Created
October 13, 2017 04:10
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Complex number library for Lua, supports all basic operations
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local complex = {} | |
do | |
function complex.init(a, b) | |
local c = {real = a, imag = b} | |
setmetatable(c, {__index = complex, | |
__add = complex.add, | |
__sub = complex.sub, | |
__mul = complex.mul, | |
__div = complex.div, | |
__pow = complex.pow, | |
__unm = complex.unm}) | |
return c | |
end | |
local function scalarDiff(a, b, tf, sf) | |
if type(b) == "table" then | |
local c = b | |
b = a | |
a = c | |
end | |
if type(b) == "table" then | |
return tf(a, b) | |
else | |
return sf(a, b) | |
end | |
end | |
local function reciprocate(z) | |
local mag = z.real * z.real + z.imag * z.imag | |
return complex(z.real / mag, -z.imag / mag) | |
end | |
function complex.add(a, b) | |
return scalarDiff(a, b, function(a, b) | |
return complex(a.real + b.real, a.imag + b.imag) | |
end, function(a, b) | |
return complex(a.real + b, a.imag) | |
end) | |
end | |
function complex.sub(a, b) | |
return complex.add(a, -b) | |
end | |
function complex.mul(a, b) | |
return scalarDiff(a, b, function(a, b) | |
return complex(a.real * b.real - a.imag * b.imag, a.real * b.imag + a.imag * b.real) | |
end, function(a, b) | |
return complex(a.real * b, a.imag * b) | |
end) | |
end | |
function complex.div(a, b) | |
if type(b) == "table" then | |
return complex.mul(a, reciprocate(b)) | |
else | |
return complex.mul(a, 1 / b) | |
end | |
end | |
function complex.pow(a, b) | |
if type(a) == "table" then | |
if type(b) ~= "table" then | |
b = complex(b, 0) | |
end | |
local arg = math.atan(a.imag / a.real) | |
local sqMag = a.real * a.real + a.imag * a.imag | |
local iC = math.pow(sqMag, b.real / 2) * math.exp(-b.imag * arg) | |
local tP = b.real * arg + 0.5 * b.imag * math.log(sqMag) | |
return complex(iC * math.cos(tP), iC * math.sin(tP)) | |
else | |
-- x^(a+bI) == x^a * E^bI == x^a * (cos(b) + Isin(b)) | |
local xa = math.pow(a, b.real) | |
return complex(xa * math.cos(b.imag), xa * math.sin(b.imag)) | |
end | |
end | |
function complex.unm(a) | |
return complex(-a.real, -a.imag) | |
end | |
setmetatable(complex, {__call=function(_, ...) return complex.init(...) end}) | |
end |
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