From 2265d38de0d60b2942ce218d2e1ae9fb7069cdb2 Mon Sep 17 00:00:00 2001 From: Maria Pais <145993408+Finarosalina@users.noreply.github.com> Date: Mon, 29 Jul 2024 10:22:14 +0000 Subject: [PATCH 1/6] v2 --- notebook/problems.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notebook/problems.ipynb b/notebook/problems.ipynb index 1ccac740..585a4e96 100644 --- a/notebook/problems.ipynb +++ b/notebook/problems.ipynb @@ -1 +1 @@ -{"cells":[{"cell_type":"markdown","id":"5dbe7b9e","metadata":{},"source":["# Calculus and Algebra problems"]},{"cell_type":"markdown","id":"519c4b12","metadata":{},"source":["## Calculus\n","\n","Calculus is not obscure. It is the language for modeling behaviors. Calculus enables us to find the rate of changes in order to optimize a function. Without calculus, we would not be able to fully understand techniques such as:\n","\n","Backpropagation in neural networks\n","\n","Regression using optimal least square\n","\n","Expectation maximization in fitting probability models"]},{"cell_type":"markdown","id":"b7e2e87a","metadata":{},"source":["### Exercise 1\n","\n","Let's say, in my office, it takes me 10 seconds (time) to travel 25 meters (distance) to the coffee machine.\n","If we want to express the above situation as a function, then it would be:\n","\n","distance = speed * time\n","\n","So for this case, speed is the first derivative of the distance function above. As speed describes the rate of change of distance over time, when people say taking the first derivative of a certain function, they mean finding out the rate of change of a function.\n","\n","**Find the speed and build the linear function on distance $(d)$ over time $(t)$, when $(t ∈ [0,10])$.**"]},{"cell_type":"code","execution_count":null,"id":"bb3e954e","metadata":{},"outputs":[],"source":["# import libraries\n","\n","\n","# Define the distance function"]},{"cell_type":"code","execution_count":null,"id":"dbc4c780","metadata":{},"outputs":[],"source":["# Plot the distance function on domain (t)"]},{"cell_type":"code","execution_count":null,"id":"4c4d4f20","metadata":{},"outputs":[],"source":["# Create a DataFrame"]},{"cell_type":"markdown","id":"1144168d","metadata":{},"source":["### Exercise 2\n","\n","It turned out that I wasn't walking a constant speed towards getting my coffee, but I was accelerating (my speed increased over time). If my initial *speed = 0*, it still took me 10 seconds to travel from my seat to my coffee, but I was walking faster and faster.\n","\n","$V_o$ = initial speed = $0$\n","\n","t = time\n","\n","a = acceleration\n","\n","**distance** = $V_o * t + 0.5 * a * (t^2)$\n","\n","**speed** = $V_o + a * t$\n","\n","The first derivative of the speed function is acceleration. I realize that the speed function is closely related to the distance function.\n","\n","**Find the acceleration value and build the quadratic function $(t ∈ [0,10])$. Also, create a graph and a table.**"]},{"cell_type":"code","execution_count":null,"id":"ec1f8bd7","metadata":{},"outputs":[],"source":["# Define and plot the quadratic funtion"]},{"cell_type":"code","execution_count":null,"id":"ba5c497b","metadata":{},"outputs":[],"source":["# Create a DataFrame"]},{"cell_type":"markdown","id":"66d4cc18","metadata":{},"source":["Before exercise 3, we'll make a brief introduction to Gradient Descent algorithm, which will have a larger explanation in future modules of the bootcamp.\n","\n","Gradient Descent algorithm is the hero behind the family of deep learning algorithms. When an algorithm in this family runs, it tries to minimize the error between the training input and predicted output. This minimization is done by optimization algorithms, and gradient descent is the most popular one.\n","\n","Let's say you have these input & output pairs:\n","\n","```py\n","# Input:\n","[\n"," [1,2],\n"," [3,4]\n","]\n","\n","# Output:\n","[\n"," [50],\n"," [110]\n","]\n","```\n","\n","We can estimate that if we multiply the input values by [10, 20], we can have the output as shown above.\n","\n","```py\n","1(10) + 2(20) = 50\n","\n","3(10) + 4(20) = 110\n","```\n","\n","When a machine learning algorithm starts running, it assigns random values and makes a prediction. \n","Let's say it assigned [1,2] values:\n","\n","```py\n","1(1) + 2(2) = 5\n","\n","3(1) + 4(2) = 11\n","```\n","\n","Once it has the predictions, it calculates the error: the difference between the real data and the predicted data. There are many ways to calculate the error, and they are called loss functions.\n","\n","Once we have this value, the optimization algorithm starts showing itself, and it sets new values which replace the initial random values. \n","\n","And, the loop continues until a condition is met. That condition can be to loop *n* times, or to loop until the error is smaller than a value."]},{"cell_type":"markdown","id":"85ef2f0b","metadata":{},"source":["It can be hard to understand **gradient descent** without understanding **gradient**. So, let's focus on what a gradient is. The gradient shows the direction of the greatest change of a scalar function. The gradient calculation is done with derivatives, so let's start with a simple example. To calculate the gradient, we just need to remember some linear algebra calculations from high school because we need to calculate derivatives.\n","\n","Let's say we want to find the minimum point of $f(x) = x^2$. The derivative of that function is $df(x)=2x$. \n","\n","The gradient of $f(x)$ at point $x=-10$\n","\n","is \n","\n","$df(-10)=-20$.\n","\n","The gradient of $f(x)$ at point $x=1$\n","\n","is \n","\n","$df(1)=2$.\n","\n","Now let’s visualize $f(x)$ and those $x=-10$ and $x=1$ points."]},{"cell_type":"code","execution_count":22,"id":"4ff7e11a","metadata":{},"outputs":[],"source":["import numpy as np\n","import seaborn as sns\n","\n","def f(x):\n"," return x**2\n","\n","def df(x):\n"," return 2*x\n","\n","def visualize(f, x=None):\n"," \n"," xArray = np.linspace(-10, 10, 100) \n"," yArray = f(xArray)\n"," sns.lineplot(x=xArray, y=yArray)\n"," \n"," if x is not None:\n"," assert type(x) in [np.ndarray, list] # x should be numpy array or list\n"," if type(x) is list: # if it is a list, convert to numpy array\n"," x = np.array(x)\n","\n"," \n"," y = f(x)\n"," sns.scatterplot(x=x, y=y, color='red')"]},{"cell_type":"code","execution_count":23,"id":"633a54fd","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=[-10, 1])"]},{"cell_type":"markdown","id":"9c187ad7","metadata":{},"source":["The red dot at x=-10 does not know the surface it stands on, and it only knows the coordinates of where it stands and the gradient of itself, which is -20. And the other red dot at x=1 does not know the surface it stands on; it only knows the coordinates of where it stands and the gradient of itself, which is 2.\n","\n","By having only this information: we can say that the red dot at x=-10 should make a bigger jump than x=1 because it has a bigger absolute gradient value. The sign shows the direction. Minus (-) shows that the red dot at x=-10 should move to the right and the other one should move to the left.\n","\n","In summary, the red dot at x=-10 (gradient: -20) should make a bigger jump to the right, and the red dot at x=1 (gradient: 2) should make a smaller jump to the left. \n","\n","We know that the jump length should be proportional to the gradient, but what is that value exactly? We don’t know. So, let’s just say that red points should move with the length of *alpha * gradient*, where alpha is just a parameter.\n","\n","We can say that the new location of the red dot should be calculated with the following formula:\n","\n","x = x - gradient * alpha"]},{"cell_type":"markdown","id":"0a7f5c3f","metadata":{},"source":["Now let's implement this with **NumPy**. Let's start with visualizing the $f(x)=x^2$ function and the $x=-10$ point."]},{"cell_type":"code","execution_count":24,"id":"e26dbdf0","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=[-10])"]},{"cell_type":"markdown","id":"6e752e19","metadata":{},"source":["The following code implements the whole logic explained before:"]},{"cell_type":"code","execution_count":25,"id":"2bdd54f1","metadata":{},"outputs":[],"source":["def gradient_descent(x, nsteps=1):\n"," \n"," \n"," # collectXs is an array to store how x changed in each iteration, so we can visualize it later\n"," \n"," collectXs = [x]\n"," \n"," # learning_rate is the value that we mentioned as alpha in the previous section\n"," \n"," learning_rate = 1e-01\n"," \n"," for _ in range(nsteps):\n"," \n"," # The following one line does the real magic\n"," # The next value of x is calculated by subtracting the gradient * learning_rate by itself\n"," # The intuition behind this line is in the previous section\n"," \n"," x -= df(x) * learning_rate \n"," collectXs.append(x)\n"," \n"," # We return a tuple that contains\n"," # x -> recent x after nsteps \n"," # collectXs -> all the x values that were calculated so far\n"," \n"," return x, collectXs"]},{"cell_type":"markdown","id":"aea74a65","metadata":{},"source":["Before running a gradient descent with 1000 steps, let's just run it twice, one step at a time, to see how x evolves. \n","We start with x=-10, and it evolves to x=-8. We know that when x=0 that is the **minimum point**, so yes, it is evolving in the correct direction."]},{"cell_type":"code","execution_count":26,"id":"0350981e","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-8.0\n"]}],"source":["x=-10\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"code","execution_count":27,"id":"f8e01e2d","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-6.4\n"]}],"source":["# The next step will start at x=-8. Let's run a gradient for 1 step\n","\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"markdown","id":"93f13b32","metadata":{},"source":["It goes to x=-6.4. Excellent. Now let's run it 1000 times"]},{"cell_type":"code","execution_count":28,"id":"b699d1fb","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-7.873484301831169e-97\n"]}],"source":["x, collectedXs = gradient_descent(x, nsteps=1000)\n","print(x)"]},{"cell_type":"code","execution_count":29,"id":"0b76ee22","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=collectedXs)"]},{"cell_type":"markdown","id":"d00d2fbb","metadata":{},"source":["### Exercise 3\n","\n","When I arrive to the coffee machine, I hear my colleague talking about the per-unit costs of producing 'product B' for the company. As the company produces more units, the per-unit costs continue to decrease until a point where they start to increase.\n","\n","To optimize the per-unit production cost at its minimum to optimize efficiency, the company would need to find the number of units to be produced where the per-unit production costs begin to change from decreasing to increasing.\n","\n","**Build a quadratic function $f(x)=0.1(x)^2−9x +4500$ on $x∈[0,100]$ to create the per-unit cost function, and make a conclusion.**"]},{"cell_type":"code","execution_count":null,"id":"7c67d8b7","metadata":{},"outputs":[],"source":["# Define and plot the function"]},{"cell_type":"markdown","id":"fbe54895","metadata":{},"source":["We saw with Gradient Descent how the red dot navigates in an environment it does not know about. It only knows the coordinates of where it is and its gradient. The red dot could find the minimum point by using only this knowledge and the gradient descent algorithm.\n","\n","**Optional:**\n","\n","Implement all the previous steps to create a gradient descent algorithm to see how the per-unit cost evolves, with a starting point of 0 units of production."]},{"cell_type":"markdown","id":"aabad82c","metadata":{},"source":["## Linear Algebra"]},{"cell_type":"markdown","id":"6753636d","metadata":{},"source":["### Exercise 1: Sum of two matrices\n","\n","Suppose we have two matrices A and B.\n","\n","```py\n","A = [[1,2],[3,4]]\n","B = [[4,5],[6,7]]\n","\n","then we get\n","A+B = [[5,7],[9,11]]\n","A-B = [[-3,-3],[-3,-3]]\n","```\n","\n","Make the sum of two matrices using Python with NumPy"]},{"cell_type":"code","execution_count":null,"id":"9e200c32","metadata":{},"outputs":[],"source":["# import numpy as np\n","\n"," \n"," \n","# Creating first matrix\n","\n"," \n","# Creating second matrix\n","\n"," \n","# Print elements\n","\n"," \n","# Adding both matrices\n"]},{"cell_type":"markdown","id":"93bfb6cc","metadata":{},"source":["### Exercise 2: Sum of two lists\n","\n","There will be many situations in which we'll have to find an index-wise summation of two different lists. This can have possible applications in day-to-day programming. In this exercise, we will solve the same problem in various ways in which this task can be performed.\n","\n","We have the following two lists:\n","\n","```py\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n","```\n","\n","Now let's use Python code to demonstrate addition of two lists."]},{"cell_type":"code","execution_count":null,"id":"867b70fc","metadata":{},"outputs":[],"source":["# Naive method\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print (\"Original list 1 : \" + str(list1))\n","print (\"Original list 2 : \" + str(list2))\n"," \n","# Using naive method to add two lists \n","res_list = []\n","for i in range(0, len(list1)):\n"," res_list.append(list1[i] + list2[i])\n"," \n","# Printing resulting list \n","print (\"Resulting list is : \" + str(res_list))"]},{"cell_type":"markdown","id":"7a063d7f","metadata":{},"source":["Now use the following three different methods to make the same calculation: sum of two lists"]},{"cell_type":"code","execution_count":null,"id":"681930a3","metadata":{},"outputs":[],"source":["# Use list comprehension to perform addition of the two lists:\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using list comprehension to add two lists\n","\n"," \n","# Printing resulting list \n"]},{"cell_type":"code","execution_count":null,"id":"a3a8a425","metadata":{},"outputs":[],"source":["# Use map() + add():\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using map() + add() to add two lists\n","\n"," \n","# Printing resulting list "]},{"cell_type":"code","execution_count":null,"id":"1708d7ee","metadata":{},"outputs":[],"source":["# Use zip() + sum():\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using zip() + sum() to add two lists\n","\n"," \n","# Printing resulting list "]},{"cell_type":"markdown","id":"1aef1bd2","metadata":{},"source":["### Exercise 3: Dot multiplication\n","\n","We have two matrices:\n","\n","```py\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n","```\n","\n","A simple technique but expensive method for larger input datasets is using *for loops*. In this exercise, we will first use nested *for loops* to iterate through each row and column of the matrices, and then we will perform the same multiplication using NumPy."]},{"cell_type":"code","execution_count":null,"id":"840e7d0e","metadata":{},"outputs":[],"source":["# Using a for loop input two matrices of size n x m\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n"," \n","res = [[0 for x in range(3)] for y in range(3)]\n"," \n","# Explicit for loops\n","for i in range(len(matrix1)):\n"," for j in range(len(matrix2[0])):\n"," for k in range(len(matrix2)):\n"," \n"," # Resulting matrix\n"," res[i][j] += matrix1[i][k] * matrix2[k][j]\n"," \n","print(res)"]},{"cell_type":"code","execution_count":null,"id":"db6c3355","metadata":{},"outputs":[],"source":["# Import libraries\n","\n"," \n","# Input two matrices\n","\n"," \n","# This will return dot product\n","\n"," \n","# Print resulting matrix\n"]},{"cell_type":"markdown","id":"785f6c30","metadata":{},"source":["Source:\n","\n","https://www.youtube.com/channel/UCXq-PLvYAX-EufF5RAPihVg\n","\n","https://www.geeksforgeeks.org/\n","\n","https://medium.com/@seehleung/basic-calculus-explained-for-machine-learning-c7f642e7ced3\n","\n","https://blog.demir.io/understanding-gradient-descent-266fc3dcf02f"]}],"metadata":{"interpreter":{"hash":"d3463682613d55fcbb64853e38cc3520a7f67bdf8d6940e781ddcdc423122719"},"kernelspec":{"display_name":"Python 3.9.12 ('calculus-project')","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.9.12"}},"nbformat":4,"nbformat_minor":5} +{"cells":[{"cell_type":"markdown","id":"5dbe7b9e","metadata":{},"source":["# Calculus and Algebra problems"]},{"cell_type":"markdown","id":"519c4b12","metadata":{},"source":["## Calculus\n","\n","Calculus is not obscure. It is the language for modeling behaviors. Calculus enables us to find the rate of changes in order to optimize a function. Without calculus, we would not be able to fully understand techniques such as:\n","\n","Backpropagation in neural networks\n","\n","Regression using optimal least square\n","\n","Expectation maximization in fitting probability models"]},{"cell_type":"markdown","id":"b7e2e87a","metadata":{},"source":["### Exercise 1\n","\n","Let's say, in my office, it takes me 10 seconds (time) to travel 25 meters (distance) to the coffee machine.\n","If we want to express the above situation as a function, then it would be:\n","\n","distance = speed * time\n","\n","So for this case, speed is the first derivative of the distance function above. As speed describes the rate of change of distance over time, when people say taking the first derivative of a certain function, they mean finding out the rate of change of a function.\n","\n","**Find the speed and build the linear function on distance $(d)$ over time $(t)$, when $(t ∈ [0,10])$.**"]},{"cell_type":"code","execution_count":3,"id":"bb3e954e","metadata":{},"outputs":[],"source":["# import libraries\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import pandas as pd\n","\n","# Define the distance function; speed= 25/10=2.5 >> fdis(x)=2.5*t(X)\n","def f(x):\n"," return 2.5*x\n","x=np.linspace(0,10)\n"]},{"cell_type":"code","execution_count":4,"id":"dbc4c780","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":4,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Plot the distance function on domain (t)\n","plt.plot(x,f(x))"]},{"cell_type":"code","execution_count":5,"id":"4c4d4f20","metadata":{},"outputs":[{"data":{"text/html":["
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xf(x)
00.0000000.000000
10.2040820.510204
20.4081631.020408
30.6122451.530612
40.8163272.040816
51.0204082.551020
61.2244903.061224
71.4285713.571429
81.6326534.081633
91.8367354.591837
102.0408165.102041
112.2448985.612245
122.4489806.122449
132.6530616.632653
142.8571437.142857
153.0612247.653061
163.2653068.163265
173.4693888.673469
183.6734699.183673
193.8775519.693878
204.08163310.204082
214.28571410.714286
224.48979611.224490
234.69387811.734694
244.89795912.244898
255.10204112.755102
265.30612213.265306
275.51020413.775510
285.71428614.285714
295.91836714.795918
306.12244915.306122
316.32653115.816327
326.53061216.326531
336.73469416.836735
346.93877617.346939
357.14285717.857143
367.34693918.367347
377.55102018.877551
387.75510219.387755
397.95918419.897959
408.16326520.408163
418.36734720.918367
428.57142921.428571
438.77551021.938776
448.97959222.448980
459.18367322.959184
469.38775523.469388
479.59183723.979592
489.79591824.489796
4910.00000025.000000
\n","
"],"text/plain":[" x f(x)\n","0 0.000000 0.000000\n","1 0.204082 0.510204\n","2 0.408163 1.020408\n","3 0.612245 1.530612\n","4 0.816327 2.040816\n","5 1.020408 2.551020\n","6 1.224490 3.061224\n","7 1.428571 3.571429\n","8 1.632653 4.081633\n","9 1.836735 4.591837\n","10 2.040816 5.102041\n","11 2.244898 5.612245\n","12 2.448980 6.122449\n","13 2.653061 6.632653\n","14 2.857143 7.142857\n","15 3.061224 7.653061\n","16 3.265306 8.163265\n","17 3.469388 8.673469\n","18 3.673469 9.183673\n","19 3.877551 9.693878\n","20 4.081633 10.204082\n","21 4.285714 10.714286\n","22 4.489796 11.224490\n","23 4.693878 11.734694\n","24 4.897959 12.244898\n","25 5.102041 12.755102\n","26 5.306122 13.265306\n","27 5.510204 13.775510\n","28 5.714286 14.285714\n","29 5.918367 14.795918\n","30 6.122449 15.306122\n","31 6.326531 15.816327\n","32 6.530612 16.326531\n","33 6.734694 16.836735\n","34 6.938776 17.346939\n","35 7.142857 17.857143\n","36 7.346939 18.367347\n","37 7.551020 18.877551\n","38 7.755102 19.387755\n","39 7.959184 19.897959\n","40 8.163265 20.408163\n","41 8.367347 20.918367\n","42 8.571429 21.428571\n","43 8.775510 21.938776\n","44 8.979592 22.448980\n","45 9.183673 22.959184\n","46 9.387755 23.469388\n","47 9.591837 23.979592\n","48 9.795918 24.489796\n","49 10.000000 25.000000"]},"execution_count":5,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","df=pd.DataFrame({'x':x, 'f(x)':f(x)})\n","df"]},{"cell_type":"markdown","id":"1144168d","metadata":{},"source":["### Exercise 2\n","\n","It turned out that I wasn't walking a constant speed towards getting my coffee, but I was accelerating (my speed increased over time). If my initial *speed = 0*, it still took me 10 seconds to travel from my seat to my coffee, but I was walking faster and faster.\n","\n","$V_o$ = initial speed = $0$\n","\n","t = time\n","\n","a = acceleration\n","\n","**distance** = $V_o * t + 0.5 * a * (t^2)$\n","\n","**speed** = $V_o + a * t$\n","\n","The first derivative of the speed function is acceleration. I realize that the speed function is closely related to the distance function.\n","\n","**Find the acceleration value and build the quadratic function $(t ∈ [0,10])$. Also, create a graph and a table.**"]},{"cell_type":"code","execution_count":11,"id":"ec1f8bd7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":11,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the quadratic funtion t=10, d=25 >> a=0.5 | Vo=0\n","\n","def f(t): return 0.5*0.5*(t**2)\n","t = np.linspace(0,10)\n","plt.plot(t, f(t))\n"]},{"cell_type":"code","execution_count":13,"id":"ba5c497b","metadata":{},"outputs":[{"data":{"text/html":["
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tf(t)
00.0000000.000000
10.2040820.010412
20.4081630.041649
30.6122450.093711
40.8163270.166597
\n","
"],"text/plain":[" t f(t)\n","0 0.000000 0.000000\n","1 0.204082 0.010412\n","2 0.408163 0.041649\n","3 0.612245 0.093711\n","4 0.816327 0.166597"]},"execution_count":13,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","dft=pd.DataFrame({'t':t, 'f(t)':f(t)})\n","dft.head()\n"]},{"cell_type":"markdown","id":"66d4cc18","metadata":{},"source":["Before exercise 3, we'll make a brief introduction to Gradient Descent algorithm, which will have a larger explanation in future modules of the bootcamp.\n","\n","Gradient Descent algorithm is the hero behind the family of deep learning algorithms. When an algorithm in this family runs, it tries to minimize the error between the training input and predicted output. This minimization is done by optimization algorithms, and gradient descent is the most popular one.\n","\n","Let's say you have these input & output pairs:\n","\n","```py\n","# Input:\n","[\n"," [1,2],\n"," [3,4]\n","]\n","\n","# Output:\n","[\n"," [50],\n"," [110]\n","]\n","```\n","\n","We can estimate that if we multiply the input values by [10, 20], we can have the output as shown above.\n","\n","```py\n","1(10) + 2(20) = 50\n","\n","3(10) + 4(20) = 110\n","```\n","\n","When a machine learning algorithm starts running, it assigns random values and makes a prediction. \n","Let's say it assigned [1,2] values:\n","\n","```py\n","1(1) + 2(2) = 5\n","\n","3(1) + 4(2) = 11\n","```\n","\n","Once it has the predictions, it calculates the error: the difference between the real data and the predicted data. There are many ways to calculate the error, and they are called loss functions.\n","\n","Once we have this value, the optimization algorithm starts showing itself, and it sets new values which replace the initial random values. \n","\n","And, the loop continues until a condition is met. That condition can be to loop *n* times, or to loop until the error is smaller than a value."]},{"cell_type":"markdown","id":"85ef2f0b","metadata":{},"source":["It can be hard to understand **gradient descent** without understanding **gradient**. So, let's focus on what a gradient is. The gradient shows the direction of the greatest change of a scalar function. The gradient calculation is done with derivatives, so let's start with a simple example. To calculate the gradient, we just need to remember some linear algebra calculations from high school because we need to calculate derivatives.\n","\n","Let's say we want to find the minimum point of $f(x) = x^2$. The derivative of that function is $df(x)=2x$. \n","\n","The gradient of $f(x)$ at point $x=-10$\n","\n","is \n","\n","$df(-10)=-20$.\n","\n","The gradient of $f(x)$ at point $x=1$\n","\n","is \n","\n","$df(1)=2$.\n","\n","Now let’s visualize $f(x)$ and those $x=-10$ and $x=1$ points."]},{"cell_type":"code","execution_count":null,"id":"4ff7e11a","metadata":{},"outputs":[],"source":["import numpy as np\n","import seaborn as sns\n","\n","def f(x):\n"," return x**2\n","\n","def df(x):\n"," return 2*x\n","\n","def visualize(f, x=None):\n"," \n"," xArray = np.linspace(-10, 10, 100) \n"," yArray = f(xArray)\n"," sns.lineplot(x=xArray, y=yArray)\n"," \n"," if x is not None:\n"," assert type(x) in [np.ndarray, list] # x should be numpy array or list\n"," if type(x) is list: # if it is a list, convert to numpy array\n"," x = np.array(x)\n","\n"," \n"," y = f(x)\n"," sns.scatterplot(x=x, y=y, color='red')"]},{"cell_type":"code","execution_count":null,"id":"633a54fd","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=[-10, 1])"]},{"cell_type":"markdown","id":"9c187ad7","metadata":{},"source":["The red dot at x=-10 does not know the surface it stands on, and it only knows the coordinates of where it stands and the gradient of itself, which is -20. And the other red dot at x=1 does not know the surface it stands on; it only knows the coordinates of where it stands and the gradient of itself, which is 2.\n","\n","By having only this information: we can say that the red dot at x=-10 should make a bigger jump than x=1 because it has a bigger absolute gradient value. The sign shows the direction. Minus (-) shows that the red dot at x=-10 should move to the right and the other one should move to the left.\n","\n","In summary, the red dot at x=-10 (gradient: -20) should make a bigger jump to the right, and the red dot at x=1 (gradient: 2) should make a smaller jump to the left. \n","\n","We know that the jump length should be proportional to the gradient, but what is that value exactly? We don’t know. So, let’s just say that red points should move with the length of *alpha * gradient*, where alpha is just a parameter.\n","\n","We can say that the new location of the red dot should be calculated with the following formula:\n","\n","x = x - gradient * alpha"]},{"cell_type":"markdown","id":"0a7f5c3f","metadata":{},"source":["Now let's implement this with **NumPy**. Let's start with visualizing the $f(x)=x^2$ function and the $x=-10$ point."]},{"cell_type":"code","execution_count":null,"id":"e26dbdf0","metadata":{},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXcAAAD4CAYAAAAXUaZHAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAsFElEQVR4nO3dd3yV9d3/8dcne5AESEISyCIkMmUZNuLAiVYcqDiA4tZq7bRa29vW1v4c991qq2jBBU4UUdy4wIGAJOydMEISkpAQyN75/v44hzZNE8g65zrj83w8eOTkOldyvXOdwztXrvG9xBiDUkopz+JjdQCllFI9T8tdKaU8kJa7Ukp5IC13pZTyQFruSinlgfysDgAQFRVlkpOTrY6hlFJuJTMzs8QYE93Wcy5R7snJyWRkZFgdQyml3IqI5LT3nO6WUUopD6TlrpRSHkjLXSmlPJCWu1JKeSAtd6WU8kCnLHcReVFEjojI9hbT+orI5yKSZf/Yxz5dROTvIpItIltFZKzDkjc3w549sHq17WNzs8MWpZRS7qYjW+4vAxe1mnY/8KUxJg340v45wMVAmv3fbcCzPROzleZmWL4cxoyBc86xfVy+XAteKaXsTlnuxphvgNJWk2cCi+2PFwOXt5i+xNisA3qLSFwPZf23rCyYO5fNvRN4bNo8qKmBuXNt05VSyg0YY3jko53sOFzmkO/f1X3uMcaYAvvjQiDG/ngAkNtivjz7tP8iIreJSIaIZBQXF3du6QUFUFPDtthUnp10NdtjBtkKvqDg1F+rlFIuYN3+UhZ9e4A9hRUO+f7dPqBqbHf76PQdP4wxC40x6caY9OjoNq+ebV9cHAQHc9nOrwlsqOPNkRdAcLBtulJKuYGlGw4RFuTHxSMc01tdLfeiE7tb7B+P2KfnAwkt5ou3T+tZaWmwZAkRPs3M2LOGFcPPpualJbbpSinl4sqqG/hkeyEzR/cnOMDXIcvoarm/D8yzP54HrGgxfa79rJmJQFmL3Tc9x8cHrrwSNm3imvkzqAgM5ZPUCbbpSinl4lZsyaeusZnZ4xIdtoyOnAr5BrAWGCwieSJyM/AocL6IZAHn2T8H+BjYD2QDi4C7HJIabEU+eDATrzyX5MgQlmbkOWxRSinVk5ZuyGVYXDgjBkQ4bBmnHBXSGHNdO09Nb2NeA/yku6E6Q0S4Oj2BJ1buYX9xJSnRvZy5eKWU6pTt+WXsOFzOwzOHO3Q5HrEfY9YZ8fj6CG/p1rtSysW9ueEQgX4+zBzV5omEPcYjyj0mPIhzBkezLDOPhia9kEkp5Zpq6ptYsfkwF4+IJSLE36HL8ohyB7h2XCIllXV8tfvIqWdWSikLfLytgIraRq4Zl3DqmbvJY8r9nMHRxIQH8sYPh6yOopRSbXrjh0MMjAplUkqkw5flMeXu5+vDNekJfL23mPzjNVbHUUqp/5BVVEFGzjFmj0tARBy+PI8pd4Br0m1/6izdkHuKOZVSyrne+CEXf1/hqjPinbI8jyr3hL4hTEuL5u2MXBr1wKpSykXUNjSxfFMeFwyPJapXoFOW6VHlDnDd+AQKymr5em8nByNTSikHWbmjkOPVDVznwCtSW/O4cp8+NIaoXoG88YPumlFKuYY3fjhEYt8QJg9y/IHUEzyu3P19fbgmPZ6vdhdRWFZrdRyllJfbX1zJuv2lzB6fgI+P4w+knuBx5Q4we1wizUYPrCqlrPfGD4fw8xFmOelA6gkeWe6JkSFMOy2aNzcc0gOrSinL1DY08XZmHhcOj6VfWJBTl+2R5Q5ww4RECspqWbVHD6wqpazxyfYCjlc3cP0E5x1IPcFjy336kH7EhAfy2vocq6MopbzUa+ucd0Vqax5b7n6+Plw7LpGv9xaTW1ptdRyllJfZXVhORs4xrh+f6NQDqSd4bLkDtst8QcebUUo53evrDxHg6+O0K1Jb8+hy7987mHOHxPBWRh71jXpgVSnlHNX1jby7MZ8Zp8fSNzTAkgweXe4AN0y0DQW8ckeh1VGUUl7i/c2Hqahr5PoJSZZl8Phyn5YWTULfYF5dpwdWlVKOZ4xhydocBseEMS65j2U5PL7cfX2EGyYksf5AKXuLKqyOo5TycJtyj7OzoJwbJyU5ZWjf9nh8uYNtKOAAPx/deldKOdyra3PoFejHFWMce4/UU/GKcu8bGsClp8exfGM+lXWNVsdRSnmo0qp6PtxawJVjB9Ar0M/SLF5R7gA3Tkqisq6R9zblWx1FKeWh3srIpb6pmRsnWncg9QSvKfcxCb0Z3j+cV9flYIyxOo5SysM0NRteW5/DhIF9OS0mzOo43lPuIsKciUnsLrTdx1AppXrSN3uLyS2tYc4k67fawYvKHeCy0f0JD/Jj8fcHrY6ilPIwi9ceJDoskAuGxVodBfCycg8J8OOa9AQ+3V5IUbneyEMp1TMOllSxek8xN0xIJMDPNWrVNVI40ZxJSTQZw2vrdbwZpVTPWLI2B39fsWRo3/Z4XbknRYZyzuB+vL7+kI43o5Tqtqq6Rt7OzOXiEXFOvyHHyXhduQPMnZRESWUdn2wvsDqKUsrNvbspn4raRuZNdo0DqSd4ZblPS4tmYFSoHlhVSnWLbRyZg4wYEM7YROvGkWlLt8pdRH4uIjtEZLuIvCEiQSIyUETWi0i2iCwVEWvGuzwJHx/baZEbDx1nW16Z1XGUUm5q7f6j7C2qZO6kZEvHkWlLl8tdRAYAPwXSjTEjAF9gNvAY8DdjTCpwDLi5J4L2tFnp8YQE+PLS9wesjqKUclMvrzlInxB/LhvV3+oo/6W7u2X8gGAR8QNCgALgXGCZ/fnFwOXdXIZDhAf5M+uMeD7cUkBxRZ3VcZRSbia3tJovdhVx3fhEgvx9rY7zX7pc7saYfOB/gUPYSr0MyASOG2NOjM6VB7Q5NJqI3CYiGSKSUVxc3NUY3TJvcjL1Tc28rqdFKqU6acnag7Yr313kitTWurNbpg8wExgI9AdCgYs6+vXGmIXGmHRjTHp0dHRXY3TLoOhenD04mlfX5+hpkUqpDquqa+TNDblcPCKWuIhgq+O0qTu7Zc4DDhhjio0xDcByYArQ276bBiAecOlhGH88OZniijo+2nbY6ihKKTexfGMeFbWNzJ+SbHWUdnWn3A8BE0UkRGyHiacDO4FVwCz7PPOAFd2L6FjT0qJJiQ7lpTUHdbRIpdQpNTcbXvr+ICPjI1zu9MeWurPPfT22A6cbgW3277UQ+A3wCxHJBiKBF3ogp8P4+AjzJyezNa+MjYd0tEil1Ml9m13C/uIq5k9xvdMfW+rW2TLGmIeMMUOMMSOMMXOMMXXGmP3GmPHGmFRjzNXGGJc/FeXKsfGEB/nx4pqDVkdRSrm4F787QHRYIJec7nqnP7bklVeothYa6Md14xP5ZFsBuaXVVsdRSrmorKIKvt5bzNyJSS4z+mN7XDudE82bbPsTS4ckUEq158U1Bwj08+EGF7iN3qloudv17x3MjNPjWLohl4raBqvjKKVczNHKOt7ZmM+VY+PpG+pyo6r8Fy33Fm6eOpCKukbeysizOopSysW8Zh8m/OapyVZH6RAt9xZGJ/QmPakPL605QFOznhaplLKpa2xiydoczh4cTWo/629+3RFa7q3cPHUgecdq+GxHodVRlFIu4v3NhymprOPmqQOtjtJhWu6tXDA8loS+wTz/nY4WqZSyjdn+wncHGBwTxtTUKKvjdJiWeyu+PsLNUwaSmXOMzJxSq+MopSz2TVYJuwsruHVaiktftNSalnsbrk5PICLYn4Xf7Lc6ilLKYou+2U9MeKBLjtl+MlrubQgN9GPOxCQ+21nEgZIqq+MopSyy43AZ32WXMH/KQJe/aKk190rrRHMnJ+Hv48ML3+nWu1LeatE3+wkN8OW68YlWR+k0Lfd29AsL4ooxA3g7I4+jlS4/PI5SqocdPl7DB1sLmD0+kYhgf6vjdJqW+0nccuZA6hqbeWVdjtVRlFJO9tIa2xlzrjxm+8louZ9EWkwY04f0Y8naHGrqm6yOo5RykrLqBl5ff4hLR8YR3yfE6jhdouV+CnecPYjSqnreysi1OopSykleXZ9DVX0Tt08bZHWULtNyP4VxyX05I6kPi77dT2OT3mdVKU9X29DES2sOMO20aIb1D7c6TpdpuXfAHWcNIu9YDR9tK7A6ilLKwZZl5lFSWc8dZ6VYHaVbtNw7YPqQfqT168VzX+/X+6wq5cGamg2Lvt3PqPgIJqVEWh2nW7TcO8DHR7htWgq7Csr5em+x1XGUUg7yyfYCco5Wc8dZg9xqqIG2aLl30MzRA4iLCOLZ1fusjqKUcgBjDM99vY+BUaFcMDzW6jjdpuXeQQF+PtxyZgrrD5SSmXPM6jhKqR72TVYJ2/PLueOsFHx93HurHbTcO+W68Qn0CfHn2dXZVkdRSvWwBauyiYsI4oox8VZH6RFa7p0QEuDHTVMG8sWuI+wqKLc6jlKqh2QcLGX9gVJuPTPF7QYIa49n/BRONHdSMr0C/XTfu1IeZMHqffQNDWD2+ASro/QYLfdOigjx54aJiXy49TAHdThgpdzejsNlfLX7CPMnJxMS4Gd1nB6j5d4FN08diJ+vD899rVvvSrm7Z1fvo1egH3MnJVsdpUdpuXdBv7AgZo9L4J2NeeQfr7E6jlKqi7KPVPLRtgJunJhERIj7Det7MlruXXT7WbYBhf6pW+9Kua0Fq7IJ9PPhljMHWh2lx2m5d9GA3sFcNTaeNzfkcqS81uo4SqlOyjlaxYoth7lxQhJRvQKtjtPjtNy74a6zU2lqNvxTb6StlNtZsGofvvahRTxRt8pdRHqLyDIR2S0iu0Rkkoj0FZHPRSTL/rFPT4V1NYmRIcwc3Z/X1udQorfiU8pt5B2r5p2NeVw3LoF+4UFWx3GI7m65PwV8aowZAowCdgH3A18aY9KAL+2fe6yfnJNKXWMzi77VrXel3MVzX+9D5N/HzjxRl8tdRCKAacALAMaYemPMcWAmsNg+22Lg8u5FdG2Dontx6cj+vLI2h9KqeqvjKKVOoaCshrc25DHrjAT69w62Oo7DdGfLfSBQDLwkIptE5HkRCQVijDEn7mpRCMS09cUicpuIZIhIRnGxew+j+9NzU6lpaGKh7ntXyuUtWLWPZmP4yTmeu9UO3St3P2As8KwxZgxQRatdMMZ2Z4s2725hjFlojEk3xqRHR0d3I4b10mLCuHRkf5asPchR3feulMs6fLyGpRtyuTo9wW1vfN1R3Sn3PCDPGLPe/vkybGVfJCJxAPaPR7oX0T3cO9229b7o2wNWR1FKtWPB6mwMnr/VDt0od2NMIZArIoPtk6YDO4H3gXn2afOAFd1K6CZS+4XxI916V8pledNWO3T/bJl7gNdEZCswGvgL8ChwvohkAefZP/cKP7VvvS/UM2eUcjnPrLLdh+En56RanMQ5ujUEmjFmM5DexlPTu/N93VVqvzAuG9WfJd/ncMvUFKLDPO+qN6XcUd6xat7KsG21D/DgM2Ra0itUe9i909Ooa2zSESOVciH/+DIbEeGec71jqx203HtcSnQvrhwbzyvrcigs0zFnlLLagZIqlm3M4/rxicRFeMdWO2i5O8S909NobjY8vSrL6ihKeb2nvtiLv69wlxecIdOSlrsDJPQN4dpxCSzdkEtuabXVcZTyWnuLKlix5TDzJifTL8wzx5Bpj5a7g9x9bioiwj++0q13pazy5Bd7CQ3w445p3rXVDlruDhMXEcyNE5JYlpnHvuJKq+Mo5XW255fx8bZCbpqSTJ/QAKvjOJ2WuwPddc4ggvx9+etne62OopTXeXzlHnqH+HOLh47Xfipa7g4U1SuQW85M4aNtBWzLK7M6jlJeY+2+o3yzt5ifnJ1KeJBn3Ru1o7TcHezWMwfSJ8Sfx1futjqKUl7BGMPjK3cTGx7EnElJVsexjJa7g4UF+XPX2al8m1XC9/tKrI6jlMf7fGcRmw4d597z0gjy97U6jmW03J1gzqQk4iKCePzTPdhGQVZKOUJTs+F/P9tDSlQoV58Rb3UcS2m5O0GQvy8/Oy+NzbnHWbmj0Oo4Snms5Rvz2FtUyS8uOA0/X++uN+/+6Z3oqrHxpPbrxeOf7qGhqdnqOEp5nNqGJv76+V5GxUdwyelxVsexnJa7k/j5+nD/RUPYX1LFmxtyrY6jlMd5ac1BCspquf/ioYiI1XEsp+XuRNOH9mN8cl+e+iKLqrpGq+Mo5TGOVdWzYHU25w7px6RBkVbHcQla7k4kIjwwYwgllXUs0ht6KNVjnlmVTVVdI7+5aIjVUVyGlruTjUnsw4zTY1n4zX6OVOiQwEp1V25pNUvW5nDV2HgGx4ZZHcdlaLlb4L4Lh9DQ1MzfPtdhCZTqrsc+3Y2PD/zigtOsjuJStNwtkBwVypyJySzdkMvuwnKr4yjltjJzjvHh1gJuOzPFq27E0RFa7hb56fRUwoL8eeSjXXphk1JdYIzhzx/tJDoskNvP8r4hfU9Fy90ivUMC+On0NL7NKmH13mKr4yjldj7aVsCmQ8f59QWDCQ30szqOy9Fyt9CciUkkR4bwl4920agXNinVYbUNTTz26W6GxIZxlZcPM9AeLXcLBfj5cP/FQ8k6UskbPxyyOo5SbuOlNQfJLa3hd5cMw9dHL1hqi5a7xS4cHsOklEj++vlejlfXWx1HKZd3pKKWp7/K4vxhMUxNi7I6jsvScreYiPA/PxpGWU0DT36h91tV6lSe+HQP9U3NPDhjqNVRXJqWuwsYGhfOdeMTeWVdDllFFVbHUcplbck9ztuZedw0dSDJUaFWx3FpWu4u4hfnn0ZogC8Pf7hTT41Uqg3GGP74wQ6iegVy9zmpVsdxeVruLiKyVyA/O+80vs0q4YtdR6yOo5TLWbH5MBsPHee+iwYT5qX3Re0MLXcXMmdSEmn9evHwhzuobWiyOo5SLqOitoFHPt7FqPgIZo3VUx87Qsvdhfj7+vDHy4aTW1rDP7/WUSOVOuHvX2ZRUlnHwzNH4KOnPnaIlruLmZwaxSUj41iwOpvc0mqr4yhluayiCl5ac5Br0xMYldDb6jhuo9vlLiK+IrJJRD60fz5QRNaLSLaILBWRgO7H9C6/u2QoPiL8+aOdVkdRylLGGP7wwQ5CAnz59YWDrY7jVnpiy/1eYFeLzx8D/maMSQWOATf3wDK8SlxEMPdMT2XljiJW79GDq8p7fbytkDXZR/n1hYOJ7BVodRy30q1yF5F44BLgefvnApwLLLPPshi4vDvL8Fa3TE0hJTqUh97Xg6vKO1XUNvDwhzsY3j+c6yckWR3H7XR3y/1J4D7gxKhXkcBxY8yJG4TmAQPa+kIRuU1EMkQko7hYR0VsLcDPhz/PHEHO0WoWrMq2Oo5STvfXz/dypKKOR644XceP6YIul7uIXAocMcZkduXrjTELjTHpxpj06OjorsbwaJNTo7h8dH+e+3o/+4orrY6jlNNszy9j8fcHuWFCIqP1IGqXdGfLfQpwmYgcBN7EtjvmKaC3iJwYXDkeyO9WQi/34CXDCPT34ffvbdcrV5VXaG42/O697fQNDeDXF+oNr7uqy+VujHnAGBNvjEkGZgNfGWNuAFYBs+yzzQNWdDulF4sOC+S+i4bw/b6jrNh82Oo4Sjnc6z8cYnPucX53yTAigvVK1K5yxHnuvwF+ISLZ2PbBv+CAZXiV68fb/jT904c7OValwwIrz1VUXstjn+xmSmokM0f3tzqOW+uRcjfGrDbGXGp/vN8YM94Yk2qMudoYU9cTy/Bmvj7Co1edTlmN7RJspTzVQyt2UN/UzCOXn47t5DvVVXqFqpsYEhvO7WelsCwzjzXZJVbHUarHrdxRyKc7Crn3vDQdzrcHaLm7kXvOTSM5MoTfvrtNz31XHqWitoGHVuxgSGwYt56ZYnUcj6Dl7kaC/H35y5Wnk3O0mr99sdfqOEr1mMc+3U1RRS2PXjUSf1+tpZ6ga9HNTB4UxexxCSz6Zj9bco9bHUepblu77yivrjvE/MkD9Zz2HqTl7oZ+e8lQ+oUFcd+yrdQ3Np/6C5RyUdX1jfzmna0kRYbowGA9TMvdDYUH+fPIFSPYU1TB0zo0gXJj//fZXg6VVvPolSMJDvC1Oo5H0XJ3U9OHxnDFmAEsWJXNzsPlVsdRqtMyc47x4poD3DgxkUmDIq2O43G03N3Y/1w6jN4h/vzq7S26e0a5lZr6Jn799hb6RwRz/8VDrY7jkbTc3Vif0AAeueJ0dhaU84+vsqyOo1SHPb5yN/tLqnh81kh6Bfqd+gtUp2m5u7kLh8dy5dgBLFi9j8169oxyA9/vK+GlNQeZNymJKalRVsfxWFruHuChHw2nX1ggv3xrs17cpFxaRW0Dv357K8mRIfzmYh3x0ZG03D1ARLA/j101kn3FVTyxco/VcZRq158/3EVBWQ3/d80oQgJ0d4wjabl7iGmnRTNnYhIvfHeA77J07Bnlej7dXsjSjFxuP2sQZyT1tTqOx9Ny9yC/nTGUQdGh/PLtzRyv1qGBles4Ul7LA8u3MmJAOD8/7zSr43gFLXcPEhzgy1Ozx1BaVc9v392md25SLqG52fCrZVupaWjiyWvHEOCnteMMupY9zIgBEfzi/MF8vK2QZZl5VsdRisVrD/LN3mIevGQYqf16WR3Ha2i5e6DbpqUwYWBfHnp/B/v1xtrKQjsPl/P/PtnNuUP6ceOERKvjeBUtdw/k6yM8OXs0AX4+3PPGJuoa9fRI5XzV9Y3c/cZGegf788SskXpnJSfTcvdQcRHBPDFrFDsOl/PoJ7utjqO80EMrdnCgpIonZ48msleg1XG8jpa7Bzt/WAw/npzMS2sO8sXOIqvjKC+yYnM+b2fmcfc5qUwepFehWkHL3cM9MGMIw+LC+dWyLeQdq7Y6jvIC+4or+e3ybaQn9eHe6WlWx/FaWu4eLtDPl2duGEtjk+Hu1zfp6JHKoWrqm7jr1Y0E+Pnw9+vG4Ke3zLOMrnkvMDAqlCdmjWRz7nH+8vEuq+MoD/b7FdvZe6SCJ2ePoX/vYKvjeDUtdy9x8elxzJ+SzMvfH+SjrQVWx1Ee6K2MXJZl5nHPOamcdVq01XG8npa7F3ng4qGMSezNfcu2kH2kwuo4yoNszy/j9+9tZ/KgSO7V4QVcgpa7Fwnw82HBDWMJDvDltlcyqahtsDqS8gClVfXc/komfUMD+Pt1Y/D10fPZXYGWu5eJiwjm6evHknO0ml+8tYXmZh1/RnVdY1Mz97yxkeLKOp678Qyi9Hx2l6Hl7oUmpkTy4IyhfL6ziKdXZVsdR7mxJ1buYU32Uf58+QhGJfS2Oo5qQcvdS82fkswVYwbwty/28tmOQqvjKDf03qZ8/vnNfm6cmMg16QlWx1GtaLl7KRHh/115OiMHRPCzpZvZVVBudSTlRjYdOsZ972xlYkpfHvrRcKvjqDZ0udxFJEFEVonIThHZISL32qf3FZHPRSTL/rFPz8VVPSnI35eFc9MJC/LjlsUZlFTWWR1JuYGCshpueyWT2PAgnr3hDPz1QiWX1J1XpRH4pTFmGDAR+ImIDAPuB740xqQBX9o/Vy4qJjyIRXPTOVpVxx2vZOoIkuqkqusbuXVJBjX1TTw/L50+oQFWR1Lt6HK5G2MKjDEb7Y8rgF3AAGAmsNg+22Lg8m5mVA42Mr43/3v1KDJyjnHfsq16ByfVpqZmw0/f2MzOw+X8/brRnBYTZnUkdRI9cvtxEUkGxgDrgRhjzIlLIAuBmHa+5jbgNoDERB3E32qXjuzPodJqHv90D4l9Q/jlBYOtjqRczJ8+3MkXu4p4eOZwzh3S5n9r5UK6vbNMRHoB7wA/M8b8x1E5Y9sEbHMz0Biz0BiTboxJj47WS5VdwZ1nDWL2uAT+8VU2b23ItTqOciEvfneAl78/yM1TBzJ3UrLVcVQHdKvcRcQfW7G/ZoxZbp9cJCJx9ufjgCPdi6icRUT40+UjODMtit++u43Ve/SlU/DJtgL+9NFOLhwew29nDLU6juqg7pwtI8ALwC5jzF9bPPU+MM/+eB6wouvxlLP5+9qGKBgcG8adr25k06FjVkdSFvp+Xwn3vrmZsYl9ePJaHVrAnXRny30KMAc4V0Q22//NAB4FzheRLOA8++fKjYQF+fPy/PH0Cw/kppc3kH1Eb7Ltjbbnl3HbkkySIkN4YV46wQG+VkdSnSCucGZEenq6ycjIsDqGaiXnaBVXPfs9gX6+vH3HJB2f24vYXvu1BPgK79w1mbgIfe1dkYhkGmPS23pOrz5Q7UqKDOXl+eMpr2ngxufXU1yhFzl5g8PHa7h+0XqamptZfNN4LXY3peWuTmrEgAhemj+OgrJa5rywnuPV9VZHUg50pKKWG55fT3lNA6/cPIE0PZfdbWm5q1NKT+7Lornp7C+uYt6LP+g48B7qWFU9c1/4gcKyWl6+aRwjBkRYHUl1g5a76pCpaVEsuGEsOw6XM1cL3uMcq6rnhufXs7+kiufnpXNGUl+rI6lu0nJXHXbesBievn4s2/LKmPviD5RrwXuE0qp6rn9+PdnFlTw/N50pqVFWR1I9QMtddcpFI2J55gZ7wb+gBe/uSk9ssduLfZre2NpjaLmrTrtweKx9F00Z1y9ax1EdKtgtFZXXcu0/17K/uJJFWuweR8tddckFw2NZODedrKJKrl24jqLyWqsjqU7ILa3m6ufWcvh4DS/PH6/F7oG03FWXnTO4H4tvGk9hWS2znvueQ0errY6kOiD7SAVXP7eWspoGXrt1IpMGRVodSTmAlrvqlokpkbx2ywQqahu58tk1bMsrszqSOokNB0u56tm1NDYblt4+kdF6U2uPpeWuum1UQm+W3TGZQD9frl24lq/3FlsdSbXh0+2F3Pj8eiJDA3j3rskMiQ23OpJyIC131SNS+/Vi+V2TSYoM5eaXN+h48C7EGMPLaw5w52uZDOsfzrI7J5PQN8TqWMrBtNxVj4kJD+Kt2237cO97Zyt/+XgXTc3WD0znzRqamvn9iu384YOdTB8Sw+u3TKSv3vfUK2i5qx4VFuTPiz8ex5yJSSz8Zj+3v5JJZV2j1bG8UllNAze9vIFX1x3i9mkp/HPOGTpsrxfRclc9zt/Xhz9dPoI/Xjacr3YXceWCNewv1jHhnWlPYQUzn/6OdfuP8viskTwwY6jeaMPLaLkrh5k3OZklN02guKKOmU+v4fOdRVZH8gofbDnM5c+soaq+iddvncg16QlWR1IW0HJXDjU1LYoP7plKUlQIty7J4ImVu2lsarY6lkeqa2zijx/s4J43NjG8fzgf3TOVcck6AJi30nJXDhffJ4Rld0zm2vQEnlm1j9kL15F/vMbqWB7lYEkVs55dy0trDvLjycm8futE+oUHWR1LWUjLXTlFkL8vj80ayVOzR7O7sIIZT33Lp9sLrI7l9owxvLcpn0v/8R2HSqv555wz+MNlwwnw0//a3k7fAcqpZo4ewEc/nUpSZAh3vLqRny/dTFmNjizZFUcr67jrtY38bOlmhsSG8fG9Z3Lh8FirYykX4Wd1AOV9kiJDeefOyTz9VTZPr8pm7b6jPDZrJGfp4FUdtnJHIQ++u43ymkZ+c9EQbpuWomfDqP+gW+7KEv6+Pvz8/NN4967J9AryY96LP3Dvm5so0eGDT6qwrJY7Xsnk9lcyiQ4L4v17pnDn2YO02NV/EWOsv4IwPT3dZGRkWB1DWaS2oYkFq/fx7OpsQgL8eODiIVyTnoCPFta/NDY189r6Qzyxcg8NTc3ce14at56Zgr+vbp95MxHJNMakt/mclrtyFVlFFfz23W1sOHiM0wdE8NCPhpGup/KxJruEhz/YyZ6iCqamRvHIFSNIigy1OpZyAVruym0YY1ix+TCPfrKbwvJaLh0Zx68uGExylPeVWVZRBU+s3MNnO4uI7xPMgzOGctGIWET0Lxplo+Wu3E51fSPPrd7Hom8PUN/UzDXpCdw7PY3YCM8/dzu3tJonv8ji3U15hAT4ccdZKdxyZgpB/joujPpPWu7KbR2pqOWZr7J5/YdDiAizzojn9mkpHrlbIvtIJc99vY/3NuXj4yPMm5TEnWen6iiOql1a7srt5ZZWs2D1Pt7JzKOxuZkZp8cxf8pAxib2duvdFMYY1h8o5eU1B1m5s5BAPx9mj0vk9rNSiIsItjqecnFa7spjHCmv5YXvDvD6+kNU1DUyvH84cyclccnI/vQKdJ/LNsprG3h/82FeWZvDnqIKIoL9mTMxiflTkonsFWh1POUmtNyVx6mqa+TdTfksWXuQvUWVBPv7ctGIWK4YM4BJgyJd8hTB+sZmvssuZvnGfD7bWUR9YzPD4sL58eRkfjSqv461rjpNy115LGMMmTnHWL4pnw+3HKa8tpGIYH+mD+3HBcNimZIaSViQv2X5yqob+C67hJU7Clm1+wgVdY30CfHnslH9uWJsPKPiI9x6t5KyltPLXUQuAp4CfIHnjTGPnmx+LXfVE2obmli9p5jPdhby5a4jlNU04OsjjIqPYEpqFGOT+jAqvrdDD1CWVNaxJfc4mTnHWJNdwrb8MpoN9A0N4Dz7L5xpp0XrwF6qRzi13EXEF9gLnA/kARuA64wxO9v7Gi131dMamprJOGgr2DX7StiaV/av+7km9A1mcEw4qf16MSg6lPg+IcRGBBEbHtShXSNVdY0UltdSVFZL3rEa9hVXsq+4kl0FFf8aytjPRxiT2JvJg6KYmhbFmITe+LngriLl3k5W7o44AjUeyDbG7Lcv/E1gJtBuuSvV0/x9fZg0KJJJgyL5FYOprGtke34ZW3KPsyXvOFlFlXy99wgNTf+5cRPo50NYkB+hgX4E2MvYYNtfXlXXSEVdI/WN/3mzkQA/H1KiQhmT2JsfT05mdGJvhvcPJyTAfQ7wKs/jiHffACC3xed5wITWM4nIbcBtAImJiQ6IodS/9Qr0Y2JKJBNTIv81rbGpmdxjNRw+XkNhWS2F5bWU1zRQUddIZW0jjc3/LnF/Xx96BfrRK8iP3sEBxEYEEhMexIDewcT3CdGBu5TLsWzTwhizEFgItt0yVuVQ3svP14eBUaEM9MKhDZTnc8ROwHyg5R154+3TlFJKOYkjyn0DkCYiA0UkAJgNvO+A5SillGpHj++WMcY0isjdwEpsp0K+aIzZ0dPLUUop1T6H7HM3xnwMfOyI762UUurU9MRbpZTyQFruSinlgbTclVLKA2m5K6WUB3KJUSFFpBjI6eKXRwElPRinp2iuztFcneeq2TRX53QnV5IxJrqtJ1yi3LtDRDLaGzjHSpqrczRX57lqNs3VOY7KpbtllFLKA2m5K6WUB/KEcl9odYB2aK7O0Vyd56rZNFfnOCSX2+9zV0op9d88YctdKaVUK1ruSinlgdyi3EXkahHZISLNIpLe6rkHRCRbRPaIyIXtfP1AEVlvn2+pfSjins64VEQ22/8dFJHN7cx3UES22edz+I1jReQPIpLfItuMdua7yL4Os0XkfifkekJEdovIVhF5V0R6tzOfU9bXqX5+EQm0v8bZ9vdSsqOytFhmgoisEpGd9vf/vW3Mc7aIlLV4ff/H0bnsyz3p6yI2f7evr60iMtYJmQa3WA+bRaRcRH7Wah6nrS8ReVFEjojI9hbT+orI5yKSZf/Yp52vnWefJ0tE5nUpgDHG5f8BQ4HBwGogvcX0YcAWIBAYCOwDfNv4+reA2fbHzwF3Ojjv/wH/085zB4EoJ667PwC/OsU8vvZ1lwIE2NfpMAfnugDwsz9+DHjMqvXVkZ8fuAt4zv54NrDUCa9dHDDW/jgM243nW+c6G/jQWe+njr4uwAzgE0CAicB6J+fzBQqxXeRjyfoCpgFjge0tpj0O3G9/fH9b73ugL7Df/rGP/XGfzi7fLbbcjTG7jDF72nhqJvCmMabOGHMAyMZ2g+5/EREBzgWW2SctBi53VFb78q4B3nDUMhzgXzc1N8bUAyduau4wxpjPjDGN9k/XYbtjl1U68vPPxPbeAdt7abr9tXYYY0yBMWaj/XEFsAvbPYrdwUxgibFZB/QWkTgnLn86sM8Y09Ur37vNGPMNUNpqcsv3UXtddCHwuTGm1BhzDPgcuKizy3eLcj+Jtm7G3frNHwkcb1Ekbc3Tk84EiowxWe08b4DPRCTTfpNwZ7jb/qfxi+38GdiR9ehIN2HbymuLM9ZXR37+f81jfy+VYXtvOYV9N9AYYH0bT08SkS0i8omIDHdSpFO9Lla/p2bT/gaWFevrhBhjTIH9cSEQ08Y8PbLuLLtBdmsi8gUQ28ZTDxpjVjg7T1s6mPE6Tr7VPtUYky8i/YDPRWS3/Te8Q3IBzwJ/wvaf8U/Ydhnd1J3l9USuE+tLRB4EGoHX2vk2Pb6+3I2I9ALeAX5mjClv9fRGbLseKu3HU94D0pwQy2VfF/sxtcuAB9p42qr19V+MMUZEHHYuusuUuzHmvC58WUduxn0U25+EfvYtri7fsPtUGUXED7gSOOMk3yPf/vGIiLyLbZdAt/5TdHTdicgi4MM2nnLITc07sL5+DFwKTDf2nY1tfI8eX19t6MjPf2KePPvrHIHtveVQIuKPrdhfM8Ysb/18y7I3xnwsIgtEJMoY49ABsjrwujjkPdVBFwMbjTFFrZ+wan21UCQiccaYAvtuqiNtzJOP7djACfHYjjd2irvvlnkfmG0/k2Egtt/AP7ScwV4aq4BZ9knzAEf9JXAesNsYk9fWkyISKiJhJx5jO6i4va15e0qr/ZxXtLM8p9/UXEQuAu4DLjPGVLczj7PWV0d+/vexvXfA9l76qr1fSD3Fvk//BWCXMeav7cwTe2Lfv4iMx/Z/2qG/dDr4urwPzLWfNTMRKGuxO8LR2v3r2Yr11UrL91F7XbQSuEBE+th3o15gn9Y5zjhq3N1/2EopD6gDioCVLZ57ENuZDnuAi1tM/xjob3+cgq30s4G3gUAH5XwZuKPVtP7Axy1ybLH/24Ft94Sj190rwDZgq/2NFdc6l/3zGdjOxtjnpFzZ2PYrbrb/e651Lmeur7Z+fuBhbL98AILs751s+3spxQnraCq23WlbW6ynGcAdJ95nwN32dbMF24HpyU7I1ebr0iqXAM/Y1+c2Wpzl5uBsodjKOqLFNEvWF7ZfMAVAg72/bsZ2nOZLIAv4AuhrnzcdeL7F195kf69lA/O7snwdfkAppTyQu++WUUop1QYtd6WU8kBa7kop5YG03JVSygNpuSullAfScldKKQ+k5a6UUh7o/wMz5ZLhDml7oAAAAABJRU5ErkJggg==","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=[-10])"]},{"cell_type":"markdown","id":"6e752e19","metadata":{},"source":["The following code implements the whole logic explained before:"]},{"cell_type":"code","execution_count":null,"id":"2bdd54f1","metadata":{},"outputs":[],"source":["def gradient_descent(x, nsteps=1):\n"," \n"," \n"," # collectXs is an array to store how x changed in each iteration, so we can visualize it later\n"," \n"," collectXs = [x]\n"," \n"," # learning_rate is the value that we mentioned as alpha in the previous section\n"," \n"," learning_rate = 1e-01\n"," \n"," for _ in range(nsteps):\n"," \n"," # The following one line does the real magic\n"," # The next value of x is calculated by subtracting the gradient * learning_rate by itself\n"," # The intuition behind this line is in the previous section\n"," \n"," x -= df(x) * learning_rate \n"," collectXs.append(x)\n"," \n"," # We return a tuple that contains\n"," # x -> recent x after nsteps \n"," # collectXs -> all the x values that were calculated so far\n"," \n"," return x, collectXs"]},{"cell_type":"markdown","id":"aea74a65","metadata":{},"source":["Before running a gradient descent with 1000 steps, let's just run it twice, one step at a time, to see how x evolves. \n","We start with x=-10, and it evolves to x=-8. We know that when x=0 that is the **minimum point**, so yes, it is evolving in the correct direction."]},{"cell_type":"code","execution_count":null,"id":"0350981e","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-8.0\n"]}],"source":["x=-10\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"code","execution_count":null,"id":"f8e01e2d","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-6.4\n"]}],"source":["# The next step will start at x=-8. Let's run a gradient for 1 step\n","\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"markdown","id":"93f13b32","metadata":{},"source":["It goes to x=-6.4. Excellent. Now let's run it 1000 times"]},{"cell_type":"code","execution_count":null,"id":"b699d1fb","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-7.873484301831169e-97\n"]}],"source":["x, collectedXs = gradient_descent(x, nsteps=1000)\n","print(x)"]},{"cell_type":"code","execution_count":null,"id":"0b76ee22","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=collectedXs)"]},{"cell_type":"markdown","id":"d00d2fbb","metadata":{},"source":["### Exercise 3\n","\n","When I arrive to the coffee machine, I hear my colleague talking about the per-unit costs of producing 'product B' for the company. As the company produces more units, the per-unit costs continue to decrease until a point where they start to increase.\n","\n","To optimize the per-unit production cost at its minimum to optimize efficiency, the company would need to find the number of units to be produced where the per-unit production costs begin to change from decreasing to increasing.\n","\n","**Build a quadratic function $f(x)=0.1(x)^2−9x +4500$ on $x∈[0,100]$ to create the per-unit cost function, and make a conclusion.**"]},{"cell_type":"code","execution_count":15,"id":"7c67d8b7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":15,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the function\n","def f(x):\n"," return 0.1*(x)**2 -9*x +4500\n","x=np.linspace(0,100)\n","plt.plot(x, f(x))"]},{"cell_type":"markdown","id":"fbe54895","metadata":{},"source":["We saw with Gradient Descent how the red dot navigates in an environment it does not know about. It only knows the coordinates of where it is and its gradient. The red dot could find the minimum point by using only this knowledge and the gradient descent algorithm.\n","\n","**Optional:**\n","\n","Implement all the previous steps to create a gradient descent algorithm to see how the per-unit cost evolves, with a starting point of 0 units of production."]},{"cell_type":"markdown","id":"aabad82c","metadata":{},"source":["## Linear Algebra"]},{"cell_type":"markdown","id":"6753636d","metadata":{},"source":["### Exercise 1: Sum of two matrices\n","\n","Suppose we have two matrices A and B.\n","\n","```py\n","A = [[1,2],[3,4]]\n","B = [[4,5],[6,7]]\n","\n","then we get\n","A+B = [[5,7],[9,11]]\n","A-B = [[-3,-3],[-3,-3]]\n","```\n","\n","Make the sum of two matrices using Python with NumPy"]},{"cell_type":"code","execution_count":19,"id":"9e200c32","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[[1, 2], [3, 4]]\n","[[4, 5], [6, 7]]\n","[[ 5 7]\n"," [ 9 11]]\n"]}],"source":["# import numpy as np\n","import numpy as np\n"," \n"," \n","# Creating first matrix\n","a=[[1,2], [3,4]]\n"," \n","# Creating second matrix\n","b=[[4,5], [6,7]]\n"," \n","# Print elements\n","print (a)\n","print (b)\n"," \n","# Adding both matrices\n","resultado=np.array(a)+np.array(b)\n","print(resultado)"]},{"cell_type":"markdown","id":"93bfb6cc","metadata":{},"source":["### Exercise 2: Sum of two lists\n","\n","There will be many situations in which we'll have to find an index-wise summation of two different lists. This can have possible applications in day-to-day programming. In this exercise, we will solve the same problem in various ways in which this task can be performed.\n","\n","We have the following two lists:\n","\n","```py\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n","```\n","\n","Now let's use Python code to demonstrate addition of two lists."]},{"cell_type":"code","execution_count":null,"id":"867b70fc","metadata":{},"outputs":[],"source":["# Naive method\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print (\"Original list 1 : \" + str(list1))\n","print (\"Original list 2 : \" + str(list2))\n"," \n","# Using naive method to add two lists \n","res_list = []\n","for i in range(0, len(list1)):\n"," res_list.append(list1[i] + list2[i])\n"," \n","# Printing resulting list \n","print (\"Resulting list is : \" + str(res_list))"]},{"cell_type":"markdown","id":"7a063d7f","metadata":{},"source":["Now use the following three different methods to make the same calculation: sum of two lists"]},{"cell_type":"code","execution_count":null,"id":"681930a3","metadata":{},"outputs":[],"source":["# Use list comprehension to perform addition of the two lists:\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using list comprehension to add two lists\n","\n"," \n","# Printing resulting list \n"]},{"cell_type":"code","execution_count":null,"id":"a3a8a425","metadata":{},"outputs":[],"source":["# Use map() + add():\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using map() + add() to add two lists\n","\n"," \n","# Printing resulting list "]},{"cell_type":"code","execution_count":null,"id":"1708d7ee","metadata":{},"outputs":[],"source":["# Use zip() + sum():\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using zip() + sum() to add two lists\n","\n"," \n","# Printing resulting list "]},{"cell_type":"markdown","id":"1aef1bd2","metadata":{},"source":["### Exercise 3: Dot multiplication\n","\n","We have two matrices:\n","\n","```py\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n","```\n","\n","A simple technique but expensive method for larger input datasets is using *for loops*. In this exercise, we will first use nested *for loops* to iterate through each row and column of the matrices, and then we will perform the same multiplication using NumPy."]},{"cell_type":"code","execution_count":null,"id":"840e7d0e","metadata":{},"outputs":[],"source":["# Using a for loop input two matrices of size n x m\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n"," \n","res = [[0 for x in range(3)] for y in range(3)]\n"," \n","# Explicit for loops\n","for i in range(len(matrix1)):\n"," for j in range(len(matrix2[0])):\n"," for k in range(len(matrix2)):\n"," \n"," # Resulting matrix\n"," res[i][j] += matrix1[i][k] * matrix2[k][j]\n"," \n","print(res)"]},{"cell_type":"code","execution_count":null,"id":"db6c3355","metadata":{},"outputs":[],"source":["# Import libraries\n","\n"," \n","# Input two matrices\n","\n"," \n","# This will return dot product\n","\n"," \n","# Print resulting matrix\n"]},{"cell_type":"markdown","id":"785f6c30","metadata":{},"source":["Source:\n","\n","https://www.youtube.com/channel/UCXq-PLvYAX-EufF5RAPihVg\n","\n","https://www.geeksforgeeks.org/\n","\n","https://medium.com/@seehleung/basic-calculus-explained-for-machine-learning-c7f642e7ced3\n","\n","https://blog.demir.io/understanding-gradient-descent-266fc3dcf02f"]}],"metadata":{"interpreter":{"hash":"d3463682613d55fcbb64853e38cc3520a7f67bdf8d6940e781ddcdc423122719"},"kernelspec":{"display_name":"Python 3.9.12 ('calculus-project')","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} From a3911d8cffd0e27db39ab99f72d61cab9cc817ab Mon Sep 17 00:00:00 2001 From: Maria Pais <145993408+Finarosalina@users.noreply.github.com> Date: Mon, 29 Jul 2024 16:30:14 +0000 Subject: [PATCH 2/6] proyecto_final --- notebook/problems.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notebook/problems.ipynb b/notebook/problems.ipynb index 585a4e96..554b8c31 100644 --- a/notebook/problems.ipynb +++ b/notebook/problems.ipynb @@ -1 +1 @@ -{"cells":[{"cell_type":"markdown","id":"5dbe7b9e","metadata":{},"source":["# Calculus and Algebra problems"]},{"cell_type":"markdown","id":"519c4b12","metadata":{},"source":["## Calculus\n","\n","Calculus is not obscure. It is the language for modeling behaviors. Calculus enables us to find the rate of changes in order to optimize a function. Without calculus, we would not be able to fully understand techniques such as:\n","\n","Backpropagation in neural networks\n","\n","Regression using optimal least square\n","\n","Expectation maximization in fitting probability models"]},{"cell_type":"markdown","id":"b7e2e87a","metadata":{},"source":["### Exercise 1\n","\n","Let's say, in my office, it takes me 10 seconds (time) to travel 25 meters (distance) to the coffee machine.\n","If we want to express the above situation as a function, then it would be:\n","\n","distance = speed * time\n","\n","So for this case, speed is the first derivative of the distance function above. As speed describes the rate of change of distance over time, when people say taking the first derivative of a certain function, they mean finding out the rate of change of a function.\n","\n","**Find the speed and build the linear function on distance $(d)$ over time $(t)$, when $(t ∈ [0,10])$.**"]},{"cell_type":"code","execution_count":3,"id":"bb3e954e","metadata":{},"outputs":[],"source":["# import libraries\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import pandas as pd\n","\n","# Define the distance function; speed= 25/10=2.5 >> fdis(x)=2.5*t(X)\n","def f(x):\n"," return 2.5*x\n","x=np.linspace(0,10)\n"]},{"cell_type":"code","execution_count":4,"id":"dbc4c780","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":4,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Plot the distance function on domain (t)\n","plt.plot(x,f(x))"]},{"cell_type":"code","execution_count":5,"id":"4c4d4f20","metadata":{},"outputs":[{"data":{"text/html":["
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xf(x)
00.0000000.000000
10.2040820.510204
20.4081631.020408
30.6122451.530612
40.8163272.040816
51.0204082.551020
61.2244903.061224
71.4285713.571429
81.6326534.081633
91.8367354.591837
102.0408165.102041
112.2448985.612245
122.4489806.122449
132.6530616.632653
142.8571437.142857
153.0612247.653061
163.2653068.163265
173.4693888.673469
183.6734699.183673
193.8775519.693878
204.08163310.204082
214.28571410.714286
224.48979611.224490
234.69387811.734694
244.89795912.244898
255.10204112.755102
265.30612213.265306
275.51020413.775510
285.71428614.285714
295.91836714.795918
306.12244915.306122
316.32653115.816327
326.53061216.326531
336.73469416.836735
346.93877617.346939
357.14285717.857143
367.34693918.367347
377.55102018.877551
387.75510219.387755
397.95918419.897959
408.16326520.408163
418.36734720.918367
428.57142921.428571
438.77551021.938776
448.97959222.448980
459.18367322.959184
469.38775523.469388
479.59183723.979592
489.79591824.489796
4910.00000025.000000
\n","
"],"text/plain":[" x f(x)\n","0 0.000000 0.000000\n","1 0.204082 0.510204\n","2 0.408163 1.020408\n","3 0.612245 1.530612\n","4 0.816327 2.040816\n","5 1.020408 2.551020\n","6 1.224490 3.061224\n","7 1.428571 3.571429\n","8 1.632653 4.081633\n","9 1.836735 4.591837\n","10 2.040816 5.102041\n","11 2.244898 5.612245\n","12 2.448980 6.122449\n","13 2.653061 6.632653\n","14 2.857143 7.142857\n","15 3.061224 7.653061\n","16 3.265306 8.163265\n","17 3.469388 8.673469\n","18 3.673469 9.183673\n","19 3.877551 9.693878\n","20 4.081633 10.204082\n","21 4.285714 10.714286\n","22 4.489796 11.224490\n","23 4.693878 11.734694\n","24 4.897959 12.244898\n","25 5.102041 12.755102\n","26 5.306122 13.265306\n","27 5.510204 13.775510\n","28 5.714286 14.285714\n","29 5.918367 14.795918\n","30 6.122449 15.306122\n","31 6.326531 15.816327\n","32 6.530612 16.326531\n","33 6.734694 16.836735\n","34 6.938776 17.346939\n","35 7.142857 17.857143\n","36 7.346939 18.367347\n","37 7.551020 18.877551\n","38 7.755102 19.387755\n","39 7.959184 19.897959\n","40 8.163265 20.408163\n","41 8.367347 20.918367\n","42 8.571429 21.428571\n","43 8.775510 21.938776\n","44 8.979592 22.448980\n","45 9.183673 22.959184\n","46 9.387755 23.469388\n","47 9.591837 23.979592\n","48 9.795918 24.489796\n","49 10.000000 25.000000"]},"execution_count":5,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","df=pd.DataFrame({'x':x, 'f(x)':f(x)})\n","df"]},{"cell_type":"markdown","id":"1144168d","metadata":{},"source":["### Exercise 2\n","\n","It turned out that I wasn't walking a constant speed towards getting my coffee, but I was accelerating (my speed increased over time). If my initial *speed = 0*, it still took me 10 seconds to travel from my seat to my coffee, but I was walking faster and faster.\n","\n","$V_o$ = initial speed = $0$\n","\n","t = time\n","\n","a = acceleration\n","\n","**distance** = $V_o * t + 0.5 * a * (t^2)$\n","\n","**speed** = $V_o + a * t$\n","\n","The first derivative of the speed function is acceleration. I realize that the speed function is closely related to the distance function.\n","\n","**Find the acceleration value and build the quadratic function $(t ∈ [0,10])$. Also, create a graph and a table.**"]},{"cell_type":"code","execution_count":11,"id":"ec1f8bd7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":11,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the quadratic funtion t=10, d=25 >> a=0.5 | Vo=0\n","\n","def f(t): return 0.5*0.5*(t**2)\n","t = np.linspace(0,10)\n","plt.plot(t, f(t))\n"]},{"cell_type":"code","execution_count":13,"id":"ba5c497b","metadata":{},"outputs":[{"data":{"text/html":["
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tf(t)
00.0000000.000000
10.2040820.010412
20.4081630.041649
30.6122450.093711
40.8163270.166597
\n","
"],"text/plain":[" t f(t)\n","0 0.000000 0.000000\n","1 0.204082 0.010412\n","2 0.408163 0.041649\n","3 0.612245 0.093711\n","4 0.816327 0.166597"]},"execution_count":13,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","dft=pd.DataFrame({'t':t, 'f(t)':f(t)})\n","dft.head()\n"]},{"cell_type":"markdown","id":"66d4cc18","metadata":{},"source":["Before exercise 3, we'll make a brief introduction to Gradient Descent algorithm, which will have a larger explanation in future modules of the bootcamp.\n","\n","Gradient Descent algorithm is the hero behind the family of deep learning algorithms. When an algorithm in this family runs, it tries to minimize the error between the training input and predicted output. This minimization is done by optimization algorithms, and gradient descent is the most popular one.\n","\n","Let's say you have these input & output pairs:\n","\n","```py\n","# Input:\n","[\n"," [1,2],\n"," [3,4]\n","]\n","\n","# Output:\n","[\n"," [50],\n"," [110]\n","]\n","```\n","\n","We can estimate that if we multiply the input values by [10, 20], we can have the output as shown above.\n","\n","```py\n","1(10) + 2(20) = 50\n","\n","3(10) + 4(20) = 110\n","```\n","\n","When a machine learning algorithm starts running, it assigns random values and makes a prediction. \n","Let's say it assigned [1,2] values:\n","\n","```py\n","1(1) + 2(2) = 5\n","\n","3(1) + 4(2) = 11\n","```\n","\n","Once it has the predictions, it calculates the error: the difference between the real data and the predicted data. There are many ways to calculate the error, and they are called loss functions.\n","\n","Once we have this value, the optimization algorithm starts showing itself, and it sets new values which replace the initial random values. \n","\n","And, the loop continues until a condition is met. That condition can be to loop *n* times, or to loop until the error is smaller than a value."]},{"cell_type":"markdown","id":"85ef2f0b","metadata":{},"source":["It can be hard to understand **gradient descent** without understanding **gradient**. So, let's focus on what a gradient is. The gradient shows the direction of the greatest change of a scalar function. The gradient calculation is done with derivatives, so let's start with a simple example. To calculate the gradient, we just need to remember some linear algebra calculations from high school because we need to calculate derivatives.\n","\n","Let's say we want to find the minimum point of $f(x) = x^2$. The derivative of that function is $df(x)=2x$. \n","\n","The gradient of $f(x)$ at point $x=-10$\n","\n","is \n","\n","$df(-10)=-20$.\n","\n","The gradient of $f(x)$ at point $x=1$\n","\n","is \n","\n","$df(1)=2$.\n","\n","Now let’s visualize $f(x)$ and those $x=-10$ and $x=1$ points."]},{"cell_type":"code","execution_count":null,"id":"4ff7e11a","metadata":{},"outputs":[],"source":["import numpy as np\n","import seaborn as sns\n","\n","def f(x):\n"," return x**2\n","\n","def df(x):\n"," return 2*x\n","\n","def visualize(f, x=None):\n"," \n"," xArray = np.linspace(-10, 10, 100) \n"," yArray = f(xArray)\n"," sns.lineplot(x=xArray, y=yArray)\n"," \n"," if x is not None:\n"," assert type(x) in [np.ndarray, list] # x should be numpy array or list\n"," if type(x) is list: # if it is a list, convert to numpy array\n"," x = np.array(x)\n","\n"," \n"," y = f(x)\n"," sns.scatterplot(x=x, y=y, color='red')"]},{"cell_type":"code","execution_count":null,"id":"633a54fd","metadata":{},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXcAAAD4CAYAAAAXUaZHAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAsZ0lEQVR4nO3dd3xV9f3H8dcne5AESAIJZBES2SAYNuJAUdGKAxUHUBeOaum0Wtva2tqf4/drtVW04MSJIoobFzgQkIS9EyAhgSQkBLJ3vr8/7qWNaQJZ9547Ps/HI4/cnHuS8865lzcnZ3yPGGNQSinlWXysDqCUUqr7abkrpZQH0nJXSikPpOWulFIeSMtdKaU8kJ/VAQCioqJMUlKS1TGUUsqtZGRkFBtjolt7ziXKPSkpifT0dKtjKKWUWxGRnLae090ySinlgbTclVLKA2m5K6WUB9JyV0opD6TlrpRSHuiU5S4iz4vIERHZ3mxabxH5TEQy7Z972aeLiPxDRLJEZKuIjHFY8qYm2LMHVq+2fW5qctiilFLK3bRny/1F4MIW0+4FvjDGpAJf2L8GuAhItX/MB57unpgtNDXB8uUwejScc47t8/LlWvBKKWV3ynI3xnwNlLSYPBN4yf74JeCyZtOXGJt1QE8Rie2mrP+RmQlz57K5ZzyPTJ0H1dUwd65tulJKuQFjDA99uJMdh0sd8vM7u8+9rzEm3/64AOhrf9wfyG02X5592n8Rkfkiki4i6UVFRR1ben4+VFezLSaFpydexfa+A20Fn59/6u9VSikXsG5/CYu/OcCegnKH/PwuH1A1trt9dPiOH8aYRcaYNGNMWnR0q1fPti02FoKDuXTnVwTW1/LGyOkQHGybrpRSbmDphoOEBflx0XDH9FZny73wxO4W++cj9umHgPhm88XZp3Wv1FRYsoQInyZm7FnDimFnU/3CEtt0pZRycaVV9Xy8vYCZp/cjOMDXIcvobLm/B8yzP54HrGg2fa79rJkJQGmz3Tfdx8cHrrgCNm3i6htnUB4Yyscp423TlVLKxa3YcojahiZmj01w2DLacyrk68BaYJCI5InIzcDDwPkikgmcZ/8a4CNgP5AFLAbudEhqsBX5oEFMuOJckiJDWJqe57BFKaVUd1q6IZehseEM7x/hsGWcclRIY8y1bTw1rZV5DfCTrobqCBHhqrR4Hlu5h/1FFSRH93Dm4pVSqkO2Hyplx+EyHpw5zKHL8Yj9GLPOiMPXR3hTt96VUi7ujQ0HCfTzYeaoVk8k7DYeUe59w4M4Z1A0yzLyqG/UC5mUUq6puq6RFZsPc9HwGCJC/B26LI8od4BrxiZQXFHLl7uPnHpmpZSywEfb8imvaeDqsfGnnrmLPKbczxkUTd/wQF7//qDVUZRSqlWvf3+QAVGhTEyOdPiyPKbc/Xx9uDotnq/2FnHoeLXVcZRS6gcyC8tJzznG7LHxiIjDl+cx5Q5wdZrtT52lG3JPMadSSjnX69/n4u8rXHlGnFOW51HlHt87hKmp0byVnkuDHlhVSrmImvpGlm/KY/qwGKJ6BDplmR5V7gDXjosnv7SGr/Z2cDAypZRykJU7CjheVc+1DrwitSWPK/dpQ/oS1SOQ17/XXTNKKdfw+vcHSegdwqSBjj+QeoLHlbu/rw9Xp8Xx5e5CCkprrI6jlPJy+4sqWLe/hNnj4vHxcfyB1BM8rtwBZo9NoMnogVWllPVe//4gfj7CLCcdSD3BI8s9ITKEqadF88aGg3pgVSllmZr6Rt7KyOOCYTH0CQty6rI9stwBrh+fQH5pDav26IFVpZQ1Pt6ez/Gqeq4b77wDqSd4bLlPG9yHvuGBvLo+x+ooSikv9eo6512R2pLHlrufrw/XjE3gq71F5JZUWR1HKeVldheUkZ5zjOvGJTj1QOoJHlvugO0yX9DxZpRSTvfa+oME+Po47YrUljy63Pv1DObcwX15Mz2PugY9sKqUco6qugbe2XiIGSNi6B0aYEkGjy53gOsn2IYCXrmjwOooSikv8d7mw5TXNnDd+ETLMnh8uU9NjSa+dzCvrNMDq0opxzPGsGRtDoP6hjE2qZdlOTy+3H19hOvHJ7L+QAl7C8utjqOU8nCbco+zM7+MGyYmOmVo37Z4fLmDbSjgAD8f3XpXSjncK2tz6BHox+WjHXuP1FPxinLvHRrAJSNiWb7xEBW1DVbHUUp5qJLKOj7Yms8VY/rTI9DP0ixeUe4AN0xMpKK2gXc3HbI6ilLKQ72ZnktdYxM3TLDuQOoJXlPuo+N7MqxfOK+sy8EYY3UcpZSHaWwyvLo+h/EDenNa3zCr43hPuYsIcyYksrvAdh9DpZTqTl/vLSK3pJo5E63fagcvKneAS0/vR3iQHy99l211FKWUh3lpbTbRYYFMHxpjdRTAy8o9JMCPq9Pi+WR7AYVleiMPpVT3yC6uZPWeIq4fn0CAn2vUqmukcKI5ExNpNIZX1+t4M0qp7rFkbQ7+vmLJ0L5t8bpyT4wM5ZxBfXht/UEdb0Yp1WWVtQ28lZHLRcNjnX5DjpPxunIHmDsxkeKKWj7enm91FKWUm3tn0yHKaxqYN8k1DqSe4JXlPjU1mgFRoXpgVSnVJbZxZLIZ3j+cMQnWjSPTmi6Vu4j8XER2iMh2EXldRIJEZICIrBeRLBFZKiLWjHd5Ej4+ttMiNx48zra8UqvjKKXc1Nr9R9lbWMHciUmWjiPTmk6Xu4j0B34KpBljhgO+wGzgEeDvxpgU4Bhwc3cE7W6z0uIICfDlhe8OWB1FKeWmXlyTTa8Qfy4d1c/qKP+lq7tl/IBgEfEDQoB84Fxgmf35l4DLurgMhwgP8mfWGXF8sCWfovJaq+MopdxMbkkVn+8q5NpxCQT5+1od5790utyNMYeA/wUOYiv1UiADOG6MOTE6Vx7Q6tBoIjJfRNJFJL2oqKizMbpk3qQk6hqbeE1Pi1RKddCStdm2K99d5IrUlrqyW6YXMBMYAPQDQoEL2/v9xphFxpg0Y0xadHR0Z2N0ycDoHpw9KJpX1ufoaZFKqXarrG3gjQ25XDQ8htiIYKvjtKoru2XOAw4YY4qMMfXAcmAy0NO+mwYgDnDpYRh/PCmJovJaPtx22OooSik3sXxjHuU1Ddw4OcnqKG3qSrkfBCaISIjYDhNPA3YCq4BZ9nnmASu6FtGxpqZGkxwdygtrsnW0SKXUKTU1GV74LpuRcREud/pjc13Z574e24HTjcA2+89aBPwG+IWIZAGRwHPdkNNhfHyEGyclsTWvlI0HdbRIpdTJfZNVzP6iSm6c7HqnPzbXpbNljDEPGGMGG2OGG2PmGGNqjTH7jTHjjDEpxpirjDEufyrKFWPiCA/y4/k12VZHUUq5uOe/PUB0WCAXj3C90x+b88orVFsKDfTj2nEJfLwtn9ySKqvjKKVcVGZhOV/tLWLuhESXGf2xLa6dzonmTbL9iaVDEiil2vL8mgME+vlwvQvcRu9UtNzt+vUMZsaIWJZuyKW8pt7qOEopF3O0opa3Nx7iijFx9A51uVFV/ouWezM3TxlAeW0Db6bnWR1FKeViXrUPE37zlCSro7SLlnszp8f3JC2xFy+sOUBjk54WqZSyqW1oZMnaHM4eFE1KH+tvft0eWu4t3DxlAHnHqvl0R4HVUZRSLuK9zYcprqjl5ikDrI7SblruLUwfFkN872Ce/VZHi1RK2cZsf+7bAwzqG8aUlCir47SblnsLvj7CzZMHkJFzjIycEqvjKKUs9nVmMbsLyrl1arJLX7TUkpZ7K65Kiyci2J9FX++3OopSymKLv95P3/BAlxyz/WS03FsRGujHnAmJfLqzkAPFlVbHUUpZZMfhUr7NKubGyQNc/qKlltwrrRPNnZSIv48Pz32rW+9KeavFX+8nNMCXa8clWB2lw7Tc29AnLIjLR/fnrfQ8jla4/PA4Sqludvh4Ne9vzWf2uAQigv2tjtNhWu4nccuZA6htaOLldTlWR1FKOdkLa2xnzLnymO0no+V+Eql9w5g2uA9L1uZQXddodRyllJOUVtXz2vqDXDIylrheIVbH6RQt91O4/eyBlFTW8WZ6rtVRlFJO8sr6HCrrGrlt6kCro3SalvspjE3qzRmJvVj8zX4aGvU+q0p5upr6Rl5Yc4Cpp0UztF+41XE6Tcu9HW4/ayB5x6r5cFu+1VGUUg62LCOP4oo6bj8r2eooXaLl3g7TBvchtU8Pnvlqv95nVSkP1thkWPzNfkbFRTAxOdLqOF2i5d4OPj7C/KnJ7Mov46u9RVbHUUo5yMfb88k5WsXtZw10q6EGWqPl3k4zT+9PbEQQT6/eZ3UUpZQDGGN45qt9DIgKZfqwGKvjdJmWezsF+Plwy5nJrD9QQkbOMavjKKW62deZxWw/VMbtZyXj6+PeW+2g5d4h146Lp1eIP0+vzrI6ilKqmy1clUVsRBCXj46zOkq30HLvgJAAP26aPIDPdx1hV36Z1XGUUt0kPbuE9QdKuPXMZLcbIKwtnvFbONHciUn0CPTTfe9KeZCFq/fROzSA2ePirY7SbbTcOygixJ/rJyTwwdbDZOtwwEq5vR2HS/ly9xFunJRESICf1XG6jZZ7J9w8ZQB+vj4885VuvSvl7p5evY8egX7MnZhkdZRupeXeCX3Cgpg9Np63N+Zx6Hi11XGUUp2UdaSCD7flc8OERCJC3G9Y35PRcu+k286yDSj0L916V8ptLVyVRaCfD7ecOcDqKN1Oy72T+vcM5soxcbyxIZcjZTVWx1FKdVDO0UpWbDnMDeMTieoRaHWcbqfl3gV3np1CY5PhX3ojbaXczsJV+/C1Dy3iibpU7iLSU0SWichuEdklIhNFpLeIfCYimfbPvborrKtJiAxh5un9eHV9DsV6Kz6l3EbesSre3pjHtWPj6RMeZHUch+jqlvsTwCfGmMHAKGAXcC/whTEmFfjC/rXH+sk5KdQ2NLH4G916V8pdPPPVPkT+c+zME3W63EUkApgKPAdgjKkzxhwHZgIv2Wd7CbisaxFd28DoHlwysh8vr82hpLLO6jhKqVPIL63mzQ15zDojnn49g62O4zBd2XIfABQBL4jIJhF5VkRCgb7GmBN3tSgA+rb2zSIyX0TSRSS9qMi9h9H96bkpVNc3skj3vSvl8hau2keTMfzkHM/daoeulbsfMAZ42hgzGqikxS4YY7uzRat3tzDGLDLGpBlj0qKjo7sQw3qpfcO4ZGQ/lqzN5qjue1fKZR0+Xs3SDblclRbvtje+bq+ulHsekGeMWW//ehm2si8UkVgA++cjXYvoHhZMs229L/7mgNVRlFJtWLg6C4Pnb7VDF8rdGFMA5IrIIPukacBO4D1gnn3aPGBFlxK6iZQ+YfxIt96VclnetNUOXT9b5m7gVRHZCpwO/BV4GDhfRDKB8+xfe4Wf2rfeF+mZM0q5nKdW2e7D8JNzUixO4hxdGgLNGLMZSGvlqWld+bnuKqVPGJeO6seS73K4ZUoy0WGed9WbUu4o71gVb6bbttr7e/AZMs3pFardbMG0VGobGnXESKVcyD+/yEJEuPtc79hqBy33bpcc3YMrxsTx8rocCkp1zBmlrHaguJJlG/O4blwCsRHesdUOWu4OsWBaKk1NhidXZVodRSmv98Tne/H3Fe70gjNkmtNyd4D43iFcMzaepRtyyS2psjqOUl5rb2E5K7YcZt6kJPqEeeYYMm3RcneQu85NQUT455e69a6UVR7/fC+hAX7cPtW7ttpBy91hYiOCuWF8Issy8thXVGF1HKW8zvZDpXy0rYCbJifRKzTA6jhOp+XuQHeeM5Agf1/+9uleq6Mo5XUeXbmHniH+3OKh47Wfipa7A0X1COSWM5P5cFs+2/JKrY6jlNdYu+8oX+8t4idnpxAe5Fn3Rm0vLXcHu/XMAfQK8efRlbutjqKUVzDG8OjK3cSEBzFnYqLVcSyj5e5gYUH+3Hl2Ct9kFvPdvmKr4yjl8T7bWcimg8dZcF4qQf6+VsexjJa7E8yZmEhsRBCPfrIH2yjISilHaGwy/O+ne0iOCuWqM+KsjmMpLXcnCPL35WfnpbI59zgrdxRYHUcpj7V8Yx57Cyv4xfTT8PP17nrz7t/eia4cE0dKnx48+ske6hubrI6jlMepqW/kb5/tZVRcBBePiLU6juW03J3Ez9eHey8czP7iSt7YkGt1HKU8zgtrsskvreHei4YgIlbHsZyWuxNNG9KHcUm9eeLzTCprG6yOo5THOFZZx8LVWZw7uA8TB0ZaHcclaLk7kYhw34zBFFfUslhv6KFUt3lqVRaVtQ385sLBVkdxGVruTjY6oRczRsSw6Ov9HCnXIYGV6qrckiqWrM3hyjFxDIoJszqOy9Byt8A9FwymvrGJv3+mwxIo1VWPfLIbHx/4xfTTrI7iUrTcLZAUFcqcCUks3ZDL7oIyq+Mo5bYyco7xwdZ85p+Z7FU34mgPLXeL/HRaCmFB/jz04S69sEmpTjDG8JcPdxIdFshtZ3nfkL6nouVukZ4hAfx0WirfZBazem+R1XGUcjsfbstn08Hj/Hr6IEID/ayO43K03C00Z0IiSZEh/PXDXTTohU1KtVtNfSOPfLKbwTFhXOnlwwy0RcvdQgF+Ptx70RAyj1Tw+vcHrY6jlNt4YU02uSXV/O7iofj66AVLrdFyt9gFw/oyMTmSv322l+NVdVbHUcrlHSmv4ckvMzl/aF+mpEZZHcdlablbTET4w4+GUlpdz+Of6/1WlTqVxz7ZQ11jE/fPGGJ1FJem5e4ChsSGc+24BF5el0NmYbnVcZRyWVtyj/NWRh43TRlAUlSo1XFcmpa7i/jF+acRGuDLgx/s1FMjlWqFMYY/vb+DqB6B3HVOitVxXJ6Wu4uI7BHIz847jW8yi/l81xGr4yjlclZsPszGg8e558JBhHnpfVE7QsvdhcyZmEhqnx48+MEOauobrY6jlMsor6nnoY92MSougllj9NTH9tBydyH+vj786dJh5JZU86+vdNRIpU74xxeZFFfU8uDM4fjoqY/touXuYialRHHxyFgWrs4it6TK6jhKWS6zsJwX1mRzTVo8o+J7Wh3HbXS53EXEV0Q2icgH9q8HiMh6EckSkaUiEtD1mN7ldxcPwUeEv3y40+ooSlnKGMMf399BSIAvv75gkNVx3Ep3bLkvAHY1+/oR4O/GmBTgGHBzNyzDq8RGBHP3tBRW7ihk9R49uKq810fbCliTdZRfXzCIyB6BVsdxK10qdxGJAy4GnrV/LcC5wDL7LC8Bl3VlGd7qlinJJEeH8sB7enBVeafymnoe/GAHw/qFc934RKvjuJ2ubrk/DtwDnBj1KhI4bow5cYPQPKB/a98oIvNFJF1E0ouKdFTElgL8fPjLzOHkHK1i4aosq+Mo5XR/+2wvR8preejyETp+TCd0utxF5BLgiDEmozPfb4xZZIxJM8akRUdHdzaGR5uUEsVlp/fjma/2s6+owuo4SjnN9kOlvPRdNtePT+B0PYjaKV3Zcp8MXCoi2cAb2HbHPAH0FJETgyvHAYe6lNDL3X/xUAL9ffj9u9v1ylXlFZqaDL97dzu9QwP49QV6w+vO6nS5G2PuM8bEGWOSgNnAl8aY64FVwCz7bPOAFV1O6cWiwwK558LBfLfvKCs2H7Y6jlIO99r3B9mce5zfXTyUiGC9ErWzHHGe+2+AX4hIFrZ98M85YBle5bpxtj9N//zBTo5V6rDAynMVltXwyMe7mZwSyczT+1kdx611S7kbY1YbYy6xP95vjBlnjEkxxlxljKntjmV4M18f4eErR1BabbsEWylP9cCKHdQ1NvHQZSOwnXynOkuvUHUTg2PCue2sZJZl5LEmq9jqOEp1u5U7CvhkRwELzkvV4Xy7gZa7G7n73FSSIkP47Tvb9Nx35VHKa+p5YMUOBseEceuZyVbH8Qha7m4kyN+Xv14xgpyjVfz9871Wx1Gq2zzyyW4Ky2t4+MqR+PtqLXUHXYtuZtLAKGaPjWfx1/vZknvc6jhKddnafUd5Zd1Bbpw0QM9p70Za7m7otxcPoU9YEPcs20pdQ9Opv0EpF1VV18Bv3t5KYmSIDgzWzbTc3VB4kD8PXT6cPYXlPKlDEyg39n+f7uVgSRUPXzGS4ABfq+N4FC13NzVtSF8uH92fhauy2Hm4zOo4SnVYRs4xnl9zgBsmJDBxYKTVcTyOlrsb+8MlQ+kZ4s+v3tqiu2eUW6mua+TXb22hX0Qw9140xOo4HknL3Y31Cg3goctHsDO/jH9+mWl1HKXa7dGVu9lfXMmjs0bSI9Dv1N+gOkzL3c1dMCyGK8b0Z+HqfWzWs2eUG/huXzEvrMlm3sREJqdEWR3HY2m5e4AHfjSMPmGB/PLNzXpxk3Jp5TX1/PqtrSRFhvCbi3TER0fScvcAEcH+PHLlSPYVVfLYyj1Wx1GqTX/5YBf5pdX839WjCAnQ3TGOpOXuIaaeFs2cCYk89+0Bvs3UsWeU6/lkewFL03O57ayBnJHY2+o4Hk/L3YP8dsYQBkaH8su3NnO8SocGVq7jSFkN9y3fyvD+4fz8vNOsjuMVtNw9SHCAL0/MHk1JZR2/fWeb3rlJuYSmJsOvlm2lur6Rx68ZTYCf1o4z6Fr2MMP7R/CL8wfx0bYClmXkWR1HKV5am83Xe4u4/+KhpPTpYXUcr6Hl7oHmT01m/IDePPDeDvbrjbWVhXYeLuN/Pt7NuYP7cMP4BKvjeBUtdw/k6yM8Pvt0Avx8uPv1TdQ26OmRyvmq6hq46/WN9Az257FZI/XOSk6m5e6hYiOCeWzWKHYcLuPhj3dbHUd5oQdW7OBAcSWPzz6dyB6BVsfxOlruHuz8oX358aQkXliTzec7C62Oo7zIis2HeCsjj7vOSWHSQL0K1Qpa7h7uvhmDGRobzq+WbSHvWJXVcZQX2FdUwW+XbyMtsRcLpqVaHcdrabl7uEA/X566fgwNjYa7Xtuko0cqh6qua+TOVzYS4OfDP64djZ/eMs8yuua9wICoUB6bNZLNucf560e7rI6jPNjvV2xn75FyHp89mn49g62O49W03L3ERSNiuXFyEi9+l82HW/OtjqM80JvpuSzLyOPuc1I467Roq+N4PS13L3LfRUMYndCTe5ZtIetIudVxlAfZfqiU37+7nUkDI1mgwwu4BC13LxLg58PC68cQHODL/JczKK+ptzqS8gAllXXc9nIGvUMD+Me1o/H10fPZXYGWu5eJjQjmyevGkHO0il+8uYWmJh1/RnVeQ2MTd7++kaKKWp654Qyi9Hx2l6Hl7oUmJEdy/4whfLazkCdXZVkdR7mxx1buYU3WUf5y2XBGxfe0Oo5qRsvdS904OYnLR/fn75/v5dMdBVbHUW7o3U2H+NfX+7lhQgJXp8VbHUe1oOXupUSE/7liBCP7R/CzpZvZlV9mdSTlRjYdPMY9b29lQnJvHvjRMKvjqFZ0utxFJF5EVonIThHZISIL7NN7i8hnIpJp/9yr++Kq7hTk78uiuWmEBflxy0vpFFfUWh1JuYH80mrmv5xBTHgQT19/Bv56oZJL6sqr0gD80hgzFJgA/EREhgL3Al8YY1KBL+xfKxfVNzyIxXPTOFpZy+0vZ+gIkuqkquoauHVJOtV1jTw7L41eoQFWR1Jt6HS5G2PyjTEb7Y/LgV1Af2Am8JJ9tpeAy7qYUTnYyLie/O9Vo0jPOcY9y7bqHZxUqxqbDD99fTM7D5fxj2tP57S+YVZHUifRLbcfF5EkYDSwHuhrjDlxCWQB0LeN75kPzAdISNBB/K12ych+HCyp4tFP9pDQO4RfTh9kdSTlYv78wU4+31XIgzOHce7gVv9ZKxfS5Z1lItIDeBv4mTHmB0fljG0TsNXNQGPMImNMmjEmLTpaL1V2BXecNZDZY+P555dZvLkh1+o4yoU8/+0BXvwum5unDGDuxCSr46h26FK5i4g/tmJ/1Riz3D65UERi7c/HAke6FlE5i4jw58uGc2ZqFL99Zxur9+hLp+Djbfn8+cOdXDCsL7+dMcTqOKqdunK2jADPAbuMMX9r9tR7wDz743nAis7HU87m72sbomBQTBh3vLKRTQePWR1JWei7fcUseGMzYxJ68fg1OrSAO+nKlvtkYA5wrohstn/MAB4GzheRTOA8+9fKjYQF+fPijePoEx7ITS9uIOuI3mTbG20/VMr8JRkkRobw3Lw0ggN8rY6kOkBc4cyItLQ0k56ebnUM1ULO0UqufPo7Av18eev2iTo+txexvfZrCfAV3r5zErER+tq7IhHJMMaktfacXn2g2pQYGcqLN46jrLqeG55dT1G5XuTkDQ4fr+a6xetpbGripZvGabG7KS13dVLD+0fwwo1jyS+tYc5z6zleVWd1JOVAR8pruP7Z9ZRV1/PyzeNJ1XPZ3ZaWuzqltKTeLJ6bxv6iSuY9/72OA++hjlXWMfe57ykoreHFm8YyvH+E1ZFUF2i5q3aZkhrFwuvHsONwGXO14D3Osco6rn92PfuLK3l2XhpnJPa2OpLqIi131W7nDe3Lk9eNYVteKXOf/54yLXiPUFJZx3XPrierqIJn56YxOSXK6kiqG2i5qw65cHgMT11vL/jntODdXcmJLXZ7sU/VG1t7DC131WEXDIux76Ip5brF6ziqQwW7pcKyGq7511r2F1WwWIvd42i5q06ZPiyGRXPTyCys4JpF6ygsq7E6kuqA3JIqrnpmLYePV/PijeO02D2QlrvqtHMG9eGlm8ZRUFrDrGe+4+DRKqsjqXbIOlLOVc+spbS6nldvncDEgZFWR1IOoOWuumRCciSv3jKe8poGrnh6DdvySq2OpE5iQ3YJVz69loYmw9LbJnC63tTaY2m5qy4bFd+TZbdPItDPl2sWreWrvUVWR1Kt+GR7ATc8u57I0ADeuXMSg2PCrY6kHEjLXXWLlD49WH7nJBIjQ7n5xQ06HrwLMcbw4poD3PFqBkP7hbPsjknE9w6xOpZyMC131W36hgfx5m22fbj3vL2Vv360i8Ym6wem82b1jU38fsV2/vj+TqYN7strt0ygt9731CtouatuFRbkz/M/HsucCYks+no/t72cQUVtg9WxvFJpdT03vbiBV9Yd5Lapyfxrzhk6bK8X0XJX3c7f14c/XzacP106jC93F3LFwjXsL9Ix4Z1pT0E5M5/8lnX7j/LorJHcN2OI3mjDy2i5K4eZNymJJTeNp6i8lplPruGznYVWR/IK7285zGVPraGyrpHXbp3A1WnxVkdSFtByVw41JTWK9++eQmJUCLcuSeexlbtpaGyyOpZHqm1o5E/v7+Du1zcxrF84H949hbFJOgCYt9JyVw4X1yuEZbdP4pq0eJ5atY/Zi9Zx6Hi11bE8SnZxJbOeXssLa7L58aQkXrt1An3Cg6yOpSyk5a6cIsjfl0dmjeSJ2aezu6CcGU98wyfb862O5faMMby76RCX/PNbDpZU8a85Z/DHS4cR4Kf/tL2dvgOUU808vT8f/nQKiZEh3P7KRn6+dDOl1TqyZGccrajlzlc38rOlmxkcE8ZHC87kgmExVsdSLsLP6gDK+yRGhvL2HZN48sssnlyVxdp9R3lk1kjO0sGr2m3ljgLuf2cbZdUN/ObCwcyfmqxnw6gf0C13ZQl/Xx9+fv5pvHPnJHoE+THv+e9Z8MYminX44JMqKK3h9pczuO3lDKLDgnjv7snccfZALXb1X8QY668gTEtLM+np6VbHUBapqW9k4ep9PL06i5AAP+67aDBXp8Xjo4X1bw2NTby6/iCPrdxDfWMTC85L5dYzk/H31e0zbyYiGcaYtFaf03JXriKzsJzfvrONDdnHGNE/ggd+NJQ0PZWPNVnFPPj+TvYUljMlJYqHLh9OYmSo1bGUC9ByV27DGMOKzYd5+OPdFJTVcMnIWH41fRBJUd5XZpmF5Ty2cg+f7iwkrlcw988YwoXDYxDRv2iUjZa7cjtVdQ08s3ofi785QF1jE1enxbNgWioxEZ5/7nZuSRWPf57JO5vyCAnw4/azkrnlzGSC/HVcGPVDWu7KbR0pr+GpL7N47fuDiAizzojjtqnJHrlbIutIBc98tY93Nx3Cx0eYNzGRO85O0VEcVZu03JXbyy2pYuHqfbydkUdDUxMzRsRy4+QBjEno6da7KYwxrD9Qwotrslm5s4BAPx9mj03gtrOSiY0ItjqecnFa7spjHCmr4blvD/Da+oOU1zYwrF84cycmcvHIfvQIdJ/LNspq6nlv82FeXpvDnsJyIoL9mTMhkRsnJxHZI9DqeMpNaLkrj1NZ28A7mw6xZG02ewsrCPb35cLhMVw+uj8TB0Zaf4pgUxNkZkJ+PsTGQmoqdU3wbVYRyzce4tOdhdQ1NDE0NpwfT0riR6P66VjrqsO03JXHMsaQkXOM5ZsO8cGWw5TVNBAR7M+0IX2YPjSGySmRhAX5OzdUUxMsXw5z51La5MO3p41j5Q0LWFUZRHltA71C/Ll0VD8uHxPHqLgIt96tpKzl9HIXkQuBJwBf4FljzMMnm1/LXXWHmvpGVu8p4tOdBXyx6wil1fX4+gij4iKYnBLFmMRejIrr6dADlMUVtWxZt4OM/3mKNf2Hsy1mIE0+vvSuLuO8kf2ZPnEQU0+L1oG9VLdwarmLiC+wFzgfyAM2ANcaY3a29T1a7qq71Tc2kZ59jDVZxazZV8zWvNJ/3881vncwg/qGk9KnBwOjQ4nrFUJMRBAx4UHt2jVSWdtAQVkNhaU15B2rZl9RBfuKKtiVX/7voYz9GhsYfXgPk3K2MCV7M6MP78bvyy/g7LMd+WsrL3OycnfEEahxQJYxZr994W8AM4E2y12p7ubv68PEgZFMHBjJrxhERW0D2w+VsiX3OFvyjpNZWMFXe49Q3/jDjZtAPx/CgvwIDfQjwL7f3gB1DU1U1jZQXttAXcMPbzYS4OdDclQooxN68uNJSZxOGcMuOYeQ8uP/mSk42LbvXSkncUS59wdym32dB4xvOZOIzAfmAyQkJDgghlL/0SPQjwnJkUxIjvz3tIbGJnKPVXP4eDUFpTUUlNVQVl1PeW0DFTUNNDT9p8T9fX3oEehHjyA/egYHEBMRSN/wIPr3DCauV8gPB+5qaoLnF8PcuVBdbSv2JUsgNdWZv7LycpadO2aMWQQsAttuGatyKO/l5+vDgKhQBnT30AY+PnDFFTBixA/OlsFH97Mr53FEuR8Cmt+RN84+TSnv4eMDgwbZPpSygCM2JTYAqSIyQEQCgNnAew5YjlJKqTZ0+5a7MaZBRO4CVmI7FfJ5Y8yO7l6OUkqptjlkn7sx5iPgI0f8bKWUUqemR3iUUsoDabkrpZQH0nJXSikPpOWulFIeyCVGhRSRIiCnk98eBRR3Y5zuork6RnN1nKtm01wd05VcicaY6NaecIly7woRSW9r4Bwraa6O0Vwd56rZNFfHOCqX7pZRSikPpOWulFIeyBPKfZHVAdqguTpGc3Wcq2bTXB3jkFxuv89dKaXUf/OELXellFItaLkrpZQHcotyF5GrRGSHiDSJSFqL5+4TkSwR2SMiF7Tx/QNEZL19vqX2oYi7O+NSEdls/8gWkc1tzJctItvs8zn8xrEi8kcROdQs24w25rvQvg6zROReJ+R6TER2i8hWEXlHRHq2MZ9T1tepfn8RCbS/xln291KSo7I0W2a8iKwSkZ329/+CVuY5W0RKm72+f3B0LvtyT/q6iM0/7Otrq4iMcUKmQc3Ww2YRKRORn7WYx2nrS0SeF5EjIrK92bTeIvKZiGTaP/dq43vn2efJFJF5nQpgjHH5D2AIMAhYDaQ1mz4U2AIEAgOAfYBvK9//JjDb/vgZ4A4H5/0/4A9tPJcNRDlx3f0R+NUp5vG1r7tkIMC+Toc6ONd0wM/++BHgEavWV3t+f+BO4Bn749nAUie8drHAGPvjMGw3nm+Z62zgA2e9n9r7ugAzgI8BASYA652czxcowHaRjyXrC5gKjAG2N5v2KHCv/fG9rb3vgd7AfvvnXvbHvTq6fLfYcjfG7DLG7GnlqZnAG8aYWmPMASAL2w26/01EBDgXWGaf9BJwmaOy2pd3NfC6o5bhAP++qbkxpg44cVNzhzHGfGqMabB/uQ7bHbus0p7ffya29w7Y3kvT7K+1wxhj8o0xG+2Py4Fd2O5R7A5mAkuMzTqgp4g48w7h04B9xpjOXvneZcaYr4GSFpObv4/a6qILgM+MMSXGmGPAZ8CFHV2+W5T7SbR2M+6Wb/5I4HizImltnu50JlBojMls43kDfCoiGfabhDvDXfY/jZ9v48/A9qxHR7oJ21Zea5yxvtrz+/97Hvt7qRTbe8sp7LuBRgPrW3l6oohsEZGPRWSYkyKd6nWx+j01m7Y3sKxYXyf0Ncbk2x8XAH1bmadb1p1lN8huSUQ+B2Jaeep+Y8wKZ+dpTTszXsvJt9qnGGMOiUgf4DMR2W3/H94huYCngT9j+8f4Z2y7jG7qyvK6I9eJ9SUi9wMNwKtt/JhuX1/uRkR6AG8DPzPGlLV4eiO2XQ8V9uMp7wKpTojlsq+L/ZjapcB9rTxt1fr6L8YYIyIOOxfdZcrdGHNeJ76tPTfjPortT0I/+xZXp2/YfaqMIuIHXAGccZKfccj++YiIvINtl0CX/lG0d92JyGLgg1aecshNzduxvn4MXAJMM/adja38jG5fX61oz+9/Yp48++scge295VAi4o+t2F81xixv+XzzsjfGfCQiC0Ukyhjj0AGy2vG6OOQ91U4XARuNMYUtn7BqfTVTKCKxxph8+26qI63McwjbsYET4rAdb+wQd98t8x4w234mwwBs/wN/33wGe2msAmbZJ80DHPWXwHnAbmNMXmtPikioiISdeIztoOL21ubtLi32c17exvKcflNzEbkQuAe41BhT1cY8zlpf7fn938P23gHbe+nLtv5D6i72ffrPAbuMMX9rY56YE/v+RWQctn/TDv1Pp52vy3vAXPtZMxOA0ma7Ixytzb+erVhfLTR/H7XVRSuB6SLSy74bdbp9Wsc446hxVz+wlVIeUAsUAiubPXc/tjMd9gAXNZv+EdDP/jgZW+lnAW8BgQ7K+SJwe4tp/YCPmuXYYv/YgW33hKPX3cvANmCr/Y0V2zKX/esZ2M7G2OekXFnY9itutn880zKXM9dXa78/8CC2/3wAguzvnSz7eynZCetoCrbdaVubracZwO0n3mfAXfZ1swXbgelJTsjV6uvSIpcAT9nX5zaaneXm4Gyh2Mo6otk0S9YXtv9g8oF6e3/djO04zRdAJvA50Ns+bxrwbLPvvcn+XssCbuzM8nX4AaWU8kDuvltGKaVUK7TclVLKA2m5K6WUB9JyV0opD6TlrpRSHkjLXSmlPJCWu1JKeaD/B3b+rZgWEmX9AAAAAElFTkSuQmCC","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=[-10, 1])"]},{"cell_type":"markdown","id":"9c187ad7","metadata":{},"source":["The red dot at x=-10 does not know the surface it stands on, and it only knows the coordinates of where it stands and the gradient of itself, which is -20. And the other red dot at x=1 does not know the surface it stands on; it only knows the coordinates of where it stands and the gradient of itself, which is 2.\n","\n","By having only this information: we can say that the red dot at x=-10 should make a bigger jump than x=1 because it has a bigger absolute gradient value. The sign shows the direction. Minus (-) shows that the red dot at x=-10 should move to the right and the other one should move to the left.\n","\n","In summary, the red dot at x=-10 (gradient: -20) should make a bigger jump to the right, and the red dot at x=1 (gradient: 2) should make a smaller jump to the left. \n","\n","We know that the jump length should be proportional to the gradient, but what is that value exactly? We don’t know. So, let’s just say that red points should move with the length of *alpha * gradient*, where alpha is just a parameter.\n","\n","We can say that the new location of the red dot should be calculated with the following formula:\n","\n","x = x - gradient * alpha"]},{"cell_type":"markdown","id":"0a7f5c3f","metadata":{},"source":["Now let's implement this with **NumPy**. Let's start with visualizing the $f(x)=x^2$ function and the $x=-10$ point."]},{"cell_type":"code","execution_count":null,"id":"e26dbdf0","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=[-10])"]},{"cell_type":"markdown","id":"6e752e19","metadata":{},"source":["The following code implements the whole logic explained before:"]},{"cell_type":"code","execution_count":null,"id":"2bdd54f1","metadata":{},"outputs":[],"source":["def gradient_descent(x, nsteps=1):\n"," \n"," \n"," # collectXs is an array to store how x changed in each iteration, so we can visualize it later\n"," \n"," collectXs = [x]\n"," \n"," # learning_rate is the value that we mentioned as alpha in the previous section\n"," \n"," learning_rate = 1e-01\n"," \n"," for _ in range(nsteps):\n"," \n"," # The following one line does the real magic\n"," # The next value of x is calculated by subtracting the gradient * learning_rate by itself\n"," # The intuition behind this line is in the previous section\n"," \n"," x -= df(x) * learning_rate \n"," collectXs.append(x)\n"," \n"," # We return a tuple that contains\n"," # x -> recent x after nsteps \n"," # collectXs -> all the x values that were calculated so far\n"," \n"," return x, collectXs"]},{"cell_type":"markdown","id":"aea74a65","metadata":{},"source":["Before running a gradient descent with 1000 steps, let's just run it twice, one step at a time, to see how x evolves. \n","We start with x=-10, and it evolves to x=-8. We know that when x=0 that is the **minimum point**, so yes, it is evolving in the correct direction."]},{"cell_type":"code","execution_count":null,"id":"0350981e","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-8.0\n"]}],"source":["x=-10\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"code","execution_count":null,"id":"f8e01e2d","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-6.4\n"]}],"source":["# The next step will start at x=-8. Let's run a gradient for 1 step\n","\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"markdown","id":"93f13b32","metadata":{},"source":["It goes to x=-6.4. Excellent. Now let's run it 1000 times"]},{"cell_type":"code","execution_count":null,"id":"b699d1fb","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-7.873484301831169e-97\n"]}],"source":["x, collectedXs = gradient_descent(x, nsteps=1000)\n","print(x)"]},{"cell_type":"code","execution_count":null,"id":"0b76ee22","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["visualize(f, x=collectedXs)"]},{"cell_type":"markdown","id":"d00d2fbb","metadata":{},"source":["### Exercise 3\n","\n","When I arrive to the coffee machine, I hear my colleague talking about the per-unit costs of producing 'product B' for the company. As the company produces more units, the per-unit costs continue to decrease until a point where they start to increase.\n","\n","To optimize the per-unit production cost at its minimum to optimize efficiency, the company would need to find the number of units to be produced where the per-unit production costs begin to change from decreasing to increasing.\n","\n","**Build a quadratic function $f(x)=0.1(x)^2−9x +4500$ on $x∈[0,100]$ to create the per-unit cost function, and make a conclusion.**"]},{"cell_type":"code","execution_count":15,"id":"7c67d8b7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":15,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the function\n","def f(x):\n"," return 0.1*(x)**2 -9*x +4500\n","x=np.linspace(0,100)\n","plt.plot(x, f(x))"]},{"cell_type":"markdown","id":"fbe54895","metadata":{},"source":["We saw with Gradient Descent how the red dot navigates in an environment it does not know about. It only knows the coordinates of where it is and its gradient. The red dot could find the minimum point by using only this knowledge and the gradient descent algorithm.\n","\n","**Optional:**\n","\n","Implement all the previous steps to create a gradient descent algorithm to see how the per-unit cost evolves, with a starting point of 0 units of production."]},{"cell_type":"markdown","id":"aabad82c","metadata":{},"source":["## Linear Algebra"]},{"cell_type":"markdown","id":"6753636d","metadata":{},"source":["### Exercise 1: Sum of two matrices\n","\n","Suppose we have two matrices A and B.\n","\n","```py\n","A = [[1,2],[3,4]]\n","B = [[4,5],[6,7]]\n","\n","then we get\n","A+B = [[5,7],[9,11]]\n","A-B = [[-3,-3],[-3,-3]]\n","```\n","\n","Make the sum of two matrices using Python with NumPy"]},{"cell_type":"code","execution_count":19,"id":"9e200c32","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[[1, 2], [3, 4]]\n","[[4, 5], [6, 7]]\n","[[ 5 7]\n"," [ 9 11]]\n"]}],"source":["# import numpy as np\n","import numpy as np\n"," \n"," \n","# Creating first matrix\n","a=[[1,2], [3,4]]\n"," \n","# Creating second matrix\n","b=[[4,5], [6,7]]\n"," \n","# Print elements\n","print (a)\n","print (b)\n"," \n","# Adding both matrices\n","resultado=np.array(a)+np.array(b)\n","print(resultado)"]},{"cell_type":"markdown","id":"93bfb6cc","metadata":{},"source":["### Exercise 2: Sum of two lists\n","\n","There will be many situations in which we'll have to find an index-wise summation of two different lists. This can have possible applications in day-to-day programming. In this exercise, we will solve the same problem in various ways in which this task can be performed.\n","\n","We have the following two lists:\n","\n","```py\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n","```\n","\n","Now let's use Python code to demonstrate addition of two lists."]},{"cell_type":"code","execution_count":null,"id":"867b70fc","metadata":{},"outputs":[],"source":["# Naive method\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print (\"Original list 1 : \" + str(list1))\n","print (\"Original list 2 : \" + str(list2))\n"," \n","# Using naive method to add two lists \n","res_list = []\n","for i in range(0, len(list1)):\n"," res_list.append(list1[i] + list2[i])\n"," \n","# Printing resulting list \n","print (\"Resulting list is : \" + str(res_list))"]},{"cell_type":"markdown","id":"7a063d7f","metadata":{},"source":["Now use the following three different methods to make the same calculation: sum of two lists"]},{"cell_type":"code","execution_count":null,"id":"681930a3","metadata":{},"outputs":[],"source":["# Use list comprehension to perform addition of the two lists:\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using list comprehension to add two lists\n","\n"," \n","# Printing resulting list \n"]},{"cell_type":"code","execution_count":null,"id":"a3a8a425","metadata":{},"outputs":[],"source":["# Use map() + add():\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using map() + add() to add two lists\n","\n"," \n","# Printing resulting list "]},{"cell_type":"code","execution_count":null,"id":"1708d7ee","metadata":{},"outputs":[],"source":["# Use zip() + sum():\n","\n","\n","# Initializing lists\n","\n"," \n","# Printing original lists\n","\n"," \n","# Using zip() + sum() to add two lists\n","\n"," \n","# Printing resulting list "]},{"cell_type":"markdown","id":"1aef1bd2","metadata":{},"source":["### Exercise 3: Dot multiplication\n","\n","We have two matrices:\n","\n","```py\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n","```\n","\n","A simple technique but expensive method for larger input datasets is using *for loops*. In this exercise, we will first use nested *for loops* to iterate through each row and column of the matrices, and then we will perform the same multiplication using NumPy."]},{"cell_type":"code","execution_count":null,"id":"840e7d0e","metadata":{},"outputs":[],"source":["# Using a for loop input two matrices of size n x m\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n"," \n","res = [[0 for x in range(3)] for y in range(3)]\n"," \n","# Explicit for loops\n","for i in range(len(matrix1)):\n"," for j in range(len(matrix2[0])):\n"," for k in range(len(matrix2)):\n"," \n"," # Resulting matrix\n"," res[i][j] += matrix1[i][k] * matrix2[k][j]\n"," \n","print(res)"]},{"cell_type":"code","execution_count":null,"id":"db6c3355","metadata":{},"outputs":[],"source":["# Import libraries\n","\n"," \n","# Input two matrices\n","\n"," \n","# This will return dot product\n","\n"," \n","# Print resulting matrix\n"]},{"cell_type":"markdown","id":"785f6c30","metadata":{},"source":["Source:\n","\n","https://www.youtube.com/channel/UCXq-PLvYAX-EufF5RAPihVg\n","\n","https://www.geeksforgeeks.org/\n","\n","https://medium.com/@seehleung/basic-calculus-explained-for-machine-learning-c7f642e7ced3\n","\n","https://blog.demir.io/understanding-gradient-descent-266fc3dcf02f"]}],"metadata":{"interpreter":{"hash":"d3463682613d55fcbb64853e38cc3520a7f67bdf8d6940e781ddcdc423122719"},"kernelspec":{"display_name":"Python 3.9.12 ('calculus-project')","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} +{"cells":[{"cell_type":"markdown","id":"5dbe7b9e","metadata":{},"source":["# Calculus and Algebra problems"]},{"cell_type":"markdown","id":"519c4b12","metadata":{},"source":["## Calculus\n","\n","Calculus is not obscure. It is the language for modeling behaviors. Calculus enables us to find the rate of changes in order to optimize a function. Without calculus, we would not be able to fully understand techniques such as:\n","\n","Backpropagation in neural networks\n","\n","Regression using optimal least square\n","\n","Expectation maximization in fitting probability models"]},{"cell_type":"markdown","id":"b7e2e87a","metadata":{},"source":["### Exercise 1\n","\n","Let's say, in my office, it takes me 10 seconds (time) to travel 25 meters (distance) to the coffee machine.\n","If we want to express the above situation as a function, then it would be:\n","\n","distance = speed * time\n","\n","So for this case, speed is the first derivative of the distance function above. As speed describes the rate of change of distance over time, when people say taking the first derivative of a certain function, they mean finding out the rate of change of a function.\n","\n","**Find the speed and build the linear function on distance $(d)$ over time $(t)$, when $(t ∈ [0,10])$.**"]},{"cell_type":"code","execution_count":5,"id":"bb3e954e","metadata":{},"outputs":[],"source":["# import libraries\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import pandas as pd\n","\n","# Define the distance function; speed= 25/10=2.5 >> fdis(x)=2.5*t(X)\n","def f(x):\n"," return 2.5*x\n","x=np.linspace(0,10)\n"]},{"cell_type":"code","execution_count":6,"id":"dbc4c780","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":6,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Plot the distance function on domain (t)\n","plt.plot(x,f(x))"]},{"cell_type":"code","execution_count":7,"id":"4c4d4f20","metadata":{},"outputs":[{"data":{"text/html":["
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xf(x)
00.0000000.000000
10.2040820.510204
20.4081631.020408
30.6122451.530612
40.8163272.040816
51.0204082.551020
61.2244903.061224
71.4285713.571429
81.6326534.081633
91.8367354.591837
102.0408165.102041
112.2448985.612245
122.4489806.122449
132.6530616.632653
142.8571437.142857
153.0612247.653061
163.2653068.163265
173.4693888.673469
183.6734699.183673
193.8775519.693878
204.08163310.204082
214.28571410.714286
224.48979611.224490
234.69387811.734694
244.89795912.244898
255.10204112.755102
265.30612213.265306
275.51020413.775510
285.71428614.285714
295.91836714.795918
306.12244915.306122
316.32653115.816327
326.53061216.326531
336.73469416.836735
346.93877617.346939
357.14285717.857143
367.34693918.367347
377.55102018.877551
387.75510219.387755
397.95918419.897959
408.16326520.408163
418.36734720.918367
428.57142921.428571
438.77551021.938776
448.97959222.448980
459.18367322.959184
469.38775523.469388
479.59183723.979592
489.79591824.489796
4910.00000025.000000
\n","
"],"text/plain":[" x f(x)\n","0 0.000000 0.000000\n","1 0.204082 0.510204\n","2 0.408163 1.020408\n","3 0.612245 1.530612\n","4 0.816327 2.040816\n","5 1.020408 2.551020\n","6 1.224490 3.061224\n","7 1.428571 3.571429\n","8 1.632653 4.081633\n","9 1.836735 4.591837\n","10 2.040816 5.102041\n","11 2.244898 5.612245\n","12 2.448980 6.122449\n","13 2.653061 6.632653\n","14 2.857143 7.142857\n","15 3.061224 7.653061\n","16 3.265306 8.163265\n","17 3.469388 8.673469\n","18 3.673469 9.183673\n","19 3.877551 9.693878\n","20 4.081633 10.204082\n","21 4.285714 10.714286\n","22 4.489796 11.224490\n","23 4.693878 11.734694\n","24 4.897959 12.244898\n","25 5.102041 12.755102\n","26 5.306122 13.265306\n","27 5.510204 13.775510\n","28 5.714286 14.285714\n","29 5.918367 14.795918\n","30 6.122449 15.306122\n","31 6.326531 15.816327\n","32 6.530612 16.326531\n","33 6.734694 16.836735\n","34 6.938776 17.346939\n","35 7.142857 17.857143\n","36 7.346939 18.367347\n","37 7.551020 18.877551\n","38 7.755102 19.387755\n","39 7.959184 19.897959\n","40 8.163265 20.408163\n","41 8.367347 20.918367\n","42 8.571429 21.428571\n","43 8.775510 21.938776\n","44 8.979592 22.448980\n","45 9.183673 22.959184\n","46 9.387755 23.469388\n","47 9.591837 23.979592\n","48 9.795918 24.489796\n","49 10.000000 25.000000"]},"execution_count":7,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","df=pd.DataFrame({'x':x, 'f(x)':f(x)})\n","df"]},{"cell_type":"markdown","id":"1144168d","metadata":{},"source":["### Exercise 2\n","\n","It turned out that I wasn't walking a constant speed towards getting my coffee, but I was accelerating (my speed increased over time). If my initial *speed = 0*, it still took me 10 seconds to travel from my seat to my coffee, but I was walking faster and faster.\n","\n","$V_o$ = initial speed = $0$\n","\n","t = time\n","\n","a = acceleration\n","\n","**distance** = $V_o * t + 0.5 * a * (t^2)$\n","\n","**speed** = $V_o + a * t$\n","\n","The first derivative of the speed function is acceleration. I realize that the speed function is closely related to the distance function.\n","\n","**Find the acceleration value and build the quadratic function $(t ∈ [0,10])$. Also, create a graph and a table.**"]},{"cell_type":"code","execution_count":8,"id":"ec1f8bd7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":8,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the quadratic funtion t=10, d=25 >> a=0.5 | Vo=0\n","\n","def f(t): return 0.5*0.5*(t**2)\n","t = np.linspace(0,10)\n","plt.plot(t, f(t))\n"]},{"cell_type":"code","execution_count":9,"id":"ba5c497b","metadata":{},"outputs":[{"data":{"text/html":["
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tf(t)
00.0000000.000000
10.2040820.010412
20.4081630.041649
30.6122450.093711
40.8163270.166597
\n","
"],"text/plain":[" t f(t)\n","0 0.000000 0.000000\n","1 0.204082 0.010412\n","2 0.408163 0.041649\n","3 0.612245 0.093711\n","4 0.816327 0.166597"]},"execution_count":9,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","dft=pd.DataFrame({'t':t, 'f(t)':f(t)})\n","dft.head()\n"]},{"cell_type":"markdown","id":"66d4cc18","metadata":{},"source":["Before exercise 3, we'll make a brief introduction to Gradient Descent algorithm, which will have a larger explanation in future modules of the bootcamp.\n","\n","Gradient Descent algorithm is the hero behind the family of deep learning algorithms. When an algorithm in this family runs, it tries to minimize the error between the training input and predicted output. This minimization is done by optimization algorithms, and gradient descent is the most popular one.\n","\n","Let's say you have these input & output pairs:\n","\n","```py\n","# Input:\n","[\n"," [1,2],\n"," [3,4]\n","]\n","\n","# Output:\n","[\n"," [50],\n"," [110]\n","]\n","```\n","\n","We can estimate that if we multiply the input values by [10, 20], we can have the output as shown above.\n","\n","```py\n","1(10) + 2(20) = 50\n","\n","3(10) + 4(20) = 110\n","```\n","\n","When a machine learning algorithm starts running, it assigns random values and makes a prediction. \n","Let's say it assigned [1,2] values:\n","\n","```py\n","1(1) + 2(2) = 5\n","\n","3(1) + 4(2) = 11\n","```\n","\n","Once it has the predictions, it calculates the error: the difference between the real data and the predicted data. There are many ways to calculate the error, and they are called loss functions.\n","\n","Once we have this value, the optimization algorithm starts showing itself, and it sets new values which replace the initial random values. \n","\n","And, the loop continues until a condition is met. That condition can be to loop *n* times, or to loop until the error is smaller than a value."]},{"cell_type":"markdown","id":"85ef2f0b","metadata":{},"source":["It can be hard to understand **gradient descent** without understanding **gradient**. So, let's focus on what a gradient is. The gradient shows the direction of the greatest change of a scalar function. The gradient calculation is done with derivatives, so let's start with a simple example. To calculate the gradient, we just need to remember some linear algebra calculations from high school because we need to calculate derivatives.\n","\n","Let's say we want to find the minimum point of $f(x) = x^2$. The derivative of that function is $df(x)=2x$. \n","\n","The gradient of $f(x)$ at point $x=-10$\n","\n","is \n","\n","$df(-10)=-20$.\n","\n","The gradient of $f(x)$ at point $x=1$\n","\n","is \n","\n","$df(1)=2$.\n","\n","Now let’s visualize $f(x)$ and those $x=-10$ and $x=1$ points."]},{"cell_type":"code","execution_count":10,"id":"4ff7e11a","metadata":{},"outputs":[],"source":["import numpy as np\n","import seaborn as sns\n","\n","def f(x):\n"," return x**2\n","\n","def df(x):\n"," return 2*x\n","\n","def visualize(f, x=None):\n"," \n"," xArray = np.linspace(-10, 10, 100) \n"," yArray = f(xArray)\n"," sns.lineplot(x=xArray, y=yArray)\n"," \n"," if x is not None:\n"," assert type(x) in [np.ndarray, list] # x should be numpy array or list\n"," if type(x) is list: # if it is a list, convert to numpy array\n"," x = np.array(x)\n","\n"," \n"," y = f(x)\n"," sns.scatterplot(x=x, y=y, color='red')"]},{"cell_type":"code","execution_count":11,"id":"633a54fd","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["visualize(f, x=[-10, 1])"]},{"cell_type":"markdown","id":"9c187ad7","metadata":{},"source":["The red dot at x=-10 does not know the surface it stands on, and it only knows the coordinates of where it stands and the gradient of itself, which is -20. And the other red dot at x=1 does not know the surface it stands on; it only knows the coordinates of where it stands and the gradient of itself, which is 2.\n","\n","By having only this information: we can say that the red dot at x=-10 should make a bigger jump than x=1 because it has a bigger absolute gradient value. The sign shows the direction. Minus (-) shows that the red dot at x=-10 should move to the right and the other one should move to the left.\n","\n","In summary, the red dot at x=-10 (gradient: -20) should make a bigger jump to the right, and the red dot at x=1 (gradient: 2) should make a smaller jump to the left. \n","\n","We know that the jump length should be proportional to the gradient, but what is that value exactly? We don’t know. So, let’s just say that red points should move with the length of *alpha * gradient*, where alpha is just a parameter.\n","\n","We can say that the new location of the red dot should be calculated with the following formula:\n","\n","x = x - gradient * alpha"]},{"cell_type":"markdown","id":"0a7f5c3f","metadata":{},"source":["Now let's implement this with **NumPy**. Let's start with visualizing the $f(x)=x^2$ function and the $x=-10$ point."]},{"cell_type":"code","execution_count":12,"id":"e26dbdf0","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["visualize(f, x=[-10])"]},{"cell_type":"markdown","id":"6e752e19","metadata":{},"source":["The following code implements the whole logic explained before:"]},{"cell_type":"code","execution_count":13,"id":"2bdd54f1","metadata":{},"outputs":[],"source":["def gradient_descent(x, nsteps=1):\n"," \n"," \n"," # collectXs is an array to store how x changed in each iteration, so we can visualize it later\n"," \n"," collectXs = [x]\n"," \n"," # learning_rate is the value that we mentioned as alpha in the previous section\n"," \n"," learning_rate = 1e-01\n"," \n"," for _ in range(nsteps):\n"," \n"," # The following one line does the real magic\n"," # The next value of x is calculated by subtracting the gradient * learning_rate by itself\n"," # The intuition behind this line is in the previous section\n"," \n"," x -= df(x) * learning_rate \n"," collectXs.append(x)\n"," \n"," # We return a tuple that contains\n"," # x -> recent x after nsteps \n"," # collectXs -> all the x values that were calculated so far\n"," \n"," return x, collectXs"]},{"cell_type":"markdown","id":"aea74a65","metadata":{},"source":["Before running a gradient descent with 1000 steps, let's just run it twice, one step at a time, to see how x evolves. \n","We start with x=-10, and it evolves to x=-8. We know that when x=0 that is the **minimum point**, so yes, it is evolving in the correct direction."]},{"cell_type":"code","execution_count":14,"id":"0350981e","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-8.0\n"]}],"source":["x=-10\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"code","execution_count":15,"id":"f8e01e2d","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-6.4\n"]}],"source":["# The next step will start at x=-8. Let's run a gradient for 1 step\n","\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"markdown","id":"93f13b32","metadata":{},"source":["It goes to x=-6.4. Excellent. Now let's run it 1000 times"]},{"cell_type":"code","execution_count":16,"id":"b699d1fb","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-7.873484301831169e-97\n"]}],"source":["x, collectedXs = gradient_descent(x, nsteps=1000)\n","print(x)"]},{"cell_type":"code","execution_count":17,"id":"0b76ee22","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["visualize(f, x=collectedXs)"]},{"cell_type":"markdown","id":"d00d2fbb","metadata":{},"source":["### Exercise 3\n","\n","When I arrive to the coffee machine, I hear my colleague talking about the per-unit costs of producing 'product B' for the company. As the company produces more units, the per-unit costs continue to decrease until a point where they start to increase.\n","\n","To optimize the per-unit production cost at its minimum to optimize efficiency, the company would need to find the number of units to be produced where the per-unit production costs begin to change from decreasing to increasing.\n","\n","**Build a quadratic function $f(x)=0.1(x)^2−9x +4500$ on $x∈[0,100]$ to create the per-unit cost function, and make a conclusion.**"]},{"cell_type":"code","execution_count":18,"id":"7c67d8b7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":18,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the function\n","def f(x):\n"," return 0.1*(x)**2 -9*x +4500\n","x=np.linspace(0,100)\n","plt.plot(x, f(x))"]},{"cell_type":"markdown","id":"fbe54895","metadata":{},"source":["We saw with Gradient Descent how the red dot navigates in an environment it does not know about. It only knows the coordinates of where it is and its gradient. The red dot could find the minimum point by using only this knowledge and the gradient descent algorithm.\n","\n","**Optional:**\n","\n","Implement all the previous steps to create a gradient descent algorithm to see how the per-unit cost evolves, with a starting point of 0 units of production."]},{"cell_type":"markdown","id":"aabad82c","metadata":{},"source":["## Linear Algebra"]},{"cell_type":"markdown","id":"6753636d","metadata":{},"source":["### Exercise 1: Sum of two matrices\n","\n","Suppose we have two matrices A and B.\n","\n","```py\n","A = [[1,2],[3,4]]\n","B = [[4,5],[6,7]]\n","\n","then we get\n","A+B = [[5,7],[9,11]]\n","A-B = [[-3,-3],[-3,-3]]\n","```\n","\n","Make the sum of two matrices using Python with NumPy"]},{"cell_type":"code","execution_count":19,"id":"9e200c32","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[[1, 2], [3, 4]]\n","[[4, 5], [6, 7]]\n","[[ 5 7]\n"," [ 9 11]]\n"]}],"source":["# import numpy as np\n","import numpy as np\n"," \n"," \n","# Creating first matrix\n","a=[[1,2], [3,4]]\n"," \n","# Creating second matrix\n","b=[[4,5], [6,7]]\n"," \n","# Print elements\n","print (a)\n","print (b)\n"," \n","# Adding both matrices\n","resultado=np.array(a)+np.array(b)\n","print(resultado)"]},{"cell_type":"markdown","id":"93bfb6cc","metadata":{},"source":["### Exercise 2: Sum of two lists\n","\n","There will be many situations in which we'll have to find an index-wise summation of two different lists. This can have possible applications in day-to-day programming. In this exercise, we will solve the same problem in various ways in which this task can be performed.\n","\n","We have the following two lists:\n","\n","```py\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n","```\n","\n","Now let's use Python code to demonstrate addition of two lists."]},{"cell_type":"code","execution_count":20,"id":"867b70fc","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Original list 1 : [2, 5, 4, 7, 3]\n","Original list 2 : [1, 4, 6, 9, 10]\n","Resulting list is : [3, 9, 10, 16, 13]\n"]}],"source":["# Naive method\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print (\"Original list 1 : \" + str(list1))\n","print (\"Original list 2 : \" + str(list2))\n"," \n","# Using naive method to add two lists \n","res_list = []\n","for i in range(0, len(list1)):\n"," res_list.append(list1[i] + list2[i])\n"," \n","# Printing resulting list \n","print (\"Resulting list is : \" + str(res_list))"]},{"cell_type":"markdown","id":"7a063d7f","metadata":{},"source":["Now use the following three different methods to make the same calculation: sum of two lists"]},{"cell_type":"code","execution_count":21,"id":"681930a3","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[2, 5, 4, 7, 3]\n","[1, 4, 6, 9, 10]\n","[3, 9, 10, 16, 13]\n"]}],"source":["# Use list comprehension to perform addition of the two lists:\n","\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print(list1)\n","print (list2)\n"," \n","# Using list comprehension to add two lists\n","result = [a + b for a, b in zip(list1, list2)]\n","\n"," \n","# Printing resulting list \n","print(result)"]},{"cell_type":"code","execution_count":23,"id":"a3a8a425","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[2, 5, 4, 7, 3]\n","[1, 4, 6, 9, 10]\n","[3, 9, 10, 16, 13]\n"]}],"source":["# Use map() + add():\n","from operator import add\n","\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n","# Printing original lists\n","print(list1)\n","print (list2)\n"," \n","# Using map() + add() to add two lists\n","result= list(map(add, list1, list2))\n"," \n","# Printing resulting list \n","print(result)"]},{"cell_type":"code","execution_count":24,"id":"1708d7ee","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[2, 5, 4, 7, 3]\n","[1, 4, 6, 9, 10]\n","[3, 9, 10, 16, 13]\n"]}],"source":["# Use zip() + sum():\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print(list1)\n","print (list2)\n"," \n","# Using zip() + sum() to add two lists\n","result= [sum(i) for i in zip(list1, list2)]\n","\n","# Printing resulting list \n","print(result)"]},{"cell_type":"markdown","id":"1aef1bd2","metadata":{},"source":["### Exercise 3: Dot multiplication\n","\n","We have two matrices:\n","\n","```py\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n","```\n","\n","A simple technique but expensive method for larger input datasets is using *for loops*. In this exercise, we will first use nested *for loops* to iterate through each row and column of the matrices, and then we will perform the same multiplication using NumPy."]},{"cell_type":"code","execution_count":null,"id":"840e7d0e","metadata":{},"outputs":[],"source":["# Using a for loop input two matrices of size n x m\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n"," \n","res = [[0 for x in range(3)] for y in range(3)]\n"," \n","# Explicit for loops\n","for i in range(len(matrix1)):\n"," for j in range(len(matrix2[0])):\n"," for k in range(len(matrix2)):\n"," \n"," # Resulting matrix\n"," res[i][j] += matrix1[i][k] * matrix2[k][j]\n"," \n","print(res)"]},{"cell_type":"code","execution_count":25,"id":"db6c3355","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[[24 33 28]\n"," [33 36 23]\n"," [25 29 23]]\n"]}],"source":["# Import libraries\n","\n","import numpy as np\n"," \n","# Input two matrices\n","matriz1 = ([1,7,3],[ 4,5,2],[ 3,6,1])\n","matriz2 = ([5,4,1],[ 1,2,3],[ 4,5,2])\n"," \n","# This will return dot product\n","res = np.dot(matriz1,matriz2)\n"," \n","# Print resulting matrix\n","print(res)\n"]},{"cell_type":"markdown","id":"785f6c30","metadata":{},"source":["Source:\n","\n","https://www.youtube.com/channel/UCXq-PLvYAX-EufF5RAPihVg\n","\n","https://www.geeksforgeeks.org/\n","\n","https://medium.com/@seehleung/basic-calculus-explained-for-machine-learning-c7f642e7ced3\n","\n","https://blog.demir.io/understanding-gradient-descent-266fc3dcf02f"]}],"metadata":{"interpreter":{"hash":"d3463682613d55fcbb64853e38cc3520a7f67bdf8d6940e781ddcdc423122719"},"kernelspec":{"display_name":"Python 3.9.12 ('calculus-project')","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} From 51fe32fd0fa16118d399cda3f7411d6c6a3906bd Mon Sep 17 00:00:00 2001 From: Maria Pais <145993408+Finarosalina@users.noreply.github.com> Date: Wed, 5 Mar 2025 17:39:31 +0000 Subject: [PATCH 3/6] avance 1 --- notebook/problems.ipynb | 899 +++++++++++++++++++++++++++++++++++++++- 1 file changed, 898 insertions(+), 1 deletion(-) diff --git a/notebook/problems.ipynb b/notebook/problems.ipynb index 554b8c31..66cf1da0 100644 --- a/notebook/problems.ipynb +++ b/notebook/problems.ipynb @@ -1 +1,898 @@ -{"cells":[{"cell_type":"markdown","id":"5dbe7b9e","metadata":{},"source":["# Calculus and Algebra problems"]},{"cell_type":"markdown","id":"519c4b12","metadata":{},"source":["## Calculus\n","\n","Calculus is not obscure. It is the language for modeling behaviors. Calculus enables us to find the rate of changes in order to optimize a function. Without calculus, we would not be able to fully understand techniques such as:\n","\n","Backpropagation in neural networks\n","\n","Regression using optimal least square\n","\n","Expectation maximization in fitting probability models"]},{"cell_type":"markdown","id":"b7e2e87a","metadata":{},"source":["### Exercise 1\n","\n","Let's say, in my office, it takes me 10 seconds (time) to travel 25 meters (distance) to the coffee machine.\n","If we want to express the above situation as a function, then it would be:\n","\n","distance = speed * time\n","\n","So for this case, speed is the first derivative of the distance function above. As speed describes the rate of change of distance over time, when people say taking the first derivative of a certain function, they mean finding out the rate of change of a function.\n","\n","**Find the speed and build the linear function on distance $(d)$ over time $(t)$, when $(t ∈ [0,10])$.**"]},{"cell_type":"code","execution_count":5,"id":"bb3e954e","metadata":{},"outputs":[],"source":["# import libraries\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import pandas as pd\n","\n","# Define the distance function; speed= 25/10=2.5 >> fdis(x)=2.5*t(X)\n","def f(x):\n"," return 2.5*x\n","x=np.linspace(0,10)\n"]},{"cell_type":"code","execution_count":6,"id":"dbc4c780","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":6,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Plot the distance function on domain (t)\n","plt.plot(x,f(x))"]},{"cell_type":"code","execution_count":7,"id":"4c4d4f20","metadata":{},"outputs":[{"data":{"text/html":["
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xf(x)
00.0000000.000000
10.2040820.510204
20.4081631.020408
30.6122451.530612
40.8163272.040816
51.0204082.551020
61.2244903.061224
71.4285713.571429
81.6326534.081633
91.8367354.591837
102.0408165.102041
112.2448985.612245
122.4489806.122449
132.6530616.632653
142.8571437.142857
153.0612247.653061
163.2653068.163265
173.4693888.673469
183.6734699.183673
193.8775519.693878
204.08163310.204082
214.28571410.714286
224.48979611.224490
234.69387811.734694
244.89795912.244898
255.10204112.755102
265.30612213.265306
275.51020413.775510
285.71428614.285714
295.91836714.795918
306.12244915.306122
316.32653115.816327
326.53061216.326531
336.73469416.836735
346.93877617.346939
357.14285717.857143
367.34693918.367347
377.55102018.877551
387.75510219.387755
397.95918419.897959
408.16326520.408163
418.36734720.918367
428.57142921.428571
438.77551021.938776
448.97959222.448980
459.18367322.959184
469.38775523.469388
479.59183723.979592
489.79591824.489796
4910.00000025.000000
\n","
"],"text/plain":[" x f(x)\n","0 0.000000 0.000000\n","1 0.204082 0.510204\n","2 0.408163 1.020408\n","3 0.612245 1.530612\n","4 0.816327 2.040816\n","5 1.020408 2.551020\n","6 1.224490 3.061224\n","7 1.428571 3.571429\n","8 1.632653 4.081633\n","9 1.836735 4.591837\n","10 2.040816 5.102041\n","11 2.244898 5.612245\n","12 2.448980 6.122449\n","13 2.653061 6.632653\n","14 2.857143 7.142857\n","15 3.061224 7.653061\n","16 3.265306 8.163265\n","17 3.469388 8.673469\n","18 3.673469 9.183673\n","19 3.877551 9.693878\n","20 4.081633 10.204082\n","21 4.285714 10.714286\n","22 4.489796 11.224490\n","23 4.693878 11.734694\n","24 4.897959 12.244898\n","25 5.102041 12.755102\n","26 5.306122 13.265306\n","27 5.510204 13.775510\n","28 5.714286 14.285714\n","29 5.918367 14.795918\n","30 6.122449 15.306122\n","31 6.326531 15.816327\n","32 6.530612 16.326531\n","33 6.734694 16.836735\n","34 6.938776 17.346939\n","35 7.142857 17.857143\n","36 7.346939 18.367347\n","37 7.551020 18.877551\n","38 7.755102 19.387755\n","39 7.959184 19.897959\n","40 8.163265 20.408163\n","41 8.367347 20.918367\n","42 8.571429 21.428571\n","43 8.775510 21.938776\n","44 8.979592 22.448980\n","45 9.183673 22.959184\n","46 9.387755 23.469388\n","47 9.591837 23.979592\n","48 9.795918 24.489796\n","49 10.000000 25.000000"]},"execution_count":7,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","df=pd.DataFrame({'x':x, 'f(x)':f(x)})\n","df"]},{"cell_type":"markdown","id":"1144168d","metadata":{},"source":["### Exercise 2\n","\n","It turned out that I wasn't walking a constant speed towards getting my coffee, but I was accelerating (my speed increased over time). If my initial *speed = 0*, it still took me 10 seconds to travel from my seat to my coffee, but I was walking faster and faster.\n","\n","$V_o$ = initial speed = $0$\n","\n","t = time\n","\n","a = acceleration\n","\n","**distance** = $V_o * t + 0.5 * a * (t^2)$\n","\n","**speed** = $V_o + a * t$\n","\n","The first derivative of the speed function is acceleration. I realize that the speed function is closely related to the distance function.\n","\n","**Find the acceleration value and build the quadratic function $(t ∈ [0,10])$. Also, create a graph and a table.**"]},{"cell_type":"code","execution_count":8,"id":"ec1f8bd7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":8,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the quadratic funtion t=10, d=25 >> a=0.5 | Vo=0\n","\n","def f(t): return 0.5*0.5*(t**2)\n","t = np.linspace(0,10)\n","plt.plot(t, f(t))\n"]},{"cell_type":"code","execution_count":9,"id":"ba5c497b","metadata":{},"outputs":[{"data":{"text/html":["
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tf(t)
00.0000000.000000
10.2040820.010412
20.4081630.041649
30.6122450.093711
40.8163270.166597
\n","
"],"text/plain":[" t f(t)\n","0 0.000000 0.000000\n","1 0.204082 0.010412\n","2 0.408163 0.041649\n","3 0.612245 0.093711\n","4 0.816327 0.166597"]},"execution_count":9,"metadata":{},"output_type":"execute_result"}],"source":["# Create a DataFrame\n","dft=pd.DataFrame({'t':t, 'f(t)':f(t)})\n","dft.head()\n"]},{"cell_type":"markdown","id":"66d4cc18","metadata":{},"source":["Before exercise 3, we'll make a brief introduction to Gradient Descent algorithm, which will have a larger explanation in future modules of the bootcamp.\n","\n","Gradient Descent algorithm is the hero behind the family of deep learning algorithms. When an algorithm in this family runs, it tries to minimize the error between the training input and predicted output. This minimization is done by optimization algorithms, and gradient descent is the most popular one.\n","\n","Let's say you have these input & output pairs:\n","\n","```py\n","# Input:\n","[\n"," [1,2],\n"," [3,4]\n","]\n","\n","# Output:\n","[\n"," [50],\n"," [110]\n","]\n","```\n","\n","We can estimate that if we multiply the input values by [10, 20], we can have the output as shown above.\n","\n","```py\n","1(10) + 2(20) = 50\n","\n","3(10) + 4(20) = 110\n","```\n","\n","When a machine learning algorithm starts running, it assigns random values and makes a prediction. \n","Let's say it assigned [1,2] values:\n","\n","```py\n","1(1) + 2(2) = 5\n","\n","3(1) + 4(2) = 11\n","```\n","\n","Once it has the predictions, it calculates the error: the difference between the real data and the predicted data. There are many ways to calculate the error, and they are called loss functions.\n","\n","Once we have this value, the optimization algorithm starts showing itself, and it sets new values which replace the initial random values. \n","\n","And, the loop continues until a condition is met. That condition can be to loop *n* times, or to loop until the error is smaller than a value."]},{"cell_type":"markdown","id":"85ef2f0b","metadata":{},"source":["It can be hard to understand **gradient descent** without understanding **gradient**. So, let's focus on what a gradient is. The gradient shows the direction of the greatest change of a scalar function. The gradient calculation is done with derivatives, so let's start with a simple example. To calculate the gradient, we just need to remember some linear algebra calculations from high school because we need to calculate derivatives.\n","\n","Let's say we want to find the minimum point of $f(x) = x^2$. The derivative of that function is $df(x)=2x$. \n","\n","The gradient of $f(x)$ at point $x=-10$\n","\n","is \n","\n","$df(-10)=-20$.\n","\n","The gradient of $f(x)$ at point $x=1$\n","\n","is \n","\n","$df(1)=2$.\n","\n","Now let’s visualize $f(x)$ and those $x=-10$ and $x=1$ points."]},{"cell_type":"code","execution_count":10,"id":"4ff7e11a","metadata":{},"outputs":[],"source":["import numpy as np\n","import seaborn as sns\n","\n","def f(x):\n"," return x**2\n","\n","def df(x):\n"," return 2*x\n","\n","def visualize(f, x=None):\n"," \n"," xArray = np.linspace(-10, 10, 100) \n"," yArray = f(xArray)\n"," sns.lineplot(x=xArray, y=yArray)\n"," \n"," if x is not None:\n"," assert type(x) in [np.ndarray, list] # x should be numpy array or list\n"," if type(x) is list: # if it is a list, convert to numpy array\n"," x = np.array(x)\n","\n"," \n"," y = f(x)\n"," sns.scatterplot(x=x, y=y, color='red')"]},{"cell_type":"code","execution_count":11,"id":"633a54fd","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["visualize(f, x=[-10, 1])"]},{"cell_type":"markdown","id":"9c187ad7","metadata":{},"source":["The red dot at x=-10 does not know the surface it stands on, and it only knows the coordinates of where it stands and the gradient of itself, which is -20. And the other red dot at x=1 does not know the surface it stands on; it only knows the coordinates of where it stands and the gradient of itself, which is 2.\n","\n","By having only this information: we can say that the red dot at x=-10 should make a bigger jump than x=1 because it has a bigger absolute gradient value. The sign shows the direction. Minus (-) shows that the red dot at x=-10 should move to the right and the other one should move to the left.\n","\n","In summary, the red dot at x=-10 (gradient: -20) should make a bigger jump to the right, and the red dot at x=1 (gradient: 2) should make a smaller jump to the left. \n","\n","We know that the jump length should be proportional to the gradient, but what is that value exactly? We don’t know. So, let’s just say that red points should move with the length of *alpha * gradient*, where alpha is just a parameter.\n","\n","We can say that the new location of the red dot should be calculated with the following formula:\n","\n","x = x - gradient * alpha"]},{"cell_type":"markdown","id":"0a7f5c3f","metadata":{},"source":["Now let's implement this with **NumPy**. Let's start with visualizing the $f(x)=x^2$ function and the $x=-10$ point."]},{"cell_type":"code","execution_count":12,"id":"e26dbdf0","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["visualize(f, x=[-10])"]},{"cell_type":"markdown","id":"6e752e19","metadata":{},"source":["The following code implements the whole logic explained before:"]},{"cell_type":"code","execution_count":13,"id":"2bdd54f1","metadata":{},"outputs":[],"source":["def gradient_descent(x, nsteps=1):\n"," \n"," \n"," # collectXs is an array to store how x changed in each iteration, so we can visualize it later\n"," \n"," collectXs = [x]\n"," \n"," # learning_rate is the value that we mentioned as alpha in the previous section\n"," \n"," learning_rate = 1e-01\n"," \n"," for _ in range(nsteps):\n"," \n"," # The following one line does the real magic\n"," # The next value of x is calculated by subtracting the gradient * learning_rate by itself\n"," # The intuition behind this line is in the previous section\n"," \n"," x -= df(x) * learning_rate \n"," collectXs.append(x)\n"," \n"," # We return a tuple that contains\n"," # x -> recent x after nsteps \n"," # collectXs -> all the x values that were calculated so far\n"," \n"," return x, collectXs"]},{"cell_type":"markdown","id":"aea74a65","metadata":{},"source":["Before running a gradient descent with 1000 steps, let's just run it twice, one step at a time, to see how x evolves. \n","We start with x=-10, and it evolves to x=-8. We know that when x=0 that is the **minimum point**, so yes, it is evolving in the correct direction."]},{"cell_type":"code","execution_count":14,"id":"0350981e","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-8.0\n"]}],"source":["x=-10\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"code","execution_count":15,"id":"f8e01e2d","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-6.4\n"]}],"source":["# The next step will start at x=-8. Let's run a gradient for 1 step\n","\n","x, collectedXs = gradient_descent(x, nsteps=1)\n","print(x)"]},{"cell_type":"markdown","id":"93f13b32","metadata":{},"source":["It goes to x=-6.4. Excellent. Now let's run it 1000 times"]},{"cell_type":"code","execution_count":16,"id":"b699d1fb","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["-7.873484301831169e-97\n"]}],"source":["x, collectedXs = gradient_descent(x, nsteps=1000)\n","print(x)"]},{"cell_type":"code","execution_count":17,"id":"0b76ee22","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["visualize(f, x=collectedXs)"]},{"cell_type":"markdown","id":"d00d2fbb","metadata":{},"source":["### Exercise 3\n","\n","When I arrive to the coffee machine, I hear my colleague talking about the per-unit costs of producing 'product B' for the company. As the company produces more units, the per-unit costs continue to decrease until a point where they start to increase.\n","\n","To optimize the per-unit production cost at its minimum to optimize efficiency, the company would need to find the number of units to be produced where the per-unit production costs begin to change from decreasing to increasing.\n","\n","**Build a quadratic function $f(x)=0.1(x)^2−9x +4500$ on $x∈[0,100]$ to create the per-unit cost function, and make a conclusion.**"]},{"cell_type":"code","execution_count":18,"id":"7c67d8b7","metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":18,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# Define and plot the function\n","def f(x):\n"," return 0.1*(x)**2 -9*x +4500\n","x=np.linspace(0,100)\n","plt.plot(x, f(x))"]},{"cell_type":"markdown","id":"fbe54895","metadata":{},"source":["We saw with Gradient Descent how the red dot navigates in an environment it does not know about. It only knows the coordinates of where it is and its gradient. The red dot could find the minimum point by using only this knowledge and the gradient descent algorithm.\n","\n","**Optional:**\n","\n","Implement all the previous steps to create a gradient descent algorithm to see how the per-unit cost evolves, with a starting point of 0 units of production."]},{"cell_type":"markdown","id":"aabad82c","metadata":{},"source":["## Linear Algebra"]},{"cell_type":"markdown","id":"6753636d","metadata":{},"source":["### Exercise 1: Sum of two matrices\n","\n","Suppose we have two matrices A and B.\n","\n","```py\n","A = [[1,2],[3,4]]\n","B = [[4,5],[6,7]]\n","\n","then we get\n","A+B = [[5,7],[9,11]]\n","A-B = [[-3,-3],[-3,-3]]\n","```\n","\n","Make the sum of two matrices using Python with NumPy"]},{"cell_type":"code","execution_count":19,"id":"9e200c32","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[[1, 2], [3, 4]]\n","[[4, 5], [6, 7]]\n","[[ 5 7]\n"," [ 9 11]]\n"]}],"source":["# import numpy as np\n","import numpy as np\n"," \n"," \n","# Creating first matrix\n","a=[[1,2], [3,4]]\n"," \n","# Creating second matrix\n","b=[[4,5], [6,7]]\n"," \n","# Print elements\n","print (a)\n","print (b)\n"," \n","# Adding both matrices\n","resultado=np.array(a)+np.array(b)\n","print(resultado)"]},{"cell_type":"markdown","id":"93bfb6cc","metadata":{},"source":["### Exercise 2: Sum of two lists\n","\n","There will be many situations in which we'll have to find an index-wise summation of two different lists. This can have possible applications in day-to-day programming. In this exercise, we will solve the same problem in various ways in which this task can be performed.\n","\n","We have the following two lists:\n","\n","```py\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n","```\n","\n","Now let's use Python code to demonstrate addition of two lists."]},{"cell_type":"code","execution_count":20,"id":"867b70fc","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Original list 1 : [2, 5, 4, 7, 3]\n","Original list 2 : [1, 4, 6, 9, 10]\n","Resulting list is : [3, 9, 10, 16, 13]\n"]}],"source":["# Naive method\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print (\"Original list 1 : \" + str(list1))\n","print (\"Original list 2 : \" + str(list2))\n"," \n","# Using naive method to add two lists \n","res_list = []\n","for i in range(0, len(list1)):\n"," res_list.append(list1[i] + list2[i])\n"," \n","# Printing resulting list \n","print (\"Resulting list is : \" + str(res_list))"]},{"cell_type":"markdown","id":"7a063d7f","metadata":{},"source":["Now use the following three different methods to make the same calculation: sum of two lists"]},{"cell_type":"code","execution_count":21,"id":"681930a3","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[2, 5, 4, 7, 3]\n","[1, 4, 6, 9, 10]\n","[3, 9, 10, 16, 13]\n"]}],"source":["# Use list comprehension to perform addition of the two lists:\n","\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print(list1)\n","print (list2)\n"," \n","# Using list comprehension to add two lists\n","result = [a + b for a, b in zip(list1, list2)]\n","\n"," \n","# Printing resulting list \n","print(result)"]},{"cell_type":"code","execution_count":23,"id":"a3a8a425","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[2, 5, 4, 7, 3]\n","[1, 4, 6, 9, 10]\n","[3, 9, 10, 16, 13]\n"]}],"source":["# Use map() + add():\n","from operator import add\n","\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n","# Printing original lists\n","print(list1)\n","print (list2)\n"," \n","# Using map() + add() to add two lists\n","result= list(map(add, list1, list2))\n"," \n","# Printing resulting list \n","print(result)"]},{"cell_type":"code","execution_count":24,"id":"1708d7ee","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[2, 5, 4, 7, 3]\n","[1, 4, 6, 9, 10]\n","[3, 9, 10, 16, 13]\n"]}],"source":["# Use zip() + sum():\n","\n","# Initializing lists\n","list1 = [2, 5, 4, 7, 3]\n","list2 = [1, 4, 6, 9, 10]\n"," \n","# Printing original lists\n","print(list1)\n","print (list2)\n"," \n","# Using zip() + sum() to add two lists\n","result= [sum(i) for i in zip(list1, list2)]\n","\n","# Printing resulting list \n","print(result)"]},{"cell_type":"markdown","id":"1aef1bd2","metadata":{},"source":["### Exercise 3: Dot multiplication\n","\n","We have two matrices:\n","\n","```py\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n","```\n","\n","A simple technique but expensive method for larger input datasets is using *for loops*. In this exercise, we will first use nested *for loops* to iterate through each row and column of the matrices, and then we will perform the same multiplication using NumPy."]},{"cell_type":"code","execution_count":null,"id":"840e7d0e","metadata":{},"outputs":[],"source":["# Using a for loop input two matrices of size n x m\n","matrix1 = [[1,7,3],\n"," [4,5,2],\n"," [3,6,1]]\n","matrix2 = [[5,4,1],\n"," [1,2,3],\n"," [4,5,2]]\n"," \n","res = [[0 for x in range(3)] for y in range(3)]\n"," \n","# Explicit for loops\n","for i in range(len(matrix1)):\n"," for j in range(len(matrix2[0])):\n"," for k in range(len(matrix2)):\n"," \n"," # Resulting matrix\n"," res[i][j] += matrix1[i][k] * matrix2[k][j]\n"," \n","print(res)"]},{"cell_type":"code","execution_count":25,"id":"db6c3355","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["[[24 33 28]\n"," [33 36 23]\n"," [25 29 23]]\n"]}],"source":["# Import libraries\n","\n","import numpy as np\n"," \n","# Input two matrices\n","matriz1 = ([1,7,3],[ 4,5,2],[ 3,6,1])\n","matriz2 = ([5,4,1],[ 1,2,3],[ 4,5,2])\n"," \n","# This will return dot product\n","res = np.dot(matriz1,matriz2)\n"," \n","# Print resulting matrix\n","print(res)\n"]},{"cell_type":"markdown","id":"785f6c30","metadata":{},"source":["Source:\n","\n","https://www.youtube.com/channel/UCXq-PLvYAX-EufF5RAPihVg\n","\n","https://www.geeksforgeeks.org/\n","\n","https://medium.com/@seehleung/basic-calculus-explained-for-machine-learning-c7f642e7ced3\n","\n","https://blog.demir.io/understanding-gradient-descent-266fc3dcf02f"]}],"metadata":{"interpreter":{"hash":"d3463682613d55fcbb64853e38cc3520a7f67bdf8d6940e781ddcdc423122719"},"kernelspec":{"display_name":"Python 3.9.12 ('calculus-project')","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5dbe7b9e", + "metadata": {}, + "source": [ + "# Calculus and Algebra problems" + ] + }, + { + "cell_type": "markdown", + "id": "519c4b12", + "metadata": {}, + "source": [ + "## Calculus\n", + "\n", + "Calculus is not obscure. It is the language for modeling behaviors. Calculus enables us to find the rate of changes in order to optimize a function. Without calculus, we would not be able to fully understand techniques such as:\n", + "\n", + "Backpropagation in neural networks\n", + "\n", + "Regression using optimal least square\n", + "\n", + "Expectation maximization in fitting probability models" + ] + }, + { + "cell_type": "markdown", + "id": "b7e2e87a", + "metadata": {}, + "source": [ + "### Exercise 1\n", + "\n", + "Let's say, in my office, it takes me 10 seconds (time) to travel 25 meters (distance) to the coffee machine.\n", + "If we want to express the above situation as a function, then it would be:\n", + "\n", + "distance = speed * time\n", + "\n", + "So for this case, speed is the first derivative of the distance function above. As speed describes the rate of change of distance over time, when people say taking the first derivative of a certain function, they mean finding out the rate of change of a function.\n", + "\n", + "**Find the speed and build the linear function on distance $(d)$ over time $(t)$, when $(t ∈ [0,10])$.**" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bb3e954e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.5\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "time=10\n", + "distance=25\n", + "speed=distance/time\n", + "print(speed)\n", + "def linear_function(x):\n", + " return speed*(x)\n", + "x_axis=np.linspace(0,10,500)\n", + "y_axis=linear_function(x_axis)\n", + "plt.plot(x_axis,y_axis)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "1144168d", + "metadata": {}, + "source": [ + "### Exercise 2\n", + "\n", + "It turned out that I wasn't walking a constant speed towards getting my coffee, but I was accelerating (my speed increased over time). If my initial *speed = 0*, it still took me 10 seconds to travel from my seat to my coffee, but I was walking faster and faster.\n", + "\n", + "$V_o$ = initial speed = $0$\n", + "\n", + "t = time\n", + "\n", + "a = acceleration\n", + "\n", + "**distance** = $V_o * t + 0.5 * a * (t^2)$\n", + "\n", + "**speed** = $V_o + a * t$\n", + "\n", + "The first derivative of the speed function is acceleration. I realize that the speed function is closely related to the distance function.\n", + "\n", + "**Find the acceleration value and build the quadratic function $(t ∈ [0,10])$. Also, create a graph and a table.**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ec1f8bd7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Define and plot the quadratic funtion; Vº=0, t=10, d=25, speed=a*t, distance=0.5*a*t**2: a=25/50=0.5 --> speed=0.5t, distance=0.5*0.5*t**2\n", + "def func_distance(t):\n", + " return 0.25*t**2\n", + "def func_speed(t):\n", + " return 0.5*t\n", + "x_axis=np.linspace(0,10,500)\n", + "y_axis_distance=func_distance(x_axis)\n", + "y_axis_speed=func_speed(x_axis)\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "ba5c497b", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'pd' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mNameError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[4]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m \u001b[38;5;66;03m# Create a DataFrame\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m dft=\u001b[43mpd\u001b[49m.DataFrame({\u001b[33m'\u001b[39m\u001b[33mt\u001b[39m\u001b[33m'\u001b[39m:t, \u001b[33m'\u001b[39m\u001b[33mf(t)\u001b[39m\u001b[33m'\u001b[39m:f(t)})\n\u001b[32m 3\u001b[39m dft.head()\n", + "\u001b[31mNameError\u001b[39m: name 'pd' is not defined" + ] + } + ], + "source": [ + "# Create a DataFrame\n", + "dft=pd.DataFrame({'t':t, 'f(t)':f(t)})\n", + "dft.head()\n" + ] + }, + { + "cell_type": "markdown", + "id": "66d4cc18", + "metadata": {}, + "source": [ + "Before exercise 3, we'll make a brief introduction to Gradient Descent algorithm, which will have a larger explanation in future modules of the bootcamp.\n", + "\n", + "Gradient Descent algorithm is the hero behind the family of deep learning algorithms. When an algorithm in this family runs, it tries to minimize the error between the training input and predicted output. This minimization is done by optimization algorithms, and gradient descent is the most popular one.\n", + "\n", + "Let's say you have these input & output pairs:\n", + "\n", + "```py\n", + "# Input:\n", + "[\n", + " [1,2],\n", + " [3,4]\n", + "]\n", + "\n", + "# Output:\n", + "[\n", + " [50],\n", + " [110]\n", + "]\n", + "```\n", + "\n", + "We can estimate that if we multiply the input values by [10, 20], we can have the output as shown above.\n", + "\n", + "```py\n", + "1(10) + 2(20) = 50\n", + "\n", + "3(10) + 4(20) = 110\n", + "```\n", + "\n", + "When a machine learning algorithm starts running, it assigns random values and makes a prediction. \n", + "Let's say it assigned [1,2] values:\n", + "\n", + "```py\n", + "1(1) + 2(2) = 5\n", + "\n", + "3(1) + 4(2) = 11\n", + "```\n", + "\n", + "Once it has the predictions, it calculates the error: the difference between the real data and the predicted data. There are many ways to calculate the error, and they are called loss functions.\n", + "\n", + "Once we have this value, the optimization algorithm starts showing itself, and it sets new values which replace the initial random values. \n", + "\n", + "And, the loop continues until a condition is met. That condition can be to loop *n* times, or to loop until the error is smaller than a value." + ] + }, + { + "cell_type": "markdown", + "id": "85ef2f0b", + "metadata": {}, + "source": [ + "It can be hard to understand **gradient descent** without understanding **gradient**. So, let's focus on what a gradient is. The gradient shows the direction of the greatest change of a scalar function. The gradient calculation is done with derivatives, so let's start with a simple example. To calculate the gradient, we just need to remember some linear algebra calculations from high school because we need to calculate derivatives.\n", + "\n", + "Let's say we want to find the minimum point of $f(x) = x^2$. The derivative of that function is $df(x)=2x$. \n", + "\n", + "The gradient of $f(x)$ at point $x=-10$\n", + "\n", + "is \n", + "\n", + "$df(-10)=-20$.\n", + "\n", + "The gradient of $f(x)$ at point $x=1$\n", + "\n", + "is \n", + "\n", + "$df(1)=2$.\n", + "\n", + "Now let’s visualize $f(x)$ and those $x=-10$ and $x=1$ points." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4ff7e11a", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import seaborn as sns\n", + "\n", + "def f(x):\n", + " return x**2\n", + "\n", + "def df(x):\n", + " return 2*x\n", + "\n", + "def visualize(f, x=None):\n", + " \n", + " xArray = np.linspace(-10, 10, 100) \n", + " yArray = f(xArray)\n", + " sns.lineplot(x=xArray, y=yArray)\n", + " \n", + " if x is not None:\n", + " assert type(x) in [np.ndarray, list] # x should be numpy array or list\n", + " if type(x) is list: # if it is a list, convert to numpy array\n", + " x = np.array(x)\n", + "\n", + " \n", + " y = f(x)\n", + " sns.scatterplot(x=x, y=y, color='red')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "633a54fd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "visualize(f, x=[-10, 1])" + ] + }, + { + "cell_type": "markdown", + "id": "9c187ad7", + "metadata": {}, + "source": [ + "The red dot at x=-10 does not know the surface it stands on, and it only knows the coordinates of where it stands and the gradient of itself, which is -20. And the other red dot at x=1 does not know the surface it stands on; it only knows the coordinates of where it stands and the gradient of itself, which is 2.\n", + "\n", + "By having only this information: we can say that the red dot at x=-10 should make a bigger jump than x=1 because it has a bigger absolute gradient value. The sign shows the direction. Minus (-) shows that the red dot at x=-10 should move to the right and the other one should move to the left.\n", + "\n", + "In summary, the red dot at x=-10 (gradient: -20) should make a bigger jump to the right, and the red dot at x=1 (gradient: 2) should make a smaller jump to the left. \n", + "\n", + "We know that the jump length should be proportional to the gradient, but what is that value exactly? We don’t know. So, let’s just say that red points should move with the length of *alpha * gradient*, where alpha is just a parameter.\n", + "\n", + "We can say that the new location of the red dot should be calculated with the following formula:\n", + "\n", + "x = x - gradient * alpha" + ] + }, + { + "cell_type": "markdown", + "id": "0a7f5c3f", + "metadata": {}, + "source": [ + "Now let's implement this with **NumPy**. Let's start with visualizing the $f(x)=x^2$ function and the $x=-10$ point." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e26dbdf0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "visualize(f, x=[-10])" + ] + }, + { + "cell_type": "markdown", + "id": "6e752e19", + "metadata": {}, + "source": [ + "The following code implements the whole logic explained before:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2bdd54f1", + "metadata": {}, + "outputs": [], + "source": [ + "def gradient_descent(x, nsteps=1):\n", + " \n", + " \n", + " # collectXs is an array to store how x changed in each iteration, so we can visualize it later\n", + " \n", + " collectXs = [x]\n", + " \n", + " # learning_rate is the value that we mentioned as alpha in the previous section\n", + " \n", + " learning_rate = 1e-01\n", + " \n", + " for _ in range(nsteps):\n", + " \n", + " # The following one line does the real magic\n", + " # The next value of x is calculated by subtracting the gradient * learning_rate by itself\n", + " # The intuition behind this line is in the previous section\n", + " \n", + " x -= df(x) * learning_rate \n", + " collectXs.append(x)\n", + " \n", + " # We return a tuple that contains\n", + " # x -> recent x after nsteps \n", + " # collectXs -> all the x values that were calculated so far\n", + " \n", + " return x, collectXs" + ] + }, + { + "cell_type": "markdown", + "id": "aea74a65", + "metadata": {}, + "source": [ + "Before running a gradient descent with 1000 steps, let's just run it twice, one step at a time, to see how x evolves. \n", + "We start with x=-10, and it evolves to x=-8. We know that when x=0 that is the **minimum point**, so yes, it is evolving in the correct direction." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0350981e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-8.0\n" + ] + } + ], + "source": [ + "x=-10\n", + "x, collectedXs = gradient_descent(x, nsteps=1)\n", + "print(x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f8e01e2d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-6.4\n" + ] + } + ], + "source": [ + "# The next step will start at x=-8. Let's run a gradient for 1 step\n", + "\n", + "x, collectedXs = gradient_descent(x, nsteps=1)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "id": "93f13b32", + "metadata": {}, + "source": [ + "It goes to x=-6.4. Excellent. Now let's run it 1000 times" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b699d1fb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-7.873484301831169e-97\n" + ] + } + ], + "source": [ + "x, collectedXs = gradient_descent(x, nsteps=1000)\n", + "print(x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0b76ee22", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "visualize(f, x=collectedXs)" + ] + }, + { + "cell_type": "markdown", + "id": "d00d2fbb", + "metadata": {}, + "source": [ + "### Exercise 3\n", + "\n", + "When I arrive to the coffee machine, I hear my colleague talking about the per-unit costs of producing 'product B' for the company. As the company produces more units, the per-unit costs continue to decrease until a point where they start to increase.\n", + "\n", + "To optimize the per-unit production cost at its minimum to optimize efficiency, the company would need to find the number of units to be produced where the per-unit production costs begin to change from decreasing to increasing.\n", + "\n", + "**Build a quadratic function $f(x)=0.1(x)^2−9x +4500$ on $x∈[0,100]$ to create the per-unit cost function, and make a conclusion.**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7c67d8b7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Define and plot the function\n", + "def f(x):\n", + " return 0.1*(x)**2 -9*x +4500\n", + "x=np.linspace(0,100)\n", + "plt.plot(x, f(x))" + ] + }, + { + "cell_type": "markdown", + "id": "fbe54895", + "metadata": {}, + "source": [ + "We saw with Gradient Descent how the red dot navigates in an environment it does not know about. It only knows the coordinates of where it is and its gradient. The red dot could find the minimum point by using only this knowledge and the gradient descent algorithm.\n", + "\n", + "**Optional:**\n", + "\n", + "Implement all the previous steps to create a gradient descent algorithm to see how the per-unit cost evolves, with a starting point of 0 units of production." + ] + }, + { + "cell_type": "markdown", + "id": "aabad82c", + "metadata": {}, + "source": [ + "## Linear Algebra" + ] + }, + { + "cell_type": "markdown", + "id": "6753636d", + "metadata": {}, + "source": [ + "### Exercise 1: Sum of two matrices\n", + "\n", + "Suppose we have two matrices A and B.\n", + "\n", + "```py\n", + "A = [[1,2],[3,4]]\n", + "B = [[4,5],[6,7]]\n", + "\n", + "then we get\n", + "A+B = [[5,7],[9,11]]\n", + "A-B = [[-3,-3],[-3,-3]]\n", + "```\n", + "\n", + "Make the sum of two matrices using Python with NumPy" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9e200c32", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1, 2], [3, 4]]\n", + "[[4, 5], [6, 7]]\n", + "[[ 5 7]\n", + " [ 9 11]]\n" + ] + } + ], + "source": [ + "# import numpy as np\n", + "import numpy as np\n", + " \n", + " \n", + "# Creating first matrix\n", + "a=[[1,2], [3,4]]\n", + " \n", + "# Creating second matrix\n", + "b=[[4,5], [6,7]]\n", + " \n", + "# Print elements\n", + "print (a)\n", + "print (b)\n", + " \n", + "# Adding both matrices\n", + "resultado=np.array(a)+np.array(b)\n", + "print(resultado)" + ] + }, + { + "cell_type": "markdown", + "id": "93bfb6cc", + "metadata": {}, + "source": [ + "### Exercise 2: Sum of two lists\n", + "\n", + "There will be many situations in which we'll have to find an index-wise summation of two different lists. This can have possible applications in day-to-day programming. In this exercise, we will solve the same problem in various ways in which this task can be performed.\n", + "\n", + "We have the following two lists:\n", + "\n", + "```py\n", + "list1 = [2, 5, 4, 7, 3]\n", + "list2 = [1, 4, 6, 9, 10]\n", + "```\n", + "\n", + "Now let's use Python code to demonstrate addition of two lists." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "867b70fc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original list 1 : [2, 5, 4, 7, 3]\n", + "Original list 2 : [1, 4, 6, 9, 10]\n", + "Resulting list is : [3, 9, 10, 16, 13]\n" + ] + } + ], + "source": [ + "# Naive method\n", + "\n", + "# Initializing lists\n", + "list1 = [2, 5, 4, 7, 3]\n", + "list2 = [1, 4, 6, 9, 10]\n", + " \n", + "# Printing original lists\n", + "print (\"Original list 1 : \" + str(list1))\n", + "print (\"Original list 2 : \" + str(list2))\n", + " \n", + "# Using naive method to add two lists \n", + "res_list = []\n", + "for i in range(0, len(list1)):\n", + " res_list.append(list1[i] + list2[i])\n", + " \n", + "# Printing resulting list \n", + "print (\"Resulting list is : \" + str(res_list))" + ] + }, + { + "cell_type": "markdown", + "id": "7a063d7f", + "metadata": {}, + "source": [ + "Now use the following three different methods to make the same calculation: sum of two lists" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "681930a3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2, 5, 4, 7, 3]\n", + "[1, 4, 6, 9, 10]\n", + "[3, 9, 10, 16, 13]\n" + ] + } + ], + "source": [ + "# Use list comprehension to perform addition of the two lists:\n", + "\n", + "\n", + "# Initializing lists\n", + "list1 = [2, 5, 4, 7, 3]\n", + "list2 = [1, 4, 6, 9, 10]\n", + " \n", + "# Printing original lists\n", + "print(list1)\n", + "print (list2)\n", + " \n", + "# Using list comprehension to add two lists\n", + "result = [a + b for a, b in zip(list1, list2)]\n", + "\n", + " \n", + "# Printing resulting list \n", + "print(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a3a8a425", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2, 5, 4, 7, 3]\n", + "[1, 4, 6, 9, 10]\n", + "[3, 9, 10, 16, 13]\n" + ] + } + ], + "source": [ + "# Use map() + add():\n", + "from operator import add\n", + "\n", + "\n", + "# Initializing lists\n", + "list1 = [2, 5, 4, 7, 3]\n", + "list2 = [1, 4, 6, 9, 10]\n", + "# Printing original lists\n", + "print(list1)\n", + "print (list2)\n", + " \n", + "# Using map() + add() to add two lists\n", + "result= list(map(add, list1, list2))\n", + " \n", + "# Printing resulting list \n", + "print(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1708d7ee", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2, 5, 4, 7, 3]\n", + "[1, 4, 6, 9, 10]\n", + "[3, 9, 10, 16, 13]\n" + ] + } + ], + "source": [ + "# Use zip() + sum():\n", + "\n", + "# Initializing lists\n", + "list1 = [2, 5, 4, 7, 3]\n", + "list2 = [1, 4, 6, 9, 10]\n", + " \n", + "# Printing original lists\n", + "print(list1)\n", + "print (list2)\n", + " \n", + "# Using zip() + sum() to add two lists\n", + "result= [sum(i) for i in zip(list1, list2)]\n", + "\n", + "# Printing resulting list \n", + "print(result)" + ] + }, + { + "cell_type": "markdown", + "id": "1aef1bd2", + "metadata": {}, + "source": [ + "### Exercise 3: Dot multiplication\n", + "\n", + "We have two matrices:\n", + "\n", + "```py\n", + "matrix1 = [[1,7,3],\n", + " [4,5,2],\n", + " [3,6,1]]\n", + "matrix2 = [[5,4,1],\n", + " [1,2,3],\n", + " [4,5,2]]\n", + "```\n", + "\n", + "A simple technique but expensive method for larger input datasets is using *for loops*. In this exercise, we will first use nested *for loops* to iterate through each row and column of the matrices, and then we will perform the same multiplication using NumPy." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "840e7d0e", + "metadata": {}, + "outputs": [], + "source": [ + "# Using a for loop input two matrices of size n x m\n", + "matrix1 = [[1,7,3],\n", + " [4,5,2],\n", + " [3,6,1]]\n", + "matrix2 = [[5,4,1],\n", + " [1,2,3],\n", + " [4,5,2]]\n", + " \n", + "res = [[0 for x in range(3)] for y in range(3)]\n", + " \n", + "# Explicit for loops\n", + "for i in range(len(matrix1)):\n", + " for j in range(len(matrix2[0])):\n", + " for k in range(len(matrix2)):\n", + " \n", + " # Resulting matrix\n", + " res[i][j] += matrix1[i][k] * matrix2[k][j]\n", + " \n", + "print(res)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "db6c3355", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[24 33 28]\n", + " [33 36 23]\n", + " [25 29 23]]\n" + ] + } + ], + "source": [ + "# Import libraries\n", + "\n", + "import numpy as np\n", + " \n", + "# Input two matrices\n", + "matriz1 = ([1,7,3],[ 4,5,2],[ 3,6,1])\n", + "matriz2 = ([5,4,1],[ 1,2,3],[ 4,5,2])\n", + " \n", + "# This will return dot product\n", + "res = np.dot(matriz1,matriz2)\n", + " \n", + "# Print resulting matrix\n", + "print(res)\n" + ] + }, + { + "cell_type": "markdown", + "id": "785f6c30", + "metadata": {}, + "source": [ + "Source:\n", + "\n", + "https://www.youtube.com/channel/UCXq-PLvYAX-EufF5RAPihVg\n", + "\n", + "https://www.geeksforgeeks.org/\n", + "\n", + "https://medium.com/@seehleung/basic-calculus-explained-for-machine-learning-c7f642e7ced3\n", + "\n", + "https://blog.demir.io/understanding-gradient-descent-266fc3dcf02f" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 0312080b6deae133e76ee38726390fdba4170522 Mon Sep 17 00:00:00 2001 From: Maria Pais <145993408+Finarosalina@users.noreply.github.com> Date: Thu, 6 Mar 2025 19:24:07 +0000 Subject: [PATCH 4/6] avance proyecto --- notebook/problems.es.ipynb | 386 +++++++++++++++++++++++++++++++------ notebook/problems.ipynb | 184 +++++++++++++----- 2 files changed, 465 insertions(+), 105 deletions(-) diff --git a/notebook/problems.es.ipynb b/notebook/problems.es.ipynb index 5ced765e..e56ed74a 100644 --- a/notebook/problems.es.ipynb +++ b/notebook/problems.es.ipynb @@ -4,6 +4,12 @@ "cell_type": "markdown", "id": "5dbe7b9e", "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "6d9bb464", + "metadata": {}, "source": [ "# Problemas de Cálculo y Álgebra" ] @@ -43,35 +49,140 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 61, "id": "bb3e954e", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# importa las librerías\n", - "\n", - "\n", - "# Define la función de distancia" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "dbc4c780", - "metadata": {}, - "outputs": [], - "source": [ - "# \"Graficar la función de distancia en el dominio (t)" + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "tiempo=10 # segundos\n", + "distancia =25 #metros\n", + "# distancia = velocidad *tiempo\n", + "#velocidad = d / t = 25/10 = 2.5\n", + "distancia=2.5*tiempo\n", + "\n", + "# Define la función de distancia\n", + "\n", + "def func_distancia(t):\n", + " return 2.5*t\n", + "\n", + "# \"Graficar la función de distancia en el dominio (t)\n", + "t=np.linspace(0,10,500)\n", + "d=func_distancia(t)\n", + "plt.xlabel('Tiempo (s)')\n", + "plt.ylabel('Distancia (m)')\n", + "plt.title('Distancia vs Tiempo')\n", + "plt.grid(True)\n", + "plt.plot(t,d,label='Distance (m)', color='green')\n", + "\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 56, "id": "4c4d4f20", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "
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tiempo(s)distancia (m)
00.000000.000000
10.020040.050100
20.040080.100200
30.060120.150301
40.080160.200401
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" + ], + "text/plain": [ + " tiempo(s) distancia (m)\n", + "0 0.00000 0.000000\n", + "1 0.02004 0.050100\n", + "2 0.04008 0.100200\n", + "3 0.06012 0.150301\n", + "4 0.08016 0.200401" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "# Crea un DataFrame" + "# Crea un DataFrame\n", + "data={\n", + " \"tiempo(s)\": t, \"distancia (m)\":d\n", + "}\n", + "df=pd.DataFrame(data)\n", + "df.head()" ] }, { @@ -103,19 +214,130 @@ "execution_count": null, "id": "ec1f8bd7", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# Define y grafica la función cuadrática" + "# Define y grafica la función cuadrática\n", + "#distancia=25=0.5*a*10**2 -->a= 0.5 ; distancia (d)=0.25*t**2 --> velocidad(v) =0.5*t\n", + "\n", + "def fun_velocidad(t): return 0.5**t # esta en realidad no la piden ya que dicen la función cuadrática\n", + "\n", + "def fun_cuad_distancia(t):\n", + " return 0.25*t**2\n", + "\n", + "t=np.linspace(0,10,500)\n", + "d=fun_cuad_distancia(t)\n", + "plt.xlabel('Tiempo (s)')\n", + "plt.ylabel('Distancia (m)')\n", + "plt.title('Distancia vs Tiempo con aceleración')\n", + "plt.grid(True)\n", + "\n", + "\n", + "plt.plot(t,d,label='Distance (m)', color='blue')\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 65, "id": "ba5c497b", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
tiempo(s)distancia (m)
00.000000.000000
10.020040.050100
20.040080.100200
30.060120.150301
40.080160.200401
\n", + "
" + ], + "text/plain": [ + " tiempo(s) distancia (m)\n", + "0 0.00000 0.000000\n", + "1 0.02004 0.050100\n", + "2 0.04008 0.100200\n", + "3 0.06012 0.150301\n", + "4 0.08016 0.200401" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "# Crea un DataFrame" + "# Crea un DataFrame\n", + "data2={\n", + " 'Tiempo (s)': t, 'Distancia (m)': d\n", + "}\n", + "df2=pd.DataFrame(data)\n", + "df2.head()" ] }, { @@ -193,7 +415,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": null, "id": "4ff7e11a", "metadata": {}, "outputs": [], @@ -225,20 +447,18 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": null, "id": "633a54fd", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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", + "image/png": 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", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -305,7 +523,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": null, "id": "2bdd54f1", "metadata": {}, "outputs": [], @@ -347,7 +565,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": null, "id": "0350981e", "metadata": {}, "outputs": [ @@ -367,7 +585,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": null, "id": "f8e01e2d", "metadata": {}, "outputs": [ @@ -396,7 +614,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": null, "id": "b699d1fb", "metadata": {}, "outputs": [ @@ -415,20 +633,18 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": null, "id": "0b76ee22", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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3bx7UarX5FhISYunYLaK+6f58IItzohARUbOsqvsl957ebaBU2O+1LhZ/ZytXrsSPP/6IZcuW4cCBA1iyZAk+/PBDLFmypNmvOXv2bGi1WvMtMzPTgolbTlyXALirlMgqrsKedM6JQkRETVNQXoNtqfkAgHv72O/pHcAKBeXFF180H0Xp3r07HnroIcycORPz5s0DAAQEmFZazMvLa/C8vLw882OXU6lU8PDwaHCzRc6Ol8yJsp+neYiIqGnWHjwPvVFAz2A1OmncxY5jVRYvKJWVlZDLG76sQqGA0WgEAISHhyMgIABbt241P15aWorExETExMRYOo7k1J/m+f1oDsqqa0VOQ0REtkIQBPMYxnv72uZQh6aweEEZM2YM3n77bfz22284e/Ys1qxZg48++gh33303ANMltzNmzMBbb72FdevWITk5GVOmTEFQUBDGjRtn6TiSExXiiXZ+rqiuNeL35Byx4xARkY04ll2K1NwyOCrluMtO5z65lNLSLzh//ny89tprePrpp5Gfn4+goCA88cQTmDNnjnmbl156CRUVFXj88cdRUlKCW265BRs3boSTk5Ol40iOTCbDhD4heG9jKlbtz8L9/ULFjkRERDZg1X7T+Mu4LhqoXRxETmN9MuHSKV5tRGlpKdRqNbRarU2OR8krrUbMvK0wCsC2f92GcF9XsSMREZGE1egNiH5nK0oqa7Hk0f42e3lxUz6/7ff6JAnTeDhhcN0/rtVJtnlFEhERtZytKfkoqaxFgIcTbungK3acFsGCIpL6y8N+TjKtRklERHQ19ad37undBgq5TOQ0LYMFRSR3dNHA08UBuaXV+OfkBbHjEBGRROVqq7H9hOlzwt7nPrkUC4pIVEoFxvUyLSC4cj9P8xARUeN+PpAFowD0b+uNdn5uYsdpMSwoIrqv7jr2zcfzUFheI3IaIiKSGqNRMP8Se18/+5/75FIsKCLqEuSB7m3UqDUIWFO3MiUREVG9xPQinCushJtKiZHdG59t3V6xoIisvhGv3J8JG7zim4iIrKj+6MmYnoFwcbT41GWSxoIisrt6BkGllONEXjkOZZaIHYeIiCRCW1VrnnH8vlYwtf3lWFBEpnZ2wMjugQA4WJaIiC5adzgbNXojOmnc0CvEU+w4LY4FRQLqFxBcfzgHlTq9yGmIiEgK6uc+ua9vCGSy1jH3yaVYUCRgQLgPQr1dUF6jx+/JuWLHISIikaXklOJIlhYOChnujmojdhxRsKBIgFwuw311R1FW7uNpHiKi1m5F3WdBbKQGPm4qkdOIgwVFIu7tEwK5DNh7tghnLpSLHYeIiERSozdg7SHT1BOtbe6TS7GgSESA2sm8OuXK/VkipyEiIrFsOpaHkspaBKqdMLijba5abAksKBJyf79QAMDqpCzUGowipyEiIjEs35cBAJjQJ7jVLAzYGBYUCRkW6Q9fNxUKymuwNSVP7DhERNTCzhVWYNepQshkrfv0DsCCIikOCrn5kuNlezlYloiotVleNzj21o5+CPZyETmNuFhQJGZiXWP+5+QFZBZVipyGiIhaSq3BiFV1YxAntfKjJwALiuSE+bhiUAcfCMLFSXqIiMj+bU3JR0F5DXzdVIjtohE7juhYUCRoYt1g2ZX7s6DnYFkiolahfnDsvX2C4aDgxzO/AhIU11UDLxcH5JZWY/uJC2LHISIiKztfUmX+eT+Rp3cAsKBIkkqpwPjepsGyP+3NEDkNERFZ24p9mRAEIKadD9r6uoodRxJYUCRqYn/TaZ6/UvORq60WOQ0REVmLwSiYxxxOig4VOY10sKBIVAd/N/Rv6w0jB8sSEdm17SfykaOthpeLA4Z35eDYeiwoEjaxv+k85PJ9mTAaBZHTEBGRNfxUN+/VPb2DoVIqRE4jHSwoEjayeyA8nJQ4X1KFHSc5WJaIyN7kaqvxV2o+AA6OvRwLioQ5OSgwvk/dzLKJHCxLRGRvVuzLhMEooH+4Nzpq3MWOIyksKBI3uW7A1NbUfORoq0ROQ0RElqI3GM1zn0zm4NgrsKBIXAd/d/QP94bBKGDFPg6WJSKyF9vSLiBHWw1vV0eM6BYgdhzJYUGxAfXNesW+TM4sS0RkJ5YlngMATOjDwbGNYUGxASO6BcDb1RE52mpsS+NgWSIiW5dZVIm/62aOndSfp3caw4JiA1RKBSbUDZb9sa5xExGR7Vq+LwOCANzSwZczx14FC4qNqG/Y209cQGZRpchpiIiouWoNRqzYlwWAg2OvhQXFRrT1dcWtHX0hCBdXvCQiItuz+XgeCspr4OeuQmwXzhx7NSwoNuSB/vWDZbOg03OwLBGRLao/VX9/3xA4KPgxfDX8ytiQ2C4a+LmrUFBeg83H88SOQ0RETZReUIFdpwohk11czoQax4JiQxwUcvNUyEv3cLAsEZGtqb+0+LZOfgj2chE5jbSxoNiYif1DIZcBCWcKcSq/TOw4RER0g6prDVi53zQ49qGYMJHTSB8Lio1p4+mMYZGmQVVL93CwLBGRrVh3OBvaqloEezljSCd/seNIHguKDZpS17x/TspCRY1e5DRERHQj6k/NPzggDAq5TOQ00seCYoMGtfdFuK8rymr0+PVQtthxiIjoOg5nluBIlhaOSjnu68vBsTeCBcUGyeUy8+Q+3yechSAIIiciIqJr+T7BdPRkdPdAeLs6ipzGNrCg2KgJfULg5CBHam4Zks4Vix2HiIiuorhCh/VHTEe7H+Tg2BvGgmKj1C4OGNuzDQDgB15yTEQkWauSMqHTG9GtjQeiQjzFjmMzWFBsWP1lar8n56CgvEbkNEREdDmjUTBfcfnQgDDIZBwce6NYUGxYtzZq9ArxRK1BwIp9mWLHISKiy2w/eQEZRZXwcFLirrqj3nRjWFBsXP0lxz/uOQeDkYNliYikZGnd4NgJfUPg7KgQOY1tYUGxcSPrRoRna6uxJYXr8xARSUVGYSX+SssHAPOVl3TjWFBsnJODAvfXrc+zZPdZccMQEZHZD3vOQhCAwZ380M7PTew4NocFxQ48OCAMchmw+3QhTuRxfR4iIrFV6vTmsYEPD+Slxc3BgmIH2ng6I65LAAAeRSEikoK1B7NRWq1HmI8LbuO6O83CgmInpg5sCwD45cB5aKtqxQ1DRNSKCYJg/mXxoQFhkHPdnWZhQbETA9p5o7PGHVW1Bqzaz0uOiYjEsudMEdLyyuDsoMAErrvTbCwodkImk5mPovyw5xyMvOSYiEgU9UdP7undBmpnB3HD2DAWFDsyLioIHk5KnCusxN8n8sWOQ0TU6pwvqcKm47kALp56p+ZhQbEjLo5K8yXHi3dzfR4iopa2dM85GAVgYHsfdNK4ix3HplmloJw/fx4PPvggfHx84OzsjO7du2P//v3mxwVBwJw5cxAYGAhnZ2fExsbi5MmT1ojS6jw0oC1kMmDHiQs4faFc7DhERK1Gda0By/ea1t3h0ZObZ/GCUlxcjEGDBsHBwQF//PEHjh8/jv/+97/w8vIyb/P+++/js88+w4IFC5CYmAhXV1cMHz4c1dXVlo7T6oT6uGBYhOmSth8SeBSFiKilrDucjeLKWrTxdEZspEbsODZPaekXfO+99xASEoJFixaZ7wsPDzf/vyAI+OSTT/Dqq69i7NixAIDvv/8eGo0Ga9euxcSJEy0dqdWZOrAttqTkY3VSFl6I6wR3Jw7SIiKyJkEQsHjXWQCmleYVvLT4pln8CMq6devQt29fTJgwAf7+/oiKisLXX39tfjw9PR25ubmIjY0136dWqxEdHY2EhIRGX7OmpgalpaUNbnR1t3TwRUd/N5TX6LFyf5bYcYiI7F5iehGO55TCyUGOif14abElWLygnDlzBl9++SU6duyIP//8E0899RSee+45LFmyBACQm2sa3azRNDz8pdFozI9dbt68eVCr1eZbSAh3/rXIZDI8Msh01Grx7nSuckxEZGXf7UwHAIzvHQxPF0eR09gHixcUo9GI3r1745133kFUVBQef/xxPPbYY1iwYEGzX3P27NnQarXmW2YmJyK7nruj2sDTxQGZRVVc5ZiIyIoyCiuxue7n7COD2oobxo5YvKAEBgaiS5cuDe6LjIxERoZpZHNAgGnNmLy8hh+aeXl55scup1Kp4OHh0eBG1+bsqMAD/U3Le9c3eyIisrzFu02rFg/p5IcO/ry02FIsXlAGDRqEtLS0BvedOHECYWGm1RzDw8MREBCArVu3mh8vLS1FYmIiYmJiLB2nVXsoJgxKuQyJ6UU4el4rdhwiIrtTVl2LlXXLizx6S/h1tqamsHhBmTlzJvbs2YN33nkHp06dwrJly/DVV18hPj4egGl8xIwZM/DWW29h3bp1SE5OxpQpUxAUFIRx48ZZOk6rFqh2xsjugQCARXWjy4mIyHJW7c9CeY0eHfzdMLijr9hx7IrFC0q/fv2wZs0a/PTTT+jWrRvefPNNfPLJJ5g8ebJ5m5deegnPPvssHn/8cfTr1w/l5eXYuHEjnJycLB2n1atv9OsPZ+NCWY3IaYiI7IfBKGBJwlkAprEnMhkvLbYkmSAINneJR2lpKdRqNbRaLcej3IB7/rcLBzJKMCO2I2bEdhI7DhGRXdh8PA+Pfb8famcH7Jk9DM6OCrEjSV5TPr+5Fk8rUH8UZemec6jRG0ROQ0RkH+ovQHggOpTlxApYUFqBEV0DEKR2QkG5Dr8eyhY7DhGRzTueXYqEM4VQyGWYEhMmdhy7xILSCigVckypW7jqu53psMGzekREkvLNP2cAACO7ByJQ7SxyGvvEgtJKTOofCldHBVJzy/DPyQKx4xAR2axcbTXWHTYdjX7sVl5abC0sKK2E2tkB99WtD/F1XfMnIqKmW7z7LPRGAf3DvdEj2FPsOHaLBaUVeXRQOOQy4J+TBUjN5YKLRERNVVGjx7LEcwCAx25tJ3Ia+8aC0oqEeLvgzm6midu++YfT3xMRNdXK/Zkordajna8rhkX4ix3HrrGgtDLT686X/nroPPJLq0VOQ0RkOwxGAd/tMv1y9+gt4ZDLOTGbNbGgtDJRoV7oG+aFWsPFGRCJiOj6/jyWi8yiKni5OGB872Cx49g9FpRWaHrdedOlezJQqdOLnIaIyDbUX2Dw0IAwTszWAlhQWqE7umgQ5uMCbVUtVidliR2HiEjyks4V4WBGCRwVcjwU01bsOK0CC0orpJDL8Ogg01iUb3emw2DkxG1ERNfy9Q7T2JNxUUHwc1eJnKZ1YEFppSb0DYaniwPOFVbiz2O5YschIpKsMxfK8edx089JXlrcclhQWikXRyWm1B2mXLj9NKe/JyK6iq//SYcgALGR/uiocRc7TqvBgtKKTY0Jg0opx+EsLfacKRI7DhGR5OSXVePnA6axek8MaS9ymtaFBaUV83FT4b6+punvF+44LXIaIiLpWbL7LHR6I3qHeqJvmJfYcVoVFpRWbvqtpunv/067gJQcTn9PRFSvvEaPHxJM09o/MaQ9ZDJOzNaSWFBauTAfV9zZ3TT9/dc7uIggEVG95XszzNPa3xGpETtOq8OCQnhisGlU+rrD2ThfUiVyGiIi8dUajPh2p+nS4scHt+O09iJgQSH0CPbEwPY+0BsFfMtFBImIsO5QNnK01fBzV2FcVBux47RKLCgE4OLo9OX7MlBSqRM5DRGReARBMF848MigtnBy4LT2YmBBIQDA4I6+iAz0QKXOYB4URkTUGm1Ly8eJvHK4qZSYHB0mdpxWiwWFAAAymQxPDjGNRVm0+ywXESSiVkkQBHyxzXT05IHoUKidHURO1HqxoJDZqO6BCPV2QVGFDsv3Zoodh4ioxe1NL0LSuWI4KuWYfku42HFaNRYUMlMq5Hii7ijK1/+cgU5vFDkREVHL+t/fpqMn9/YJhr+Hk8hpWjcWFGpgfO9g+LurkKOtxtqD58WOQ0TUYo6e12L7iQuQy4AnB3Nae7GxoFADTg4KTL/VdFhzwfbTMBi5iCARtQ5f1h09GdMzCKE+LiKnIRYUusID0WFQOzvgTEEFNh7NFTsOEZHVnb5Qjt+P5gAAnrqNR0+kgAWFruCmUmLqwLYAgP/9fQqCwKMoRGTfFm4/DUEAYiP9ERHgIXYcAgsKXcUjA9vCxVGBY9ml2H7igthxiIisJrukCr8cMI25e/r2DiKnoXosKNQoL1dHTOofCgD4X92cAERE9ujrf85AbxQwoJ03eod6iR2H6rCg0FU9dms7OCrk2Hu2CHvTi8SOQ0RkcQXlNfhpbwYA4OnbePRESlhQ6KoC1E64t28wAGD+XydFTkNEZHlf/3MG1bVG9AzxxK0dfcWOQ5dgQaFrempIeyjlMvxzsgAHM4rFjkNEZDHFFTrz2mPPDe0AmUwmciK6FAsKXVOItwvurltqfP5fp0ROQ0RkOd/tSkelzoCuQR4YGuEvdhy6DAsKXVf87R0glwF/pebj6Hmt2HGIiG6atqoWi3edBQA8y6MnksSCQtfV1tcVd/UMAsCxKERkH5bsPouyGj06a9wR1yVA7DjUCBYUuiHPDO0AmQz481geUnNLxY5DRNRs5TV6fLcrHQAQP7QD5HIePZEiFhS6IR383TGyWyAA4HOORSEiG/ZDwjmUVNainZ8rRnUPFDsOXQULCt2wZ4aa5gj4LTkHp/LLRU5DRNR0lTo9vvnnDADgmds7QMGjJ5LFgkI3LDLQA3d00UAQgM85FoWIbNCPezJQWKFDmI+LeWwdSRMLCjXJ88M6AgDWHc7mURQisimVOj0WbDct3RF/WwcoFfwIlDLuHWqSbm3UiI3UwCgAn23lURQish0/JJxDYYUOod4uuLt3G7Hj0HWwoFCTzYg1HUVZfyQbp/LLRE5DRHR9lTo9Fu4wjT15dmgHOPDoieRxD1GTdWujRlzdWJRPt/KKHiKSvu8TzqGoQoe2PhdnxyZpY0GhZpkR2wkAsOFINk7k8SgKEUlXRY0eX5mPnnTk2BMbwb1EzdIlyAMjugbUHUXhWBQikq4lCWdRVKFDuK8rxvbilTu2ggWFmu35urEovyfnIC2XR1GISHrKGxw94ZU7toR7ipotMtADI7vXH0U5IXYcIqIrLNl91jRr7CVripFtYEGhm/L8MNNYlN+Tc3E8m2v0EJF0lFbXmo+ePDeMY09sDfcW3ZTOAe4Y3cO0lsVHm9NETkNEdNE3/6RDW1WLDv5uGMOjJzaHBYVu2sw7OkEuA7ak5ONARrHYcYiIUFShw7d1a+7MuqMT19yxQSwodNPa+7lhfO9gAMBHmzgWhYjEt3D7aVToDOhad8Uh2R4WFLKI54Z1hINChp2nCpCw7SCQmAikpQHFPKJCRC0rv7QaSxLOAgD+FdcZch49sUksKGQRId4umBjpDQD48NstEAYMACIigIkTgcxMkdMRUWvy+bZTqK41ok+YF27r7Cd2HGomFhSyjOJiPPPT+1DV1iApuAv+btfXdP+mTcD06TySQkQtIrOoEj/tzQAAvBDXCTIZj57YKqsXlHfffRcymQwzZsww31ddXY34+Hj4+PjAzc0N48ePR15enrWjkDXl5UHz+xpMPbABAPDhrQ/CiLofDJs2Ady/RNQCPtt6ErUGAYM6+GBge1+x49BNsGpB2bdvHxYuXIgePXo0uH/mzJlYv349Vq1ahe3btyM7Oxv33HOPNaOQtWm1AIAnE3+Ga00ljgV0wMbOA694nIjIWs5cKMfPB7IAmMaekG2zWkEpLy/H5MmT8fXXX8PLy8t8v1arxbfffouPPvoIQ4cORZ8+fbBo0SLs3r0be/bssVYcsja1GgDgXVWKaft/BWA6iqKXyRs8TkRkLf/ddAJGAYiN9EdUqNf1n0CSZrWCEh8fj1GjRiE2NrbB/UlJSaitrW1wf0REBEJDQ5GQkNDoa9XU1KC0tLTBjSRGowHi4gAA0/eugVelFmd8QrC6e6zpfo1G5IBEZM+OZJXgt+QcyGTAv4bz6Ik9sEpBWb58OQ4cOIB58+Zd8Vhubi4cHR3h6enZ4H6NRoPc3NxGX2/evHlQq9XmW0hIiDVi083w8gK++QaIi4OHrhLxCSsBAJ8MexTVC74yPU5EZCXvbUwFANwd1QYRAR4ipyFLsHhByczMxPPPP48ff/wRTk5OFnnN2bNnQ6vVmm+ZvGxVmkJCgOXLgZQUPPjpK2jjqkSuoxsWZ+jFTkZEduyfkxew61QhHBVyzLqjk9hxyEIsXlCSkpKQn5+P3r17Q6lUQqlUYvv27fjss8+gVCqh0Wig0+lQUlLS4Hl5eXkICGh8tj+VSgUPD48GN5IoLy8gIgJOAwdg5siuAID/bTsFbWWtyMGIyB4ZjQLe/cN09OTBAWEI9nIRORFZisULyrBhw5CcnIxDhw6Zb3379sXkyZPN/+/g4ICtW7ean5OWloaMjAzExMRYOg6J6O6oNuiscUdptR5fbj8tdhwiskMbknNwLLsUbiolnhnaQew4ZEFKS7+gu7s7unXr1uA+V1dX+Pj4mO+fNm0aZs2aBW9vb3h4eODZZ59FTEwMBgwYYOk4JCKFXIaXRnTGtCX7sWhXOh4e2BYBasuc9iMi0umN+O8m0yrqjw9uB29XR5ETkSWJMpPsxx9/jNGjR2P8+PEYPHgwAgIC8Msvv4gRhaxsaIQ/+rX1Qo3eiE+2cCFBIrKcFfsycK6wEr5uKky7JVzsOGRhMkEQBLFDNFVpaSnUajW0Wi3Ho9iApHNFGP9lAuQyYNPMwejg7y52JCKyceU1etz2wd8oKK/BG2O7YkpMW7Ej0Q1oyuc31+Ihq+sT5o07umhgFGAezEZEdDO+2n4aBeU1CPNxwcR+oWLHIStgQaEW8cqdEVDIZdiSko+E04VixyEiG5arrcZX/5wBALwyIgKOSn6U2SPuVWoR7f3cMDna9FvOO7+nwGi0uTOLRCQRH21OQ3WtEX3CvDCiW+PTU5DtY0GhFvP8sI5wUymRfF6LdYezxY5DRDYoJacUq5JMCwL+e2QkZDKZyInIWlhQqMX4uKnw1G3tAQAf/JmG6lqDyImIyNbM+yMVggCM6h6IPmFcQsOesaBQi5p2SzgC1U44X1KFRbvOih2HiGzI9hMXsOPEBTgoTHMskX1jQaEW5eSgwL/iTD9Y/rftFIoqdCInIiJbYDAKmPd7CgDgoQFtEebjKnIisjYWFGpxd0e1QZdAD5TV6PEpJ28johvwc1IWUnPL4OGkxLOc0r5VYEGhFieXy/DqqEgAwNLEDJzKLxM5ERFJWXmNHh/UTWn/zNAO8OKU9q0CCwqJYmAHX8RGamAwCnhzQ4rYcYhIwv637RQulJkmZZs6sK3YcaiFsKCQaP5vVCQcFDJsP3EB21LzxY5DRBKUWVSJb3amAwD+b2QkVEqFyImopbCgkGjCfV3xyCDTAl9v/nYctQajyImISGrm/ZECnd6IQR18cEcXjdhxqAWxoJConhnaAT6ujjhzoQI/JJwTOw4RScieM4X4PTkXchnw2ugunJStlWFBIVF5ODnghbrLjj/ZcgLFvOyYiIC68WnHAQCT+ociIoAr17c2LCgkuvv7hSAiwB2l1Xp8zMuOiQjA6qRMHMsuhbuTErPu6CR2HBIBCwqJTiGXYc6YLgCAHxMzkJbLy46JWrOy6lp88Kfpl5Xnh3WEj5tK5EQkBhYUkoSB7X0xvKvpsuP/rDsGQeBqx0St1adbTqKgvAbhvq6YEtNW7DgkEhYUkoxXR3WBSilHwplC/JacI3YcIhLBibwyLNp9FgAwd0wXOCr5MdVacc+TZIR4u5hXO377txRU6vQiJyKiliQIpiOoBqOAO7pocFtnf7EjkYhYUEhSnhzSHsFezsjRVuOLbafEjkNELeiPo7nYfboQjko55ozuInYcEhkLCkmKk4MCr9X9YPp6RzrSCypETkRELaFSp8dbdZcVPzmkPUK8XURORGJjQSHJieuiweBOftAZjHh9PQfMErUG/9t2GtnaarTxdMZTQ9qLHYckgAWFJEcmk2HumC5wUMjwd9oFbE3hOj1E9uxsQQW+2nEGgGnGWGdHrrdDLCgkUe393DDtlnYAgNc3HEOVziByIiKyBkEQ8J/1x6AzGHFrR9N0A0QACwpJ2LNDOyBQ7YTMoioOmCWyUxuP5uLvtAtwUMjwn7u6cr0dMmNBIclyVSkxt26G2YU7TuNUfrnIiYjIkspr9Hh9/cWBse393ERORFLCgkKSNrxrAIZG+KPWIODVtckcMEtkRz7efAK5pdUI9XZB/O0dxI5DEsOCQpImk8nw+l1d4eQgx54zRVh76LzYkYjIAo5nl2Jx3Yyxb4ztCicHDoylhlhQSPJCvF3w7NCOAEwzzGora0VOREQ3w2gU8H9rk2EwChjVPZAzxlKjWFDIJjx2azt08HdDQbkO7/+ZKnYcIroJy/dl4mBGCVwdL07MSHQ5FhSyCY5KOd4c2w0AsGxvBg5mFIuciIiao6C8Bu9tNP2SMSuuMwLUTiInIqliQSGbEdPeB/f0bgNBAGb/koxag1HsSETURG+sPw5tVS26BHpgakyY2HFIwlhQyKa8OqoLvF0dkZpbZp55kohsw7bUfKw7nA25DHhvfA8oFfwIoqvjvw6yKd6ujuZVTj/dehJnLnBuFCJbUFGjx6trjwIApt0Sju7BapETkdSxoJDNGdsryLSYoN6I2b8kw2jk3ChEUvfhpjScL6lCsJczZt7RSew4ZANYUMjmyGQyvD2uG5wdFEhML8KK7WlAaiqQmAikpQHFHEBLJCUHM4rNc568c3d3uDgqxQ1ENoEFhWxSiLcLXogz/Rb2zm/Hkd93IDBgABARAUycCGRmipyQiABApzfilZ+TIQjAPVFtMLiTn9iRyEawoJDNeqSLJ3pW5KJMqcKcO568+MCmTcD06TySQiQBX+04jbS8Mni7OuJVznlCTcCCQjZLcSEf81a8DaVBj42dB+G3zoMuPrhpE5CXJ144IsKJvDJ8ttW0Evmc0aYr8IhuFAsK2S6tFl0upOPpPasAAHPueAqFzh4NHicicegNRry46jB0BiOGRfhjbK8gsSORjWFBIdulNl2m+MzuFYjIT0ehqyfmXnqqR83LGInE8vU/6TicpYWHkxLv3NMdMplM7EhkY1hQyHZpNEBcHByNenzw+ydQGA3YEDkYf3QaCMTFmR4nohZ3Mq8MH28+AQCYM6YrNB6czp6ajgWFbJeXF/DNN0BcHLrnncZTdad6Xhs9A0XzF5geJ6IWpTcY8a/VR6AzGDE0wh/je7cROxLZKBYUsm0hIcDy5UBKCp59Nx6dPB1Q4OCCuUklYicjapW+2ZmOw5klcHdS4p27eWqHmo8FhWyflxcQEQHVwAH48MH+UMhlWH84GxuP5oidjKhVOZVfho/qT+2M7sKViummsKCQXekR7IknBrcDAPx7zVHkl1WLnIiodag1GDFzxWHo9Ebc1tkP9/YJFjsS2TgWFLI7z8d2RESAO4oqdJj9czIEgWv1EFnb/K0nkXxeC08XB7w3vgdP7dBNY0Ehu6NSKvDJxF5wVMixNTUfK/Zx2nsiazqYUYwv/j4NAHhrXDdetUMWwYJCdikiwMO8Vs+bG44jo7BS5ERE9qlSp8eslYdhMAoY2ysIo3twQjayDBYUslvTb22H/m29UaEzYNbKQzAYeaqHyNLm/Z6K9IIKBHg44Y27uokdh+wICwrZLYVchv/e1xOujgrsP1eMr3acETsSkV3ZfuICfthzDgDw4YSeULs4iJyI7AkLCtm1EG8XzB3TFQDw0eY0HD3P9XmILKGoQocXVx0GADw8sC1u6egrciKyNywoZPcm9A1GXBcNag0CnvvpICpq9GJHIrJpgiDgpdWHkV9Wgw7+bnh5RITYkcgOsaCQ3ZPJZHhvfA8EeDjhTEEFXl9/TOxIRDbt+4Rz2JKSD0eFHJ9NjIKzo0LsSGSHWFCoVfBydcRH9/eETAas3J+FDUeyxY5EZJNSckrx9u8pAIDZIyPQJchD5ERkr1hQqNUY2N4XT9/WHgAw+5dkZBbx0mOipqjSGfDcTweh05sWAnx4YFuxI5Eds3hBmTdvHvr16wd3d3f4+/tj3LhxSEtLa7BNdXU14uPj4ePjAzc3N4wfPx55eXmWjkJ0hRmxndArxBNl1XrMWHEIeoNR7EhENuOt347jZH45/NxV+OBezhZL1mXxgrJ9+3bEx8djz5492Lx5M2praxEXF4eKigrzNjNnzsT69euxatUqbN++HdnZ2bjnnnssHYXoCg5158zdVEoknSvGZ1tPih2JyCZsPJqLHxMzAAAf3dcTPm4qkRORvZMJVl6o5MKFC/D398f27dsxePBgaLVa+Pn5YdmyZbj33nsBAKmpqYiMjERCQgIGDBhw3dcsLS2FWq2GVquFhwfPf1LT/XroPJ5ffggyGfD9o/1xa0c/sSMRSVZGYSVGzf8HZdV6PDG4HWaPjBQ7Etmopnx+W30MilZrmnfC29sbAJCUlITa2lrExsaat4mIiEBoaCgSEhIafY2amhqUlpY2uBHdjLG92mBS/xAIAjBj+SHklXLVY6LG1OgNiF92AGXVevQO9cS/hncWOxK1ElYtKEajETNmzMCgQYPQrZtpCuTc3Fw4OjrC09OzwbYajQa5ubmNvs68efOgVqvNt5CQEGvGplZi7piuiAz0QGGFDs/+dJDjUYga8c5vKUg+r4WXiwM+f6A3HBS8toJahlX/pcXHx+Po0aNYvnz5Tb3O7NmzodVqzbfMTK5OSzfPyUGB/03uDTeVEnvTi/DR5hNiRyKSlA1HsrEkwTSV/Uf390KQp7PIiag1sVpBeeaZZ7BhwwZs27YNwcHB5vsDAgKg0+lQUlLSYPu8vDwEBAQ0+loqlQoeHh4NbkSWEO7rinfHdwcA/O/v09iWli9yIiJpSC+owCs/JwMAnrqtPW7v7C9yImptLF5QBEHAM888gzVr1uCvv/5CeHh4g8f79OkDBwcHbN261XxfWloaMjIyEBMTY+k4RNc1ukcQHhoQBgCYteIQzpdUiZyISFzVtQbE/3gA5TV69G/rjRfu6CR2JGqFLF5Q4uPjsXTpUixbtgzu7u7Izc1Fbm4uqqpMP/TVajWmTZuGWbNmYdu2bUhKSsIjjzyCmJiYG7qCh8gaXh0die5t1CiurMVTS5NQXWsQOxKRKARBwL9/ScbxnFL4uDris0lRUHLcCYnA4v/qvvzyS2i1Wtx2220IDAw031asWGHe5uOPP8bo0aMxfvx4DB48GAEBAfjll18sHYXohqmUCnz5YG94uTjgSJYWr609CitfgU8kSd8nnMMvB89DIZdh/gNRCFA7iR2JWimrz4NiDZwHhaxl58kCTPkuEUYBePvubpgcHSZ2JKIWsze9CA98vQd6o4BXR0Vi+q3txI5EdkZS86AQ2ZJbOvripbql4/+z7hiSjmYAqalAYiKQlgYUF4uckMg68kqr8fSPB6A3ChjTMwjTbgm//pOIrIgFhegyTwxuh5HdA1BrEPD0dwnI7xsDDBgAREQAEycCvMyd7IxOb8RTS5NQUF6DiAB3vDe+O9fZIdGxoBBdRiaT4f1hYehYVYg8Rzc8PW42ahRK04ObNgHTp/NICtkNQRAwd91RHMgogYeTEgsf6gMXR6XYsYhYUIga41ZSgIU/zIZ7dTn2B3fFq3HxMA/W2rQJ4OrbZCcW7z6Ln/ZmQiYDPp0YhTAfV7EjEQFgQSFqnFaLdsXZ+OLX9yA3GrCqxx34pt/dDR4nsnU7TlzAmxuOAwD+fWckbo/gZGwkHSwoRI1RqwEAg88exGt/fQMAeOf2R7CtXd8GjxPZqlP55YhfdgBGAZjQJxjTb+WgWJIWFhSixmg0QFwcAODhpPWYdOgPCDI5nr3rJZy4a6LpcSIbVVKpw/Ql+1BWrUffMC+8dXc3DoolyWFBIWqMlxfwzTdAXBxkAF7fvBDRGckoV7lgWvSjKHRwETshUbPUGoyIX3YAZwsr0cbTGQse6gOVUiF2LKIrsKAQXU1ICLB8OZCSAsfdO7HgpTEI9VQhs1SH6d/v53T4ZHPqp7HfdaoQLo4KfDO1L3zdVGLHImoUCwrRtXh5meY/iY6GV6+u+O7RAVA7O+BgRgmeX34QBqPNTcRMrdhnW09hVVIW5DLg8weiEBnImbhJulhQiJqgg78bvnqoDxwVcvx5LA9v/5YidiSiG7I6KQsfbzkBAHhzXDcMjeA4KpI2FhSiJopu54MP7+sJAPhuVzq+3ZkuciKia9t5sgCv/HwEAPDUbe25xhTZBBYUoma4q2cQXq5bs+et345j49EckRMRNS41txRPLU0yr7HzYlxnsSMR3RAWFKJmenJIO0yODoUgAM8tP4SE04ViRyJqILOoElO+3YuyGj36h3vjwwk9IJfzcmKyDSwoRM0kk8nw+l1dcUcXDXR6Ix77fj+OnucMsyQNF8pq8OC3icgvq0FnjTu+4uXEZGNYUIhuglIhx/xJUYgO90Z5jR5Tv9uLMxfKxY5FrZy2qhZTvtuLc4WVCPZyxvfT+sPTxVHsWERNwoJCdJOcHEzzSXRr44HCCh0e+nYvcrRVYseiVqq61oDHluxHSk4pfN0csXRaNDQeTmLHImoyFhQiC3B3csDiR/oj3NcV50uqMOXbvSiu0Ikdi1qZWoMRzyw7gL1ni+CuUmLJo/3R1perE5NtYkEhshBfNxV+mNYfAR5OOJlfjge/TYS2slbsWNRK6A1GzFhxCFtS8qFSyvHN1L7oGsRFLcl2saAQWVCwlwuWTu8PH1dHHMsuxZTvElFazZJC1mUwCvjXqsP47UgOHBQyLHiwD6Lb+Ygdi+imsKAQWVgHf3f8+Fg0vFwccDhLi0cW7UN5bgGQmgokJgJpaUBxsdgxyU4YjQJe/vkI1h7KhlIuwxcP9MbtEf5ixyK6aSwoRFYQEeCBpdOjoXZ2QNK5Yjz65i+o7NELGDDAtLbPxIlAZqbYMcnGGY0C/m9tMlYnZUEhl2H+pCjEdQ0QOxaRRbCgEFlJ1yA1fpgQCXdDDfa6t8G08XNQ6VC3cuymTcD06TySQs1mNAqYs+4oftqbCbkM+Oi+nrize6DYsYgshgWFyIp6yCuwZNm/4VZTiYSwnpg64Q2UOTqbHty0CcjLEzcg2SSDUcArvxzB0j0ZkMmAD+7tibG92ogdi8iiWFCIrEmrRe/sNHy/8jW4V5djX0hXPHj/2yhxcjM/TtQUtQYjZq44hJX7s8xHTsb3CRY7FpHFsaAQWZPadJln7+w0/LT8/+BVqcXhoE6YNPEdFDp7mB8nuhE6vWmek3WHTQNiP3+gN+6OYjkh+8SCQmRNGg0QFwcA6JZ3Gst/+jd8y4uRommH+x/7HHkuXiIHJFtRXWvAEz/sx5/H8uCokGPhQ30wkmNOyI6xoBBZk5cX8M035pLSueAcVi57GYG6Mpxy9sY9y45x7R66Lm1lLR76NhHb0i7AyUGObx/ui2GRGrFjEVmVTBAEQewQTVVaWgq1Wg2tVgsPDw+x4xBdX3GxaUCsVguo1chUqfHQ6lScLayEt6sjvnu4H3qFeIqdkiQoR1uFqd/txYm8crg7KfHt1H7oH+4tdiyiZmnK5zcLCpFICspr8OjifTiSpYWLowJfPtgHQzr5iR2LJORUfhmmfLsX2dpqaDxUWPJof0QE8Gce2a6mfH7zFA+RSHzdVPjpsQG4taMvKnUGTFu8D2sOZokdiyQi6Vwx7l2QgGxtNdr5ueLnpwaynFCrwoJCJCJXlemQ/bheQdAbBcxccRifbDkBGzywSRa07nA2Jn29ByWVtYgK9cTPTw5EsJeL2LGIWhQLCpHIHJVyfHRfLzwxpB0A4JMtJ/H88kOorjWInIxamiAI+GTLCTz300Ho9EbERvrjx+nR8HJ1FDsaUYtTih2AiAC5XIbZd0aina8r/m/NUaw7nI2Mokp8NaUP/PVVFwfYenoC/v6mq4PIrlTXGvDS6iNYdzgbAPD44HZ4eUQEFHKZyMmIxMFBskQSk3C6EE/9mISSyloEuTngm/1L0OXXZRc3iIszXbocEiJeSLKo/LJqPPFDEg5mlEApl+Gtcd0wsX+o2LGILI6DZIlsWEx7H6x5ehDaeTshu7wW97S/B2u63HZxAy40aFf2ny3C6M924mBGCdTODvh+Wn+WEyKwoBBJUrivK9YMD8CQM/tR7eCEmWP+hbmxT0Anrzsry4UGbZ4gCFi0Kx0Tv9qD/LIadNK4YW38IAxs7yt2NCJJYEEhkih1dTm+W/0GnttlOr2zpM8YTJr0DvLc6ibp4kKDNqtSp8eMFYfw+vrj0BsFjO4RiDVPD0K4r6vY0YgkgwWFSKrUaigEI2btXIZvV78Oj+pyJAV3waiHP8X28N5caNBGncgrw91f7Mavh7KhkMvw2ugumD8pCq4qXrNAdCkWFCKpumShwWGn92H9khmIyE9HgasXpt73Bt46VokaPS9FthWCIOCHPecwZv5OpOWVmSfqm3ZLOGQyXqlDdDkWFCKpumyhwbCSXKz94QVMuXAYAPDNvhyM/3I3TnOxQckrrtDh8R+S8Nrao6jRGzGkkx/+eP5WrqlDdA28zJhI6i5baBAaDTbn6PDS6sMorqyFs4MCr43ugkn9Q/ibuAT9c/ICXlx1BLml1XBQyPDyiAg8Oigccs5vQq0QFwskagVytdWYueIQEs4UAgBu7eiLefd0RzBqOLGbBJRW1+Kd31KwfF8mAKCdnys+mxiFbm04dohaLxYUolbCYBTw3c50fLgpDTV6I1wd5Pj36S144KePYP79nBO7tbi/0/Ix+5dk5GirAQBTY8Lw8p0RcHHkQFhq3VhQiFqZMxfK8dLyA9h/vgwAMPDsYby16Qu0KzZNm464OGD5ch5JsbLC8hrM+yMVq5NMq1KH+bjgvfE9MKCdj8jJiKSBM8kStTLt/NywYpgf5mz5Ck611djdtidGPPoFPrz1QVQpVZzYzcoMRgE/Jp7D0P9ux+qkLMhkwKODwvHH87eynBA1E483EtkJRVkpHk1ah2Gn92Ju7JP4u31ffD5wItZ0vR1ztn6NuJIScFim5R3OLMFrvx7FkSzTxHmRgR54a1xX9AnjFTpEN4OneIjsRWoqEBkJABAAbOo4AG8Mexzn1f4AgFuDnDH73r7oEuTR8MogDqRtlhxtFT7adAKrD2RBEAB3lRIvxHXCgwPCoFTw4DRRYzgGhag1Ki4GJk40nc6pU6VU4fOY+/DVgHtRK1dAJgPGdfTErDUfI2TDzxefy4G0N0xbWYv/bT+FxbvOokZvBADcE9UGr4yMgL+7k8jpiKSNBYWotcrMNK10fElJQVwczv33C/w3uQzrDpsGzTrqa/HQwd/w5J7V8KssMW/HgbRXV6nTY+mec/hi22loq2oBAP3beuOVkRHoHcqvGdGNYEEhas0amditvnQk7zyMdz/fgF1tewEAVLU1mHT4Tzyx92cElhUCKSlARARPAV2itLoWPyScw7c701FUoQMAdNK44eURERga4c/J8YiagAWFiBqXmAhhwADsCO+Nj295AIeCIgAADoZajD/6F558aRLadghu9ChMazsFVFheg8W7z2Lx7rMoq9YDAEK9XfDM0A4Y3zsYCs4ES9RkLChE1LjLBtLuDuuJ+TH3Y09YDwCADMBt2nRM2bQYQ84cgByX/HhoJaeAjmSVYMnuc1h/JBu6ujEmHfzd8MztHTC6RyAHwBLdBBYUImpcIwNpAWB/m0h8MeZpbFOHm+8LK87GQwd/x91H/4JPVSng6gocPgzU1trdqZ9KnR4bj+bi+4RzOJRZYr6/R7AaT9/WHnFdArh2DpEFsKAQ0dVdZSAtvvkGZ09k4od3FmFl91iUObkBAJQGPYZkHMa44VG4Y+WXcPrzj4vPu+su4LPPgKoqmystBqOA3acLsObgefx5NBcVOgMAwFEhx+gegZgysC16hXiKG5LIzrCgENG1XW0gbd0poEoHFdZ2uQ0/9RyB5MCO5qe51VQi7kQC7jiViFvz0+D2/SJTQdmyxbSBqyvw8cdATIyptHh7AzU1QFmZJMqLTm/E3vQibEnJw+/JOcgvqzE/Furtgvv6BmNi/1D4uqlEy0hkz2ymoHzxxRf44IMPkJubi549e2L+/Pno37//dZ/HgkJkJY2cAjrlE4w1//kSa4/l47xaY77fEUZEazMQu3cjBp09hPY1xZD99BPw6afAnj3Apf8/YwYwaBDg5wc4OQEKhekmkwFKJSCXAy4uQEWFqTTVH41Rq4GwsJt6S9klVdhzphBbU/Kx48QFlNXozY95ujhgdI9A3B3VBr1DvXhFDpGV2URBWbFiBaZMmYIFCxYgOjoan3zyCVatWoW0tDT4+/tf87ksKERW1NgpoPXrYRxzF/YHd8GfnWKwtX1/nPUOavA0H9SiX/FZ9E/ahj7DB6Dz3r/hlLDLVFQWLgSeeML036efBtzdTaXE19f0X09PUyl56qmLR2MAIDYW+PJLoEOHG4quNxhxpqACBzOKkZhehL3pRcgqrmqwja+bI4ZG+OOOLgEY0skPjkoOeiVqKTZRUKKjo9GvXz98/vnnAACj0YiQkBA8++yzeOWVV675XBYUIiu7/BSQ0Qh07Wp+WABw+vvV2Pr5Mmxr1xcHgzqjxqHhaRG50YBweQ0iijIR6euMtieT0aZTKNq08YWvwgh5RGfThgEBgEoFPPZYw3JSLzbWdIlz3ZEUQRCgrapFVnEVzpdUIaOwEqm5ZUjNLcXJvHLoDMaGOWRA1yA1hnTyw7BIf/QM9uSAVyKRSL6g6HQ6uLi4YPXq1Rg3bpz5/qlTp6KkpAS//vprg+1rampQU3PxXHFpaSlCQkJYUIhaSmNX/6xfD4wZAwCoUSiR/PUK7F34E/aGdMORzn1QpL96CXCUCdC4KKF2kMHdUQF3Rxk8/lgPB4O+wXYGuQJlKleUDRmKMqUTSqv1yC+tNg9obYyrowJdg9ToH+6N/uHe6B3mBTcV10UlkoKmFBRRvmsLCgpgMBig0Wga3K/RaJCamnrF9vPmzcPrr7/eUvGI6HJeXqajGJee+tmzx3R0Y8sWqAx69PVzRN/E1Xg6cTWEdetxYdJDSPn0G6R8tQxp4x9C5pE0nA+PRF6tDDpBhswKAzIBAHWlpPsdV//7c2sA1DS4y9fNEW08ndHGyxmdNO6IDPRAZIAHgr2ceYSEyA7YxK8Vs2fPxqxZs8x/rj+CQkQtKCTENFHbpVPgT59uGluyaZOpsAwbBmzdClniHvgP6A1/jSOG7P0ZeO1h4OWXgfXrUWsEcnUC8t19UForoNQgQ1mtEWUffgy9vOGPJLlghHtNJdzn/h88OrWDu5MDfN0cEeTpDCcHhShfBiJqGaIUFF9fXygUCuTl5TW4Py8vDwEBAVdsr1KpoFLxsj8i0Xl5XXmZcH1pKSsDHn4YiI8HPvnENDg2O9tUWurLy549cAgNRQiAED93wAkXx6C4a68+BqVXEBCmufIxIrJbogxfd3R0RJ8+fbB161bzfUajEVu3bkVMTIwYkYiouby8TAsM9utnutpm+XJg/35T8ai/Cic5GXj+eeDQISA42DTdvlJp2kYuN82f8uWXpu0vFRsLLFhw05caE5HtEfUy46lTp2LhwoXo378/PvnkE6xcuRKpqalXjE25HK/iIbIxxcVAfj5gMJiuCGrBeVCISDokP0gWAO6//35cuHABc+bMQW5uLnr16oWNGzdet5wQkQ1q7NRQY/z8rJ+FiGwCp7onIiKiFtGUz29OoUhERESSw4JCREREksOCQkRERJLDgkJERESSw4JCREREksOCQkRERJLDgkJERESSw4JCREREksOCQkRERJIj2lT3N6N+8tvS0lKRkxAREdGNqv/cvpFJ7G2yoJSVlQEAQkJCRE5CRERETVVWVga1Wn3NbWxyLR6j0Yjs7Gy4u7tDJpNZ9LVLS0sREhKCzMxMu1znh+/P9tn7e+T7s332/h7t/f0B1nuPgiCgrKwMQUFBkMuvPcrEJo+gyOVyBAcHW/Xv8PDwsNt/eADfnz2w9/fI92f77P092vv7A6zzHq935KQeB8kSERGR5LCgEBERkeSwoFxGpVJh7ty5UKlUYkexCr4/22fv75Hvz/bZ+3u09/cHSOM92uQgWSIiIrJvPIJCREREksOCQkRERJLDgkJERESSw4JCREREktPqCsrbb7+NgQMHwsXFBZ6eno1uk5GRgVGjRsHFxQX+/v548cUXodfrr/m6RUVFmDx5Mjw8PODp6Ylp06ahvLzcCu+gaf7++2/IZLJGb/v27bvq82677bYrtn/yySdbMPmNa9u27RVZ33333Ws+p7q6GvHx8fDx8YGbmxvGjx+PvLy8Fkp8486ePYtp06YhPDwczs7OaN++PebOnQudTnfN50l9/33xxRdo27YtnJycEB0djb17915z+1WrViEiIgJOTk7o3r07fv/99xZK2nTz5s1Dv3794O7uDn9/f4wbNw5paWnXfM7ixYuv2F9OTk4tlLhp/vOf/1yRNSIi4prPsaX919jPE5lMhvj4+Ea3t4V9t2PHDowZMwZBQUGQyWRYu3Ztg8cFQcCcOXMQGBgIZ2dnxMbG4uTJk9d93aZ+HzdVqysoOp0OEyZMwFNPPdXo4waDAaNGjYJOp8Pu3buxZMkSLF68GHPmzLnm606ePBnHjh3D5s2bsWHDBuzYsQOPP/64Nd5CkwwcOBA5OTkNbtOnT0d4eDj69u17zec+9thjDZ73/vvvt1DqpnvjjTcaZH322Wevuf3MmTOxfv16rFq1Ctu3b0d2djbuueeeFkp741JTU2E0GrFw4UIcO3YMH3/8MRYsWIB///vf132uVPffihUrMGvWLMydOxcHDhxAz549MXz4cOTn5ze6/e7duzFp0iRMmzYNBw8exLhx4zBu3DgcPXq0hZPfmO3btyM+Ph579uzB5s2bUVtbi7i4OFRUVFzzeR4eHg3217lz51oocdN17dq1QdadO3dedVtb23/79u1r8N42b94MAJgwYcJVnyP1fVdRUYGePXviiy++aPTx999/H5999hkWLFiAxMREuLq6Yvjw4aiurr7qazb1+7hZhFZq0aJFglqtvuL+33//XZDL5UJubq75vi+//FLw8PAQampqGn2t48ePCwCEffv2me/7448/BJlMJpw/f97i2W+GTqcT/Pz8hDfeeOOa2w0ZMkR4/vnnWybUTQoLCxM+/vjjG96+pKREcHBwEFatWmW+LyUlRQAgJCQkWCGhZb3//vtCeHj4NbeR8v7r37+/EB8fb/6zwWAQgoKChHnz5jW6/X333SeMGjWqwX3R0dHCE088YdWclpKfny8AELZv337Vba7280iK5s6dK/Ts2fOGt7f1/ff8888L7du3F4xGY6OP29K+EwRBACCsWbPG/Gej0SgEBAQIH3zwgfm+kpISQaVSCT/99NNVX6ep38fN0eqOoFxPQkICunfvDo1GY75v+PDhKC0txbFjx676HE9PzwZHJGJjYyGXy5GYmGj1zE2xbt06FBYW4pFHHrnutj/++CN8fX3RrVs3zJ49G5WVlS2QsHneffdd+Pj4ICoqCh988ME1T8klJSWhtrYWsbGx5vsiIiIQGhqKhISEloh7U7RaLby9va+7nRT3n06nQ1JSUoOvvVwuR2xs7FW/9gkJCQ22B0zfk7awrwDT/gJw3X1WXl6OsLAwhISEYOzYsVf9eSMFJ0+eRFBQENq1a4fJkycjIyPjqtva8v7T6XRYunQpHn300WsuTGtL++5y6enpyM3NbbCP1Go1oqOjr7qPmvN93Bw2uVigNeXm5jYoJwDMf87Nzb3qc/z9/Rvcp1Qq4e3tfdXniOXbb7/F8OHDr7vY4gMPPICwsDAEBQXhyJEjePnll5GWloZffvmlhZLeuOeeew69e/eGt7c3du/ejdmzZyMnJwcfffRRo9vn5ubC0dHxijFIGo1GcvvrcqdOncL8+fPx4YcfXnM7qe6/goICGAyGRr/HUlNTG33O1b4npb6vANPK6zNmzMCgQYPQrVu3q27XuXNnfPfdd+jRowe0Wi0+/PBDDBw4EMeOHbP6wqhNFR0djcWLF6Nz587IycnB66+/jltvvRVHjx6Fu7v7Fdvb8v5bu3YtSkpK8PDDD191G1vad42p3w9N2UfN+T5uDrsoKK+88gree++9a26TkpJy3YFctqQ57zkrKwt//vknVq5ced3Xv3T8TPfu3REYGIhhw4bh9OnTaN++ffOD36CmvL9Zs2aZ7+vRowccHR3xxBNPYN68eZKdiro5++/8+fMYMWIEJkyYgMcee+yazxV7/5FJfHw8jh49es0xGgAQExODmJgY858HDhyIyMhILFy4EG+++aa1YzbJnXfeaf7/Hj16IDo6GmFhYVi5ciWmTZsmYjLL+/bbb3HnnXciKCjoqtvY0r6zNXZRUF544YVrNlwAaNeu3Q29VkBAwBUjkeuv7ggICLjqcy4fGKTX61FUVHTV59ys5rznRYsWwcfHB3fddVeT/77o6GgApt/gW+ID7mb2aXR0NPR6Pc6ePYvOnTtf8XhAQAB0Oh1KSkoaHEXJy8uz2v66XFPfX3Z2Nm6//XYMHDgQX331VZP/vpbef1fj6+sLhUJxxRVT1/raBwQENGl7qXjmmWfMA+ab+pu0g4MDoqKicOrUKSulsxxPT0906tTpqlltdf+dO3cOW7ZsafJRR1vad8DFz7W8vDwEBgaa78/Ly0OvXr0afU5zvo+bxWKjWWzM9QbJ5uXlme9buHCh4OHhIVRXVzf6WvWDZPfv32++788//5TUIFmj0SiEh4cLL7zwQrOev3PnTgGAcPjwYQsns7ylS5cKcrlcKCoqavTx+kGyq1evNt+Xmpoq2UGyWVlZQseOHYWJEycKer2+Wa8hpf3Xv39/4ZlnnjH/2WAwCG3atLnmINnRo0c3uC8mJkaygyyNRqMQHx8vBAUFCSdOnGjWa+j1eqFz587CzJkzLZzO8srKygQvLy/h008/bfRxW9t/9ebOnSsEBAQItbW1TXqe1PcdrjJI9sMPPzTfp9Vqb2iQbFO+j5uV1WKvZCPOnTsnHDx4UHj99dcFNzc34eDBg8LBgweFsrIyQRBM/7i6desmxMXFCYcOHRI2btwo+Pn5CbNnzza/RmJiotC5c2chKyvLfN+IESOEqKgoITExUdi5c6fQsWNHYdKkSS3+/q5my5YtAgAhJSXliseysrKEzp07C4mJiYIgCMKpU6eEN954Q9i/f7+Qnp4u/Prrr0K7du2EwYMHt3Ts69q9e7fw8ccfC4cOHRJOnz4tLF26VPDz8xOmTJli3uby9ycIgvDkk08KoaGhwl9//SXs379fiImJEWJiYsR4C9eUlZUldOjQQRg2bJiQlZUl5OTkmG+XbmNL+2/58uWCSqUSFi9eLBw/flx4/PHHBU9PT/OVcw899JDwyiuvmLfftWuXoFQqhQ8//FBISUkR5s6dKzg4OAjJyclivYVreuqppwS1Wi38/fffDfZXZWWleZvL3+Prr78u/Pnnn8Lp06eFpKQkYeLEiYKTk5Nw7NgxMd7CNb3wwgvC33//LaSnpwu7du0SYmNjBV9fXyE/P18QBNvff4Jg+rANDQ0VXn755Sses8V9V1ZWZv6sAyB89NFHwsGDB4Vz584JgiAI7777ruDp6Sn8+uuvwpEjR4SxY8cK4eHhQlVVlfk1hg4dKsyfP9/85+t9H1tCqysoU6dOFQBccdu2bZt5m7Nnzwp33nmn4OzsLPj6+govvPBCgxa9bds2AYCQnp5uvq+wsFCYNGmS4ObmJnh4eAiPPPKIufRIwaRJk4SBAwc2+lh6enqDr0FGRoYwePBgwdvbW1CpVEKHDh2EF198UdBqtS2Y+MYkJSUJ0dHRglqtFpycnITIyEjhnXfeaXC06/L3JwiCUFVVJTz99NOCl5eX4OLiItx9990NPvSlYtGiRY3+e7304Kct7r/58+cLoaGhgqOjo9C/f39hz5495seGDBkiTJ06tcH2K1euFDp16iQ4OjoKXbt2FX777bcWTnzjrra/Fi1aZN7m8vc4Y8YM89dDo9EII0eOFA4cONDy4W/A/fffLwQGBgqOjo5CmzZthPvvv184deqU+XFb33+CYDoCDkBIS0u74jFb3Hf1n1mX3+rfh9FoFF577TVBo9EIKpVKGDZs2BXvPSwsTJg7d26D+671fWwJMkEQBMudMCIiIiK6eZwHhYiIiCSHBYWIiIgkhwWFiIiIJIcFhYiIiCSHBYWIiIgkhwWFiIiIJIcFhYiIiCSHBYWIiIgkhwWFiIiIJIcFhYiIiCSHBYWIiIgkhwWFiIiIJOf/Ab6hq3qyBK1CAAAAAElFTkSuQmCC", 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" + "
" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -452,12 +668,55 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 80, "id": "7c67d8b7", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " unidades costes\n", + "10 1.001001 4491.091191\n", + "11 1.101101 4490.211332\n", + "12 1.201201 4489.333478\n", + "13 1.301301 4488.457627\n", + "14 1.401401 4487.583780\n", + "el valo) más bajo de costes es de 4297.500202905609\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# Definir y graficar la función" + "# Definir y graficar la función\n", + "def costes_min(x): return 0.1*x**2-9*x+4500\n", + "x=np.linspace(0,100,1000)\n", + "y=costes_min(x)\n", + "plt.plot(x,y,label='costes/unidad fabricada', color='brown')\n", + "plt.grid(True)\n", + "plt.xlabel('unidades frabicadas')\n", + "plt.ylabel('costes')\n", + "\n", + "plt.tight_layout()\n", + "plt.title('Evolucion costes/unidad fabricada')\n", + "\n", + "data={\n", + " \"unidades\":x, \"costes\":y\n", + "}\n", + "df_costes=pd.DataFrame(data)\n", + "df_costes=df_costes[df_costes[\"unidades\"]>=1]\n", + "minimo_coste=df_costes['costes'].min()\n", + "print(df_costes.head())\n", + "print(f\"el valo) más bajo de costes es de {minimo_coste}\")" ] }, { @@ -548,7 +807,17 @@ "execution_count": null, "id": "867b70fc", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original list 1 : [2, 5, 4, 7, 3]\n", + "Original list 2 : [1, 4, 6, 9, 10]\n", + "Resulting list is : [3, 9, 10, 16, 13]\n" + ] + } + ], "source": [ "# Naive method\n", "\n", @@ -669,7 +938,15 @@ "execution_count": null, "id": "840e7d0e", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[24, 33, 28], [33, 36, 23], [25, 29, 23]]\n" + ] + } + ], "source": [ "# Usando un bucle for para ingresar dos matrices de tamaño n x m\n", "matrix1 = [[1,7,3],\n", @@ -729,11 +1006,8 @@ } ], "metadata": { - "interpreter": { - "hash": "d3463682613d55fcbb64853e38cc3520a7f67bdf8d6940e781ddcdc423122719" - }, "kernelspec": { - "display_name": "Python 3.9.12 ('calculus-project')", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -747,7 +1021,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.12" + "version": "3.11.4" } }, "nbformat": 4, diff --git a/notebook/problems.ipynb b/notebook/problems.ipynb index 66cf1da0..57962d06 100644 --- a/notebook/problems.ipynb +++ b/notebook/problems.ipynb @@ -43,7 +43,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 17, "id": "bb3e954e", "metadata": {}, "outputs": [ @@ -112,19 +112,9 @@ "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "[]" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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" + ], + "text/plain": [ + " time speed distance\n", + "0 0.00 0.000 0.0\n", + "1 0.01 0.005 0.0\n", + "2 0.02 0.010 0.0\n", + "3 0.03 0.015 0.0\n", + "4 0.04 0.020 0.0" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ "# Create a DataFrame\n", - "dft=pd.DataFrame({'t':t, 'f(t)':f(t)})\n", + "import pandas as pd\n", + "data= {\n", + " 'time':x_axis, 'speed':y_axis_speed, 'distance':y_axis_distance\n", + "}\n", + "dft=pd.DataFrame(data)\n", + "dft=dft.round(3)\n", "dft.head()\n" ] }, @@ -243,7 +321,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "id": "4ff7e11a", "metadata": {}, "outputs": [], @@ -275,13 +353,13 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "id": "633a54fd", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -322,13 +400,13 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, "id": "e26dbdf0", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -351,7 +429,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "id": "2bdd54f1", "metadata": {}, "outputs": [], @@ -394,7 +472,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "id": "0350981e", "metadata": {}, "outputs": [ @@ -414,7 +492,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "id": "f8e01e2d", "metadata": {}, "outputs": [ @@ -443,7 +521,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 26, "id": "b699d1fb", "metadata": {}, "outputs": [ @@ -462,13 +540,13 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 27, "id": "0b76ee22", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -497,23 +575,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 28, "id": "7c67d8b7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 18, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -573,7 +651,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 29, "id": "9e200c32", "metadata": {}, "outputs": [ @@ -629,7 +707,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "id": "867b70fc", "metadata": {}, "outputs": [ @@ -673,7 +751,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "id": "681930a3", "metadata": {}, "outputs": [ @@ -709,7 +787,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 32, "id": "a3a8a425", "metadata": {}, "outputs": [ @@ -744,7 +822,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 33, "id": "1708d7ee", "metadata": {}, "outputs": [ @@ -799,10 +877,18 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "id": "840e7d0e", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[24, 33, 28], [33, 36, 23], [25, 29, 23]]\n" + ] + } + ], "source": [ "# Using a for loop input two matrices of size n x m\n", "matrix1 = [[1,7,3],\n", @@ -827,7 +913,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 35, "id": "db6c3355", "metadata": {}, "outputs": [ From 6bb51806b09fa87c624f9259a1e7903108da3bd3 Mon Sep 17 00:00:00 2001 From: Maria Pais <145993408+Finarosalina@users.noreply.github.com> Date: Fri, 7 Mar 2025 20:39:53 +0000 Subject: [PATCH 5/6] proyecto --- notebook/problems.es.ipynb | 320 +++++++++++++++++++++++++++++-------- 1 file changed, 251 insertions(+), 69 deletions(-) diff --git a/notebook/problems.es.ipynb b/notebook/problems.es.ipynb index e56ed74a..3ce69a1c 100644 --- a/notebook/problems.es.ipynb +++ b/notebook/problems.es.ipynb @@ -49,17 +49,17 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 21, "id": "bb3e954e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 61, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, @@ -103,7 +103,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 22, "id": "4c4d4f20", "metadata": {}, "outputs": [ @@ -171,7 +171,7 @@ "4 0.08016 0.200401" ] }, - "execution_count": 56, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -211,23 +211,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "id": "ec1f8bd7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 58, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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", 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", 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" ] @@ -258,7 +258,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 24, "id": "ba5c497b", "metadata": {}, "outputs": [ @@ -326,7 +326,7 @@ "4 0.08016 0.200401" ] }, - "execution_count": 65, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } @@ -415,7 +415,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "id": "4ff7e11a", "metadata": {}, "outputs": [], @@ -447,7 +447,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 26, "id": "633a54fd", "metadata": {}, "outputs": [ @@ -494,7 +494,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 27, "id": "e26dbdf0", "metadata": {}, "outputs": [ @@ -523,7 +523,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 28, "id": "2bdd54f1", "metadata": {}, "outputs": [], @@ -565,7 +565,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 29, "id": "0350981e", "metadata": {}, "outputs": [ @@ -585,7 +585,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "id": "f8e01e2d", "metadata": {}, "outputs": [ @@ -614,7 +614,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "id": "b699d1fb", "metadata": {}, "outputs": [ @@ -633,7 +633,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 32, "id": "0b76ee22", "metadata": {}, "outputs": [ @@ -668,7 +668,7 @@ }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 40, "id": "7c67d8b7", "metadata": {}, "outputs": [ @@ -676,18 +676,18 @@ "name": "stdout", "output_type": "stream", "text": [ - " unidades costes\n", + " unidades costos\n", "10 1.001001 4491.091191\n", "11 1.101101 4490.211332\n", "12 1.201201 4489.333478\n", "13 1.301301 4488.457627\n", "14 1.401401 4487.583780\n", - "el valo) más bajo de costes es de 4297.500202905609\n" + "El valor más bajo de costes es 4297.500202905609, lo que se corresponde a fabricar 45.04504504504505 unidades.\n" ] }, { "data": { - "image/png": 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", + "image/png": 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Nm+Lzzz+HTCZDWFgYHBwcMGPGjHzX/yHZCmPs2LHYsmULunbtin79+qFBgwZITEzErl27sGzZMtSrV6/AWQYMGIDExES0atUKlStXxr179/Dbb7/B09NT9dl7enpCKpXil19+wbNnzyCTydCqVSvY2NhgwoQJmDJlCtq0aYP27dsjMjISS5YsQcOGDfHll18CAA4dOoThw4eja9euqFmzJrKzs7Fu3TpIpVJ07twZwMvz6z755JM8Fyv4+/ujSpUq6N+/P8aOHQupVIrVq1fD2toa9+/fL5bPU09PD9OmTcPgwYPRqlUrdO/eHdHR0VizZk2evUKffvoptm3bhk6dOiEwMBDR0dFYtmwZateurbbn6bPPPsPHH3+Mb7/9Fnfv3kXt2rWxbdu2Dz4f7NNPP8W6detgbm6O2rVr49SpUzhw4ACsrKzyXT4rKwu+vr7o1q2bamw++eQTtG/fvkjbL8ifveL+jMzMzNCsWTPMmjULCoUClSpVQkhISJ69qUSFJtbluERl2btud4J8bvugVCoFR0dHAYAwbdq0fNcZHx8v9O3bV6hYsaKgr68veHh45Hv7CLxxuxNBEISQkBDB3d1d0NfXF1xdXYX169e/9ZYaq1evFurXry/IZDLB0tJSaN68uSCXy1Xz37zdSUGzve1WFm/LnJ+nT58Kw4cPFypVqiTo6+sLlStXFoKDg4UnT54UKsuWLVsEf39/wcbGRtDX1xeqVKkiDB48WIiNjVVbbsWKFYKzs7MglUrz3Ppk0aJFgpubm6CnpyfY2toKX331lZCUlKSaf+fOHaFfv36Ci4uLYGBgIFSoUEFo2bKlcODAAUEQXo65jY2N2m0vXnf+/HmhUaNGqnzz5s176+1OAgMD8/z8m+P05u1Oci1ZskRwcnISZDKZ4O3tLRw9ejTPzyqVSuHnn38WqlatKshkMqF+/frCv//+m++tdJ4+fSr06tVLMDMzE8zNzYVevXqpbv1S1NudJCUlqcbUxMRECAgIEG7cuJHntiS5n8+RI0eEQYMGCZaWloKJiYkQFBQkPH36VG2db/vccue9vt7c9/WuP3sl8Rk9ePBA6NSpk2BhYSGYm5sLXbt2FR49elTg3xei/EgEoRTPaCYiKifOnj2LRo0a4dq1a4W+EpmIqKh4jh0RUQn5+eefWeqIqFRxjx0RERGRluAeOyIiIiItwWJHREREpCVY7IiIiIi0BO9jVwBKpRKPHj2CqanpOx+WTkRERFTcBEHA8+fP4eDgkOdZ2W9isSuAR48ewdHRUewYREREVI7FxMSgcuXK71yGxa4Acu9mHxMTAzMzsxLZhkKhQEhICPz9/aGnp1ci26CC4VhoFo6H5uBYaA6OheYojbFISUmBo6NjgZ70w2JXALmHX83MzEq02BkZGcHMzIy/pCLjWGgWjofm4FhoDo6F5ijNsSjI6WC8eIKIiIhIS7DYEREREWkJFjsiIiIiLcFiR0RERKQlWOyIiIiItASLHREREZGWYLEjIiIi0hIsdkRERERagsWOiIiISEuw2BERERFpCRY7IiIiIi2hMcVu5syZkEgkGDVqlNr0U6dOoVWrVjA2NoaZmRmaNWuGjIwM1fzExEQEBQXBzMwMFhYW6N+/P1JTU9XWcfnyZTRt2hQGBgZwdHTErFmzSuMtEREREZUqjSh2YWFhWL58OerWras2/dSpU2jTpg38/f1x9uxZhIWFYfjw4dDR+f/YQUFBuHbtGuRyOf79918cPXoUgwYNUs1PSUmBv78/qlativPnz2P27NmYPHkyfv/991J7f0RERESlQVfsAKmpqQgKCsKKFSswbdo0tXmjR4/GiBEj8O2336qmubq6qr6/fv069u/fj7CwMHh7ewMAfvvtN7Rr1w5z5syBg4MDNmzYgKysLKxevRr6+vqoU6cOwsPDMW/ePLUCSERERFTWiV7shg0bhsDAQPj5+akVu4SEBJw5cwZBQUFo0qQJoqKi4ObmhunTp+OTTz4B8HKPnoWFharUAYCfnx90dHRw5swZdOrUCadOnUKzZs2gr6+vWiYgIAC//PILkpKSYGlpmSdTZmYmMjMzVa9TUlIAAAqFAgqFotg/g9x1v/5fEg/HQrNwPDQHx0JzcCw0R8Tq1ci6fBnP3N1hXqVKiWyjMOMsarHbuHEjLly4gLCwsDzz7ty5AwCYPHky5syZA09PT/z555/w9fXF1atXUaNGDcTFxcHGxkbt53R1dVGhQgXExcUBAOLi4uDk5KS2jK2trWpefsVuxowZmDJlSp7pISEhMDIyKtqbLSC5XF6i66eC41hoFo6H5uBYaA6OhbiEnBxkrF4NITUVRxwdoVurVolsJz09vcDLilbsYmJiMHLkSMjlchgYGOSZr1QqAQCDBw9G3759AQD169fHwYMHsXr1asyYMaPEsk2YMAFjxoxRvU5JSYGjoyP8/f1hZmZWIttUKBSQy+Vo3bo19PT0SmQbVDAcC83C8dAcHAvNwbHQDLFHj+J4aipgbIyAoUMhMzQske3kHjksCNGK3fnz55GQkAAvLy/VtJycHBw9ehSLFi1CZGQkAKB27dpqP1erVi3cv38fAGBnZ4eEhAS1+dnZ2UhMTISdnZ1qmfj4eLVlcl/nLvMmmUwGmUyWZ7qenl6J/wKVxjaoYDgWmoXjoTk4FpqDYyGu+3v2AAB0PT0hMzQssbEozHpFuyrW19cXV65cQXh4uOrL29sbQUFBCA8Ph7OzMxwcHFQFL9fNmzdRtWpVAICPjw+Sk5Nx/vx51fxDhw5BqVSiUaNGqmWOHj2qdnxaLpfD1dU138OwRERERO+TmZyMB4cOAQB0X9tJJTbR9tiZmprC3d1dbZqxsTGsrKxU08eOHYtJkyahXr168PT0xB9//IEbN25gy5YtAF7uvWvTpg0GDhyIZcuWQaFQYPjw4ejRowccHBwAAF988QWmTJmC/v37Y/z48bh69Sp+/fVXzJ8/v3TfMBEREWmN+/v3Q6lQwLxmTWTb24sdR0X0q2LfZdSoUXjx4gVGjx6NxMRE1KtXD3K5HC4uLqplNmzYgOHDh8PX1xc6Ojro3LkzFi5cqJpvbm6OkJAQDBs2DA0aNEDFihUxceJE3uqEiIiIiuzOjh0AgGrt2+O2uFHUaFSxCw0NzTPt22+/VbuP3ZsqVKiAv/76653rrVu3Lo4dO/ah8YiIiIjwLCoKT69cgURXF1XatcPt06fFjqSiEU+eICIiIioronfuBAA4NG0KgwoVRE6jjsWOiIiIqICUOTmI3r0bAODcsaO4YfLBYkdERERUQHEnTyIjIQEyCws4NGsmdpw8WOyIiIiICij3MGzVwEBIX3tcqaZgsSMiIiIqgKyUFMQcPAgAcO7QQeQ0+WOxIyIiIiqA+/v3Q5mVBfMaNWD5xpOxNAWLHREREVEB3Hl1GNa5QwdIJBKR0+SPxY6IiIjoPVKio/EkPBwSqRTVPv1U7DhvxWJHRERE9B7Ru3YBAOw/+QSG1tYip3k7FjsiIiKid1Dm5KiKnaZeNJGLxY6IiIjoHeLPnEF6XBz0zcxQqUULseO8E4sdERER0Tvc2bYNAFC1bVtIZTKR07wbix0RERHRW2QmJ6vuXefSubPIad6PxY6IiIjoLe7t3QtlVhYsXF019t51r2OxIyIiInqLqO3bAQAun3+usfeuex2LHREREVE+kq5fR1JEBHT09DT63nWvY7EjIiIiykfu3rrKrVpBZmEhbpgCYrEjIiIiekNOZibu7t4NAHDu1EnkNAXHYkdERET0hgeHDyMrJQVGdnawa9JE7DgFxmJHRERE9Ibce9c5degAHalU5DQFx2JHRERE9Jq02FjEnjwJAHDu2FHcMIXEYkdERET0muidOwFBgE3DhjCtUkXsOIXCYkdERET0iqBUqt27rqxhsSMiIiJ6JSEsDGkPHkDX2BiOrVuLHafQWOyIiIiIXsndW1etXTvoGhqKnKbwWOyIiIiIAGQ9f46YkBAAgHMZPAwLsNgRERERAQDu7duHnMxMmFevDisPD7HjFAmLHRERERH+/951zp06QSKRiJymaFjsiIiIqNxLvnULT69cgURXF06ffSZ2nCJjsSMiIqJyL+rV3rpKLVrAwMpK5DRFx2JHRERE5VpOVhbu7t4NAHDp1EnkNB+GxY6IiIjKtYehochMSoJBxYqw/+QTseN8EBY7IiIiKtdub94M4OVFEzq6uiKn+TAsdkRERFRupT58iLhTpwAA1Tt3FjnNh2OxIyIionIrautWQBBg5+MDE0dHseN8MBY7IiIiKpeU2dm48+oRYi5duoicpniw2BEREVG59OjoUWQkJEBmaYnKrVqJHadYsNgRERFRuXR7yxYAgHPHjpDq64ucpniw2BEREVG5kx4Xh9hjxwAALlpw0UQuFjsiIiIqd6K2bYOgVMLG2xtmTk5ixyk2LHZERERUrihzclSPENOWiyZysdgRERFRuRJ38iTSY2Ohb2YGx9atxY5TrFjsiIiIqFyJenXRRLX27aFrYCBymuLFYkdERETlRsbjx3gQGgoAqK5lh2EBFjsiIiIqR+7s2AEhOxsVPT1hUaOG2HGKHYsdERERlQuCUvnyEWLQvosmcrHYERERUbkQf/YsUmNioGdigqoBAWLHKREsdkRERFQu5D5pompgIHSNjEROUzJY7IiIiEjrvUhKwoMDBwAA1bt2FTlNyWGxIyIiIq0XvXMnlAoFKtSpgwq1aokdp8RoTLGbOXMmJBIJRo0apZrWokULSCQSta8hQ4ao/dyb8yUSCTZu3Ki2TGhoKLy8vCCTyVC9enWsXbu2FN4RERERaQJBEFT3rtPWiyZy6YodAADCwsKwfPly1K1bN8+8gQMHYurUqarXRvkcE1+zZg3atGmjem1hYaH6Pjo6GoGBgRgyZAg2bNiAgwcPYsCAAbC3t0eAlp44SURERP/v8fnzSImOhtTQENXatRM7TokSvdilpqYiKCgIK1aswLRp0/LMNzIygp2d3TvXYWFh8dZlli1bBicnJ8ydOxcAUKtWLRw/fhzz589nsSMiIioHbv3zDwCgWmAg9ExMRE5TskQ/FDts2DAEBgbCz88v3/kbNmxAxYoV4e7ujgkTJiA9PT3fdVSsWBEfffQRVq9eDUEQVPNOnTqVZ90BAQE4depU8b4RIiIi0jgvnj5FTEgIAKBGt24ipyl5ou6x27hxIy5cuICwsLB853/xxReoWrUqHBwccPnyZYwfPx6RkZHYtm2bapmpU6eiVatWMDIyQkhICIYOHYrU1FSMGDECABAXFwdbW1u19dra2iIlJQUZGRkwNDTMs93MzExkZmaqXqekpAAAFAoFFArFB7/v/OSut6TWTwXHsdAsHA/NwbHQHByLgru1dSuU2dmwrFMHpjVrFvtnVhpjUZh1i1bsYmJiMHLkSMjlchi85QG8gwYNUn3v4eEBe3t7+Pr6IioqCi4uLgCAH3/8UbVM/fr1kZaWhtmzZ6uKXVHMmDEDU6ZMyTM9JCQk33P8ipNcLi/R9VPBcSw0C8dDc3AsNAfH4t0EpRIZf/4JAEhzc8PevXtLbFslORb5Ha18G9GK3fnz55GQkAAvLy/VtJycHBw9ehSLFi1CZmYmpFKp2s80atQIAHD79m1VsXtTo0aN8NNPPyEzMxMymQx2dnaIj49XWyY+Ph5mZmb57q0DgAkTJmDMmDGq1ykpKXB0dIS/vz/MzMyK9H7fR6FQQC6Xo3Xr1tDT0yuRbVDBcCw0C8dDc3AsNAfHomDiTpzAsaQk6JmaIvCbb6D7lr/3P0RpjEXukcOCEK3Y+fr64sqVK2rT+vbtCzc3N4wfPz5PqQOA8PBwAIC9vf1b1xseHg5LS0vIZDIAgI+PT56GLpfL4ePj89Z1yGQy1c+/Tk9Pr8R/gUpjG1QwHAvNwvHQHBwLzcGxeLfoV8+Fde7QAYYltGMmV0mORWHWK1qxMzU1hbu7u9o0Y2NjWFlZwd3dHVFRUfjrr7/Qrl07WFlZ4fLlyxg9ejSaNWumui3K7t27ER8fj8aNG8PAwAByuRw///wzvvnmG9U6hwwZgkWLFmHcuHHo168fDh06hE2bNmHPnj2l+n6JiIio9KTHxeFhaCgAoHo5uGgil+i3O3kbfX19HDhwAAsWLEBaWhocHR3RuXNn/PDDD6pl9PT0sHjxYowePRqCIKB69eqYN28eBg4cqFrGyckJe/bswejRo/Hrr7+icuXKWLlyJW91QkREpMVub9kCQamETcOGMH/L6VvaSKOKXeirZg0Ajo6OOHLkyDuXb9OmjdqNid+mRYsWuHjx4ofGIyIiojJAqVConjRRo3t3kdOULtHvY0dERERUnB6GhiLj8WMYWFmhsq+v2HFKFYsdERERaZVbmzYBAJw//xxSfX2R05QuFjsiIiLSGs/v3UPcyZOARILqXbuKHafUsdgRERGR1ri9eTMAwKFpU5hUqiRymtLHYkdERERaISczE3e2bwdQvm5x8joWOyIiItIK9+VyZCYnw8jODg7NmokdRxQsdkRERKQVbm/cCACo3rUrdPJ5glV5wGJHREREZV7yzZt4fPEiJLq6cOncWew4omGxIyIiojLv1j//AAAqt2oFQ2trkdOIh8WOiIiIyjRFaiqid+0CUP6eNPEmFjsiIiIq0+7s3Ins9HSYOTvDtlEjseOIisWOiIiIyixBEHDr778BADW/+AISiUTkROJisSMiIqIyK/70aaRER0PX2BhO7duLHUd0LHZERERUZt18tbfOuUMH6Bkbi5xGfCx2REREVCalPXqEh4cPAwBq9OghchrNwGJHREREZdKtf/6BoFTCtnFjmLu4iB1HI7DYERERUZmTk5mJqK1bAby8aIJeYrEjIiKiMufe/v3ITEqCkZ0dKjVvLnYcjcFiR0RERGXOzb/+AvDy3DodXV2R02gOFjsiIiIqU55cvozEq1eho6dXrp8Lmx8WOyIiIipTcm9IXKVtWxhUqCByGs3CYkdERERlxovERNzbtw8AULNnT5HTaB4WOyIiIiozorZuhVKhQIU6dVCxbl2x42gcFjsiIiIqE5TZ2bj1zz8AeIuTt2GxIyIiojLh4ZEjSI+NhczCAlXbthU7jkZisSMiIqIyIfcWJy6dO0Mqk4mcRjOx2BEREZHGe3b7NuJPn4ZERwfVu3cXO47GYrEjIiIijRe5YQMAoFLLljCpVEnkNJqLxY6IiIg0WmZyMqJ37QIAuH75pchpNBuLHREREWm0qK1bkfPiBSxcXWHTsKHYcTQaix0RERFpLGV2tuqiCddevSCRSEROpNlY7IiIiEhjPTh4EOlxcZBVqIBq7dqJHUfjsdgRERGRxopctw4AUL1rV97ipABY7IiIiEgjJV67hscXL0Kiq4saPXqIHadMYLEjIiIijXRj/XoAQJWAABjZ2IicpmxgsSMiIiKNk/H4Me7v3QuAtzgpDBY7IiIi0ji3Nm2CMjsbFT09UbFuXbHjlBksdkRERKRRcrKycPuffwBwb11hsdgRERGRRrm3bx9ePH0KQ1tbOPr5iR2nTGGxIyIiIo0hCAIiX100UbNnT+jo6YmcqGxhsSMiIiKN8fjCBSRFREAqk6F6165ixylzWOyIiIhIY+TekLjap59CZmEhbpgyiMWOiIiINELao0d4cPAgAF40UVQsdkRERKQRbv71FwSlEraNGsGiZk2x45RJLHZEREQkOkVaGm5v2QIAcOvdW+Q0ZReLHREREYkuautWKJ4/h5mTExyaNRM7TpnFYkdERESiUmZnqy6acOvdGxId1pOi4idHREREooo5cABpjx5BZmmJau3bix2nTGOxIyIiItEIgoAba9cCAGr06AFdAwNxA5VxLHZEREQkmicXL+LplSvQ0ddHzZ49xY5T5rHYERERkWiu//EHAMDps89gYGUlcpqyT2OK3cyZMyGRSDBq1CjVtBYtWkAikah9DRkyRO3n7t+/j8DAQBgZGcHGxgZjx45Fdna22jKhoaHw8vKCTCZD9erVsfbVLl8iIiISz/N791Q3JHYLDhY5jXbQFTsAAISFhWH58uWoW7dunnkDBw7E1KlTVa+NjIxU3+fk5CAwMBB2dnY4efIkYmNj0bt3b+jp6eHnn38GAERHRyMwMBBDhgzBhg0bcPDgQQwYMAD29vYICAgo+TdHRERE+bqxbh0gCHBo1gzmLi5ix9EKou+xS01NRVBQEFasWAFLS8s8842MjGBnZ6f6MjMzU80LCQlBREQE1q9fD09PT7Rt2xY//fQTFi9ejKysLADAsmXL4OTkhLlz56JWrVoYPnw4unTpgvnz55faeyyItIcPkXX0KARBEDsKERFRictMTsadHTsAcG9dcRJ9j92wYcMQGBgIPz8/TJs2Lc/8DRs2YP369bCzs8Nnn32GH3/8UbXX7tSpU/Dw8ICtra1q+YCAAHz11Ve4du0a6tevj1OnTsHPz09tnQEBAWqHfN+UmZmJzMxM1euUlBQAgEKhgEKh+JC3m6/sjAyEdO2K7PR0xHXsCPvGjYt9G1RwuWNcEmNNhcfx0BwcC82hDWMRuXEjcjIyYF6zJip4eZXZ91IaY1GYdYta7DZu3IgLFy4gLCws3/lffPEFqlatCgcHB1y+fBnjx49HZGQktm3bBgCIi4tTK3UAVK/j4uLeuUxKSgoyMjJgaGiYZ7szZszAlClT8kwPCQlROxRcrNzdgbNncWr+fBjwXy4aQS6Xix2BXsPx0BwcC81RVsdCyM5Gxqvz3TPq1cO+ffvEDVQMSnIs0tPTC7ysaMUuJiYGI0eOhFwuh8Fb7lkzaNAg1fceHh6wt7eHr68voqKi4FKCx+InTJiAMWPGqF6npKTA0dER/v7+aoeCi1OSqysOdOmCnMhIfFyzJsyrVy+R7dD7KRQKyOVytG7dGnp6emLHKfc4HpqDY6E5yvpY3N21C2HPn8PA2hqB48ZBpwy+h1ylMRa5Rw4LQrRid/78eSQkJMDLy0s1LScnB0ePHsWiRYuQmZkJqVSq9jONGjUCANy+fRsuLi6ws7PD2bNn1ZaJj48HANjZ2an+mzvt9WXMzMzy3VsHADKZDDKZLM90PT29Ehs0SxcXSGvXRs61a7i1bh18Xl38QeIpyfGmwuN4aA6OheYoi2MhCAJurV8PAHD78kvISupIWCkrybEozHpFu3jC19cXV65cQXh4uOrL29sbQUFBCA8Pz1PqACA8PBwAYG9vDwDw8fHBlStXkJCQoFpGLpfDzMwMtWvXVi1z8NWl1K8v4+PjU0LvrOj0Xj30+N6ePUh/o4wSERFpg/jTp5F88yZ0DQ1RvWtXseNoHdGKnampKdzd3dW+jI2NYWVlBXd3d0RFReGnn37C+fPncffuXezatQu9e/dGs2bNVLdF8ff3R+3atdGrVy9cunQJ//33H3744QcMGzZMtcdtyJAhuHPnDsaNG4cbN25gyZIl2LRpE0aPHi3WW38rqaMjKjZooPYwZCIiIm1y/dW5dc6ffw59c3Nxw2gh0W938jb6+vo4cOAA/P394ebmhv/973/o3Lkzdu/erVpGKpXi33//hVQqhY+PD7788kv07t1b7b53Tk5O2LNnD+RyOerVq4e5c+di5cqVGnsPO9dXF07c2rQJWc+fi5yGiIio+CRFRiL2+HFIdHTg1quX2HG0kui3O3ldaGio6ntHR0ccOXLkvT9TtWpV7N27953LtGjRAhcvXvzQeKXC/pNPYO7igmdRUbi9eTNq9+sndiQiIqJicX3NGgCAo78/TBwdRU6jnTR2j115JdHRgVvfvgCAyHXrkPPqRstERERlWdqjR7j3akdM7f79RU6jvVjsNFC1wEAYWlsjIyEB9/bsETsOERHRB7v+xx8QcnJg5+ODCq8ucKTix2KngaT6+nB9de7B9bVrISiVIiciIiIquszkZERt3QoAqMVTjEoUi52Gqt6tG3SNjfHs9m08OnZM7DhERERFdvOvv5CTkQHLWrVgp4G3G9MmLHYaSt/UFDW6dQPw/yebEhERlTXZGRm4+ddfAF6eWyeRSEROpN1Y7DSY65dfQqKri4SwMDy5fFnsOERERIUWtW0bMpOSYOLoCMfWrcWOo/VY7DSYkZ0dqrVrB4B77YiIqOxRZmfjxh9/AADcgoOho6tRd1nTSix2Gq7Wq1ufPDhwAM/v3RM5DRERUcHd/+8/pD18CFmFCnDu1EnsOOUCi52Gs6hZE/ZNm0JQKnH91b96iIiINJ0gCIhYtQoA4BoUBF0DA5ETlQ8sdmVA7tMn7mzfjozHj0VOQ0RE9H6xJ04gOTISuoaGqNGjh9hxyg0WuzLApmFDVPT0hDIrC5Hr1okdh4iI6L2ur14NAHDp0gUyCwtxw5QjLHZlgEQiQe0BAwAANzduRFZKisiJiIiI3u7p1auIP3MGEl1duAUHix2nXGGxKyMqNW8Oi5o1kZ2Whpt//y12HCIiorfKPbeuWrt2MLa3FzlN+cJiV0ZIdHRUD02OXLcO2RkZIiciIiLKK+XePcTI5QD4+DAxsNiVIVXatIGJoyMyk5JUz9wjIiLSJNdXrQIEAQ7Nm8OiRg2x45Q7LHZliI6urupfP9fXrEFOVpbIiYiIiP5fWmwsonfuBADUGThQ5DTlE4tdGePcoQMMra2RHheHu3v2iB2HiIhI5fratVBmZ8OmYUNY168vdpxyicWujJHKZKorjCJWroQyJ0fkRERERMCLp08RtWULAMB98GCR05RfLHZlUPVu3aBvZobnd+/iwYEDYschIiLCjXXrkPPiBSq4u8O2cWOx45RbLHZlkJ6xMWoGBQEArq1YAUEQRE5ERETlWVZKCm69uhWX++DBkEgkIicqv1jsyijXL7+ErqEhkq5fR+yJE2LHISKicuzmX39BkZoK8xo1UKlFC7HjlGssdmWUzMICLl27AgAiVqwQOQ0REZVXirQ01eMu6wwcCIkOq4WY+OmXYbX69IGOri4Szp3D4wsXxI5DRETl0O3Nm5GZnAyTKlVQpU0bseOUeyx2ZZiRrS2cOnQAAFxbuVLkNEREVN7kZGbixtq1AIA6AwZARyoVNxCx2JV1tfr3h0RHB4+OHEHS9etixyEionLkzs6dyHj8GEZ2dqj22WdixyGw2JV5ZlWrqnZ9X12+XOQ0RERUXiizsxGxahUAoFbfvpDq64uciAAWO61QZ/BgQCJBjFyO5Fu3xI5DRETlwL29e5H24AFkFSrApXNnsePQKyx2WsCienVU8fcHwL12RERU8gSlEtde3ZHBrXdv6BoaipyIcrHYaYk6rx7fcn//fjyLihI5DRERabOYAweQcucO9MzMULNnT7Hj0GtY7LSEpasrKvv6AoKg+lcUERFRcROUSlxduhQA4PrFF9AzMRE5Eb2OxU6LuA8ZAgC4t2cPUu7dEzkNERFpoweHDiH55k3oGhvDtVcvsePQG1jstEiF2rXh0Lw5BKUSEb//LnYcIiLSMoIg/P/euqAgyCwsxA1EebDYaZncvXbRu3cjNSZG5DRERKRNHhw6hKQbN6BrZAS34GCx41A+WOy0TMW6dWH/8ccQcnJ4rh0RERWb1/fW1eTeOo3FYqeF3L/6CsDLO4KnPXokchoiItIGDw8fRtL169xbp+FY7LSQdf36sG3cGEJ2NiL4DFkiIvpAgiDgSu7eui++gIGlpciJ6G2KVOwuXLiAK1euqF7v3LkTHTt2xHfffYesrKxiC0dF5/Fqr13Utm1Ij4sTOQ0REZVlj44cQVJEBHQNDeHWp4/YcegdilTsBg8ejJs3bwIA7ty5gx49esDIyAibN2/GuHHjijUgFY2NtzdsvL2hVCgQsXq12HGIiKiMEgQBV5YsAQDU6NmTe+s0XJGK3c2bN+Hp6QkA2Lx5M5o1a4a//voLa9euxdatW4szH32A3HPtbm/ejPSEBJHTEBFRWfTo2DEkXrsGqaEhavXtK3Yceo8iFTtBEKBUKgEABw4cQLt27QAAjo6OePLkSfGlow9i26gRrOvXhzIrCxG8QpaIiApJEARcfbW3rmaPHjCoUEHkRPQ+RSp23t7emDZtGtatW4cjR44gMDAQABAdHQ1bW9tiDUhFJ5FI4DF8OICXe+3SYmNFTkRERGVJ7PHjeHrlCqQGBjy3rowoUrFbsGABLly4gOHDh+P7779H9erVAQBbtmxBkyZNijUgfRjbRo1g07AhlAoF72tHREQF9vqVsDW6d4dhxYoiJ6KC0C3KD9WtW1ftqthcs2fPhlQq/eBQVHwkEgnqDh+OA8HBuLN1K2r37w+TSpXEjkVERBou9sQJPL10CVKZjOfWlSEfdB+78+fPY/369Vi/fj0uXLgAAwMD6OnpFVc2KiY23t6w8/GBMjsb15YvFzsOERFpOEEQcPm33wAA1bt3h6G1tciJqKCKVOwSEhLQsmVLNGzYECNGjMCIESPg7e0NX19fPH78uLgzUjHwGDYMAHBnxw48v39f5DRERKTJHoaGIvHqVUgNDVFnwACx41AhFKnYff3110hNTcW1a9eQmJiIxMREXL16FSkpKRgxYkRxZ6RiYF2/Puw/+QRCTg6uLlsmdhwiItJQglKp2lvnGhQEAysrkRNRYRSp2O3fvx9LlixBrVq1VNNq166NxYsXY9++fcUWjopX7l67u7t3I+XuXXHDEBGRRoqRy5EcGQk9ExOeW1cGFanYKZXKfM+l09PTU93fjjRPxbp14dC8OQSlEldfXelERESUS5mTg8uLFgEAXHv3hszCQtxAVGhFKnatWrXCyJEj8ejRI9W0hw8fYvTo0fD19S22cFT86n79NQDg7p49eBYVJXIaIiLSJPf27kXKnTvQNzODW+/eYsehIihSsVu0aBFSUlJQrVo1uLi4wMXFBU5OTkhJScFvr47Lk2aqUKsWKvv5Aa89+4+IiEipUKj+XqjVrx/0TU1FTkRFUaRi5+joiAsXLmDPnj0YNWoURo0ahb179+LChQuoXLlykYLMnDkTEokEo0aNyjNPEAS0bdsWEokEO3bsUJsnkUjyfG3cuFFtmdDQUHh5eUEmk6F69epYu3ZtkTJqC4+hQwEA9/fvR/LNmyKnISIiTRC9axdS79+HrEIF1PziC7HjUBEVqdj9+eefyMrKQuvWrfH111/j66+/hp+fH7KysvDnn38Wen1hYWFYvnw56tatm+/8BQsWQCKRvPXn16xZg9jYWNVXx44dVfOio6MRGBiIli1bIjw8HKNGjcKAAQPw33//FTqntrB0dUWVgAAAwOXFi0VOQ0REYsvJylI9ZaJ2//7QMzYWOREVVZGKXd++ffHs2bM8058/f46+hbyCJjU1FUFBQVixYgUsLS3zzA8PD8fcuXOxevXqt67DwsICdnZ2qi8DAwPVvGXLlsHJyQlz585FrVq1MHz4cHTp0gXz588vVE5t4zF0KCCR4MGBA0i8dk3sOEREJKKorVuRHhsLQ2tr1OjRQ+w49AGK9EgxQRDy3YP24MEDmJubF2pdw4YNQ2BgIPz8/DBt2jS1eenp6fjiiy+wePFi2NnZvXMdAwYMgLOzM4YMGYK+ffuq8p06dQp+fn5qywcEBOR7yDdXZmYmMjMzVa9TUlIAAAqFAgqFolDvr6By11tS63+TUdWqqNKuHe7v2YOL8+ejGa+SVSntsaB343hoDo6F5ijOsch58QJXXz2VyK1/fwhSKce4EErj96Iw6y5Usatfv77qPDZfX1/o6v7/j+fk5CA6Ohpt2rQp8Po2btyICxcuICwsLN/5o0ePRpMmTdChQ4e3rmPq1Klo1aoVjIyMEBISgqFDhyI1NVV1o+S4uDjY2tqq/YytrS1SUlKQkZEBQ0PDPOucMWMGpkyZkmd6SEgIjIyMCvz+ikIul5fo+l+nrFUL2LcP8adOYfeiRZA6O5fatsuC0hwLej+Oh+bgWGiO4hgLxfHjyHr8GBILC0QaGeHm3r3FkKz8Kcnfi/T09AIvW6hil3vuWnh4OAICAmBiYqKap6+vj2rVqqFz584FWldMTAxGjhwJuVyudug0165du3Do0CFcvHjxnev58ccfVd/Xr18faWlpmD179gc9AWPChAkYM2aM6nVKSgocHR3h7+8PMzOzIq/3XRQKBeRyOVq3bl2qz9u9cP8+ojZtgtHZs2g1bNg7z2UsL8QaC8ofx0NzcCw0R3GNRXZ6OvbOng0A8BoxAs7t2xdXxHKjNH4vco8cFkShit2kSZMAANWqVUOPHj0gk8kKl+w158+fR0JCAry8vFTTcnJycPToUSxatAhfffUVoqKiYPHGzRE7d+6Mpk2bIjQ0NN/1NmrUCD/99BMyMzMhk8lgZ2eH+Ph4tWXi4+NhZmaW7946AJDJZPm+Nz09vRL/n1lpbON1dYcOxd1du5B4+TISjh9H5VatSm3bmq60x4LejeOhOTgWmuNDxyJy40ZkJiXBxNERNT7/HDoc1yIryd+Lwqy3SOfYtWrVCo8fP1bd2uTs2bP466+/ULt2bQwaNKhA6/D19cWVK1fUpvXt2xdubm4YP348KlasiMGDB6vN9/DwwPz58/HZZ5+9db3h4eGwtLRUFTMfHx/sfWO3slwuh4+PT4FyajtDa2u4fvklIlauxKWFC+HQvDl0pFKxYxERUQnLTE7G9VcXJtb9+muWOi1RpGL3xRdfYNCgQejVqxfi4uLg5+cHd3d3bNiwAXFxcZg4ceJ712Fqagp3d3e1acbGxrCyslJNz++CiSpVqsDJyQkAsHv3bsTHx6Nx48YwMDCAXC7Hzz//jG+++Ua1/JAhQ7Bo0SKMGzcO/fr1w6FDh7Bp0ybs2bOnKG9dK9Xu1w+3/vkHz27dwr19++D06adiRyIiohJ2bcUKKFJTYeHqiqpt24odh4pJkW53cvXqVXz00UcAgE2bNsHDwwMnT57Ehg0bSvXmv3p6eli8eDF8fHzg6emJ5cuXY968eapDxgDg5OSEPXv2QC6Xo169epg7dy5WrlyJgFf3cSNA39wctfv1AwBcWbQIOVlZIiciIqKSlBYbi5t//QUA8Bw9GhKdItUB0kBF2mOnUChUhzoPHDiA9q9OtnRzc0NsbGyRw7ztvLlcgiCovW7Tpk2BrsJt0aLFey/CKO9cv/wSkevXIzUmBne2beN9jIiItNjVpUuhzMqCTcOGsP/kE7HjUDEqUkWvU6cOli1bhmPHjkEul6vK1aNHj2BlZVWsAal06BoZoc6rcxqvLluG7IwMkRMREVFJeBYVhTvbtwMA6o0axbshaJkiFbtffvkFy5cvR4sWLdCzZ0/Uq1cPwMtblOQeoqWyp3rXrjCuVAkZjx/j5oYNYschIqIScHnhQghKJSq3agVrT0+x41AxK9Kh2BYtWuDJkydISUlRewzYoEGDSvwGvlRypPr68Bg2DKe/+w4Rq1aherdu0C+h+/YREVHpe3L5MmIOHIBERwd1R44UOw6VgCKfLSmVSpGdnY3jx4/j+PHjePz4MapVqwYbG5vizEelrNqnn8K8enVkpaTg+po1YschIqJiIggCLr16TrpT+/awqF5d5ERUEopU7NLS0tCvXz/Y29ujWbNmaNasGRwcHNC/f/9CPfaCNI+OVIq6r57acWPdOmQ8fixyIiIiKg5xJ08i/uxZ6OjpwWPYMLHjUAkpUrEbM2YMjhw5gt27dyM5ORnJycnYuXMnjhw5gv/973/FnZFKWeVWrWBVrx5yMjJwZfFiseMQEdEHEpRKhC9YAACo0bMnjB0cxA1EJaZIxW7r1q1YtWoV2rZtCzMzM5iZmaFdu3ZYsWIFtmzZUtwZqZRJJBLUf1XQo7ZuxbOoKJETERHRh7j/339IioiArrEx6gwcKHYcKkFFKnbp6emwtbXNM93GxoaHYrWETYMGqOzr+/Jfea/OySAiorJHqVDg0sKFAIBaffrAoEIFkRNRSSpSsfPx8cGkSZPw4sUL1bSMjAxMmTKFz2DVIp6jR0MileLh4cNIOHdO7DhERFQEt7dsQer9+5BVqAC34GCx41AJK1KxW7BgAU6cOIHKlSvD19cXvr6+cHR0xIkTJ/Drr78Wd0YSiZmTE6p36QIAuDhnTp4nfxARkWbLev5cda60x9Ch0DM2FjkRlbQiFTsPDw/cunULM2bMgKenJzw9PTFz5kzcvn0bderUKe6MJCL3oUOha2iIp1euICYkROw4RERUCBGrViEzKUntH+qk3Yp0g+IZM2bA1tYWA984AXP16tV4/Pgxxo8fXyzhSHyGFSuiVr9+uLJ4McLnz0elli0h1dcXOxYREb1HWmwsIv/8EwDgOWYMdPT0RE5EpaFIe+yWL18ONze3PNNznyFL2sUtOBgGFSsiNSYGtzdtEjsOEREVwOWFC5GTmQkbb29UatlS7DhUSopU7OLi4mBvb59nurW1NWJjYz84FGkWPWNj1H11M8urS5ci6/lzkRMREdG7JF6/jujduwEA9b/5BhKJROREVFqKVOxyL5R404kTJ+DAmx5qJefPP4eZszMyk5MRsWqV2HGIiOgtBEHAxdmzAUFA1XbtYOXhIXYkKkVFKnYDBw7EqFGjsGbNGty7dw/37t3D6tWrMXr06Dzn3ZF20NHVhefo0QCAyD//RHpcnMiJiIgoP4+OHUP8mTPQ0dNDvVGjxI5DpaxIF0+MHTsWT58+xdChQ5GVlQUAMDAwwPjx4zFhwoRiDUiao1LLlrBu0ACPz5/H5d9+Q+Pp08WOREREr1FmZyN8zhwAgOuXX8KkUiWRE1FpK9IeO4lEgl9++QWPHz/G6dOncenSJSQmJmLixInFnY80iEQiQf1vvgEA3Nm5E4nXr4uciIiIXndn+3Y8i4qCvrk56gwaJHYcEkGRil0uExMTNGzYEO7u7pDJZMWViTRYxbp1UbVtW0AQcOGXX3jTYiIiDaFIS8Pl334DALh/9RX0zcxETkRi+KBiR+WT55gxkMpkSAgLw4ODB8WOQ0REAK6vWYMXT5/CxNERNbp3FzsOiYTFjgrN2MFB9bzBi3PmIOfVeZZERCSO9Ph4XF+7FsDL53zzRvLlF4sdFUntAQNUNy2+uWGD2HGIiMq18AULkJORgYqennD09xc7DomIxY6KRM/YWHUZ/dVly/AiMVHcQERE5dSTy5dxd9cuAECDb7/lzYjLORY7KjLnDh1gWasWFKmpuLxokdhxiIjKHUEQcH7mTACAU/v2vBkxsdhR0Ul0dNDg228BAFGbNyP51i2RExERlS/39+7F00uXoGtoiHqvbiJP5RuLHX0QG29vOLZuDUGpxIVZs3j7EyKiUiJkZeHKr78CAGoPHAgjGxuRE5EmYLGjD1b/f/+Djp4e4k6exKOjR8WOQ0RULiiOHkVGQoLanQqIWOzog5k4OsK1Vy8AwMXZs6FUKERORESk3dJjY6F49Q/p+t98A10DA5ETkaZgsaNi4T54MGQVKiAlOhq3/vlH7DhERFrt8q+/AtnZqOjlxdubkBoWOyoWeiYmqPf11wCAy4sX8/YnREQl5PGFC4jZvx+QSOA5bhxvb0JqWOyo2Dh37gwLV1coUlJw6dUJvUREVHwEpVJ1exPdBg1g6eYmciLSNCx2VGx0pFJ4f/89ACBq61Y8vXpV5ERERNoleudOJF67Bl1jY+i3bi12HNJALHZUrGwaNEC1Tz8FBAHnfv4ZglIpdiQiIq2Q9fw5wufPBwDUGjAAElNTkRORJmKxo2Ln+b//QdfICE8vXUL0zp1ixyEi0gpXFi3Ci6dPYVqtGmp++aXYcUhDsdhRsTOysYH7kCEAgPD585H1/LnIiYiIyrbkmzdx8++/AQDe330HHT09kRORpmKxoxLh2qsXTKtVw4unT3FlyRKx4xARlVmCIODc9OkQcnLg6OcH+48/FjsSaTAWOyoRUn19NJgwAQBwc8MGJN++LXIiIqKy6d6ePUg4dw5SAwN4jR8vdhzScCx2VGIcPvkElVu1gpCTg/M//8znyBIRFZIiLQ0X58wBANQZOBDGDg4iJyJNx2JHJcpr3Djo6Osj/swZxISEiB2HiKhMubp0KTIeP4aJoyNq9e0rdhwqA1jsqESZODqidv/+AIALs2YhOz1d5ERERGXDs9u3cWPdOgBAg+++g1QmEzkRlQUsdlTiavfvDyN7e6THxeHq77+LHYeISOMJgoBzM2ZAyM5GpRYtUKlZM7EjURnBYkclTtfQUHUhxY01a/AsKkrkREREmi0mJATxp09DR18fDb79Vuw4VIaw2FGpqNyqFRyaN4cyOxthP/3ECymIiN5CkZaGC7NmAQBqDxgAE0dHkRNRWcJiR6VCIpHA+/vvITUwQEJYGO7u3i12JCIijXRlyRKkx8XBuFIl1TnKRAXFYkelxqRSJdUTKS7Mno3M5GRxAxERaZikGzcQ+eqCCe8ffoCugYHIiaisYbGjUuUWHAxzFxdkJibi0q+/ih2HiEhjKHNycHbKlJdPmPD35wUTVCQsdlSqpPr68P7xRwDA7c2b8eTyZZETERFphqgtW/D08mXoGhurLjgjKiwWOyp1tg0bwql9e0AQEDZlCpTZ2WJHIiISVcbjxwifPx8AUG/kSBjZ2IiciMoqFjsSRf1vvoG+mRmSbtzAzb//FjsOEZGoLsyaBcXz56hQpw5q9Oghdhwqw1jsSBQGVlbwHD0aAHB54UKkx8eLnIiISByxJ07g3t69kOjo4KNJk6AjlYodicowjSl2M2fOhEQiwahRo/LMEwQBbdu2hUQiwY4dO9Tm3b9/H4GBgTAyMoKNjQ3Gjh2L7DcO7YWGhsLLywsymQzVq1fH2rVrS+6NUIG5dOkCq3r1kJ2ejvMzZ4odh4io1GW/eIGwn34CANT44gtUqFNH5ERU1mlEsQsLC8Py5ctRt27dfOcvWLAAEokkz/ScnBwEBgYiKysLJ0+exB9//IG1a9di4sSJqmWio6MRGBiIli1bIjw8HKNGjcKAAQPw33//ldj7oYKR6Ojgo4kTIZFKERMSggeHDokdiYioVEWsWIHUmBgY2tig3tdfix2HtIDoxS41NRVBQUFYsWIFLC0t88wPDw/H3LlzsXr16jzzQkJCEBERgfXr18PT0xNt27bFTz/9hMWLFyMrKwsAsGzZMjg5OWHu3LmoVasWhg8fji5dumD+q5NUSVyWbm6o1acPACBs2jQoUlPFDUREVEqe3bmDiJUrAQANvv0WeiYmIicibaArdoBhw4YhMDAQfn5+mDZtmtq89PR0fPHFF1i8eDHs7Ozy/OypU6fg4eEBW1tb1bSAgAB89dVXuHbtGurXr49Tp07Bz89P7ecCAgLyPeSbKzMzE5mZmarXKSkpAACFQgGFQlGUt/leuestqfVrMreBA3EvJARpMTG4MHcuvL77TtQ85XksNBHHQ3NwLIqPoFTizKRJUGZnw+6TT2DXsmWhPleOheYojbEozLpFLXYbN27EhQsXEBYWlu/80aNHo0mTJujQoUO+8+Pi4tRKHQDV67i4uHcuk5KSgoyMDBgaGuZZ74wZMzBlypQ800NCQmBkZPT+N/YB5HJ5ia5fU+X4+wOrViFq82Y8tLSEtGpVsSOV27HQVBwPzcGx+HCK06eRdeECoK+PZz4+2LdvX5HWw7HQHCU5Funp6QVeVrRiFxMTg5EjR0Iul8Mgn0em7Nq1C4cOHcLFixdLPduECRMwZswY1euUlBQ4OjrC398fZmZmJbJNhUIBuVyO1q1bQ09Pr0S2oenCnj7F3R07oCeXo/XGjZDq64uSg2OhWTgemoNjUTzS4+Px3/TpAADPUaNQ44svCr0OjoXmKI2xyD1yWBCiFbvz588jISEBXl5eqmk5OTk4evQoFi1ahK+++gpRUVGwsLBQ+7nOnTujadOmCA0NhZ2dHc6ePas2P/7VbTNyD93a2dmppr2+jJmZWb576wBAJpNBJpPlma6np1fiv0ClsQ1N1WDsWMQdO4bnd+7g5tq1qDtsmKh5yvNYaCKOh+bgWBSdIAi4+PPPyE5Lg1W9enD78ssPur0Jx0JzlORYFGa9ol084evriytXriA8PFz15e3tjaCgIISHh+P777/H5cuX1eYDwPz587FmzRoAgI+PD65cuYKEhATVeuVyOczMzFC7dm3VMgcPHlTbtlwuh4+PT+m8USowmYUFGrw6vy7i99/x7PZtkRMRERWve/v24dGRI9DR00PjqVN5zzoqdqLtsTM1NYW7u7vaNGNjY1hZWamm53fBRJUqVeDk5AQA8Pf3R+3atdGrVy/MmjULcXFx+OGHHzBs2DDVHrchQ4Zg0aJFGDduHPr164dDhw5h06ZN2LNnTwm/QyqKKgEBuLt7Nx6GhuLMpElovW4dJDqiX7xNRPTBXiQl4fyMGQCAOoMGwbx6dZETkTYq039jSqVS/Pvvv5BKpfDx8cGXX36J3r17Y+rUqaplnJycsGfPHsjlctSrVw9z587FypUrERAQIGJyehuJRALvH36ArpERnoSH49Y//4gdiYioWFz45RdkJibCvEYN1B4wQOw4pKVEv93J60JDQ985XxCEPNOqVq2KvXv3vvPnWrRoIcpFGFQ0xvb28Bw9GuemT0f4vHmo1KIFjO3txY5FRFRkj44dw93duwGJBI2mThXt4jDSfmV6jx1prxo9eqCipyey09NxdtKkfEs9EVFZoEhLw9lXt9By7dULFd/ylCWi4sBiRxpJoqODxtOmQUdfH7EnTuDOtm1iRyIiKpJLv/6K9NhYGFeuzMeGUYljsSONZebkhHojRgAALsyahbTYWJETEREVTsK5c7j5118AgEaTJ0O3hG9yT8RiRxrNtXdvVPT0hCI1lYdkiahMUaSl4fQPPwCCAJfOnWHH22xRKWCxI42mI5XykCwRlUnh8+YhNSYGRvb28Bo3Tuw4VE6w2JHG4yFZIipr4k6fxq2NGwEAjX/6CXomJiInovKCxY7KBB6SJaKyQpGa+vIQLIAa3bvzECyVKhY7KhN4SJaIyooLs2erroL1/N//xI5D5QyLHZUZPCRLRJru0bFjiNqyBQDQeNo06Bkbi5yIyhsWOypTXj8ke2biRAhKpdiRiIgAAFkpKTgzaRIAoOaXX8K2YUORE1F5xGJHZUruIVmpgQHiTp7Ezb//FjsSEREA4PzMmciIj4dJlSrwHDVK7DhUTrHYUZlj5uSE+q/OWwmfOxfPoqJETkRE5d2DQ4cQvXMnIJHAZ/p06Boaih2JyikWOyqTavTsCfuPP0ZOZiZOfvstcrKyxI5EROVUxpMnqkOwtfr0gbWXl8iJqDxjsaMySSKRoNG0adA3N0dSRASuLl0qdiQiKocEQcCZiRORmZgIi5o1UffVBV5EYmGxozLLyMYGH736V3LEypV4fPGiyImIqLy5vWkTHh05Ah19fTT55RdI9fXFjkTlHIsdlWlVAgJQrX17CEolTk2YAEVamtiRiKicSImOxoVZswAAnqNGwaJmTZETEbHYkRbw/u47GNnbIzUmRvU/WSKikqRUKHBy/HjkvHgB28aN4dqrl9iRiACw2JEW0Dc1hc+MGYBEgqgtW/Dg0CGxIxGRlruyZAkSr12DvpkZfKZPh0SHf52SZuCfRNIKtg0bolafPgCAM5MmIePJE3EDEZHWenzhAiJWrgQAfDR5Mozs7ERORPT/WOxIa9QdMQIWNWsiMzERpyZM4FMpiKjYKVJTcfLV/1+c2rdHlYAAsSMRqWGxI60h1dfHx7Nnq55KcX3tWrEjEZEWEQQBZ6dORdqDBzCuVAne338vdiSiPFjsSKuYV6+OBt9+CwC49OuveHrlisiJiEhbRO/YgXt79kAilaLJzJnQMzEROxJRHix2pHVcunRBlYAACNnZODF2LBSpqWJHIqIyLiU6GmHTpwMAPIYN49MlSGOx2JHWkUgk+GjyZBg7OCA1JgZnp06FIAhixyKiMionMxPH//c/5GRkwLZRI9QeMEDsSERvxWJHWknfzAxNZs2CRCrFvT17Xj6cm4ioCC7OmYPkyEjILC3hM3MmdKRSsSMRvRWLHWkt6/r14TFsGADg3LRpSLl7V9xARFTmPDh0CDf/+gsA0Pjnn2FkYyNyIqJ3Y7EjrVZ7wADYfvQRsjMycOKbb5CTlSV2JCIqI9JiY3H61ZWvbn36oFKzZiInIno/FjvSajpSKXxmzoTMwgJJ16/j4ty5YkciojJAmZ2Nk+PGISslBRXq1EG9kSPFjkRUICx2pPWMbG3R+NXVbDfXr8f9//4TORERaborixfj8YUL0DU2xsdz5kCqry92JKICYbGjcqFSixao1a8fAOD0jz/yfDsiequHR47g2u+/A3j5yDDTKlVETkRUcCx2VG7UGzkSNt7eyE5Lw/HRo5GdkSF2JCLSMKkPH+LUq5uc1/ziC1Rr107kRESFw2JH5YaOri4+njMHBlZWSL55E+emTRM7EhFpkJysLBwfPRpZKSmw8vBA/bFjxY5EVGgsdlSuGFpb4+PZsyHR0cGdHTsQtW2b2JGISENcmDkTideuQd/cHJ/Mm8fz6qhMYrGjcse2USN4DB8O4OX97ZJu3BA5ERGJLfrff3Hrn38AiQRNfvkFxg4OYkciKhIWOyqX6gwcCPumTZGTmYljo0cj6/lzsSMRkUie3b6Ns5MnAwDcBw+GQ9Om4gYi+gAsdlQuSXR00GTmTBjZ2yP1/n2c/u47CEql2LGIqJQp0tJwbPRo5GRkwM7HB+5Dh4odieiDsNhRuSWzsMAn8+ZBR08PDw4dwtXly8WORESlSBAEnP7uO6TcuQNDW1s0mTWLz4GlMo/Fjsq1inXrouGPPwJ4eUPSh6Gh4gYiolJz7fffEXPgAHT09PDJvHkwqFBB7EhEH4zFjso9l86dUaN7d0AQcHL8eDy/d0/sSERUwh4eOYLLv/0GAPD+4QdYe3qKG4iomLDYEQHw+vZbWNevD0VqKk6MHg3hxQuxIxFRCUmJjsbJceMAQUCN7t1RvUsXsSMRFRsWOyIAUn19fDJ/PgxtbPD8zh1kbtnCiymItJAiNRVHR4yAIjUV1l5e8Hr1lAkibcFiR/SKobU1mv76K3T09JATEYHrq1aJHYmIipGgVOLkt9+qLpbgTYhJG7HYEb2mYt268PruOwDAtSVL8ODwYZETEVFxubpsGR4ePgwdfX00+/VXGFpbix2JqNix2BG9walTJ+g2avTyYopx45B886bYkYjoA8XI5biyeDEA4KOJE2Hl4SFyIqKSwWJHlA/9Tz+FdcOGyE5Px5Fhw/Di6VOxIxFRESVeu4aTr86lqxkUBOdOnURORFRyWOyI8iGRStFkzhyYVq2KtEePcHTECORkZoodi4gKKT0+HkeGD0fOixew//hjeI0bJ3YkohLFYkf0Fvrm5mi+eDH0zMzwJDwcZyZOhCAIYsciogLKTk/HkeHDkZGQAHMXF3w8dy50dHXFjkVUoljsiN7BzMkJTefNg0Qqxd1//8W1338XOxIRFYCgVOLUhAlIioiAzNISzZcsgb6pqdixiEocix3Re9j5+MD7++8BAJcXLsT9kBCRExHR+1xauFD1uLBmCxfCpHJlsSMRlQoWO6ICqNG9O2p++SUA4NSECXh69arIiYjobe7s2IGIFSsAAI1++gnWXl4iJyIqPRpT7GbOnAmJRIJRo0appg0ePBguLi4wNDSEtbU1OnTogBs3bqj9nEQiyfO1ceNGtWVCQ0Ph5eUFmUyG6tWrY+3ataXwjkjbeI0dC/umTZHz4gWODB2K1JgYsSMR0Rviz57F2UmTAAB1Bg2C02efiZyIqHRpRLELCwvD8uXLUbduXbXpDRo0wJo1a3D9+nX8999/EAQB/v7+yMnJUVtuzZo1iI2NVX117NhRNS86OhqBgYFo2bIlwsPDMWrUKAwYMAD//fdfabw10iI6urr4ZM4cWLi64sXTpzg8ZAgyk5PFjkVEryTfvImjI0ZAmZ2NKgEBqPv112JHIip1ohe71NRUBAUFYcWKFbC0tFSbN2jQIDRr1gzVqlWDl5cXpk2bhpiYGNy9e1dtOQsLC9jZ2am+DAwMVPOWLVsGJycnzJ07F7Vq1cLw4cPRpUsXzJ8/vzTeHmkZPRMTtFi2DEZ2dnh+9y6ODBuG7BcvxI5FVO6lx8Xh8JAhUDx/DusGDeAzYwYkOqL/FUdU6kS/7nvYsGEIDAyEn58fpk2b9tbl0tLSsGbNGjg5OcHR0THPOgYMGABnZ2cMGTIEffv2hUQiAQCcOnUKfn5+assHBASoHfJ9U2ZmJjJfu2dZSkoKAEChUEChUBT2LRZI7npLav1UcO8bCz1LS3yyaBEO9+2LJ+HhODF2LHxmz4ZEKi3NmOUGfzc0h6aORVZKCg4PHoyM+HiYOjujybx5UOroQKlhOYuTpo5FeVQaY1GYdYta7DZu3IgLFy4gLCzsrcssWbIE48aNQ1paGlxdXSGXy6H/2kObp06dilatWsHIyAghISEYOnQoUlNTMWLECABAXFwcbG1t1dZpa2uLlJQUZGRkwNDQMM82Z8yYgSlTpuSZHhISAiMjo6K+3QKRy+Ulun4quPeNhbR7dyjWrMHDQ4ewY/hw6H/6qeofFFT8+LuhOTRpLITsbLxYswbK6GhITE2R3aULDpw4IXasUqNJY1HeleRYpKenF3hZ0YpdTEwMRo4cCblcrnbo9E1BQUFo3bo1YmNjMWfOHHTr1g0nTpxQ/cyPP/6oWrZ+/fpIS0vD7NmzVcWuKCZMmIAxY8aoXqekpMDR0RH+/v4wMzMr8nrfRaFQQC6Xo3Xr1tDT0yuRbVDBFGYsYmrUwOnx45F96hRq+/jAtXfvUkpZfvB3Q3No2lgISiXOfPcdYqKjoWtsjJYrV8LC1VXsWKVC08aiPCuNscg9clgQohW78+fPIyEhAV6vXYaek5ODo0ePYtGiRcjMzIRUKoW5uTnMzc1Ro0YNNG7cGJaWlti+fTt69uyZ73obNWqEn376CZmZmZDJZLCzs0N8fLzaMvHx8TAzM8t3bx0AyGQyyGSyPNP19PRK/BeoNLZBBVOQsXD+9FNkPnmCi7Nn4/K8eTC2tYXTp5+WUsLyhb8bmkNTxuLinDmI2b8fEl1dNPv1V1i7u4sdqdRpylhQyY5FYdYrWrHz9fXFlStX1Kb17dsXbm5uGD9+PKT5nK8kCAIEQVA7/+1N4eHhsLS0VBUzHx8f7N27V20ZuVwOHx+fYngXRIBbcDDSY2MRuX49Tn/3HfRNTFCpRQuxYxFptYhVq3B9zRoAQONp02DH/6cTARCx2JmamsL9jX9dGRsbw8rKCu7u7rhz5w7++ecf+Pv7w9raGg8ePMDMmTNhaGiIdu3aAQB2796N+Ph4NG7cGAYGBpDL5fj555/xzTffqNY5ZMgQLFq0COPGjUO/fv1w6NAhbNq0CXv27CnV90vaSyKRwGv8eGQmJ+Puv//i+JgxaLF8OWwbNhQ7GpFWur1pE8LnzQMAeP7vf7xXHdFrNPZacAMDAxw7dgzt2rVD9erV0b17d5iamuLkyZOwsbEB8HLX5OLFi+Hj4wNPT08sX74c8+bNw6RXN6cEACcnJ+zZswdyuRz16tXD3LlzsXLlSgQEBIj11kgLSXR00HjaNFRq0QI5mZk4MmwYEiMixI5FpHXu7duHs1OnAgBqDxyI2v36iZyISLOIfruT14WGhqq+d3BwyHMI9U1t2rRBmzZt3rveFi1a4OLFix8aj+iddPT08PHcuQgdMgQJYWE4PGgQ/P78E+bOzmJHI9IKD48exclvvwUEATW6d0e9kSPFjkSkcTR2jx1RWaRrYIDmixahQp06yExKwuGBA5H26JHYsYjKvITz53F81CgI2dmo2q4dvH/4gbcXIsoHix1RMct9OoWZszPS4+JwaOBAZDx5InYsojIrMSICR4YORU5mJhyaN4fPzz/zqRJEb8HfDKISYFChAlr+/juM7O3x/O5dHBowAC8SE8WORVTmJN24gUMDBkCRmgobb298Mm8edHh7D6K3YrEjKiHG9vbwXbUKhjY2eHbrFg7174/M5GSxYxGVGcm3buHQgAHIevYMVnXrovnixdB9xw3tiYjFjqhEmVatCt/Vq2FQsSKSb95kuSMqoGe3b+Ngv37ITEpChTp10HL5cuiZmIgdi0jjsdgRlTAzJ6eX5c7KCkk3buDwoEHIKsTjYYjKm2d37rwsdYmJsKxVC61WrIB+CT3OkUjbsNgRlQJzFxe0Wr0aMktLJF679rLcPX8udiwijZNy7x4O9euHF0+fwsLVFa1WroS+ubnYsYjKDBY7olJiUb06Wq1aBX1zczy9coV77ojekHL3Lg727YuMx49hUbMmWq1aBZmFhdixiMoUFjuiUmTp6grf3HJ3+TIO9uuHF0lJYsciEl3yrVs40Ls3MuLjX+7hXrkSBpaWYsciKnNY7IhKmWWtWvBdswayChWQdP06Dvbpg4zHj8WORSSaxIgIHOzTR3X41XftWhhYWYkdi6hMYrEjEoGlqyv8/vjj5a1Qbt/GgeBgpMXGih2LqNQ9Dg9/eaFEcjKsPDzgt2YNDCpUEDsWUZnFYkckEnNnZ/j98cfLmxjfu4cDwcFIffBA7FhEpSb+7FkcHjAAiufPYd2gAS+UICoGLHZEIjKtUgWt//wTJo6OSHv4EPLevfEsKkrsWEQl7tGxYwgdMgTZGRmw8/FBy2XLeJ86omLAYkckMmMHB/j9+SfMnJ2RER8Pea9eeHL5stixiEpM9O7dODJ8uOrZr80XL4aukZHYsYi0AosdkQYwsrGB359/wsrDA1nPnuFgv354dOyY2LGIit31tWtx6ttvIWRno9qnn6LpggWQymRixyLSGix2RBrCwNISrVatgv3HHyMnIwNHhg9H9K5dYsciKhaCIODinDm4OHs2AMC1d2/4zJgBqb6+yMmItAuLHZEG0TM2RrNFi1A1MBBCdjZOTZiA62vXih2L6IMoFQqc/v57XF+zBgDgOWYMvMaNg0SHfwURFTf+VhFpGKm+PprMnAnXXr0AABdnz8aFWbMgKJUiJyMqPEVaGo6OGIHonTshkUrReNo01O7fHxKJROxoRFqJxY5IA0l0dOA1fjw8x4wBANz44w8cGzUK2enpIicjKrj0uDjIe/XCo6NHITUwQLOFC+HcqZPYsYi0GosdkYaSSCSo3b8/mvzyC3T09PDg4EEc6NMH6QkJYkcjeq/Ea9fwX48eSI6MhIGVFXzXrEGlFi3EjkWk9VjsiDRctU8/he/q1ZBZWiLx2jWE9OyJpBs3xI5F9FYPDh2CPDgYGY8fw7x6dQRs3IiKdeuKHYuoXGCxIyoDrL284P/XXzBzclId3np49KjYsYjUCIKA62vX4uiIEcjJyID9xx+j9fr1MHZwEDsaUbnBYkdURphWqQL/DRtg+9FHyE5Px9Fhw3B9zRoIgiB2NCLkZGbizMSJL29nIgio0b07mi9ZAn1TU7GjEZUrLHZEZYi+uTlaLF8Ol86dISiVuDhnDk6OHcuLKkhU6XFxOBAcjDvbtr288GfcOHj/+CN0dHXFjkZU7rDYEZUxUn19fDRlCrx/+AESXV3c27cPIUFBSH3wQOxoVA4lnD+P/d264emVK9A3M0OL5cvhFhzM25kQiYTFjqgMkkgkqNmzJ3xXr4aBlRWSb97E/m7dEHvypNjRqJwQBAE3//oLB/v1w4unT2FRsybabNoE+yZNxI5GVK6x2BGVYTYNGqDNpk2o4O6OrGfPEDp4MK6tWMGbGVOJys7IwJkffsC56dMhZGejatu28N+wASaOjmJHIyr3WOyIyjgjOzu0/vNPOHfqBEGpxKUFCxD61Vd4kZgodjTSQsr4eBwMCsKdHTsg0dFB/W++QZPZs6FrZCR2NCICix2RVpDKZGj0009oNHUqpDIZYo8fx77OnREfFiZ2NNISgiAgescOZCxZgpQ7d2BQsSJarVyJWn378nw6Ig3CYkekJSQSCVw6d0bAP//AzNkZGQkJONSvH64sXQplTo7Y8agMU6Sl4dSECTg3eTKgUMDWxwfttm2DbaNGYkcjojew2BFpGYsaNdDmn3/g1KEDBKUSVxYtwuGBA5EeHy92NCqDEiMisL9bN9zdvRsSqRR6/v5oungxDKysxI5GRPlgsSPSQrpGRvD5+Wc0nj4dUkNDxJ85gz0dO+Lunj1iR6MyQpmdjavLl+O/nj3x/O5dGNraosXKldBv0QISHf7VQaSp+NtJpMWcO3ZE282bUcHdHYqUFJwcNw7Hv/kGmcnJYkcjDfb83j3Ie/fG5YULIWRnw7F1a7TduhUV69cXOxoRvQeLHZGWM3Nygv/69fAYNgwSqRT39+3D3k6d8Oj4cbGjkYYRBAG3N23C3s6d8fTSJeiZmMBnxgx8Mn8+DCwtxY5HRAXAYkdUDujo6cFj6FD4b9gAMycnZCQkIHTwYJyZNAlZKSlixyMNkBoTg0MDBuDslCnIyciATcOGaLd9O5zat+dVr0RlCIsdUTli5eGBNps3o+aXXwIAorZswZ727REjl4ucjMSizM7G9bVrsadjR8SfPg2pTIb6Y8fCd/VqGDs4iB2PiAqJxY6onNE1NIT3hAnw++MPmFarhozHj3Fs1CgcHTGCV86WM0k3biDkiy9wcfZs5Lx4AduPPkK77dtRq08fXiBBVEbxN5eonLLx9ka7bdtQZ/BgSHR18eDgQexp3x6RGzZAmZ0tdjwqQYrUVFyYNQv7u3dH4rVr0DM1xUdTpqDV6tUwrVpV7HhE9AFY7IjKMalMhnojRqDt5s2w8vCAIjUV53/+Gfu7duVTK7SQIAiI3rULuwMDceOPP15e8ernh09370b1Ll14Lh2RFtAVOwARic+iZk203rABUZs349LChUi+eRMH+/RB1bZtUf+bb2BkZyd2RPpASdev49z06Xh88SIAwLRqVTSYMAEOTZuKnIyIihOLHREBAHSkUtTo0QNV2rTB5YULcXvzZtzbtw8PQkNRu18/uAUHQ8/YWOyYVEjpcXG4vHgxonfsgKBUQmpoCPfBg+EWHAypvr7Y8YiomPFQLBGpkVlYoOHEiQjYtAnW9esjJyMDVxYvxu62bXHz77+hVCjEjkgFkPX8OcIXLMDudu1wZ9s2CEolqrRpg09370adgQNZ6oi0FPfYEVG+KtSqBb916xATEoLwBQuQev8+zk2bhht//gnPUaPg6O/Pc7I0UE5mJm798w+uLV+uesKItZcXPP/3P1h7eoqajYhKHosdEb2VRCJBlYAAVG7VCre3bMHVpUuRev8+jo8ZAwtXV7gPHgzH1q15awwNkP3iBW5v3ozrq1Yh4/FjAICZszM8R49GpZYtWcKJygkWOyJ6Lx09PdTs2RNO7dvjxh9/4PratUiOjMTxMWNgXr066gwejCoBAdCRSsWOWu5kZ2Tg9qZNiFi9Gi+ePAEAGNnZwX3IEDh36gQdXf5vnqg84W88ERWYnrExPIYORc0vvkDkhg2IXLcOz27fxsmxY3F1yRK4BQej2mefQdfAQOyoWu9FYiJubdyIWxs34sXTpwAAYwcH1Bk4EE4dO/IcOqJyisWOiApNZmGBusOGwa13b9zcsAE3/vgDKdHRODt5Mi79+itqdO+OGj16wNDaWuyoWudZVBQi161D9K5dyMnMBAAYV6qEOoMGwal9exY6onKOxY6Iikzf1BTuQ4bAtVcv3N68GTc3bEDao0e4umwZIlatQtV27VCje3dY1a3Lc7w+gDI7G4+OHsWtTZsQe+yYanqFOnXg1qcPqrRuDR09PRETEpGmYLEjog+mZ2yMWn36wPXLL/Hg4EHc+PNPPAkPR/TOnYjeuRPmNWrApXNnOH32GWQWFmLHLTNSHz5E1NatuLN9OzISEl5OlEhQuVUruAUHw9rLi4WZiNSw2BFRsdHR1UWVgABUCQjAk8uXcevvv3E/JATPbt3ChZkzET5vHhx9fVHts89g5+PDw4b5UKSmIubAAdzdswdxp04BggAAkFlawrljR7h07QozPs+ViN5CY+5RMHPmTEgkEowaNUo1bfDgwXBxcYGhoSGsra3RoUMH3LhxQ+3n7t+/j8DAQBgZGcHGxgZjx45F9hsPMA8NDYWXlxdkMhmqV6+OtWvXlsI7IirfKtatC58ZM9Dp8GF4//ADLN3coMzKwr19+3Bk6FBsb94cZyZORNzp01Dm5IgdV1TZL17g/n//4djIkdjatClOf/894k6eBAQBdj4++HjuXHQ8dAj1v/mGpY6I3kkj9tiFhYVh+fLlqFu3rtr0Bg0aICgoCFWqVEFiYiImT54Mf39/REdHQyqVIicnB4GBgbCzs8PJkycRGxuL3r17Q09PDz///DMAIDo6GoGBgRgyZAg2bNiAgwcPYsCAAbC3t0dAQIAYb5eoXNE3M0PNnj1Rs2dPJF67hjs7d+L+f//hxZMniNq6FVFbt8LAygoOzZrBoVkz2DdpAj0TE7Fjl7iMx4/x6OhRPAwNReypU8jJyFDNM3N2RtW2bVHt009hWqWKiCmJqKwRvdilpqYiKCgIK1aswLRp09TmDRo0SPV9tWrVMG3aNNSrVw93796Fi4sLQkJCEBERgQMHDsDW1haenp746aefMH78eEyePBn6+vpYtmwZnJycMHfuXABArVq1cPz4ccyfP5/FjqiUVahTBxXq1IHX+PF4fO4c7u3bh/shIXjx9CnubN+OO9u3Q0dXF9YNGsChWTPYfvQRTJydxY5dLHIyM/Hk0iXEnz2LR8eOIfHqVbX5Rvb2L8tcu3awcHPjuXNEVCSiF7thw4YhMDAQfn5+eYrd69LS0rBmzRo4OTnB0dERAHDq1Cl4eHjA1tZWtVxAQAC++uorXLt2DfXr18epU6fg5+entq6AgAC1Q75vyszMROar2wgAQEpKCgBAoVBAUULPycxdb0mtnwqOY1E6Knh5oYKXF+qNG4fHFy4g9tgxxB47htR79xB/5gziz5wBAOgaG0OoXBnXHj2Crbc3LFxdoWtoKHL698t69gxJERF4cvEiEs6fR+Lly3mes2tZp87LvZTNm8PC1VVV5t48nURT8HdDc3AsNEdpjEVh1i1qsdu4cSMuXLiAsLCwty6zZMkSjBs3DmlpaXB1dYVcLof+qxOu4+Li1EodANXruLi4dy6TkpKCjIwMGObzF8SMGTMwZcqUPNNDQkJgZGRUuDdZSHK5vETXTwXHsShltWsDtWvD8MkT5ERGIufWLeTcu4fstDQgMhIRkZGIAACJBBJra0grVYKOgwN07O0hqVgRElNTUfZyCUolhKQkKJ88gTIuDsoHD6B89AhCUlKeZSWmptBxcoK0enVIXV2RZWqKuwDu3rkD3LlT6tmLir8bmoNjoTlKcizS09MLvKxoxS4mJgYjR46EXC6HwTvuUh8UFITWrVsjNjYWc+bMQbdu3XDixIl3/syHmjBhAsaMGaN6nZKSAkdHR/j7+8PMzKxEtqlQKCCXy9G6dWvo8X5UouJYaA4hJwdPIiJwcuNGWKWlIfHyZWQmJkJISEB2QgJw8aJqWamhIUyrVIFJlSowcXSEQcWKMKhYEYbW1jCwsoKsQgXoGhpCUojHnikVCijS0pCVnIyMx4/x4vFjZLz6SnvwAM/v30daTEyePXG5jB0dYeXuDmtvb1h7e8OkSpUyfYiVvxuag2OhOUpjLHKPHBaEaMXu/PnzSEhIgJeXl2paTk4Ojh49ikWLFiEzMxNSqRTm5uYwNzdHjRo10LhxY1haWmL79u3o2bMn7OzscPbsWbX1xsfHAwDs7OxU/82d9voyZmZm+e6tAwCZTAaZTJZnup6eXon/ApXGNqhgOBYaQE8P1h4e0IuJwSft2kFXVxcZjx8jKSICiRERSLp+Hcm3biHt4UPkZGQgOTISyZGR71yl1NAQekZG0DUyUr+p76vbiuQoFMhOTYUiLe2the1NOvr6MK1aFeYuLqhQu/bLcwlr1YK+uXmR37om4++G5uBYaI6SHIvCrFe0Yufr64srV66oTevbty/c3Nwwfvx4SPP5V7UgCBAEQXX+m4+PD6ZPn46EhATY2NgAeLkr1MzMDLVr11Yts3fvXrX1yOVy+Pj4lMTbIqISJJFIYGRjAyMbG1Rq0UI1PScrC2kPHyLl7l08v3cPaY8e/f8etidPkPHkieqq05yMjJffv3q+akHoGhvDyMbm5d4/a+uXGeztYVatGkyrVYORnR10CrEnkIiopIhW7ExNTeHu7q42zdjYGFZWVnB3d8edO3fwzz//wN/fH9bW1njw4AFmzpwJQ0NDtGvXDgDg7++P2rVro1evXpg1axbi4uLwww8/YNiwYao9bkOGDMGiRYswbtw49OvXD4cOHcKmTZuwZ8+eUn/PRFQypPr6MHNygpmTU77zBUFATmYmsjMykJ2ervrKycwEXh0azT1EKtHVhZ6xsepL19gYOrqiX2dGRFQgGvt/KwMDAxw7dgwLFixAUlISbG1t0axZM5w8eVK1d04qleLff//FV199BR8fHxgbGyM4OBhTp05VrcfJyQl79uzB6NGj8euvv6Jy5cpYuXIlb3VCVI5IJBLoGhhA18AAsLQUOw4RUYnRqGIXGhqq+t7BwSHPIdT8VK1a9b3LtWjRAhdfO8maiIiISBtpzCPFiIiIiOjDsNgRERERaQkWOyIiIiItwWJHREREpCVY7IiIiIi0BIsdERERkZZgsSMiIiLSEix2RERERFqCxY6IiIhIS7DYEREREWkJFjsiIiIiLcFiR0RERKQlWOyIiIiItASLHREREZGW0BU7QFkgCAIAICUlpcS2oVAokJ6ejpSUFOjp6ZXYduj9OBaaheOhOTgWmoNjoTlKYyxy+0duH3kXFrsCeP78OQDA0dFR5CRERERUXj1//hzm5ubvXEYiFKT+lXNKpRKPHj2CqakpJBJJiWwjJSUFjo6OiImJgZmZWYlsgwqGY6FZOB6ag2OhOTgWmqM0xkIQBDx//hwODg7Q0Xn3WXTcY1cAOjo6qFy5cqlsy8zMjL+kGoJjoVk4HpqDY6E5OBaao6TH4n176nLx4gkiIiIiLcFiR0RERKQlWOw0hEwmw6RJkyCTycSOUu5xLDQLx0NzcCw0B8dCc2jaWPDiCSIiIiItwT12RERERFqCxY6IiIhIS7DYEREREWkJFjsiIiIiLcFipyEWL16MatWqwcDAAI0aNcLZs2fFjqT1ZsyYgYYNG8LU1BQ2Njbo2LEjIiMj1ZZ58eIFhg0bBisrK5iYmKBz586Ij48XKXH5MXPmTEgkEowaNUo1jWNReh4+fIgvv/wSVlZWMDQ0hIeHB86dO6eaLwgCJk6cCHt7exgaGsLPzw+3bt0SMbF2ysnJwY8//ggnJycYGhrCxcUFP/30k9rzQjkWJefo0aP47LPP4ODgAIlEgh07dqjNL8hnn5iYiKCgIJiZmcHCwgL9+/dHampqieZmsdMA//zzD8aMGYNJkybhwoULqFevHgICApCQkCB2NK125MgRDBs2DKdPn4ZcLodCoYC/vz/S0tJUy4wePRq7d+/G5s2bceTIETx69Aiff/65iKm1X1hYGJYvX466deuqTedYlI6kpCR8/PHH0NPTw759+xAREYG5c+fC0tJStcysWbOwcOFCLFu2DGfOnIGxsTECAgLw4sULEZNrn19++QVLly7FokWLcP36dfzyyy+YNWsWfvvtN9UyHIuSk5aWhnr16mHx4sX5zi/IZx8UFIRr165BLpfj33//xdGjRzFo0KCSDS6Q6D766CNh2LBhqtc5OTmCg4ODMGPGDBFTlT8JCQkCAOHIkSOCIAhCcnKyoKenJ2zevFm1zPXr1wUAwqlTp8SKqdWeP38u1KhRQ5DL5ULz5s2FkSNHCoLAsShN48ePFz755JO3zlcqlYKdnZ0we/Zs1bTk5GRBJpMJf//9d2lELDcCAwOFfv36qU37/PPPhaCgIEEQOBalCYCwfft21euCfPYRERECACEsLEy1zL59+wSJRCI8fPiwxLJyj53IsrKycP78efj5+amm6ejowM/PD6dOnRIxWfnz7NkzAECFChUAAOfPn4dCoVAbGzc3N1SpUoVjU0KGDRuGwMBAtc8c4FiUpl27dsHb2xtdu3aFjY0N6tevjxUrVqjmR0dHIy4uTm0szM3N0ahRI45FMWvSpAkOHjyImzdvAgAuXbqE48ePo23btgA4FmIqyGd/6tQpWFhYwNvbW7WMn58fdHR0cObMmRLLpltia6YCefLkCXJycmBra6s23dbWFjdu3BApVfmjVCoxatQofPzxx3B3dwcAxMXFQV9fHxYWFmrL2traIi4uToSU2m3jxo24cOECwsLC8szjWJSeO3fuYOnSpRgzZgy+++47hIWFYcSIEdDX10dwcLDq887v/1kci+L17bffIiUlBW5ubpBKpcjJycH06dMRFBQEABwLERXks4+Li4ONjY3afF1dXVSoUKFEx4fFjggv9xRdvXoVx48fFztKuRQTE4ORI0dCLpfDwMBA7DjlmlKphLe3N37++WcAQP369XH16lUsW7YMwcHBIqcrXzZt2oQNGzbgr7/+Qp06dRAeHo5Ro0bBwcGBY0FvxUOxIqtYsSKkUmmeq/vi4+NhZ2cnUqryZfjw4fj3339x+PBhVK5cWTXdzs4OWVlZSE5OVlueY1P8zp8/j4SEBHh5eUFXVxe6uro4cuQIFi5cCF1dXdja2nIsSom9vT1q166tNq1WrVq4f/8+AKg+b/4/q+SNHTsW3377LXr06AEPDw/06tULo0ePxowZMwBwLMRUkM/ezs4uz0WQ2dnZSExMLNHxYbETmb6+Pho0aICDBw+qpimVShw8eBA+Pj4iJtN+giBg+PDh2L59Ow4dOgQnJye1+Q0aNICenp7a2ERGRuL+/fscm2Lm6+uLK1euIDw8XPXl7e2NoKAg1fcci9Lx8ccf57ntz82bN1G1alUAgJOTE+zs7NTGIiUlBWfOnOFYFLP09HTo6Kj/NS2VSqFUKgFwLMRUkM/ex8cHycnJOH/+vGqZQ4cOQalUolGjRiUXrsQuy6AC27hxoyCTyYS1a9cKERERwqBBgwQLCwshLi5O7Gha7auvvhLMzc2F0NBQITY2VvWVnp6uWmbIkCFClSpVhEOHDgnnzp0TfHx8BB8fHxFTlx+vXxUrCByL0nL27FlBV1dXmD59unDr1i1hw4YNgpGRkbB+/XrVMjNnzhQsLCyEnTt3CpcvXxY6dOggODk5CRkZGSIm1z7BwcFCpUqVhH///VeIjo4Wtm3bJlSsWFEYN26cahmORcl5/vy5cPHiReHixYsCAGHevHnCxYsXhXv37gmCULDPvk2bNkL9+vWFM2fOCMePHxdq1Kgh9OzZs0Rzs9hpiN9++02oUqWKoK+vL3z00UfC6dOnxY6k9QDk+7VmzRrVMhkZGcLQoUMFS0tLwcjISOjUqZMQGxsrXuhy5M1ix7EoPbt37xbc3d0FmUwmuLm5Cb///rvafKVSKfz444+Cra2tIJPJBF9fXyEyMlKktNorJSVFGDlypFClShXBwMBAcHZ2Fr7//nshMzNTtQzHouQcPnw4378jgoODBUEo2Gf/9OlToWfPnoKJiYlgZmYm9O3bV3j+/HmJ5pYIwmu3sCYiIiKiMovn2BERERFpCRY7IiIiIi3BYkdERESkJVjsiIiIiLQEix0RERGRlmCxIyIiItISLHZEREREWoLFjog0UmhoKCQSSZ7nw75u7dq1sLCw+OBtVatWDQsWLPjg9bxNXFwcWrduDWNj4w/O26dPH3Ts2PGdy7Ro0QKjRo36oO0URw4iKn26YgcgIspPkyZNEBsbC3Nzc7GjfLD58+cjNjYW4eHhpfJ+tm3bBj09vRLfDhFpHhY7ItJI+vr6sLOzEztGsYiKikKDBg1Qo0aNty6jUCiKrYxVqFChWNZDRGUPD8USUbHL79Cmp6cnJk+erHotkUiwcuVKdOrUCUZGRqhRowZ27dqlmp/fodi1a9eiSpUqMDIyQqdOnfD06VO1bURFRaFDhw6wtbWFiYkJGjZsiAMHDqgtk5CQgM8++wyGhoZwcnLChg0b8uRPTk7GgAEDYG1tDTMzM7Rq1QqXLl1Szb906RJatmwJU1NTmJmZoUGDBjh37txbP4utW7fizz//hEQiQZ8+fVTvf+nSpWjfvj2MjY0xffp05OTkoH///nBycoKhoSFcXV3x66+/5rveKVOmqPINGTIEWVlZqnlvHorNzMzE+PHj4ejoCJlMhurVq2PVqlUAUKBt5uTkYMyYMbCwsICVlRXGjRuHN59GuX//fnzyySeqZT799FNERUWp5mdlZWH48OGwt7eHgYEBqlatihkzZuT73oio6FjsiEg0U6ZMQbdu3XD58mW0a9cOQUFBSExMzHfZM2fOoH///hg+fDjCw8PRsmVLTJs2TW2Z1NRUtGvXDgcPHsTFixfRpk0bfPbZZ7h//75qmT59+iAmJgaHDx/Gli1bsGTJEiQkJKitp2vXrkhISMC+fftw/vx5eHl5wdfXV5UtKCgIlStXRlhYGM6fP49vv/32rXvbwsLC0KZNG3Tr1g2xsbFqpWny5Mno1KkTrly5gn79+kGpVKJy5crYvHkzIiIiMHHiRHz33XfYtGmT2joPHjyI69evIzQ0FH///Te2bduGKVOmvPVz7t27N/7++28sXLgQ169fx/Lly2FiYgIABdrm3LlzsXbtWqxevRrHjx9HYmIitm/frraNtLQ0jBkzBufOncPBgweho6ODTp06QalUAgAWLlyIXbt2YdOmTYiMjMSGDRtQrVq1t2YmoiISiIiKWdWqVYX58+erTatXr54wadIk1WsAwg8//KB6nZqaKgAQ9u3bJwiCIBw+fFgAICQlJQmCIAg9e/YU2rVrp7bO7t27C+bm5u/MUqdOHeG3334TBEEQIiMjBQDC2bNnVfOvX78uAFDlPXbsmGBmZia8ePFCbT0uLi7C8uXLBUEQBFNTU2Ht2rXv3O7rOnToIAQHB6tNAyCMGjXqvT87bNgwoXPnzqrXwcHBQoUKFYS0tDTVtKVLlwomJiZCTk6OIAiC0Lx5c2HkyJFq71kulxc475vbtLe3F2bNmqV6rVAohMqVKwsdOnR46zoeP34sABCuXLkiCIIgfP3110KrVq0EpVJZ4BxEVHjcY0dEoqlbt67qe2NjY5iZmeXZe5br+vXraNSokdo0Hx8ftdepqan45ptvUKtWLVhYWMDExATXr19X7bG7fv06dHV10aBBA9XPuLm5qV2peunSJaSmpsLKygomJiaqr+joaNWhxTFjxmDAgAHw8/PDzJkz1Q45Foa3t3eeaYsXL0aDBg1gbW0NExMT/P7772p7HAGgXr16MDIyUvscUlNTERMTk2d94eHhkEqlaN68+VtzvGubz549Q2xsrNpnr6urmyf7rVu30LNnTzg7O8PMzEy1Ny53PX369EF4eDhcXV0xYsQIhISEvOfTIaKiYLEjomKno6OT5xwshUKRZ7k3D19KJBLVobui+Oabb7B9+3b8/PPPOHbsGMLDw+Hh4aF2/tn7pKamwt7eHuHh4WpfkZGRGDt2LICXh1CvXbuGwMBAHDp0CLVr185zaLIgjI2N1V5v3LgR33zzDfr374+QkBCEh4ejb9++hcr/JkNDw3fOL65tfvbZZ0hMTMSKFStw5swZnDlzBgBU6/Hy8kJ0dDR++uknZGRkoFu3bujSpUvR3hQRvRWviiWiYmdtbY3Y2FjV65SUFERHR3/QOmvVqqUqC7lOnz6t9vrEiRPo06cPOnXqBOBlSbt7965qvpubG7Kzs3H+/Hk0bNgQABAZGal2gYaXlxfi4uKgq6v7znPAatasiZo1a2L06NHo2bMn1qxZo9puUZ04cQJNmjTB0KFDVdPy2xt46dIlZGRkqErb6dOnYWJiAkdHxzzLenh4QKlU4siRI/Dz8yv0Ns3NzWFvb48zZ86gWbNmAKD6DL28vAAAT58+RWRkJFasWIGmTZsCAI4fP55nW2ZmZujevTu6d++OLl26oE2bNkhMTORVvETFiHvsiKjYtWrVCuvWrcOxY8dw5coVBAcHQyqVftA6R4wYgf3792POnDm4desWFi1ahP3796stU6NGDWzbtg3h4eG4dOkSvvjiC7U9gK6urmjTpg0GDx6MM2fO4Pz58xgwYIDaXi0/Pz/4+PigY8eOCAkJwd27d3Hy5El8//33OHfuHDIyMjB8+HCEhobi3r17OHHiBMLCwlCrVq0Pen+5+c+dO4f//vsPN2/exI8//oiwsLA8y2VlZaF///6IiIjA3r17MWnSJAwfPhw6Onn/l16tWjUEBwejX79+2LFjB6KjoxEaGqq6OKIg2xw5ciRmzpyJHTt24MaNGxg6dKhaGba0tISVlRV+//133L59G4cOHcKYMWPU1jFv3jz8/fffuHHjBm7evInNmzfDzs6uWG4wTUT/j8WOiIrdhAkT0Lx5c3z66acIDAxEx44d4eLi8kHrbNy4MVasWIFff/0V9erVQ0hICH744Qe1ZebNmwdLS0s0adIEn332GQICAlR7lXKtWbMGDg4OaN68OT7//HMMGjQINjY2qvkSiQR79+5Fs2bN0LdvX9SsWRM9evTAvXv3YGtrC6lUiqdPn6J3796oWbMmunXrhrZt277zqtSCGjx4MD7//HN0794djRo1wtOnT9X2pOXy9fVFjRo10KxZM3Tv3h3t27dXu5XMm5YuXYouXbpg6NChcHNzw8CBA5GWllbgbf7vf/9Dr169EBwcDB8fH5iamqrtndTR0cHGjRtx/vx5uLu7Y/To0Zg9e7baOkxNTTFr1ix4e3ujYcOGuHv3Lvbu3ZtvGSWiopMIb54IQ0RERERlEv+pRERERKQlWOyIiIiItASLHREREZGWYLEjIiIi0hIsdkRERERagsWOiIiISEuw2BERERFpCRY7IiIiIi3BYkdERESkJVjsiIiIiLQEix0RERGRlmCxIyIiItIS/wf7QMFgq2GJqwAAAABJRU5ErkJggg==", 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" ] @@ -698,25 +698,26 @@ ], "source": [ "# Definir y graficar la función\n", - "def costes_min(x): return 0.1*x**2-9*x+4500\n", + "def costos_min(x): return 0.1*x**2-9*x+4500\n", "x=np.linspace(0,100,1000)\n", - "y=costes_min(x)\n", - "plt.plot(x,y,label='costes/unidad fabricada', color='brown')\n", + "y=costos_min(x)\n", + "plt.plot(x,y,label='costos/unidad fabricada', color='brown')\n", "plt.grid(True)\n", "plt.xlabel('unidades frabicadas')\n", - "plt.ylabel('costes')\n", + "plt.ylabel('costos')\n", "\n", "plt.tight_layout()\n", - "plt.title('Evolucion costes/unidad fabricada')\n", + "plt.title('Evolucion costos/unidad fabricada')\n", "\n", "data={\n", - " \"unidades\":x, \"costes\":y\n", + " \"unidades\":x, \"costos\":y\n", "}\n", - "df_costes=pd.DataFrame(data)\n", - "df_costes=df_costes[df_costes[\"unidades\"]>=1]\n", - "minimo_coste=df_costes['costes'].min()\n", - "print(df_costes.head())\n", - "print(f\"el valo) más bajo de costes es de {minimo_coste}\")" + "df_costos=pd.DataFrame(data)\n", + "df_costos=df_costos[df_costos[\"unidades\"]>=1]\n", + "minimo_coste=df_costos['costos'].min()\n", + "print(df_costos.head())\n", + "unidad_min_coste = df_costos[df_costos[\"costos\"] == minimo_coste][\"unidades\"].values[0]\n", + "print(f\"El valor más bajo de costes es {minimo_coste}, lo que se corresponde a fabricar {unidad_min_coste} unidades.\")\n" ] }, { @@ -731,6 +732,100 @@ "Implementa todos los pasos anteriores para crear un algoritmo de descenso por gradientes y ver cómo evoluciona el costo por unidad, comenzando desde 0 unidades de producción." ] }, + { + "cell_type": "code", + "execution_count": null, + "id": "e8f3f3b5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9\n", + "1.782\n", + "44.99999992726549\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#algortimo descenso gradientes\n", + "import numpy as np\n", + "import seaborn as sns\n", + "\n", + "def f(x): return 0.1*x**2-9*x+4500\n", + "\n", + "def df(x):\n", + " return 0.2*x-9\n", + "\n", + "def visualize(f, x=None):\n", + " \n", + " xArray = np.linspace(0, 100, 1000) \n", + " yArray = f(xArray)\n", + " sns.lineplot(x=xArray, y=yArray)\n", + " \n", + " if x is not None:\n", + " assert type(x) in [np.ndarray, list] # x debería ser un array de numpy o una lista\n", + " if type(x) is list: # Si es una lista, convertir en un array de numpy\n", + " x = np.array(x)\n", + "\n", + " \n", + " y = f(x)\n", + " sns.scatterplot(x=x, y=y, color='red')\n", + "\n", + "visualize(f, x=[0, 100])\n", + "\n", + "def gradient_descent(x, nsteps=1):\n", + " \n", + " # collectXs es un array para almacenar cómo cambió x en cada iteración, para poder visualizarlo más tarde\n", + " \n", + " collectXs = [x]\n", + " \n", + " # learning_rate es el valor que mencionamos como alpha en la sección anterior\n", + " \n", + " learning_rate = 1e-01\n", + " \n", + " for _ in range(nsteps):\n", + " \n", + " # La siguiente línea hace la verdadera magia\n", + " # El siguiente valor de x se calcula restando el gradiente * learning_rate de sí mismo\n", + " # La intuición detrás de esta línea está en la sección anterior\n", + " \n", + " x -= df(x) * learning_rate \n", + " collectXs.append(x)\n", + " \n", + " # Retornamos una tupla que contiene\n", + " # x -> el valor reciente de x después de nsteps \n", + " # collectXs -> todos los valores de x que se calcularon hasta ahora\n", + " \n", + " return x, collectXs\n", + "\n", + "x=0\n", + "x, collectedXs = gradient_descent(x, nsteps=1)\n", + "print(x)\n", + "\n", + "# Ejecutemos un descenso por gradientes durante 1 paso.\n", + "\n", + "x, collectedXs = gradient_descent(x, nsteps=1)\n", + "print(x)\n", + "\n", + "x, collectedXs = gradient_descent(x, nsteps=1000)\n", + "print(x)\n", + "\n", + "visualize(f, x=collectedXs)\n", + "\n" + ] + }, { "cell_type": "markdown", "id": "aabad82c", @@ -762,25 +857,50 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 50, "id": "9e200c32", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Matriz A:\n", + "[[1 2]\n", + " [3 4]]\n", + "\n", + "Matriz B:\n", + "[[4 5]\n", + " [6 7]]\n", + "\n", + "Resultado de la suma (C = A + B):\n", + "[[ 5 7]\n", + " [ 9 11]]\n" + ] + } + ], "source": [ - "# import numpy as np\n", - "\n", - " \n", - " \n", "# Crear la primera matriz\n", + "A = np.array([[1, 2], [3, 4]])\n", "\n", - " \n", - "# Crear la segunda matriz\n", + "# segunda matrices\n", + "\n", + "B = np.array([[4, 5], [6, 7]])\n", + "\n", + "# Sumar las dos matrices\n", + "C = A + B\n", "\n", - " \n", "# Imprimir elementos\n", "\n", + "print(\"Matriz A:\")\n", + "print(A)\n", + "print(\"\\nMatriz B:\")\n", + "print(B)\n", + "# Sumar ambas matrices\n", + "print(\"\\nResultado de la suma (C = A + B):\")\n", + "print(C)\n", " \n", - "# Sumar ambas matrices\n" + "\n" ] }, { @@ -822,9 +942,10 @@ "# Naive method\n", "\n", "# Inicializando listas\n", - "list1 = [2, 5, 4, 7, 3]\n", - "list2 = [1, 4, 6, 9, 10]\n", - " \n", + "# Definir dos listas\n", + "list1 = [2, 5, 4, 7,3]\n", + "list2 = [1,4, 6, 9, 10]\n", + "\n", "# Imprimir listas originales\n", "print (\"Original list 1 : \" + str(list1))\n", "print (\"Original list 2 : \" + str(list2))\n", @@ -848,68 +969,127 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 51, "id": "681930a3", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original list 1 : [2, 5, 4, 7, 3]\n", + "Original list 2 : [1, 4, 6, 9, 10]\n", + "Resultado de la suma de las listas:\n", + "[3, 9, 10, 16, 13]\n" + ] + } + ], "source": [ "# Usar comprensión de listas para realizar la suma de las dos listas:\n", - "\n", - "\n", "# Inicializando listas\n", + "list1 = [2, 5, 4, 7,3]\n", + "list2 = [1,4, 6, 9, 10]\n", "\n", - " \n", "# Imprimir listas originales\n", + "print (\"Original list 1 : \" + str(list1))\n", + "print (\"Original list 2 : \" + str(list2))\n", "\n", - " \n", "# Usando comprensión de listas para sumar dos listas\n", "\n", + "suma_listas = [list1[i] + list2[i] for i in range(len(list1))]\n", + "\n", + "# Imprimir lista resultante\n", + "print(\"Resultado de la suma de las listas:\")\n", + "print(suma_listas)\n", + " \n", + "\n", + "\n", + " \n", + "\n", " \n", - "# Imprimir lista resultante\n" + "\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 52, "id": "a3a8a425", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original list 1 : [2, 5, 4, 7, 3]\n", + "Original list 2 : [1, 4, 6, 9, 10]\n", + "Resultado de la suma de las listas:\n", + "[3, 9, 10, 16, 13]\n" + ] + } + ], "source": [ "# Usar map() + add():\n", "\n", - "\n", "# Inicializando listas\n", + "list1 = [2, 5, 4, 7,3]\n", + "list2 = [1,4, 6, 9, 10]\n", "\n", - " \n", "# Imprimir listas originales\n", + "print (\"Original list 1 : \" + str(list1))\n", + "print (\"Original list 2 : \" + str(list2))\n", "\n", " \n", "# Usando map() + add() para sumar dos listas\n", + "suma_listas = list(map(lambda x, y: x + y, list1, list2))\n", "\n", - " \n", - "# Imprimir lista resultante" + "# Imprimir lista resultante\n", + "print(\"Resultado de la suma de las listas:\")\n", + "print(suma_listas)\n", + " " ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 53, "id": "1708d7ee", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original list 1 : [2, 5, 4, 7, 3]\n", + "Original list 2 : [1, 4, 6, 9, 10]\n", + "Resultado de la suma de las listas:\n", + "[3, 9, 10, 16, 13]\n" + ] + } + ], "source": [ "# Usar zip() + sum():\n", "\n", "\n", "# Inicializando listas\n", + "list1 = [2, 5, 4, 7,3]\n", + "list2 = [1,4, 6, 9, 10]\n", "\n", - " \n", "# Imprimir listas originales\n", + "print (\"Original list 1 : \" + str(list1))\n", + "print (\"Original list 2 : \" + str(list2))\n", "\n", - " \n", "# Usando zip() + sum() para sumar dos listas\n", "\n", + "suma_listas = [sum(i) for i in zip(list1, list2)]\n", + "\n", + "# Imprimir lista resultante\n", + "print(\"Resultado de la suma de las listas:\")\n", + "print(suma_listas)\n", + "\n", + " \n", + "\n", " \n", - "# Imprimir lista resultante" + "\n", + " \n" ] }, { @@ -976,11 +1156,13 @@ "metadata": {}, "outputs": [], "source": [ - "# Importar bibliotecas\n", - "\n", - " \n", "# Ingresar dos matrices\n", - "\n", + "matrix1 = [[1,7,3],\n", + " [4,5,2],\n", + " [3,6,1]]\n", + "matrix2 = [[5,4,1],\n", + " [1,2,3],\n", + " [4,5,2]]\n", " \n", "# Esto devolverá el producto punto\n", "\n", From c4d853400367bb059c95ca9445e5b8ed45b566da Mon Sep 17 00:00:00 2001 From: Maria Pais <145993408+Finarosalina@users.noreply.github.com> Date: Mon, 10 Mar 2025 18:44:22 +0000 Subject: [PATCH 6/6] =?UTF-8?q?mejora=20ortogr=C3=A1fica=20eje=203?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- notebook/problems.es.ipynb | 97 ++++++++------------------------------ 1 file changed, 20 insertions(+), 77 deletions(-) diff --git a/notebook/problems.es.ipynb b/notebook/problems.es.ipynb index 3ce69a1c..2a4b91d7 100644 --- a/notebook/problems.es.ipynb +++ b/notebook/problems.es.ipynb @@ -211,7 +211,7 @@ }, { "cell_type": "code", - 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