testDiscrete.m 35.7 KB
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 1 2 3 4 5 6 function [tests] = testDiscrete() %testQuantity Summary of this function goes here % Detailed explanation goes here tests = functiontests(localfunctions); end  Jakob Gabriel committed Jun 04, 2019 7 8 9 10 11 12 13 14 15 16  function testScalarPlusMinusQuantity(testCase) syms z myGrid = linspace(0, 1, 7); f = quantity.Discrete(quantity.Symbolic([1; 2] + zeros(2, 1)*z, ... 'variable', {z}, 'grid', {myGrid})); testCase.verifyError(@() 1-f-1, ''); testCase.verifyError(@() 1+f+1, ''); end  17 18 19 20 21 22 23 24 25 26 27 28 function testNumericVectorPlusMinusQuantity(testCase) syms z myGrid = linspace(0, 1, 7); f = quantity.Discrete(quantity.Symbolic([1+z; 2+sin(z)] + zeros(2, 1)*z, ... 'variable', {z}, 'grid', {myGrid})); a = ones(size(f)); testCase.verifyEqual(on(a-f), 1-f.on()); testCase.verifyEqual(on(f-a), f.on()-1); testCase.verifyEqual(on(a+f), f.on()+1); testCase.verifyEqual(on(f+a), f.on()+1); end  Jakob Gabriel committed May 27, 2019 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 function testUnitaryPluasAndMinus(testCase) syms z zeta qSymbolic = quantity.Symbolic(... [1+z*zeta, -zeta; -z, z^2], 'grid', {linspace(0, 1, 21), linspace(0, 1, 41)},... 'variable', {z, zeta}, 'name', 'q'); qDiscrete = quantity.Discrete(qSymbolic); qDoubleArray = qSymbolic.on(); testCase.verifyEqual(on(-qSymbolic), -qDoubleArray); testCase.verifyEqual(on(-qDiscrete), -qDoubleArray); testCase.verifyEqual(on(+qSymbolic), +qDoubleArray); testCase.verifyEqual(on(+qDiscrete), +qDoubleArray); testCase.verifyEqual(on(+qDiscrete), on(+qSymbolic)); testCase.verifyEqual(on(-qDiscrete), on(-qSymbolic)); end  Ferdinand Fischer committed May 15, 2019 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 function testConcatenate(testCase) t = linspace(0, pi)'; A = quantity.Discrete({sin(t); cos(t)}, 'grid', {t}, 'gridName', 't'); B = quantity.Discrete({tan(t); exp(t)}, 'grid', {t}, 'gridName', 't'); AB = [A, B]; AB_ = [A', B']; ABA = [A, B, A]; testCase.verifyTrue(all(size(AB) == [2, 2])); testCase.verifyTrue(all(size(AB_) == [1, 4])); testCase.verifyTrue(all(size(ABA) == [2, 3])); t = linspace(0, pi, 13)'; C = quantity.Discrete({sin(t); cos(t)}, 'grid', {t}, 'gridName', 't');  62 AC = [A; C];  Ferdinand Fischer committed May 15, 2019 63   64 testCase.verifyTrue(all(size(AC) == [4, 1]));  Ferdinand Fischer committed May 15, 2019 65   66 67 A0s = [A, zeros(2,3)]; testCase.verifyTrue(all(all(all(A0s(:, 2:end).on() == 0))))  Ferdinand Fischer committed May 15, 2019 68 69 70  end  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 function testExp(testCase) % 1 spatial variable syms z zeta s1d = quantity.Discrete(quantity.Symbolic(... 1+z*z, 'grid', {linspace(0, 1, 21)}, 'variable', {z}, 'name', 's1d')); testCase.verifyEqual(s1d.exp.on(), exp(s1d.on())); % diagonal matrix s2dDiag = quantity.Discrete(quantity.Symbolic(... [1+z*zeta, 0; 0, z^2], 'grid', {linspace(0, 1, 21), linspace(0, 1, 41)},... 'variable', {z, zeta}, 'name', 's2dDiag')); testCase.verifyEqual(s2dDiag.exp.on(), exp(s2dDiag.on())); end function testExpm(testCase) syms z zeta mat2d = quantity.Discrete(quantity.Symbolic(... ones(2, 2) + [1+z*zeta, 3*zeta; 2+5*z+zeta, z^2], 'grid', {linspace(0, 1, 21), linspace(0, 1, 41)},... 'variable', {z, zeta}, 'name', 's2d')); mat2dMat = mat2d.on(); mat2dExpm = 0 * mat2d.on(); for zIdx = 1 : 21 for zetaIdx = 1 : 41 mat2dExpm(zIdx, zetaIdx, :, :) = expm(reshape(mat2dMat(zIdx, zetaIdx, :, :), [2, 2])); end end testCase.verifyEqual(mat2d.expm.on(), mat2dExpm, 'RelTol', 100*eps); end function testSqrt(testCase) % 1 spatial variable quanScalar1d = quantity.Discrete((linspace(0,2).^2).', 'size', [1, 1], 'grid', linspace(0, 1), ... 'gridName', 'z', 'name', 's1d'); quanScalarRoot = quanScalar1d.sqrt(); testCase.verifyEqual(quanScalarRoot.on(), linspace(0, 2).'); % 2 spatial variables quanScalar2d = quantity.Discrete((linspace(0, 2, 21).' + linspace(0, 2, 41)).^2, 'size', [1, 1], ... 'grid', {linspace(0, 1, 21), linspace(0, 1, 41)}, ... 'gridName', {'z', 'zeta'}, 'name', 's2d'); quanScalar2dRoot = quanScalar2d.sqrt(); testCase.verifyEqual(quanScalar2dRoot.on(), (linspace(0, 2, 21).' + linspace(0, 2, 41))); % diagonal matrix quanDiag = [quanScalar1d, 0*quanScalar1d; 0*quanScalar1d, (2)*quanScalar1d]; quanDiagRoot = quanDiag.sqrt(); testCase.verifyEqual(quanDiagRoot(1,1).on(), quanScalarRoot.on()); testCase.verifyEqual(quanDiagRoot(1,2).on(), 0*quanDiagRoot(1,2).on()); testCase.verifyEqual(quanDiagRoot(2,1).on(), 0*quanDiagRoot(2,1).on()); testCase.verifyEqual(quanDiagRoot(2,2).on(), sqrt(2)*quanDiagRoot(1,1).on(), 'AbsTol', 10*eps); %testCase.verifyEqual(1, 0); end function testSqrtm(testCase) quanScalar1d = quantity.Discrete((linspace(0,2).^2).', 'size', [1, 1], 'grid', linspace(0, 1), ... 'gridName', 'z', 'name', 's1d'); quanScalar2d = quantity.Discrete((linspace(0, 2, 21).' + linspace(0, 2, 41)).^2, 'size', [1, 1], ... 'grid', {linspace(0, 1, 21), linspace(0, 1, 41)}, ... 'gridName', {'z', 'zeta'}, 'name', 's2d'); % diagonal matrix - 1 spatial variable quanDiag = [quanScalar1d, 0*quanScalar1d; 0*quanScalar1d, (2)*quanScalar1d]; quanDiagRoot = quanDiag.sqrt(); % only works for diagonal matrices quanDiagRootMatrix = quanDiag.sqrtm(); testCase.verifyEqual(quanDiagRootMatrix.on(), quanDiagRoot.on()); % full matrix - 1 spatial variable quanMat1d = [quanScalar1d, 4*quanScalar1d; quanScalar1d, (2)*quanScalar1d]; quanMat1dMat = quanMat1d.on(); quanMat1dReference = 0*quanMat1dMat; for zIdx = 1:size(quanMat1dReference, 1) quanMat1dReference(zIdx, :, :) = sqrt(reshape(quanMat1dMat(zIdx, :), [2, 2])); end testCase.verifyEqual(quanMat1d.sqrtm.on(), quanMat1dReference, 'AbsTol', 10*eps); % full matrix - 2 spatial variables quanMat2d = [quanScalar2d, 4*quanScalar2d; quanScalar2d, (2)*quanScalar2d]; quanMat2dMat = quanMat2d.on(); quanMat2dReference = 0*quanMat2dMat; for zIdx = 1:size(quanMat2dMat, 1) for zetaIdx = 1:size(quanMat2dMat, 2) quanMat2dReference(zIdx, zetaIdx, :, :) = ... sqrt(reshape(quanMat2dMat(zIdx, zetaIdx, :), [2, 2])); end end testCase.verifyEqual(quanMat2d.sqrtm.on(), quanMat2dReference, 'AbsTol', 10*eps); end function testDiag2Vec(testCase) % quantity.Symbolic syms z myMatrixSymbolic = quantity.Symbolic([sin(0.5*z*pi)+1, 0; 0, 0.9-z/2]); myVectorSymbolic = diag2vec(myMatrixSymbolic); testCase.verifyEqual(myMatrixSymbolic(1,1).valueContinuous, myVectorSymbolic(1,1).valueContinuous); testCase.verifyEqual(myMatrixSymbolic(2,2).valueContinuous, myVectorSymbolic(2,1).valueContinuous); testCase.verifyEqual(numel(myVectorSymbolic), size(myMatrixSymbolic, 1)); % quantity.Discrete myMatrixDiscrete = quantity.Discrete(myMatrixSymbolic); myVectorDiscrete = diag2vec(myMatrixDiscrete); testCase.verifyEqual(myMatrixDiscrete(1,1).on(), myVectorDiscrete(1,1).on()); testCase.verifyEqual(myMatrixDiscrete(2,2).on(), myVectorDiscrete(2,1).on()); testCase.verifyEqual(numel(myVectorDiscrete), size(myMatrixDiscrete, 1)); end function testVec2Diag(testCase) % quantity.Symbolic syms z myMatrixSymbolic = quantity.Symbolic([sin(0.5*z*pi)+1, 0; 0, 0.9-z/2]); myVectorSymbolic = quantity.Symbolic([sin(0.5*z*pi)+1; 0.9-z/2]); testCase.verifyEqual(myMatrixSymbolic.on(), myVectorSymbolic.vec2diag.on()); % quantity.Discrete myMatrixDiscrete = quantity.Discrete(myMatrixSymbolic); myVectorDiscrete = quantity.Discrete(myVectorSymbolic); testCase.verifyEqual(myMatrixDiscrete.on(), myVectorDiscrete.vec2diag.on()); end function testInvert(testCase) myGrid = linspace(0, 1, 21); % scalar fScalar = quantity.Discrete((myGrid.').^2, 'grid', myGrid, 'gridName', 'x'); fScalarInverse = fScalar.invert(fScalar.gridName{1}); testCase.verifyEqual(fScalarInverse.on(fScalar.on()), myGrid.'), end function testSolveAlgebraic(testCase) myGrid = linspace(0, 1, 21); % scalar fScalar = quantity.Discrete((1+myGrid.').^2, 'grid', myGrid, 'gridName', 'x', ... 'size', [1, 1]); solutionScalar = fScalar.solveAlgebraic(2, fScalar.gridName{1}); testCase.verifyEqual(solutionScalar, sqrt(2)-1, 'AbsTol', 1e-3); % array % fArray = quantity.Discrete([2*myGrid.', myGrid.' + ones(numel(myGrid), 1)], ... % 'grid', myGrid', 'gridName', 'x', 'size', [2, 1]); % solution = fArray.solveAlgebraic([1; 1], fArray(1).gridName{1}); % testCase.verifyEqual(solution, 0.5); end function testSolveDVariableEqualQuantityConstant(testCase) %% simple constant case quan = quantity.Discrete(ones(51, 1), 'grid', linspace(0, 1, 51), ... 'gridName', 'z', 'size', [1, 1], 'name', 'a'); solution = quan.solveDVariableEqualQuantity(); [referenceResult1, referenceResult2] = ndgrid(linspace(0, 1, 51), linspace(0, 1, 51)); testCase.verifyEqual(solution.on(), referenceResult1 + referenceResult2, 'AbsTol', 10*eps); end function testSolveDVariableEqualQuantityNegative(testCase) syms z zeta assume(z>0 & z<1); assume(zeta>0 & zeta<1); myParameterGrid = linspace(0, 1, 51); Lambda = quantity.Symbolic(-0.1-z^2, ...%, -1.2+z^2]),...1+z*sin(z) 'variable', z, ... 'grid', myParameterGrid, 'gridName', 'z', 'name', '\Lambda'); %% myGrid = linspace(-2, 2, 101); sEval = -0.9; solveThisOdeDiscrete = solveDVariableEqualQuantity(... diag2vec(quantity.Discrete(Lambda)), 'variableGrid', myGrid); solveThisOdeSymbolic = solveDVariableEqualQuantity(... diag2vec(Lambda), 'variableGrid', myGrid); testCase.verifyEqual(solveThisOdeSymbolic.on({sEval, 0.5}), solveThisOdeDiscrete.on({sEval, 0.5}), 'RelTol', 5e-4); end function testSolveDVariableEqualQuantityComparedToSym(testCase) %% compare with symbolic implementation syms z assume(z>0 & z<1); quanBSym = quantity.Symbolic([1+z], 'grid', {linspace(0, 1, 21)}, ... 'gridName', 'z', 'name', 'bSym', 'variable', {z}); quanBDiscrete = quantity.Discrete(quanBSym.on(), 'grid', {linspace(0, 1, 21)}, ... 'gridName', 'z', 'name', 'bDiscrete', 'size', size(quanBSym)); solutionBSym = quanBSym.solveDVariableEqualQuantity(); solutionBDiscrete = quanBDiscrete.solveDVariableEqualQuantity(); %solutionBSym.plot(); solutionBDiscrete.plot(); testCase.verifyEqual(solutionBDiscrete.on(), solutionBSym.on(), 'RelTol', 1e-6); end function testSolveDVariableEqualQuantityAbsolut(testCase) %% compare with symbolic implementation syms z assume(z>0 & z<1); quanBSym = quantity.Symbolic([1+z], 'grid', {linspace(0, 1, 51)}, ... 'gridName', 'z', 'name', 'bSym', 'variable', {z}); quanBDiscrete = quantity.Discrete(quanBSym.on(), 'grid', {linspace(0, 1, 51)}, ... 'gridName', 'z', 'name', 'bDiscrete', 'size', size(quanBSym)); solutionBDiscrete = quanBDiscrete.solveDVariableEqualQuantity(); myGrid = solutionBDiscrete.grid{1};  Ferdinand Fischer committed May 24, 2019 265 solutionBDiscreteDiff = solutionBDiscrete.diff(1, 's');  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 quanOfSolutionOfS = zeros(length(myGrid), length(myGrid), 1); for icIdx = 1 : length(myGrid) quanOfSolutionOfS(:, icIdx, :) = quanBSym.on(solutionBDiscrete.on({myGrid, myGrid(icIdx)})); end %% testCase.verifyEqual(solutionBDiscreteDiff.on({myGrid(2:end-1), myGrid}), quanOfSolutionOfS(2:end-1, :), 'AbsTol', 1e-3); end function testMtimesDifferentGridLength(testCase) %% a = quantity.Discrete(ones(11, 1), 'grid', linspace(0, 1, 11), 'gridName', 'z', ... 'size', [1, 1], 'name', 'a'); b = quantity.Discrete(ones(5, 1), 'grid', linspace(0, 1, 5), 'gridName', 'z', ... 'size', [1, 1], 'name', 'b'); ab = a*b; % syms z c = quantity.Symbolic(1, 'grid', linspace(0, 1, 21), 'variable', z, 'name', 'c'); ac = a*c; %% %% testCase.verifyEqual(ab.on(), ones(11, 1)); testCase.verifyEqual(ac.on(), ones(21, 1)); end function testDiff1d(testCase) %% 1d constant = quantity.Discrete([2*ones(11, 1), linspace(0, 1, 11).'], 'grid', linspace(0, 1, 11), ... 'gridName', 'z', 'name', 'constant', 'size', [2, 1]);  Ferdinand Fischer committed May 24, 2019 296   297 298 constantDiff = diff(constant); testCase.verifyEqual(constantDiff.on(), [zeros(11, 1), ones(11, 1)], 'AbsTol', 10*eps);  Ferdinand Fischer committed May 24, 2019 299 300 301 302 303 304 305 306 307 308 309 310 311  z = linspace(0,pi)'; sinfun = quantity.Discrete(sin(z), 'grid', z, 'gridName', 'z'); % do the comparison on a smaller grid, because the numerical derivative is % very bad a the boundarys of the domain. Z = linspace(0.1, pi-0.1)'; testCase.verifyTrue(numeric.near(sinfun.diff().on(Z), cos(Z), 1e-3)); testCase.verifyTrue(numeric.near(sinfun.diff(2).on(Z), -sin(Z), 1e-3)); testCase.verifyTrue(numeric.near(sinfun.diff(3).on(Z), -cos(Z), 1e-3));  312 313 314 315 316 317 318 319 end function testDiffConstant2d(testCase) %% 2d [zNdgrid, zetaNdgrid] = ndgrid(linspace(0, 1, 11), linspace(0, 1, 21)); myQuantity = quantity.Discrete(cat(3, 2*ones(11, 21), zNdgrid, zetaNdgrid), ... 'grid', {linspace(0, 1, 11), linspace(0, 1, 21)}, ... 'gridName', {'z', 'zeta'}, 'name', 'constant', 'size', [3, 1]);  Ferdinand Fischer committed May 24, 2019 320 321 myQuantityDz = diff(myQuantity, 1, 'z'); myQuantityDzeta = diff(myQuantity, 1, 'zeta');  Jakob Gabriel committed May 30, 2019 322 323 324 325 myQuantityDZzeta = diff(myQuantity, 1); myQuantityDZzeta2 = diff(myQuantity, 1, {'z', 'zeta'}); testCase.verifyEqual(myQuantityDZzeta.on(), myQuantityDZzeta2.on());  326 327 328 329  % constant testCase.verifyEqual(myQuantityDz(1).on(), zeros(11, 21)); testCase.verifyEqual(myQuantityDzeta(1).on(), zeros(11, 21));  Jakob Gabriel committed May 30, 2019 330 testCase.verifyEqual(myQuantityDZzeta(1).on(), zeros(11, 21));  331 332 333 334  % zNdgrid testCase.verifyEqual(myQuantityDz(2).on(), ones(11, 21), 'AbsTol', 10*eps); testCase.verifyEqual(myQuantityDzeta(2).on(), zeros(11, 21), 'AbsTol', 10*eps);  Jakob Gabriel committed May 30, 2019 335 testCase.verifyEqual(myQuantityDZzeta(2).on(), zeros(11, 21), 'AbsTol', 10*eps);  336 337 338 339  % zetaNdgrid testCase.verifyEqual(myQuantityDz(3).on(), zeros(11, 21), 'AbsTol', 10*eps); testCase.verifyEqual(myQuantityDzeta(3).on(), ones(11, 21), 'AbsTol', 10*eps);  Jakob Gabriel committed May 30, 2019 340 testCase.verifyEqual(myQuantityDZzeta(3).on(), zeros(11, 21), 'AbsTol', 10*eps);  341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 end function testOn(testCase) %% init data gridVecA = linspace(0, 1, 27); gridVecB = linspace(0, 1, 41); [value] = createTestData(gridVecA, gridVecB); a = quantity.Discrete(value, 'size', [2, 3], ... 'grid', {gridVecA, gridVecB}, 'gridName', {'z', 'zeta'}, 'name', 'A'); %% testCase.verifyEqual(value, a.on()); testCase.verifyEqual(permute(value, [2, 1, 3, 4]), ... a.on({gridVecB, gridVecA}, {'zeta', 'z'})); testCase.verifyEqual(createTestData(linspace(0, 1, 100), linspace(0, 1, 21)), ... a.on({linspace(0, 1, 100), linspace(0, 1, 21)}), 'AbsTol', 100*eps); testCase.verifyEqual(createTestData(linspace(0, 1, 24), linspace(0, 1, 21)), ... a.on({linspace(0, 1, 24), linspace(0, 1, 21)}, {'z', 'zeta'}), 'AbsTol', 24*eps); testCase.verifyEqual(permute(createTestData(linspace(0, 1, 21), linspace(0, 1, 24)), [2, 1, 3, 4]), ... a.on({linspace(0, 1, 24), linspace(0, 1, 21)}, {'zeta', 'z'}), 'AbsTol', 2e-4); function [value] = createTestData(gridVecA, gridVecB) [zGridA , zetaGridA] = ndgrid(gridVecA, gridVecB); value = ones(numel(gridVecA), numel(gridVecB), 2, 3); value(:,:,1,1) = 1+zGridA; value(:,:,2,1) = 1+zetaGridA; value(:,:,2,2) = 1+2*zGridA - zetaGridA.^2; value(:,:,1,2) = 1+zGridA + zetaGridA.^2; value(:,:,2,3) = 1+zeros(numel(gridVecA), numel(gridVecB)); end end function testOn2(testCase) zeta = linspace(0, 1); eta = linspace(0, 1, 71)'; z = linspace(0, 1, 51); [ZETA, ETA, Z] = ndgrid(zeta, eta, z); a = quantity.Discrete(cat(4, sin(ZETA.*ZETA.*Z)+ETA.*ETA, ETA+cos(ZETA.*ETA.*Z)), ... 'size', [2 1], 'grid', {zeta, eta, z}, 'gridName', {'zeta', 'eta', 'z'}); testCase.verifyEqual(a.on({zeta, eta, z}), ... permute(a.on({eta, zeta, z}, {'eta', 'zeta', 'z'}), [2, 1, 3, 4])); testCase.verifyEqual([a(1).on({zeta(2), eta(3), z(4)}); a(2).on({zeta(2), eta(3), z(4)})], ... [sin(zeta(2)*zeta(2)*z(4))+eta(3)*eta(3); eta(3)+cos(zeta(2)*eta(3)*z(4))]); end function testMtimesZZeta2x2(testCase) gridVecA = linspace(0, 1, 101); [zGridA , ~] = ndgrid(gridVecA, gridVecA); a = quantity.Discrete(ones([size(zGridA), 2, 2]), 'size', [2, 2], ... 'grid', {gridVecA, gridVecA}, 'gridName', {'z', 'zeta'}, 'name', 'A'); syms zeta assume(zeta>=0 & zeta>=1) gridVecB = linspace(0, 1, 100); b = quantity.Symbolic((eye(2, 2)), 'variable', zeta, ... 'grid', gridVecB); c = a*b; %% testCase.verifyEqual(c.on(), a.on()); end function testMTimesPointWise(testCase) syms z zeta Z = linspace(0, 1, 501)'; ZETA = Z; P = quantity.Symbolic([z, z^2; z^3, z^4] * zeta, 'grid', {Z, ZETA}); B = quantity.Symbolic([sin(zeta); cos(zeta)], 'grid', ZETA); PB = P*B; p = quantity.Discrete(P); b = quantity.Discrete(B); pb = p*b; end function testMldivide(testCase) %% scalar example s = linspace(0, 1, 21); vL = quantity.Discrete(2*ones(21, 1), ... 'size', [1, 1], 'grid', {s}, 'gridName', {'asdf'}); vR = quantity.Discrete((linspace(1, 2, 21).').^2, ... 'size', [1, 1], 'grid', {s}, 'gridName', {'asdf'}); vLdVR = vL \ vR; %% matrix example t = linspace(0, pi); s = linspace(0, 1, 21); [T, ~] = ndgrid(t, s); KL = quantity.Discrete(permute(repmat(2*eye(2), [1, 1, size(T)]), [3, 4, 1, 2]), ... 'size', [2 2], 'grid', {t, s}, 'gridName', {'t', 's'}); KR = quantity.Discrete(permute(repmat(4*eye(2), [1, 1, size(T)]), [3, 4, 1, 2]), ... 'size', [2 2], 'grid', {t, s}, 'gridName', {'t', 's'}); KLdKR = KL \ KR; %% testCase.verifyEqual(vLdVR.on(), 2 .\ (linspace(1, 2, 21).').^2); testCase.verifyEqual(KLdKR.on(), permute(repmat(2*eye(2), [1, 1, size(T)]), [4, 3, 1, 2])); end function testMrdivide(testCase) %% scalar example s = linspace(0, 1, 21); vL = quantity.Discrete(2*ones(21, 1), ... 'size', [1, 1], 'grid', {s}, 'gridName', {'asdf'}); vR = quantity.Discrete((linspace(1, 2, 21).').^2, ... 'size', [1, 1], 'grid', {s}, 'gridName', {'asdf'}); vLdVR = vL / vR; %% matrix example t = linspace(0, pi); s = linspace(0, 1, 21); [T, ~] = ndgrid(t, s); KL = quantity.Discrete(permute(repmat(2*eye(2), [1, 1, size(T)]), [3, 4, 1, 2]), ... 'size', [2 2], 'grid', {t, s}, 'gridName', {'t', 's'}); KR = quantity.Discrete(permute(repmat(4*eye(2), [1, 1, size(T)]), [3, 4, 1, 2]), ... 'size', [2 2], 'grid', {t, s}, 'gridName', {'t', 's'}); KLdKR = KL / KR; %% testCase.verifyEqual(vLdVR.on(), 2 ./ (linspace(1, 2, 21).').^2); testCase.verifyEqual(KLdKR.on(), permute(repmat(0.5*eye(2), [1, 1, size(T)]), [4, 3, 1, 2])); end function testInv(testCase) %% scalar example s = linspace(0, 1, 21); v = quantity.Discrete((linspace(1, 2, 21).').^2, ... 'size', [1, 1], 'grid', {s}, 'gridName', {'asdf'}); vInv = v.inv(); %% matrix example t = linspace(0, pi); s = linspace(0, 1, 21); [T, ~] = ndgrid(t, s); K = quantity.Discrete(permute(repmat(2*eye(2), [1, 1, size(T)]), [3, 4, 1, 2]), ... 'size', [2 2], 'grid', {t, s}, 'gridName', {'t', 's'}); kInv = inv(K); %% testCase.verifyEqual(vInv.on(), 1./(linspace(1, 2, 21).').^2) testCase.verifyEqual(kInv.on(), permute(repmat(0.5*eye(2), [1, 1, size(T)]), [3, 4, 1, 2])) end function testCumInt(testCase) %% t = linspace(pi, 1.1*pi, 51)'; s = t; [T, S] = ndgrid(t, t); syms sy tt a = [ 1, sy; tt, 1]; b = [ sy; 2*sy]; A = zeros([size(T), size(a)]); B = zeros([length(s), size(b)]); for i = 1:size(a,1) for j = 1:size(a,2) A(:,:,i,j) = subs(a(i,j), {sy, tt}, {S, T}); end end for i = 1:size(b,1) B(:,i) = subs(b(i), sy, s); end % compute the numeric version of the volterra integral K = quantity.Discrete(A, 'size', size(a), 'grid', {t, s}, 'gridName', {'t', 's'}); x = quantity.Discrete(B, 'size', size(b), 'grid', {s}, 'gridName', 's'); f = K.volterra(x); fCumInt = cumInt(K*x, 'intGridName', 's', 'boundaryGridName', 't'); testCase.verifyEqual(fCumInt.on(), f.on(), 'AbsTol', 10*eps); end function testCumIntWithLowerAndUpperBoundSpecified(testCase) %% t = linspace(pi, 1.1*pi, 51)'; s = t; [T, S] = ndgrid(t, t); syms sy tt a = [ 1, sy; tt, 1]; A = zeros([size(T), size(a)]); for i = 1:size(a,1) for j = 1:size(a,2) A(:,:,i,j) = subs(a(i,j), {sy, tt}, {S, T}); end end % compute the numeric version of the volterra integral K = quantity.Discrete(A, 'size', size(a), 'grid', {t, s}, 'gridName', {'t', 's'}); fCumInt2Bcs = cumInt(K, 'intGridName', 's', 'boundaryGridName', {'zeta', 't'}); fCumInt2Cum = cumInt(K, 'intGridName', 's', 'boundaryGridName', 't') ... - cumInt(K, 'intGridName', 's', 'boundaryGridName', 'zeta'); testCase.verifyEqual(fCumInt2Bcs.on(), fCumInt2Cum.on(), 'AbsTol', 10*eps); end function testVolterra(testCase) %% t = linspace(pi, 1.1*pi, 51)'; s = t; [T, S] = ndgrid(t, t); syms sy tt a = [ 1, sy; tt, 1]; b = [ sy; 2*sy]; A = zeros([size(T), size(a)]); B = zeros([length(s), size(b)]); for i = 1:size(a,1) for j = 1:size(a,2) A(:,:,i,j) = subs(a(i,j), {sy, tt}, {S, T}); end end for i = 1:size(b,1) B(:,i) = subs(b(i), sy, s); end %% int_0_t a(t,s) * b(s) ds % compute symbolic version of the volterra integral v = int(a*b, sy, t(1), tt); V = quantity.Symbolic(v, 'grid', t, 'gridName', 'tt'); V = V.subs('tt', 't'); % compute the numeric version of the volterra integral K = quantity.Discrete(A, 'size', size(a), 'grid', {t, s}, 'gridName', {'t', 's'}); x = quantity.Discrete(B, 'size', size(b), 'grid', {s}, 'gridName', 's'); f = K.volterra(x); testCase.verifyTrue(numeric.near(V.on(), f.on(), 1e-2)); %% int_s_t a(t,s) * b(s) ds v = int(a*b, sy, sy, tt); V = quantity.Symbolic(subs(v, {tt, sy}, {'t', 's'}), 'grid', {t, s}); f = K.volterra(x, 'fixedLowerBound', false); testCase.verifyTrue( numeric.near(f.on(), V.on(), 1e-2) ); %% int_s_t a(t,s) * c(t,s) ds c = [1, sy+1; tt+1, 1]; C = zeros([size(T), size(c)]); for i = 1:numel(c) C(:,:,i) = double(subs(c(i), {tt sy}, {T S})); end y = quantity.Discrete(C, 'size', size(c), 'grid', {t s}, 'gridName', {'t' 's'}); v = int(a*c, sy, sy, tt); V = quantity.Symbolic(subs(v, {tt, sy}, {'t', 's'}), 'grid', {t, s}); f = K.volterra(y, 'variable', 's', 'fixedLowerBound', false); testCase.verifyTrue( numeric.near(f.on(), V.on(), 1e-3) ); end function testAtIndex(testCase) z = linspace(0,1).'; a = sin(z * pi); A = quantity.Discrete({a}, 'grid', {z}, 'gridName', {'z'}); testCase.verifyEqual(a(end), A.atIndex(end)); testCase.verifyEqual(a(1), A.atIndex(1)); testCase.verifyEqual(a(23), A.atIndex(23));  627 628 629 630 631 632 633 y = linspace(0,2,51); b1 = sin(z * pi * y); b2 = cos(z * pi * y); B = quantity.Discrete({b1; b2}, 'grid', {z, y}, 'gridName', {'z', 'y'}); B_1_y = B.atIndex(1,1); b_1_y = [sin(0); cos(0)];  Ferdinand Fischer committed May 28, 2019 634 testCase.verifyTrue(numeric.near(B_1_y, b_1_y));  635 636 637 638 639 640  B_z_1 = B.atIndex(':',1); testCase.verifyTrue(all(B_z_1(:,1,1) == 0)); testCase.verifyTrue(all(B_z_1(:,:,2) == 1));  641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 end function testGridJoin(testCase) s = linspace(0, 1); z = linspace(0, 1, 71)'; t = linspace(0, 1, 51); [Z, T, S] = ndgrid(z, t, s); a = quantity.Discrete(cat(4, sin(Z.*Z.*S), cos(Z.*T.*S)), ... 'size', [2 1], 'grid', {z, t, s}, 'gridName', {'z', 't', 's'}); b = quantity.Discrete(ones(numel(s), numel(t)), ... 'size', [1 1], 'grid', {s, t}, 'gridName', {'p', 's'}); c = quantity.Discrete(ones(numel(t), 2, 2), ... 'size', [2 2], 'grid', {t}, 'gridName', {'p'}); [gridJoinedAB, gridNameJoinedAB] = gridJoin(a, b); [gridJoinedCC, gridNameJoinedCC] = gridJoin(c, c); [gridJoinedBC, gridNameJoinedBC] = gridJoin(b, c); testCase.verifyEqual(gridNameJoinedAB, {'p', 's', 't', 'z'}); testCase.verifyEqual(gridJoinedAB, {s, s, t, z}); testCase.verifyEqual(gridNameJoinedCC, {'p'}); testCase.verifyEqual(gridJoinedCC, {t}); testCase.verifyEqual(gridNameJoinedBC, {'p', 's'}); testCase.verifyEqual(gridJoinedBC, {s, t}); end function testGridIndex(testCase) z = linspace(0, 2*pi, 71)'; t = linspace(0, 3*pi, 51); s = linspace(0, 1); [Z, T, S] = ndgrid(z, t, s); a = quantity.Discrete(cat(4, sin(Z.*Z.*S), cos(Z.*T.*S)), ... 'size', [2 1], 'grid', {z, t, s}, 'gridName', {'z', 't', 's'}); idx = a.gridIndex('z'); testCase.verifyEqual(idx, 1); idx = a.gridIndex({'z', 't'}); testCase.verifyEqual(idx, [1 2]); idx = a.gridIndex({'z', 's'}); testCase.verifyEqual(idx, [1 3]); idx = a.gridIndex('t'); testCase.verifyEqual(idx, 2); end  Ferdinand Fischer committed May 29, 2019 698 function testMTimes(testCase)  699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 % multiplication of a(z) * a(z)' % a(z) \in (3, 2), z \in (100) z = linspace(0, 2*pi)'; a = cat(3, [z*0, z, sin(z)], [z.^2, z.^3, cos(z)]); % dim = (100, 3, 2) aa = misc.multArray(a, permute(a, [1, 3, 2]), 3, 2, 1); % dim = (100, 3, 3) A = quantity.Discrete(a, 'size', [3, 2], 'grid', z, 'gridName', {'z'}); AA = A*A'; testCase.verifyTrue(numeric.near(aa, AA.on())); z = linspace(0, 2*pi, 31); t = linspace(0, 1, 13); v = linspace(0, 1, 5); [z, t] = ndgrid(z, t); [v, t2] = ndgrid(v, t(1,:)); % scalar multiplication of b(z, t) * b(v, t) b = z .* t; b1b1 = misc.multArray(b, b, 4, 3, [1, 2]); B1 = quantity.Discrete(b(:,:,1,1)', 'size', [ 1, 1 ], 'gridName', {'t', 'z'}, 'grid', {t(1,:), z(:,1)}); B1B1 = B1*B1; testCase.verifyTrue(numeric.near(b1b1', B1B1.on())); % vector multiplication of b(z, t) * b(v, t) b2 = cat(3, z .* t, z*0 +1); b2b2 = misc.multArray(b2, permute(b2, [1 2 4 3]), 4, 3, [1, 2]); b2b2 = permute(b2b2, [2 1 3 4]); B2 = quantity.Discrete(b2, 'size', [ 2, 1 ], 'gridName', {'z', 't'}, 'grid', {z(:,1), t(1,:)}); B2B2 = B2*B2'; testCase.verifyTrue(numeric.near(b2b2, B2B2.on())); c2 = cat(4, sin(z), sin(t), cos(z)); b2c2 = misc.multArray(b2, c2, 4, 3, [1 2]); C2 = quantity.Discrete(c2, 'size', [1 3], 'gridName', {'z', 't'}, 'grid', {z(:,1), t(1,:)}); B2C2 = B2 * C2; testCase.verifyTrue(numeric.near(permute(b2c2, [2 1 3 4]), B2C2.on())); % matrix b(z,t) * b(z,t) b = cat(4, cat(3, z .* t, z*0 +1), cat(3, sin( z ), cos( z .* t ))); bb = misc.multArray(b, b, 4, 3, [1, 2]); bb = permute(bb, [2 1 3 4]); B = quantity.Discrete(b, 'size', [ 2, 2 ], 'gridName', {'z', 't'}, 'grid', {z(:,1), t(1,:)}); BB = B*B; testCase.verifyTrue(numeric.near(bb, BB.on)); % matrix multiplication with one commmon and one distinct domain c = cat(4, cat(3, v .* t2, v*0 +1), cat(3, sin( v ), cos( v .* t2 )), cat(3, cos( t2 ), tan( v .* t2 ))); bc = misc.multArray(b, c, 4, 3, 2); bc = permute(bc, [ 1 2 4 3 5 ]); B = quantity.Discrete(b, 'size', [ 2, 2 ], 'gridName', {'z', 't'}, 'grid', {z(:,1), t(1,:)}); C = quantity.Discrete(c, 'size', [2, 3], 'gridName', {'v', 't'}, 'grid',{v(:,1), t2(1,:)}); BC = B*C; testCase.verifyTrue(numeric.near(bc, BC.on));  Ferdinand Fischer committed May 29, 2019 754 755 756 757 758 759 760 761 762 763 764 %% z = linspace(0,1).'; a = quantity.Discrete({sin(z * pi), cos(z* pi)}, 'grid', {z}, ... 'gridName', 'z', 'name', 'a'); aa = a.' * a; %% testCase.verifyTrue( numeric.near( aa(1,1).on() , sin(z * pi) .* sin(z * pi))); testCase.verifyTrue( numeric.near( aa(1,2).on() , sin(z * pi) .* cos(z * pi))); testCase.verifyTrue( numeric.near( aa(2,2).on() , cos(z * pi) .* cos(z * pi))); %% test multiplicatin with constants:  Ferdinand Fischer committed Jun 03, 2019 765 766 C = [3 0; 0 5]; c = quantity.Discrete(C, 'gridName', {}, 'grid', {}, 'name', 'c');  Ferdinand Fischer committed May 29, 2019 767 768 testCase.verifyTrue( numeric.near( squeeze(double(a*c)), [sin(z * pi) * 3, cos(z * pi) * 5])); testCase.verifyTrue( numeric.near( squeeze(double(a*[3 0; 0 5])), [sin(z * pi) * 3, cos(z * pi) * 5]));  Ferdinand Fischer committed Jun 03, 2019 769 testCase.verifyTrue( numeric.near( double(c*c), C*C));  Ferdinand Fischer committed May 29, 2019 770 771 772 773 774 775 776 777 778 779  %% test multiplication with a scalar: s = quantity.Discrete(42, 'gridName', {}, 'grid', {}', 'name', 's'); testCase.verifyTrue( numeric.near( squeeze(double(42 * a)), [sin(z * pi) * 42, cos(z * pi) * 42])); testCase.verifyTrue( numeric.near( squeeze(double(a * 42)), [sin(z * pi) * 42, cos(z * pi) * 42])); testCase.verifyTrue( numeric.near( squeeze(double(s * a')), [sin(z * pi) * 42, cos(z * pi) * 42])); testCase.verifyTrue( numeric.near( squeeze(double(a * s)), [sin(z * pi) * 42, cos(z * pi) * 42])); %% test  Ferdinand Fischer committed Jun 03, 2019 780 781 782   783 784 end  Ferdinand Fischer committed May 23, 2019 785 786 787 788 789 790 791 792 793 794 795 function testIsConstant(testCase) C = quantity.Discrete(rand(3,7), 'gridName', {}); testCase.verifyTrue(C.isConstant()); z = linspace(0, pi)'; A = quantity.Discrete(sin(z), 'grid', z, 'gridName', 'z'); testCase.verifyFalse(A.isConstant()); end  796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 function testMTimesConstant(testCase) myGrid = linspace(0, 2*pi)'; a = cat(3, [myGrid*0, myGrid, sin(myGrid)], [myGrid.^2, myGrid.^3, cos(myGrid)]); % dim = (100, 3, 2) c = rand(2, 3); % dim = (2, 3) A = quantity.Discrete(a, 'size', [3, 2], 'grid', myGrid, 'gridName', {'z'}); C = quantity.Discrete(c, 'gridName', {}); ac = misc.multArray(a, c, 3, 1); % dim = (100, 3, 3) AC = A*C; Ac = A*c; ca = permute(misc.multArray(c, a, 2, 2), [2, 1, 3]); CA = C*A; cA = c*A; verifyTrue(testCase, numeric.near(Ac.on(), ac)); verifyTrue(testCase, numeric.near(AC.on(), ac)); verifyTrue(testCase, numeric.near(cA.on(), ca, 1e-12)); verifyTrue(testCase, numeric.near(CA.on(), ca, 1e-12)); end function testMPower(testCase) %% z = linspace(0,1).'; a = sin(z * pi); A = quantity.Discrete({a}, 'grid', {z}, 'gridName', 'z'); aa = sin(z * pi) .* sin(z * pi); AA = A^2; verifyTrue(testCase, numeric.near(aa, AA.on())); end function testPlus(testCase) %%  838 z = linspace(0,1,31).';  839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 zeta = linspace(0,1,51); [zGrid, zetaGrid] = ndgrid(z, zeta); a = sin(z * pi); aLr = sin(zeta * pi); b = cos(z * pi); c = zeta; bc = cos(zGrid * pi) + zetaGrid; azZeta = sin(zGrid * pi) + sin(zetaGrid * pi); bzZeta = cos(zGrid * pi) + cos(zetaGrid * pi); AB = quantity.Discrete({a, b}, 'grid', {z}, 'gridName', 'blub'); A = quantity.Discrete({a}, 'grid', {z}, 'gridName', 'z'); ALr = quantity.Discrete({aLr}, 'grid', {zeta}, 'gridName', 'z'); B = quantity.Discrete({b}, 'grid', {z}, 'gridName', 'z'); C = quantity.Discrete({c}, 'grid', {zeta}, 'gridName', 'zeta'); AZZETA = quantity.Discrete({azZeta}, 'grid', {z, zeta}, 'gridName', {'z', 'zeta'}); BZZETA = quantity.Discrete({bzZeta}, 'grid', {z, zeta}, 'gridName', {'z', 'zeta'}); ABAB = AB + AB; BC = B+C; AB = A+B; ABZZETA = AZZETA + BZZETA; ALrA = ALr+A; %% testCase.verifyEqual(a+a, ABAB(1).on()); testCase.verifyEqual(b+b, ABAB(2).on()); testCase.verifyEqual(a+b, AB.on()); testCase.verifyEqual(bc, BC.on()); testCase.verifyEqual(azZeta+bzZeta, ABZZETA.on());  869 870 871 testCase.verifyEqual(a+a, ALrA.on(z), 'RelTol', 1e-3); %% additional test  Jakob Gabriel committed May 17, 2019 872 a = quantity.Discrete(zGrid, 'grid', {z, zeta}, ...  873  'gridName', {'z', 'zeta'}, 'name', 'a');  Jakob Gabriel committed May 17, 2019 874 b = quantity.Discrete(zetaGrid.', 'grid', {zeta, z}, ...  875 876 877  'gridName', {'zeta', 'z'}, 'name', 'b'); c = a + b; cMat = c.on();  Jakob Gabriel committed May 17, 2019 878 cMatReference = zGrid + zetaGrid;  879 %%  Jakob Gabriel committed May 17, 2019 880 881 testCase.verifyEqual(numel(cMat), numel(cMatReference)); testCase.verifyEqual(cMat(:), cMatReference(:));  882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 end function testInit(testCase) %% z = linspace(0,1).'; t = linspace(0,1,101); v = {sin(z * t * pi); cos(z * t * pi)}; V = cat(3, v{:}); b = quantity.Discrete(v, 'grid', {z, t}, 'gridName', {'z', 't'}); c = quantity.Discrete(V, 'grid', {z, t}, 'gridName', {'z', 't'}); d = quantity.Discrete(V, 'gridName', {'z', 't'}); %% verifyTrue(testCase, misc.alln(b.on() == c.on())); verifyTrue(testCase, misc.alln(b.on() == d.on())); end function testInt(testCase) %% % z = linspace(0,1).'; % t = linspace(0,1,101); % v = {sin(z * t * pi); cos(z * t * pi)}; % b = quantity.Discrete(v, 'grid', {z, t}, 'gridNames', {'z', 't'}); z = linspace(0, 2*pi, 701)'; t = linspace(0, 3*pi, 501); F = {@(z,t) sin(z*t), @(z,t) cos(z*t)}; a = quantity.Discrete(cat(3, sin(z*t), cos(z*t)), ... 'size', [2 1], 'grid', {z, t}, 'gridName', {'z', 't'}); At = int(a, 'z'); Anumt = []; for tau = t Anumt = [Anumt; ... integral(@(z)F{1}(z,tau), z(1), z(end)), ... integral(@(z)F{2}(z,tau), z(1), z(end))]; end verifyTrue(testCase, numeric.near(At.on(), Anumt, 1e-3)); Az = int(a, 't'); AnumZ = []; for zeta = z' AnumZ = [AnumZ; ... integral(@(t)F{1}(zeta,t), t(1), t(end)), ... integral(@(t)F{2}(zeta,t), t(1), t(end))]; end verifyTrue(testCase, numeric.near(Az.on(), AnumZ, 1e-3)); A = int(a); Anum = [integral2(@(z,t) sin(z.*t), z(1), z(end), t(1), t(end)); ... integral2(@(z,t) cos(z.*t), z(1), z(end), t(1), t(end))]; verifyTrue(testCase, numeric.near(A.on(), Anum, 1e-2)); end function testNDGrid(testCase) %% z = linspace(0,1).'; t = linspace(0,1,101); b = quantity.Discrete({sin(z * t * pi); cos(z * t * pi)}, 'grid', {z, t}, 'gridName', {'z', 't'}); % #TODO end function testDefaultGrid(testCase) v = quantity.Discrete.value2cell( rand([100, 42, 2, 3]), [100, 42], [2, 3]); g = quantity.Discrete.defaultGrid([100, 42]); testCase.verifyEqual(g{1}, linspace(0, 1, 100).'); testCase.verifyEqual(g{2}, linspace(0, 1, 42)); end function testValue2Cell(testCase) v = rand([100, 42, 2, 3]); V = quantity.Discrete( quantity.Discrete.value2cell(v, [100, 42], [2, 3]), 'gridName', {'z', 't'} ); verifyTrue(testCase, misc.alln(v == V.on())); end function testMtimesDifferentGrid(testCase) %% zetaA = linspace(0, 1, 21); zA = linspace(0, 1); [zetaAGrid, zAGrid] = ndgrid(zetaA, zA); zX = linspace(0, 1, 21); tX = linspace(1, 2, 31); [zXGrid, tXGrid] = ndgrid(zX, tX); a = quantity.Discrete({sin(zetaAGrid * pi), cos(zAGrid* pi)}, ... 'grid', {zetaA, zA}, 'gridName', {'zeta', 'z'}); x = quantity.Discrete({zXGrid; tXGrid}, ... 'grid', {zX, tX}, 'gridName', {'z', 't'}); ax = a * x; ax2 = x.' * a.'; % calculate reference result with stupid for loops referenceResult = zeros(numel(zA), numel(zetaA), numel(tX)); aMat = a.on(); xMat = x.on({zA, tX}); for zIdx = 1:numel(zA) for zetaIdx = 1:numel(zetaA) for tIdx = 1:numel(tX) referenceResult(zIdx, zetaIdx, tIdx) = ... reshape(aMat(zetaIdx, zIdx, :, :), [1, 2]) ... * reshape(xMat(zIdx, tIdx, :), [2, 1]); end end end %% testCase.verifyEqual(referenceResult, ax.on(), 'AbsTol', 1e-12); testCase.verifyEqual(referenceResult, permute(ax2.on(), [1, 3, 2]), 'AbsTol', 1e-12); %% end function testZeros(testCase) z = quantity.Discrete.zeros([2, 7, 8], {linspace(0,10)', linspace(0, 23, 11)}, 'gridName', {'a', 'b'}); 
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