JNB05A_ProblemaIngenieria.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Prob_Ingenieria.ipynb","version":"0.3.2","provenance":[]},"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"}},"cells":[{"metadata":{"id":"d92DmvpM6T80","colab_type":"text"},"cell_type":"markdown","source":["# Matrices en NumPy\n","\n","Además de arreglos, NumPy tiene otro tipo de dato que son las matrices.  Cuando trabajamos con arreglos, vimos que los operadores matemáticos +, -, *, / y otras funciones operan sobre cada elemento.  Con matrices, sabemos que los operadores matemáticos son muy diferentes, la multiplicación por ejemplo."]},{"metadata":{"id":"LmG8tG4n6T83","colab_type":"code","colab":{}},"cell_type":"code","source":["import numpy as np"],"execution_count":0,"outputs":[]},{"metadata":{"id":"gI8K9ke16T9A","colab_type":"code","colab":{}},"cell_type":"code","source":["matriz1 = np.matrix([[8, 2], [7, 3]])  # se puede abreviar el np.matrix como np.mat"],"execution_count":0,"outputs":[]},{"metadata":{"id":"lJaUcjW96T9F","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":50},"outputId":"56fe2e08-5c62-4433-d61d-6d27b2fbb2ca","executionInfo":{"status":"ok","timestamp":1552662762014,"user_tz":360,"elapsed":414,"user":{"displayName":"Julio Ayala","photoUrl":"https://lh5.googleusercontent.com/-HJnYqzIf1xY/AAAAAAAAAAI/AAAAAAAAAP8/r2VPTM2GaBQ/s64/photo.jpg","userId":"04825294589197241048"}}},"cell_type":"code","source":["matriz1"],"execution_count":4,"outputs":[{"output_type":"execute_result","data":{"text/plain":["matrix([[8, 2],\n","        [7, 3]])"]},"metadata":{"tags":[]},"execution_count":4}]},{"metadata":{"id":"dTBNq-zD6T9P","colab_type":"text"},"cell_type":"markdown","source":["## Invertir la matriz"]},{"metadata":{"id":"eYHcRoP36T9Q","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":50},"outputId":"977ca7ee-6381-426a-d919-31dc014c374a","executionInfo":{"status":"ok","timestamp":1552662764208,"user_tz":360,"elapsed":632,"user":{"displayName":"Julio Ayala","photoUrl":"https://lh5.googleusercontent.com/-HJnYqzIf1xY/AAAAAAAAAAI/AAAAAAAAAP8/r2VPTM2GaBQ/s64/photo.jpg","userId":"04825294589197241048"}}},"cell_type":"code","source":["matriz1.I"],"execution_count":5,"outputs":[{"output_type":"execute_result","data":{"text/plain":["matrix([[ 0.3, -0.2],\n","        [-0.7,  0.8]])"]},"metadata":{"tags":[]},"execution_count":5}]},{"metadata":{"id":"f1dNJQPl6T9V","colab_type":"text"},"cell_type":"markdown","source":["## Prueba de que es la matriz invertida\n","\n","I es un atributo de las matrices que genera la matriz invertida"]},{"metadata":{"id":"p5xFm1Ji6T9W","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":50},"outputId":"0173758c-65c5-43f9-cdfd-38f33631fa7c","executionInfo":{"status":"ok","timestamp":1552662769170,"user_tz":360,"elapsed":611,"user":{"displayName":"Julio Ayala","photoUrl":"https://lh5.googleusercontent.com/-HJnYqzIf1xY/AAAAAAAAAAI/AAAAAAAAAP8/r2VPTM2GaBQ/s64/photo.jpg","userId":"04825294589197241048"}}},"cell_type":"code","source":["matriz1 * matriz1.I"],"execution_count":6,"outputs":[{"output_type":"execute_result","data":{"text/plain":["matrix([[1.00000000e+00, 0.00000000e+00],\n","        [3.33066907e-16, 1.00000000e+00]])"]},"metadata":{"tags":[]},"execution_count":6}]},{"metadata":{"id":"dwKPZUxm6T9f","colab_type":"text"},"cell_type":"markdown","source":["## Otra forma de multiplicar matrices"]},{"metadata":{"id":"iNYzXoKd6T9g","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":118},"outputId":"0dfc11e2-551f-4de0-ed86-970fd6b804ac","executionInfo":{"status":"ok","timestamp":1552662835736,"user_tz":360,"elapsed":367,"user":{"displayName":"Julio Ayala","photoUrl":"https://lh5.googleusercontent.com/-HJnYqzIf1xY/AAAAAAAAAAI/AAAAAAAAAP8/r2VPTM2GaBQ/s64/photo.jpg","userId":"04825294589197241048"}}},"cell_type":"code","source":["x = np.array([[8, 2], [7, 3]])\n","y = np.array([[3], [4]])\n","print(x)\n","print(y)\n","x * y"],"execution_count":7,"outputs":[{"output_type":"stream","text":["[[8 2]\n"," [7 3]]\n","[[3]\n"," [4]]\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([[24,  6],\n","       [28, 12]])"]},"metadata":{"tags":[]},"execution_count":7}]},{"metadata":{"id":"To9kxRvL6T9l","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":50},"outputId":"472518a2-ed38-4f2e-841d-6dc9607ff42d","executionInfo":{"status":"ok","timestamp":1552662845775,"user_tz":360,"elapsed":452,"user":{"displayName":"Julio Ayala","photoUrl":"https://lh5.googleusercontent.com/-HJnYqzIf1xY/AAAAAAAAAAI/AAAAAAAAAP8/r2VPTM2GaBQ/s64/photo.jpg","userId":"04825294589197241048"}}},"cell_type":"code","source":["z = np.mat(x) * np.mat(y)\n","z"],"execution_count":8,"outputs":[{"output_type":"execute_result","data":{"text/plain":["matrix([[32],\n","        [33]])"]},"metadata":{"tags":[]},"execution_count":8}]},{"metadata":{"id":"dCTXJcOB6T9q","colab_type":"text"},"cell_type":"markdown","source":["##  Problema de ingeniería"]},{"metadata":{"id":"G_7UWWV76T9s","colab_type":"text"},"cell_type":"markdown","source":["### Enunciado del problema\n","\n","Se midió la velocidad vertical de un cohete en tres tiempos diferentes, los resultados se ven en la siguiente tabla:\n","\n","\n","| Tiempo, t (s) | Velocidad, v (m/s) |\n","|---------------|--------------------|\n","|       5       |       106.8        |\n","|---------------|--------------------|\n","|       8       |        177.2       |\n","|---------------|--------------------|\n","|    12         |        279.2       |\n","|---------------|--------------------|\n","\n","\n","\n","![image.png](attachment:image.png)\n","\n","<center>Figura 1.  Un cohete lanzado al espacio</center>\n","\n","\n","La velocidad se aproxima por un polinomio como:  \n","\n","<center>v(t) = at<sup>2</sup> + bt + c</center>\n","\n","Desarrolle las ecuaciones en forma de matrices para encontrar los valores de a, b y c\n"]},{"metadata":{"id":"UZV52M9_6T9u","colab_type":"text"},"cell_type":"markdown","source":["###  Solución del problema\n","\n","El polinomio pasará por los tres puntos (t1, v1), (t2, v2) y (t3, v3).  \n","\n","De la tabla anterior establecemos:\n","\n","<center>t1 = 5s, v1 = 106 m/s</center>\n","<center>t2 = 8s, v2 = 177.2 m/s</center>\n","<center>t3 = 12s, v3 = 279.2 m/s</center>\n","\n","Usando nuestro polinomio tenemos:\n","\n","<center>v(t1) = v1 = a*t1<sup>2</sup> + b*t1 + c</center>\n","<center>v(t2) = v2 = a*t2<sup>2</sup> + b*t2 + c</center>\n","<center>v(t3) = v3 = a*t3<sup>2</sup> + b*t3 + c</center>\n","\n","Sustituyendo los datos:\n","\n","<center>a(5<sup>2</sup>) + b(5) + c = 106</center>\n","<center>a(8<sup>2</sup>) + b(8) + c = 177.2</center>\n","<center>a(12<sup>2</sup>) +b(12) + c = 279.2</center>\n","\n","o\n","\n","<center>25a + 5b + c = 106</center>\n","<center>64a + 8b + c = 177.2</center>\n","<center>144a + 12b + c = 279.2</center>\n","\n","Esto en forma matricial es:\n","\n","$$ \\left[ \\begin{array}{ccc} 25a &  5b & c \\\\ 64a &  8b & c \\\\ 144a & 12b & c \\\\ \\end{array} \\right]\n","= \\left[  \\begin{array}{c} 106  \\\\  177.2  \\\\  279.2 \\\\ \\end{array} \\right]$$\n","\n","\n","\n","Que es equivalente a:\n","\n","$$ \\left[ \\begin{array}{ccc} 25 &  5 & 1 \\\\ 64 &  8 & 1 \\\\ 144 & 12 & 1 \\\\ \\end{array} \\right]\n","\\left[ \\begin{array}{ccc} a \\\\ b \\\\ c \\\\ \\end{array} \\right]\n","= \\left[  \\begin{array}{c} 106  \\\\  177.2  \\\\  279.2 \\\\ \\end{array} \\right]$$\n","\n","\n","Esto tiene el formato\n","\n","A * B = C   donde A, B y C son matrices\n","\n","Para despejar por B, necesitamos multiplicar ambos lados por la inversa de A (A<sup>-1</sup>), dando\n","\n","A * A<sup>-1</sup> * B = C * A<sup>-1</sup>\n","\n","B = C * A<sup>-1</sup>\n","\n","ya que una matriz multiplicada por su inversa da la matriz identidad\n","\n","Resolviendo en Python:\n"]},{"metadata":{"id":"QeKSKwo66T9v","colab_type":"code","colab":{}},"cell_type":"code","source":["A = np.array([[25, 5, 1], [64, 8, 1], [144, 12, 1]])\n","C = np.array([[106], [177.2], [279.2]])"],"execution_count":0,"outputs":[]},{"metadata":{"id":"I6rbITEQ6T9z","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":84},"outputId":"ee4a00a0-cc2c-484d-fd14-e6fc9811392e","executionInfo":{"status":"ok","timestamp":1552663062140,"user_tz":360,"elapsed":522,"user":{"displayName":"Julio Ayala","photoUrl":"https://lh5.googleusercontent.com/-HJnYqzIf1xY/AAAAAAAAAAI/AAAAAAAAAP8/r2VPTM2GaBQ/s64/photo.jpg","userId":"04825294589197241048"}}},"cell_type":"code","source":["#  La matriz de los coeficientes a, b, y c se encuentra\n","#\n","try:\n","    B = np.mat(A).I * np.mat(C)\n","    print(\"Los coeficientes a, b y c son:\\n\", B)\n","except:\n","    print(\"Hubo un error, puede que la matriz A no tenga inversa \")"],"execution_count":11,"outputs":[{"output_type":"stream","text":["Los coeficientes a, b y c son:\n"," [[ 0.25238095]\n"," [20.45238095]\n"," [-2.57142857]]\n"],"name":"stdout"}]},{"metadata":{"id":"Yi4CC0_a6T94","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":34},"outputId":"40d7c3c7-1bdf-4fbf-c0dc-40da0479ef85","executionInfo":{"status":"ok","timestamp":1552663135719,"user_tz":360,"elapsed":436,"user":{"displayName":"Julio Ayala","photoUrl":"https://lh5.googleusercontent.com/-HJnYqzIf1xY/AAAAAAAAAAI/AAAAAAAAAP8/r2VPTM2GaBQ/s64/photo.jpg","userId":"04825294589197241048"}}},"cell_type":"code","source":["#  Comprobacion para t = 5s\n","\n","t = 5\n","a = float(B[0])\n","b = float(B[1])\n","c = float(B[2])\n","v = a * t**2 + b * t + c\n","print(\"La velocidad para t = 5s es:  \", v)"],"execution_count":12,"outputs":[{"output_type":"stream","text":["La velocidad para t = 5s es:   105.99999999999979\n"],"name":"stdout"}]},{"metadata":{"id":"xUdwZxIZ6T-A","colab_type":"text"},"cell_type":"markdown","source":["# Solución usando el sub-módulo numpy.linalg\n","\n","Otra forma de resolverlo, sin tener que recurrir a matrices, es con una sub-librería de NumPy.  Esta sub-librería se llama numpy.linalg\n","\n","Utilizando esta, resolveremos el problema desde el principio"]},{"metadata":{"id":"ZkvOfrSd6T-D","colab_type":"code","colab":{},"outputId":"10273744-30c9-4871-826f-b05c495db306"},"cell_type":"code","source":["A = np.array([[25, 5, 1], [64, 8, 1], [144, 12, 1]])\n","C = np.array([106, 177.2, 279.2])\n","\n","# Usando la librería indicada\n","\n","try:\n","              B = np.linalg.solve(A,C)\n","              print(\"Los coeficientes a, b y c son:  \", B)\n","except:\n","              print(\"Hubo un error, es posible que la matriz A no tenga una inversa\")"],"execution_count":0,"outputs":[{"output_type":"stream","text":["Los coeficientes a, b y c son:   [ 0.25238095 20.45238095 -2.57142857]\n"],"name":"stdout"}]},{"metadata":{"id":"nkPZsGdK6T-V","colab_type":"text"},"cell_type":"markdown","source":["# Visualizando la solución\n","\n","Como reza el dicho:  \"Una imagen vale más que mil palabras!\"\n","\n","Utilizaremos el módulo MatPlotLib para visualizar la velocidad del cohete versus el tiempo\n","\n","Para esto necesitamos generar los datos de tiempo y velocidad.  Aprovecharemos las facilidades de NumPy para hacer esto.  Ahora que ya tenemos los valores de a, b y c, podemos establecer la ecuación exacta:\n","\n","<center>v(t) = at<sup>2</sup> + bt + c</center>\n","\n","y con los valores encontrados:\n","\n","<center>v(t) = 0.2524t<sup>2</sup> + 20.4524t - 2.5714</center>\n","\n","Con NumPy:"]},{"metadata":{"id":"72Duvhqa6T-Y","colab_type":"code","colab":{},"outputId":"1f774663-b8b6-499e-cd93-eafcb27c360d"},"cell_type":"code","source":["tiempo = np.arange(5, 13, 0.5)\n","velocidad =0.2524 * tiempo**2 + 20.4524 * tiempo - 2.5714\n","velocidad"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([106.0006, 117.5519, 129.2294, 141.0331, 152.963 , 165.0191,\n","       177.2014, 189.5099, 201.9446, 214.5055, 227.1926, 240.0059,\n","       252.9454, 266.0111, 279.203 , 292.5211])"]},"metadata":{"tags":[]},"execution_count":14}]},{"metadata":{"id":"l8O4FXfl6T-t","colab_type":"text"},"cell_type":"markdown","source":["Usando el módulo MatPlotLib"]},{"metadata":{"id":"MwacEkuf6T-z","colab_type":"code","colab":{},"outputId":"1e3a0398-55a3-44ca-8052-6284cf79d5fb"},"cell_type":"code","source":["import matplotlib.pyplot as plt\n","\n","plt.plot(tiempo, velocidad)\n","plt.title(\"Velocidad vrs Tiempo para el intervalo 5 <= t <= 12 segundos\")\n","plt.xlabel(\"Tiempo (s)\")\n","plt.ylabel(\"Velocidad (m/s)\")\n","plt.show()"],"execution_count":0,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"metadata":{"id":"LJRDu9CK6T_D","colab_type":"text"},"cell_type":"markdown","source":["Si ahora quisiéramos graficar la aceleracion en este mismo período, sabemos que:\n","\n","$a(t) = dv(t)/dt$\n","\n","para nuestro caso:\n","\n","$a(t) = 2 * 0.2524t + 20.4524$\n","\n","$a(t) = 0.5048t +20.4524$\n","\n","Con NumPy esto es:"]},{"metadata":{"id":"TYr6mifI6T_G","colab_type":"code","colab":{}},"cell_type":"code","source":["aceleracion = 0.5048 * tiempo + 20.4524"],"execution_count":0,"outputs":[]},{"metadata":{"id":"tzOViMqT6T_Q","colab_type":"text"},"cell_type":"markdown","source":["Y para graficarlo"]},{"metadata":{"id":"Lq6kP3KB6T_T","colab_type":"code","colab":{},"outputId":"c8584fd6-584e-4e01-95f9-c6d46e5bb9b1"},"cell_type":"code","source":["plt.plot(tiempo, aceleracion, color = \"red\")\n","plt.title(\"Aceleración vrs Tiempo para el intervalo 5 <= t <= 12 segundos\")\n","plt.xlabel(\"Tiempo (s)\")\n","plt.ylabel(\"Aceleración (m/sˆ2)\")\n","plt.show()"],"execution_count":0,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"metadata":{"id":"F0gzbDVL6T_e","colab_type":"text"},"cell_type":"markdown","source":["# Multiples líneas en una gráfica\n","\n","Podemos graficar las dos variables en una sola gráfica"]},{"metadata":{"id":"fyIDkmWX6T_f","colab_type":"code","colab":{},"outputId":"912289de-40f3-48bb-dffd-c5d039b3d621"},"cell_type":"code","source":["plt.plot(tiempo, velocidad, label = \"velocidad\")\n","plt.plot(tiempo, aceleracion, label = \"Aceleración\", color = \"red\")\n","plt.title(\"Velocidad y Aceleración vrs Tiempo\")\n","plt.xlabel(\"Tiempo (s)\")\n","plt.legend()\n","plt.show()"],"execution_count":0,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"metadata":{"id":"iK4QD0Ox6T_l","colab_type":"text"},"cell_type":"markdown","source":["Viendo las gráficas individuales, parecería que la de velocidad es lineal y la de aceleración cambia bastante.  Colocando ambos trazos en una sola gráfica vemos que la aceleración no cambia mucho y por eso parece que la gráfica de la velocidad es lineal"]}]}