Module:Temperament data

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Note: Do not invoke this module directly; use the corresponding template instead: Template:Temperament data.

This module depends on the following other modules: Module: Rational Module: Utils

Todo: add documentation

---

local rat = require('Module:Rational')
local p = {}

-- Complex number functions (1st element = real and 2nd element = imaginary)
local function cadd(a, b)
	return {(a[1] + b[1]), (a[2] + b[2])}
end

local function csub(a, b)
	return {(a[1] - b[1]), (a[2] - b[2])}
end

local function cmul(a, b)
	return {(a[1] * b[1] - a[2] * b[2]), (a[1] * b[2] + a[2] * b[1])}
end

local function cdiv(a, b)
	return {(a[1] * b[1] + a[2] * b[2])/(b[1]*b[1] + b[2]*b[2]), (a[2] * b[1] - a[1] * b[2])/(b[1]*b[1] + b[2]*b[2])}
end

local function matadd(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(b[1]) do
			result[i][j] = cadd(a[i][j], b[i][j])
		end
	end
	return result
end

local function matsub(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(b[1]) do
			result[i][j] = csub(a[i][j], b[i][j])
		end
	end
	return result
end

local function matmul(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(b[1]) do
			result[i][j] = {0, 0}
			for k = 1, #(a[1]) do
				result[i][j] = cadd(result[i][j], cmul(a[i][k], b[k][j]))
			end
		end
	end
	return result
end


local function scalarmatmul(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(a[1]) do
			result[i][j] = cmul(a[i][j], b)
		end
	end
	return result
end

function p.matinv(a)
	dbl_identity = {}
	for i = 1, #a do
		dbl_identity[i] = {}
		for j = 1, #a do
			if i == j then
				dbl_identity[i][j] = {2, 0}
			else
				dbl_identity[i][j] = {0, 0}
			end
		end
	end
	
	xn = scalarmatmul(a, {0.0001, 0})
	
	for i = 1, 30 do
		xn = matmul(xn, matsub(dbl_identity, matmul(a, xn)))
	end
	return xn
end

return p