"
922 | ]
923 | },
924 | "execution_count": 34,
925 | "metadata": {},
926 | "output_type": "execute_result"
927 | }
928 | ],
929 | "source": [
930 | "# Esta celda da el estilo al notebook\n",
931 | "from IPython.core.display import HTML\n",
932 | "css_file = '../static/styles/style.css'\n",
933 | "HTML(open(css_file, \"r\").read())"
934 | ]
935 | }
936 | ],
937 | "metadata": {
938 | "anaconda-cloud": {},
939 | "kernelspec": {
940 | "display_name": "Python [default]",
941 | "language": "python",
942 | "name": "python3"
943 | },
944 | "language_info": {
945 | "codemirror_mode": {
946 | "name": "ipython",
947 | "version": 3
948 | },
949 | "file_extension": ".py",
950 | "mimetype": "text/x-python",
951 | "name": "python",
952 | "nbconvert_exporter": "python",
953 | "pygments_lexer": "ipython3",
954 | "version": "3.5.2"
955 | },
956 | "widgets": {
957 | "state": {
958 | "d8f76be24aa9464ab37ea1b7fb8c7806": {
959 | "views": [
960 | {
961 | "cell_index": 70
962 | }
963 | ]
964 | }
965 | },
966 | "version": "1.2.0"
967 | }
968 | },
969 | "nbformat": 4,
970 | "nbformat_minor": 0
971 | }
972 |
--------------------------------------------------------------------------------
/notebooks/02-NumPy.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "![\"AeroPython\"](\"../static/aeropython_name_mini.png\")
"
8 | ]
9 | },
10 | {
11 | "cell_type": "markdown",
12 | "metadata": {},
13 | "source": [
14 | "# 02-NumPy"
15 | ]
16 | },
17 | {
18 | "cell_type": "markdown",
19 | "metadata": {},
20 | "source": [
21 | "_Hasta ahora hemos visto los tipos de datos más básicos que nos ofrece Python: integer, real, complex, boolean, list, tuple... Pero ¿no echas algo de menos? Efectivamente, los __arrays__. _\n",
22 | "\n",
23 | "_Durante esta nos adentraremos en el paquete NumPy: veremos como los arrays mejoran la eficiencia de nuestro código, aprenderemos a crearlos y a operar con ellos_."
24 | ]
25 | },
26 | {
27 | "cell_type": "markdown",
28 | "metadata": {},
29 | "source": [
30 | "## ¿Qué es un array? "
31 | ]
32 | },
33 | {
34 | "cell_type": "markdown",
35 | "metadata": {},
36 | "source": [
37 | "Un array es un __bloque de memoria que contiene elementos del mismo tipo__. Básicamente:\n",
38 | "\n",
39 | "* nos _recuerdan_ a los vectores, matrices, tensores...\n",
40 | "* podemos almacenar el array con un nombre y acceder a sus __elementos__ mediante sus __índices__.\n",
41 | "* ayudan a gestionar de manera eficiente la memoria y a acelerar los cálculos.\n",
42 | "\n",
43 | "\n",
44 | "---\n",
45 | "\n",
46 | "| Índice | 0 | 1 | 2 | 3 | ... | n-1 | n |\n",
47 | "| ---------- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n",
48 | "| Valor | 2.1 | 3.6 | 7.8 | 1.5 | ... | 5.4 | 6.3 |\n",
49 | "\n",
50 | "---\n",
51 | "\n",
52 | "__¿Qué solemos guardar en arrays?__\n",
53 | "\n",
54 | "* Vectores y matrices.\n",
55 | "* Datos de experimentos:\n",
56 | " - En distintos instantes discretos.\n",
57 | " - En distintos puntos del espacio.\n",
58 | "* Resultado de evaluar funciones con los datos anteriores.\n",
59 | "* Discretizaciones para usar algoritmos de: integración, derivación, interpolación...\n",
60 | "* ... "
61 | ]
62 | },
63 | {
64 | "cell_type": "markdown",
65 | "metadata": {},
66 | "source": [
67 | "## ¿Qué es NumPy?"
68 | ]
69 | },
70 | {
71 | "cell_type": "markdown",
72 | "metadata": {},
73 | "source": [
74 | "NumPy es un paquete fundamental para la programación científica que __proporciona un objeto tipo array__ para almacenar datos de forma eficiente y una serie de __funciones__ para operar y manipular esos datos.\n",
75 | "Para usar NumPy lo primero que debemos hacer es importarlo:"
76 | ]
77 | },
78 | {
79 | "cell_type": "code",
80 | "execution_count": null,
81 | "metadata": {
82 | "collapsed": false
83 | },
84 | "outputs": [],
85 | "source": []
86 | },
87 | {
88 | "cell_type": "markdown",
89 | "metadata": {},
90 | "source": [
91 | "## Nuestro primer array"
92 | ]
93 | },
94 | {
95 | "cell_type": "markdown",
96 | "metadata": {},
97 | "source": [
98 | "¿No decíamos que Python era fácil? Pues __creemos nuestros primeros arrays__:"
99 | ]
100 | },
101 | {
102 | "cell_type": "code",
103 | "execution_count": null,
104 | "metadata": {
105 | "collapsed": false
106 | },
107 | "outputs": [],
108 | "source": [
109 | "# Array de una dimensión"
110 | ]
111 | },
112 | {
113 | "cell_type": "code",
114 | "execution_count": null,
115 | "metadata": {
116 | "collapsed": false
117 | },
118 | "outputs": [],
119 | "source": [
120 | "# Podemos usar print"
121 | ]
122 | },
123 | {
124 | "cell_type": "code",
125 | "execution_count": null,
126 | "metadata": {
127 | "collapsed": false
128 | },
129 | "outputs": [],
130 | "source": [
131 | "# Comprobar el tipo de mi_primer_array"
132 | ]
133 | },
134 | {
135 | "cell_type": "code",
136 | "execution_count": null,
137 | "metadata": {
138 | "collapsed": false
139 | },
140 | "outputs": [],
141 | "source": [
142 | "# Comprobar el tipo de datos que contiene"
143 | ]
144 | },
145 | {
146 | "cell_type": "markdown",
147 | "metadata": {},
148 | "source": [
149 | "Los arrays de una dimensión se crean pasándole una lista como argumento a la función `np.array`. Para crear un array de dos dimensiones le pasaremos una _lista de listas_:"
150 | ]
151 | },
152 | {
153 | "cell_type": "code",
154 | "execution_count": null,
155 | "metadata": {
156 | "collapsed": false
157 | },
158 | "outputs": [],
159 | "source": [
160 | "# Array de dos dimensiones"
161 | ]
162 | },
163 | {
164 | "cell_type": "markdown",
165 | "metadata": {},
166 | "source": [
167 | "Esto sería una buena manera de definirlo, de acuerdo con el [PEP 8 (indentation)](http://legacy.python.org/dev/peps/pep-0008/#indentation)."
168 | ]
169 | },
170 | {
171 | "cell_type": "markdown",
172 | "metadata": {},
173 | "source": [
174 | "### Funciones y constantes de NumPy"
175 | ]
176 | },
177 | {
178 | "cell_type": "markdown",
179 | "metadata": {},
180 | "source": [
181 | "Hemos dicho que NumPy también incorporá __funciones__. Un ejemplo sencillo:"
182 | ]
183 | },
184 | {
185 | "cell_type": "code",
186 | "execution_count": null,
187 | "metadata": {
188 | "collapsed": false
189 | },
190 | "outputs": [],
191 | "source": [
192 | "# Suma"
193 | ]
194 | },
195 | {
196 | "cell_type": "code",
197 | "execution_count": null,
198 | "metadata": {
199 | "collapsed": false
200 | },
201 | "outputs": [],
202 | "source": [
203 | "# Máximo"
204 | ]
205 | },
206 | {
207 | "cell_type": "code",
208 | "execution_count": null,
209 | "metadata": {
210 | "collapsed": false
211 | },
212 | "outputs": [],
213 | "source": [
214 | "# Seno"
215 | ]
216 | },
217 | {
218 | "cell_type": "markdown",
219 | "metadata": {},
220 | "source": [
221 | "Y algunas __constantes__ que podemos neccesitar:"
222 | ]
223 | },
224 | {
225 | "cell_type": "code",
226 | "execution_count": null,
227 | "metadata": {
228 | "collapsed": false
229 | },
230 | "outputs": [],
231 | "source": []
232 | },
233 | {
234 | "cell_type": "markdown",
235 | "metadata": {},
236 | "source": [
237 | "## Funciones para crear arrays"
238 | ]
239 | },
240 | {
241 | "cell_type": "markdown",
242 | "metadata": {},
243 | "source": [
244 | "### Rangos"
245 | ]
246 | },
247 | {
248 | "cell_type": "markdown",
249 | "metadata": {},
250 | "source": [
251 | "#### np.arange"
252 | ]
253 | },
254 | {
255 | "cell_type": "markdown",
256 | "metadata": {},
257 | "source": [
258 | "NumPy, dame __un array que vaya de 0 a 5__:"
259 | ]
260 | },
261 | {
262 | "cell_type": "code",
263 | "execution_count": null,
264 | "metadata": {
265 | "collapsed": false
266 | },
267 | "outputs": [],
268 | "source": []
269 | },
270 | {
271 | "cell_type": "markdown",
272 | "metadata": {},
273 | "source": [
274 | "__Mira con atención el resultado anterior__, ¿hay algo que deberías grabar en tu cabeza para simpre?\n",
275 | "__El último elemento no es 5 sino 4__"
276 | ]
277 | },
278 | {
279 | "cell_type": "markdown",
280 | "metadata": {},
281 | "source": [
282 | "NumPy, dame __un array que vaya de 0 a 10, de 3 en 3__:"
283 | ]
284 | },
285 | {
286 | "cell_type": "code",
287 | "execution_count": null,
288 | "metadata": {
289 | "collapsed": false
290 | },
291 | "outputs": [],
292 | "source": []
293 | },
294 | {
295 | "cell_type": "markdown",
296 | "metadata": {},
297 | "source": [
298 | "#### np.linspace"
299 | ]
300 | },
301 | {
302 | "cell_type": "markdown",
303 | "metadata": {},
304 | "source": [
305 | "Si has tenido que usar MATLAB alguna vez, seguro que esto te suena:"
306 | ]
307 | },
308 | {
309 | "cell_type": "code",
310 | "execution_count": null,
311 | "metadata": {
312 | "collapsed": false
313 | },
314 | "outputs": [],
315 | "source": []
316 | },
317 | {
318 | "cell_type": "markdown",
319 | "metadata": {},
320 | "source": [
321 | "En este caso sí que se incluye el último elemento."
322 | ]
323 | },
324 | {
325 | "cell_type": "markdown",
326 | "metadata": {},
327 | "source": [
328 | "Nota: \n",
329 | "También puedes probar `np.logspace()`\n",
330 | "
"
331 | ]
332 | },
333 | {
334 | "cell_type": "markdown",
335 | "metadata": {},
336 | "source": [
337 | "### reshape"
338 | ]
339 | },
340 | {
341 | "cell_type": "markdown",
342 | "metadata": {},
343 | "source": [
344 | "Con `np.arange()` es posible crear \"vectores\" cuyos elementos tomen valores consecutivos o equiespaciados, como hemos visto anteriormente. ¿Podemos hacer lo mismo con \"matrices\"? Pues sí, pero no usando una sola función. Imagina que quieres crear algo como esto:\n",
345 | "\n",
346 | "\\begin{pmatrix}\n",
347 | " 1 & 2 & 3\\\\ \n",
348 | " 4 & 5 & 6\\\\\n",
349 | " 7 & 8 & 9\\\\\n",
350 | " \\end{pmatrix}\n",
351 | " \n",
352 | "* Comenzaremos por crear un array 1d con los valores $(1,2,3,4,5,6,7,8,9)$ usando `np.arange()`.\n",
353 | "* Luego le daremos forma de array 2d. con `np.reshape(array, (dim0, dim1))`."
354 | ]
355 | },
356 | {
357 | "cell_type": "code",
358 | "execution_count": null,
359 | "metadata": {
360 | "collapsed": false
361 | },
362 | "outputs": [],
363 | "source": [
364 | "a = np.arange(1,10)\n",
365 | "M = np.reshape(a, [3,3])\n",
366 | "M"
367 | ]
368 | },
369 | {
370 | "cell_type": "code",
371 | "execution_count": null,
372 | "metadata": {
373 | "collapsed": false
374 | },
375 | "outputs": [],
376 | "source": [
377 | "# También funciona como método\n",
378 | "N = a.reshape([3,3])\n",
379 | "N"
380 | ]
381 | },
382 | {
383 | "cell_type": "markdown",
384 | "metadata": {},
385 | "source": [
386 | "Nota: \n",
387 | "No vamos a entrar demasiado en qué son los métodos, pero debes saber que están asociados a la programación orientada a objetos y que en Python todo es un objeto. Lo que debes pensar es que son unas funciones especiales en las que el argumento más importante (sobre el que se realiza la acción) se escribe delante seguido de un punto. Por ejemplo: `.método(argumentos)`\n",
388 | "
"
389 | ]
390 | },
391 | {
392 | "cell_type": "markdown",
393 | "metadata": {},
394 | "source": [
395 | "## Operaciones"
396 | ]
397 | },
398 | {
399 | "cell_type": "markdown",
400 | "metadata": {},
401 | "source": [
402 | "### Operaciones elemento a elemento"
403 | ]
404 | },
405 | {
406 | "cell_type": "markdown",
407 | "metadata": {},
408 | "source": [
409 | "Ahora que pocas cosas se nos escapan de los arrays, probemos a hacer algunas operaciones. El funcionamiento es el habitual en FORTRAN y MATLAB y poco hay que añadir:"
410 | ]
411 | },
412 | {
413 | "cell_type": "code",
414 | "execution_count": null,
415 | "metadata": {
416 | "collapsed": false
417 | },
418 | "outputs": [],
419 | "source": [
420 | "#crear un arra y y sumarle un número\n",
421 | "arr = np.arange(11)\n",
422 | "arr + 55"
423 | ]
424 | },
425 | {
426 | "cell_type": "code",
427 | "execution_count": null,
428 | "metadata": {
429 | "collapsed": false
430 | },
431 | "outputs": [],
432 | "source": [
433 | "#multiplicarlo por un número\n",
434 | "arr * 2"
435 | ]
436 | },
437 | {
438 | "cell_type": "code",
439 | "execution_count": null,
440 | "metadata": {
441 | "collapsed": false
442 | },
443 | "outputs": [],
444 | "source": [
445 | "#elevarlo al cuadrado\n",
446 | "arr ** 2"
447 | ]
448 | },
449 | {
450 | "cell_type": "code",
451 | "execution_count": null,
452 | "metadata": {
453 | "collapsed": false
454 | },
455 | "outputs": [],
456 | "source": [
457 | "#calcular una función\n",
458 | "np.tanh(arr)"
459 | ]
460 | },
461 | {
462 | "cell_type": "markdown",
463 | "metadata": {},
464 | "source": [
465 | "Entrenamiento: \n",
466 | "Puedes tratar de comparar la diferencia de tiempo entre realizar la operación en bloque, como ahora, y realizarla elemento a elemento, recorriendo el array con un bucle.\n",
467 | "
"
468 | ]
469 | },
470 | {
471 | "cell_type": "markdown",
472 | "metadata": {},
473 | "source": [
474 | "__Si las operaciones involucran dos arrays también se realizan elemento a elemento__"
475 | ]
476 | },
477 | {
478 | "cell_type": "code",
479 | "execution_count": null,
480 | "metadata": {
481 | "collapsed": false
482 | },
483 | "outputs": [],
484 | "source": [
485 | "#creamos dos arrays\n",
486 | "arr1 = np.arange(0,11)\n",
487 | "arr2 = np.arange(20,31)"
488 | ]
489 | },
490 | {
491 | "cell_type": "code",
492 | "execution_count": null,
493 | "metadata": {
494 | "collapsed": false
495 | },
496 | "outputs": [],
497 | "source": [
498 | "#los sumamos\n",
499 | "arr1 + arr2"
500 | ]
501 | },
502 | {
503 | "cell_type": "code",
504 | "execution_count": null,
505 | "metadata": {
506 | "collapsed": false
507 | },
508 | "outputs": [],
509 | "source": [
510 | "#multiplicamos\n",
511 | "arr1 * arr2"
512 | ]
513 | },
514 | {
515 | "cell_type": "markdown",
516 | "metadata": {},
517 | "source": [
518 | "#### Comparaciones"
519 | ]
520 | },
521 | {
522 | "cell_type": "code",
523 | "execution_count": null,
524 | "metadata": {
525 | "collapsed": false
526 | },
527 | "outputs": [],
528 | "source": [
529 | "# >,<\n",
530 | "arr1 > arr2"
531 | ]
532 | },
533 | {
534 | "cell_type": "code",
535 | "execution_count": null,
536 | "metadata": {
537 | "collapsed": false
538 | },
539 | "outputs": [],
540 | "source": [
541 | "# ==\n",
542 | "arr1 == arr2 # ¡ojo! los arrays son de integers, no de floats"
543 | ]
544 | },
545 | {
546 | "cell_type": "markdown",
547 | "metadata": {},
548 | "source": [
549 | "Nota: \n",
550 | "Por cierto, ¿qúe ocurrirá si los arrays con los que se quiere operar no tiene la misma forma? ¿apuestas? Quizá más adelante te interese buscar algo de información sobre __broadcasting__.\n",
551 | "
"
552 | ]
553 | },
554 | {
555 | "cell_type": "markdown",
556 | "metadata": {},
557 | "source": [
558 | "## Álgebra lineal"
559 | ]
560 | },
561 | {
562 | "cell_type": "markdown",
563 | "metadata": {},
564 | "source": [
565 | "_Una vez hemos visto el manejo básico de arrays en Python con NumPy, es hora de pasar a operaciones más interesantes como son las propias del Álgebra Lineal._\n",
566 | "\n",
567 | "_Los productos escalares y las inversiones de matrices están por todas partes en los programas científicos e ingenieriles, así que vamos a estudiar cómo se realizan en Python._"
568 | ]
569 | },
570 | {
571 | "cell_type": "markdown",
572 | "metadata": {},
573 | "source": [
574 | "Como sabemos, las operaciones del álgebra lineal aparecen con mucha frecuencia a la hora de resolver sistemas de ecuaciones en derivadas parciales y en general al linealizar problemas de todo tipo, y suele ser necesario resolver sistemas con un número enorme de ecuaciones e incógnitas. Gracias a los arrays de NumPy podemos abordar este tipo de cálculos en Python, ya que todas las funciones están escritas en C o Fortran y tenemos la opción de usar bibliotecas optimizadas al límite."
575 | ]
576 | },
577 | {
578 | "cell_type": "markdown",
579 | "metadata": {},
580 | "source": [
581 | "El paquete de álgebra lineal en NumPy se llama `linalg`, así que importando NumPy con la convención habitual podemos acceder a él escribiendo `np.linalg`. Si imprimimos la ayuda del paquete vemos que tenemos funciones para:\n",
582 | "\n",
583 | "* Funciones básicas (norma de un vector, inversa de una matriz, determinante, traza)\n",
584 | "* Resolución de sistemas\n",
585 | "* Autovalores y autovectores\n",
586 | "* Descomposiciones matriciales (QR, SVD)\n",
587 | "* Pseudoinversas"
588 | ]
589 | },
590 | {
591 | "cell_type": "code",
592 | "execution_count": null,
593 | "metadata": {
594 | "collapsed": false
595 | },
596 | "outputs": [],
597 | "source": [
598 | "import numpy as np"
599 | ]
600 | },
601 | {
602 | "cell_type": "code",
603 | "execution_count": null,
604 | "metadata": {
605 | "collapsed": false
606 | },
607 | "outputs": [],
608 | "source": [
609 | "help(np.linalg)"
610 | ]
611 | },
612 | {
613 | "cell_type": "markdown",
614 | "metadata": {},
615 | "source": [
616 | "Recordemos que si queremos usar una función de un paquete pero no queremos escribir la \"ruta\" completa cada vez, podemos usar la sintaxis `from package import func`:"
617 | ]
618 | },
619 | {
620 | "cell_type": "code",
621 | "execution_count": null,
622 | "metadata": {
623 | "collapsed": false
624 | },
625 | "outputs": [],
626 | "source": []
627 | },
628 | {
629 | "cell_type": "markdown",
630 | "metadata": {},
631 | "source": [
632 | "El producto matricial usual (no el que se hace elemento a elemento, sino el del álgebra lineal) se calcula con la misma función que el producto matriz-vector y el producto escalar vector-vector: con la función `dot`, que **no** está en el paquete `linalg` sino directamente en `numpy` y no hace falta importarlo."
633 | ]
634 | },
635 | {
636 | "cell_type": "code",
637 | "execution_count": null,
638 | "metadata": {
639 | "collapsed": false
640 | },
641 | "outputs": [],
642 | "source": [
643 | "np.dot"
644 | ]
645 | },
646 | {
647 | "cell_type": "markdown",
648 | "metadata": {},
649 | "source": [
650 | "Una consideración importante a tener en cuenta es que en NumPy no hace falta ser estricto a la hora de manejar vectores como si fueran matrices columna, siempre que la operación sea consistente. Un vector es una matriz con una sola dimensión: por eso si calculamos su traspuesta no funciona."
651 | ]
652 | },
653 | {
654 | "cell_type": "code",
655 | "execution_count": null,
656 | "metadata": {
657 | "collapsed": false
658 | },
659 | "outputs": [],
660 | "source": [
661 | "M = np.array([\n",
662 | " [1, 2],\n",
663 | " [3, 4]\n",
664 | "])\n",
665 | "v = np.array([1, -1])"
666 | ]
667 | },
668 | {
669 | "cell_type": "code",
670 | "execution_count": null,
671 | "metadata": {
672 | "collapsed": false
673 | },
674 | "outputs": [],
675 | "source": [
676 | "# ¡La traspuesta del vector no incrementa las dimensiones!"
677 | ]
678 | },
679 | {
680 | "cell_type": "code",
681 | "execution_count": null,
682 | "metadata": {
683 | "collapsed": false
684 | },
685 | "outputs": [],
686 | "source": []
687 | },
688 | {
689 | "cell_type": "markdown",
690 | "metadata": {},
691 | "source": [
692 | "El mismo resultado se obtiene usando el operador `@`, nuevo en Python 3.5:"
693 | ]
694 | },
695 | {
696 | "cell_type": "code",
697 | "execution_count": null,
698 | "metadata": {
699 | "collapsed": false
700 | },
701 | "outputs": [],
702 | "source": []
703 | },
704 | {
705 | "cell_type": "markdown",
706 | "metadata": {},
707 | "source": [
708 | "Para hacer comparaciones entre arrays de punto flotante se pueden usar las funciones `np.allclose` y `np.isclose`. La primera comprueba si todos los elementos de los arrays son iguales dentro de una tolerancia, y la segunda compara elemento a elemento y devuelve un array de valores `True` y `False`."
709 | ]
710 | },
711 | {
712 | "cell_type": "code",
713 | "execution_count": null,
714 | "metadata": {
715 | "collapsed": false
716 | },
717 | "outputs": [],
718 | "source": [
719 | "u, v"
720 | ]
721 | },
722 | {
723 | "cell_type": "code",
724 | "execution_count": null,
725 | "metadata": {
726 | "collapsed": false
727 | },
728 | "outputs": [],
729 | "source": [
730 | "np.allclose(u, v)"
731 | ]
732 | },
733 | {
734 | "cell_type": "code",
735 | "execution_count": null,
736 | "metadata": {
737 | "collapsed": false
738 | },
739 | "outputs": [],
740 | "source": [
741 | "np.isclose(0.0, 1e-8, atol=1e-10)"
742 | ]
743 | },
744 | {
745 | "cell_type": "markdown",
746 | "metadata": {},
747 | "source": [
748 | "### Ejercicios"
749 | ]
750 | },
751 | {
752 | "cell_type": "markdown",
753 | "metadata": {},
754 | "source": [
755 | "1- Hallar el producto de estas dos matrices y su determinante:\n",
756 | "\n",
757 | "$$\\begin{pmatrix} 1 & 0 & 0 \\\\ 2 & 1 & 1 \\\\ -1 & 0 & 1 \\end{pmatrix} \\begin{pmatrix} 2 & 3 & -1 \\\\ 0 & -2 & 1 \\\\ 0 & 0 & 3 \\end{pmatrix}$$"
758 | ]
759 | },
760 | {
761 | "cell_type": "code",
762 | "execution_count": null,
763 | "metadata": {
764 | "collapsed": false
765 | },
766 | "outputs": [],
767 | "source": [
768 | "from numpy.linalg import det"
769 | ]
770 | },
771 | {
772 | "cell_type": "code",
773 | "execution_count": null,
774 | "metadata": {
775 | "collapsed": false
776 | },
777 | "outputs": [],
778 | "source": [
779 | "A = np.array([\n",
780 | " ...\n",
781 | "])\n",
782 | "B = np.array([\n",
783 | " ...\n",
784 | "])\n",
785 | "print(A)\n",
786 | "print(B)"
787 | ]
788 | },
789 | {
790 | "cell_type": "code",
791 | "execution_count": null,
792 | "metadata": {
793 | "collapsed": false
794 | },
795 | "outputs": [],
796 | "source": []
797 | },
798 | {
799 | "cell_type": "code",
800 | "execution_count": null,
801 | "metadata": {
802 | "collapsed": false
803 | },
804 | "outputs": [],
805 | "source": []
806 | },
807 | {
808 | "cell_type": "markdown",
809 | "metadata": {},
810 | "source": [
811 | "2- Resolver el siguiente sistema:\n",
812 | "\n",
813 | "$$ \\begin{pmatrix} 2 & 0 & 0 \\\\ -1 & 1 & 0 \\\\ 3 & 2 & -1 \\end{pmatrix} \\begin{pmatrix} 1 & 1 & 1 \\\\ 0 & 1 & 2 \\\\ 0 & 0 & 1 \\end{pmatrix} \\begin{pmatrix} x \\\\ y \\\\ z \\end{pmatrix} = \\begin{pmatrix} -1 \\\\ 3 \\\\ 0 \\end{pmatrix} $$"
814 | ]
815 | },
816 | {
817 | "cell_type": "code",
818 | "execution_count": null,
819 | "metadata": {
820 | "collapsed": false
821 | },
822 | "outputs": [],
823 | "source": [
824 | "M = ..."
825 | ]
826 | },
827 | {
828 | "cell_type": "code",
829 | "execution_count": null,
830 | "metadata": {
831 | "collapsed": false
832 | },
833 | "outputs": [],
834 | "source": [
835 | "x = ..."
836 | ]
837 | },
838 | {
839 | "cell_type": "code",
840 | "execution_count": null,
841 | "metadata": {
842 | "collapsed": false
843 | },
844 | "outputs": [],
845 | "source": [
846 | "np.allclose(np.dot(M, x), np.array([-1, 3, 0]))"
847 | ]
848 | },
849 | {
850 | "cell_type": "markdown",
851 | "metadata": {},
852 | "source": [
853 | "3- Hallar la inversa de la matriz $H$ y comprobar que $H H^{-1} = I$ (recuerda la función `np.eye`)"
854 | ]
855 | },
856 | {
857 | "cell_type": "code",
858 | "execution_count": null,
859 | "metadata": {
860 | "collapsed": false
861 | },
862 | "outputs": [],
863 | "source": [
864 | "H = np.array(\n",
865 | "[[ 2, 4, 7, 12, 21, 38],\n",
866 | " [ 71, 128, 265, 512, 1035, 2048],\n",
867 | " [ 4109, 8206, 16399, 32784, 65553, 131090],\n",
868 | " [ 262145, 524308, 1048577, 2097174, 4194305, 8388632],\n",
869 | " [ 16777271, 33554488, 67108921, 134217786, 268435515, 536870972],\n",
870 | " [ 1073741855, 2147483680, 4294967329, 8589934626, 17179869219, 34359738404]]\n",
871 | ")\n",
872 | "print(H)"
873 | ]
874 | },
875 | {
876 | "cell_type": "code",
877 | "execution_count": null,
878 | "metadata": {
879 | "collapsed": false
880 | },
881 | "outputs": [],
882 | "source": []
883 | },
884 | {
885 | "cell_type": "code",
886 | "execution_count": null,
887 | "metadata": {
888 | "collapsed": false
889 | },
890 | "outputs": [],
891 | "source": []
892 | },
893 | {
894 | "cell_type": "code",
895 | "execution_count": null,
896 | "metadata": {
897 | "collapsed": false
898 | },
899 | "outputs": [],
900 | "source": [
901 | "np.isclose(np.dot(Hinv, H), np.eye(6))"
902 | ]
903 | },
904 | {
905 | "cell_type": "code",
906 | "execution_count": null,
907 | "metadata": {
908 | "collapsed": false
909 | },
910 | "outputs": [],
911 | "source": [
912 | "np.set_printoptions(precision=3)\n",
913 | "print(np.dot(Hinv, H))"
914 | ]
915 | },
916 | {
917 | "cell_type": "markdown",
918 | "metadata": {},
919 | "source": [
920 | "¡No funciona! Y no solo eso sino que los resultados varían de un ordenador a otro.
"
921 | ]
922 | },
923 | {
924 | "cell_type": "markdown",
925 | "metadata": {},
926 | "source": [
927 | "4- Comprobar el número de condición de la matriz $H$."
928 | ]
929 | },
930 | {
931 | "cell_type": "code",
932 | "execution_count": null,
933 | "metadata": {
934 | "collapsed": false
935 | },
936 | "outputs": [],
937 | "source": []
938 | },
939 | {
940 | "cell_type": "markdown",
941 | "metadata": {},
942 | "source": [
943 | "La matriz está mal condicionada.
"
944 | ]
945 | },
946 | {
947 | "cell_type": "markdown",
948 | "metadata": {},
949 | "source": [
950 | "## Secciones de arrays"
951 | ]
952 | },
953 | {
954 | "cell_type": "markdown",
955 | "metadata": {},
956 | "source": [
957 | "Hasta ahora hemos visto cómo acceder a elementos aislados del array, pero la potencia de NumPy está en poder acceder a secciones enteras. Para ello se usa la sintaxis `inicio:final:paso`: si alguno de estos valores no se pone toma un valor por defecto. Veamos ejemplos:"
958 | ]
959 | },
960 | {
961 | "cell_type": "code",
962 | "execution_count": null,
963 | "metadata": {
964 | "collapsed": false
965 | },
966 | "outputs": [],
967 | "source": [
968 | "M = np.arange(36, dtype=float).reshape(4, 9)\n",
969 | "M"
970 | ]
971 | },
972 | {
973 | "cell_type": "code",
974 | "execution_count": null,
975 | "metadata": {
976 | "collapsed": false
977 | },
978 | "outputs": [],
979 | "source": [
980 | "# De la segunda a la tercera fila, incluida"
981 | ]
982 | },
983 | {
984 | "cell_type": "code",
985 | "execution_count": null,
986 | "metadata": {
987 | "collapsed": false
988 | },
989 | "outputs": [],
990 | "source": [
991 | "# Hasta la tercera fila sin incluir y de la segunda a la quinta columnas saltando dos"
992 | ]
993 | },
994 | {
995 | "cell_type": "markdown",
996 | "metadata": {},
997 | "source": [
998 | "### Ejercicio"
999 | ]
1000 | },
1001 | {
1002 | "cell_type": "markdown",
1003 | "metadata": {},
1004 | "source": [
1005 | "Pintar un tablero de ajedrez usando la función `plt.matshow`."
1006 | ]
1007 | },
1008 | {
1009 | "cell_type": "code",
1010 | "execution_count": null,
1011 | "metadata": {
1012 | "collapsed": false
1013 | },
1014 | "outputs": [],
1015 | "source": [
1016 | "tablero = ..."
1017 | ]
1018 | },
1019 | {
1020 | "cell_type": "code",
1021 | "execution_count": null,
1022 | "metadata": {
1023 | "collapsed": false
1024 | },
1025 | "outputs": [],
1026 | "source": [
1027 | "%matplotlib inline\n",
1028 | "import matplotlib.pyplot as plt\n",
1029 | "\n",
1030 | "plt.matshow(tablero, cmap=plt.cm.gray_r)"
1031 | ]
1032 | },
1033 | {
1034 | "cell_type": "markdown",
1035 | "metadata": {},
1036 | "source": [
1037 | "## Entrada/Salida"
1038 | ]
1039 | },
1040 | {
1041 | "cell_type": "markdown",
1042 | "metadata": {},
1043 | "source": [
1044 | "Con E/S (I/O en inglés) entendemos leer y escribir datos archivos. Es algo que necesitaremos hacer con relativa frecuencia, y en NumPy es muy sencillo de hacer. Para el caso de la **lectura** se usa la función `np.loadtxt`."
1045 | ]
1046 | },
1047 | {
1048 | "cell_type": "markdown",
1049 | "metadata": {},
1050 | "source": [
1051 | "Para practicar, vamos a leer el archivo `temperaturas.csv` que contiene datos diarios de temperaturas en Nueva York entre el 1 de enero de 2013 y el 1 de enero de 2014, obtenidos gratuitamente de http://ncdc.noaa.gov/. Como los hemos descargado en formato CSV habrá que tener algunas precauciones a la hora de leer el archivo."
1052 | ]
1053 | },
1054 | {
1055 | "cell_type": "code",
1056 | "execution_count": null,
1057 | "metadata": {
1058 | "collapsed": false
1059 | },
1060 | "outputs": [],
1061 | "source": [
1062 | "#!head ../static/temperaturas.csv # Esta línea no funciona en Windows\n",
1063 | "!type ../static/temperaturas.csv"
1064 | ]
1065 | },
1066 | {
1067 | "cell_type": "code",
1068 | "execution_count": null,
1069 | "metadata": {
1070 | "collapsed": false
1071 | },
1072 | "outputs": [],
1073 | "source": [
1074 | "# Saltamos una línea\n",
1075 | "# Solo columnas 2, 3 y 4\n",
1076 | "# Separados por comas"
1077 | ]
1078 | },
1079 | {
1080 | "cell_type": "markdown",
1081 | "metadata": {},
1082 | "source": [
1083 | "La primera columna es un entero con formato \"AAAAMMDD\" que vamos a ignorar. Las temperaturas están medidas en décimas de grado Celsius, así que hay que pasarlas a grados Celsius. Vamos a calcular también la temperatura media."
1084 | ]
1085 | },
1086 | {
1087 | "cell_type": "code",
1088 | "execution_count": null,
1089 | "metadata": {
1090 | "collapsed": false
1091 | },
1092 | "outputs": [],
1093 | "source": []
1094 | },
1095 | {
1096 | "cell_type": "markdown",
1097 | "metadata": {},
1098 | "source": [
1099 | "Como vamos a ignorar la columna de las fechas tenemos que crear un dominio para el eje x. Simplemente construiremos un array de enteros desde 0 hasta 365."
1100 | ]
1101 | },
1102 | {
1103 | "cell_type": "code",
1104 | "execution_count": null,
1105 | "metadata": {
1106 | "collapsed": false
1107 | },
1108 | "outputs": [],
1109 | "source": []
1110 | },
1111 | {
1112 | "cell_type": "markdown",
1113 | "metadata": {},
1114 | "source": [
1115 | "Supongamos que ahora queremos guardar nuestra tabla de datos en un archivo txt, para poder cargarlo ya modificado más adelante. Una manera fácil de hacerlo sería con otra función de NumPy: `np.savetxt`. Lo usaremos con los argumentos opcionales `fmt='%.5f', newline = '\\r\\n'` para obtener un fichero *bonito* que podamos entender de un vistazo."
1116 | ]
1117 | },
1118 | {
1119 | "cell_type": "code",
1120 | "execution_count": null,
1121 | "metadata": {
1122 | "collapsed": false
1123 | },
1124 | "outputs": [],
1125 | "source": [
1126 | "matriz_datos = np.zeros([366, 4])\n",
1127 | "matriz_datos[:, 0] = x\n",
1128 | "matriz_datos[:, 1] = Tmax\n",
1129 | "matriz_datos[:, 2] = Tmin\n",
1130 | "matriz_datos[:, 3] = Tavg\n",
1131 | "\n",
1132 | "print(matriz_datos[:10])\n",
1133 | "\n",
1134 | "np.savetxt('archivo_datos.txt', matriz_datos, fmt='%.5f', newline = '\\r\\n')"
1135 | ]
1136 | },
1137 | {
1138 | "cell_type": "markdown",
1139 | "metadata": {},
1140 | "source": [
1141 | "### Ejercicio"
1142 | ]
1143 | },
1144 | {
1145 | "cell_type": "markdown",
1146 | "metadata": {},
1147 | "source": [
1148 | "Y ahora representamos la evolución de la temperatura media (por ejemplo de color negro), indicando \"Daily summaries\" en el título, \"Days\" en el eje x y \"Temperature (C)\" en el eje y. Podemos crear una zona rellena entre la máxima y la mínima con la función `fill_between(x, max, min)` (por ejemplo de color #4f88b1). Si los límites del eje x no quedan como queremos podemos usar la función `set_xlim(xmin, xmax)`."
1149 | ]
1150 | },
1151 | {
1152 | "cell_type": "code",
1153 | "execution_count": null,
1154 | "metadata": {
1155 | "collapsed": false
1156 | },
1157 | "outputs": [],
1158 | "source": [
1159 | "plt.plot(x, Tavg, 'k')\n",
1160 | "plt.xlim(0, 366)\n",
1161 | "plt.fill_between(x, Tmin, Tmax, facecolor='#4f88b1', edgecolor='none')\n",
1162 | "plt.title(\"Resúmenes diarios\")\n",
1163 | "plt.xlabel(\"Días\")\n",
1164 | "plt.ylabel(\"Temperatura (C)\")"
1165 | ]
1166 | },
1167 | {
1168 | "cell_type": "markdown",
1169 | "metadata": {},
1170 | "source": [
1171 | "---"
1172 | ]
1173 | },
1174 | {
1175 | "cell_type": "markdown",
1176 | "metadata": {},
1177 | "source": [
1178 | "_Ya hemos aprendido a efectuar algunas operaciones útiles con NumPy e incluso hemos hecho nuestro primer ejercicio de lectura de datos. Estamos en condiciones de empezar a escribir programas más interesantes, pero aún queda lo mejor._\n",
1179 | "\n",
1180 | "* [Álgebra lineal en Python con NumPy en Pybonacci](http://pybonacci.org/2012/06/07/algebra-lineal-en-python-con-numpy-i-operaciones-basicas/)"
1181 | ]
1182 | },
1183 | {
1184 | "cell_type": "markdown",
1185 | "metadata": {},
1186 | "source": [
1187 | "Si te ha gustado esta clase:\n",
1188 | "\n",
1189 | "\n",
1190 | "\n",
1191 | "\n",
1192 | "---"
1193 | ]
1194 | },
1195 | {
1196 | "cell_type": "markdown",
1197 | "metadata": {},
1198 | "source": [
1199 | "#### ¡Síguenos en Twitter!"
1200 | ]
1201 | },
1202 | {
1203 | "cell_type": "markdown",
1204 | "metadata": {},
1205 | "source": [
1206 | "##### ![\"Licencia](\"http://i.creativecommons.org/l/by/4.0/88x31.png\")
Curso AeroPython por Juan Luis Cano Rodriguez y Alejandro Sáez Mollejo se distribuye bajo una Licencia Creative Commons Atribución 4.0 Internacional."
1207 | ]
1208 | },
1209 | {
1210 | "cell_type": "markdown",
1211 | "metadata": {},
1212 | "source": [
1213 | "##### "
1214 | ]
1215 | },
1216 | {
1217 | "cell_type": "markdown",
1218 | "metadata": {},
1219 | "source": [
1220 | "---\n",
1221 | "_Las siguientes celdas contienen configuración del Notebook_\n",
1222 | "\n",
1223 | "_Para visualizar y utlizar los enlaces a Twitter el notebook debe ejecutarse como [seguro](http://ipython.org/ipython-doc/dev/notebook/security.html)_\n",
1224 | "\n",
1225 | " File > Trusted Notebook"
1226 | ]
1227 | },
1228 | {
1229 | "cell_type": "code",
1230 | "execution_count": null,
1231 | "metadata": {
1232 | "collapsed": false
1233 | },
1234 | "outputs": [],
1235 | "source": [
1236 | "%%html\n",
1237 | "\n",
1238 | ""
1239 | ]
1240 | },
1241 | {
1242 | "cell_type": "code",
1243 | "execution_count": null,
1244 | "metadata": {
1245 | "collapsed": false
1246 | },
1247 | "outputs": [],
1248 | "source": [
1249 | "# Esta celda da el estilo al notebook\n",
1250 | "from IPython.core.display import HTML\n",
1251 | "css_file = '../static/styles/style.css'\n",
1252 | "HTML(open(css_file, \"r\").read())"
1253 | ]
1254 | }
1255 | ],
1256 | "metadata": {
1257 | "anaconda-cloud": {},
1258 | "kernelspec": {
1259 | "display_name": "Python [default]",
1260 | "language": "python",
1261 | "name": "python3"
1262 | },
1263 | "language_info": {
1264 | "codemirror_mode": {
1265 | "name": "ipython",
1266 | "version": 3
1267 | },
1268 | "file_extension": ".py",
1269 | "mimetype": "text/x-python",
1270 | "name": "python",
1271 | "nbconvert_exporter": "python",
1272 | "pygments_lexer": "ipython3",
1273 | "version": "3.5.2"
1274 | }
1275 | },
1276 | "nbformat": 4,
1277 | "nbformat_minor": 0
1278 | }
1279 |
--------------------------------------------------------------------------------
/notebooks/PX - Sistema Cerrado.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "# Problema X Termodinámica\n",
8 | "\n",
9 | "### Definición de los sistemas y entorno \n",
10 | "Se tiene un sistema cerrado formado por un globo de goma elástica lleno de hidrógeno. \n",
11 | "El sistema de hidrógeno encerrado por el globo (sistema $h$ en lo sucesivo) está envuelto por aire en condiciones ambiente. El aire de este entorno está encerrado por un cilindro ($c$) con émbolo ($E$), conformando otro sistema cerrado. El sistema de aire (sistema $a$ en lo sucesivo) y el sistema $h$ de su interior, se encuentran rodeados por una atmósfera de aire de condiciones conocidas."
12 | ]
13 | },
14 | {
15 | "cell_type": "markdown",
16 | "metadata": {},
17 | "source": [
18 | "### Datos Geométricos y Estructurales conocidos\n",
19 | "- **Fronteras del Sistema $a$ **\n",
20 | " - Cilindro ($c$):\n",
21 | " - $L_0=30cm$ (altura total del cilindro)\n",
22 | " - $\\phi_c=20cm$ (diámetro total del cilindro)\n",
23 | " - Cilindro perfecto, indeformable y sin rozamiento con el émbolo\n",
24 | " - El cilindro es perfectamente diatérmano\n",
25 | " - Émbolo ($e$):\n",
26 | " - Espesor despreciable ($\\delta_e\\approx0$)\n",
27 | " - $\\phi_e=20cm=\\phi_c$ (diámetro total del émbolo)\n",
28 | " - Émbolo perfecto, sin rozamiento e indeformable, que encaja perfectamente en el cilindro\n",
29 | " - El émbolo es perfectamente diatérmano\n",
30 | " - El émbolo tiene una masa $m_e$ desconocida\n",
31 | "- ** Fronteras del Sistema $h$**\n",
32 | " - El material elástico del que está hecho el globo tiene una masa de $m_g=2g$\n",
33 | " - La masa de globo $m_g$ ocupa un volumen despreciable\n",
34 | " - El globo de goma tiene un diámetro mínimo $\\phi_{h_0}$ hasta el cual no se aplica sobrepresión alguna en su interior. A partir de ahí se sigue una relación lineal (ley elástica) tal que por cada centímetro de variación de diámetro se requieren 15 mmHg de sobrepresión: $$\\Delta P=k·(\\phi_{h_1}-\\phi_{h_0}) $$ Donde\n",
35 | " - $\\phi_{h_0}=5 cm \\equiv$ Diámetro mínimo\n",
36 | " - $\\phi_{h_1}=15cm \\equiv$ Diámetro inicial\n",
37 | " - $k=15 \\frac {mmHg}{cm} \\equiv$ Constante Elástica\n",
38 | " 
\n",
39 | " - El globo se considera perfectamente diatérmano\n",
40 | " - En todo momento consideraremos que el globo es esférico e indeformable, de diámetro variable\n"
41 | ]
42 | },
43 | {
44 | "cell_type": "markdown",
45 | "metadata": {},
46 | "source": [
47 | "### Datos Termodinámicos y Propiedades Termodinámicas Iniciales\n",
48 | "- **Entorno:**\n",
49 | " - Atmósfera de aire, ideal\n",
50 | " - Temperatura inicial: $T_\\infty=15ºC$\n",
51 | " - Presión inicial: $P_\\infty=1bar$\n",
52 | "- **Sistema $a$:**\n",
53 | " - Aire en condiciones atmósfericas inicialmente\n",
54 | " - Émbolo a distancia $L_1 = L_0$ de la base del cilindro inicialmente\n",
55 | "- **Sistema $h$:**\n",
56 | " - Globo con diámetro $\\phi_{h_1}$ inicialmente\n",
57 | "- **Propiedades termodinámicas y constantes**: \n",
58 | " - Aire como gas ideal:\n",
59 | " - Se asume aire compuesto al $78\\% N_2$ y $22\\% O_2$\n",
60 | " - Masas moleculares disponibles: $M_N=14 \\frac{g}{mol}$ y $M_O=16 \\frac{g}{mol}$\n",
61 | " - Coeficiente de dilatación adiabático: $\\gamma_a=1.4$\n",
62 | " - Hidrógeno como gas ideal:\n",
63 | " - Masa molecular del hidrógeno: $M_H=1 \\frac{g}{mol}$\n",
64 | " - Coeficiente de dilatación adiabático: $\\gamma_h=1.411$\n",
65 | " - Constante universal de los gases ideales: $\\overline{R}=8.3114 \\frac{J}{mol·K}$"
66 | ]
67 | },
68 | {
69 | "cell_type": "markdown",
70 | "metadata": {},
71 | "source": [
72 | "### Proceso Termodinámico y Apartados\n",
73 | "|Estado Inicial: | Estado Final:|\n",
74 | "|-----------------------------------------------------------|--------------|\n",
75 | "|- Sistema $a$ en condiciones atmosféricas y émbolo a $L_0$| Se suelta el émbolo y se deja llegar al equilibrio termodinámico a los sistema $a$ y $h$|\n",
76 | "|- Globo a $\\phi_{h1}$ | El proceso es rápido. Se deja suficiente tiempo hasta el atemperamiento de todos los sistemas|\n",
77 | "Se pide obtener:\n",
78 | "1. Propiedades termodinámicas que resuelven el estado inicial de ambos sistemas\n",
79 | "2. Condición de flotabilidad del globo en función de la masa del émbolo $m_e$"
80 | ]
81 | },
82 | {
83 | "cell_type": "markdown",
84 | "metadata": {},
85 | "source": [
86 | "### **Primer Paso:** Conversión de los datos a Sistema Internacional y obtención de las constantes básicas\n",
87 | "En primer lugar, se calculan las constantes de los gases a partir de la constante universal y las masas moleculares. Todas las unidades se pasan a SI. Todas. Sin excepción!"
88 | ]
89 | },
90 | {
91 | "cell_type": "markdown",
92 | "metadata": {},
93 | "source": [
94 | "##### Obtención de las Constantes de los Gases"
95 | ]
96 | },
97 | {
98 | "cell_type": "code",
99 | "execution_count": 1,
100 | "metadata": {
101 | "collapsed": false
102 | },
103 | "outputs": [],
104 | "source": [
105 | "## Constantes de los Gases:\n",
106 | "# Masas moleculares\n",
107 | "M_O = 16 #g/mol - Masa molecular del oxígeno\n",
108 | "M_N = 14 #g/mol - Masa molecular del nitrógeno\n",
109 | "M_H = 1 #g/mol - Masa molecular del hidrógeno\n",
110 | "\n",
111 | "M_a = 0.78*2*M_N + 0.22*2*M_O #masa molecular del aire en g/mol\n",
112 | "M_h = 2*M_H #masa molecular del sistema hidrógeno (diatómico) en g/mol\n",
113 | "\n",
114 | "# Constante de los Gases\n",
115 | "R_u = 8.3114 #J/mol/K - Constante universal de los gases\n",
116 | "R_a = R_u/M_a * 1000 #J/kg/K\n",
117 | "R_h = R_u/M_h * 1000 #J/kg/K"
118 | ]
119 | },
120 | {
121 | "cell_type": "markdown",
122 | "metadata": {},
123 | "source": [
124 | "##### Ley Elástica y Condiciones Iniciales del Globo\n"
125 | ]
126 | },
127 | {
128 | "cell_type": "code",
129 | "execution_count": 2,
130 | "metadata": {
131 | "collapsed": true
132 | },
133 | "outputs": [],
134 | "source": [
135 | "import numpy as np"
136 | ]
137 | },
138 | {
139 | "cell_type": "code",
140 | "execution_count": 3,
141 | "metadata": {
142 | "collapsed": true
143 | },
144 | "outputs": [],
145 | "source": [
146 | "#Ley elástica del globo\n",
147 | "mmHg2Pa = 101325/760 #conversión de mmHg a Pa\n",
148 | "K = 15*mmHg2Pa*100 #constante elástica en Pa/m\n",
149 | "phi_h0 = 0.05 #diámetro mínimo en m"
150 | ]
151 | },
152 | {
153 | "cell_type": "code",
154 | "execution_count": 4,
155 | "metadata": {
156 | "collapsed": true
157 | },
158 | "outputs": [],
159 | "source": [
160 | "def delta_p(phi_h):\n",
161 | " if phi_h<=phi_h0:\n",
162 | " return 0\n",
163 | " else:\n",
164 | " return K*(phi_h - phi_h0)"
165 | ]
166 | },
167 | {
168 | "cell_type": "code",
169 | "execution_count": 5,
170 | "metadata": {
171 | "collapsed": false
172 | },
173 | "outputs": [],
174 | "source": [
175 | "#Obtención del volumen inicial del globo:\n",
176 | "phi_h1 = 0.15 #diámetro inicial del globo en metros\n",
177 | "V_h1 = np.pi/6*(phi_h1**3) # Volumen inicial del sistema de hidrógeno (globo) en m3\n",
178 | "\n",
179 | "#Masa del globo\n",
180 | "m_g = 0.002 #kg\n",
181 | " \n",
182 | "#Condiciones Ambiente:\n",
183 | "T_inf = 15 + 273.15 #Temperatura ambiente en K\n",
184 | "P_inf = 1e5 #Presión ambiente en Pa\n",
185 | "\n",
186 | "#Aceleración de la gravedad:\n",
187 | "grav = 9.8 #m/s2"
188 | ]
189 | },
190 | {
191 | "cell_type": "markdown",
192 | "metadata": {},
193 | "source": [
194 | "##### Obtención de las ligaduras Geométricas"
195 | ]
196 | },
197 | {
198 | "cell_type": "code",
199 | "execution_count": 6,
200 | "metadata": {
201 | "collapsed": true
202 | },
203 | "outputs": [],
204 | "source": [
205 | "#Condiciones geométricas del problema:\n",
206 | "L1 = 0.3 # distancia inicial entre émbolo y base del cilindro en metros\n",
207 | "phi_c = 0.2 #diámetro del cilindro\n",
208 | "\n",
209 | "#Obtención del Volumen inicial del aire\n",
210 | "V_a1 = L1*np.pi/4*phi_c**2 - V_h1#Volumen incial del sistema aire en m3"
211 | ]
212 | },
213 | {
214 | "cell_type": "markdown",
215 | "metadata": {},
216 | "source": [
217 | "### Segundo Paso: Resolución del Estado Termodinámico inicial a ambos sistemas"
218 | ]
219 | },
220 | {
221 | "cell_type": "markdown",
222 | "metadata": {},
223 | "source": [
224 | "##### Sistema $a$\n",
225 | "El cilindro es perfectamente diatérmano y el proceso se puede considerar cuasiestático, con lo que la temperatura se mantendrá siempre constante e igual al valor de la temperatura ambiente (ejerce de baño térmico): el proceso del sistema $a$ es **Isotermo**.\n",
226 | "Además, el estado inicial se adquiere llenando el cilindro de aire atmósférico y tapándolo con el émbolo sin dejaro caer. La presión será, por tanto, la del ambiente, y el volumen el máximo posible (émbolo a distancia $L_0$ de la base del cilindro)."
227 | ]
228 | },
229 | {
230 | "cell_type": "code",
231 | "execution_count": 7,
232 | "metadata": {
233 | "collapsed": false
234 | },
235 | "outputs": [
236 | {
237 | "name": "stdout",
238 | "output_type": "stream",
239 | "text": [
240 | "Masa del Sistema Aire: 0.00923kg\n"
241 | ]
242 | }
243 | ],
244 | "source": [
245 | "import eq_state \n",
246 | "## Sistema Aire en Estado Inicial (1):\n",
247 | "# Se considera estado de equilibrio. Como las fronteras son diatérmanas:\n",
248 | "T_a1 = T_inf\n",
249 | "\n",
250 | "# Como está en condiciones atmosféricas:\n",
251 | "P_a1 = P_inf\n",
252 | "\n",
253 | "#Como el volumen es conocido por ligaduras geométricas, la ecuación de estado nos da la masa:\n",
254 | "m_a = eq_state.solve_m(R=R_a, P=P_inf, T=T_inf, V=V_a1)\n",
255 | "rho_a1 = m_a/V_a1 #densidad del aire en 1\n",
256 | "print('Masa del Sistema Aire: {0:1.5f}kg'.format(m_a))"
257 | ]
258 | },
259 | {
260 | "cell_type": "markdown",
261 | "metadata": {},
262 | "source": [
263 | "##### Sistema $h$\n",
264 | "El sistema del hidrógeno se resuelve de manera análoga al sistema de aire: la temperatura $T_{h_1}$ es directa al estar $a$ y $h$ atemperados. La presión del sistema se puede calcular a través de la ley elástica del globo, y ésta a su vez se obtiene con el diámetro (inicialmente $\\phi_{h_1}$ es dato, con lo que se tiene también el volumen del globo)."
265 | ]
266 | },
267 | {
268 | "cell_type": "code",
269 | "execution_count": 8,
270 | "metadata": {
271 | "collapsed": false
272 | },
273 | "outputs": [
274 | {
275 | "name": "stdout",
276 | "output_type": "stream",
277 | "text": [
278 | "Masa de 1.77086e-04kg y presión de 119998Pa en el Sistema Hidrógeno\n"
279 | ]
280 | }
281 | ],
282 | "source": [
283 | "## Sistema Hidrógeno en Estado Inicial (1):\n",
284 | "#Como es diatérmano:\n",
285 | "T_h1 = T_inf\n",
286 | "\n",
287 | "#La presión se puede obtener mediante balance de fuerzas y la sobrepresión debida al globo:\n",
288 | "P_h1 = P_a1 + delta_p(phi_h1)\n",
289 | "\n",
290 | "#Con la presión,la temperatura y el volumen (debido al diámetro):\n",
291 | "m_h = eq_state.solve_m(R=R_h, P=P_h1, T=T_h1, V=V_h1)\n",
292 | "print('Masa de {0:1.5e}kg y presión de {1:6.0f}Pa en el Sistema Hidrógeno'.format(m_h, P_h1))"
293 | ]
294 | },
295 | {
296 | "cell_type": "markdown",
297 | "metadata": {},
298 | "source": [
299 | "### Tercer Paso: Condición de Flotabilidad\n",
300 | "La condición de flotabilidad depende de igualar el peso del peso del globo (incluyendo la masa de la goma elástica) al peso que tendría la masa de aire que ocupase su lugar: $$E=P$$ Donde: $$E=\\rho_{a_1}·V_{h_1}·g$$ $$ P=(m_h + m_g)·g$$ La densidad del aire se obtiene de la ecuación de estado: $$P=\\rho ·R_g ·T$$Por tanto:"
301 | ]
302 | },
303 | {
304 | "cell_type": "code",
305 | "execution_count": 9,
306 | "metadata": {
307 | "collapsed": false
308 | },
309 | "outputs": [
310 | {
311 | "name": "stdout",
312 | "output_type": "stream",
313 | "text": [
314 | "Empuje neto sobre el globo: -0.00045N\n"
315 | ]
316 | }
317 | ],
318 | "source": [
319 | "##Condición de Flotabilidad:\n",
320 | "# Peso total del Sistema Hidrógeno y Globo:\n",
321 | "P = (m_h + m_g)*grav\n",
322 | "\n",
323 | "#Empuje del aire sobre h+g:\n",
324 | "E = rho_a1*V_h1*grav\n",
325 | "\n",
326 | "print('Empuje neto sobre el globo: {0:4.5f}N'.format(E-P))"
327 | ]
328 | },
329 | {
330 | "cell_type": "markdown",
331 | "metadata": {},
332 | "source": [
333 | "Para obtener la condición de flotabilidad hay que igualar el peso al empuje $E=P$. Como el peso del sistema hidrógeno + globo es **constante**, la densidad del aire será el elemento que regule la flotabilidad del globo. La densidad del aire a su vez depende de la **presión del aire** a través de la ecuación de estado, y la presión del sistema aire se obtiene por **balance de fuerzas en el émbolo**. Por lo tanto:"
334 | ]
335 | },
336 | {
337 | "cell_type": "markdown",
338 | "metadata": {},
339 | "source": [
340 | "#### Balance de Fuerzas al Émbolo (Ec. 1)\n",
341 | "$$P_{a_2} = P_\\infty + m_e·\\frac{g}{A_c}$$"
342 | ]
343 | },
344 | {
345 | "cell_type": "markdown",
346 | "metadata": {},
347 | "source": [
348 | "#### Balance de Fuerzas al Globo (Ec. 2)\n",
349 | "$$P_{h_2} = P_{a_2} + K·(\\phi_{h_2} - \\phi_{h_0})$$"
350 | ]
351 | },
352 | {
353 | "cell_type": "markdown",
354 | "metadata": {},
355 | "source": [
356 | "#### Ecuación de Estado al Hidrógeno (Ec. 3)\n",
357 | "$$P_{h_2}·V_{h_2}=m_h·R_h·T_{h_2}$$"
358 | ]
359 | },
360 | {
361 | "cell_type": "markdown",
362 | "metadata": {},
363 | "source": [
364 | "#### Flotabilidad (Ec. 4)\n",
365 | "$$\\frac{P_{a_2}}{R_a·T_{a_2}}·\\frac{\\pi}{6}·\\phi³_{h_2}·g = (m_h + m_g)·g$$"
366 | ]
367 | },
368 | {
369 | "cell_type": "markdown",
370 | "metadata": {},
371 | "source": [
372 | "Para resolver la masa del émbolo que hace que el globo flote ($E=P$), sustituiremos las ecuaciones **1 y 2** en **3** y asumiremos una masa inicial del émbolo. El resultado del volumen del sistema de hidrógeno debe cumplir la ecuación **4**.\n",
373 | "De esta forma, si la diferencia entre la presión de la **Ec. 1** y la de la **Ec. 4** es pequeña $(\\approx 10^{-6})$."
374 | ]
375 | },
376 | {
377 | "cell_type": "markdown",
378 | "metadata": {
379 | "collapsed": false
380 | },
381 | "source": [
382 | "#### Iterando para resolver $m_e$"
383 | ]
384 | },
385 | {
386 | "cell_type": "code",
387 | "execution_count": 10,
388 | "metadata": {
389 | "collapsed": false
390 | },
391 | "outputs": [
392 | {
393 | "name": "stdout",
394 | "output_type": "stream",
395 | "text": [
396 | "Masa del émbolo que resuelve la condición de flotabilidad: 33.00kg\n",
397 | "La condición de presiones es P_h2=129547Pa; P_a2=110294Pa\n"
398 | ]
399 | }
400 | ],
401 | "source": [
402 | "residual = 1\n",
403 | "m_e = 5\n",
404 | "while residual>1e-6:\n",
405 | " m_e += 0.2\n",
406 | " P_a2 = P_inf + m_e*grav/(np.pi/4*phi_c**2)\n",
407 | " phi_h2 = ((m_h + m_g)/(P_a2/R_a/T_inf)*6/np.pi)**(1/3)\n",
408 | " \n",
409 | " P_h2 = eq_state.solve_P(R=R_h, V=np.pi/6*phi_h2**3, m=m_h, T=T_inf)\n",
410 | " residual = (P_a2 + K*(phi_h2 - phi_h0) - P_h2)/P_h2\n",
411 | " \n",
412 | "print('Masa del émbolo que resuelve la condición de flotabilidad: {0:4.2f}kg'.format(m_e))\n",
413 | "print('La condición de presiones es P_h2={0:6.0f}Pa; P_a2={1:6.0f}Pa'.format(P_h2, P_a2))"
414 | ]
415 | },
416 | {
417 | "cell_type": "markdown",
418 | "metadata": {},
419 | "source": [
420 | "#### Resolviendo el Sistema de manera interactiva:\n",
421 | "La siguiente función resuelve el sistema de cuatro ecuaciones anterior para cada valor de masa $m_e$ que seleccionemos con el deslizador. "
422 | ]
423 | },
424 | {
425 | "cell_type": "code",
426 | "execution_count": 11,
427 | "metadata": {
428 | "collapsed": true
429 | },
430 | "outputs": [],
431 | "source": [
432 | "%matplotlib inline\n",
433 | "from ipywidgets import interact\n",
434 | "import matplotlib.pyplot as plt\n",
435 | "from matplotlib import patches"
436 | ]
437 | },
438 | {
439 | "cell_type": "code",
440 | "execution_count": 12,
441 | "metadata": {
442 | "collapsed": true
443 | },
444 | "outputs": [],
445 | "source": [
446 | "m_a = P_a1*V_a1/R_a/T_a1"
447 | ]
448 | },
449 | {
450 | "cell_type": "code",
451 | "execution_count": 13,
452 | "metadata": {
453 | "collapsed": false
454 | },
455 | "outputs": [],
456 | "source": [
457 | "def embolo(m_e3):\n",
458 | " \n",
459 | " P_a3 = P_inf + m_e3*grav/(np.pi/4*phi_c**2)\n",
460 | " V_a3 = eq_state.solve_V(R=R_a, m=m_a, P=P_a3, T=T_inf)\n",
461 | " \n",
462 | " V_h3 = (m_h + m_g)/(P_a2/R_a/T_inf)\n",
463 | " \n",
464 | " L = (V_a3 + V_h3)/(np.pi/4*phi_c**2)\n",
465 | " \n",
466 | " P_h3 = P_a3 + K*((V_h3/np.pi*6)**(1/3)-phi_h0)\n",
467 | " \n",
468 | " width = phi_c/2\n",
469 | " piston_height = 0.3\n",
470 | " emb_heigth = 0.01\n",
471 | " R = phi_c/2\n",
472 | " \n",
473 | " fig, ax = plt.subplots(1, 3)\n",
474 | "\n",
475 | " embolo_down = patches.Rectangle((0, 0), width, L, alpha=1-L)\n",
476 | " embolo_up = patches.Rectangle((0, L), width, piston_height-L, alpha=0.1)\n",
477 | " piston = patches.Rectangle((0, L), width, emb_heigth, color='black')\n",
478 | "\n",
479 | " fig.set_figwidth(10)\n",
480 | " ax[0].add_patch(embolo_down)\n",
481 | " ax[0].add_patch(embolo_up)\n",
482 | " ax[0].add_patch(piston)\n",
483 | " \n",
484 | " ax[0].set_xlim(0, width)\n",
485 | " ax[0].set_ylim(0, piston_height)\n",
486 | " ax[0].axes.get_xaxis().set_visible(False)\n",
487 | " ax[0].axes.get_yaxis().set_visible(False)\n",
488 | " \n",
489 | " ax[0].text(width/5, L/2,\n",
490 | " '$P_h={0:6.0f} Pa$ \\n$P_a={1:6.0f} Pa$'.format(P_h3, P_a3),\n",
491 | " size=12)\n",
492 | " \n",
493 | " m_e3_ = np.linspace(0.01, 300, 100)\n",
494 | " \n",
495 | " P_a3_ = P_inf + m_e3_*grav/(np.pi/4*phi_c**2)\n",
496 | " V_a3_ = eq_state.solve_V(R=R_a, m=m_a, P=P_a3_, T=T_inf) \n",
497 | " \n",
498 | " ax[1].plot(m_e3_, V_a3_)\n",
499 | " ax[1].plot(m_e3, V_a3, 'ro')\n",
500 | " ax[1].set_ylabel('$V_{a3}\\ (m^{3})$', size=12)\n",
501 | " ax[1].set_xlabel('$m_{e3}\\ (kg)$', size=12)\n",
502 | " \n",
503 | " \n",
504 | " ax[2].plot(m_e3_, P_a3_)\n",
505 | " ax[2].plot(m_e3, P_a3, 'ro')\n",
506 | " ax[2].set_ylabel('$P_{a3}\\ (Pa)$', size=12)\n",
507 | " ax[2].set_xlabel('$m_{e3}\\ (kg)$', size=12)\n",
508 | " \n",
509 | " plt.tight_layout()"
510 | ]
511 | },
512 | {
513 | "cell_type": "code",
514 | "execution_count": 14,
515 | "metadata": {
516 | "collapsed": false
517 | },
518 | "outputs": [
519 | {
520 | "data": {
521 | "image/png": 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j4eOP4Z574s5GREREiurpp+GOO2DQIGjbNu5sKhYV3iIiUuIOOgh69IC+feGr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522 | "text/plain": [
523 | ""
524 | ]
525 | },
526 | "metadata": {},
527 | "output_type": "display_data"
528 | }
529 | ],
530 | "source": [
531 | "i = interact(embolo, m_e3=(0.01, 300))"
532 | ]
533 | }
534 | ],
535 | "metadata": {
536 | "anaconda-cloud": {},
537 | "kernelspec": {
538 | "display_name": "Python [default]",
539 | "language": "python",
540 | "name": "python3"
541 | },
542 | "language_info": {
543 | "codemirror_mode": {
544 | "name": "ipython",
545 | "version": 3
546 | },
547 | "file_extension": ".py",
548 | "mimetype": "text/x-python",
549 | "name": "python",
550 | "nbconvert_exporter": "python",
551 | "pygments_lexer": "ipython3",
552 | "version": "3.5.2"
553 | },
554 | "widgets": {
555 | "state": {
556 | "39297bbfbee3433dade3d731441b98c1": {
557 | "views": [
558 | {
559 | "cell_index": 33
560 | }
561 | ]
562 | }
563 | },
564 | "version": "1.2.0"
565 | }
566 | },
567 | "nbformat": 4,
568 | "nbformat_minor": 1
569 | }
570 |
--------------------------------------------------------------------------------
4 | 
5 |
6 | ## [Juan Luis Cano](http://es.linkedin.com/in/juanluiscanor) y [Álex Sáez](https://www.linkedin.com/in/alejandrosaezm)
7 |
8 | __Charla de introducción a Python en la Universidad Alfonso X el Sabio__
9 | __5 de diciembre de 2016__
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11 | Charla-taller introductorio a Python científico (NumPy, matplotlib y SciPy) dirigida a los alumnos de las asignaturas de Termodinámica (2º) y Motores (3º) del grado en Ingeniería Aeroespacial.
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13 | Impartido con la colaboración del Profesor [Marcos A. Rodríguez Jiménez](https://www.linkedin.com/in/marcos-antonio-rodr%C3%ADguez-jim%C3%A9nez-50615446).
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