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
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
|
import unittest
from polymatrix.polystruct import init_equation, init_poly_matrix
from polymatrix.utils import variable_to_index
class TestPolyMatrix(unittest.TestCase):
@staticmethod
def assert_term_in_eq(result, degree, eq_idx, row_idx, value, monoms=None):
if monoms is None:
monoms = tuple()
assert degree in result.terms, f'could not find {degree} in {result.terms}'
degree_terms = result.terms[degree]
key = eq_idx, monoms, row_idx
assert key in degree_terms, f'could not find {key} in {degree_terms}'
# eq_terms = degree_terms[key]
# assert row_idx in eq_terms, f'could not find {row_idx} in {eq_terms}'
assert degree_terms[key] == value, f'value {degree_terms[key]} and {value} do not match'
def test_param_matrix_param_d0_vector_degree_d0(self):
"""
param = [a11 a21 a31 a41 v11 v21]
"""
n_var = 2
mat = init_poly_matrix(degrees=(0,), shape=(n_var, n_var))
vec = init_poly_matrix(degrees=(0,), shape=(n_var, 1))
eq = init_equation(
terms = [(mat, vec)],
n_var = n_var,
)
result = eq.create()
offset_dict = eq.offset_dict
# a11 v11
self.assert_term_in_eq(
result = result,
degree = 2,
eq_idx = 0,
row_idx = (offset_dict[(mat, 0)], offset_dict[(vec, 0)]),
value = 1,
)
# a12 v21
self.assert_term_in_eq(
result = result,
degree = 2,
eq_idx = 0,
row_idx = (offset_dict[(mat, 0)]+2, offset_dict[(vec, 0)]+1),
value = 1,
)
# a21 v11
self.assert_term_in_eq(
result = result,
degree = 2,
eq_idx = 1,
row_idx = (offset_dict[(mat, 0)]+1, offset_dict[(vec, 0)]),
value = 1,
)
# a22 v21
self.assert_term_in_eq(
result = result,
degree = 2,
eq_idx = 1,
row_idx = (offset_dict[(mat, 0)]+3, offset_dict[(vec, 0)]+1),
value = 1,
)
def test_param_matrix_d0_param_vector_d01(self):
"""
param = [a11 a21 a31 a41 v011 v021 v111 v112 v121 v122]
"""
n_var = 2
mat = init_poly_matrix(degrees=(0,), shape=(n_var, n_var))
vec = init_poly_matrix(degrees=(0,1), shape=(n_var, 1))
eq = init_equation(
terms = [(mat, vec)],
n_var = n_var,
)
result = eq.create()
offset_dict = eq.offset_dict
# a11 v011
self.assert_term_in_eq(
result = result,
degree = 2,
eq_idx = 0,
row_idx = (offset_dict[(mat, 0)], offset_dict[(vec, 0)]),
value = 1,
)
# a11 v011
self.assert_term_in_eq(
result = result,
degree = 2,
eq_idx = 0,
monoms=(0,),
row_idx = (offset_dict[(mat, 0)], offset_dict[(vec, 1)]),
value = 1,
)
def test_param_matrix_d0_const_vector_d0(self):
"""
param = [a11 a21 a31 a41]
"""
n_var = 2
mat = init_poly_matrix(degrees=(0,), shape=(n_var, n_var))
vec = init_poly_matrix(subs={0: {(0, 0, 0): 1, (1, 0, 0): 1}}, shape=(n_var, 1))
eq = init_equation(
terms = [(mat, vec)],
n_var = n_var,
)
result = eq.create()
offset_dict = eq.offset_dict
# a11
self.assert_term_in_eq(
result = result,
degree = 1,
eq_idx = 0,
row_idx = (offset_dict[(mat, 0)],),
value = 1,
)
# a21
self.assert_term_in_eq(
result = result,
degree = 1,
eq_idx = 1,
row_idx = (offset_dict[(mat, 0)]+1,),
value = 1,
)
def test_param_matrix_d0_const_vector_d1(self):
"""
param = [a11 a21 a31 a41]
"""
n_var = 2
mat = init_poly_matrix(degrees=(0,), shape=(n_var, n_var))
vec = init_poly_matrix(subs={1: {(0, 0, 0): 1, (0, 0, 1): 0, (1, 0, 0): 0, (1, 0, 1): 1}}, shape=(n_var, 1))
eq = init_equation(
terms = [(mat, vec)],
n_var = n_var,
)
result = eq.create()
offset_dict = eq.offset_dict
# a11
self.assert_term_in_eq(
result = result,
degree = 1,
eq_idx = 0,
monoms=(0,),
row_idx = (offset_dict[(mat, 0)],),
value = 1,
)
# a12
self.assert_term_in_eq(
result = result,
degree = 1,
eq_idx = 0,
monoms=(1,),
row_idx = (offset_dict[(mat, 0)]+2,),
value = 1,
)
# a21
self.assert_term_in_eq(
result = result,
degree = 1,
eq_idx = 1,
monoms=(0,),
row_idx = (offset_dict[(mat, 0)]+1,),
value = 1,
)
def test_const_matrix_const_vector_degree_0(self):
"""
param = [a11 a21 a31 a41]
"""
n_var = 2
mat = init_poly_matrix(subs={0: {(0, 0, 0): 1, (0, 1, 0): 1, (1, 0, 0): 1, (1, 1, 0): 1}}, shape=(n_var, n_var))
vec = init_poly_matrix(subs={0: {(0, 0, 0): 1, (1, 0, 0): 1}}, shape=(n_var, 1))
eq = init_equation(
terms = [(mat, vec)],
n_var = n_var,
)
result = eq.create()
offset_dict = eq.offset_dict
self.assert_term_in_eq(
result = result,
degree = 0,
eq_idx = 0,
row_idx = tuple(),
value = 2,
)
def test_skew_symmetric_param_matrix_const_vector(self):
"""
param = [a11 a21 a31 a41]
"""
def skew_symmetric(degree, poly_row, poly_col, monom):
if poly_row == poly_col:
return poly_row, poly_col, monom, 0
elif poly_col < poly_row:
return poly_col, poly_row, monom, -1
n_var = 2
mat = init_poly_matrix(
degrees=(0,),
re_index=skew_symmetric,
shape=(n_var, n_var),
)
vec = init_poly_matrix(subs={0: {(0, 0, 0): 1, (1, 0, 0): 1}}, shape=(n_var, 1))
eq = init_equation(
terms = [(mat, vec)],
n_var = n_var,
)
result = eq.create()
offset_dict = eq.offset_dict
self.assert_term_in_eq(
result = result,
degree = 1,
eq_idx = 0,
row_idx = (offset_dict[(mat, 0)] + 2,),
value = 1,
)
self.assert_term_in_eq(
result = result,
degree = 1,
eq_idx = 1,
row_idx = (offset_dict[(mat, 0)] + 2,),
value = -1,
)
def test_const_matrix_d0_param_gradient_vector_d1(self):
"""
param = [v11 v12 v21 v22]
"""
def gradient(degree, p_row, p_col, monom):
if degree == 1:
factor = sum(p_row==e for e in monom) + 1
if monom[-1] < p_row:
n_p_row = monom[-1]
n_monom = sorted(monom + (p_row,), reverse=True)
if p_row <= monom[-1]:
n_p_row = p_row
n_monom = monom
return n_p_row, p_col, n_monom, factor
n_var = 2
mat = init_poly_matrix(
subs={0: {(0, 0, 0): 1, (0, 1, 0): 1, (1, 0, 0): 1, (1, 1, 0): 1}},
shape=(n_var, n_var),
)
vec = init_poly_matrix(
degrees=(1,),
re_index=gradient,
shape=(n_var, 1),
)
eq = init_equation(
terms = [(mat, vec)],
n_var = n_var,
)
result = eq.create()
offset_dict = eq.offset_dict
self.assert_term_in_eq(
result = result,
degree = 1,
monoms=(0,),
eq_idx = 0,
row_idx = (offset_dict[(vec, 1)],),
value = 2,
)
self.assert_term_in_eq(
result = result,
degree = 1,
monoms=(1,),
eq_idx = 0,
row_idx = (offset_dict[(vec, 1)]+2,),
value = 1,
)
self.assert_term_in_eq(
result = result,
degree = 1,
monoms=(0,),
eq_idx = 1,
row_idx = (offset_dict[(vec, 1)]+2,),
value = 1,
)
|
