*rename

1 files changed, 266 insertions, 0 deletions

diff --git a/Data/BuiltIn/Libraries/lua-addons/addons/libs/matrices.lua b/Data/BuiltIn/Libraries/lua-addons/addons/libs/matrices.lua
new file mode 100644
index 0000000..5931aad
--- /dev/null
+++ b/Data/BuiltIn/Libraries/lua-addons/addons/libs/matrices.lua
@@ -0,0 +1,266 @@
+--[[
+Library for a matrix data structure and operations defined on it.
+]]
+
+_libs = _libs or {}
+
+require('tables')
+require('maths')
+require('vectors')
+
+local table, math, vector = _libs.tables, _libs.maths, _libs.vectors
+
+matrix = {}
+
+_libs.matrices = matrix
+
+_meta = _meta or {}
+_meta.M = _meta.M or {}
+_meta.M.__index = matrix
+_meta.M.__class = 'Matrix'
+
+-- Constructor for vectors.
+-- matrix.m is the row-dimension
+-- matrix.n is the column-dimension
+function M(t)
+    t.rows, t.cols = #t, #t[1]
+    return setmetatable(t, _meta.M)
+end
+
+-- Returns a transposed matrix.
+function matrix.transpose(m)
+    local res = {}
+    for i, row in ipairs(m) do
+        for j, val in ipairs(row) do
+            res[j][i] = val
+        end
+    end
+
+    res.rows, res.cols = m.cols, m.rows
+    return res
+end
+
+-- Returns the identity matrix of dimension n.
+function matrix.identity(n)
+    local res = {}
+    for i = 1, n do
+        res[i] = {}
+        for j = 1, n do
+            res[i][j] = i == j and 1 or 0
+        end
+    end
+
+    res.rows, res.cols = n, n
+    return setmetatable(res, _meta.M)
+end
+
+-- Returns the row and column number of the matrix.
+function matrix.dimensions(m)
+    return m.rows, m.cols
+end
+
+-- Returns the vector of the diagonal of m.
+function matrix.diag(m)
+    local res = {}
+    for i, row in ipairs(m) do
+        res[i] = row[i]
+    end
+
+    res.n = m.rows
+    return setmetatable(res, _meta.V)
+end
+
+-- Return a matrix scaled by a constant.
+function matrix.scale(m, k)
+    local res = {}
+    for i, row in ipairs(m) do
+        res[i] = {}
+        for j, val in ipairs(row) do
+            res[i][j] = val*k
+        end
+    end
+
+    res.rows, res.cols = m.rows, m.cols
+    return setmetatable(res, _meta.M)
+end
+
+-- Returns m scaled by -1 (every value negated.
+function matrix.negate(m)
+    return m:scale(-1)
+end
+
+_meta.M.__unm = matrix.negate
+
+-- Returns the nth row of a matrix as a vector.
+function matrix.row(m, n)
+    return V(m[n], n)
+end
+
+-- Returns the nth column of a matrix as a vector.
+function matrix.column(m, n)
+    local res = {}
+    for i, col in ipairs(m) do
+        res[i] = col[n]
+    end
+
+    res.n = m.m
+    return setmetatable(res, _meta.V)
+end
+
+-- Returns the determinant of a matrix.
+function matrix.det(m)
+    if m.rows == 2 then
+        return m[1][1]*m[2][2] - m[1][2]*m[2][1]
+    end
+
+    local acc = 0
+    for i, val in ipairs(m[1]) do
+        acc = acc + (-1)^i * m:exclude(1, i):det()
+    end
+
+    return acc
+end
+
+-- Returns a matrix with one row and column excluded.
+function matrix.exclude(m, exrow, excol)
+    local res = {}
+    local ik = 1
+    local jk = 1
+    for i, row in ipairs(m) do
+        if i ~= exrow then
+            res[ik] = {}
+            for j, val in ipairs(row) do
+                if j ~= excol then
+                    res[ik][jk] = val
+                    jk = jk + 1
+                end
+            end
+            ik = ik + 1
+        end
+    end
+end
+
+-- Returns two matrices added.
+function matrix.add(m1, m2)
+    local res = {}
+    for i, row in ipairs(m1) do
+        res[i] = {}
+        for j, val in ipairs(row) do
+            res[i][j] = val + m2[i][j]
+        end
+    end
+
+    res.rows, res.cols = m1.rows, m1.cols
+    return setmetatable(res, _meta.M)
+end
+
+_meta.M.__add = matrix.add
+
+-- Returns m1 subtracted by m2.
+function matrix.subtract(m1, m2)
+    local res = {}
+    for i, row in ipairs(m1) do
+        res[i] = {}
+        for j, val in ipairs(row) do
+            res[i][j] = val - m2[i][j]
+        end
+    end
+
+    res.rows, res.cols = m1.rows, m1.cols
+    return setmetatable(res, _meta.M)
+end
+
+_meta.M.__sub = matrix.subtract
+
+-- Return a matrix multiplied by another matrix or vector.
+function matrix.multiply(m1, m2)
+    local res = {}
+
+    local cols = {}
+    for i, col in ipairs(m2[1]) do
+        cols[i] = {}
+    end
+    for i, row in ipairs(m2) do
+        for j, val in ipairs(row) do
+            cols[j][i] = val
+        end
+    end
+
+    local acc
+    for i, row in ipairs(m1) do
+        res[i] = {}
+        for c, col in ipairs(cols) do
+            acc = 0
+            for j, val in ipairs(col) do
+                 acc = acc + m1[i][c]*m2[j][c]
+            end
+
+            res[i][c] = acc
+        end
+    end
+
+    res.rows, res.cols = m1.rows, m2.cols
+    return setmetatable(res, _meta.M)
+end
+
+_meta.M.__mul = matrix.multiply
+
+-- Returns an inline string representation of the matrix.
+function matrix.tostring(m)
+    local str = '['
+    for i, row in ipairs(m) do
+        if i > 1 then
+            str = str..', '
+        end
+        str = str..'['
+
+        for j, val in ipairs(row) do
+            if j > 1 then
+                str = str..', '
+            end
+            str = str..tostring(val)
+        end
+        str = str..']'
+    end
+
+    return str..']'
+end
+
+_meta.M.__tostring = matrix.tostring
+
+-- Returns a multiline string representation of the matrix.
+function matrix.tovstring(m)
+    local str = ''
+    for i, row in ipairs(m) do
+        if i > 1 then
+            str = str..'\n'
+        end
+        for j, val in ipairs(row) do
+            if j > 1 then
+                str = str..' '
+            end
+            str = str..tostring(val)
+        end
+    end
+
+    return str
+end
+
+function matrix.vprint(m)
+    if log then
+        log(m:tovstring())
+    end
+end
+
+--[[
+Copyright © 2013, Windower
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+    * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
+    * Neither the name of Windower nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL Windower BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+]]