Lecture 11_Gradient Descent Algorithm.ipynb

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    "# <center><font color=navy> Big Data Economics</font></center>\n",
    "## <center><font color=navy> Gradient Descent Algorithm</font> </center>\n",
    "### <center> Ali Habibnia</center>\n",
    "\n",
    "    \n",
    "<center> Assistant Professor, Department of Economics, </center>\n",
    "<center> and Division of Computational Modeling & Data Analytics at Virginia Tech</center>\n",
    "<center> habibnia@vt.edu </center> \n"
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    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "\n",
    "Gradient descent, also known as **steepest descent**, is an iterative optimization algorithm for finding a ***local*** minimum of differentiable objective functions. At each iteration, gradient descent operates by moving the current solution in the direction of the negative gradient of the function (the direction of \"steepest descent\").\n",
    "\n",
    "<img src=\"images/error.jpg\"  width=\"500\">\n",
    "\n",
    "> What is gradient? \n",
    "- “A gradient measures how much the output of a function changes if you change the inputs a little bit.” — Lex Fridman (MIT)\n",
    "- You can also think of a gradient as the slope of a function. \n",
    "- Said it more mathematically, a gradient is a partial derivative with respect to its inputs.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "See [Gradient: definition and properties](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-b-chain-rule-gradient-and-directional-derivatives/session-35-gradient-definition-perpendicular-to-level-curves/)\n",
    "\n",
    "</div>\n",
    "\n",
    "\n"
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    "### Optimization \n",
    "\n",
    "Optimization refers to the task of minimizing/maximizing an objective function f(x) parameterized by x.\n",
    "\n",
    "***There are three kinds of optimization algorithms:***\n",
    "\n",
    "- Optimization algorithm that is not iterative and simply solves for one point.\n",
    "- Optimization algorithm that is iterative in nature and converges to acceptable solution regardless of the parameters initialization such as gradient descent applied to logistic regression.\n",
    "- Optimization algorithm that is iterative in nature and applied to a set of problems that have non-convex cost functions such as neural networks. Therefore, parameters’ initialization plays a critical role in speeding up convergence and achieving lower error rates.\n"
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    "Optimization algorithms can be broadly categorized into gradient-based and gradient-free methods. Here's an overview of each category along with some commonly used algorithms:\n",
    "\n",
    "### Gradient-Based Optimization Algorithms\n",
    "\n",
    "These algorithms use the gradient (or derivative) of the objective function to guide the search for the optimum. They are typically used when the gradient information is available and reliable.\n",
    "\n",
    "1. **Gradient Descent**: The simplest form, moving in the direction of the negative gradient to minimize the objective function.\n",
    "   \n",
    "2. **Stochastic Gradient Descent (SGD)**: A variant of gradient descent where the gradient is computed using a randomly selected subset of data instead of the full dataset, useful for large-scale problems.\n",
    "\n",
    "3. **Mini-batch Gradient Descent**: Intermediate between gradient descent and SGD, where the gradient is computed on a small, randomly selected subset of the data.\n",
    "\n",
    "4. **Momentum**: Builds on gradient descent by incorporating a fraction of the previous update step, adding inertia to overcome local minima and smooth out the path.\n",
    "\n",
    "5. **Nesterov Accelerated Gradient (NAG)**: A refined version of the momentum method that looks ahead by calculating the gradient at a position slightly ahead in the direction of the momentum.\n",
    "\n",
    "6. **Adagrad**: Adapts the learning rate to the parameters, performing smaller updates for parameters associated with frequently occurring features.\n",
    "\n",
    "7. **RMSprop**: Modifies Adagrad to improve its performance in online and non-stationary settings by using a moving average of squared gradients.\n",
    "\n",
    "8. **Adam (Adaptive Moment Estimation)**: Combines ideas from RMSprop and Momentum, computing adaptive learning rates for each parameter.\n",
    "\n",
    "9. **BFGS and L-BFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno)**: Quasi-Newton methods that approximate the Hessian matrix to guide the search.\n",
    "\n",
    "10. **Conjugate Gradient**: Designed for solving large linear systems and unconstrained optimization problems, particularly useful for quadratic objectives.\n",
    "\n",
    "### Gradient-Free Optimization Algorithms\n",
    "\n",
    "These methods do not require gradient information and are suitable for non-differentiable, discontinuous, or noisy objective functions.\n",
    "\n",
    "1. **Simulated Annealing**: Inspired by the annealing process in metallurgy, this method probabilistically accepts worse solutions early on to escape local minima, gradually reducing the acceptance rate as it converges.\n",
    "\n",
    "2. **Genetic Algorithms**: Inspired by the process of natural selection, this approach uses operations such as mutation, crossover, and selection to evolve a set of solutions towards the optimum.\n",
    "\n",
    "3. **Particle Swarm Optimization (PSO)**: Simulates the social behavior of birds or fish, where a \"swarm\" of candidate solutions is guided towards the optimum by the collective experience of the swarm.\n",
    "\n",
    "4. **Differential Evolution**: A population-based algorithm that uses the differences between randomly selected solutions to drive the optimization process.\n",
    "\n",
    "5. **Evolution Strategies**: Similar to genetic algorithms but focuses more on the mutation operation and often uses self-adaptation techniques to adjust strategy parameters.\n",
    "\n",
    "6. **Ant Colony Optimization**: Inspired by the foraging behavior of ants, this method is particularly effective for discrete optimization problems like the traveling salesman problem.\n",
    "\n",
    "7. **Cuckoo Search**: Uses a metaphor of cuckoo birds laying eggs in the nests of other host birds, combined with the idea of Lévy flights for global and local search.\n",
    "\n",
    "8. **Bayesian Optimization**: Uses a probabilistic model to predict the objective function and applies Bayesian inference to update the model and select the next point to evaluate.\n",
    "\n",
    "9. **Nelder-Mead Simplex Method**: A direct search method that maintains a simplex of solutions, iteratively replacing the worst point in the simplex with a better one.\n",
    "\n",
    "10. **Random Search**: A baseline method where the search space is sampled randomly. It's surprisingly effective for some high-dimensional problems where structured methods might struggle.\n",
    "\n",
    "Each of these algorithms has its own strengths and weaknesses and is suitable for different types of optimization problems. The choice of algorithm depends on the specific characteristics of the problem, such as the nature of the objective function, the dimensionality of the search space, and the availability of derivative information."
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    "### Why Gradient Descent? \n",
    "\n",
    "- Gradient descent is by far the most popular optimization strategy, used in machine learning. \n",
    "- It can be combined with every algorithm and is easy to understand and implement.\n",
    "- It is an optimization algorithm, based on a convex function, that tweaks it’s parameters iteratively to minimize a given function to its local minimum.\n",
    "- It is simply used to find the values of a functions parameters (coefficients) that minimize a loss/cost function as far as possible.\n",
    "- It is a first-order optimization algorithm. This means it only takes into account the first derivative when performing the updates on the parameters. \n",
    "\n",
    "> You start by defining the initial parameters values and from there on Gradient Descent iteratively adjusts the values, using calculus, so that they minimize the given loss function. On each iteration, we update the parameters in the opposite direction of the gradient of the objective function w.r.t the parameters where the gradient gives the direction of the steepest ascent. \n",
    "\n",
    "— — — — — — — — — — — — — \n",
    "\n",
    "**Forward propagation**\n",
    "1. Initialise parameters (one-time)\n",
    "2. Feed data\n",
    "3. Compute ŷ\n",
    "4. Compute loss\n",
    "\n",
    "**Backpropagation**\n",
    "5. Compute partial differentials\n",
    "6. Update parameters\n",
    "\n",
    " — — — — — — — — — — — — —\n",
    "\n",
    "Repeat until convergence\n",
    "\n",
    "<img src=\"images/update_rule.png\"  width=\"300\">\n",
    "\n",
    "\n",
    "\n",
    "> When Gradient Descent can’t decrease the cost-function anymore and remains more or less on the same level, we say it has converged.\n",
    "\n"
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    "### Multivariable Calculus Review\n",
    "We will be covering some of the most relevant concepts from multivariable calculus for this lecture, and show how they can be extended to deal with matrices of training data."
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    "### Partial Derivatives\n",
    "The derivative of a function of 2 variables $f(x, y)$ w.r.t. either one of its variables is defined as \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{\\partial}{\\partial x} f(x, y) &:= \\lim_{h \\to 0} \\frac{f(x + h, y) - f(x, y)}{h}\\\\\n",
    "\\frac{\\partial}{\\partial y} f(x, y) &:= \\lim_{h \\to 0} \\frac{f(x, y + h) - f(x, y)}{h}\n",
    "\\end{aligned}\n",
    "$$"
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    "---\n",
    "### Directional Derivatives\n",
    "Before we define the gradient, we discuss the closely related concept of a directional derivative.\n",
    "\n",
    "The directional derivative of a function $f(x, y)$ at $(x_0, y_0)$ moving in the direction of a unit vector $u = [a, b]$ is \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "D_{u} f(x_0, y_0) := \\lim_{h \\to 0} \\frac{f(x_0 + ha, y_0 + hb) - f(x_0, y_0)}{h}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This simply tells us how the scalar output of $f$ will change when we move in an arbitrary direction that is not necesarily axis-aligned. It can be written as \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "D_{u} f(x, y) = \\left[\\frac{\\partial}{\\partial x} f(x, y), \\frac{\\partial}{\\partial y} f(x, y)\\right] \\cdot u\n",
    "\\end{aligned}\n",
    "$$"
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   "source": [
    "---\n",
    "### Gradient\n",
    "This is perhaps the term you will hear most often in the context of neural networks. The gradient is informally defined as the vector pointing in the direction of steepest increase for a given function. Thus, if we would like to minimize a loss function such as mean squared error (MSE), we move in the opposite direction of the gradient, i.e. in the direction of the negative gradient.\n",
    "\n",
    "Now the gradient is simply defined as \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\nabla f(x, y) := \\left[\\frac{\\partial}{\\partial x} f(x, y), \\frac{\\partial}{\\partial y} f(x, y)\\right]\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Note that this is a vector-field (vector-valued function), and not a scalar-valued function!"
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    "### Gradient Descent"
   ]
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   "source": [
    "#### Introduction"
   ]
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    "Gradient descent is an algorithm used to the find local minimums of any differentiable function. More formally, given a differentiable function $f(x),$ the gradient descent algorithms helps us compute $x^*$ such that $f'(x^*) = 0$ and $x^*$ is a minimum of $f(x).$ A function can have many local minimums $x_{1}^{*}, x_{2}^{*}, \\ldots, x_{k}^{*},$ the gradient descent algorithm will converge to one of them depending on the its starting position and learning rate (discussed below). \n",
    "\n",
    "The name \"Gradient Descent\" hints at how this algorithm works. The algorithms requires 1) knowing the $\\textbf{gradient}$ (partial derivatives) of the function and 2) using the gradient to determine the direction of steepest $\\textbf{descent}.$ The idea is that we will begin somewhere on the function, for example $f(x_{1})$, and then climb down the function as quickly as possible towards the first valley (local minimum) where $f'(x^*) = 0.$ The gradient descent algorithm essentially describes the sequence of steps to take to go from $x_{1}$ to a local minimum $x^*.$\n",
    "\n",
    "Gradient descent (or a variation) is very commonly used to train machine learning models by minimizing some objective function. Many of the objective functions in machine learning are hard to minimize analytically, but we can approximate the minimum using gradient descent. "
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    "#### Algorithm intuition\n",
    "\n",
    "Suppose we have a single variable function $f(x)$ that has a single global minimum (for example a parabola that opens upwards) at $x^*.$ Our goal is to approximate $x^*$ through an itterative algorithm. The first step is to pick a starting point (initial value) for the algorithm, $x_{1}.$ We will randomly guess $x_{1}$ and note that either $x_{1} < x^*$, or $x_{1} > x^*$ (we can get really lucky and have $x_{1} = x^*,$ but this is very unlikely). Since $x^*$ is the global minimum, we know that $f(x^*) < f(x_{1}),$ that is our starting point is above the minimum. Starting at $x_{1}$ we want to take a sequence of steps to get down to $x^*.$ The gradient descent algorithm characterizes the set of steps to take to get from $x_{1}$ down to $x^*.$\n",
    "\n",
    "Without loss of generality assume our starting position $x_{1} < x^*,$ and let us discuss how to get down towards $x^*.$ Recall that we can compute the gradient of $f(x)$ since we assume the function is differentiable. Suppose we find $f'(x_{1}) < 0,$ that indicates that if we take a step right to $x_{2} > x_{1}$ then we will move down the function since $f(x_{2}) < f(x_{1}).$ This is exactly what we want (moving down the function), so we want to take a step to the right of $x_{1}.$ But how large of a step should we take? Well it makes sense to say the step size will depend on the steepness of the descent. The steeper the descent at $x_{1}$, the larger the step size should be as it indicates we have a long way to go before getting to the minimum. More formally the step size will be proportional to the gradient at $x_{1}.$\n",
    "\n",
    "Once we get from $x_{1}$ to $x_{2}$, we repeat the same logic as above. Suppose $f'(x_2) < 0$ again, so we need to take a step towards $x_{3} > x_{2}$ to further go down the function. Again our step size will be proportional to $f'(x_2).$ Repeating this process will result in a sequence of steps $x_{1}, x_{2}, \\ldots, x_{T}.$ For large values of $T$ we expect $x_{T} \\approx x^*.$ The diagram below more formally describes the intuition behind gradient descent."
   ]
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    "<img src=\"images/gradd.jpg\"  width=\"600\">"
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    "The diagram above formally shows a single step of the gradient descent algorithm from $x_{1}$ to $x_{2}$ To determine $x_{2}$ we take a step to the right of $x_{1}$ that is proportional to $f'(x_{1}).$ Mathematically speaking, the sign of $f'(x_{1})$ indicates the direction of the steepest ascent at $x_{1}$ (magnitude of f'(x_{1}) is measure of steepness), but since we want to descend (its called gradient $\\textbf{descent}$) we use $-f'(x_{1}).$ Gradient descent relies on a parameter $\\eta$ called the learning rate, let us talk about this more. "
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    "### Thinking about the learning rate\n",
    "\n",
    "- How big the steps are that Gradient Descent takes into the direction of the local minimum are determined by the so-called learning rate. \n",
    "- It determines how fast or slow we will move towards the optimal weights.\n",
    "- In order for Gradient Descent to reach the local minimum, we have to set the learning rate to an appropriate value, which is neither too low nor too high.\n",
    "- This is because if the steps it takes are too big, it maybe will not reach the local minimum because it just bounces back and forth between the convex function of gradient descent like you can see on the left side of the image below. \n",
    "- If you set the learning rate to a very small value, gradient descent will eventually reach the local minimum but it will maybe take too much time like you can see on the right side of the image.\n",
    "\n",
    "The learning rate $\\eta$ and the steepest descent $-f'(x_{1})$ together determine the step size towards the minimum. Hence the learning rate determines the size of the steps. If $\\eta$ is large then we will take large steps down towards to the minimum. Similarly if $\\eta$ is small it will take longer to converge towards the minimum as the step size is smaller. Does this mean we should pick a really large $\\eta$ to coverge fast towards $x^*?$ No, this is not a good idea. $\\eta$ too large or too small can cause covergence problems as illustrated by the diagram below.\n",
    "\n",
    "<img src=\"images/learningrate.jpg\"  width=\"600\">"
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    "Note that $J(w)$ is the function that we want to minimize in the above diagram. On the left figure $\\eta$ is very large which leads to taking very big steps. These big steps essentially have trouble locating the minimum because they are jumping over it. On the right figure $\\eta$ is very small leading to tiny steps towards the minimum. The algorithm finds a minimum, but its only a local minimum (global minimum is ideal). For the right figure imagine the step size was a bit larger, then the algorithm could jump over the local minimum and possiblly converge into the global minimum. \n",
    "\n",
    "***So how you do pick the best $\\eta$? This is often done using \"cross validation\".***\n",
    "\n",
    "A good way to make sure that Gradient Descent runs properly is by plotting the cost function as Gradient Descent runs. You put the number of iterations on the x-axes and the value of the cost-function at the y-axes. This enables you to see the value of your cost function after each iteration of gradient descent. \n",
    "\n",
    "\n",
    "<img src=\"images/eta.png\"  width=\"300\">\n",
    "\n"
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   "source": [
    "### Examples: "
   ]
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    "#### Example by hand:\n",
    "\n",
    "Find the local minima of the function y=(x+5)² starting from the point x=3\n",
    "\n",
    "<img src=\"images/ex1.png\"  width=\"300\">\n",
    "\n",
    "**Solution:** We know the answer just by looking at the graph. y = (x+5)² reaches it’s minimum value when x = -5 (i.e when x=-5, y=0). Hence x=-5 is the local and global minima of the function.\n",
    "\n",
    "\n",
    "Now, let’s see how to obtain the same numerically using gradient descent.\n",
    "\n",
    "- Step 1 : Initialize x =3. Then, find the gradient of the function, dy/dx = 2*(x+5).\n",
    "\n",
    "- Step 2 : Move in the direction of the negative of the gradient. But wait, how much to move? For that, we require a learning rate. Let us assume the learning rate → 0.01\n",
    "\n",
    "- Step 3 : Let’s perform 2 iterations of gradient descent\n",
    "\n",
    "<img src=\"images/ex2.png\"  width=\"500\">\n",
    "\n",
    "- Step 4 : We can observe that the X value is slowly decreasing and should converge to -5. \n"
   ]
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    "# Gradient descent in Python :\n",
    "# Step 1 : Initialize parameters\n",
    "cur_x = 3 # The algorithm starts at x=3\n",
    "rate = 0.01 # Learning rate\n",
    "precision = 0.00001 #This tells us when to stop the algorithm\n",
    "previous_step_size = 1 #\n",
    "max_iters = 10000 # maximum number of iterations\n",
    "iters = 0 #iteration counter\n",
    "df = lambda x: 2*(x+5) #Gradient of our function\n",
    "#  lambda operator or lambda function is used for creating small, one-time and anonymous function objects in Python."
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     "text": [
      "Iteration 1 \n",
      "X value is 2.84\n",
      "Iteration 2 \n",
      "X value is 2.6832\n",
      "Iteration 3 \n",
      "X value is 2.529536\n",
      "Iteration 4 \n",
      "X value is 2.37894528\n",
      "Iteration 5 \n",
      "X value is 2.2313663744\n",
      "Iteration 6 \n",
      "X value is 2.0867390469119997\n",
      "Iteration 7 \n",
      "X value is 1.9450042659737599\n",
      "Iteration 8 \n",
      "X value is 1.8061041806542846\n",
      "Iteration 9 \n",
      "X value is 1.669982097041199\n",
      "Iteration 10 \n",
      "X value is 1.5365824551003748\n",
      "Iteration 11 \n",
      "X value is 1.4058508059983674\n",
      "Iteration 12 \n",
      "X value is 1.2777337898784\n",
      "Iteration 13 \n",
      "X value is 1.152179114080832\n",
      "Iteration 14 \n",
      "X value is 1.0291355317992152\n",
      "Iteration 15 \n",
      "X value is 0.9085528211632309\n",
      "Iteration 16 \n",
      "X value is 0.7903817647399662\n",
      "Iteration 17 \n",
      "X value is 0.6745741294451669\n",
      "Iteration 18 \n",
      "X value is 0.5610826468562635\n",
      "Iteration 19 \n",
      "X value is 0.44986099391913825\n",
      "Iteration 20 \n",
      "X value is 0.3408637740407555\n",
      "Iteration 21 \n",
      "X value is 0.23404649855994042\n",
      "Iteration 22 \n",
      "X value is 0.1293655685887416\n",
      "Iteration 23 \n",
      "X value is 0.026778257216966764\n",
      "Iteration 24 \n",
      "X value is -0.07375730792737258\n",
      "Iteration 25 \n",
      "X value is -0.1722821617688251\n",
      "Iteration 26 \n",
      "X value is -0.2688365185334486\n",
      "Iteration 27 \n",
      "X value is -0.36345978816277963\n",
      "Iteration 28 \n",
      "X value is -0.45619059239952403\n",
      "Iteration 29 \n",
      "X value is -0.5470667805515336\n",
      "Iteration 30 \n",
      "X value is -0.6361254449405029\n",
      "Iteration 31 \n",
      "X value is -0.7234029360416929\n",
      "Iteration 32 \n",
      "X value is -0.8089348773208591\n",
      "Iteration 33 \n",
      "X value is -0.8927561797744419\n",
      "Iteration 34 \n",
      "X value is -0.9749010561789531\n",
      "Iteration 35 \n",
      "X value is -1.055403035055374\n",
      "Iteration 36 \n",
      "X value is -1.1342949743542665\n",
      "Iteration 37 \n",
      "X value is -1.2116090748671813\n",
      "Iteration 38 \n",
      "X value is -1.2873768933698377\n",
      "Iteration 39 \n",
      "X value is -1.361629355502441\n",
      "Iteration 40 \n",
      "X value is -1.4343967683923922\n",
      "Iteration 41 \n",
      "X value is -1.5057088330245443\n",
      "Iteration 42 \n",
      "X value is -1.5755946563640535\n",
      "Iteration 43 \n",
      "X value is -1.6440827632367725\n",
      "Iteration 44 \n",
      "X value is -1.711201107972037\n",
      "Iteration 45 \n",
      "X value is -1.7769770858125964\n",
      "Iteration 46 \n",
      "X value is -1.8414375440963444\n",
      "Iteration 47 \n",
      "X value is -1.9046087932144176\n",
      "Iteration 48 \n",
      "X value is -1.9665166173501292\n",
      "Iteration 49 \n",
      "X value is -2.0271862850031264\n",
      "Iteration 50 \n",
      "X value is -2.0866425593030637\n",
      "Iteration 51 \n",
      "X value is -2.1449097081170025\n",
      "Iteration 52 \n",
      "X value is -2.2020115139546625\n",
      "Iteration 53 \n",
      "X value is -2.257971283675569\n",
      "Iteration 54 \n",
      "X value is -2.312811858002058\n",
      "Iteration 55 \n",
      "X value is -2.3665556208420164\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 461 \n",
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      "Iteration 481 \n",
      "X value is -4.999518238161995\n",
      "The local minimum occurs at -4.999518238161995\n"
     ]
    }
   ],
   "source": [
    "# Step 2 : Run a loop to perform gradient descent :\n",
    "# Stop loop when difference between x values from 2 consecutive iterations is less than 0.000001 or when number of iterations exceeds 10,000\n",
    "while previous_step_size > precision and iters < max_iters:\n",
    "    prev_x = cur_x #Store current x value in prev_x\n",
    "    cur_x = cur_x - rate * df(prev_x) #Grad descent\n",
    "    previous_step_size = abs(cur_x - prev_x) #Change in x\n",
    "    iters = iters+1 #iteration count\n",
    "    print(\"Iteration\",iters,\"\\nX value is\",cur_x) #Print iterations\n",
    "    \n",
    "print(\"The local minimum occurs at\", cur_x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example with two parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration: 0, x: 4.00, step_x: -0.06, z: 4.00, step_z: -0.08\n",
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      "iteration: 471, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 472, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 473, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 474, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 475, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 476, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 477, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 478, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 479, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 480, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 481, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 482, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 483, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 484, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 485, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 486, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 487, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 488, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 489, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 490, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 491, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 492, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 493, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 494, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 495, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 496, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 497, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 498, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n",
      "iteration: 499, x: 1.00, step_x: -0.00, z: 0.00, step_z: -0.00\n"
     ]
    }
   ],
   "source": [
    "# For the following function: \n",
    "# y = x**2 + z**2 - 2x + 2\n",
    "# def y(x, z):\n",
    "#   return x**2 + z**2 -2*x + 2\n",
    "\n",
    "# the partial derivatives are:\n",
    "# dy/dx = 2x -2\n",
    "# dy/dz = 2z\n",
    "\n",
    "# the following function runs gradient descent for 40 iterations specifically for this example, with an initial guess of x = 4, z = 4 and a learning rate (alpha) of 0.1\n",
    "\n",
    "# The algorithm converges on the minimum within 39 iterations\n",
    "\n",
    "def gradient_descent(x=4, z = 4, alpha=0.01):\n",
    "  for i in range(500):\n",
    "    # the step is alpha * dy/dx\n",
    "    step_x = alpha * (2*x - 2)\n",
    "    step_z = alpha * 2*z\n",
    "    print(\"iteration: {}, x: {:.2f}, step_x: -{:.2f}, z: {:.2f}, step_z: -{:.2f}\".format(i, x, step_x, z, step_z))\n",
    "    # we move x down the slope by moving in the opposite direction to the gradient\n",
    "    x = x - step_x\n",
    "    z = z - step_z\n",
    "\n",
    "gradient_descent(4, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression using Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s apply the things learnt above on linear regression problem. Here’s a recap of linear regression:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kmjc6sragwoR"
   },
   "source": [
    "\n",
    "Our model is $y(x) = wx + b$. Parameters are $v = (w, b)$\n",
    "We are given training pairs $(x^1, y^1), (x^2, y^2), \\ldots, (x^n, y^n)$.\n",
    "\n",
    "We want to find $w$ and $b$ which minimize the following \n",
    "cost/loss function:\n",
    "\n",
    "$$\n",
    "C(w, b) = \\frac{1}{n} \\sum_{i = 1}^{n} C_i(w, b) = \\frac{1}{2n} \\sum_{i = 1}^{n} \\| y(x^i) - y^i\\|^2\n",
    "$$\n",
    "\n",
    "where\n",
    "$C_i(w, b) = \\frac{1}{2} | y(x^i) - y^i|^2 = \\frac{1}{2} | wx^i + b - y^i|^2$ is the loss of the model for $i$ th training pair.\n",
    "\n",
    "\n",
    "<p>Let’s calculate gradients,</p>\n",
    "\n",
    "$$\n",
    "\\nabla C = \\frac{1}{n} \\sum_{i = 1}^{n} \\nabla C_i\n",
    "$$\n",
    "\n",
    "where $\\nabla C_i$ is computed using:\n",
    "\n",
    "$$\n",
    "\\nabla C_i = \\left( \\frac{\\partial C_i}{\\partial w}, \\frac{\\partial C_i}{\\partial b}  \\right) = \\left( (wx^i + b - y^i)x^i, (wx^i + b - y^i) \\right)\n",
    "$$\n",
    "\n",
    "Update rule is\n",
    "\n",
    "$$v \\rightarrow v' = v -\\eta \\nabla C = v -\\frac{\\eta}{n} \\sum_{i = 1}^{n} \\nabla C_i$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GFG2fm77e7_p"
   },
   "source": [
    "\n",
    "\n",
    "Here $\\eta$ is called *learning rate*. If it is too small, algorithm can be very slow and might take too many iterations to converge. If it is too large, algorithm might not even converge.\n",
    "\n",
    "![alt text](https://www.jeremyjordan.me/content/images/2018/02/Screen-Shot-2018-02-24-at-11.47.09-AM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***See:*** How to Implement Linear Regression With Gradient Descent and Stochastic Gradient Descent From Scratch With Python\n",
    "\n",
    "https://github.com/chasinginfinity/ml-from-scratch/blob/master/02%20Linear%20Regression%20using%20Gradient%20Descent/Linear%20Regression%20using%20Gradient%20Descent.ipynb\n",
    "\n",
    "https://machinelearningmastery.com/implement-linear-regression-stochastic-gradient-descent-scratch-python/\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More Examples:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Single variable\n",
    "\n",
    "Suppose we have a single variable and differentiable function $f(x).$ Given a initial value $x_{1}$ the gradient descent describes the steps required to coverge towards a local minimum $x^*$ such that $f'(x^*) = 0.$ In the above section we determined that $x_{2} = x_{1} - \\lambda f'(x_{1}),$ where $\\lambda$ is the learning rate parameter. This formula can be generalized to $$x_{t+1} = x_{t} - \\lambda f'(x_{t}),$$ for itteration $t.$ Given initial value $x_{1}$ and large number of itterations $T,$ this algorithm will generate $x_{1}, x_{2}, \\ldots, x_{T},$ where $x_{T} \\approx x^*.$ That is $x_{t+1}$ converges towards $x^*$ as $t$ gets very large. Notice that at convergence $f'(x_{t}) \\approx 0$ and hence $|x_{t+1} - x_{t}| \\approx 0.$ Therefore a common stopping criteria for gradience descent is to itterate until $|x_{t+1} - x_{t}|$ is a very small number. For example we can keep itterating gradient descent until $|x_{t+1} - x_{t}| < 0.001.$\n",
    "\n",
    "#### Multiple variables\n",
    "Consider a multiple variable and differentiable function $f(x_{1},x_{2},\\ldots, x_{n}).$ Our goal is to apply gradient descent and find a minimum $(x_{1}^{*}, x_{2}^{*}, \\ldots, x_{n}^{*}).$ This function has partial derivatives stored in the gradient vector $(\\frac{df(x)}{dx_{1}}, \\ldots, \\frac{df(x)}{dx_{n}}).$ The direction of the gradient vector indicates direction of steepest ascent, and the length of the gradient vector is a mesuare of the steepness. We can easily generalize the gradient descent to multiple variables as follows:\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    x_{1}^{t+1} \\\\ \n",
    "    \\vdots \\\\\n",
    "    x_{n}^{t+1}\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "    x_{1}^{t} \\\\ \n",
    "    \\vdots \\\\\n",
    "    x_{n}^{t}\n",
    "\\end{bmatrix}\n",
    "-\n",
    "\\lambda\n",
    "\\begin{bmatrix}\n",
    "    \\frac{df(x_{1})}{dx_{1,t}} \\\\ \n",
    "    \\vdots \\\\\n",
    "    \\frac{df(x_{n})}{dx_{n,t}} \\\\ \n",
    "\\end{bmatrix},\n",
    "$$\n",
    "where $t$ is the gradient descent itteration. Now the stopping criteria can depend on the euclidean distance between the now and previous itteration, that is stop if $\\sqrt{(x_{1}^{t+1} - x_{1}^{t})^2 + \\ldots + (x_{n}^{t+1} - x_{n}^{t})^2} < 0.001.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Minimizing single variable function\n",
    "\n",
    "Consider the following single variable function $$f(x) = 0.1x^2 + sin(0.1x^2)$$ and suppose we find its minimum using gradient descent. Gradient descent requires us to compute the first derivative which is $$f'(x) = 0.2x + 0.2xcos(0.1x^2).$$ The plot for f(x) is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Matrix computations\n",
    "from numpy import *\n",
    "\n",
    "# Plotting\n",
    "from matplotlib.pyplot import *\n",
    "\n",
    "# Change size of figures\n",
    "#fig_size = [9,7]\n",
    "#rcParams[\"figure.figsize\"] = fig_size\n",
    "\n",
    "# Define function f(x)\n",
    "def f(x):\n",
    "    \n",
    "    # f(x) = 0.1x^2 + sin(0.1x^2)\n",
    "    return 0.1*x**2 + sin(0.1*x**2)\n",
    "\n",
    "# Plot function on given range\n",
    "# Second arguments allows for seperate points to be ploted on f(x)\n",
    "def plotf(x, xdots, label):\n",
    "\n",
    "    # Compute y-values\n",
    "    y = f(x)\n",
    "\n",
    "    # Plot (x, f(x))\n",
    "    plot(x,y)\n",
    "    xlabel(\"x\")\n",
    "    ylabel(\"f(x)\")\n",
    "    title(label)\n",
    "    \n",
    "    # Plot points on f(x)\n",
    "    plot(xdots, f(xdots), 'bo')\n",
    "    show()\n",
    "    \n",
    "# Plot f(x) from [-10,10]\n",
    "x = arange(-10, 10, 0.1)\n",
    "plotf(x, np.array([]), \"Single Variable Function\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that f(x) has a global minimum at x = 0, but there are also seem to be two local minimums near -5.5 and 5.5. Ideally we want to be able to start anywhere from [-10,10] and use gradient descent to go down towards the minimum of 0. We will see that finding the global minimum depends on initial starting point and learning rate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Derivative of f(x) is f'(x) (denoted by df below)\n",
    "# f'(x) = 0.2x + 0.2xcos(0.1x^2)\n",
    "def df(x):\n",
    "    return 0.2*x + 0.2*x*cos(0.1*(x**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have defined f(x) and f'(x), let us run gradient descent for different initial values and learning parameters and try to compute the global minimum. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gradient descent for single variable\n",
    "# Depends on f(x), f'(x), x_1, and lambda\n",
    "def grad_descent(df,x_prev,learn_rate, sequence):\n",
    "\n",
    "    # Epsilon threshold \n",
    "    epsilon = 0.1\n",
    "    \n",
    "    # Itterations number\n",
    "    grad_itter = 1\n",
    "\n",
    "    # First itteration of gradient descent\n",
    "    x_next = x_prev - learn_rate*df(x_prev)\n",
    "    \n",
    "    # Save first itteration\n",
    "    sequence = np.append(sequence, x_next)\n",
    "\n",
    "    # while abs(x_{t+1} - x_{t}) > threshold, keep itterating gradient descent\n",
    "    while abs(x_next - x_prev) > epsilon:\n",
    "\n",
    "        # Update x_{t}\n",
    "        x_prev = x_next\n",
    "\n",
    "        # Gradient descent step\n",
    "        # Set new x_{t+1} = x_{t} - lambda*f'(x_{t})\n",
    "        x_next = x_prev - learn_rate*df(x_prev)\n",
    "        \n",
    "        # Save itteration \n",
    "        sequence = np.append(sequence, x_next)\n",
    "        \n",
    "        # Increment itteration\n",
    "        grad_itter += 1\n",
    "        \n",
    "    # Output converged x_{T}\n",
    "    return (x_next, sequence, grad_itter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using ideal learning rate\n",
    "\n",
    "The example below uses a good learning rate for this context, $\\lambda = 1.$ Gradient descent coverges to the global minimum in 20 itterations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum x-value from gradient descent: 0.09765189469685362\n",
      "Number of gradient descent itterations: 7\n"
     ]
    }
   ],
   "source": [
    "# Output vector (min x-value, (x_1,..,x_T)) from gradient descent\n",
    "# Initial value x1 = 8 and learn rate lambda = 1\n",
    "grad_output = grad_descent(df,3,1, np.array([3]))\n",
    "\n",
    "# Plot including converging sequence on f(x)\n",
    "plotf(x, grad_output[1], \"x1 = 3 and lambda = 1 Finds Global Minimum\")\n",
    "\n",
    "# Print gradient descent solution\n",
    "print('Minimum x-value from gradient descent: %s' %grad_output[0])\n",
    "print('Number of gradient descent itterations: %s' %grad_output[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using a small learning rate\n",
    "\n",
    "The example below uses a smaller than ideal learning rate of $\\lambda = 0.1.$ Not only does this increase the number of gradient descent itterations to 105, but the algorithm coverges to one of the local minimums. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum x-value from gradient descent: -6.56845833092785\n",
      "Number of gradient descent itterations: 7\n"
     ]
    }
   ],
   "source": [
    "# Initial value x1 = 8 and learn rate lambda = 1\n",
    "grad_output = grad_descent(df,-8,0.1, np.array([-8]))\n",
    "\n",
    "# Plot including converging sequence on f(x)\n",
    "plotf(x, grad_output[1], \"x1 = -8 and lambda = 0.1 Finds Local Minimum\")\n",
    "\n",
    "# Print gradient descent solution\n",
    "print('Minimum x-value from gradient descent: %s' %grad_output[0])\n",
    "print('Number of gradient descent itterations: %s' %grad_output[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Small learning rate but starting close to global minimum\n",
    "\n",
    "The example below uses a small learning rate (for this context) of $\\lambda = 0.1,$ but starts the algoirthm at $x_{1} = -5.$ The key point is that the initial value is now slight beyond the local minimum. Hence even with a small learning rate we are able to eventually converge to the global minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum x-value from gradient descent: -4.980114361554693\n",
      "Number of gradient descent itterations: 1\n"
     ]
    }
   ],
   "source": [
    "# Initial value x1 = 8 and learn rate lambda = 1\n",
    "grad_output = grad_descent(df,-5,0.1, np.array([-5]))\n",
    "\n",
    "# Plot including converging sequence on f(x)\n",
    "plotf(x, grad_output[1], \"x1 = -5 and lambda = 0.1 Finds Global Minimum\")\n",
    "\n",
    "# Print gradient descent solution\n",
    "print('Minimum x-value from gradient descent: %s' %grad_output[0])\n",
    "print('Number of gradient descent itterations: %s' %grad_output[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initial value and learning rate are important\n",
    "\n",
    "From the above exercises of changing the initial value and learning rate we can conclude that gradient descent is not guranteed to converge to the global minimum. Having a really low learning rate can make convergence slower (more itterations before finding minimum) and make it more likely to get stuck at local minimums. A very high learning rate may be even more problematic as gradient descent may never coverge (try $\\lambda$ = 6 in the code). The initial value is also important for finding the global minimum. If we start close to the global minimum, we are more likely to find it in the above example even with a smaller than ideal learning rate.\n",
    "\n",
    "The diagram below shows even with multiple variables different initial values can lead to different local minimums from gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MDhkeqO453vrFixc4A+SEYcUBfu4Mvm0NFj0c0xxkRmoNNxUwRZBAD4IEdUC0cN46OzsL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SlEj5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b+wJYeQknabPO9INweUFtoFwImkSM6zkERCvJyI9WU7x8okzZedDjUHarF/cIhRfqKwRBAU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gdn3m9CnIRmkGY1jD9AZ4cfXqaxcvXGA8uLu5eemBi0qK48OjpbUVCCiH+0cLi0sAK2Dw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\nSlWUOOWylD/syDb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efDoN97aDPlzsgVs30J/f+ta3ZmdnT58+zcMMh9slP2qT4r1iD+9X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\nS5Gvz9DQECgLfTh+/DgWDJEVX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fkKuGO1WqHP1dTU5OXlUdoJHAh3lz4X7s5OHZUFow+s\nJCYGCny8sLBQBqEigUJsa1gTTCGZQcIVB7Rdsk34uIWGDszMzGCEIdswER//+MdNJhNfW+ue3gy4\nQ09PT3t7O6AqhnTPnj1k8QJWmJychLycn5/HlZWVlY2NjXyllQ8MeohMyE0xzFi0zKEBC89ms1HJ\nHtqXxK9wZmhoqLa2liKV4hwsjh7iLd7+xZoi3ATOSROfYFXgYmNjY52dnVVVVfjkGd9Om8fBK4Fp\nwCIh7yH1WSQF71vAwiBxAX1F+bMpKIDKlKP/4MhtbW19fX2QQ/8/e+cWE1f1/fFJW+jQYaAwQjsz\n3CnlahVKScMlUg2QmKolQY2aGC8xPqgPxifDs+9N7IPxEhMNsdRWY0pq0JYAhbZyFRSEQaQUhjsM\ndyil5v/NrH93zm+4CMMw9PL9PEwOM4c55+yzZ6/v2mevtWCfcFEQIgcPHpRUHBiy4RbL96vpYhc6\nOzuNRmN4eDiMmbJham2my2ILbYUtT9lyCZ7s7e3Fd0ZERMhKEWmKVVerbB9QkzD5zc3N/v7+sF6Z\nmZkWiyUwMFAKvmz8e6Dwfv75Z9wRyA7c6B9//BFfEhMTI6XahoaG8M24KadPn8bdycjI0D2kzy+0\nCdfRwaASxsbG0Mjob5JwDJoYLYwfgjw1u3HjxtmzZ9Fin376Kdr/Uc7LSfVAyM7PPWC0UvP58kBd\nkjvBBp87d66trQ3mGRa0vr4ew/1WJsZXJtjWxrhqpwRgyI8cOSKLz9dx3VxmC1ShKVm3ERISgi+B\nsJidnYVLhzenpqagLTD44qJU8CcuHzsfPnxYKlBAT2BPjNRQHnq9HmO3JN7WOafiXeIwdauVGnFb\nH2gTh0iD4P2uri60Q2xsrGRqWjVfp9smZNWsGCr7kzbPFV4hX/52gjPJzc0NCgqSZtGtyF2xEXWI\nm4K2TUxMHBwchI2UrGv4ktDQUBwCnU3nLCuqJh4esiWTLhcluhA6qa6uDgJC6tTY7faRkZGTJ09C\ntqJXo+tOT0+judCNOXBRPRCy894PxmubzXbx4kVZagCLixEKdis6OvrVV1+9c+eOVE+WNJFiVNwr\ncyBLDlVopVoAKO+LZFHrydWj37Wkw1rvrAwyDHKCA0EHSKibrGCXmqJSnbympuann36COcRIDT8Y\nI7Wvr29qaqrOGVOgVjNoMyquX/ZsU020ag5K+X5YUGkWnNVK59sjBURcEC9fTWzg9Q8nUJBpaWkv\nv/yyrGndSiFKiUh0iSyV4BH0NHjeUCc4RGNjI+6Od7KM79SvT22YTKaioqKmpqbKykp0QvRA/O7Q\nCO+++y5+C+gM6Jx5eXn4hX722WecaaB6IGSHgS3MzMw0GAy///47RigMT+np6bATMiEBlxevML1w\nzSU8T7dGxuX1gQ2orq6Gxw+zHRYWhqPAKEo8BY51+fJlqQmSlZWVlJTkRuDAf6adUPkr5aEMvHkY\nRegDmV3AttVqLSgoQCN899134eHhkt7qhx9+kMzNycnJuHyJEcWfOudiTO1UhM6tvOAueZ8kWlUy\nIsD/hncuRVJ099Jgr9QKnrUi6okMDichwQ0NDVevXsUlo0GKi4vRT1adCXDjqnGZCwsLcKbn5ubk\njuNPmEn0BLyie2AfaDtJX/FQTjysBL/Ejz76qKSkRFb2tLS0fPzxx1JmT3qXjxPPikXCTNWEuGkw\ntMZAjKvSB9oNbc7EzT6/sNlsX3zxxXPPPQcHuqKiAtbo9ddfh5GAbcCfMMw4KPbp7u7G6Cmhm569\nTJfTVteFA01NTfX09IyOjsLrxenB7YuMjBR5MTg4CPMGe9bX1zcxMYGdZa5eKlVKsg3sGR0dLSv+\nVpZEX5mKdFXrK3/KWg2xnZOTkzJrouYDJOzCsyUhVuYskkdXHR0dEFLQczgfnENubq7MpWuvy+1n\nWPhfyAKIErStSDrcfRhOu90O7Qg1iUOjh2C3sbGxkydPonkfnV8iGr+pqUlaANrx0KFD2nxooKys\n7PTp06WlpZJ2hXDugZAd0t3/68KKSVCGYZ2NTYExEcYPQyGMbl1dHbxqGRBhKWGZBgYGrl+/Dvtt\nNpu3yaNyOW0xxjiNW7dutbW1SWnQY8eOWSwWmVSQxyuQEWLUk5OTJQ3z+Pg4/gv/Ozw8jBOGsMBA\nb7VapS5Xdna2pEgKDg6WKQQJqtStKFDpotjE/8b/BgQEyJS+yWRa/xI8ePcVS0tLuBeQDrLYIi4u\n7ujRo3Ituv/NZrHFAN39+/c/88wzOBYaE30gLCxMJCOu/ciRI1CTEBa6e+seHqmUzGiBDCcu8k6t\nd2GSKKoHQh4tlGvuMg0AswFrgeGypaUFtlx0hkesxfrPEXAUm83W0NCQlpaWmJgIY6lWXbgM3HLm\nssRdCnHJEjboCbyTlZU156SqqurixYtS9AF2VyJBIAJgDiWHlbYgtSBLLtACsNbYJyEhAfuvWnZk\n+8wnLgeqCDJoamqqsrKypqbmWSdQchITqHJLb71ui/ZacL2xsbHaiRmIMLlwibB96DNEEaoHQsh/\nI/l/xHyqLIQwun/88Qekg9FohDff2NjotfPBmcCuP/nkk7p7wSZqcnjVYmPy7EalZvL19RXjKsF1\nUgMM+kNWcvT29mIDxhi+O+wxxEFSUpKswQwPD8e2aJH+/n5Y7pSUFJyJLEKUsH4vTz5BQpWUlISG\nhsbHx3/wwQfQUjrN4lbZDSfmwZKYK9dwqGdJ2kpdItSoIcj2/gS47oGQ+5axsbELFy7AKZeH3Hl5\neXDiR0ZGDh06dOXKFZhbybUHW5udnS2WdeM2Q/vwXuIpxPJpzbDkgRDRoLJKr+PWr0wDtdaqhfXP\nEydjt9tv3ryJ662rq8M/zs7O4sJxjbDWcrEQIvhUFmPK6cmDFe0JeCTuQAkgWYOJMxkcHIR6g7hB\ny0PTWCwWb1bNZpXITQGhWVZWdvbsWejsEydOvPHGG7Kgki1D9UDIQ4sUAYKtgjU1mUywUnNzcwsL\nC8HBwfiou7sb2zCf8Mv9/PzcMyqyjuGvv/5yOBzyiAGetJTRgrFsb2+HFccGjhIdHY0DbbZCtHv1\nkZXOkNJf0A04E5vNlpqaCvXQ2toKTYMzDwoKkkVwAQEBEiCK81RBLpAXnprJl3oKAwMDeG1sbERz\nwQ6lpKTgjqgK2l57sk71sNkeLnNgKoDIm1KP6oEQsgNonXVlBbUDn/r9itvthgHD116/fr2qqion\nJwfffOnSJVjoF198Ed82Pz9fW1srKaRgL/Hp22+/7TX1AMkCa11XVweFZDAYrFZrQkLCvn37JGRR\nqptOTEzAoZSindPT05KwC9vyJcnJydAWOGGIDKPRuJUbMT4+Xl9fD9USGRkJdXLw4MGYmBiVWsMj\n9c+oHraprbRxT+qhEltv63DdAyH3sbrXRPqtWv7bZQc3/GzsPzk5CRcfogHmsKysDDZbPpKcynq9\nHvsMDg7+/fffm03ltME3V+JwOK5cuTIyMvLEE0+EhYUFBwermA6J6ZfdAgMDo6KiJN+DZNrAq1S1\nhoxoaWnp7u6WzFGStxt6QmptyGn4+vpqs2+pdakqCBMbdrsdoqGzsxNHLygowL9DiCjnVTvr4BIb\n4oVeQTbCFuOeCNUDIQ+JjNgOiyJumSy1U3YU9tLf3395ebmjowPOd05Ojtf8Nth+HAvWWpIWuLiM\nK9deSHCHnLwK2nz88celKOiNGzeampp8fHxKS0sXFxexW1pampSHMBgMZrMZ0kTFtgizs7P9/f24\n6pKSErRAcXGxNvuQNtchfdkH4odDqB4IIR4G9g+2U7JQq9w7YpJhRBsaGnp7e48fP56UlLSVZEcb\nPBPZeOyxx1566SWlbDZuJCSXs9ai44QzMzOzsrLwPRMTEzIz0dXVVVNTg8vs6enBscLDwx0Oh8xz\niJDCVdfW1h49evStt96Kj483Go2rzgPRPlFPUD0QsgMowyDR85JQVhsEyCbyAlar1Waz/frrr7Ca\ngYGBCQkJMLHw0YODgy9cuHDt2jUYUVhZfAr7un6VinVu9NLS0vDwMLb9/PxMJpOLCoFMwTvaguba\ndR7gVuBcAAAHI0lEQVSb9e9dAj1UWdGgoCDJDBEXF3f79m1ZlDo2NoYdGhsb0QIzMzP9/f34yN/f\n/4UXXjh27NjevXulc8rKBvZJQv7/V8ZVk2QHXV7pfp1O4PxhZE9PTz9w4IBK0sdW8gLLy8u9vb0D\nAwO4I2azOSIiArYcFjQgIKCtrQ3bkvbRYrHExsa6d1PGx8dhm6empsQAp6ampqWlyUdQFXa7HTIF\n0uTpp5/WWmiX5zVu94f1E3hLqYjm5ubW1lZoBdX95ufnJyYm0DhQVHgfb8Y5WaeEKSGceyBk+6Wr\ncwi+evXqt99+W1BQAONUUVHR0NDw3nvvhYSEqJKMZLtBU8fExEgtUElAJBGbICMjQwUUqJg3Nw5x\n69atsrKyTz75RK/Xnz9/vry8XKkHuP7V1dWQF5AvMNW+vr7r1wJ1u6etXG0qWZUgj6BsIF5zc3Mh\nnlRqy3kn+K/R0dG+vj6dcxkpp8QIoXogOz/3AJf3888/h9NZVFSkc9Z0Li4uTkxMfOWVV5hw12t3\nQbsSUPunTA6JjFOx8u4V4pJoiKCgIH9/f4PBMDQ0pL4nNDT01KlT33//vcu6RS/MuIBffvnl2rVr\n6enpr732motw2ecE5wktK3kkdZoK4CunQ9hdySMFI1jIjgHP77fffmtvb8/OzhYPOC4uLj4+/syZ\nM1NTU2wfbwoI3b1KQvLgQL26zAC5LR2kgrbLBIa8+vj4QFJ4eapJFop2dXUtLCxAN+Tn50uqyrXm\nLbTZoHXOHFY3b96sr6+XumWEcO6BEO8xMzNTXV2t1+slpQ/EREBAQGRkJNxQeIRFRUV05u5bnbHZ\nf4REgGc/MDCA17m5Ofj0uN3oAJI7AV+7vLzsMh2yHWfuwuHDhyFY13lWstYEQ3d3d3l5+dDQkNls\nllTZhHDugRAvsbi42NPTA8UgVYZ1zuC6oKAgbNTU1FA6PEzExMQUFhaWlZWdO3cOd/nZZ5+FdGht\nbcWrREOEhYVJrchtEj0S9LHoRIp8AugGyYW1WUkE0RMbGxsYGOjeZAwhnHsgxH0mnERERKgAfbxi\nXMaf/f39XPewI/MK2wQMrSgGsdnw17GRnp4O4y2q8cSJEzpnfqrtWJZ4586dzs7Oy5cvQzpAnmZl\nZSUkJKxak9Pl0GudicViGRsb6+joYBclVA+EeM9KYcyF/zc9PQ1z0tvb+9VXXxkMBvm0ubl51sn8\n/DznhL3A+vbPI9ZRvmSvE+372vsr1TS2ieHh4a+//rqwsDAkJOTPP/+sqKgwmUxms9mNWQdtN0Yf\nZsQ7oXogxKvqQecM9IdEgBuXlpamQgTxDnxE91ISEbIqMPO3b9+OioqyWq2jo6MQrFvM2YA+vGfP\nHigelk4gVA+EeJXdu3cHBAQYjUb4o5IhWGbOe3p6MKxDTOB9WauPd8bHx7FDeHi4x91i8ugICJ1m\nLeRWclfonI9aIETy8/NNJhP7IaF6IMQbqHQCISEhoaGhk5OTUlIZ4zs8QvyJkR1aATtAOlRUVNTV\n1UVERNTW1hYUFCQnJ9PbI25MFdy9e1d6lO5eCa4t9uFgJ2xbQvVAiPfUg2zs27cvPj6+qqoK6kGm\ngrExMjKCHZ5//nmohJ6enkuXLp06dSojI6O0tPT8+fMWi0VVUCRkg6DP5ObmnjlzRudcmHn8+HEu\nqSGE6oE8qGAEf+qpp6AempqaZA38xMQEFENWVlZOTs6///7b3t6+sLCQmJjo5+cHnVFZWYlP4fBx\nrphsCqPRWFhYmJ6evry8bDAYrFbrqgEXhJCNw0lgsmP4+PhAJeTl5ZWXl0MWTE9P19fXz8zMvPPO\nOzLJ3N3dvbS05Ovru2vXLogGh8PR19cnU9AUEGQTw9yuXRANUKgpKSnR0dGrpocihHDugTwwmM3m\n999//5tvvvnyyy+xDenw5ptvQlJguJeQTr1ev3v3boz1skheMgux3cgWoXoghOqBPNiDeExMzIcf\nftjf3z83N2exWA4cOADXECoBcmH//v12u/3u3buSKNDgRHdv3SVbjxBCqB7II4o8lZAE1VpZsGfP\nnujo6La2tsXFRbzvcDj27t0LbUGvkRBCdn7oZhOQnUJbtNBlQwo8JiYm6vX6jo4OSAebzRYXFxcV\nFeV2kWhCCCEeG8CZaZXcn0AiLC0t1dTUNDc3BwcHT05O5ufnJyUlcd0DIYRQPRCypnr418k///zj\ncDgsFktYWBilAyGEUD0QQggh5MGDnhwhhBBCqB4IIYQQQvVACCGEEKoHQgghhFA9EEIIIYTqgRBC\nCCGE6oEQQgghVA+EEEIIoXoghBBCCNUDIYQQQqgeCCGEEEL1QAghhBBC9UAIIYQQqgdCCCGEUD0Q\nQgghhOqBEEIIIVQPhBBCCCFUD4QQQgiheiCEEEII1QMhhBBCqB4IIYQQQvVACCGEEKoHQgghhBCq\nB0IIIYR4iv8LAAD//1F9kTSVSYdMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import Image, display\n",
    "display(Image(filename='GradDescentMult.png', embed=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Minimizing multiple variable function\n",
    "\n",
    "Let us consider the following straight forward bivariate function $$f(x,y) = x^2 + y^2 + 1.$$ Since this a function of two variables, we have have the following partial derivatives $$\\frac{df(x)}{dx} = f_{x} = 2x \\text{ and } \\frac{df(y)}{dy} = f_{y} = 2y.$$ Note that its easy to argue that the global minimum of $f(x,y)$ is (0,0) since $f(0,0) = 1$ and $f(x,y) \\ge 1.$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting f(x,y) in 3D\n",
    "\n",
    "The 3D plot for f(x,y) and the corresponding countour plots are shown below. This function is essentially a 3D parabola. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
    "\n",
    "# f(x,y) = x^2 + y^2 + 1\n",
    "def f(x, y):\n",
    "    return x**2 + y**2 + 1\n",
    "\n",
    "# (X,Y) grid on [-5,5]\n",
    "x = np.arange(-5, 5, 0.25)\n",
    "y = np.arange(-5, 5, 0.25)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "# Z = x^2 + y^2 + 1\n",
    "Z = f(X, Y)\n",
    "\n",
    "# Plot (X,Y,Z) in 3D\n",
    "fig = plt.figure()\n",
    "\n",
    "fig = plt.figure(figsize=(12, 8)) \n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# Plot the surface\n",
    "surf = ax.plot_surface(X, Y, Z, cmap=cm.RdBu, linewidth=0, antialiased=False)\n",
    "\n",
    "# Customize the z axis\n",
    "ax.zaxis.set_major_locator(LinearLocator(10))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
    "\n",
    "# Add a color bar which maps values to colors\n",
    "fig.colorbar(surf, shrink=0.7, aspect=5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XqifasbQn4jMwdAypP46drJZSojR0gHp80VPijYhYA5hlLyxXziMzvZDp9UQ93uj9xur09yWlV+/RmozQn3NxXInleP9HzzD7TKllCRVMB1dKLu1qolB12NST5R0XHknWGCyamLaLoSonHR0HVsibYjrPDTis7UzTX6jywmCBtoTBL18aQlMEliMZKFSxXPfUOztDyqbNULFK1XaJagpzkrEz/iJnGmmbXuZBKeMV4wjFO6niDd5JFoZMQk6BEAIRbzjlNkTiqJE4sqED7CpuKYcsZZCjhzxRj6VREo1eWmQd/e6yZYt81SId1anYLmkhKFRt8hWLiKbQmoyeUbhFCIGmCBQhuHpJK5t7MqzX0jTHjVoBoc2mnlGuW9o2nh56IgIr5NmqTTqi056M0BjVuW/XIK/oauL65a10j5bpHi1x3bJWOk8xWXEmWI7LUKFK0bTRFEFHKhroQh7pOshyDreYGU8TFJEEoqEdEa1fzyikPhBCgB5FbYgi021eMVExgyzncEoZUA2URIPnqQe0p8vExInGuIHtulQsh7ZkhKimENUUmuIGQ4UKQ8UqHWeoPzFd5YblbeO3M2Vvzm2waPL0wVEWNcVZ1OzVBMyKRy6EUPHWcjwkpbz9TPfXljB4YSDPz57v41C2wsr2JJmyxVWLW1jempzRTBVXSjIlk9GS13uiOW7QGDd87+FwPKSU3tC2OOLFKqUEzfAmLOONXq+SkJBZxvPUE6iRBNLt9MIupQxubhByg56DkWgaLz4KCpYj0VTGz/WYrlGoWuO552NecVRXKZnOUfMJZ0pHMsIT3SN8b8shEoZKOqpx9eKW8ePOVmjlD4DngWlpyKAqgqLpoCuCd21cAAge2jvEQKFKW8KYMREvmTaDhQqW48XBWxORQE5kepkEGdziqJcuKBREvBEl3uiVbgfwohNybiIUFZFohESj1xumlPE89ZEeUDREohEl0ey70yGlpGTZ5PMWbckoEU2hYjvoqjIupEIITNulYrlenBumzcFrSRi895KFPD+QZ0FDjKimjIdUTnU+T4uQCyHmA7cBn8Nbgf2MiWoqN65oH0+Gd1zJ9cvaZqzBlO16YZRC1UZXBXMbYoGrAINa7LswjCxmvIlLPYLSOMeLfQc8/SskRGgGIt2OSLV5GVTFEWR+CCc/5KUwJlu8KmEfHBFRyzfXFMFgoeIlU2gKyYiGlFA0LYqmg+W4xHWVZGRmOi2uavdSP6fi7U+XUn0B+ChwwoYMQog7gDsAurq6jnrOrM0EH9uHZEzE3drs8UwgpSRftRkqVJAymGEUL3xSws0PIyt5AESsASXZHHrfIXWJl/qYgliqNjE/iiyOIofyoEdRki2IeNqXsEsyopOM6F62iKbQmy3jSq/KMqIqNMV0jFloOT2V8/qMhVwIcTswIKXcLIS49kTbSSm/DHwZvDa2Y49nKxY/3N5LTFN484Z5xzV+pkTVclwG8xVKlkNUU2lPRWblC5osUkpkJY+bGwKr7FVaplpRks1hX5OQswahGagNHch0G7KYwS2M4I4egmw/SqoFkWj2ZaLe0JTayl0ujpS0RCKBzVabDo/8CuA1QohbgSiQFkJ8W0r59lO98GCmzI939OK4kmvWdM6aZylrvcGHCl57z9ZkhIbo5JrwzwZSSi/7JD/otSBV9Vr4pDHMPJkk3iimgqzWeqKbZWS19r9ZOfJnmV4vGdfxenyP33Zqt10QCiiKF7oa/1MQqndbqBrC8BZ0IFJb2MGIHvmLxLy/MPR1UoRQEMlmRKLJqzrOD+Fm+yE/5HnoyeZZ/wxVRTC/KTE+dxbVVFqSkUCN2GEahFxK+efAnwPUPPI/noyIbzmc5d5dAzRGdX5j3VxaErOTjmQ7LgM1Lzymq7SnooHpTCiliyxlcfND3jJgWgSlaZ4X/w7YD8dPpHSRhSxuMYtbzCFLeS93uZjDLeVqecz5I20HjotAGFHQ9WMEWvUulorqTcRpilft6DreCjoTBd+pCb5TW0jj2KXZjjqcQMSSKPE0Ip5GSaQR8RRKIu09lmhASTUFuiJythBCeC0ioklktYSbH/Ra6uaHEMlmT9Rn+XOK19pjF6u217X5mNPRcSW9uTItCYOYPvvfoS+/mlzF5u4XB1jSHOc1qztnbbiSr1gM1mLhQfLCpXSRxVHc/LBXvKNHUZoX1FKz/LfPD7xRSQE3N4ybHcLNDeNka7fzIy8XaU2vCWIarX2BJ5bxtOcJT/SMa7fRz2ydy+PZOyboR7z/CbfLYxebPG5+BKdv/3EXXxbJRtR0C0pDK0q6BaWhBTXdikiem6MxEYmjRhYizTJufsibGC0MIxLNXthllkOMiRN0IrRdF9txOZQp0xgzaJnBzLrj4ctSb/PPWye/9fMHuGZpy6wMUVwpGcxXyFft2go9sUCU1kspvVSs7IC3qo4RQ0m1ed0GzyEBl9LFzY3gDB3CGTrs/T/SB2blyEaKipJurolbK2q6BZFsHPdoMeqvwZe0TdxS3htJFLO1i9Ywbm4IJzt89Mo+iorS2I7aOhe1dZ7319xxznnw0qri5geRpSxjTb+UdFsgwlauKxkqVsnVKj9nQmcCtWbnhgsvklue2Twrx6raDn25Cpbj0hQ3aI7P7pXyRLiVghf/syqegKc7fEu7mk2klMj8KPbQoZpwe+I9LlqqhtrcidoyF6WxzRPthhZE4tzySL2J7uKR0UhmEHekD2foELJa8+QVFaWpA7V1LlpN3JXmjkCI2kwjbRM3N+AJuqJ6Yp5oDsT5U6haDOQrSKA9GSUVnb5RQ6CEfKYXX4ajJzSVWnl9EPLCpVXFzfZ5fb9VHaWhw+uBEoAf4EwgpcTNDuH07cfu3Yfdtx9ZynlPKqon2q3zxj1Npan9nBCi00VKiSyMHhm5DB3GHjp0ZPSiR9A6ulA7F6F1LkZtm3dWf57SLHvnU7XkVTQ3dAZiRGs5Lv25ChXbIRXVaZumCdJzZvHlMQpVm8FClZiu0pGOovnszUnH9jyI4igIxRPwZHOgypOnAyklbmYAu3c/Tl9NuMsFAEQs6YnLnEVobQs80T7HQgNnihACkWpGSTWjL14LTBjlDPZ4F8y+/dib7qMKoOlo7TVhn7MYtW3+WfWZCyOG0rrIS9PN9uMOH0BEEt75dczC1LOJrirMa4wxUmv1UbEc5qSjM5beXJce+WRKVscKfVI+N7nyMixGvB4T0kUkmrw+KGfRySTNKvbh3VgHd2H37PIyRsCbeOxcjNa5CHXOYpR0i++e0rmCWy7WRN27mLojfd4Tmo42dynaghXo81egJBt9tXM68RaPrp1rruO1rGho973momTa9OcquFLSkY6SjJy+PWdVaMV1JcoMVXpOJ26lgDvaC46JiCa9YZ9+/EWj6w03P4LV/TzWwRdx+rq91Dsjij5vGdr85WidixGpplC4A4JbLeH0dWMf2o118EVkIQOA0tyJvmAFWtcqLwxzFowQpevg5gaRhREQwoufJ/11ImzHpTdXpmq7NMZ0WhKR07LnrBHykWKViu0Q0VSimnrCdCA/kY7txe1KWS9u1zgHpQ4Xrz0WJzOItXcbVvfz4x6e0tiOtuA89AUrUDu6zup47NmCN28xiH1w15ELsXQR8RR61yr0xWtR5yyqe1GXtomb6fPaWuhR1KZ5XuqpX/ZIyVChSrZiETdUOlOxKTukZ4WQD+Qr2K5LUzxC2bRxpaQ5HgmMdz5ekZnp9YZ2qVbPG6jjE8ItF7D2bsfavQVn6BAgUDu60BetRu9ahZJu9tvEkDNEVstYB1/E6n4eu+clsE1EIo2xdD360g2ozR1+m3jaBPGczJZNBgtVDFVhTkNsSgWJdS/kluMyXGvk7rWSdOjPV+hMT+2DmCmkY+GO9gbm6n8mSNv0wia7t2If2g3SRWmZg7F0A/rS81HiJ+yNFlLneN/9C1h7tnqiLl2U5jkYy9ajLzkfJTEtXapnnaNHyRHUprmISNw3e0qmTV+ujEDQ2RB7WcPAE1G3Qu64kqLpFfIA42t0CiHozZZpihu+NrIZL+rJ9IGU3uSKz/G400FKidO7D3P3s1j7d4JlIhINnle2bD1qU/16ZSGnx/hobM9WnMEeEAJtzhL0ZRvQF6/1vX/46eBW8rV5K6tWTORfuqtpO/Rmy9iupD01uXzzuhRyy3Hpy5WJaCoVy6ExppOOGeNZK4cyJVoSXkeyYtUmqqsz1u72eEjbxB09jKwWwYh7V/k6m8x0qyWsl57FfOFp3OwQ6BH0xWsxlm1A7VxY12GhkOnDyQ5h7d6CuWcrMj+KMGLoyy/AWHkxamOb3+ZNCek6uNkBZHHEq+VomuvbHNZYj5aK5UyqYLHuhNxxvb4F6ZhOY8ygULWoWA7NiQgCzyPvz5VpTkTIli1s1x0Pu8wGbimLO3oYwMtZTdRXhoYzOkB15+NYu7eAY6O2LcBYdUndelohs4OUEqdvH+bzv8ba/xxIF23uUoy1V6DNX1ZXF35ZLeKMHvbmBJIt3nnswzkspWSgUCFfsUnXiodOZEfdFQSpikJHOkqklkA/WjJRhKAvVyZhaOPZKocyJaK6Smd6dpL/pXRxM/3e1VyPobbMD+xCsscipcQ+tBtzx+PYh14CVUNfup7I6ktRW+b4bV5IHSBq4RVtzhLcUh7zxU2YL/ya0r3fRGlow1h7GcayDXVxTohIArV9qRc7LwzjmCXU5gWz7sgIIWhPRtEUr3jIlXLKTmlgPfKJVCyHXMWiPRWlaNoUKhapqM5I0URTxeyJuG3iDB8Eq1K7grfXhQciXQdrzzaq2x7BzQwgYkmMVa/AWHkJSizht3khdY50bKx9O6jueBx3+DAiEsdY/Qoiay5HRPyrrpwK4yNsIVCa5qHE/JnQHylVGSmaJAyNzvTLxbzuQisnYyBfIWFoxA119kIp5RzuyCEAlOZ5KLHgz95L18HavZXq1odwc8MoTR1E1l2JvmTdWVVZGhIMvLDLfqo7HsM+8ALoESJrLsNYczlK1L8MkckirSrOyEGwqrU0xXZfQi2ZkslQserlmqdjR/VoqbvQyokwbYeK7ZCcpdJ7KV3cbL9XJaZHUVsWBH7YKF0H66VnPQHPj6K0zCF+/VvRFq6sixFESH3ihV0Wo81ZjDPcS2XLg1S3PEh15+NEVl2Kse4KlGhwR4BCj6C2L/GKiPJDONWSFzqd5RL/xriBEDBYqNKbLTOnIXbKhlt145G7UlI2HYaKFZrjkWltDXkivFBKD1hlL1WpoSPQQihdB2vXM1S2PoQsZFBb5xG54JVoC86rq4nYkLMHZ6Sf6tYHsfbuAE3HWHUJkXVXBT6k55YyXpqiECjN833JaslVvHa4UU1lboNXBVr3oRUpJRXLASEmnTx/JkizhDN0wMsNb5rnLV4QUKSUXoxy8/24uWHUtvlELrgObf7yUMBDAoGTGaC65SGsvdtAM4isu5LIuisCPbqVVtWbE7OrXpuN5OxXMReqFn25mpg3xlAVpX6EvGI5vhb5ePHwHlA01NaFgc4Nd0b6KD/xM5y+/ShNHUQ33oi2YEUo4CGBxMkMUNl0P3b3c4hEA7FX3Iq2aHVgf6/SdXFHepCVvG8pimNiHtNV5jcl6iNGnimbDBWqzEnHfGmI5RaGvSpNPYba2hXYSUFZLVN55leYzz+FMCJEr3gNxoqN59QqOiH1h9rYTuKGt2L37qP85M8p/eq7aHOXEr3sNtTGdr/NexlCUVBaFuBmepGFYVzHQmme3S6RyYhOewpyZevEdgbJI89XLPprGSnHS72ZSbyOcP3IwjAimkJpnh9IUZTSxXrpWSpP34uslDBWXkzkohvqIisgJGQi0nUwX3iayub7wTIx1lxG9IJXBrJHkbcy07C3PKMRR21dgFBm18mTUqKcILQSGHezZNr05ytEayv6zK6Iu7gjh5DlnLc6d2NnIId69uAhKk/8FGewB7V9AbGbfhu1da7fZoWEnBZCUYmsvhR98Voqm+7D3PEY1p6tRC+5GX3p+kCdg97KTK2g6rgjh3AG9nlh11mM8Z+0dD8IHnnVdujJlNAVhXmN8dntl+I63qSmWaotvxa8hlfSrFB5+l7MF55GxBJEL74Jfdn6QGfQhIRMFXuwh8rjP8UZOoTasZDYla8LZB8XWS3iDB0EgSfms7ikXGCzVmzXpWe0BMD8xjjaLLaklY6NM9QNVsVLMYo3zNqxJ4vdf4DSQ/+NLGQwVl9K9MLrAzn0DAmZDqR0vRTaX9+DdCyir7gFY+UlwXOurKqnHa7jifkstcQNZEGQlJK+bBnHlT6J+H6wTJSWLt9Kck+EdB2vmGLLg4hkI4nb3o/W0eW3WWcN0nGwMlnsYgG3auKaJq5Zxa2aSHPsvvcnNA3FMFAiBooR8W4bBoqhe/fjMYzmZhQ9bDZ2pgihYJy3EW3BeZQf+RGVx3+KfXAXsatejxILzipbQo+gti3CGezGGer2EiMi/uXG++aRP/300wzkK+SrNp1nuCDpVJGOjTO4H5yaiAdsGTY3N0Lpof/GGTiIvmwDsctuD73wKeCUSpS6D1Du6cEcGsYaGcYcHsEcGcEcHsYaHsEcHQXXndbjaukURnMLekszRksLRnMzRkszeksL0blziC9ciN5UX10y/URKF/O5p6g8fQ/CiBK7+g3o81f4bdZRSMfCGewGx6x55jMr5oELrdz38OMMF6s0xw2aE7OXpz3uidsmSsvCQJUMSymxdm+h/MTPvMKny1+DsfR8v80KJNJ1qQ4OUt7fTam7m3L3AUrd3ZT2d2MODh61rdA09JqojgnsmNhqqRRqxPOyRcRA0Y0J3rd3XzqO562b5gTv/YgH7xSLmCOjRy4SIyOYI8OYQ8O4lcpRtmipFLGFXcQXLvT+X7SQ+MKFROfNCz36E+CM9FF68L9xR/sxVl9G9OIbA9Vq2RPz/V476BkOswRKyC+86CL5/bsfJBnRZrWHuHQd7wO3qiitwfLEZbVM+bGfYO3bjtqxkPi1v4WSbPTbrMBgZXPktm8nv2MnuZ07yT/3PE6hMP68mkgQX9hFbOFC4osWEuvqIt7VhdHWhpZO+eYFO6US5tAw5UOHKHd3U6pdcMrdBzCHhsa3E5pGcsVyUmvXkFqzhvS6tUTnzg299xrStrwJ/+eeQGnqIH7tb6E2d/pt1jhHiXnbQoQxM2IeKCFft+FCedcDjzCvMX7KZjDThZSu90GbFZTWBSjR4MTEneFeir/8DrKQJXLhdUTOvzqQOeyzSbV/gOyWLWS3biX77BZKe/d5TygKiWVLSa9ZQ2LF8nHP1mgJXrbRqbALBcoHDlDa301x717yO58j//wLuOUyAEZbKw3r19OwYQMNF2wgvmTxOf+7sA7uovzIj5BmhdgVr8VYfoHfJo0jbQtncB+4Lmr74hmpCA+UkJ+/4UK5efOmWVs0WUqJO3wQWcmjNC8IVN8Ua/9OSg/+ABGJEr/uLefshKZ0XfLPPc/wI48w/PAj48KtxuOkz19HwwUbSJ9/PqlVK1Fj9dHj+nSQtk1x7z5y27eT3eJdxMZCRXpTEy1XXUnL1VfRePHFqNHgto6YSdxygdID/4XTuw9jzeVEL7k5MBc4aZs4A/tACE/Mp7lzYqCE/Ez7kU8FKaXXlrI4gtLQiZJqmZXjngopJeb2R6k8fQ9q2wLir3pboGblZwO3WiWzaTNDDz/CyKOPeaEGVaVhw3parryChgsvJLlsKUILTN3arCOlpNLbS/aZZxl94klGHn8Cp1RCiUZpesUltFx9Fc1XXI7R1OS3qbOKdB0qT92N+dwTaF0riV/7W4HpiSTNsjf61wzUtkXTurjzOSvkbm4QNzeASLagNgYjpiZdx4uH79qMvngdsavfEKjJm5nEKZcZevAhhh98mJGnnsItl1HjcZouu5SWq66k+fLL0RuCM2IKGq5lkdn8DMMPP8LwI49iDgyAopBet46Wq6+i/VU3EOkIXs+SmaL63JNUnvw5SnMniVe9AyURjN+OW8njDh1ARBIorV3TVrx3Tgq5W8rgjhxCxNJe75QAxFBltUzxV9/FObyXyPpriFx0/VlfoSmlJLtlC/0/u4uhXz2AUyphtLXSctVVXpjgogtRjOC2Mw0qUkoKL+6qifojFHe9BIpC0yUX03HbrbRcffU5EX6xDr5I6YH/QuhREje+IzDrz7rFUdzRw4h4A0rTvGnRn3NOyN1KEXeoGxGJobQuDIRYuoUMxXv+Azc34k3UrLjQb5NmFHNkhL6f/JS+n/yUyqHDqPE4bTdcT8ett5DeEKxeGmcD5Z4e+u+6m/6f/5xqXz9qMkn7ja9i7m+8gcSypX6bN6M4w70U7/sWslohft2b0RcEI9/czQ3g5gYRqVbUho4z3t85JeTStnAG9nj9xNsXT2uM6nRxcsMU7/oa0qqSuOGtaHOW+G3SjCClJL9jJ4d/8AMGf/kA0rJouPBCOl99G62vvPasnqgMCtJ1yTzzDP0//TlDDzyAWzVpuGADc3/zN2i59hqUs3TOwS3mKN73LdzRAeLXvhF98Rq/TfLm6EYPI0sZlJYFZ7zW7zkj5FJKLwXIqqK2LwnEBIgz2k/xF18H6ZK46V1nZcdCKSWjTz3Fga9+jdz2HajxOB2338rc33gD8UWL/DbvnMXKZun7yc/o/dGPqRw+jNHeTtc730Hna25Hifh/bkw30qxQvOebOIMHiV31hkCkJ0rp4gzsB7uK2rH0jDomnjNC7mT7kfmhwDTBcoYOU7z7G6CqJG5+N2rT2TURJaVk9Mmn6P7KneR37iTS0cH8d7yNjltvQUsEp2r2XEc6DiOPP8HBb36b3LZtGG1tLPjtdzDnNa8+6wRdWlWK9/0nTu8+ole8msjKS/w2yUtL7N8DWgS1fdFph3pnTMiFEAuAbwIdgAS+LKX8p5O9ZqaE3C3ncYcPIBJNqE3+e73OcC/Fu74GukHi1vegpoOR+jgdSCkZffwJuu/8GvmdzxHp7GDBb/82nbffGk5cBhgpJZlNm+n+yp3ktm7FaGtlwTveTudrX3tWTYxK26L0q+9hH3zRm49aebHfJnlLSA4fRCSbURtPb0J2JoV8DjBHSvmMECIFbAZeJ6V87kSvmQkhH4+Lq5oXUvF5ctMZHaB411dB1Uje9j6U1Owv3DoTSCkZeexxDtz5NfLPPU9kzhy63vVOOm67NewVUkdIKcls3syBr36N7LNbMFpbWfCOt9H5utedNYIuHZvS/d/B7nmJ2NWvx1juf3KBk+lFFkZOO14+a6EVIcT/Av8qpbzvRNtMt5BLKXGH9iPNSiDi4m4hQ+Gn/w5SkrjtfagNrb7aM10UXtrN7r/9O3LbtnsC/p530XHrLWft5Nm5QmbzM3R/9Wtkn3kGo62VJX/wIdpuuP6syCqStkXpvm9j9+4lfv1b0Reu8tce6XqVn7aJ2rlsypWfsyLkQohFwMPAWill7pjn7gDuAOjq6rqou7t72o7rFkZwM70oTXNREv5WuEmzSuHnX8HNj5K8/Q7U5jNPOfIb1zQ58PX/4OB/fBMtnWLRB36HjttvCwX8LCPzzLPs/ad/ofDCC7RcdSXL/vRPiLQFb4WeqSItk+Jdd+JkBkje9n7fkw2kVcXp34OIJlFaFkzpgjnjQi6ESAIPAZ+TUv7oZNtOp0c+NokgjLF8cf+8COk6lO77T+xDu4nf9E70ect8s2W6yG3fwa7P/TWlfftov+Vmlv7hH6A3+D+JHDIzSNvm0H99n/3//mWEbrDkQx+k8zWvrnvv3C3lKfzkSyBdkq/5AErC39+wmx/CzfajNM9DiTdO+nUnEvJpCSQLIXTgh8B/nkrEp5OxHE0Apcnflp9SSipP3oXds4vY5a+uexF3ymX2fP6f2PL+38EplVj7+X9g5ac/GYr4WY7QNOa/7a1c9J/fJrliOS/9n79h+wc/RPnQIb9NOyOUeIrEje/0vPN7v4U0q77aI5ItYMS8PlCOdcb7O2MhF5563gk8L6X8xzO2aArIUgZZLXqLJs/iatbHw9z5BObzT2GsuzIQM+RnwujTm9j81ndw6Hv/xZw3vJ6LvvNtmi+/zG+zQmaR2IL5nP/Ff2H5n32U/HPPs/ktb6fnu99DOo7fpp02anMH8evejDs6QOnB7yNd/96LEAK1aR64Lm6m74z3Nx0e+RXAO4DrhBBban+3TsN+T4q0LdxMHyKSQPgcF7cOvEDlqV+gLVxN9OIbfbXlTLCLRXZ97q/Z/sEPIVSV87/0RZZ/9I/RkmE++LmIUBTmvP51bPzed2jceBF7v/DPbHn/Byjt3++3aaeNPn850ctuxz74IpWnfuGrLUKPoKTbkOUcbil7Rvs649kqKeWjwKzHNNxsHyB9D6m4+RFKD/0AtXUO8Wt/0/e0x9Ol3NPDjo/8CeUDB1nwzrfT9d73njVpaCFnRqSjnTX/8HcM3nsfu//h8zzzrvey6rOfpuXqq/w27bSIrLoENzuEufNx1PYFGEvX+2aLSLVCOec5pdHkabcTqUvVkdUSspxDJFt9DalIx6b0wPcBiF/3Ft/DO6dLdus2trz3DqyREc7/l39i8e/9bijiIUchhKD9phu56NvfJL5wITs/+mdeqMWHyvDpIHrJTagdXZQf+1+c7NCpXzBDCCG84iDXxs0Pn/Z+6k7IpZQ42T5QNZSUv/nZ1WcfwBnsIX7l61FS9dnYv//ue9j2e7+Plkqx4c6v0LjxIr9NCgkwkfY21n/pi7Recw17v/DP7P7bv8e1bb/NmjJCUYlf+0aEolJ+6Af+xssjcUSsAZkfOu2Jz/oT8nIOzDJKut3X5Z3s/gNUtz2MvuLCQHRZmypSSvZ/+au8+KnPkF63lg13foV417m5zFzI1FBjMVb99V+x4J1vp/dHP2bnH/0x9oSFsOsFJdlI7IrX4gz2UN36kL+2NHg9mNzcwOm9fjqNmWmklN4b1SKIKeReTrsdVpXyQz9AJBqIvWLG53WnHbda5YVPfpoDd36NjttuZd0/fyFclSdkSghFYfHv/S4rPvYXZDZtZsv7fofy4cN+mzVl9MVr0Zeup/rsg9iD/qVYCs1AJJuQxQzSqkz59fUl5MVRsE0v3dDHCc7Kpvtw86PEr/4NhBH1zY7TwS4W2fb7H2bw3vtY9LsfYMUnPhb2SAk5bTpfczvr/uWfMIeH2PKe91F4abffJk2Z2GW3I2JJyg//AOn4FyZSUm0gFNzs1L3yuhFyKaU3GaDHEFH/Fil2hnu9fPHVr0Cbs9g3O04Hu1hkx4f/iNyOHaz8q8/S9dvvrPuKvRD/abzoQjZ81asE3f7BD1Hcvcdvk6aEiMSIXfFa3Mwg5nNP+meHqiGSLchKHmlNrWCpfoS8nAfHREm1+CY+UkrKT/4cYcSIXni9LzacLk6pxI4Pf4TczudY9Vefpf1VN/htUshZRHzhQtb/v39F6Drbfu/3607M9a7z0OavoPLsA7ilvG92KMlmQOAWppZJUxdCLqX03phqIM5wqaQzwdq3A6dvP5GNNyAi9bNkmWvbPPdnf0Fu505W/eVnaLvulX6bFHIWElswn/X/9kWErrP9Qx+mcrjXb5OmRPTSW8GxqWw6YePWGUeoGiLRiCxmp5TBUhdCjlnyMlX89MZtk8qv70ZpnoOx4mU9awKLlJJdn/trRp/6NSv+7E9pu/46v00KOYuJLZjPun/+PK5psv3Df4iVPbOKxdlEbWjFWHMZ1kvPYA/2+GaHkmwBJG5hZPKvmTlzpg83PwyKikg0+mZDddsjyGKW2GW3+Zr2OFX2f+nfGbjrFyy84/10vuZ2v80JOQdILFnCmr/7v1R6+9j5xx/FqfjboGoqRDdci4glqTzxM6R0fbFB6BFELIUsjE46vz3wiiRtE1nJIxLNvpW/u+Ui1W2Poi9eh9a5yBcbTofBX/6Kg9/4Jp2vey1d73mX3+aEnEM0XLCBlZ/+JLntO9jzj7PaS++MEEaU6MU34gz2YO9/3jc7lGQrSAc5yR4swRfyUgbA1wUjzJ2Pg2MTubB+whKV3l5e+uv/S2rNapb9yUfC7JSQWaft+utY8M530Pe/P2Xgvvv9NmfS6Es3oKRbqGx9yL8WBEYMtAhuTf9ORaCFXEqJW8x4HQ41f3KdpVmh+tyTaItWozbWx2op0rZ54ZOfRjoOK//yM+FKPiG+sfCO95Fau4aX/vr/1k3BkFAUIudfhTt8GPuQP3nxQgiURCOY5UmlIgZayDFL4Fj+xsaffwqsKtH11/hmw1TZ/9U7yW3bzvI/+yixefP8NifkHEbRNFb+5WcAeOHjn6qbviz6sg2IRNrX0n0R9xZxmYxXHmghd4sZEAoi6k/KobRNzB2Po81f4fs6f5Mls2kzB7/xTTpuv432m+q3N3rI2UNs7lyW//mfkt+5k+4vf9VvcyaFUDUi667C6duP3bffJxt0RDTple2fIsQTWCGXruu1qo2nfcsSMV/cjKwUiay/2pfjTxU7n+eFT3+GWNcCln3kD/02JyRknPZX3UDna17NwW9+i8zmZ/w2Z1IY512EiCaobn3YNxtEvAlcG1ktnnS74Ap5tQDSRcT8WyPSfHETatv8uslU6f7a1zGHhln5mU+jxuN+mxMSchRL/+jDROfMYc8/fr4ulowTmoGx6hLsnpdwCxl/bIglQShe19eTEFwhrxS8sErEH0FyRvpxR/vRl23w5fhTpXzgIIe//wM6X307qVUr/TYnJORlqLEYiz/4uxR376HvJz/125xJ4Z3/EmvfDl+OL4SCiCSQlcJJwyuBFHIppZc7Hk36ljtu7d0GQkFfvNaX40+Vvf/6RRTDYNEH7vDblJCQE9J63StJb1jP/n//Mnbh5OGCIKCmW1Bb52Hu2eabDSKWAscC+8TZK4EUcqwqOLZvXQ6llFh7t6HNXYIS86/T4mTJbd/B8EMPs+Cdb8doafHbnJCQEyKEYOmHP4Q1muHQ977ntzmTQl9yPu7wYd+WhBvTQVk+cTOvQAq5rHgG+yXkzmAPbn4Ufcn5vhx/quz/8lfQmxqZ96Y3+m1KSMgpSa1aReu119Lzne9hZU8e+w0C+pJ1gMDyySsXqg56FLdy4lWYAinkbqUAetR7Az5g7d8Jioq+aLUvx58K+edfIPPrp1nwjreHE5whdcPCO96LUyxy+Ic/9NuUU6Ik0qidCz1d8AkRTXp1NScgcEIupQSr4tskJ4DTuxe1fUFdrP7Tf9ddCMOg87Wv8duUkJBJk1i6lIaLLmTgrrv9K4OfAtr85bij/bhlf+L6wji5HgZOyLGrXtqh7k+/b2lWcIZ762L1H9eyGLjnPlqvvgotGfxYfkjIRDpuvYXywYPkd/iTETIVtE5PDxy/ioOMGGjGCZ8PnJBL01t4VBj+CLnd1w1Sjn9xQWbk8Sews1k6br3Fb1NCQqZM6yuvRYlE6L/rbr9NOSVq2zzQdOy+fb4cX6gaWufyEz4fPCG3yiCUk159ZhK7bx8oKmr7Al+OPxUG7robvamJpldc4rcpISFTRkskaH3lNQzedz+uafptzkkRiorW3oXd64+Qn4rgCblZ8SY6fWq76vTuQ22b71u3xcliZXMMP/oo7TfdiAi7G4bUKe233IydzzP86GN+m3JK1DmLvTh5JXj574ETcuwqQo/4cmjpOjgjfajtXb4cfypkNm9G2jZtN9RPj/SQkGNpuvhitHSK0Sf9W71+smg1XXCGg7cWaaCEXLoOuI5vaYduIQOug9rY6svxp0J+x06EYZBcGZbjh9QvQlVJrVlLbod/qX2TRamtR+D6VBh0MgIl5IytGu1TfNzNDgOgNARfyHPbd5A6bwWKHuwQUEjIqUivXUNp7z7swokLXoKAiCVBN8Z1IkgESshlTch988hrV1olHWwhdy2LwosvkFpXH31gQkJORnrdWpCS/HP+rZE5GYQQKOlW3FzokZ8cu+aR+yXkuWEwoohosCski7t341ZN0mtDIQ+pf1JrVoMQ5Oogn1xtaAlDK6dizCNH9ScLw80OoaZbAr9QcX7nc0DtBAgJqXO0ZJL4woWB98gBlHQLbiGDdIK1ZF2ghBzpglB9E1JplhHRhC/Hngrm0DAoCpH2dr9NCQmZFiJz5mAOBc/TPRYRTYCUk1oQeTYJlpC7Lij+ecPSMn1LfZwKVi6Llkr5tgReSMh0ozeksOugE+K4PpyNQi6EuFkI8aIQYrcQ4s9Oe0dSelWdPiGtKuj+ZMxMBTubQ2/wbwm8kJDpRks3YGWzfptxSsaEXFrBqkQ9Y9UUQqjAF4FbgNXAW4QQpxe8la7vQl4fHnkOvSHttxkhIdOG3tCAUyzi2sGKPb+MmqN3NoZWLgF2Syn3SilN4HvAa09rT9IFv+Lj0gXLQtSFR55FS4dCHnL2oNUcEzsX7PDKWeuRA/OAgxPu99QeOwohxB1CiE1CiE2Dg4PH3ZHXl9inGLmUgARF9ef4U8CpVlEiwR85hIRMFjXi9f53K8HydI9FqDV9OFezVqSUX5ZSbpRSbmxrazvuNkJRPK/cB4SieiI+lsseYPRUKvBVcCEhU8HOe5540EeaY5540Ebu0yHkh4CJPV/n1x6bOkKpecb+IHQjcLGv46Gl09h1MDEUEjJZrGwOoaqoiWAX443rQ8Dm0qZDyJ8GlgshFgshDODNwE9Oa09C+OaRA6BH6kPIG+pjhj8kZLJYtXmfoBfjjelD0JIizriEUkppCyE+CNwDqMDXpJSn18rMb49cM5B2sCYxjofekMbO5f02IyRk2rBzdZJSG9DQyrTUwksp7wLuOuMdCf9i5FC7ypp14JGn0zilEm446RlylmBl6iMT60iMPFjnXaBKA4WignSRrk8Tnok0bjH4IYv4woUAFPfu9dmSkJAzR0pJcc8eYl3BX17RLWS8XPJQyE/C2PJqjj+ZI2pDK25uxFvgIsCk1q4BvJ7kISH1TuVgD3Y267WzDThubggl3Rq4WH6ghHysD7l0/IlTKw0tIF3c/Kgvx58s0Y4OjLa2ulhVJSTkVIy1r60LIc8OoTa0+G3GywiUkKPWJhB8yuUeW1AiiCuAHEt67RryddC/OSTkVOR27ESNx4kvWuS3KSdFOjZuIRPIFcQCJuTe3Kv0KbQy9gUFcQWQY0mtXUvl0GHMkRG/TQkJOSPyO3aSWrP6SNVkQHHzIyAlSjr0yE+KEMJbHcinFEAlGkdE4zgj/b4cfyqkz18HQObpTT5bEhJy+pijoxR27ya9bp3fppySMV1QGo5fme4ngRJyAKFHkVbFt+Or7Qtx+vb7dvzJkl67hkhHBwN33+O3KSEhp83gffeD49B2w3V+m3JKnL79oBmoLZ1+m/IygifkRhRs07fMEW3OYtz8SODTEIWi0H7zTYw89WvM4eDH9ENCjkf/Xb8ged4KEkuX+m3KKbF796F1LPTSpANG4IQcPeb975NXrnUuArwvLeh03HIzOA4D997ntykhIVOmuHcfhedfoP2WW/w25ZS45SJuZgB1ziJfji+lxK2cuFFe4IRcGJ6QS7Psy/GV5k4wonUh5PHFi0itXkX/Xb/w25SQkCkz8Iu7QVVpv/FVfptySsbCrVrnYn8MsKu4Q90nfDp4Qq5qoOq+CblQFLTORXURJwdov/UWirteorDrJb9NCQmZNNK26b/7HpovfQVGS7Pf5pwSu3cvaDpq28uWWpgVTqWHgRNyAGHEkdVibaGJ2Uebtxw3N1wX2SvtN96IGo9z8D++6bcpISGTpv8Xd2MODDDndae3mNhsIqWLdeB5tDlLfIuPy2rxpIveBFPIY0lwHbD88cr1xWtAKFh7t/ly/KmgN6SZ+6bfYvD+X1J4abff5oSEnBLXsui+8+skV62k+aor/TbnlDh93chiDn3p+b4cX0qJrBQQ0eQJtwmmkEc8g92yP6vgKLEk2twlWHu3+TYqmArz3/oW1GSSfV/8N79NCQk5Jb0/+jHV3l4W3fH+wPUsOR7W3u2g6uhdK/0xwCyD6yCiqRNuEkwhVzUwYsiKfz239SXn4+ZHcQZ7fLNhsujpNAvf8y5Gn3iCkSef9NuckJATYmVzdH/1ThovuZimyy7125xTIl0Ha/8O9K6VvrWudWs6KKKJE24TSCEHUKIpsCq+levri1aDqmHtCX54BWDub/0m0fnz2PuFf0HawVoYNiRkjAN3fg27UGTpH3yoLrxx+9AeZKXkW1gFQFYKYMQRyomXjwiskI/Fg2TZH69cGFG0Bedh7dlaF6sGKYbBkt//IKV9++j5znf9Nick5GXkn3+ewz/4IZ2veTWJZcEvAAIwd21CRGJo85f7cnxpm2BVUE4SH4cACzl6FDQDt+RfhWVk7eXIagnzxc2+2TAVWq65mtbrr2P/l74ctrgNCRR2ocjzH/8kRmsri3/3//PbnEnhZAaw9z+PseoVXrjXB2RN/0T85MvgBVbIhRAo8UYwS0jbn+XXtI6FqJ2LqG5/BOkEP1whhGDFn/8pRnsbL3ziU9gFfyaLQ0ImIqVk99/9HZXDvaz87KfRG4K/pBtAdevDoGkYay7z5fhSStxSBhGJI7STrxEaWCEHEIlGANxixjcbIuuvQRZzWLu3+GbDVNBSKVZ+9jNU+vt56W/+ti6ybkLObgZ+cTcDd9/Lwve+h4YN6/02Z1K4+VGsPdswzrsY5SSTjDOKWQbbRMSbTrlpsIVc1RGRJLKU9bE4aBlq61yq2x4J/BJwYzScv45F738vg/fdT//Pfu63OSHnMKUDB3jpb/+ehgsvoOvdv+23OZOmuu0REILIOv/y3N3SKAgFETtx2uEYgRZyqHnljuVVNvlxfCGIrL8GNzeMta9+VuRZ8M530HDRhez++3+kuDf4fWNCzj6cSpUXPv4pFF1n5ac/FfiFI8ZwS3nMl55BX34BSsKfMJB0XWQph4ilJ1VNGnwhj6VAUZEF/1bC0RauQmnqoLL5fqRPy9BNFaGqrPzMp1BjMXb80R9THQr+qkchZw/ScXjxU5+hsGsX533y40Q62v02adJUNt8HUhI5/yrfbJClDEgXpRZePhXBF3KhIBLNyEoeafkz6SmEQuzSW5H5Uao7HvPFhtMh0tbG2s//PVYmw44//Ah2wZ9RTci5hZSSPf/4BYYefJClH/4QLXVQhj+GPdiDtetZjDWXofq0pJuUErcw7LX0NuKTek3ghRxASTYDwntzPqHNXYq2aDXVrQ8FftGJiaRWrWL1X3+O0p69PPfnf4FrBj8nPqS+Ofgf3+LwD37I/Le9lXlvfpPf5kwaKV0qT/wcEUsQ3XCtf3ZU8mCbKKmWSRdN1YWQC1VDJBqRxYyvaYCxS24BKak8XV/LqzVfdinLP/bnZH79NM/9WSjmITNHz3e+y/5/+xJtN93I4g/+rt/mTAlr91acwYNEL77RW6nMB6SUuPkhUA1EbPLx+boQcgAl2QJIX71yJdVEZN2VWHu2YddJv/IxOm+7lWV/+lFGHnuc5/78Y6GYh0w7Pd/5Lnv/6V9ovf46Vn7y4wilbuQFaVapPH0Patt89GUb/DPELIFZnpI3DnUk5EKPIKIpZGHU1zTAyPlXIxJpyk/8rC6KhCYy9w2vY9mf/gkjjz7Gjo/8SVgwFDItSCnp/uqd4yK+6rOfRmj+VEKeLpVnfoksF4heehtC+CeLbn4IFBURb5zS6+pGyAGUdBtIx3uzPiF0g9hlr8Yd6aP67AO+2XG6zH3D61nx8b8gu/kZtrzvdygfPuy3SSF1jFut8sKnPkP3V+6k47ZbWfnZ+hNxu3cf5s4nMFZegta+wDc7ZLWIrBRQki1THs3UlZALI4aINSALw751RQTQF65CX3Eh1W0PY/cf8M2O06Xz1bez9p8/jzk0xJb3vI/c9u1+mxRSh5ijo2z74IcYvOdeFv1/H2DFJz6GUmciLs0KpYd/iJJuJnrJzf7ZISVOth9UDZGaerZMXQk5gNLQDhLc3ICvdsRecSsi0UD5oR/4lhZ5JjRt3MiGr/47aiLB1t/9fQbuvc9vk0LqiOLefWx5z/spvPgiq/7PX9H1rnfWRVvaYyk/+XNkMUvsmt9E6CfvZzKTyHLei42n208rtFN3Qi40A5Fs9jJYzIp/dhhR4lf/Bm5hlPLjP/XNjjMhvmgRF9z5FVKrV/HCJz5F91e/FvZmCTklo0/9mi3v/x2cSoXz/+3/0Xb9dX6bdFqYe7ZivfQskfXX+BtSkS5uth+0yJRj42PUnZBDLVauqLjZPl+FR5uzmMiGV2Lt3oK56xnf7DgT9MZGzv+Xf6L9lpvp/spXeeHjnwwnQUOOi3Rder77Pbb/4UeIdnZwwde/SnrNar/NOi2c7BDlx/4XtaOLyAWv9NUWWRgBx0Rp7DztUU1dCrlQVJR0uzc54GO/coDIhmtR5yym/PhP6jJeDt6iFOd96hMs+t0PMPirB9j05rcy/MijfpsVEiBK3d1s/cDvsfcL/0zLFZez/t+/RLSz02+zTgtZLVO679sIRSV+7Rsn1ctkxmyxTdzcICKaPOXiESejLoUcQCSawIjhZvp8nfgUikL8ujejxNOU7v9P3Jx/PWHOBCEEXb/9Ti742lfQGxrY+ccf5fmPfxJzdNRv00J8xLVtDvzHN9n89t+mtG8vKz75cVb/7d+gJX1q7XqGSMem+Mvv4OZHiV//VpRko3+2SIk76mWNKY1zz2hf9SvkQqA2zQPp4o72+hpiUaIJ4je9E1yX4r3fQlbLvtlypqRWreKCb3yNhb/zfoYefIhNb3orA/fcG8bOz0EKL77Ilve8j/3/70u0XHkFG7/3HTpvu7UuJzXBE87yYz/B6d1H7KrXo81Z7K89xVFktYjS0IHQ9DPa1xkJuRDi74QQLwghtgkhfiyEaDwja6Z6fD2C0tDuNdQq52bz0C9DbWglfsNbcfMjFH/13brpXX48FF1n4XvezYXf/AaxBfN54ZOfZudH/oRKf7/fpoXMAm61yr5/+xLPvPt9VAeHWP03/4fVf/05jBZ/mkhNF9VtD2O99AyRC16J4Wf1JrWQSrYfEUl40YUz5Ew98vuAtVLK84FdwJ+fsUVTRCRbQI/hZnp9r7TU5iwmduVrcQ7vpfzYT+rei00sWcyGL3+JpX/4B2Q2P8PmN7+Nwz/6H6Tr+m1ayAyR3bqNze98Fwe/8U06brmZjf/1HVpfea3fZp0x5t7tVDfdh77kfCIX+Jtlc1RIpWnutIxwzkjIpZT3SinH1PNJYP4ZWzRFhBCozXPBdT0x91k8jeUXEll/DdauzVS3POirLdOBUFXmvflNXPSdb5Fas5rd//dvefZd72H44Ud8/6xDpo/inj089xcfZ+sdH8CtVln7T5/nvE98DD1dH+trngy7bz/lh3+I2tFF7KrX+x4aOhJSaT/lWpyTRUzXySiE+CnwX1LKb5/g+TuAOwC6urou6u7unpbjjuHmh3Cz/SiNc2ptb/1DSpfywz/C2r2F6CU3+7pc1HQipWTgnnvp/vJXqBw6TPK8FXS99920XH217ydHyOlR3L2H7ju/xtCvHkCNx5n3pjey4J1vR41Prg920LEHDlK8++so8QYSt70PJebvJK20KjgDexFGHKV14ZTPGyHEZinlxpc9fiohF0LcDxwvz+hjUsr/rW3zMWAj8AY5iSvDxo0b5aZNmyZl+GSRUuIOH0BWiqjtixFGbFr3P2V7XIfyg/+NtW8H0UtvI+LTStwzgWvbDNx9Dwe+/g0qPYdILF/Owve9h5arr6qrjnfnMoVdL3Hgzq8z9OCD4wI+7y1vrpsV7ieDPXjIE/FogsSt7/Vt2bYxpOvgDOwF10XtWIJQpz7BedpCPokdvwv4HeB6KWVpMq+ZCSEHL7XIGdgDQkFtX+Jrfih4X1zpV9/D7n7+rPLMx5C2zcC993Hga9+gfPAgiWXL6Hrvu2m99ppQ0ANK4cUX6b7z6ww/9DBqIsG8N7+JeW9+41kRQpmI3d9N8Z5vIiIxkre9z9c0wzGckR5kKYvSuvC0c8ZnRMiFEDcD/whcI6UcnOzrZkrIwesg5gzuR8TSKM3zfR/ye575D7D2bSdywSuJXHCd7zZNN9K2Gbjvfk/QDxwgvngx533qE6RWrTzu9rkdOxn4xd1YmQydr3stTRe/7HcZMo1Ix2HkiSc5/IMfMvrEk6jJJPPe/EbmvensE3AA+/Aeivd9GyXRQOKWd6MkGvw2Cbc4ijt6GJFqQ204/fVLTyTkZ9qq7F+BCHBfTZyelFJ+4Az3eUaISAIl3Y6bG0AWR7ysFj/tUVRi1/4WaDrVZx9A2hbRi286q8RcaBodt9xM+42vYvD+X3L4v39w0sV2d33u/zD3t34TNRaj+9+/jFut0nLlFbNo8bmBlcnQ97O76P3Rj6gcOozR2srC33k/837rN9FSKb/NmxGsAy9Q+tX3UNItnojHTr9acrqQVgU301vTprYZOcYZCbmUctl0GTKdiFQrwizhZvpAi5xR6eu02KMoxK56HULTMbc/iizlvdlztb5afp4Koaq033Qj7TfdeMJtzJERFF1n7hteD0D22S1UenqQjoNQ/Q2FnQ24ts3oE0/S97OfM/LoY0jbpuGCDSz+3f+Plmuvqbs2s1Oh+sKvqTz+M9SWOcRv+m2UqP8TttKxcIYOgFBRmufNmAN3Vn6rQgiU5vk4g/twhw8i2hb5PvkphEL0stsR8RTVzffjFjLEb3grSrQ+S51PF3NoiNiiRTx566tpufZq7HyexPLloYifAdJxyO3YydADDzBw971Yo6PoTU3MfeNv0nnbbSSWLfXbxBlFui6Vp+/B3PEY2vwVxF/5JoQR8dssb3Jz6AC4DmrbotOa3Jws05Z+OBVmMkY+EelYOAP7QEovk2WacjbPFHPvdsoP/xAlniZ+0ztRG1r9NmlWKB84yL5/+xIdt9yM0drC/i99mXlveTPNl13qt2l1h1OpMPrUrxl+5FFGHn0UazSD0DSar7yCzttupenyy85q73sMaZmUHvpv7O7nMVZfSvQVt/ie5AC11rRDB7x88ZYulNj0hLJmKkYeaISqo7Z24Qzswxnq9sRc8f8tG0vWoSQaKN3/nxR/8u/Eb3ir730fZoPcjh0ITaPl6qsASK1eTXHPXppecclRWS6ubSNU9ayaR5gOzJERRh59nOGHH2b010/jVquoiQTNl19Gy9VX0Xz5ZWhJ/2PCs4VbzFG6/9s4w72BSvEdq9yU1SJK09xpE/GT4YuqubM4ChB61BPzwW6coYOobQt9XVx1DK2ji+Srf4fifd+iePc3iF12O8bKi/02a0YRmoZb9hqK2YUiQtNwCoWXpSr2fOvb9P30ZzRceCENG9bTsGE90XkzF18MKlY2S3bLVnJbtpLdsoX88y+AlEQ6Ouh8zatpufoqGi7YgKLP3JA9qNiDPZR++R1ktUL8hrehdx0/Q8oP3NyAl2aYbkOZhj4qk8GX0Mq6DRfKx558inR09n6AbimLO9KDiKZQWhYERhRktUzpge9jH3oJffmFxC67DaH7H9+bCSp9fez9wj9TOnCASFsb8UWLaL/lZlIrzztqu6EHH6L/Zz8nu3Ubds5rhma0tdKwfj2pNatJrV1LcsUK1OjZ8zlJ16W0fz/5Hc+R27mT3LZtlPbuA0DoOqk1q2nceBGtV19FYsWKwPx+ZxspJeYLv6by5F2IeIrEDW9DbZnjt1njuIURL0Ml0YTSOGfav6cZKwg6HdZfcKH80b0PMa8xTlSfvXiWmx/GzfYhYg0zOoM8VaTrUn32V1S3PISSbiZ27W+htc1625pZo9LbS2HXLppecelJxXhM3LLPbvE8023bqPZ5HRiFqhJbtJD4woXEFnYRX7iQ+MIuYl0LA90r27Usygd7KB84QGl/9/j/pX37cEpePZ2WSpFau8YbjaxfT2r1KpTI2XPROl3ccpHyoz/GPvAC2rzlxK79zUAlC4znis+gsxgoId+4caP8wT0PIoEFjXE0dfZCHW5uEDc3gIg3oDQFR8wB7N69lB76AbJUIHLR9UTWhSXvx2IOD5PbsZP8jp0U9+2jvL+b8uHD4BxpG2y0tRLr6iLe1YXR1obR3ITR0oLe0oLR0ozR3IxiTP/Et3QcrEwGc3gEc2QYc3gEa9j7v9zTQ7n7wHFtjS9cSHzRIpKrV5Feu4bYggXh934MVs9LlB/+IbJaJnrxTRhrLg1EiHQMt5jBHT2EiCRRWhfMmG2BE/LHnnyKnkwJQ1WY1xhHmUVBPSLmjdPWRnK6kNUy5cf+F2vfDtTORcSv+c1AlBcHGdeyqPQconSg2/Nyuw9Q6u6mfLAHO3v8pQC1VAq9pRk9lUIYBooRQYkYKEbtL2Kg6AaKoSNtB9c0a39V3GrttmXhVk2cYhFzZAQrk4HjtPhVYjFi8+Z6F5eFC2sjiS5iC7oCPXoIAtK2qGy6D3Pn4yiN7cRf+UbU5mAtMeeWMrgjh7yCn9auGb3ABE7IN23aRLFq05srk4xodKSisyqoTnYAmR8MpGcupcTa/SzlJ34GQiF2xWsxlqzz26y6xLUsrJHRcQ/ZHDniJZsjI9j5PK5pIseEuvpywRaadkTcx0R/wn01FvO8/eZmz+Mf8/6bmzCam8+aToKzjTPST+nB7+OO9nuphRffdMYr6Uw34+GUSBylZeGMj6QCmX6YiGi0JCIMF6sYqklzYvbigGpDO64QuLkBXClrMfNgDNWEEBjLL0TtWEj5wf+m/MB/YR98kdiltyEi/hY21RuKrhPpaD9py4CQYCFdF/O5J6lsuhehR4jf+A70Beed+oWzjFsYxs30eZ54S5ev4TDfk6obYzqm7TBSMtFUZVYzWZR0GwgFN9uHO+R4ExQBKCYYQ023kLj9/VS3PEh1y0PYPS8RvfhG9OUXBOaiExIyndgDB6k88VOcocNoC84jdtXrA9EvZSJSSmR+EDc3WJvYnO/7+ei7kAshaE9Fsd0yA/kKqhAkIrNnlpJqAUXBHT2MM7gPtWVhoIZvQlGJXng9+sLVlB//KeVHfoz5wtNEL3s1Wts8v80LCZkW3HKBytP3YL30LCKeInbtG9GXrAtUyBNqFZujvchSJlBzbIEp0XddyaFsCdN2Zz0tEcCtFHCHD4KieGJuRGf1+JPBi51vofL0PchyEf28i4hufFWgUrBCQqaCdB3M556i8swvwbGJrL2cyIZrA1lLIV0Hd/igV7GZbkOk2mZdxAMZI5+IogjmNMQ4NFricLbM/MYYhjZ7Yq5Ek4i2xThD3TiD+1BaFvjeNfFYvNj5BegLV1F59gHMnU9g79tJ5KIbMFZeHKashdQVdu9eyk/8HHe0H23ecqKX3oraODNtXs8UaVs4w91gVb2y+1mq2BzDlRLTPvGi54HxyMewHJeejFcYMa8xjjGLOebg/xc2FZzRfspP/Byndy9K8xxil956TvRsCalv3PwolU33Yu3djkg2Erv0NrSulYEIURwPaVY8TXBdXxw8V0p6s2UqlsOy9nTw0g9PRNV2OJQpowhPzPXZFvMJQyiRakVJtwf3RyYl9v6dlJ/6BbKYRZu/guhF16O2hvHzkGDhlvJUtz2M+fyvQQgi519N5PyrAjUndSxuOY870uNbyFVKSW+uTMl0aE9FaYgZ9SPkABXL4XC2hCIEc/3wzCdOakQS3rJxAV4IQtoW5nNPUt36MNIsoy04j8gFrzyrS/1D6gO3mKO67RHMF58G10VffgHRC68LxBJsJ0JK6TW/yg+BHkVt6Zr1C44rJX01EW9LRmiIGcEsCDoVVcvhULaMEDCvYXZj5lBLMyplcEd7QVFRmucHfmJRmhWqzz+Fuf0xZLWENm+5J+gdXX6bFnKO4RYynoDv2lwT8A1E1l+DmvZ3+cVTIR0LZ7gHzFKt+VXnrKcXjoVTytYREYeAVnZOhqrtcDhbRkqY1xgjMstiDt6ae87wQbBNL8ySag1sqGUMaVYxX/g11e2PICsltLlLiWy4FrVzUeBtD6lv3PzoEQGXEn3FhUTXX42SavbbtFPiVgpeKEVKlKY5KPHGWbfBcWsxcduhIxUlNaG2pm6FHMC0XQ5nS7hSMrdh9lMToRY3H+1FlrN1EWoZQ1qmJ+jbHkFWiqht8zHWXI6+eE2gip9C6h974CDmjsew9j8HQmCsuIjI+VehpIKbMDDGUaEULYLassCXFEjHlRzOlqjaLp3pKMnI0eGcuhZy8LJZDmVKOFIyNx0jZsy+iEopkcVRb1FnRUVtmY+IBDvUMoa0Tcxdz2LufBw3N4xIpImsvgzjvI2nLPuXroszcAC1Y2YbAoXUH9J1sPY/h7njcZzBg2BEMc7bSGT1pXXT7O2oUEq80esj7kMqr+26HM6UMR2XOenYcQsj617IAWzH5VC2jO24dJ7gjc4G0izjjPTUQi3+FAacLlK62Ad3Ud3xOE7vXtB09CXnewtanGBNUzc/SunRH+MM9BC78nUYS8+fZatDgoZbymO+uAnzxU3IYhYl3YKx5jKM5RcEspjnRLjlHO7oYZAuSuNclESjL3ZYjsvhmrbNaYgRP4GjGviCoMmgqQrzGmP0Zsv05sq0JiM0RPXZr64yYqjtS3Azvbi5QSjnUZvmIozgN7QSQkHvWonetRJnuJfqc0/ijvbDSVb4FpE4iVe9g+IvvoaIHEm/cisl3NwwauvcMExzDiBdB/vQHsxdm7G7nwfpos1dinHZ7WgLzqurgjTp2LiZPmQ562WlNM9D6P5Uc5cth75sGYlkbsPpRRvqSsgBNMXrX96fqzBUqGLaLm3JyOyLuaKiNs/HjaVxR3txBvbWcs7b6ib8oLbMIX7V65HSPennJ4wIztBhpG2hz18BeMVI1S0PIs0KbnYIfcn5Xk5wAFsbhJw+UkqcocNYe7Zg7dmGrBQRkTjG2ssxVl4c+AyUY5FSIss53EyvV+CTbqslL/hzzuYrFgP5CpoimNMQP+3MvLoTcgBFCDrTUYaLJpmyiVULtajK7Ic3lFgaEUl4V/f8EE4553nndRI7Byb1I7Z6do039HeGDlPd+Tja/OUYyy9EmhXs3n2gT/+qOyH+4OZHMfdsxdq9FTc7CIqK1rUSY9kGtPnL62Ki/1ikbeFmDiMrBdBjqG1zffPCpZSMlExGSyZRXWXOGepX/X0bNYQQtCYjGJrCQL5CT6bEnIbYrBcOwZh3Pg833lDrorjfyz9t6Kj7kIOULjgO9uE9RNZcDoC1fye4DkKL4Iz2ozZ1oC9c5bOlIWeKW8pjdT+PtWcrTn83AGrnImLrrkBftKZue+GPJylk+wHpnZfJFl/ntfJVm9GSSSqq0z4NEYW6FfIx0lEdXRH05sr0jBaZ41NGC9Qab3Us9dKYCiM4lQJK4xyUWMoXe6YDIRTcSg5ZLaMt8MIqdt9+RCSGM9pHZetDRC+6PpCN/0NOjpQSNzOAfeBFrAPP4wz0ABKlsY3IxldhLDm/LlIHT4a0qp4XXi15acNNc084qT+bpCIagijJiDYtF5S6F3KAmKExvylBb7bMoWyZ1kSEhtjsT4JCzTtvnIOMNeCMHsYdPoCMpjwvoI5m8wGczCDmzieQ1TJqizeh6WSHEEaUyPlXo3V0oXetpPzUL9Dmr6ibzJ1zGWmb2If3YR98EatnF7KQAUBtnUvkwuvQF65Caeqo++9Sug5ufgiZHwYhvJTCRFNg3pcQ4qhCnzPlrBByAENVmN8YZyBfYahYpWJ7TWZmc1HniYhIHLVjCTI/jJsfwunfg0g2eZMrSn187Eo8jZJuxtq3A2ekj2rbfLQ5i1AaWhExbw7AyQ6BEAghapOmR0JbbrkAioISCdes9Avp2DiDPdi9+3D69mP3d4Njg6ajzV2Kvv4atPnL6ybn+1SMh1FyA174L97gOVEnycqaTkzbJVsxiWgqEU2ZtUr0+lCUSaIq3iToaNlkpGhStUt0pqO+lPWDF5YQ6TZEohE3N+iFW4pZlHQrItkc+OwWYUSIrLuSyLorcYs53GIWtdFb+7L6zK/Ql6zDfO5J9KUbvO2PeT/V7Y9hbn8UpbkDrXMx2pxFqJ2LAt+vpp6RtoUzcBC7bx92336cgYOecANKcyfGyovR5q9Am7O4LicsT4SUElkpeHFwuwpGHLWxc1ZTgnNlk9GySSqiU7EcqpZDY1zMSvfWuioImgol06Y/X8F1Ja3JCGkf8s2PRVoV3Ew/sloAzfA8hWjKd7umiqyWMXdvwe7bj7H8QrQFy497UXKGDmMdfBG7bx9O/0FwLACUxnbU9gWorfNQW+eiNneeVaIyW0jp4uZGcIYO4QwdxhnswRnsAdcBBEpLZ+0Cuhi1c+FZOzLyzqs+ZLXo23klpaQ/X6ExZhDV1fF1iJvjXkLGdHFWVHZOFdt16c9VKFsOyYhGWzLqS4risbiVPG7GP8/BD6Rj4wwd9kS9dz/OUA+yWvaeVFSUpvZxYdda53lx2lDcx5FS4uZHcAYP4QwfHhdvrKq3gaqhNneidi5C61yE1rGwbrNMJot0LC+xoJgBoXphy2TTrI50i1WbkmWTMDRURYxnzQkhOJwt0RA1prUCPVBCvmLtBrnlmU0nLEOdTqSUZMomw0UTTRF0pKPEdP8F4mWxvFgKJdV21gv6GFJKZCFzxJus/S/NmrgLBSXdjNLQipJuQWloQU23ePH5eCrwYanTxa2WcLPDuNkh3NwwbnYYJzeEmx0G2/Q2GhPtlrmobfNQW+aiNLXXfarrZJGOhZsfRhZHQUpEstkLV87y3NNgoULFckhHdbJli6a4QSqqM6apvbkyLYnItIZ2A1WiX7YcvrH5IL+xbi4dyZnN5BBC0BSPENU1+nNlDmXKNMYMWhKGryENIYQXJ483eD/KwjBOOY+IJj1BP0uHwWMIIRCpJpRUE/ritUBN3POjnsc53IuTHcTNDmMf2j0e5wVA0z1xTzaixNOIRBolnkLE0yiJNEo8DUY0cCEraVu4pRyymPP+L+VxizlkKYdbyOLmhpHV0pEXCOG9x3QrWuci1KYO1NZ555RoT0Ta5hEBRyJiDSgNbQht9rPBLMcd78aqKgJXShz3iFMsa/8YqoLluBSrNqmoPmMRAV888vUXXCTv+OIPqFgOt63qYGX77ORZu65kqFglV7EwVIUOHydCj0W6DrIwglsY9jz0SNxrxhVJBE6QZhspXU/8csM4Wc87dXPDuIUMspQ7EqKZiKajxFKISAxhRL0wgxFFGDFEJOo9ZkS9nGJV9YSx9icUZfw2igJSguOA6yBd739c98htx0ZWy0izMuGvjKxOuF0qHBltHGWngZJII+Kp8RGHMvZ/qikMLwHSruLmhpClLCC9DoWp1sCk8xaqFv25CnFDQ1MFyYiOoSr05cokDI1cxaIxZpCOnXnmzIyGVoQQHwH+HmiTUg6davuNGzfKBx97kh/v6OVQrsLlC5u5anHzrAlWsWozkK/gSElz3KAp7q93PhHpusjiCG5+GFwbjJjnoUeTgbExaEjb8rzbUu6Ih1vMIct5T0gnCmq1XJsMnCGEcuQiEYmOXzyUWBIRT9VE2xs1KIk06LPfJ6hekFbFE/ByFhBetXSqJRAFPRPJVyxURRA3NEZLVRxXkjA0DmU9IW9OGNPmMM5YaEUIsQC4ETgwldclIxpvuWAe9+4a5PHuEQaLVW5f1UlkGmd4T0QiotGlxxksVBkpmRSqNu2pqC8LVhyLUBSviU+yGVnM4OaHcIcPgB5BSbYg4g1nbXz4dBGajkg3o6QntwKNtK0jnrNl1jxsB6SLdCZ63Da4LiiK57ELBdSJXrvmPadqR7x+LThOQT0ipURWS8jCMLKS9y6MyRZPwGcpF3yqTCzsiRsaw8UqLbpKc9ygOTE7o4bpGLd9Hvgo8L9TPriicMt57bQnI/xy9yDfeuYgv7FuDk2xmb/iqopCZzrmeecFr1dLY0ynORHxrYhoIkIoXgw90YQsZT1BHz0M2X6UZDMi0RwOu08ToeneQrrx+m2dcLYhpVubKxgGq+JdLFNt3m+9jn7nxao9rh+zJeJwhkIuhHgtcEhKufVUXogQ4g7gDoCurq6Jj7NxfiOtcYP/2dnLNzYd5K0XzJ/xSdAxPO88wXCxSqZsUajatCWjvi1acSxCCESiERFvQFaLyMKw1wM9N4SIpVGSTWDEQy8wpC6RtolbHPUmMF0HtIjXDyWAI0/TdlGEty7CRKSUmI7LYL6Cpiq0JWd/ov2UaiWEuB/oPM5THwP+Ai+sckqklF8GvgxejPzY5xc1x3nXxi6e6B6hNT67MTBVEbSnoqQiGgOFKr21SYrWZGRWqrImgxACEU1CNOk1AiqOIIsZnHLW+/HXMmDOxWyGkPpirApTFke8lrKAiKW8UWYAJ/ddKRmttZxNRTQ60kenCAshEAgaYsa09k+ZyPP9eQ7lKid8/pRCLqW84XiPCyHWAYuBMW98PvCMEOISKWXf6RjbGNO5ZWXHKbeTUs7Ilx0zNLqaVDK1Ev8DIzZNcYPGuBGIcMsYQo94jbnSHchyFrcw4jXKz/YhYmlEvDGQJ0TIuY20KrjFjJd94tqgaLXwSVMg499SSoqmzVChiu1KUhGNlhNECgxNmdYKzjFMx+X+lwbZ1ptjXvrEvdNPO34gpdwOtI/dF0LsBzZOJmvlTBHCy9vc3ptjYVOcxmlI65m476Z4hGREZ6g2GZqrWLQmIySM6Wk5OV0IRfE6usUbwSqPnySylAVV9xoGxRsDk6YVcu4hXbuWRZQBy0u/FNGUFy4McHuKqu0wVKhSthwMVWFuQ3RWChgn0p+v8r/P9TJSsrhsYRNXLmrhnSfYNhiB4CmQKVvsGiyQrVjsGiry0nCR167unPYQiK4qzGmIUapdkftyFaKaSmsyEojslokIIbxSfyOObOz00u5KGW/FovyQl8IYbwxDLyGzwnjopJRBlvOA9LKuGjq80WKAJy9t12Wk6DlvihC0+dCnSUrJ5kNZHtg9RExXePOGeSxqOnmB4LR9olLKRdO1r+ORKVvsHi7Sn6/SFNNZ1pogU7G5rKsJXVUYKppENIXUNE9Sxg2NBU0quYrFSNGkJ1MaH2JpAVxsVggFEW+AeAPSsbyMl2LGC71k+rx89FgaEUvWTTvdkOAjpeulDZZzyHLOm7hUVK91c7wx8K0nXCnJlk1GSiZSQkNMpzkemfXeTEXT5q4XBtgzXGRpS4LbVnYQN07tfNXFmey6kie6RxgoVHnbBfNRFcFDe4eZk4rQmjD4wfbDGKpCT6bMlYtbOH9OelqPL4Q3kZGM6IyWquQrNq2neE3JtHFcOWOTH5NBqHotJ70FrApuqVYJWcnDKF4cPZbyhD2AMcqQYCNdx/O8y3nvNyVdL+87mvRGf9Fk4DJPjkVK6TlpJRPHlcQNldZEdEbi3adiuGTy7Wd6MB2X65e1snF+46RHAnUh5IoiuGpxCz9/vp//3n6YrsYYuYrFDcvb+J+dfbQlDK5b1sahbJnH9o+wuj35shSh6UBVBK3JKM0JecrJTwHkKhaZsklT3LsI+IUXeomhGjFkQ6cXTy/nPe8p0weZPtBjXkl7LAVaWG0YcnykY9XEO4esFAHped6xtPcXTQRevMET8ELVZqTkLd4e1RQ6U9EZXybyZIkaTTGdlW1JLpzfQNsUc9DrQshdKUlGNN60YR73vzTIY/tHuGJRM3tGSriu5LplbQAoQpCOajhSos5QZsvYcU5FzNCYZ2iUTJtcxSIZ0SlbDlFN8b1Z11g8nYYOpFVFlnO45bzXiTE3AKqGiCQ9jyqaDOPq5zBeyKSMrOS9ft9WLQVO1b2wSSxdV3UMxwq4oSp0pqMzmshQthx29udZ0hwnFdHQVXFcQVeE4Kbz2k+wl5NTF0KuCO+NF0wHV0ou7WqiUHXY1JPlHRfOH99usGhi2t6X49cPa+wLylcskhENx5W4rqRqO2TLJgO2SzKi0RSQlEahRxB6G0q6zStdrxaOeFyljLeREUNEkijRpHc7AHaHnBjpusjSKEKPIiJTW41JSgm2eeR3UC15IRO85QtFut2rZ9CD113yZPgh4AB7h4vc/eIA8xtj9OYqpKMa1yxpnfZj1oWQg+dJaopAEYKrl7SyuSfDei1Nc9zAlZJcxWZTzyjXLW2rrR85cx75qeyUUlK2HAbyFRIRjXRMR1MUOlJRJNCfq4x3RAsSXul6EySavBPaLONWCt5JnR/EyQ96MdBIwjupI3HQQ2H3AyklWF4jMITizXWMjZysMm6mD5FsQY0kTnoujAu3WfImK6vF8ZWcUI0jse5Ioi5HZn4JeNlyiOkquarNJV1NbJzfyFCxyqP7R3iie4TLFjZPq0bVjZADxHSVG5a3jd/OlL0f3GDR5OmDoyxqirOo2UvT8UNcxr4YIbxKUUNVkDAeH5fSi61HdRXHlb5dbCaDEAIicdRIHGhHOrbXIqBS8E76Sn5sQy8jwYgjjLjXNjbMhplxZHEEt5hFGFGv2ZdZRm2a4z1nm57XPLGH+7Gvrxa93t5m6Ug3SEX1vsNUiyfePvT5ni5cKclXLDJla9YEfOx8fmD3EL35Cr+xbi6ZssVYGXtL3ODSriZ+9nw/qztSNNQWoZgOe+r2jOtIRniie4TvbTlEwlBJRzWuXtwCzFzl56mo2A6aorwsp32iwFcsB9t10RQRWBE/HkLVxtMaoTbpVS2Ne3Lkh8Z/sGgGQvf6gKPXWrqG4j5tSCkR0RRqvBGhqF7Lhmwf0jZBSmSliNLQiTN84ITngnRdpFX1BNuIeyGYs6Bzo+24ZCsW2bKFKyURbXY8cDjiPJZtB8eVbOvNcuG8Br65+SCvWNBE3FDpTEVZ3prg2UNZrl06fSGWuj27WhIG771kIc8P5FnQEBufRJz4w+3LV3hxsMBlXc0znk4kpaRquwyUKyQjOpoiKFk2yYhXTGDaDrmKTcV2SBoaqWjdfvRALbVxorC7nleIWfL6fpulWh/pGqruxWyNqBeO0SPeY3UuHH4ghICJPblVzRNxRUNW8l7mSK2a90Sfr4gm0eYsnw1zZ4WK5ZApey2pARKGRmNMJ6qrs/obMx0XKeHShU1s782xoDHGxvmN3L97kNes7sSVkrZEhKGiietKhJie6EF9qwmwqra60NgCGRM/lP0jJZ7oHmV7b45rl7aypmPmSoKFEDTGDFIRjdGSSdWWtCQiWI7LcLGK5bioilcpFpRViaYToSiIaAKiRybXpGMjrcp4LFdalSMhGQAhvFRHzfCER4t4w3ndqIsUNr8Zc1pkcdTLMlIUnMIISqoVt1aUY/e+hNo872VLB54NF9CxXiiZkkXFdhDCK+RpjBm+NLuTUmKoXs8VQ1VY2BRn6+EcaztTPHFglF2DBVa0JclXbWzXRZnGYiNfhHwgV2G0aNKUmL7JvuP9MC9d2MyCxhj3vzTIz57v55lDWW5Y3sbckzSfOVNURaE1GR2/sPSMemswzmmIjfdqON5wt2p7ccqzSeSFqiFUr2PjGNJ1wKp6om6bYFc9kS/njn6xqteWYdNrt3Vv8k3Tz1pPXkrpNZOyLaRjgWN5oQ/9+L9XIYTXBracR23oqP2uFNxsnzdvoeq1pe3igZ6PmSq265IrW+QqFrYr0RRBa8IrpZ9OcZwqQggsx6VQtVnYFCcZ0XjqwChDJZMrFzXz/ECep3syVCyHm1acXprhCY/tx5qdibnL5aUf/Dc+8fp1XLvq1N0OzxQpJdv78jy0d4ii6bC2M8U1S1qnvZz/RMfOV22yZRNNUU7YGrcvV6ZQtYloCg1Rg2RE8/VHOdtI6YJlIu2qJ+6WiXRML4PieJN2quYJlaLVVu3Rjn9bKF5Wh0+T3yC9VYZcB1y7tgKRfdRt6djjAg5Hn49K4xyU5MtXPhoTZifTh9AjKImml23j5gaQtonaPL/uhXwsEyxbtiia3u8hpqs0xPTANbN7aO8QharNoVyFhoiOEPCb589FEYKDmTILGk+/XcGMrtk5Vdauv0Cuft8/s6s3z83nz+Gjt6+meRYWkqjaDk90j/L0wQxCwMULGnnFgqZZa4JVrNqoijju8RzXm2XPVrxZdgEkoxrpqE5Um904X9CQ0vUWOLY9YZe2BY7pPebatYWRT5yhAYwLOopyRNzHbiO8UlyEF+459v6YII8tjT5+ztRuS+lljriul3MtvaXixvKvT2qTqnkXnrEL07Ejj5Ok/LmlHG62FxFrGM88UdJt42taSqs6vpB3vWI5LrmKRb7mfY8V/aWjhi9l9KdCSskDe4YYLppctaSFzlSU+14apC1hsGFuwxnvP1BCvnHjRvnEk7/m6w/v4csP7CYZ0fjo7au5Zf3cWRGsTNni4b1DPDdQIKIpvGKBl+cZhB+GlJKK7ZKvWOSrFlKCrgpSUZ1URA/MQhdBwwtLOC/3fE8gsEcec8d2wMvFunb/KJGfeLsm+ELUvH71yIVCGRsJ1G4rWm2tzwmjhjP8rbuFEdxSBiWaOhJGOQtaFruupGDa5CsWZcu7QMV1lXSAvG8pJS8OFhgqmlxZy5Ybw7TdcS1xa0kQsWlyFgMn5Js2bQJgd3+ez/xoO9sPZrjqvDY+9tq1dJ7B0GMq9BeqPLJ3mN3DRWK6ymVdTVwwryEwYunWihlyFYtK7Qcd1RSSUZ1kRAtk98WQkNPBlZKSaZOv2JRMGwloiiAd1UlFg+PASCnZPVzkkX3DDBRM2hIG79rYddwuia48dU+mqRJYIQcvrPDdJ/bzr/fuQlUEH775PH7j4q5ZixEfzlZ4eN8w+0dLJA2Vyxc1s35Ow6y3sDwZ3iSKRb5iYzqeFxnTVVJRnaRxbsXTQ84OxuLe+YoX93YlqEKQjGqkIjoRn/sSTURKyf7REg/vHaY3X6UxpnPVomZWdaRmrdWG5bgYmhpcIR+jZ6TEX/54O0/tGeb8rkY+/tq1rJjmlrQn48BoiYf3DdOT9XoiXLGomXUd6cCJZNV2KFTt8bihwOubnoxoJEJRDwkwY+JdrNoUqjaOlCjCy/tORXVis5z3PRkOZso8vHeYg9ky6YinC2s707Pm6GVLJv90z4scGinx5fddelwhD1Qe+fzmOF96zyX85JlDfOEXL/CX/7ODb37gsln7Yrua4rytMTZ+5f3FCwMkdJVlrclTv3gWiWgqEU2lOW5QtV3yVYtCxaZo2iQMjTkNwW7iH3LukqtYDBaq485HKqoRN7RANJA7HhXb4ftbD2FoCq9a3sb6uelZD2l+94lu/ndzD2+9fNEJt/HFIxdCDALds37gl9MKzPgao3VG+Jm8nPAzOZrw83g5s/WZLJRSth37oC9CHhSEEJuON0w5lwk/k5cTfiZHE34eL8fvzyQYU8EhISEhIadNKOQhISEhdc65LuRf9tuAABJ+Ji8n/EyOJvw8Xo6vn8k5HSMPCQkJORs41z3ykJCQkLonFPKQkJCQOicU8hpCiI8IIaQQotVvW/xGCPF3QogXhBDbhBA/FkI0+m2THwghbhZCvCiE2C2E+DO/7fEbIcQCIcQDQojnhBA7hRB/4LdNQUAIoQohnhVC/MwvG0Ihx/uBAjcCB/y2JSDcB6yVUp4P7AL+3Gd7Zh0hhAp8EbgFWA28RQix2l+rfMcGPiKlXA1cCvxe+JkA8AfA834aEAq5x+eBj3JsV/9zFCnlvVLKsQbfTwLz/bTHJy4Bdksp90opTeB7wGt9tslXpJS9UspnarfzeOI1z1+r/EUIMR+4Dfiqn3ac80IuhHgtcEhKudVvWwLKe4Bf+G2ED8wDDk6438M5LloTEUIsAi4AnvLZFL/5Ap4TeIpVRGaWQDXNmimEEPcDncd56mPAX+CFVc4pTvaZSCn/t7bNx/CG0/85m7aFBBshRBL4IfBhKWXuVNufrQghbgcGpJSbhRDX+mnLOSHkUsobjve4EGIdsBjYWuuwOB94RghxiZSybxZNnHVO9JmMIYR4F3A7cL08N4sNDgELJtyfX3vsnEYIoeOJ+H9KKX/ktz0+cwXwGiHErUAUSAshvi2lfPtsGxIWBE1ACLEf2CilPKc7uwkhbgb+EbhGSjnotz1+IITQ8CZ6r8cT8KeBt0opd/pqmI8Iz9v5D2BESvlhn80JFDWP/I+llLf7cfxzPkYeclz+FUgB9wkhtgghvuS3QbNNbbL3g8A9eJN63z+XRbzGFcA7gOtqv4stNW80xGdCjzwkJCSkzgk98pCQkJA6JxTykJCQkDonFPKQkJCQOicU8pCQkJA6JxTykJCQkDonFPKQkJCQOicU8pCQkJA65/8HzCOQymQTVuQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Function for contour plot with points on it\n",
    "def contour_plot(x_seq,y_seq, x1):\n",
    "\n",
    "    # Contour plots for f(x,y) = x^2 + y^2 + 1\n",
    "    figure(1)\n",
    "    CS = contour(X, Y, Z, cmap=cm.RdBu)\n",
    "    clabel(CS, inline=1, fontsize=10)\n",
    "    \n",
    "    # Initial point\n",
    "    plot(x1[0],x1[1],'ro')\n",
    "    \n",
    "    # Sequence of points from gradient descent itterations\n",
    "    plot(x_seq,y_seq,'ro')\n",
    "    title('Contour plot for f(x,y)')\n",
    "    show()\n",
    "\n",
    "# Contour plot with no points\n",
    "contour_plot([],[],[[],[]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding global minimum using gradient descent\n",
    "\n",
    "For this example the gradient descent algorithm is simplified to\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    x^{t+1} \\\\ \n",
    "    y^{t+1}\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "    x^{t} \\\\ \n",
    "    y^{t}\n",
    "\\end{bmatrix}\n",
    "-\n",
    "\\lambda\n",
    "\\begin{bmatrix}\n",
    "    2x^{t} \\\\ \n",
    "    2y^{t} \\\\ \n",
    "\\end{bmatrix},\n",
    "$$\n",
    "\n",
    "where $t$ is the gradient descent itteration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Partial derivatives\n",
    "\n",
    "# df/dx = 2x\n",
    "def dfdx(x,y):\n",
    "    return 2*x\n",
    "\n",
    "# df/dy = 2y\n",
    "def dfdy(x,y):\n",
    "    return 2*y\n",
    "\n",
    "# Gradient vector [df/dx, df/dy]\n",
    "def grad_vector(x,y):\n",
    "    return np.array([dfdx(x,y), dfdy(x,y)])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gradient descent for multiple variable\n",
    "def grad_descent_mult(df,x_prev,learn_rate):\n",
    "    \n",
    "    # Epsilon threshold \n",
    "    epsilon = 0.001\n",
    "    \n",
    "    # Itterations number\n",
    "    grad_itter = 1\n",
    "    \n",
    "    # Save itteration \n",
    "    seq_x = []\n",
    "    seq_y = []\n",
    "\n",
    "    # First itteration of gradient descent\n",
    "    x_next = np.subtract(x_prev, learn_rate*df(x_prev[0],x_prev[1]))\n",
    "    \n",
    "    # Save starting itteration\n",
    "    seq_x = np.append(seq_x, x_next[0])\n",
    "    seq_y = np.append(seq_y, x_next[1])\n",
    "    \n",
    "    # Itterate until abs(x_{t+1} - x_{t}) < epsilon\n",
    "    # abs(x_{t+1} - x_{t}) is defined as euclidean distance \n",
    "    while np.linalg.norm(np.subtract(x_next,x_prev)) > epsilon:\n",
    "        \n",
    "        # Update x_{t}\n",
    "        x_prev = x_next\n",
    "\n",
    "        # Gradient descent step\n",
    "        # Set new x_{t+1} = x_{t} - lambda*[df/dx df/dy]\n",
    "        x_next = x_prev - learn_rate*df(x_prev[0],x_prev[1])\n",
    "        \n",
    "        # Increment itteration\n",
    "        grad_itter += 1\n",
    "        \n",
    "        # Update sequence of itterations\n",
    "        seq_x = np.append(seq_x, x_next[0])\n",
    "        seq_y = np.append(seq_y, x_next[1])\n",
    "    \n",
    "    # gradient descent output\n",
    "    return (x_next, grad_itter, seq_x,seq_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum (x,y) from gradient descent: [0.0010156  0.00033853]\n",
      "Number of gradient descent itterations: 17\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Gradient desecent with x1 = [6,2] and learn rate lambda = 0.2\n",
    "grad_output = grad_descent_mult(grad_vector, np.array([6,2]), 0.2)\n",
    "\n",
    "# Print gradient descent solution\n",
    "print('Minimum (x,y) from gradient descent: %s' %grad_output[0])\n",
    "print('Number of gradient descent itterations: %s' %grad_output[1])\n",
    "\n",
    "# Convergence sequence (x_t,y_t) on contour plot\n",
    "contour_plot(grad_output[2],grad_output[3], np.array([6,2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected the gradient descent in multiple variables converges close to the global minimum of (0,0). The contour plot shows the sequence of $(x_t,y_t)$ resulting from gradient descent that coverge to (0,0) from the initial value. Feel free to play around with the initial value and learning rate above. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "Gradient descent is a first order (requires first derivative) optimization algorithm used to minimize a given objective function. The algorithm depends on the initial value and the learning rate. The idea behind gradient descent is that it takes a seqeuence of steps to go from the starting position to a local minimum. An initial value that is somewhat close to the global minimum is ideal. Too small a learning rate makes it more likely for the algorithm to get stuck at a local minimum. Whereas too high a learning rate makes it more likely that the algorithm will skip over the global minimum. As we discussed in this notebook, the gradient descent can be applied to any first differentiable function (single or multiple variabe) to approximate the minimums (can be local minimums) even if analytical ($f'(x) = 0$ solve for x) solutions are difficult. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}