File size: 11,632 Bytes
389d072 |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 |
from visma.matrix.checks import isMatrix, dimCheck, multiplyCheck, isEqual
from visma.matrix.operations import simplifyMatrix, addMatrix, subMatrix, scalarAdd, scalarSub, scalarMult, scalarDiv, gauss_elim, row_echelon
from visma.matrix.structure import DiagMat, IdenMat
from visma.functions.constant import Constant
from tests.tester import getTokens
from visma.io.parser import tokensToString
####################
# matrix.structure #
####################
def test_strMatrix():
mat = getTokens("[1+x, 2; \
3 , 4]")
assert mat.__str__() == "[{1.0}+{x},{2.0};{3.0},{4.0}]"
def test_traceMat():
mat = getTokens("[1, 2, 3; \
3, 4, 7; \
4, 6, 9]")
mat.isSquare()
trace = mat.traceMat()
assert tokensToString(trace) == "14.0"
mat = getTokens("[7, 5; \
2, 0]")
mat.isSquare()
trace = mat.traceMat()
assert tokensToString(trace) == "7.0"
def test_isSquare():
mat = getTokens("[1, 0, 3; \
2, 1, 2]")
assert not mat.isSquare()
mat = getTokens("[1, 2; \
x, z]")
assert mat.isSquare()
mat = getTokens("[1, 2; \
1, 3; \
1, 4]")
assert not mat.isSquare()
def test_transposeMat():
mat = getTokens("[1, 3; \
2, 6]")
matTranspose = mat.transposeMat()
assert matTranspose.__str__() == "[{1.0},{2.0};{3.0},{6.0}]"
mat = getTokens("[5,8,2;\
12,30,9;\
4,17,7]")
matTranspose = mat.transposeMat()
assert matTranspose.__str__() == "[{5.0},{12.0},{4.0};{8.0},{30.0},{17.0};{2.0},{9.0},{7.0}]"
mat = getTokens("[5,8,2;\
2,3,4]")
matTranspose = mat.transposeMat()
assert matTranspose.__str__() == "[{5.0},{2.0};{8.0},{3.0};{2.0},{4.0}]"
mat = getTokens("[1, 2; \
3, 4]")
matTranspose = mat.transposeMat()
assert matTranspose.__str__() == "[{1.0},{3.0};{2.0},{4.0}]"
def test_isDiagonal():
mat = getTokens("[1, 0; \
0, z]")
assert mat.isDiagonal()
mat = getTokens("[1+x, 0+y; \
0, z]")
assert not mat.isDiagonal()
mat = getTokens("[1, 2; \
1, 3; \
1, 4]")
assert not mat.isDiagonal()
mat = DiagMat([3, 3], [[Constant(1)], [Constant(5)], [Constant(2)]])
assert mat.isDiagonal()
mat = IdenMat([2, 2])
assert mat.isDiagonal()
def test_isIdentity():
mat = getTokens("[1, 0; \
0, 1]")
assert mat.isIdentity()
mat = getTokens("[1+x, 0+y; \
0, 1]")
assert not mat.isIdentity()
mat = getTokens("[1, 2; \
1, 3; \
1, 4]")
assert not mat.isIdentity()
#################
# matrix.checks #
#################
def test_isMatrix():
mat = getTokens("[1, 2, 3; \
x, z, 3]")
assert isMatrix(mat)
mat = getTokens("[1, 2; \
1, 3; \
1]")
assert mat == [] # not a matrix; returns empty matrix
def test_dimCheck():
matA = getTokens("[2, x; \
3, y]")
matB = getTokens("[1, 2, x; \
2, 3, y]")
assert not dimCheck(matA, matB)
matA = getTokens("[2, x; \
3, y]")
matB = getTokens("[1, 2; \
2, 3]")
assert dimCheck(matA, matB)
def test_multiplyCheck():
matA = getTokens("[2, x; \
3, y; \
3, y]")
matB = getTokens("[2, x; \
3, y]")
assert multiplyCheck(matA, matB)
matA = getTokens("[2, x, 1; \
3, y, z]")
matB = getTokens("[1, 2; 2, 3]")
assert not multiplyCheck(matA, matB)
def test_isEqual():
matA = getTokens("[1, 2; \
x, z]")
matB = getTokens("[1, 2; \
x, z]")
assert isEqual(matA, matB)
matA = getTokens("[2, x, 1; \
3, y, z]")
matB = getTokens("[1, 2; 2, 3]")
assert not isEqual(matA, matB)
#####################
# matrix.operations #
#####################
def test_simplifyMatrix():
mat = getTokens("[x + y + x, x^2 + x^2; \
1 + 4/2 , z^3/z^2 ]")
matRes = simplifyMatrix(mat)
assert matRes.__str__() == "[2{x}+{y},2{x}^{2.0};{3.0},{z}]"
mat = getTokens("[1 + x^2 + 2]")
matRes = simplifyMatrix(mat)
assert matRes.__str__() == "[{3.0}+{x}^{2.0}]"
def test_addMatrix():
matA = getTokens("[2x + y, 2x]")
matB = getTokens("[-x, -x]")
matSum = addMatrix(matA, matB)
# assert matSum.__str__() == "[2{x}+{y}]" # BUG: Strange simplification for matSum
matA = getTokens("[ x , x^2; \
3 + x^2, xy ]")
matB = getTokens("[ y + 1 , x^2; \
2 - x^2, xy - 1 ]")
matSum = addMatrix(matA, matB)
assert matSum.__str__() == "[{x}+{y}+{1.0},2{x}^{2.0};{5.0},2{x}{y}-{1.0}]"
def test_subMatrix():
matA = getTokens("[y, 2x]")
matB = getTokens("[-x, -x]")
matSub = subMatrix(matA, matB)
assert matSub.__str__() == "[{y}--1.0{x},3.0{x}]"
def test_scalarAddMatrix():
mat = getTokens("[1, 2; \
2, 1]")
const = 2
matSum = scalarAdd(const, mat)
assert matSum.__str__() == "[{3.0},{2.0};{2.0},{3.0}]"
mat = getTokens("[1, 2, 3;\
4, 5, 6;\
7, 8, 9]")
const = 3
matSum = scalarAdd(const, mat)
assert matSum.__str__() == "[{4.0},{2.0},{3.0};{4.0},{8.0},{6.0};{7.0},{8.0},{12.0}]"
def test_scalarSubMatrix():
mat = getTokens("[8,6;\
1,9]")
const = 2
matSub = scalarSub(const, mat)
assert matSub.__str__() == "[{6.0},{6.0};{1.0},{7.0}]"
mat = getTokens("[5,8,2;\
12,30,9;\
4,17,7]")
const = 10
matSub = scalarSub(const, mat)
assert matSub.__str__() == "[{-5.0},{8.0},{2.0};{12.0},{20.0},{9.0};{4.0},{17.0},{-3.0}]"
def test_scalarMultMatrix():
mat = getTokens("[1, 2]")
const = 2
matSum = scalarMult(const, mat)
assert matSum.__str__() == "[{2.0},{4.0}]"
mat = getTokens("[2,4;\
-5,7]")
const = 2
matSum = scalarMult(const, mat)
assert matSum.__str__() == "[{4.0},{8.0};{-10.0},{14.0}]"
def test_scalarDivMatrix():
mat = getTokens("[4, 2]")
const = 2
matSum = scalarDiv(const, mat)
assert matSum.__str__() == "[{2.0},{1.0}]"
mat = getTokens("[48,36;\
24,-3]")
const = 6
matSum = scalarDiv(const, mat)
assert matSum.__str__() == "[{8.0},{6.0};{4.0},{-0.5}]"
def test_multiplyMatrix():
"""
# FIXME: Fixing addition fixes multiplication
matA = getTokens("[1, 0; 0, 1]")
matB = getTokens("[2; 3]")
matPro = multiplyMatrix(matA, matB)
# assert matPro.__str__() == ""
matA = getTokens("[1, 2; x, 2; 3, y]")
matB = getTokens("[2, x; 3, y]")
matPro = multiplyMatrix(matA, matB)
# assert matPro.__str__() == ""
matA = getTokens("[2, x, 1; \
3, y, z]")
matB = getTokens("[1, 2; 2, 3; 5, 6]")
matPro = multiplyMatrix(matA, matB)
# assert matPro.__str__() == ""
"""
pass
def test_determinant():
mat = getTokens('[1,2;3,4]')
if mat.isSquare():
a = ''
for i in mat.determinant():
a += i.__str__()
assert a == "{-2.0}"
mat = getTokens('[1,2,3;4,5,6;7,8,9]')
if mat.isSquare():
a = ''
for i in mat.determinant():
a += i.__str__()
assert a == "{0}"
mat = getTokens('[1]')
if mat.isSquare():
a = ''
for i in mat.determinant():
a += i.__str__()
assert a == "{1.0}"
def test_inverse():
mat = getTokens("[5, 7, 9;\
4, 3, 8;\
7, 5, 6]")
if mat.isSquare():
assert mat.inverse().__str__() == "[{-0.20977011494252873},{0.028735632183908046},{0.27586206896551724};{0.3023255813953489},{-0.3139534883720931},{-0.03779069767441861};{-0.009111617312072894},{0.22779043280182235},{-0.12300683371298407}]"
mat = getTokens("[4, 5;\
7, 3]")
if mat.isSquare():
assert mat.inverse().__str__() == "[{-0.1301859799713877},{0.21745350500715305};{0.303951367781155},{-0.17325227963525833}]"
mat = getTokens("[4, 5, 6, 8;\
3, 25, 4, 6;\
5, 1, 8, 4;\
1, 3, 5, 8]")
if mat.isSquare():
assert mat.inverse().__str__() == "[{0.49400000000000005},{-0.044000000000000004},{-0.08600000000000001},{-0.42400000000000004};{-0.057142857142857134},{0.049999999999999996},{0.014285714285714284},{0.0047619047619047615};{-0.40131578947368424},{0.03947368421052632},{0.25},{0.2565789473684211};{0.21321177223288548},{-0.03854766474728087},{-0.15067178502879078},{0.01599488163787588}]"
mat = getTokens("[1,1;1,1]")
if mat.isSquare():
assert mat.inverse().__str__() == "-1"
def test_cofactor():
mat = getTokens('[1,2;3,4]')
if mat.isSquare():
assert str(mat.cofactor()) == '[{4.0},{-3.0};{-2.0},{1.0}]'
mat = getTokens('[1,2,3;0,4,5;1,0,6]')
if mat.isSquare():
assert str(mat.cofactor()) == '[{24.0},{5.0},{-4.0};{-12.0},{3.0},{2.0};{-2.0},{-5.0},{4.0}]'
mat = getTokens('[1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16]')
if mat.isSquare():
assert str(mat.cofactor()) == '[{0},{0},{0},{0};{0},{0},{0},{0};{0},{0},{0},{0};{0},{0},{0},{0}]'
def test_echelon():
mat = getTokens("[1, 4, 2;\
5, 7, 6;\
2, 4, 9]")
assert row_echelon(mat).__str__() == "[{1.0},{4.0},{2.0};{0.0},{-13.0},{-4.0};{0.0},{0.0},{6.24}]"
mat = getTokens("[1, 2, 3, 1;\
4, 5, 6, 1;\
7, 8, 9, 2]")
assert row_echelon(mat).__str__() == "[{1.0},{2.0},{3.0},{1.0};{0.0},{-3.0},{-6.0},{-3.0};{0.0},{0.0},{0.0},{1.0}]"
mat = getTokens("[1, 2, 3, 1;\
4, 5, 6, 1;\
7, 8, 9, 1;\
2, 3 ,1 ,4]")
assert row_echelon(mat).__str__() == "[{1.0},{2.0},{3.0},{1.0};{0.0},{-3.0},{-6.0},{-3.0};{0.0},{0.0},{-3.02},{2.99};{0.0},{0.0},{0.0},{0.0}]"
mat = getTokens("[6,2,8,26;\
3,5,2,8;\
0,8,2,-7]")
assert row_echelon(mat).__str__() == "[{6.0},{2.0},{8.0},{26.0};{0.0},{4.0},{-2.0},{-5.0};{0.0},{0.0},{6.0},{3.0}]"
def test_multi_variable_solve():
mat = getTokens("[1, 2, 3, 1;\
4, 5, 6, 1;\
7, 8, 2, 2]")
assert gauss_elim(mat).__str__() == "[{-1.14};{1.2799999999999998};{-0.14285714285714285}]"
mat = getTokens("[6,2,8,26;\
3,5,2,8;\
0,8,2,-7]")
assert gauss_elim(mat).__str__() == "[{4.0};{-1.0};{0.5}]"
#######################
# Operator Overloading
#######################
def test_addoverload():
matA = getTokens("[ x , x^2; \
3 + x^2, xy ]")
matB = getTokens("[ y + 1 , x^2; \
2 - x^2, xy - 1 ]")
matSum = matA + matB
assert matSum.__str__() == "[{x}+{y}+{1.0},2{x}^{2.0};{5.0},2{x}{y}-{1.0}]"
def test_suboverload():
matA = getTokens("[y, 2x]")
matB = getTokens("[-x, -x]")
matSub = matA - matB
assert matSub.__str__() == "[{y}--1.0{x},3.0{x}]"
|