1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
|
-- tkz_elements_matrices.lua
-- date 2024/03/25
-- version 2.20c
-- Copyright 2024 Alain Matthes
-- This work may be distributed and/or modified under the
-- conditions of the LaTeX Project Public License, either version 1.3
-- of this license or (at your option) any later version.
-- The latest version of this license is in
-- http://www.latex-project.org/lppl.txt
-- and version 1.3 or later is part of all distributions of LaTeX
-- version 2005/12/01 or later.
-- This work has the LPPL maintenance status “maintained”.
-- The Current Maintainer of this work is Alain Matthes.
-- ----------------------------------------------------------------------------
matrix={}
function matrix: new (value)
local type = 'matrix'
local rows = #value
local cols = #value[1]
local set = value
local det = determinant(value)
local o = {set = set,
rows = rows,
cols = cols,
det = det,
type = type }
setmetatable(o, self)
self.__index = self
return o
end
function matrix.__mul(m1,m2)
if getmetatable(m1) ~= matrix then return k_mul_matrix(m1, m2) end
if getmetatable(m2) ~= matrix then return k_mul_matrix(m2, m1) end
return mul_matrix(m1,m2)
end
function matrix.__add(m1,m2)
return add_matrix(m1,m2)
end
function matrix.__sub(m1,m2)
return add_matrix(m1,k_mul_matrix(-1, m2))
end
function matrix.__pow( m, num )
if num =='T' then
return transposeMatrix(m)
else
if num == 0 then
return matrix:new( #m,"I" )
end
if num < 0 then
local i; m,i = inv_matrix ( m )
if not m then return m, i end
num = -num
end
local mt = m
for i = 2,num do
mt = mul_matrix(mt,m)
end
return mt
end
end
function matrix.__tostring( A )
local mt = (A.type=='matrix' and A.set or A)
local k = {}
for i = 1,#mt do
local n = {}
for j = 1,#mt[1] do
n[j] = display(mt[i][j])
end
k[i] = table.concat(n, " ")
end
return table.concat(k)
end
function matrix.__eq( A , B )
local mt1 = (A.type=='matrix' and A.set or A)
local mt2 = (B.type=='matrix' and B.set or B)
if A.type ~= B.type then
return false
end
if #mt1 ~= #mt2 or #mt1[1] ~= #mt2[1] then
return false
end
for i = 1,#mt1 do
for j = 1,#mt1[1] do
if mt1[i][j] ~= mt2[i][j] then
return false
end
end
end
return true
end
function matrix : square(n,...)
local m = {}
local t = table.pack(...)
if n*n == #t then
for i = 1, n do
m[i] = {}
for j = 1, n do
m[i][j] = t[n*(i-1)+j]
end
end
return matrix : new (m)
else
return nil
end
end
function matrix: vector (...)
local m = {}
local t = table.pack(...)
for i = 1, #t do
m[i] = {}
m[i][1] = t[i]
end
return matrix : new (m)
end
function matrix : homogenization ()
return homogenization_ (self)
end
function matrix : htm_apply (...)
local obj,nb,t
local tp = table.pack(...)
obj = tp[1]
nb = tp.n
if nb == 1 then
if obj.type == "point" then
return htm_apply_ ( self,obj )
elseif obj.type == "line" then
return htm_apply_L_ (self,obj)
elseif obj.type == "triangle" then
return htm_apply_T_ (self,obj)
elseif obj.type == "circle" then
return htm_apply_C (self,obj)
elseif obj.type == "square"
or obj.type == "rectangle"
or obj.type == "quadrilateral"
or obj.type == "parallelogram" then
return htm_apply_Q (self,obj)
end
else
t = {}
for i=1,tp.n do
table.insert(t , htm_apply_ ( self , tp[i]))
end
return table.unpack ( t )
end
end
function matrix: k_mul (n)
return k_mul_matrix(n, self)
end
function matrix : get (i,j)
return get_element_( self,i,j )
end
function matrix: inverse ()
return inv_matrix (self)
end
function matrix: adjugate ()
return adjugate_ (self)
end
function matrix: transpose ()
return transposeMatrix (self)
end
function matrix: is_diagonal ()
return isDiagonal_ (self)
end
function matrix: is_orthogonal ()
return isOrthogonal_ (self)
end
function matrix: diagonalize () -- return two matrices D and P
return diagonalize_ (self)
end
function matrix: print (style,fmt)
local style = (style or 'bmatrix')
local fmt = (fmt or 0)
return print_matrix (self,style,fmt)
end
function matrix: identity (n)
return id_matrix (n)
end
-------------------------
-- homogeneous transformation matrix
function matrix : htm (phi,a,b,sx,sy)
local tx = (a or 0)
local ty = (b or 0)
local sx = (sx or 1)
local sy = (sy or 1)
local phi = (phi or 0)
return matrix : square (3,sx*math.cos(phi),-math.sin(phi),tx,math.sin(phi),sy*math.cos(phi),ty,0,0,1)
end
-------------------------
function matrix: is_orthogonal ()
return isOrthogonal_ (self)
end
return matrix
|