+ -- Modules not exported by this package.
+ -- Other-modules:
+
+ -- Extra tools (e.g. alex, hsc2hs, ...) needed to build the source.
+ -- Build-tools:
+