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Mahdi Dibaiee 2016-11-04 23:09:14 +03:30
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#### joe made this: http://goel.io/joe
#### haskell ####
dist
dist-*
cabal-dev
*.o
*.hi
*.chi
*.chs.h
*.dyn_o
*.dyn_hi
.hpc
.hsenv
.cabal-sandbox/
cabal.sandbox.config
*.prof
*.aux
*.hp
*.eventlog
.stack-work/
cabal.project.local
.HTF/

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GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The GNU General Public License is a free, copyleft license for
software and other kinds of works.
The licenses for most software and other practical works are designed
to take away your freedom to share and change the works. By contrast,
the GNU General Public License is intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users. We, the Free Software Foundation, use the
GNU General Public License for most of our software; it applies also to
any other work released this way by its authors. You can apply it to
your programs, too.
When we speak of free software, we are referring to freedom, not
price. Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
them if you wish), that you receive source code or can get it if you
want it, that you can change the software or use pieces of it in new
free programs, and that you know you can do these things.
To protect your rights, we need to prevent others from denying you
these rights or asking you to surrender the rights. Therefore, you have
certain responsibilities if you distribute copies of the software, or if
you modify it: responsibilities to respect the freedom of others.
For example, if you distribute copies of such a program, whether
gratis or for a fee, you must pass on to the recipients the same
freedoms that you received. You must make sure that they, too, receive
or can get the source code. And you must show them these terms so they
know their rights.
Developers that use the GNU GPL protect your rights with two steps:
(1) assert copyright on the software, and (2) offer you this License
giving you legal permission to copy, distribute and/or modify it.
For the developers' and authors' protection, the GPL clearly explains
that there is no warranty for this free software. For both users' and
authors' sake, the GPL requires that modified versions be marked as
changed, so that their problems will not be attributed erroneously to
authors of previous versions.
Some devices are designed to deny users access to install or run
modified versions of the software inside them, although the manufacturer
can do so. This is fundamentally incompatible with the aim of
protecting users' freedom to change the software. The systematic
pattern of such abuse occurs in the area of products for individuals to
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have designed this version of the GPL to prohibit the practice for those
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stand ready to extend this provision to those domains in future versions
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Finally, every program is threatened constantly by software patents.
States should not allow patents to restrict development and use of
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avoid the special danger that patents applied to a free program could
make it effectively proprietary. To prevent this, the GPL assures that
patents cannot be used to render the program non-free.
The precise terms and conditions for copying, distribution and
modification follow.
TERMS AND CONDITIONS
0. Definitions.
"This License" refers to version 3 of the GNU General Public License.
"Copyright" also means copyright-like laws that apply to other kinds of
works, such as semiconductor masks.
"The Program" refers to any copyrightable work licensed under this
License. Each licensee is addressed as "you". "Licensees" and
"recipients" may be individuals or organizations.
To "modify" a work means to copy from or adapt all or part of the work
in a fashion requiring copyright permission, other than the making of an
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earlier work or a work "based on" the earlier work.
A "covered work" means either the unmodified Program or a work based
on the Program.
To "propagate" a work means to do anything with it that, without
permission, would make you directly or secondarily liable for
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To "convey" a work means any kind of propagation that enables other
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a computer network, with no transfer of a copy,

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slope-field
===========
I was studying [this course on Integration](https://www.edx.org/course/calculus-1b-integration-mitx-18-01-2x) when I encountered
slope fields and I found them interesting!
So I thought I would give it a shot and try to write a program to draw slope fields myself!
In order to read a mathematical function definition from input, I wrote [mathexpr](/mdibaiee/mathexpr).
Get Started
-----------
If you don't already, install [Haskell Platform](https://www.haskell.org/platform/).
```
git clone https://github.com/mdibaiee/slope-field
cd slope-field
stack install
slope-field
```
Examples
--------
Parameters:
- dy/dx: derivative of the function you are trying to visualize
- range: range of numbers to draw
- estimation size: size of `deltax` which is used to draw the slope corresponding to a small point, `0.03` is usually a good number, but you might want to try out larger numbers to get a more detailed picture on some examples
```
dy/dx =
x + y
range - format: (lower, upper):
(-10, 10)
estimation size:
0.03
```
![x plus y](https://github.com/mdibaiee/slope-field/blob/master/xpy.png?raw=true)
```
dy/dx =
x * y
range - format: (lower, upper):
(-10, 10)
estimation size:
0.03
```
![x times y](https://github.com/mdibaiee/slope-field/blob/master/xty.png?raw=true)
```
dy/dx =
-y
range - format: (lower, upper):
(-10, 10)
estimation size:
0.03
```
![minus y](https://github.com/mdibaiee/slope-field/blob/master/minusy.png?raw=true)
```
dy/dx =
y/x
range - format: (lower, upper):
(-10, 10)
estimation size:
0.1
```
![y divided by x](https://github.com/mdibaiee/slope-field/blob/master/ydx.png?raw=true)

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import Distribution.Simple
main = defaultMain

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{-# LANGUAGE ScopedTypeVariables #-}
module Main where
import Lib
import System.IO
import Graphics.Rendering.Chart
import Graphics.Rendering.Chart.Backend.Cairo
import Control.Lens
import Data.Default.Class
main :: IO ()
main = do
putStrLn "dy/dx = "
math <- getLine
putStrLn "range - format: (lower, upper): "
(lower, upper) :: (Int, Int) <- read <$> getLine
putStrLn "estimation size: "
s <- read <$> getLine
let pts = points (lower, upper)
field = slopeField math pts s
let chart = toRenderable layout
where
layout = layout_title .~ "slope field"
$ layout_plots .~ [vectors]
$ def
vectors = plotVectorField
$ plot_vectors_values .~ field
$ plot_vectors_scale .~ 0
$ plot_vectors_style . vector_head_style . point_radius .~ 0
$ def
renderableToFile def "slope-field.png" chart
putStrLn "created file slope-field.png"
return ()

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name: slope-field
version: 0.1.0.0
synopsis: Visualize mathematical function's slope fields
description: Visualize mathematical function's slope fields
homepage: https://github.com/mdibaiee/slope-field
license: GPL-3
license-file: LICENSE
author: Mahdi Dibaiee
maintainer: mdibaiee@aol.com
copyright: 2016 Mahdi Dibaiee
category: Web
build-type: Simple
-- extra-source-files:
cabal-version: >=1.10
library
hs-source-dirs: src
exposed-modules: Lib
build-depends: base >= 4.7 && < 5
, mathexpr >= 0.3.0.0
, data-default-class
default-language: Haskell2010
executable slope-field
hs-source-dirs: app
main-is: Main.hs
ghc-options: -threaded -rtsopts -with-rtsopts=-N
build-depends: base
, slope-field
, Chart
, Chart-cairo
, lens
, data-default-class
default-language: Haskell2010
source-repository head
type: git
location: https://github.com/mdibaiee/slope-field

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module Lib
( points
, slopeField
) where
import Numeric.MathExpr
import Data.Default.Class
type Range = (Int, Int)
points :: Range -> [(Double, Double)]
points (lower, upper) =
let range = [lower..upper]
in [ (fromIntegral x, fromIntegral y) | x <- range, y <- range ]
slopeField :: String -> [(Double, Double)] -> Double -> [((Double, Double), (Double, Double))]
slopeField math pts diff =
let d x y = evaluate def math [("x", x), ("y", y)]
half = diff / 2
res = map (\(x, y) -> ((x - half, y), (half, d x y * diff))) pts
inf = 1/0
in filter (\((x0, y0), (x, y)) -> x < inf && y < inf && x > -inf && y > -inf) res

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# This file was automatically generated by 'stack init'
#
# Some commonly used options have been documented as comments in this file.
# For advanced use and comprehensive documentation of the format, please see:
# http://docs.haskellstack.org/en/stable/yaml_configuration/
# Resolver to choose a 'specific' stackage snapshot or a compiler version.
# A snapshot resolver dictates the compiler version and the set of packages
# to be used for project dependencies. For example:
#
# resolver: lts-3.5
# resolver: nightly-2015-09-21
# resolver: ghc-7.10.2
# resolver: ghcjs-0.1.0_ghc-7.10.2
# resolver:
# name: custom-snapshot
# location: "./custom-snapshot.yaml"
resolver: lts-7.6
# User packages to be built.
# Various formats can be used as shown in the example below.
#
# packages:
# - some-directory
# - https://example.com/foo/bar/baz-0.0.2.tar.gz
# - location:
# git: https://github.com/commercialhaskell/stack.git
# commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
# - location: https://github.com/commercialhaskell/stack/commit/e7b331f14bcffb8367cd58fbfc8b40ec7642100a
# extra-dep: true
# subdirs:
# - auto-update
# - wai
#
# A package marked 'extra-dep: true' will only be built if demanded by a
# non-dependency (i.e. a user package), and its test suites and benchmarks
# will not be run. This is useful for tweaking upstream packages.
packages:
- '.'
- '../mathexpr'
# Dependency packages to be pulled from upstream that are not in the resolver
# (e.g., acme-missiles-0.3)
extra-deps:
- mathexpr-0.3.0.0
# Override default flag values for local packages and extra-deps
flags: {}
# Extra package databases containing global packages
extra-package-dbs: []
# Control whether we use the GHC we find on the path
# system-ghc: true
#
# Require a specific version of stack, using version ranges
# require-stack-version: -any # Default
# require-stack-version: ">=1.1"
#
# Override the architecture used by stack, especially useful on Windows
# arch: i386
# arch: x86_64
#
# Extra directories used by stack for building
# extra-include-dirs: [/path/to/dir]
# extra-lib-dirs: [/path/to/dir]
#
# Allow a newer minor version of GHC than the snapshot specifies
# compiler-check: newer-minor

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main :: IO ()
main = putStrLn "Test suite not yet implemented"

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