example_interview.ipynb 1.38 MB
 Theresa Pollinger committed Mar 08, 2018 1 2 3 { "cells": [ {  4  "cell_type": "markdown",  Theresa Pollinger committed Mar 08, 2018 5 6  "metadata": {}, "source": [  Theresa Pollinger committed Apr 06, 2018 7  "**Hello, user! I am TheInterview, your partial differential equations and simulations expert.**\n",  8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  "Let's set up a model and simulation together.\n", "\n", "To get explanations, enter explain . \n", "To see a recap of what we know so far, enter recap . \n", "To interactively visualize ther current theory graph, enter tgwiev or tgview mpd. \n", "Otherwise, you can always answer with LaTeX-type input.\n", "\n", "\n", "How many dimensions does your model have?\n", "\n", "\n", "I am just assuming it's 1, since that is all we can currently handle.\n", "\n", "\n", "\n", "\n", "What is the domain you would like to simulate for? Ω : type ❘ = [?;?], e.g. \\Omega = [0.0;1.0]\n", "By the way, you can always try and use LaTeX-type input.\n"  Theresa Pollinger committed Mar 08, 2018 26 27 28 29  ] }, { "cell_type": "code",  30  "execution_count": 1,  Theresa Pollinger committed Mar 08, 2018 31  "metadata": {},  32 33  "outputs": [ {  34 35 36 37 38  "data": { "text/markdown": [ "we will just assume that the variable is called x for now.\n", "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 39 40  "\n", "Which variable(s) are you looking for? / What are the unknowns in your model? u : Ω ⟶ ??, e.g., u : Ω ⟶ ℝ ?\n"  41 42 43 44  ] }, "metadata": {}, "output_type": "display_data"  45 46  } ],  Theresa Pollinger committed Mar 08, 2018 47  "source": [  Theresa Pollinger committed Apr 10, 2018 48  "Ω = [0.0;1.0]\n"  Theresa Pollinger committed Mar 08, 2018 49 50 51 52  ] }, { "cell_type": "code",  53  "execution_count": 2,  Theresa Pollinger committed Mar 08, 2018 54  "metadata": {},  55 56  "outputs": [ {  57 58  "data": { "text/markdown": [  59  "Ok, s : Ω ⟶ ℝ\n",  Theresa Pollinger committed Apr 06, 2018 60  "\n",  61 62  "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 63  "Would you like to name additional parameters like constants or functions (that are independent of your unknowns)? c : ℝ = ? or f : Ω ⟶ ℝ = ?\n"  64 65 66 67  ] }, "metadata": {}, "output_type": "display_data"  68 69  } ],  Theresa Pollinger committed Mar 08, 2018 70  "source": [  71  "s : Ω ⟶ ℝ"  Theresa Pollinger committed Mar 08, 2018 72 73 74 75  ] }, { "cell_type": "code",  76  "execution_count": 3,  Theresa Pollinger committed Mar 08, 2018 77  "metadata": {},  78 79  "outputs": [ {  80 81 82  "data": { "text/markdown": [ "Ok, f = [ x : Ω] x\n",  Theresa Pollinger committed Apr 06, 2018 83 84 85  "\n", "\n", "\n",  86 87 88 89 90  "Would you like to declare more parameters?\n" ] }, "metadata": {}, "output_type": "display_data"  91 92  } ],  Theresa Pollinger committed Mar 08, 2018 93 94 95 96 97 98  "source": [ "f = x" ] }, { "cell_type": "code",  99  "execution_count": 4,  Theresa Pollinger committed Mar 08, 2018 100  "metadata": {},  101 102  "outputs": [ {  103 104 105  "data": { "text/markdown": [ "Ok, α = [ x : Ω] -5.0\n",  Theresa Pollinger committed Apr 06, 2018 106 107 108  "\n", "\n", "\n",  109 110 111 112 113  "Would you like to declare more parameters?\n" ] }, "metadata": {}, "output_type": "display_data"  114 115  } ],  Theresa Pollinger committed Mar 08, 2018 116 117 118 119 120 121  "source": [ "\\alpha = -5.0" ] }, { "cell_type": "code",  122  "execution_count": 5,  Theresa Pollinger committed Mar 08, 2018 123  "metadata": {},  124 125  "outputs": [ {  126 127 128 129 130  "data": { "text/markdown": [] }, "metadata": {}, "output_type": "display_data"  131 132  } ],  Theresa Pollinger committed Mar 08, 2018 133 134 135 136 137 138  "source": [ "y" ] }, { "cell_type": "code",  139  "execution_count": 6,  140 141 142 143  "metadata": { "scrolled": true }, "outputs": [  Theresa Pollinger committed Apr 10, 2018 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  { "name": "stderr", "output_type": "stream", "text": [ "I did not catch that. Could you please rephrase?\n", "Details: MMT server error: unbound token: ·.
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info.kwarc.mmt.api.SourceError of level 2
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source error (object-parser) at http://mathhub.info/MitM/smglom/calculus/differentialequations#15.0.15:15.0.15\n", "\n", "
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\n", "\n" ]  296 297  } ],  Theresa Pollinger committed Mar 08, 2018 298 299 300 301 302 303  "source": [ "k = x \\cdot x" ] }, { "cell_type": "code",  304  "execution_count": 7,  Theresa Pollinger committed Mar 08, 2018 305  "metadata": {},  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  "outputs": [ { "data": { "text/markdown": [ "These are the things we know so far about your problem:\n", "\n", "\n", "\n", "\n", "\n", "\n", "domain: {'name': 'Ω', 'theoryname': 'ephdomain', 'axes': OrderedDict([('x', '[0.0;1.0]')]), 'from': '0.0', 'to': '1.0', 'boundary_name': 'Ω', 'viewname': 'ephdomainASmDomain'}\n", "\n", "\n", "\n", "\n", "\n", "\n", "unknowns: OrderedDict([('s', {'theoryname': 's', 'string': 's : Ω ⟶ ℝ', 'type': 'Ω ⟶ ℝ', 'codomain': 'ℝ', 'viewname': 'sASmUnknown'})])\n", "\n", "\n", "\n", "\n", "\n", "\n", "parameters: OrderedDict([('f', {'theoryname': 'f', 'string': 'f = x', 'parsestring': 'f = [ x : Ω] x', 'type': '{ : Ω } Ω', 'viewname': 'fASmParameter'}), ('α', {'theoryname': 'α', 'string': 'α = -5.0', 'parsestring': 'α = [ x : Ω] -5.0', 'type': '{ : Ω } ℝ', 'viewname': 'αASmParameter'})])\n", "\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "recap" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {},  349 350  "outputs": [ {  351 352 353 354 355 356  "data": { "text/markdown": [ "f = x\n", "α = -5.0\n", "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 357  "\n",  358 359 360 361 362  "Let's talk about your partial differential equation(s). What do they look like? Δu = 0.0, or laplace_operator Ω ℝ u = f ?\n" ] }, "metadata": {}, "output_type": "display_data"  363 364  } ],  Theresa Pollinger committed Mar 08, 2018 365 366 367 368 369 370  "source": [ "n" ] }, { "cell_type": "code",  371  "execution_count": 9,  Theresa Pollinger committed Mar 21, 2018 372 373 374  "metadata": { "scrolled": true },  375 376  "outputs": [ {  377 378 379 380  "data": { "text/markdown": [ "Ok, \n", " \n",  381  " \n",  382 383  " \n", " \n",  384  " \n",  385 386 387  " \n", " \n", " \n",  388  " \n",  389 390 391 392 393 394 395 396 397 398  " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n",  399  " \n",  400 401 402 403 404  " \n", " \n", " \n", " \n", " \n",  405  " \n",  406 407 408 409 410 411 412 413  " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n",  Theresa Pollinger committed Apr 06, 2018 414  " \n",  415 416 417 418 419 420 421 422 423 424  " \n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 425  "\n",  426 427 428 429 430 431  "These are all the PDEs needed.\n", "Let's discuss your boundary conditions. What do they look like? u(x) = f(x) or u(1.0) = \\alpha ?\n" ] }, "metadata": {}, "output_type": "display_data"  432 433  } ],  Theresa Pollinger committed Mar 08, 2018 434  "source": [  435  "Δs = \\alpha"  Theresa Pollinger committed Mar 08, 2018 436 437 438 439  ] }, { "cell_type": "code",  440  "execution_count": 10,  Theresa Pollinger committed Mar 08, 2018 441  "metadata": {},  442 443  "outputs": [ {  444 445  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 446 447 448 449 450 451 452 453 454  "Ok \n", "\n", "\n", "\n", "These are all the boundary conditions needed.\n", "\n", "\n", "\n", "Do you know something about the operator Δ? Is it e.g. linear, or not elliptic ? \n"  455 456 457 458  ] }, "metadata": {}, "output_type": "display_data"  459 460  } ],  Theresa Pollinger committed Mar 08, 2018 461  "source": [  462  "s = f"  Theresa Pollinger committed Mar 08, 2018 463 464 465 466  ] }, { "cell_type": "code",  467  "execution_count": 11,  Theresa Pollinger committed Mar 08, 2018 468  "metadata": {},  469 470  "outputs": [ {  471 472  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 473 474  "OK!\n", "do you know anything else?\n"  475 476 477 478  ] }, "metadata": {}, "output_type": "display_data"  479 480  } ],  Theresa Pollinger committed Mar 08, 2018 481 482 483 484 485 486  "source": [ "linear" ] }, { "cell_type": "code",  487  "execution_count": 12,  Theresa Pollinger committed Mar 08, 2018 488  "metadata": {},  489 490  "outputs": [ {  491 492  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 493 494  "OK!\n", "do you know anything else?\n"  495 496 497 498  ] }, "metadata": {}, "output_type": "display_data"  499 500  } ],  Theresa Pollinger committed Mar 08, 2018 501 502 503 504 505 506  "source": [ "elliptic" ] }, { "cell_type": "code",  507  "execution_count": 13,  Theresa Pollinger committed Mar 08, 2018 508  "metadata": {},  509 510  "outputs": [ {  511 512  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529  "\n", "\n", "\n", "These are the things we know so far about your problem:\n", "\n", "\n", "\n", "\n", "\n", "\n", "domain: {'name': 'Ω', 'theoryname': 'ephdomain', 'axes': OrderedDict([('x', '[0.0;1.0]')]), 'from': '0.0', 'to': '1.0', 'boundary_name': 'Ω', 'viewname': 'ephdomainASmDomain'}\n", "\n", "\n", "\n", "\n", "\n", "\n",  530  "unknowns: OrderedDict([('s', {'theoryname': 's', 'string': 's : Ω ⟶ ℝ', 'type': 'Ω ⟶ ℝ', 'codomain': 'ℝ', 'viewname': 'sASmUnknown'})])\n",  Theresa Pollinger committed Apr 10, 2018 531 532 533 534 535 536 537 538 539 540 541 542 543  "\n", "\n", "\n", "\n", "\n", "\n", "parameters: OrderedDict([('f', {'theoryname': 'f', 'string': 'f = x', 'parsestring': 'f = [ x : Ω] x', 'type': '{ : Ω } Ω', 'viewname': 'fASmParameter'}), ('α', {'theoryname': 'α', 'string': 'α = -5.0', 'parsestring': 'α = [ x : Ω] -5.0', 'type': '{ : Ω } ℝ', 'viewname': 'αASmParameter'})])\n", "\n", "\n", "\n", "\n", "\n", "\n",  544  "pdes: {'pdes': [{'theoryname': 'ephemeral_pde1', 'string': 'Δs = α', 'lhsstring': 'Δs', 'rhsstring': 'α', 'rhsstring_expanded': '-5.0', 'viewname': 'ephemeral_pde1ASmPDE', 'op': 'Δ', 'lhsparsestring': ' [ anys : Ω ⟶ ℝ ] Δ anys ', 'rhsparsestring': ' α'}]}\n",  Theresa Pollinger committed Apr 10, 2018 545 546 547 548 549 550  "\n", "\n", "\n", "\n", "\n", "\n",  551  "bcs: {'theoryname': 'ephbcs', 'bcs': [{'name': 'bc0', 'string': 's = f', 'lhsstring': 's', 'rhsstring': 'f', 'rhsstring_expanded': 'x', 'type': ('Dirichlet',), 'on': ('x',), 'measure': (2,)}], 'viewname': 'ephbcsASmBCsRequired', 'measure_given': 2}\n",  Theresa Pollinger committed Apr 10, 2018 552 553 554 555 556 557 558 559 560 561 562 563 564 565  "\n", "\n", "\n", "\n", "\n", "\n", "props: {'theoryname': 'ephBoundaryValueProblem', 'viewname': 'ephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem', 'ops': [{'name': 'Δ', 'props': ['elliptic'], 'linear': True}]}\n", "\n", "\n", "\n", "\n", "\n", "\n", "sim: {'type': None}\n",  566 567 568 569 570 571 572  "\n", "\n", "\n", "## Solving\n", "\n", "\n", "\n",  Theresa Pollinger committed Apr 10, 2018 573  "Would you like to try and solve the PDE using the Finite Difference Method in ExaStencils? If yes, you can provide a configuration name, or we'll just use your name.\n"  574 575 576 577  ] }, "metadata": {}, "output_type": "display_data"  578 579  } ],  Theresa Pollinger committed Mar 08, 2018 580 581 582 583 584 585  "source": [ "n" ] }, { "cell_type": "code",  586  "execution_count": 14,  Theresa Pollinger committed Mar 08, 2018 587  "metadata": {},  588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678  "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generated ExaStencils input; running ExaStencils\n", "Ran ExaStencils; preparing visualization\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", " \n", " my plot\n", " \n", "\n", " \n", "\n", "\n", " \n", " \n", " \n", "
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