{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# OOP in Action: The Samuelson Accelerator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Co-author: Natasha Watkins**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Paul Samuelson’s (1939) multiplier-accelerator model\n", "\n", "This lecture creates nonstochastic and stochastic versions of Paul\n", "Samuelson’s celebrated multiplier accelerator model, as described in\n", "[[Sam39]](zreferences.ipynb#samuelson1939)\n", "\n", "Samuelson used a **second-order linear difference equation** to\n", "represent a model of national output based on three components:\n", "\n", "- a **national output identity** asserting that national outcome is the\n", " sum of output devoted to consumption plus investment plus government\n", " purchases \n", "- a Keynesian **consumption function** asserting that consumption at\n", " time $t$ is equal to a constant called the **marginal\n", " propensity to consume** times national output at time $t-1$ \n", "- an investment **accelerator** asserting that investment at time\n", " $t$ equals a constant called the **accelerator coefficient**\n", " times the difference in output between period $t-1$ and\n", " $t-2$ \n", "- the idea that consumption plus investment plus government purchases\n", " constitute **aggregate demand** that automatically call forth an\n", " equal amount of **aggregate supply** \n", "\n", "\n", "(To read about linear difference equations see\n", "[here](https://en.wikipedia.org/wiki/Linear_difference_equation) or\n", "chapter IX of [[Sar87]](zreferences.ipynb#sargent1987))\n", "\n", "Samuelson used the model to analyze how particular values of the\n", "marginal propensity to consume and the accelerator coefficient might\n", "give rise to transient **business cycles** in national output with\n", "alternative dynamic properties:\n", "\n", "- smooth convergence to a constant level of output \n", "- damped business cycles that eventually converge to a constant level\n", " of output \n", "- persistent business cycles that neither dampen nor explode \n", "\n", "\n", "Later in the lecture we present an extension to Samuelson’s model that\n", "simply adds a random shock to the right side of the national income\n", "identity (the random shock represents random fluctuations in aggregate demand\n", "\n", "This modification makes national output become governed by a second-order\n", "**stochastic linear difference equation** that, with appropriate parameter values,\n", "gives rise to recurrent irregular business cycles.\n", "\n", "(To read about stochastic linear difference equations see chapter XI of\n", "[[Sar87]](zreferences.ipynb#sargent1987))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Structure of the model\n", "\n", "In more detail, let’s assume that\n", "\n", "- $\\{G_t\\}$ is a sequence of levels of government expenditures.\n", " We’ll start by setting $G_t = G \\forall t$ \n", "- $\\{C_t\\}$ is a sequence of levels of aggregate consumption\n", " expenditures, a key endogenous variable in the model \n", "- $\\{I_t\\}$ is a sequence of rates of investment, another key\n", " endogenous variable \n", "- $\\{Y_t\\}$ is a sequence of levels of national income, yet\n", " another endogenous variable \n", "- $a$ is the marginal propensity to consume in the Keynesian\n", " consumption function $C_t = a Y_{t-1} + \\gamma$ \n", "- $b$ is the “accelerator coefficient” in the “investment\n", " accerator” $I_t = b (Y_{t-1} - Y_{t-2})$ \n", "- $\\{\\epsilon_{t}\\}$ is an IID sequence standard normal random variables \n", "- $\\sigma \\geq 0$ is a “volatility”\n", " parameter — setting $\\sigma = 0$ recovers the nonstochastic case\n", " that we’ll start with \n", "\n", "\n", "The model combines the consumption function\n", "\n", "\n", "\n", "
 $$\n", "C_t = a Y_{t-1} + \\gamma\n", "$$\n", "\n", " (1)
with the investment accelerator\n", "\n", "\n", "\n", "
 $$\n", "I_t = b (Y_{t-1} - Y_{t-2})\n", "$$\n", "\n", " (2)
and the national income identity\n", "\n", "\n", "\n", "
 $$\n", "Y_t = C_t + I_t + G_t\n", "$$\n", "\n", " (3)
- The parameter $a$ is peoples’ *marginal propensity to consume*\n", " out of income - equation [(1)](#equation-consumption) asserts that people consume a fraction of\n", " math:a in (0,1) of each additional dollar of income \n", "- The parameter $b > 0$ is the investment accelerator coefficient - equation\n", " [(2)](#equation-accelerator) asserts that people invest in physical capital when\n", " income is increasing and disinvest when it is decreasing \n", "\n", "\n", "Equations [(1)](#equation-consumption), [(2)](#equation-accelerator), and [(3)](#equation-income_identity)\n", "imply the following second-order linear difference equation for national income:\n", "\n", "
 $$\n", "Y_t = (a+b) Y_{t-1} - b Y_{t-2} + (\\gamma + G_t)\n", "$$\n", "\n", "
or\n", "\n", "\n", "\n", "
 $$\n", "Y_t = \\rho_1 Y_{t-1} + \\rho_2 Y_{t-2} + (\\gamma + G_t)\n", "$$\n", "\n", " (4)
where $\\rho_1 = (a+b)$ and $\\rho_2 = -b$\n", "\n", "To complete the model, we require two **initial conditions**\n", "\n", "If the model is to generate time series for $t=0, \\ldots, T$, we\n", "require initial values\n", "\n", "
 $$\n", "Y_{-1} = \\bar Y_{-1}, \\quad Y_{-2} = \\bar Y_{-2}\n", "$$\n", "\n", "
We’ll ordinarily set the parameters $(a,b)$ so that starting from\n", "an arbitrary pair of initial conditions\n", "$(\\bar Y_{-1}, \\bar Y_{-2})$, national income $Y_t$ converges to\n", "a constant value as $t$ becomes large\n", "\n", "We are interested in studying\n", "\n", "- the transient fluctuations in $Y_t$ as it converges to its\n", " **steady state** level \n", "- the **rate** at which it converges to a steady state level \n", "\n", "\n", "The deterministic version of the model described so far — meaning that\n", "no random shocks hit aggregate demand — has only transient fluctuations\n", "\n", "We can convert the model to one that has persistent irregular\n", "fluctuations by adding a random shock to aggregate demand" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Stochastic version of the model\n", "\n", "We create a **random** or **stochastic** version of the model by adding\n", "a random process of **shocks** or **disturbances**\n", "$\\{\\sigma \\epsilon_t \\}$ to the right side of equation [(4)](#equation-second_order),\n", "leading to the **second-order scalar linear stochastic difference\n", "equation**:\n", "\n", "\n", "\n", "
 $$\n", "Y_t = G_t + a (1-b) Y_{t-1} - a b Y_{t-2} + \\sigma \\epsilon_{t}\n", "$$\n", "\n", " (5)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mathematical analysis of the model\n", "\n", "To get started, let’s set $G_t \\equiv 0$, $\\sigma = 0$, and\n", "$\\gamma = 0$.\n", "\n", "Then we can write equation [(5)](#equation-second_stochastic) as\n", "\n", "
 $$\n", "Y_t = \\rho_1 Y_{t-1} + \\rho_2 Y_{t-2}\n", "$$\n", "\n", "
or\n", "\n", "\n", "\n", "
 $$\n", "Y_{t+2} - \\rho_1 Y_{t+1} - \\rho_2 Y_t = 0\n", "$$\n", "\n", " (6)
To discover the properties of the solution of [(6)](#equation-second_stochastic2),\n", "it is useful first to form the **characteristic polynomial**\n", "for [(6)](#equation-second_stochastic2):\n", "\n", "\n", "\n", "
 $$\n", "z^2 - \\rho_1 z - \\rho_2\n", "$$\n", "\n", " (7)
where $z$ is possibly a complex number\n", "\n", "We want to find the two **zeros** (a.k.a. **roots**) – namely\n", "$\\lambda_1, \\lambda_2$ – of the characteristic polynomial\n", "\n", "These are two special values of $z$, say $z= \\lambda_1$ and\n", "$z= \\lambda_2$, such that if we set $z$ equal to one of\n", "these values in expresssion [(7)](#equation-polynomial),\n", "the characteristic polynomial [(7)](#equation-polynomial) equals zero:\n", "\n", "\n", "\n", "
 $$\n", "z^2 - \\rho_1 z - \\rho_2 = (z- \\lambda_1 ) (z -\\lambda_2) = 0\n", "$$\n", "\n", " (8)
Equation [(8)](#equation-polynomial_sol) is said to **factor** the characteristic polynomial\n", "\n", "When the roots are complex, they will occur as a complex conjugate pair\n", "\n", "When the roots are complex, it is convenient to represent them in the\n", "polar form\n", "\n", "
 $$\n", "\\lambda_1 = r e^{i \\theta}, \\ \\lambda_2 = r e^{-i \\theta}\n", "$$\n", "\n", "
where $r$ is the *amplitude* of the complex number and\n", "$\\theta$ is its *angle*.\n", "\n", "These can also be represented as\n", "\n", "
 $$\n", "\\lambda_1 = r (cos (\\theta) + i \\sin (\\theta))\n", "$$\n", "\n", "
 $$\n", "\\lambda_2 = r (cos (\\theta) - i \\sin(\\theta))\n", "$$\n", "\n", "
(To read about the polar form, see\n", "[here](https://www.varsitytutors.com/hotmath/hotmath_help/topics/polar-form-of-a-complex-number))\n", "\n", "Given **initial conditions** $Y_{-1}, Y_{-2}$ we want to generate\n", "a **solution** of the difference equation [(6)](#equation-second_stochastic2)\n", "\n", "It can be represented as\n", "\n", "
 $$\n", "Y_t = \\lambda_1^t c_1 + \\lambda_2^t c_2\n", "$$\n", "\n", "
where $c_1$ and $c_2$ are constants that depend on the two\n", "initial conditions and on $\\rho_1, \\rho_2$\n", "\n", "When the roots are complex, some algebra that exploits the fact that the\n", "roots appear as a complex conjugate pair implies that\n", "\n", "
 $$\n", "Y_t = \\tilde c_1 r^t \\cos(\\theta t + \\tilde c_1)\n", "$$\n", "\n", "
where $\\tilde c_1, \\tilde c_2$ is a pair of constants chosen to\n", "satisfy the given initial conditions for $Y_{-1}, Y_{-2}$\n", "\n", "This formula shows that when the roots are complex, $Y_t$ displays\n", "oscillations with **period** $\\check p =\n", "\\frac{2 \\pi}{\\theta}$ and **damping factor** $r$\n", "\n", "**Remark:** Following [[Sam39]](zreferences.ipynb#samuelson1939), we want to choose the parameters\n", "$a, b$ of the model so that the absolute values (of the possibly\n", "complex) roots $\\lambda_1, \\lambda_2$ of the characteristic\n", "polynomial are both strictly less than one:\n", "\n", "
 $$\n", "| \\lambda_j | < 1 \\quad \\quad \\text{for } j = 1, 2\n", "$$\n", "\n", "
**Remark:** When both eigenvalues $\\lambda_1, \\lambda_2$ have\n", "absolute values strictly less than one, the absolute value of the larger\n", "one governs the rate of convergence to the steady state of the non\n", "stochastic version of the model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Things this lecture does\n", "\n", "1. Writes a function to generate simulations of a $\\{Y_t\\}$\n", " sequence as a function of time. Say about 40 or 80 periods. The\n", " function checks that $a, b$ are set so that\n", " $\\lambda\\_1, \\lambda\\_2$ are less than\n", " unity in absolute value (also called “modulus”). The function also\n", " tells us whether the roots are complex, and, if they are complex,\n", " returns both their real and complex parts; if the roots are both\n", " real, the function returns their values. The function requires that\n", " we put in initial conditions for $Y_{-1}, Y_{-2}$ \n", "1. The lecture produces a version of a graph in chapter IX, p. 189, of\n", " [[Sar87]](zreferences.ipynb#sargent1987). The\n", " graph maps values of $\\rho_1, \\rho_2$ into various regions –\n", " including ones that produce complex roots and therefore “cycles” in\n", " the outputs. We can use versions of this graph to help us guide how\n", " to set $a,b$ \n", "1. We use our function written to simulate paths that are stochastic\n", " (when $\\sigma >0$) \n", "1. We have written the function in a way that allows us to input\n", " $\\{G_t\\}$ paths of a few simple forms – e.g., one time jumps\n", " in $G$ at some time; and a permanent jump in $G$ that\n", " occurs at some time \n", "1. We proceed to use the Samuelson multiplier-accererator model as a\n", " laboratory to make a simple OOP example that eventually can follow\n", " the example of the Solow model class in [this lecture](https://lectures.quantecon.org/py/python_oop.html).\n", " One lesson from\n", " doing this is that in writing the function and class to simulate the\n", " model, the “state” that determines next period’s $Y_{t+1}$ is\n", " now not just the current value $Y_t$ but also the once lagged\n", " value $Y_{t-1}$. This involves a little more bookkeeping than is\n", " required in the Solow model class definition \n", "1. We use the Samuelson multiplier-accelerator model as a vehicle for\n", " teaching how we can gradually add more and more fun features to the\n", " class. We want to have a method in the class that automatically\n", " generates a simulation, either nonstochastic ($\\sigma=0$) or\n", " stochastic ($\\sigma > 0$) \n", "1. We also show how to map the Samuelson model into a simple instance of\n", " the LinearStateSpace class described [here](https://lectures.quantecon.org/py/linear_models.html).\n", " We can use a LinearStateSpace instance to do various things that we did above with\n", " our homemade function and class. Among other things, we show by\n", " example that the eigenvalues of the matrix $A$ that we use to\n", " form the instance of the LinearStateSpace class for the Samuelson\n", " model equal the roots of the characteristic polynomial [(7)](#equation-polynomial) for the\n", " Samuelson multiplier accelerator model. Here is the formula for the\n", " matrix $A$ in the linear state space system in the case that\n", " government expenditures are a constant $G$: \n", "\n", "\n", "
 $$\n", "A = \\begin{bmatrix} 1 & 0 & 0 \\cr\n", " \\gamma + G & \\rho_1 & \\rho_2 \\cr\n", " 0 & 1 & 0 \\end{bmatrix}\n", "$$\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let’s get to work\n", "\n", "We’ll start by drawing an informative graph from page 189 of [[Sar87]](zreferences.ipynb#sargent1987)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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D69atsXr16jJPhfrhhx/w3//+F02bNoWhoSEyMjIAVLxv/u233yBJEm7duiWfN3PmTEiS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def param_plot():\n", "\n", " \"\"\"this function creates the graph on page 189 of Sargent Macroeconomic Theory, second edition, 1987\"\"\"\n", "\n", " fig, ax = plt.subplots(figsize=(12, 8))\n", " ax.set_aspect('equal')\n", "\n", " # Set axis\n", " xmin, ymin = -3, -2\n", " xmax, ymax = -xmin, -ymin\n", " plt.axis([xmin, xmax, ymin, ymax])\n", "\n", " # Set axis labels\n", " ax.set(xticks=[], yticks=[])\n", " ax.set_xlabel(r'$\\rho_2$', fontsize=16)\n", " ax.xaxis.set_label_position('top')\n", " ax.set_ylabel(r'$\\rho_1$', rotation=0, fontsize=16)\n", " ax.yaxis.set_label_position('right')\n", "\n", " # Draw (t1, t2) points\n", " rho1 = np.linspace(-2, 2, 100)\n", " ax.plot(rho1, -abs(rho1) + 1, c='black')\n", " ax.plot(rho1, np.ones_like(rho1) * -1, c='black')\n", " ax.plot(rho1, -(rho1**2 / 4), c='black')\n", "\n", " # Turn normal axes off\n", " for spine in ['left', 'bottom', 'top', 'right']:\n", " ax.spines[spine].set_visible(False)\n", "\n", " # Add arrows to represent axes\n", " axes_arrows = {'arrowstyle': '<|-|>', 'lw': 1.3}\n", " ax.annotate('', xy=(xmin, 0), xytext=(xmax, 0), arrowprops=axes_arrows)\n", " ax.annotate('', xy=(0, ymin), xytext=(0, ymax), arrowprops=axes_arrows)\n", "\n", " # Annotate the plot with equations\n", " plot_arrowsl = {'arrowstyle': '-|>', 'connectionstyle': \"arc3, rad=-0.2\"}\n", " plot_arrowsr = {'arrowstyle': '-|>', 'connectionstyle': \"arc3, rad=0.2\"}\n", " ax.annotate(r'$\\rho_1 + \\rho_2 < 1$', xy=(0.5, 0.3), xytext=(0.8, 0.6),\n", " arrowprops=plot_arrowsr, fontsize='12')\n", " ax.annotate(r'$\\rho_1 + \\rho_2 = 1$', xy=(0.38, 0.6), xytext=(0.6, 0.8),\n", " arrowprops=plot_arrowsr, fontsize='12')\n", " ax.annotate(r'$\\rho_2 < 1 + \\rho_1$', xy=(-0.5, 0.3), xytext=(-1.3, 0.6),\n", " arrowprops=plot_arrowsl, fontsize='12')\n", " ax.annotate(r'$\\rho_2 = 1 + \\rho_1$', xy=(-0.38, 0.6), xytext=(-1, 0.8),\n", " arrowprops=plot_arrowsl, fontsize='12')\n", " ax.annotate(r'$\\rho_2 = -1$', xy=(1.5, -1), xytext=(1.8, -1.3),\n", " arrowprops=plot_arrowsl, fontsize='12')\n", " ax.annotate(r'${\\rho_1}^2 + 4\\rho_2 = 0$', xy=(1.15, -0.35),\n", " xytext=(1.5, -0.3), arrowprops=plot_arrowsr, fontsize='12')\n", " ax.annotate(r'${\\rho_1}^2 + 4\\rho_2 < 0$', xy=(1.4, -0.7),\n", " xytext=(1.8, -0.6), arrowprops=plot_arrowsr, fontsize='12')\n", "\n", " # Label categories of solutions\n", " ax.text(1.5, 1, 'Explosive\\n growth', ha='center', fontsize=16)\n", " ax.text(-1.5, 1, 'Explosive\\n oscillations', ha='center', fontsize=16)\n", " ax.text(0.05, -1.5, 'Explosive oscillations', ha='center', fontsize=16)\n", " ax.text(0.09, -0.5, 'Damped oscillations', ha='center', fontsize=16)\n", "\n", " # Add small marker to y-axis\n", " ax.axhline(y=1.005, xmin=0.495, xmax=0.505, c='black')\n", " ax.text(-0.12, -1.12, '-1', fontsize=10)\n", " ax.text(-0.12, 0.98, '1', fontsize=10)\n", "\n", " return fig\n", "\n", "param_plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_3_0.png](_static/figures/sam_3_0.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Explanation of the graph\n", "\n", "The graph portrays regions in which the $(\\lambda_1, \\lambda_2)$\n", "root pairs implied by the $(\\rho_1 = (a+b), \\rho_2 = - b)$\n", "difference equation parameter pairs in the Samuelson model are such that:\n", "\n", "- $(\\lambda_1, \\lambda_2)$ are complex with modulus less than\n", " $1$ - in this case, the $\\{Y_t\\}$ sequence displays damped\n", " oscillations \n", "- $(\\lambda_1, \\lambda_2)$ are both real, but one is strictly\n", " greater than $1$ - this leads to explosive growth \n", "- $(\\lambda_1, \\lambda_2)$ are both real, but one is strictly\n", " less than $-1$ - this leads to explosive oscillations \n", "- $(\\lambda_1, \\lambda_2)$ are both real and both are less than\n", " $1$ in absolute value - in this case, there is smooth\n", " convergence to the steady state without damped cycles \n", "\n", "\n", "Later we’ll present the graph with a red mark showing the particular\n", "point implied by the setting of $(a,b)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function to describe implications of characteristic polynomial" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def categorize_solution(rho1, rho2):\n", " \"\"\"this function takes values of rho1 and rho2 and uses them to classify the type of solution\"\"\"\n", "\n", " discriminant = rho1 ** 2 + 4 * rho2\n", " if rho2 > 1 + rho1 or rho2 < -1:\n", " print('Explosive oscillations')\n", " elif rho1 + rho2 > 1:\n", " print('Explosive growth')\n", " elif discriminant < 0:\n", " print('Roots are complex with modulus less than one; therefore damped oscillations')\n", " else:\n", " print('Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n" ] } ], "source": [ "### Test the categorize_solution function\n", "\n", "categorize_solution(1.3, -.4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function for plotting $Y_t$ paths\n", "\n", "A useful function for our work below" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_y(function=None):\n", " \"\"\"function plots path of Y_t\"\"\"\n", " plt.subplots(figsize=(12, 8))\n", " plt.plot(function)\n", " plt.xlabel('Time $t$')\n", " plt.ylabel('$Y_t$', rotation=0)\n", " plt.grid()\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Manual or “by hand” root calculations\n", "\n", "The following function calculates roots of the characteristic polynomial\n", "using high school algebra\n", "\n", "(We’ll calculate the roots in other ways later)\n", "\n", "The function also plots a $Y_t$ starting from initial conditions\n", "that we set" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rho_1 is 1.42\n", "rho_2 is -0.5\n", "Two real roots: \n", "[-0.6459687576256715, -0.7740312423743284]\n", "Absolute values of roots are less than one\n" ] }, { "data": { "image/png": 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TKienj928OehSAAAApkWYRuic6BnUd585rvftXKM1S5mVBgAA4UWYRuh86dEjMhmz0gAA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\nvkbSQ7mZ64s/925Jd0tSY2P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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from cmath import sqrt\n", "\n", "##=== This is a 'manual' method ===#\n", "\n", "def y_nonstochastic(y_0=100, y_1=80, alpha=.92, beta=.5, gamma=10, n=80):\n", "\n", " \"\"\"Takes values of parameters and computes roots of characteristic polynomial.\n", " It tells whether they are real or complex and whether they are less than unity in absolute value.\n", " It also computes a simulation of length n starting from the two given initial conditions for national income\"\"\"\n", "\n", " roots = []\n", "\n", " rho1 = alpha + beta\n", " rho2 = -beta\n", "\n", " print('rho_1 is ', rho1)\n", " print('rho_2 is ', rho2)\n", "\n", " discriminant = rho1 ** 2 + 4 * rho2\n", "\n", " if discriminant == 0:\n", " roots.append(-rho1 / 2)\n", " print('Single real root: ')\n", " print(''.join(str(roots)))\n", " elif discriminant > 0:\n", " roots.append((-rho1 + sqrt(discriminant).real) / 2)\n", " roots.append((-rho1 - sqrt(discriminant).real) / 2)\n", " print('Two real roots: ')\n", " print(''.join(str(roots)))\n", " else:\n", " roots.append((-rho1 + sqrt(discriminant)) / 2)\n", " roots.append((-rho1 - sqrt(discriminant)) / 2)\n", " print('Two complex roots: ')\n", " print(''.join(str(roots)))\n", "\n", " if all(abs(root) < 1 for root in roots):\n", " print('Absolute values of roots are less than one')\n", " else:\n", " print('Absolute values of roots are not less than one')\n", "\n", " def transition(x, t): return rho1 * x[t - 1] + rho2 * x[t - 2] + gamma\n", "\n", " y_t = [y_0, y_1]\n", "\n", " for t in range(2, n):\n", " y_t.append(transition(y_t, t))\n", "\n", " return y_t\n", "\n", "plot_y(y_nonstochastic())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "rho_1 is 1.42\n", "rho_2 is -0.5\n", "Two real roots:\n", "[-0.6459687576256715, -0.7740312423743284]\n", "Absolute values of roots are less than one\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_11_2.png](_static/figures/sam_11_2.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reverse engineering parameters to generate damped cycles\n", "\n", "The next cell writes code that takes as inputs the modulus $r$ and\n", "phase $\\phi$ of a conjugate pair of complex numbers in polar form\n", "\n", "
 $$\n", "\\lambda_1 = r \\exp(i \\phi), \\quad \\lambda_2 = r \\exp(- i \\phi)\n", "$$\n", "\n", "
- The code assumes that these two complex numbers are the roots of the\n", " characteristic polynomial \n", "- It then reverse engineers $(a,b)$ and $(\\rho_1, \\rho_2)$,\n", " pairs that would generate those roots " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a, b = (0.6346322893124001+0j) (0.9024999999999999-0j)\n", "rho1, rho2 = (1.5371322893124+0j) (-0.9024999999999999+0j)\n" ] } ], "source": [ "### code to reverse engineer a cycle\n", "### y_t = r^t (c_1 cos(phi t) + c2 sin(phi t))\n", "###\n", "\n", "import cmath\n", "import math\n", "\n", "def f(r, phi):\n", " \"\"\"\n", " Takes modulus r and angle phi of complex number r exp(j phi)\n", " and creates rho1 and rho2 of characteristic polynomial for which\n", " r exp(j phi) and r exp(- j phi) are complex roots.\n", "\n", " Returns the multiplier coefficient a and the accelerator coefficient b\n", " that verifies those roots.\n", " \"\"\"\n", " g1 = cmath.rect(r, phi) # Generate two complex roots\n", " g2 = cmath.rect(r, -phi)\n", " rho1 = g1 + g2 # Implied rho1, rho2\n", " rho2 = -g1 * g2\n", " b = -rho2 # Reverse engineer a and b that validate these\n", " a = rho1 - b\n", " return rho1, rho2, a, b\n", "\n", "## Now let's use the function in an example\n", "## Here are the example paramters\n", "\n", "r = .95\n", "period = 10 # Length of cycle in units of time\n", "phi = 2 * math.pi/period\n", "\n", "## Apply the function\n", "\n", "rho1, rho2, a, b = f(r, phi)\n", "\n", "print(\"a, b = \", a, b)\n", "print(\"rho1, rho2 =\", rho1, rho2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "a, b = (0.6346322893124001+0j) (0.9024999999999999-0j)\n", "rho1, rho2 = (1.5371322893124+0j) (-0.9024999999999999+0j)\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAAUBAMAAAB7d4cqAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( 1.5371322893124, \\quad -0.9024999999999999\\right )$$" ], "text/plain": [ "(1.5371322893124, -0.9024999999999999)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Print the real components of rho1 and rho2\n", "\n", "rho1 = rho1.real\n", "rho2 = rho2.real\n", "\n", "rho1, rho2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "(1.5371322893124, -0.9024999999999999)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Root finding using numpy\n", "\n", "Here we’ll use numpy to compute the roots of the characteristic\n", "polynomial" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "r, phi = 0.95 0.6283185307179586\n", "p1, p2 = (0.95, 0.6283185307179586) (0.95, -0.6283185307179586)\n", "a, b = (0.6346322893124001+0j) (0.9024999999999999-0j)\n", "rho1, rho2 = 1.5371322893124 -0.9024999999999999\n" ] } ], "source": [ "r1, r2 = np.roots([1, -rho1, -rho2])\n", "\n", "p1 = cmath.polar(r1)\n", "p2 = cmath.polar(r2)\n", "\n", "print(\"r, phi =\", r, phi)\n", "print(\"p1, p2 = \", p1, p2)\n", "# print(\"g1, g2 = \", g1, g2)\n", "\n", "print(\"a, b =\", a, b)\n", "print(\"rho1, rho2 =\", rho1, rho2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "r, phi = 0.95 0.6283185307179586\n", "p1, p2 = (0.95, 0.6283185307179586) (0.95, -0.6283185307179586)\n", "a, b = (0.6346322893124001+0j) (0.9024999999999999-0j)\n", "rho1, rho2 = 1.5371322893124 -0.9024999999999999\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Roots are complex with modulus less than one; therefore damped oscillations\n", "Roots are [ 0.85+0.27838822j 0.85-0.27838822j]\n", "Roots are complex\n", "Roots are less than one\n" ] }, { "data": { "image/png": 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Mo6B2VMgx4icS9Hn01rMX6+cvMXMaAID5iDCNgkkkU9p5aLRiWzyy3n1Bi0YnEnpgKzOn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\nHQAAAPMRYbqASmFnmrF4AAAAhUOYLqD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "##=== This method uses numpy to calculate roots ===#\n", "\n", "\n", "def y_nonstochastic(y_0=100, y_1=80, alpha=.9, beta=.8, gamma=10, n=80):\n", "\n", " \"\"\" Rather than computing the roots of the characteristic polynomial by hand as we did earlier, this function\n", " enlists numpy to do the work for us \"\"\"\n", "\n", " # Useful constants\n", " rho1 = alpha + beta\n", " rho2 = -beta\n", "\n", " categorize_solution(rho1, rho2)\n", "\n", " # Find roots of polynomial\n", " roots = np.roots([1, -rho1, -rho2])\n", " print('Roots are', roots)\n", "\n", " # Check if real or complex\n", " if all(isinstance(root, complex) for root in roots):\n", " print('Roots are complex')\n", " else:\n", " print('Roots are real')\n", "\n", " # Check if roots are less than one\n", " if all(abs(root) < 1 for root in roots):\n", " print('Roots are less than one')\n", " else:\n", " print('Roots are not less than one')\n", "\n", " # Define transition equation\n", " def transition(x, t): return rho1 * x[t - 1] + rho2 * x[t - 2] + gamma\n", "\n", " # Set initial conditions\n", " y_t = [y_0, y_1]\n", "\n", " # Generate y_t series\n", " for t in range(2, n):\n", " y_t.append(transition(y_t, t))\n", "\n", " return y_t\n", "\n", "plot_y(y_nonstochastic())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "Roots are complex with modulus less than one; therefore damped oscillations\n", "Roots are [ 0.85+0.27838822j 0.85-0.27838822j]\n", "Roots are complex\n", "Roots are less than one\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_17_1.png](_static/figures/sam_17_1.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reverse engineered complex roots: example\n", "\n", "The next cell studies the implications of revese engineered complex\n", "roots\n", "\n", "We’ll generate an **undamped** cycle of period 10" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a, b = 0.6180339887498949 1.0\n", "Roots are complex with modulus less than one; therefore damped oscillations\n", "Roots are [ 0.80901699+0.58778525j 0.80901699-0.58778525j]\n", "Roots are complex\n", "Roots are less than one\n" ] }, { "data": { "image/png": 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KR7/9AbLVWCiK9AIgDJxkpbHQ6CZjymBTBjskRgEL5giotV2O/E1IPQLxl7ko\nVgRORs4SWCjnM7NZho7ZdPMMCJ0zttlkZKmxkLoxmybFDFAdErNjs3I+N1WKGZDNCPPCEbuWKrK0\nNqOEBXME1DsO5qcUMtmLYjlTL/rsRbGcqaMxQNYOGPfILbF3s5ihDon1jjv1fgZkq7FQre1OvZ8B\n2Vub0exn2RF/9Y6L2aINe4oUMyBbazNKWDBPieMFaDs+R7EmQEqJWsedKt9PkbXNctqoPDBoj50R\nx6weUbQ0S42Foosws80mJVv72fTvWIAwvWC7nY0eBrWOM3WKGRCuzWbPg+Nlo4FVVLBgnpJ6REn4\nQHaiWF3Xh+MFkUQXsuIpSykjqcYCZEzItKdPYwGyZbN6ZJG/QmYe5EZls6VK2MAqCLIg/qLbz1Tg\nynRCm0XjzIa/LxvrMypYME9JLaIkfABYzkj+Wi2i19HAILqQAZs1eh78QEZnswyIP88P0Oh50UWx\nWtmJYkUxz5arBTT7HvpeFoRMRDcZ1QICGZYqNZ3IbJahaklRReWXBw/ms/JYMipYME9JFEX+FVmJ\nYo2K/HPkb1yiaMChUFEs3/Ao1k53+nrCiqVKAY4foNU3uxNn3/PRcfzIbswA8x8ySykjqcYCZKur\nZGRR+Qx1lYyiuhSQnbUZNSyYp6QeUWkcQOUwmx/Fiqo0DhAKmVYGolhRNJNQLFYKkHI0d02lFkGR\nf0VWDpgo1+awq6Thkb+O48Pxg4iipYNmTIbbLAhkZO8LFjPUibMeQUUuIHtVuaKCBfOURNF5R5GV\nKNawyH+Em6XpCz/KCPNilW02KVlpLBTljdlSRuqkR9VMAsiOkGn2PAQymkDTUkZs5voBmn0vUptl\nwcmIEhbMUxJt5C8bQibqaClg/sKvR2iz7Ii/6OeZ6XmSqpU4i7/xifTGLCNt2KNOZQTMt9koxWx6\nm82X88hZwvi1GTUsmKek3nFQsC2Upyy+DmRHyNTbEUb+MhfF4uu4camzzSZmp8tR+UmJqsXz7t9h\numOmHjUeiyDve6aQQ9G2jM/7jjL907IEjs3kjV+bUcOCeUpUEv60HZ6ADEWxOi4qhRwK9vTTLytC\nptZxIQQwF0FzhKwJmWgfFplts1He9/Q2myupKJbZQibKlIyCbWG2ZGfGZlE4ZkKITJQXjbK6FKAe\nzJs9z6KGBfOURFUXEcjOa9+oSuMAwPLwkYz5NlMCZFqODdNYzLZZrePAtgSqRXvq3zVTsFHO5zJh\nMyCaQ9nO9G54AAAgAElEQVSywk6c5qdLRSf+AGC5an49/ihvfwBgqWp+w5dRdamIbJahBlZRwYJ5\nSuodJ5LWu8DohbTpm2VULZ4BYK5sw85ALlZURf4BIJ+zMF/OZ8JmCxHd/gDZKGFY77go2hZKEaSY\nAdloLKQif1GdA1mYZypXPop24kA2bBbljRkwqsrFjA8L5imJMsJcLuRQzucykZIRlc2EEDiWic0y\nuqg8kA0hE7nNMtDwJeyMGJ3NsiBkah0H1aIdSYoZkA2b1TtOZClmwGA/M/7cjC6HGcjGGRA1LJin\npN5xIsn3U2Rls4xq0QPZWPhRFaxXZKFtcSw2M36eRdNMQpEFm0XVgEOxVCkYX4e51nGHlRqiYLFS\nMD6VsdZxI0sxA0Kb7XRduH4Qye/LAiyYp2DY4YmjWBMRZYQZyMahXIuoYL0iCzaLem1mw2bRRpjD\nyJ/pQib6qHyt4yAwuBNn5DarFtBzA3Qcc3sYqBuzqFLM1ONvFblmDocF8xQ0+x68QHIUawL8QKLR\niy4fFzDfZgCnFxyFqCPMS5mIYkV9Y1ZEo+cZHcWKIyqv9klTiSMqD5hdjz/6G7Ns9H2IEhbMU7AT\nYcF6henir9F1IWW0NjM9iuV4AdqOH7mTYXIUS0oZw01GMQNRrIij8oPKPzWD97TIo/IZKGEYfVTe\nfPFXj+FmFjC/jG2UsGCegihLMClUFEtKM4XM0GYxRLEcz8wolmolvhBB+3XFYqVodBSr6/pwvCBy\nxwwwN4olpUS9G+3tTxZqfocPJTnyNwlRR5izUI8/8qh8BhyzqGHBPAVRtt5VLFVVFMuP7HdSohZD\nVF4tfFNzsaJsi61YHtjM1MdFcdjM9AOm2ffgBzLyAABgrpMROp0eO2YTEnVUftnwtQlEH5UfzTNz\nb2ejhgXzFERdsB4w31OOumA9YP4Bo66zF8o8z8Ylyk5iipHNzDxg6u34nFlTc793uvE5ZqauzbhS\nzABz1+awwECEN7PhA0Jz51kcsGCeglHnHb7CHJc4ovLmi79oC9YD5h8wsUSYVWMhUx2zCFs8K0xP\nLxilmLFjNi5xBJqqRRuFnGXsudlxfDh+EGmgKWcJHJsx//F3lLBgnoKoOzwBvFkeBdOjWPUYDmXT\nu0rGImQMj/zFEZVfKOdhGRzFimM/K9o5VIu2selSo6BJdDYTwuw27HE4s4D5RQaihgXzFNQ7DmZL\nNuxcdGbMQhTLEsBsRMXXgSxEsaKPlqpHl6a+kB5G5SN0ZiuFHAq2Zew8i7r1LgBYhkexom7xrDBZ\nyETdsU5hss3qw+BcdE4GoBq+mGmzOGDBPAVRl60CshDFCstWWRF1eAKyEcUq2BbK+Vxkv7No5zBb\ntI3dLOvt6CN/Qgiju0rGUfUHMLurZKw2M3Se1WMSzCbXlo8rwrxk8DyLAxbMUxB1IXEgC1GsaNti\nAxmIYg3mWVQdnhSLVXM3y1rHHa6lKDFZyNQ6LoSINsUMMNtmw6h8hI+xABjumEWfkgGoeWZmWt7Q\nZhGmmAFmr804YME8BVEX+QfCKNZypWBu/lrELZ4VS1Vzm5fEcZMBmN25LurOiIqlatHYeVbvOJgr\n5ZGL8PYHAJarRWwZOs9qHQe2JSJNMQPC/cxc8RdPVH6pUjT2JiO+qHwRtY4D39AGVlHDgnkK6t3o\nI8yAivyZuVlG3RhBYbKnvBNxwXrFYqVodK58lM1xFKZH/nhtToZqix357U+liNttx8gGVvWOi6Jt\noVyILsUMCJ2MtuOj55rXw2B4kxFxDvNSpQApze1hEDUsmKeg3o4+wgyMNksTiS3yVykaLGSiLViv\nMDl/La6ovMniL661uVgpoN5x4fnmdeKMbz8rwPUlmn3z2rCHnRHjmWeAmW9Zah0nLJ0XQ4oZYKbN\n4oAF8xFx/QDNvhfjVbmZEziOvG/AbCFTiyH1BwhvMmodU6NY8Ym/jqFRrLjW5qgTp3lt2OPczwAz\nq9jUYrsxM1f8Rd0WW2F606+oYcF8RIaNEWK49jVV/PVcHz034CjWBIQdnqJ/KAmMoliNnnlRrLhS\nf0xuLFSPMSoPmCxk4nFmATNry+9047sxA4AtA98YxHXLaHpVrqhhwXxE4ihYrzA1ihXXYw/A3ChW\nq+/BC2S8USzDNks/kNjpxpUuZW7kLzbxVzFX/NVjyvs2OfJX67ixBZoA8/YzIImovHlrMw5YMB+R\nOJpJKEyNYqki/yz+xmfUTCLOyJ9Zm2Wj60LKmNamoZE/xwvQ6nsx7WfmNhaKLfJn6H4GxPuOBTDX\nZnHMM/U7TdMaccGC+YgMuxVF/GoVCEu9ADCufJWKys/HeCibZrM4o/LLg3lmWgnDuDqJAeZ24qx3\nY7RZ1cxoadfx0feCePczw4RMmGLmRt4ZEQDmyjZsSxhnMyB8KBnH2sznLCzM5I1bm3ERmWAWQpSE\nEC8IIV4VQrwphPibg6//n0KIK0KIVwb/PBrVZ6ZJXHURgd1XmGZN4rgK1gO7I3+m2oyj8uNSizMq\nb2jOX5w3GcdmChDCxLUZnzNbLuQwU8gZN8+awxSz6G0mhDCyq6TnB2j0vFjWJmDum6k4iLLaeh/A\nN6WULSFEHsB5IcSfDv7bfyOl/IMIPyt14uq8A4xSMkxb+HEeMKaKv7hz5QFzbRbHPJst2sjnzIti\n1drx2SxnCSyU88al/sTVrlhhopCpt5VjFp/NTFubO934giaA2Q2soiayCLMMaQ3+NT/4x7x6VQNq\nHQf5nEAl4uLrgMlRrPii8sZGsdrxHcqlfA6VQs6467g4o/LDKJZhB8woKs/ib1zijMoDZpYXjTNo\nApjZITHOm1nAzLUZF5HmMAshckKIVwBsAvielPL5wX/6O0KI14QQ3xFCFKP8zLTYGbwoj7rDE2Bu\nFKvecVHO51DKR+9kmBrFqg+iC/Mx5PwBZnaVjDMqD5jZWGgYlY/hxgwYNBYyzjGLV/yZ6ZipeRaX\nY2be2tyJ8X0BYKbN4iLKlAxIKX0AjwohFgD8kRDiMwB+HcCHAAoAvgvgrwP4W7t/TgjxbQDfBoAT\nJ05gbW0tymGNTavVGvuz19/roSCD2MZasYE3L17D2tqHsfz+qJjEZm9f7qOci89mJeHhnSs3sLa2\nHcvvj4pJbPbGhT5mbOD8038Ry1jyfh8X399Ibc2NyyQ2e+WCA0sAP3nufCwOreV0ceWD8ceTFpPY\n7MeXwwPzjZeew7odvc38bg832/Gt/aiYxGYvvBc6s2+/8iJulqJ/P+80+/jgtm+UzZ75IKz5fuH1\nV9C8Er3NurU+NnY8o2z28mZos8vvvA7cjD7Y1NpycLvt4gdPPQUrhv0yKiaxWVxEKpgVUsq6EGIN\nwM9LKX9r8OW+EOL/APDX9vj+7yIU03jsscfk6upqHMM6lLW1NYz72f/o3WdxcgZYXX08lrHc++rT\nKM6VsLr607H8/qiYxGb/19UX8THZw+rqE7GM5YF3noUQ8f1NomISm/3Rhy/jeLs+9vdPyu9dfREb\njfj+JlExic2erL2OYxsf4hvf+EYsY/nDmy/j1evx/U2iYhKbPdt5G4XLV/FzP7sai5PxZO11XH3j\nQ6Ns9vr314G3LuAXvrUaectiAHim8zZefOYqvv71r8fyN4mKSWx25UdXgNfewr/yjXPDNxRR8pq/\njj9/7wIeP/cEinb04jIqJrHZrZfeB37yGr517nE8uDQT+Vgu21fw/15+C1/48tnYbpiiYBKbxUWU\nVTKODyLLEEKUAXwLwDtCiHsHXxMAfgnAG1F9ZprUY2qJqliqFIws9xXXVRxg5oOPWkwlmBSLlYJx\nV+VxdUZUmGgz1eI5LmG2VCngdseBH5jzrKXWcVEp5GIRy0A4zxwvQNsxp4FVreNCiBhTzAaCT9X8\nN4FhrnxMZ6epteXjIMqVfi+Ap4QQrwF4EWEO8x8D+CdCiNcBvA5gGcDfjvAzU6MWUxtZRfh4waxD\nOa5OYgozbRZPkX+FspmU5giZuFo8K5arBbT6HvqeOUImbpstVQqQcpQrbQL1bsxr08BqSTsdB3Ol\nPHJWPI7ZsoHir9ZxYFsCs8VYEgKMrS0fB5H9BaSUrwH4wh5f/2ZUn0GFsPh6vJuliS9XawlE5WuD\nKFZcG3LS1DoOTi9XYvv9S5UCHD/s8jZbiu9vkyS1jouTC+XYfv/iro5i987H9zlJUo+p9a5isTqy\nmWrMpDv1mFo8K3ZH/uK4ik+DWkytxBWLBnb7U22x47r9MbW8aBxwp78j0HZ8uL6MXfyZFMUKAomd\nbrxRrEUTo1jteKPyJh4wcadLDRsLGRSRiavFs0JFS01KmYrbZiauzVoCgSbALJslccsImLU244IF\n8xFQtXHjzZM0a7Ns9FwEMr7cNeCjUSwTcP0Azb7HQmZCajHnMC8ZWCe9FneE2Ugh48a6n5m4NuO+\nyVgy1JmN8x2LOl9MWptxwYL5CMRdsB4wL4oVd/F1wLwDpj7sJpmAkDFknvVcHz034CjWBCSRYmba\n2gSSiDCbdQYA8dtsvhzmR5uUwxz325+CbWG2ZBuzn8UJC+YjEHfBesC8KFbcBesB84RM3A04APNs\nlsjaNEz8tfoevCDeFLNjhjlm/jDFLD6bzRRyKNqWUc1L4o4wW5bAsZm8MfsZEP/bH8DMrpJxwIL5\nCNRj7u0O7IouGLJZ7iQQlR9dx5lhsyTmmXLMtgyZZ6qcVJw2U6/8jZlnCazNfM7CXMk2Zj9rdF1I\nGa/NhBBGCRnHCx8Xx+nMAuaVfQwflyZhMzPWZpywYD4CSUT+lg0r9ZJE5O+YYZE/lSsfp81mCjbK\n+Zwxkb8k1qZlCaOq2CSxNgFguVo0Z20mcGMGAEtVc9oW17tqnsUdLTXHZl3HR98LYo3KA2bNszhh\nwXwEVBQrzkk8V7ZhW8KYSTzKYY7PZvmchfmyOddxKvIX58MiwKwShrUE8r4Bs64wk1ibwGCeGeKY\n1RKIygNmrc0kbjIAYNGgevxJObMm7WdxwoL5CNQ6DmaLNvK5+MwnhMAxozZLB5YIr7PjxKSFP4pi\nxbxZVg20GQuZsUkiKg+YabNEhIwpTkYCN2aAoWdAAs5szbAGVnHAgvkI1DtObG0qd2Pawp8v52HF\n3FDEtChWPidQKeRi/RwThUzcV5gm2WwkZOK+9jVpP0swKm+YzZJYmztdF64fxPo5SZBYVL5SgBdI\nNLperJ+jOyyYj0DcbbEVpm2WbLPJUKW+4urwpDDLZu6gukC8TsaSQY9k1OPSJFJ/ah0HQaB/FCux\nqHy1gK7ro+PoL2R2ugndmA1+v4rO6kxiKRkGthSPAxbMRyDumqUKs4RMvM0kFGZFseIvJwSomwwz\nNsrkHLMiGj3PmCjWXMmGHWOKGRDazA8kGj031s9JgnrHRc4SmCvZsX6OSY04kovKm/NgPmmbmaI3\n4oIF8xEID+WEhIwhUaxaO7kIsylRrFrMBesVi5Uiem5gRBQrKcdscRCRqRlwwNQ6TuxRP8Cs+tWq\n+1r8tz/mCJlax0HBtlDOx59iBphhs/rgf8N8AnWYATPWZpywYD4CcbeqVKgoluOZEMVyYl/0wCiK\ntdM1IYqVXIQZMCUik9BNxsBmW0bYzE1oPzNnntU7bkL7mUniz03EyRilF+hvs1pCKWYmrc04YcE8\nIZ4foNnzEon8qYVvQi5WvZtMhHnZoM2ynlB6gUkHTNxtZBVLJgmZhFLMRt1L9b81i7vFs8Kk/Swp\nmw3XpgG3s/VuMjYbOWb62yxOWDBPyE4C3dcUpkT++p6PjuMnYjNTIjJSysTEn0mbZWJ53wY9kkku\nV36QW6r52gSSS8szaW3G3RZbET6U1v8MAJKzWSmfQ7VoG7E244QF84SMGiMkKWT0nsRJlcYBzDlg\nOo4Pxw+SFTKaO2bBIBUnqUd/gP5rExhclSdgM9VMxoSyj0lF5atFG4WcZYSQSSrCnLMEjs2Y8fg7\nKZsBZhUZiAsWzBOSVDkhwJwoVlKlcQBzoli1hOoJA6MHbLpvlo2ei0AmszYXynlYBkSxXD9As+8l\nsjaLdg6zhkSxkorKCyGMqS1f67ixd+BUmCL+koowA+bYLE5YME9IUmVeAHOiWKqVeBI2MyWKlWRU\nvlLIoWBb+s+zBNemZUgUq95JppW4woS2xT3XR88NElmbgBlCJkwxSyYqD4Q2031tAslGmE3qKhkX\nLJgnJMloqSlRrCSj8qZEsZKcZ0III7pKJmkzwIyukkmuTcAM8Zf0PFuqFrCluc1afQ9eIBNxZgEz\nSrL6wxQzjjBTgQXzhCTVehcYRbF0L11VSyGKpb/4Sy5aCgwiMpofMEmuTUBFsfS2WdLzbKlSwJbm\n8yzJGzNACRm9bZbkjRlghvhrdF3IhFLMAHVu9iGl/j0M4oIF84TUOi5sS6BajLfDk2Kpqv9mmXhE\nxogDJtnI31K1qP0BM0wvSMhmy9Wi9o5ZPfG1acA86ya8NitFA24ykl2bS9Ui6l0XvsYNrIbnZkKB\npuVKEa4v0ezr38AqLlgwT4jKw4q7+LrCBE+53nFQylsoxdzhSbFYKWqfi6WiWElFS81IyUj2UDZj\nbSY7zxarYSdOnaNYSed9L1ULaDs+eq6fyOfFwShoktx+JqXePQxqKUTlAf3f/8QJC+YJqbWTe7UK\nhNEFE4TMQjmZRQ+oCLPuNnMwW7SRzyWzRM0Qfw4sAcyWkrn9WawUUO+48Hx9O3HWkr7JqBTg+hKN\nnr5RrKHNEtrTTCgvmmTVH8AMmw1vGRPowgmMqiXprjfihAXzhISdd5ITzGYImWSdDBOiWDtdFwsJ\nRbCAcJ51DIhizZfzsKxkbn9GnTj1bcNe67jI5wQqhaRuf0wQMglH5Y2yWXKOGaB3bfnE01gMmGdx\nw4J5QpLqvqYwIYpVT7A0DmBOFCtpmwF6RxdqCbUSV5ghZJJPMQP0bixUazso53OJpZiZsTbTiZbq\nvDbTqPoD6L0244YF84QkVbBeYUYUy0ks3w8wQ8jUUnDMAL3z10Lxl/w807lSRuL7mQFdJZNqi60w\nQcjUOy5mSzbsBFPMAP1tlmSKmSlNv+KEBfMESClTi2LpfCinEZUHoHWZtHrHSSwaA4wcsy2N51mt\nnezaNEX8Jbo2DciTTLIBB2DKPEv2xmxx8Fk6l2StDeZZUilm5UIO5XxO63kWNyyYJ6Dr+nC85Do8\nAaPrmB1NI8xSStQTLL4O7LJZV0+bAeG1b5I2U3O6obHNkhYy6u+j8zyrJxxhNsFmSd+YzZZsWEJ3\nmyV7Btg5C7MlW2ubJf32BwjXp842ixsWzBOQdJF/AJgrhZ+laz5uo+fBD2Si0YW5srKZngvf8wM0\nel6i4m84zzTeLJM+lHWfZ0Dyed/lfA62JbSeZ0nfmFmWwGwpr7nNknVmgXBP03ttJhuVB8I9Ted5\nFjcsmCeg1k62BBMAzJXD/CVdJ3HSDTgAYK6kbKank6E8/CTFn8qT09Ux67k+uq6PY5Xk5lnRtlDI\nWdrOMyll4kJGCBEeytoLmWQjf3NlW9u1CaRls7y2axNIPgAA6O9kxA0L5gmopxph1nMSpxKVL+sd\nLR21Ek9OyJTyORRtS1ubJV3qC1Diz9Z2bbYdH64vUziUbW2FTBBI7HSTjcoDAyGj6doEgHo72ag8\nMJhnmq5NIKWofFnftZkELJgnYNSqMrlJPKt5tDTpxggAkM9ZmCnktN0s04jKA8C8xpE/1a6YrzDH\nJ+m22Aqd51mz5yGQvDYnwfUDNPteOvNM07UJpBiV13SeJQEL5gmoJ9ytCAgfL1SL+j5eGB3KyV8t\n6WqzNKLyQLhZamuzhFuJK3SeZ2lE5QHN5xnvZxMzTDFL8KEkoLcz23N99NxkCwwAes+zJGDBPAHD\nAybBNs+A3ldLSXd4Uuh8tZRW5E/nq/JRG9kUIsya5pamcfsD6J1ekHSLZ4UJ+9l8gmUyAZWPq6vN\n0nNmW30PQaBvl9w4YcE8AbWOi0ohh4KdrNl09pRrHRdCpLVZ6mmzNDdLXW02yvtOPh+3qfHaBNK4\nydD3AVtqAQCN97PRPEs+aNLqe1p2yU26y59irmRDSqDZ13N9xg0L5glIIwkf0HuzrHcczJXyyCVU\nfF2ht/hzYFsC1WIyHZ4UJkT+Uslh1nSepZUrz/NscubKeXQcH66O4q+dlvgLHcGWhuIvvZsMvR/M\nxw0L5glIumC9QufruDRK4wB6pxfUBgXrhUjaydA58ueglLdQyucS/dxQ/HmQUr8rzNTyvst59L0A\nPddP9HOjILWo/ODxd1PD9ZnmjRmg54P5elpRec2rcsUNC+YJSLrIv0L3CHMqUXnNI3+p3WR0XT3F\nX1prs2zD8QP0PQ0jfx0Hs0Ub+VzCKWZaiz8HlhgJi6TQOfKXRnUpYFc9fg3PgfRuMvSuyhU3LJgn\nIE3xp+vL1TRK4wCjkkI6Pl5I02ZeINFx9Iv8pbU25zUWMvWOg4VUbsz0jWLVOg7my3lYCaeYqXmm\n4zlQ67jI5wQqhWRvf3S2WVpReZ1tlgQsmCcgtfQCjV+u1trpReUDCbQd/TzlpFvvKvQWMmml/uh7\nwKQXlWebTYrOa1M5s8mnmOnrzNbaDsr5XCopZoCe8ywJWDCPiR9INHopCRmNX66mF5XXt9VzWhHm\n4Wap4XVcaDMWMpOQZuoPoKeQCW3Ga3MSUtvPNF6baQbnAD3XZhKwYB6Tna4LKZN/7AHoO4kdL0Db\n8VMWf3rZTEqZaj4uoOcBUx88lEyaOY07caZ1KM/r7MymdWOm8dqspXVjpvHaTMuZnS3aEELPtZkE\nLJjHJK0kfEDfa5Jh2aqEH3sA+joZXdeH4yXf4QnQ18kIAok6R5gnJjWbaTrPgDBwwmtzMnZScswq\nBRuW0HNtplWRyxqUM9VxniUBC+YxSSsJH9D35WpdtURNM8KsmadcT6lsFaCv+Gv2PQQypbWpqZDx\n/ACNnpfSfqbnPAPSSy+YKeSQs4TGNkveybAsgVlNa37XU3LMAL2rcsUNC+YxSavIP7DrJb5mk1gV\nrE+6XTGgb/WCtNoVA/peYaa5NnXNlVcP7hYS7sAJAEXbQiFnaTfP+p6PjuOn4mQIIQaVf/SymZQS\n9Y6L+RRsBgyqJWm2NoFBilkKaxOAlvMsKVgwj0laBesBfV/i1whE5XWzWbo3GXrPszTWZtHOoZS3\nNHTMVCvx5J0MIYSWddLTaoutmCvZ2q3NjuPD8YNUIsxAeA7oZrM0U8wA1ShNL5slBQvmMUk3iqVn\ntLSeUsF6AMO20rodymnmyudzFmYKOe3mWZpReSB0aHU7lNPczwA9hUyaaxPQsxnTyGbpREt1bMPe\n7KWXYgZwSsZBsGAek1rHQc4Sw2vrJNH15WqakT87Zw0eL7DNJkHHzbKe9qGspZAhMM80EzKqlTjb\nbHzSj8rruDYJOGaazbOkYME8JrVBTlHSxdcBfV+u1jsOCraFcsLF1xVzJVu7zbLeTj/yp52TMRQy\n6V2Va2czCoeyZgEAClF53WyW/jzTeG2mUCUDUE6GXjZLChbMY5JWwXqFrp7ysZl0nAxAT0+51nFR\nKeRQsNNZmjrOs3rHgRCj1KWk0THCPBJ/aR3KNpoark0gZSGjq834xmxsUo/Kl220+h48P0jl8ynD\ngnlM0ipYr5jT8OVqWg04FHpulukUrFfoKP5qHRfz5TxyVkqOmaZCxh7cXKWBnvMs7WipfjZLPyqf\nR8fx4Wok/lKfZ4MiAy0NOwvHDQvmMamlLGTmyxqmF6QdldfSyUinYL1C1/SCdJ1Z/a7KlWOW2u1P\nKVybUspUPv8o1DsOSnkLpZRSzObLefTcAH3PT+Xzj4JKl0rrHFDlRZsarc+0o/Kjkqz62CwpIhPM\nQoiSEOIFIcSrQog3hRB/c/D1h4UQzwsh1oUQvy+ESO9km4J6St2KFLpGsdIWMvq9xE/XZvNl/So+\nhN3X0lub84PUH73EX7r72Xw5D8cP0Pf0ifzV097PNKyTXu86mC3ayOdSSjHTsLxovePAEqNIb9Lo\nWl40CaKcxX0A35RSfh7AowB+XgjxVQC/CeA7UsozAGoA/kqEn5kY9a6TSnk0hY75uPVOet2KAD1T\nMtJqvauYK+fR7LkIAn3EX+oR5lIeXiDRcTSK/KVtMw2FTC3t/UzDBlb1jouFVG/M9CvJWh+kmFmp\npZjpWZI1CSITzDKkNfjX/OAfCeCbAP5g8PXfBfBLUX1mUvRcHz03GF5VpIFuL1fDDk/pp2S0+p6G\n4i/deRZIoO3oM9dq7fS6YgH6Cpm0uq8BugoZJ915pqHNah0nlU6vCh3XZtrpn7r2fUiCSO9JhBA5\nIcQrADYBfA/AJQB1KaU6fa8DOBnlZyZB2kn4gH4vV1t9D14gUxZ/NqQEmpo8XggCGUaYUxV/+rV6\nTv2hZEm/nL/UHTNNhUyq7ws0XJthVJ6Ck6GPzepp20zDtZkUkT6RllL6AB4VQiwA+CMAn9zr2+78\nghDi2wC+DQAnTpzA2tpalMMam1artednX2+GIvXGlQtY615OeFQhm9fDyftn3/8hqoV0rmr2Yj+b\nbXdDm3343mWsrb2f8KhCbg5s9uRTT+P4DJ33rfvZrO1KSAnc+uA9rK3dTH5gAN77MDxYfvD0s3hg\nlr7N/ECi7fiobVzH2tpm8gMDcGUrTMX44bMv4OaxdB6E7cV+NgOAWruPxtZGanvtpXpos/Mv/ATN\nK+lU6tiLg2y21ejggWI/NZvdaIV76nM/fhXyAz1strHdQWnOSs1mt3uhzV589Q1Ubr+byhj24iCb\n3djsYrYoUrNZ1wsl2k/eeBcn2unonb04yGZJEcuqk1LWhRBrAL4KYEEIYQ+izPcD+GCP7/8ugO8C\nwGOPPSZXV1fjGNahrK2tYa/PfuHKbeBHz+LxLz2Kc2eWkx8YgK0fX8c/fedVfO5LX8GDSzOpjGEv\n9rPZWx80gB8+jS8/+hmsfube5AcGoPfGh/idN36MTz36JXz6vvlUxrAX+9ns/dsd4PtP4Yuf+QRW\nHwO9qe8AACAASURBVHsg+YEByF/cwj985Xl8/NOfx1dOL6Uyhr3Yz2a32w7w5Pfw+U+ewerZh5Mf\nGIBj79fxWy/9CI984jNY/eSJVMawF/vZzPECOH/2p/jMxx/G6uqZ5AcG4IFbLfzGcz/EqTOfxOqj\ndC4d97MZAHT//E/xU488iNXVveJA8bPR6OG/P/993H/6DFa/8lAqY9iLg2zmPv09rDz0MayufjbZ\nQQ1o9z1g7V/i3gdPY/Xrj6Qyhr04yGb/w4tP4eGTC1hd/UKygxoQBBLW9/8E95x8EKurP5XKGPbi\nIJslRZRVMo4PIssQQpQBfAvA2wCeAvDLg2/7NQD/PKrPTAqVy6OuxNJgXrNrEjXOtF76AvqVx9kZ\nzjMCV5iaXPs2KNhM17VJYZ5pkifZc304XsD72QRIKdHouanOs5lCDrYltFmbQLgm0pxnliW0LDKQ\nBFEqwHsB/K4QIodQiP8/Uso/FkK8BeD/FkL8bQAvA/idCD8zESiIP/VyVZdX5TSEjGY2IzDP5jUr\nKUTJZroImeHaTHM/0ywfl4KTUbQtFHKWNmuz5wZwfZnqPBMiFH+62Cx0MrxUg3NAuDfoYrMkieyv\nIqV8DcBddwhSyssAvhzV56QBDfGnV0RGHYTpOhmaRf4GgivNzXIoZHSZZ0ObpTfPZnVzZnvpz7Oi\nnUMpr4/4G86zUno2C8WfPg2sRk5G2uJPn2ZMHceHH6TrZAB6NmNKAjqvegijJs5sipuldte+BNJY\n9HMy0o/8qVbJ2swzAodyPmdhppDTZ54RiDCrz9fGZgQizIBmNqMyzzRqKc7zjDYsmMeg0XUxU8il\n1q0I0K/Lk1r4sylulrNFG0JodO1L4CbDzlmoFvWJyJA5lDVqkkPmUNZJyBCZZ7Nlferxk5lnGom/\n0U0GAZtpsjaThAXzGDR6bqpNSwCgUrBhCY0if10Ps0UbuZS6FQHh44VQ/Glis54HIUKhnyZzJf2u\nfdNen3NlnZyMcJyp20yjq3IlUmnYTJO1SWWeaZRewPsZbVgwj8FOyq9WAf1eru50030drZjXLIo1\nW7RTa4mq0G2e5SyBmUK69Y91isjsEImW6hRh3iGQYgbotZ+N5hkBm+myn3V4nlGGBfMYNLrpv1oF\n9Hq52ui5qeZ8K/S6jqPhZGg1z7oe5ko2hCDgZGhywDR6LvI5gVI+3e1ft7UJEHEydLEZoZQMbfYz\nAu9Y1Od3HB+uJp2Fk4IF8xg0eulHmAHNrpaoiD+NrpZ4nk1O2nVeFVqlFwxuzNJ3MvSaZwXbQilP\n4Caj60HKuxrmkkMJ+7QDJ3PlPPpegJ7rpzqOcaDwjmX35+vinCUFC+YxoHMo6xRd8GiIP42uysnc\nZOgUxSKQLgWEV5j6RLE8EvuZspke4o/Ifla24fgB+h79yF+j56GUt1C003Yywj21qYFzRqEiF6Bf\nnfSkYME8BuraN230En8ui78JIRNh1mmeESjyD4TzrNlzEQQ6iD+XzH7mBxIdR4PIX4/IfqZRh0Qq\nzqxOJVkpVOQC9JpnScKC+RCCQKJJoEoGoF96AQmblTQqw9QlYrNyHq2+p5H4I2CzUh6BBNoO/blG\n5sZMMyFDYp7pZDNCZwCgh/gjYzON5lmSsGA+hLbjIZDp5xQB+kT+gkCi1adzhdnqe/A0eLxA5ap8\nrmRDSqDZ10P80Thg9LnCJPO+YChkNLBZz6Mxz4ZdJTWwWZfIfqbV2iRybmq0NpOEBfMhUCnBBIQ5\nfzq8XG32PEgiToY65FrExZ/nB4ScDH0iMlTKF+oUxdqhciiX9ekqScXJmNco8rdDJPVnXrv9jJDN\nNJhnScKC+RCGnXcITGJdhMyoNA4Bmw2EAfUHWepBCol5ponN+p6PnhvQmGearE2A83GPApm8b+3m\nWfpOhi77GUDoHUtZ3WTQt1mSsGA+BCp1EQF9rpZGRf4p2EyPqyWa84z2ZjlyMgjYTIk/4muz5/pw\nvIDIPNMjiiWlJCf+tBDMnPc9MVTmWTmfg20JLeZZkrBgPgQqdREBfTZLUuKvpIf4G91kpG+zeV2c\nDGLpUoBGa5Pn2dj03ACuL0nMs9mSHkGT0MmgUcGmaFso5Czy8wygU5FLCKFVM6akYMF8CGpjorBZ\n6uIpcxrL5FBMYyE/zyilsWhyhTlcmwTm2WxJE5sNnYz0bVbK51C0LfL7Wcfx4Qc0nIxQ/Nnk9zNV\nkYuCMwvo1YwpKVgwH4LamGi8kNYjIqM2JhI208bJGNhshpDNiB/KlCLM1aImNxmEIsz5nIWZQo7n\n2YToEPmjdAYAejT9UhW5yNhMg3mWNCyYD0FFP6oEIjK65JbSSmMZ2Iy4k0GpGsts0YYQ9K99KR3K\nds5CtUg/IkMpAADoUSqT0jwD9Ij8UXrHAgCzZfr1+CmdAYAeTkbSsGA+hEbPxWzRRs4SaQ9FnzzJ\nrgshgGohfSejWrRhCQ2cDEKRP8sSA/FH22bUDuW5Ev1rX3KHsgbNmKjNs3kNIn+j1B9CNiO+n1FK\nZQTUPKO9NpOGBfMhUCm+DoxertLP+fMwW7RhEXAy1OMF8jbrerAEUCnk0h4KAD2iC9QOZR3asFPK\n+wY0iTATyvsGoMl+RifvG1BReeI2I/RYHgj/dtTnWdKwYD6ERs8dPk5JG11erlIp8q/QQvwNHnsI\nkb6TAeiRv9boucjnBEp5GtuYHuKP2qGsgc0I3f4A+uxnAM+zSaCUygjoMc+ShsZJQxh64o/+FSaV\n4uuK8IU0cZsRqVmqmNfgqlzZjJSTQd1mPRcF20IpT+MmY14Hmw1EA5XAiS77GUBN/HmQUqY9lH2h\nVJELCP92fS9Az/XTHgoZWDAfQqNHo42sQg9PmUb9TYUOnjKVmqUKLaKlPTrpUoAeV5gNIm2xFXMl\nDWzW81DKWyjaNJwMtZ/pIP4oORmOH6DvBWkPZV8oprEAowZRDAvmQ2l0XTKvowFdxB9Bm1EXf9Tm\nmQ75uETaFSu0mGdE2mIr5sp5NHsugoCw+CN2+zNXzsMLJLqEI3+NrotKIYd8jobE0KHpl9o7ZonM\nNV1KsiYJjdlMmDAlg84Bo8PL1R1iB4wO177UbBaKP9o2o9JGVjFXzqPV98iLP1KOWSmPQIY1aKlC\nLQCgQ4fEHWKpjPMaiL+dLp2KXIA+9fiThAXzAfiBRLNP7ApTi2tfWpulFjYjmPfd6nvwfLpXmNQO\n5bmSDSmBZp+ukKEXLaXf6pnePAvHQnlPo7efaWAzQhW5AD3mWdKwYD6A1rAEE61JTNnj8/wAbcen\ntVmW8ui6PhzS+Wv0cpgB2vlr5PJxNYjIkMv71uGqvOvRSv3RoIEVvf2MfgMrShW5gPDhN0DbmU0a\nFswHMCqNQ2cSU3+52iRW5xUYCZkm0QPG8QJ0XWJOhgZXmOTycUsa2Ixa3rcWTgbNCDN5m/F+NhHk\nbmY1mGdJw4L5AKh1eALov1ylVn8ToH/t2yRW5xWgnyfZG9wYUJpn1G0mpSQn/ka5pTRtBlBMY9FA\n/BGbZzqIP4oVuQDa8yxpWDAfgJoolB58UJ/ESiyQshnxzVKJBVo2o33tS62ZBDByzKjm/PXcAK4v\naR3KxPMkQyeD0wsmpdH1SO1nsyXaQROA3oPcom2hkLNIz7OkYcF8ANRa7wL0xR/JqDxxJ2NkM0KH\nMvGrcmrtigH6KRkjJ4OQzdTtD9F51nF8+AExJ4P42gyCwU0GobVZyudQtC2yNgPoVeQKOwvbZPez\nNDhUMAshPimEuCKEsAb/bgkhnhRC/Gr8w0sXaoXEgd3ij6bXR/FQpn5VTq1dMUDfySB9+0P0UFbj\nomSzalGPmwxKNsvnLMwUcmRt1nI8SEkraAKokqw0bUaxIhegRz3+JDlUMEsp3wbwDoBfHHzp7wJ4\nV0r5e3EOjAIUr33niV/7khR/xK99Kc4zFR2iajOKNxmzRRtC0HVmdwiuTTtnoVqk24ad4jwDwr8h\n1bVJ8QwAwr8hVZtRrMgF0J5naTBuGPA7AP5LIUQewFkA34xvSHRodF0IAVQLdKKl1FMySIo/4mWY\nKKb+VAo2LMFR+UmwLDEQf0TnGcG1CYTOGa/NyZgr03UyhjYjdMsIDOYZVZsRrMgF0HYy0mCsHGYp\n5ZMA7gfwPwL4d6SULgAIIY7FOLbUafQ8zBZtWEQ67wAaXJV3PVgCqBRyaQ9lSDmfg20JDYQMnc3S\nsgRmCbd6bhAsXwjQbo9NMe8boH3tSzEtDyA+zwhWSgIG84yozejeZNhoEl2baTDJo79nAPwDKeXN\nXV/7TsTjIQW1uogA/ZerqpyQEHScjPDxAt3NstF1YVsC5TwdJwNQLcXp2gygdyhTbsNONsJMeW2y\n+JuYBlnxR3g/43mmBZMI5k8BeEX9ixDi5wF8Qgjx1yIfFREaPVplXgD6L1eplcZRUL+OmyfmZACD\na1+i+biNnouCbaFEzMkIr8rprk0ApLqJASpPkug8Iyv+KO9n9MpkAsT3M4LlWAHlZHiQUqY9FBJM\nIpg/DeCNXf++BeAfSyl/K9oh0YFa610FZU95h1iRfwVlT3mnS6tdsYLyPCO9NonOs0bPQylvoWiz\nkzEuSmCRczJI72dEo6WD/Yyi+COb+lO24fgB+l6Q9lBIMJZgFkI8AKAupWzt+vLnALway6iIsEOs\nLqIi3CyJesrEivwrqKcXUMsrBaiLP3dYMYYS1PNxqUWwAOLzrOuiUsghn6PVskDtZ5TFX5XYnjZf\nzsMLJLqun/ZQ7oJqutSoJCvN9Zk04z76e19KefqOL28B+I+FEJ+Mflg0CIuv05rAAO2Xq9TayCoo\nl8eh1kZWMVe26dqM4PsCQIk/qs4s0bVZzqPV9xAEBMUf1bVZyiOQQKtPb641ei5mizZyhB7LAyMx\nSnFPo1iRC6BfkjVpjuw2Syn/hZTy1wZ1mo2E7qFM9+Uq3UOZcv4aUZuVCD9go2qzso1W34Pn07vC\n3CG8n0kJNAmKP7opZnRbPTcIp5gBNEtlUqzIBdCvypU0tO6ZCOH5AdqOT3SzpHyFSTMlg3Q+LtE0\nlrlyHl3Xh0Mwfy20GcG1OdgvSEb+uh7N1B/C176U9zOAqM16Lrmcb4B2PX7KwTmAppORBiyY96FJ\ntM4rQPflquMF6Lp0nYy+F6BHMX+NaBRL5a81qR4wBA9lym3YqaYXzBOOYtG9MSMsmMmKP8I2oz7P\nCK7NNGDBvA9qgpB8JEP05aoSVvMzBG02EFdNYleYPddH3wtoHjBEr32llGTFH/U8SZKHMuE8SbLz\nTIk/YmsTCMdE89ykK/4aXaI2I+xkpAEL5n2gWhoHoPtylbLNqG6WVF9HA3Q3y54bwPUlzXlWonnt\nGzoZRNMLynSvfammsVA9AwC6jhnl2x+6FbloBk3SggXzPgzbyBIWMtQiMlTbFQN0I39U2xUDhG1G\n+vaHppDpOD78QNK0WYmmMxsEEk2CzauA0R5LbW0CKiWD3n6m8qpJ2oxoSkbRzqGUt0jaLA1YMO/D\nKPJHb+GTjZZSjjATjZZqEWGmOs94bY4N1da7AF0no+14CCTNtVkt0rzJ8AOJZp9mU6F8zsJMIUdu\nngF0874B2g/mk4YF8z7QFn80rzApi795oldLpOcZ0aty0qk/RNfm0GYE1+Zs0YYQ9NYm5Xlm5yxU\ni/TaY7d6dG9mAZpNcihX5AJoV+VKGhbM+0BZ/JGNYg3TCwjajGyEObQZya51VCPMhNdmpWDDEgRt\nRnhtWpYYiD+iNiO4NoHQOSM3z4Y3GURtVqbnZFCuyAUM5hkxm6UFC+Z9aHQ95CyBSiGX9lDugq74\n0yC3lNoBQzjyN1PIwbYEvXlGOO/bsgTJ9tiU01iAQatnamuTcBoLQLMNu4rKUzwDAJoRZsrnJsAR\n5t2wYN6HMAnfhhC0Ou8AdF+u7nRd5HMCpTy9aVW0LRRyFjlPmfK1rxCC5GZJOcIM0GzDTl78EcyT\npOzMAkTFH3WbEdzPKJ8BAM21mRb0lA0RqLaRBUYvV6lNYlVOiKKTQVn8FWwLpTy9mwyA5nUc5bxv\ngGYbdvpChuA869FNYwFUhJmazWivzXmKNiNckQtQtz+0bJYWLJj3gWotSQXNKBbNdsWKubJNz2Zd\nmi/KFXNlmvOsnM+hYNPcvihGZEbij2ZKBuVoKd2rcpr7GUA39WeuRNBmhCtyAaN5Rq2zcBrQPHEI\nQLXIv4JktJRou2IFTSFDs2apgqqQYZtNRqProlLIwc7R3PIp5uOqv2GV6J5Gcp5RT5cq59HsuQgC\nOuKP/I1ZKQ8/kOg4ftpDSZ1Idk8hxANCiKeEEG8LId4UQvzVwdf/hhDihhDilcE/vxDF5yUB/Qgz\nxStMumksgHIyiNmM+jwr06tesKOFzWjNM8opZoASf/RsNlu0kbPopZgB4X7W6nvkxJ8QQLVA18kI\nZFhjmwo6OBkAvQfzaRBVuMED8F9LKT8J4KsA/jMhxKcG/+07UspHB//8SUSfFztUO+8o6EaYCdus\nZKNJTPyRT2MhKGTIO2ZEI3+k12bZRqvvwfODtIcypNGlvjZtSAk0+3TWZ6PnYbZowyLrZNB7ME+5\nIhewuyoXHZulRSSCWUp5U0r5k8H/3wTwNoCTUfzutGh0PczPUN4sKV5hEj9gCDoZzS7N1ruKeYpX\n5V2PdOrPfDmPjuPDJSf+aNsMAFqkxJ87bKdMEYodEhtdl/y5CRCzGeGKXMBuJ4OOzdIi8t1ACHEK\nwBcAPA/gLID/XAjxqwBeQhiFru3xM98G8G0AOHHiBNbW1qIe1li0Wi2sra3BCyS6ro+tm+9jbW0j\nlbEcRut2H9sNLzVbDccxsBkA1Np97Ny6ibW17VTHtB/1TQf1tounnnoq1c1pt81uNdpolfup/x33\nY+umg74X4MnvP4VCjobNNmodVAKLrM02rocHy59+/4eYK9Cw2QdbXSwUBVmbfXAjtNmTa+dxz0x6\neda7bfbezS4AkLXZ+xuhc/GD88/iobn0opO7bXbpeg+WJ8na7Mp2mIf7F8++iI1FGja7cLWHPAKy\nNru8E9rsRy/8BO2r6TmQu22WFpH+rxdCVAH8MwD/hZSyIYT43wD8BgA5+L9/H8B/dOfPSSm/C+C7\nAPDYY4/J1dXVKIc1Nmtra1hdXcVWqw88+ed49FMfx+rjp1IZy2G82H8Hf3HjMr7+9a+nKv6UzXqu\nD+/P/gyf/vhprK6upDaeg3gbl/AnV97B4+d+JtUybspmUkr0vven+MQjD2F19ROpjecg3i9exT9b\nfxNf+PLXcHy2mNo4lM0AwP2LJ3HmofuwuvqZ1MZzELWXr+Mfv/0qPvvFL+Ph5Upq49hts+CFH+D0\n/YtYXX00tfEchPvWBn779Zfwyc99CZ+9fz61cey22W+++jROLpSxuvpYauM5iOKlbfwvLz+Hj3/6\nUTz+yFJq49hts3/4zjO4b9bC6upXUxvPQSzf2MHfe/E8Tn/iM1j91InUxrHbZr975QWcsBysrp5L\nbTwHcWqrjb/17BoeOvMJrH7h/tTGsdtmaRGZKy+EyCMUy/9ESvmHACCl3JBS+lLKAMBvA/hyVJ8X\nJ9RfrQLh2DxCL1epP1wARldLVMoK9dwAri9pz7PB35OKzaSU9CvYULz2JZ7GosZG6dqXfDUWYvsZ\nQD/1R61NUjajvp+pM6BDx2ZpEVWVDAHgdwC8LaX8B7u+fu+ub/u3ALwRxefFTYN4b3eA3stVyu2K\nFdSEDPX6m8AumxGZZx3Hhx9I0nnf1NZmEEg0e7Rz5Unm41K3GbG1CejxuBQgNs+IP5afLdF7KJkW\nUZ3UZwH8hwBeF0K8MvjafwfgLwshHkWYknEVwH8a0efFii4RZiAUqvemd4M5RI8IM60DRot5RuyA\nod5GFqD3qrzleAgkr81J8AOJZo9+UyGAztoEVFSers2qRYI3GcSdjHzOwkwhR2qepUUkgllKeR7A\nXom02pSR240e4o/WwtdC/ClPmYiQ0WKeDaNYbLNx4bU5OdTWZqtHu10xAMwWbQhBZ216foC245Oe\nZ3bOQrVIq0469TQWgGapzDSg2fYpZdRi0uI6jojXpzZt0jYjFsXSYZ7NE4tijVJ/2GbjQr1dMRBG\n/ixBaG0qx4xwiplliYH4o2Gz5vAMoGszYND0i8g8c7wAXdcnfQYANJsxpQEL5j0YbZZ0J/E8MfE3\nvConvFlSEzKj9AK6NqPnZNCfZ+V8DrYlyDws0mE/E0JgrpwnY7PRfkbXZsCgTjqRtamLzSi1Ydfh\nxgygNc/ShAXzHux0XeRzAqU8XfNQe7mqw7WverxA5VDWYbMs2hYKOYuezQjPMyX+qBwwDV2EDKFm\nTDrMM4BtdhQoOWY6nJtAOD4qNksTuoowRdSrVaqddwB6L1cbPRcF20q1vvFhFO0cSnmLjs0GGxDl\nbmKh+KNzHaeP+CNksx79NBZgcO1LZm3ST2MBaF2Vj2xGfJ6V8nTmmQYVuQCaXXLTgAXzHlBv8QzQ\ne7ka1nmlbTOAWkTGQylvoWjTdTIAWg8+RuKPD5hxUfOdfJ4kqbWpkc2ozDMNymQCyskgYjNtIsx0\nHLM0YcG8B2GEmfaiB+htltQ3SoCekKG+UQLALKGcv52ui0ohBztHe+uiJP7UVWqV+J5Gaj/T5SaD\n0NrUR/wRmmcapOUB4fiaPRdBINMeSqrQPnVSIhR/tCcwQO06jnaRfwUlT5l6YwRF+KqciM2I13lV\nkEov6LmYLdrIWXRTzAB6+5kQQLWgg5NBxGa6ROXLebT6Hgnxp0OlJCCcZ4EE2g6NuZYWLJj3QJtD\nmZKnrEm0lFKEeUeTeTZfzqNJJYpFvMi/Yp5U5I9+ihlA6yV+o+dhtmjD0sDJaPU9eH6Q9lCw03WR\nswRmCtRTzGxICTT76Ys/HRoxAbtry6dvszRhwbwHO5rk41I7YLQ5lCkJGeLX5AAtJ0OHIv8ArVfl\njZ5L+mGpYq6UR8fx4RIQf7oETVRkskVA/Kn9jPJjeYBWedFGj35FLoCWzdKE9l8pJXTKxyVzKGuU\n903GZrqk/gxsJiWBK0xNIsxz5Tz6XoCe66c9FG3EH6VWz9rMs8EYKexp2uxnZUI206AiF0BrnqUJ\nC+Y76Lk+HC/QZLOkkfMnpdRoswxzS0mIP23SWGy4vkTPJRD502WeDZzHJoErzEZPjxszSte+2txk\nDJ0MCjbTZD9TXXIJ3JrpcjNLyZlNExbMd6DLq1WAzsvVnhvA9aU2m6UfSHScdCN/oZOhyaFM6YDp\neuQfyAC0OiTq8yCXzqGs04NcgMg802U/U44ZGSdDA5sNz4D0bZYmLJjvYFh8XZNJTOHlqi71NwE6\nQqbj+PADTZwMItGFIBjcZGiyNoH0babGwGtzMnZ0iZYSWZtqDFrYjFIAQJcbs6GTkb7N0oQF8x3o\nUhoHoHOFqUtjBGC3kKHhZOhhMxpRrJbjQcr/v733j5Hsyu77vreqXv2u7qrpni4OOeQMZ7qGWmq1\nS3IpLrXkapu7VrJSDK8COJAV21kkChYBFEQyZDiSEcCODQOO40gxgkDISitrASmrKLIUyYIlmFpz\nTPaQy19L7vI3u2c4w+FwODNV1b/q56tX7+aP915VTU93df1479137z0fgJiZZrPrzeG975z7Peee\nI0v2Jxp7s29z7HUlKcmIyN50nkGWQCZawZ8U77OoHTIksFk+FQ0fIBoKmPchS8N6IDoqliytcYDR\nQCYiNpNgnS1GpE5SlsEIQHRulTc6cowrBkZsJnhvWn0bTbMvxTobHGYjcMiQpU1mIZUAY+IPs4A8\nHbkS8RjyqWjcmRIJBcz7kCn4i4pTlqnuOzI2G5T+RN9mUVGxBjaTobwgIrfKB3tThjIW9/+raJvt\ndeRZZ/lUAjEmfm92rT46PVuKdRaLMRRS0RiPLUtHLiBabWxFQQHzPnYlellGpT2ObHXfQBRsJlHd\nd1Rs1pHnMBuVQ4ZMmYyMEUcixoQHMjKtM8ZYJNqL7kmUyQCiMVJcpo5cAFBIJ4SvM9FQwLwPmdK+\nUbm5KpPCHJX6NZmcciEdjQsfMpVLpRIxJOMx4SlMmdaZF/yJPmQMMxnRtxngTnyNyt6UYJ0B0ZiS\nK5PfBKJxyBANBcz72O30kEzEkDaiPd4TiM7NVe/zZZgmNgj+RB8yJAr+0kYcqURMvM3cz5fhYpET\n/CXEO+W2PDYDotFbXqYLucCwt7xIZMrMAq7NRK8ziTKzgHfIoBpmYoRdSYrwgejcXN3tWEgbMaQS\n0T9kGPEYssm4+EOG++KR4ZABRENdkOl+ARAx5U+aQEa88rcjm82itM5k2pvC/aY8ogngHTJIYSZG\ncFrjyPGijMrNVVkGI3hE4mXZ7iGXjMOIy7EFF9JRUEudz89LcsgoZMQrMtI5ZQr+piYS7zPpVPno\nrDNpbBaBdSYaObx1iMjSF9EjCjdXZWny77GYMYQfMmRpweQRBZvtdnoopBKIx5jQ55iUxYg4ZcaA\nfFKOQ8YiHTKmJgp7U6bLpUA01plsGbPFjIFG1xI+WVgkFDDvQ5ZpRR6FtPg0iSzTijwiUVvakWud\nRSFVvtu25FpnkdibFgqpBGKSHDIWMuJv4u+2LcQYkEtGv8QMiMj7TKI2mYDznI2uBatvC3sG+eq+\nDXAO7HX1rWOmgHkfux3JnHIEWgo5dd9ybHrAeVlGwmaSvCiBiNis05Om5huIyiFDssNsFEoyXAGA\nMUkOGWkDLbOPntDgrwcjzpA25AgpvHfvnkCVWb7Sn2g0GRCJHKs7RByFWSKnHIGbq/IpzBEIZKRT\nmCOglkoZ/FngXFwKU751ZqBr2ej0+sKeQbYsYxRaZXo2k+mQAYi9MC9TRy4gOnMfREIB8wiccwmD\nv4gEMjI5mHQCO60IBMwyrTP3YCY2+LOkuSADOHvT7Nvo9AQqf23JbJYW3/lHxnUGiA1kZMzMAoJt\nJlFHLmDkkEEBMwEApg30+lyql+Wi4JIM55AhV3nBYsbAXtdCX+DlBdnKWBYzBvo2R0Ng/ZpsVvOa\ncwAAIABJREFUB7PFCDhl53KpPOssCmqpbDaLwjqTLTMbCZtJNBYbiIbNREMB8witnhNAyeSUS9kk\nGl0LpiVGxer0gb4t1yGjmE2Cc3FO2XYzGTLZrJRNAgC2BSrzu5IFMp7NtlqmsGeQrSRjaDPRwZ88\nNitGYG/K1vWnlHWeVfQ6k8oH5MTbTDQUMI/QcsUzuZyys4i322KcspSHjMHGF2OzjgVwLk8LJgAo\nZsXazOYce125UpiibQbIV/c9CJibdMiYlMgczCRaZ8NDhuC9SetMKihgHkHG4E+0ujA8ZMhnM1En\n5ZYl3zor5cTarC3hOhOtyvdtjqbZl2qdeYcMsZkMuUrMoqGWSnqYbVLd96SkjTjSRkzoIUM0FDCP\n0PQCZokWsWhFRsZDRkmwujCwmYROWbjNJKqTFK3ItGXMmOXE2syyOdo9uQ4ZC2kDMSZYLZWsHteI\nx1BIJcRnfyR6nwHOO41KMggAI2qpRIt4oMgIqscdqKUSvSxLglWs4TqTxymLz2TId5gVrZbKmMlw\nxsUzge8z51eZ1lksxrCYMYStM7PPYVq2VOsMAIo5cRfmZezIBTh+QGT2RzQUMI/QklBhLkZG+ZPI\nZhmxKpaU6ywjth7Xe0fLdEkmbcSRMeLC96ZMNmOMuU6ZbDYNjvInyGYSHmYBxw+IspnXkUsmvwk4\nfoBKMggAcioyom+Ve4qMTA6mkE64KUyxyp9MNku4KUxRNmtKeDADnAOtqL3plWfKF8gYwmpLZSyX\nAoDFrDiFWcbDLCB2b0p7MMsZdOmPcGj1gIwRRzIhj1myyTiS8ZhwtVSmkcWxmKNiibLZIJCRLfgT\n+LKUsfQHgFi1VFKbRUItlWxvCrWZhPcLAMdm4jIZzq+y7U0qySAGtCwu3QJ2UpgGtgUqMrlkHIm4\nXEupKFSRcRxMXkIHI06RcX6VTS0tRUDFki34E7s3nV9lW2dCbSZpSUYpa4i7LC/twczAdrsndOKr\nSOSKcgKm1ZOvpggQrcjI96IERNuMo5BKIB5jQj5/VkSrpYwB+aSMhwxxexOQb3+K3puAjIGMSIXZ\n+VU2mxWzSex2LFj98Id+ydiRC3DWWd92pvvqCAXMIzgKs1wLGBCvLsj2ogREK3/yvSgBz2bi0r6F\nVAIx6Q4ZYjMZMeZ0npCJYs6xmQgVS9Ya5lLWQMvso2v1Q/9seUt/xI16lrEjFxCNgS8ioYB5hFZP\nvgUMiFYX5CtjAcSrpTLVfHuUsklxpT8SZzK2WyZsW0Dw5woAjMl1yChlkzD7NlqmiOAPSMQYMoZk\nhwyBbR9lLf0ROYxJxk5JQDSG5IiEAuYRZFWYnZurAgMZyV6UgHi1VMZ1Vswa2Ota6AlIYbZ6XLob\n5YBjM5sDewJSmLLarCRwpLhnMxkPGYAgm1lAMhFDWtpDhgibyXnIKAoexiQaCphHkNXBeGqpqBSm\nrDbr9Gx0emJULBlt5jllMSlMWUt/xDmYpqSHWZFqaVPSw2xJ4KhnWX2ASLVUxo5cgPiJr6KR6/9W\ngHDOpVZLLZuj0Q1fxZLXwQhUZCS9XCpySI6spT+lnFi1VEqbCVZLZSzLE6mWNi0upc3ErjPJ96ag\n0jzRUMDs0jT7sLl8FxeA4eS6sBUZ2+ZoS+tgxI0tlv5lKcRmch5mB4EMqfITI3J0vazlUt7BTMg6\nk9Rmi96lP1HrTMK96dyJELPOogAFzC677gKQcRGLCv4apgUO+S4uAEObha0u9AeHDPlsNlQXRKml\n8tpMjCov5zoTXVsqo83Eq/Ly2ayQSiARYwIVZvlsFo8xLKT1HY9NAbPLbscNmCVcxMPbvuEuYpkP\nGSVBdZIN9/KXjOtM1MHM6tvo9OVcZ8WMwNpSSTMZXj2ssEyGhDZLG3GkEjFS5afAG/olqoZZxsws\nILYlq2goYHbZbbuBjIROWdSt8oHNJHQwohSZwcFMwpelKFV+ryPvOhukMEO2mWnZMCU9ZCQTMeRT\nCbpfMCWlbFJM9kfSGmZAXHtRWRVmQGxLVtFQwOwyUEsldMqibpUPgz/5Nr4otXSnLW8mIz9IYYpZ\nZzLexI/HGBYz4Ssye57NsvLZDBAz8KXT66Nny7k3AQhRSznn0g5iAsS1F5X7YCauJatoKGB2kdkp\nD9K+IS9imYO/tBFHxoiHrsh4BzMZ15mTwgxfXdiRuPQHEDNYiGw2PTKX5QHDITlh0u710edyvs8A\nTy0VcMiQtLUo4GUyqCRDa2Sux03EYyikE+ErzBIHf4CYWiyZVXlAjLowLP2R02Yi1NJdictYADFq\n6bAsT06bOQOsBO1Nep9NjMwduQAqySAA7LgbX8aRxYAoRUbul6WIjS9z3TfgrTNBhwypbUYXcqdB\nhFoqu8IsQi1VY2/2Qh36Jf/eNNA0+zCt8Ce+ioYCZpfdTg/puKPWyogQtdTd+HlZDxkiFBnpnbIR\net9S2R2MGIVZ7nVWyhrCyqVkXWelrIHtNgV/01DMJmFaNtohTnyVfW8Wc+LaPopGzugwAHbbPWQN\nJvoxZkaIWtrpIZNwLjbJiBBFpt0DA5BPSnrIoNrSqRGjMMuf/dntWLD64alYXsZsUWK1tG/zwd8j\nDOTfm+G3MJR9b4ocKS4a3wJmxti9jLFnGGPvMMbeYoz9kvv1Y4yxpxljG+6vJb8+0092Oz1k5XxP\nAhCkYrUtZBNyBsuAc1ky7IlFux0LmQQQk/WQkXPWWbgqloUYA3LJeGif6SelrIGW2UfXEqFiyflS\n85xyqMGfAmopEO7kOtnrvofdksI70MrckQsYnSxMCvM8WAB+hXP+KQCPA/hFxtiDAH4VwHc55xUA\n33X/HDl225bUCrMo5U92m223TNh2uCnMnOQ2M/s2Wma4wV824XTpkBExgUwPcQZkDEkPGQKGMamj\nloZvM1kvfotoySq/zUhhnhvO+XXO+ffd3+8BeAfAPQC+BuDb7rd9G8DP+vWZfuI4ZTkdMuAs4r2Q\nU5g7bflVeZsPB2OEwU67h4zE60yEU5bfZl7wF56D8fam7IeMMFWsnXYPCea0nJSRYjb8Q4Z3CCxI\nqsqLGGDltXyU1mYa1zAHEu4wxk4DeBjAiwDKnPPrgBNUM8ZWDvj+bwD4BgCUy2WcP38+iMcay9mM\niXTGEvLZflC95mzCf/dX/xELqXCc5Ee3WjiesqW12Q3XZn/5zHMo58Ip5798vY1MrC+tzT664Rwu\n/urZF3B6MZzA4uLVDrJxedfZlZqjxj/z/Eu4fiwcm713uYNsgktrs0s7js2effH72PsgnFP525td\nZA15bXa94Yglz7/6Q+B6ODb74ftdpOIcz68/G8rn+c12x7HZS6+/hXz9/VA+87UNEwwcr790ATEJ\nD7Rdy8nIvvrmu7irdSm0z200GsL3pu+7ijGWB/BvAPwy53x3EoWDc/5NAN8EgEcffZSvra35/VhH\nsrYGnD9/HiI+2w92Xr+G33vndTz48KNYXSmE8pnd555GKWtLazP73Rv4rTdewbkfexgP3xdOaf0/\nevkZHE92pbVZ5lIN/8dr38PZBz+DL1aOh/KZ/+sPn0Mx1pTWZsc/3sG/eHkdp889iLVPnwjlM3/z\nvRewaG5La7MztRb+yQvP4OSZB7D26L2hfObvXXkZi7tVaW1Wb5r4tfWnceLUWaw9cX8on/knn7yG\nhZvXpbWZadn45fN/geP3nMbaWiWUz3x66w3kP/wQX37qqVA+z28450ie/0scu+terK19KrTPjUJ8\n5qusxhgz4ATLv885/2P3yzcYYyfcf38CwE0/P5NwCDvta9scWy0ThaR8J2QPEfVr9YbcNhvWloZo\ns6bkNhNQkiG7zYq58EfX15omFpKhfZzvLGYMMEbrbBqSiRhyyTjZbAoYY9qOx/azSwYD8C0A73DO\nf33kX/0ZgK+7v/86gD/16zOJIQOnHFLv0u12z5lWJPkFNiC8+rWu1cde15L6ZRn2rXLOOWqSOxgR\ndZKyO+VCKoFEjJHNpiAeY1hIG6HWltYkFwCA8Fuyyv4+A8QMsIoCfirMTwD4uwC+zBh73f3nZwD8\ncwA/xRjbAPBT7p8JnxkGMuEs4nqzCwBSb/yw+0luNd3LHhIfMoYthcKxmTdRqiCx8pdJxpFKxEKz\nmQrZH8ZY6OOxZc/+AOEPsKo3TSzIbrOQB1jJfjADvDa2+inMvtUwc87XARy2Cr7i1+cQBxN2G6Za\nw/kcmTf+QtpAjIWnltYUOGQkEzHkU4nQ1lndW2cSHzIAV5Gh7M9UhKn8DbM/cnYu8AjTZpxzJ/hb\nkrOriEfYamm9aeLeY3LvzVI2iY2bDdGPETo06U8Rcsk4jDgLbePXm17AHMrHBUIsxrCYCU9dGNpM\n7pdlmENyVDhkAAhVLVUh+wMg1DpJFbI/QLg2a3QtmH1b+nUW5iGjr0D2BxAzWTgKUMCsCIwxLGbC\nW8Q1ZYK/8NQFVQLmMIfkeDaTPu0booNRIfsDhDu6vtpQ5ZCRHAT/QaOCaAI4E1/D8gHbLROcy7/O\nPNEkzImvUYACZoUohan8KeOUjdAmsFUbagR/YaqlqqyzUi68Mew1RQKZMN9nqhxmi9nkYDBG0FRV\n2ZtZA7udHvohTHxVRWgqZQ1YNkejG97QryhAAbNChKv8dbGQdm6yy0zYNovHGLJyl0mGq5YqojCH\nmcJUxWaUyZieUtZwSiWs4Ce+qmKzYjYJzp1x8kFTU0Y0Cb8laxSggFkhwq0tNbGUT4XyWUESps3q\nTROlbFLK6U6jlLJGaBfY6s0u0kYMKYlHYwNDtTSMFKZ3UTKvgFPuWjbaZj/wz1JF+St6Y4vbwe9P\nZWrlc163pDBspsY6E9EqMwpQwKwQYSsyx3KS53wRrs1qDRNLCthsMZvEbseC1Q9exao1TSzlFDiY\nZZKwbI69EFKYqmR/itkwAxk1sj/FTHjtRZU5ZIQ4WGh4yAj8owIl7JasUYECZoUo5kJUsZQJmA20\nzD66VvAqlko2AxBKraQqNhv0SQ/hQpYq2Z9SqAGzKtmf8AZY1RsmMkYcqbgaNgujZMo7ZOQl78ZS\nDNFmUYICZoUoZZMw+zZaIaUwVVBLw6zFqjdNHMvLb7MwRz2rEjCHmcJUxWZh7k1Vsj/FEJU/VdZZ\nmGppvWliMWNIn/0Z2Cyk0ryoQAGzQoSlyNg2x5YyL8vwAhl1DhmewhyCzRQJZMKuk6S9OR01VWyW\nC1ctXVJAAAhTLVXFByxmqCSDkJywFJndTg+WzdVwMIOTcrA26/Vt7LR7itjMS/uGUV7QVcJmYaql\nVVUOGWGrpQoEf2HaTJW9uZBOIB5j4RzMGmrYLBGPYSGdoJIMQl7CUmS8OqxlBeokw1IXvNSVGrWl\n4ayzlmmh07PJZlNgu5PElFL+Qkj71hpdLCsQyGSMOJKJWCiBTL2hhirPGAtteEldEVUecLIZpDAT\n0hJW/ZrXGkeFl2VYNvMOGSoof8VcODfxvZ6lKthsMWOAseDXmTeA4ZgCnUWSiRhyyXjgNuv1bex2\nLCVsxhgLZTw25xy1pqmEaAIAi1kjnENG01RinQHehERSmAlJGdSWBq0wN9QJmAc3pAOux1XpkFFI\nOS3Lgn5ZqmSzeIxhIW0EvzcVOpgB7sCXgPeml/1RoSQD8AYLBXvIcDoL2UrsTSAcmznZn55SezOs\nqZJRgQJmhShmwuleUB+UF8i/8TPJOFKJWPBqqUKBDGMslPHYdeUCmRBtpsA6A9yR4rQ3pyKMYUzK\nrbMQ9uZO28v+qGQzUpgJSUkmYsinEiEof07zdXU2fjLw9jj1hlo2C2PUs3qBTPBDclTK/gDhDBZS\nL/gLYZ0puDdDe58pIgAUs8lQ+spHCQqYFSMMdaHWNJFPJZBKxAP9nLAISy1lbHiRSXbCqF9T7WAW\npvKnilNezARvs6p7mFUn+AvjfabW3gxDLVXxYLbXtdALYeJrVKCAWTFCURcUuR3tUQpBXai6k8Ti\nkjes9yiGUPNXa5hIxp2siQqEszdVC2RIYZ4WTy0NcuJrdXAhV5ELbNkkOj0bnV5wQ7+U25shXf6O\nEhQwK0ZYaqkqChbgbPzAnbIivXE9SiFlMpbySTDJxxV7hJX9KSiU/SlljUHtZ1DUmyZiCmV/SlkD\nls3R6FqBfYZ69wuCb/uoUjtWQM/x2BQwK0YYaqkq04o8wlBLVZm+5uH04Axe+VPKZtkkGl0LphVc\nClOVARwexWwSnAO7Ad7GrymY/QGCVf7qTXPQ9k8Fwhhg5R0ySgodzAC9pv1RwKwYpawR/AU2RSY8\neZSyBrbbvUBTmLVmVylVvpg10LVstM0AU5jKBcxuCjPANmnKHTJCGCmuygAOj1DU0oaJ5ZxK2Z/g\n1dJ600QhnUAyoUbYFebo+qigxv85YkAxm8Rux4IVUCE+51yp5uuAs/H7NsduJ9gUJjnl6ag3u8pl\nMoBglT8Vsz9AsCqWenszeOWv3uwqlckYHsxob06KN/eBSjIIaRkMLwkohenciuVKbfzFTLAbv29z\nbLd7ih0ywlL+VLKZG/wFmAFSL/sTvPJXVS77E45aqtLeHM4woL05KWEcZqMGBcyKUQp4EdcV6/MK\nBG+zrZYJztVpWwUEr5Z2en00zb5igUywKpaa2Z8w1FJFFeYAD2aklk5PTTEBIJeMw4gHP/E1SlDA\nrBhDhTmYRVxT7HY0MNoeJxibqda2Cgi+JENJm7l/l6D2porZn6DVUqtvY7ulVvZnkDEL8KKkaoeM\ntBFHxogHflFSpb3pTHxNYocUZkJWhmnfYBax10tyWSEHE7RaOhiMoNIhI2Dlrzbo80o2m5SBzRRa\nZwvpBOIxFtje9P5fLCtks0Q8hoV0IjCbtc0+WmZfqYAZCHY8tpf9UWlvAvqNx6aAWTFCU/4U2vhh\n2UyVJv8AsOilMANK+9aa6h0yMkYcyUQswHWm1mAEwFWxApwqqWImAwi27eNgbypmsyDHY++2LVg2\nV26dFbNJqmEm5KUY8PSdWlM95W8xY4CxAOu+FXTKqUQc2WQ8BJupc8jwgr/twLI/6h3MAOdwFtz7\nTL1DBuCNrqf32TQEOcBKRQEA8AZYkcJMSEohlUAiFlwhfr1pIpuMI22o0bAeAOIxhoV0cBvfC2S8\nlLwqlLLJwHoKK+uUAxz1rGL2BwjHZqodMoJUSweiiSIT6zyCHGClogAAeHuTFGZCUpxC/GDVBdWC\nGCDY+rV600QxayARV2u7BTnqudY0YcQZFtKJQH6+KIK2GaBW9gcIdm/WFOz6AwRbW1pX8H4BEKzN\nVN2b3sEsyKFfUUItD04ACF5dUG3TA8HaTN1DRoDKX8MZV6zKJDGPoNVS1bI/QDhqqWrZn2I2GVjp\nj8qZjJ12D7btf/CnbsbMQK/P0Qxw4muUoIBZQYK9JKNW83WPYqDqgloT6zyCVktVXGdOnSRlf6Yh\nULW02VUy+1PKJt02g/5PfPWyP4WUWtmfxYwBmwO7Hf/3p6oBczGEnt9RQq23BAEg2FqsWsNUrnYN\ncJW/AC9jqVYjCQSrltaaXSwruM6CTGFWG10l92Yxm0SnZ6PT81/FUq03rkcpwMvftYYjmqiY/QGC\nufxdbXSRTyWUzP4AwTUZiBoUMCtIUIoM51zhkozgLv3Vm6Zy6UvAWWc77R76AaUwVVNjAMdmls3R\n6Fq+/2xlg78A2z6qepgNcuCLatMkPbxDRhDrTN33WfAjxaMEBcwKUsoFozA3zT5My1Z243t/Pz+x\nbY6tlpqBTDGbBOfAbgATxeoNNR1MkIqMuk45OLVUeZsFsDfVFU3cSZy0ziYmyHUWRShgVpBi1kDX\nstH2uRC/ruiNcmB04/t7Ut5u92BzRW0WkCLTtfrY61pKOuVSQAGz2tmf4FQsdbM/3sRXUksnJfhM\nhno2C3p0fdSggFlBgtr4qjZfB4JT/lScvuZRDKjmz6slVzOQCeaQoXT2J6B63L7NUVc2+xOsKq+i\nDwhydL2qh4zhpT9SmAlJCcopq9p8HQhOkVF1+howqpYGdDBT0sEEc5hVO/sTjM2cy5dks2noWn00\nFM3+LKQNxJj/7zPOubKZDCMeQyGVoBpmQl6CUktVbb4OjJyUfVeY1Q1kiplgVCyVD2ZBKX8qZ38W\nA19n6tksm4zDiLMA32fq7c1YjGExgJasja4Fs28r6TcBoJjTZzw2BcwKElhJhsoqVi4YtbQ6GCOr\noM1onU2Nd8gIzmbqBTJpI46MEfc/+6PoWGzAm/jq/8AXlfcmEMyoZ5X3JqDXeGwKmBUkqFqserOL\ntBFDNqlWL0kgQJs1vEli6jmYQjrhpjCDyWQsK3jISMRjKKQTgamlqqpYQYzHrit8mAWCaS9aU9xm\nQbQXVd9mwU3ijBoUMCvIopf2DUCRWcqllGtYDwAZI45kPOb7xq83u1hIJ5BMqLfVYjFHxfK/Vr6L\neIxhIa3WuGKPIAa+kFOeHpVLzAC4e5MuMU9DMYABVqofZp3JwqQwE5KSSsSRTcYDUWRUfVE6Kcxg\nFBkVp695BDEeu940UcomEYupdzADglJLveyPWuOKPZyR4sFclCwp+k4rBaGWNhQP/gKwmeqHjCBH\n10cNCpgVpRSAIqNywAwEU4ulh838d8qqOmQgOLVUxVpcD8dm/l+UXEgnYMTVdINBvc8Symd/gros\nr+b+LGaT2OtYsPr+Dv2KImq+KYhg1FLlA5kg1AXVA+ZgakvVtxmts2kIqh5X7exP0m2d59/o+nrT\nRCmndvan3euj0/Nv6Fe9YSJjxJFR8O4PoNe0PwqYFaWUTfq+gNV3ykGoWKofMgLKZChaiwsEo5bq\nsDd32j3Yto/Bn6Lj1z1KWQO9PkfLx4mvOrzPAGDHR9+p/N4cdJiigJmQFL9rS1umhXavr3Qg49RJ\n+mcz2+bYUv1lGZTyp7TN/E9hqp/9ScLmwF7H8u1nKh/IBND2kWw2PTVFJyN66DQemwJmRfG7ttS7\n7LGsaB0W4H8Kc7fTg2Vz5dO+nZ7tWwqz17ex0+4pW+8HjIx69lHFqjW7SjvlIKaX1pqmkq0LPYIY\nklNrdBUPmP0f9VxrdpU+zAY5UjxqUMCsKKWsgZ12D32fUpgqT8XyKGUNWDZHo+uPiqV62ypgdDy2\nPy9LbziFypkMvxWZlmmh07OVHYwA+K/82TbHVktxtTQXkFqqsM2CUEud0h/amypAAbOiFLNJcA7s\n+qRi1bUKZHy2mdIOxl/lT4dDxnDanz/rTPVWX8BIb3mfbLbbccQElQMZv9eZadnY61hK28zL/vhl\nM865BiUZ3t6kgJmQlOHGp0BmUvw+Kas+RhbwP2DW4ZAxWGc+DRbSymY+rbOqBocMv9VSz/YqiyZ+\nr7OW2UfXspXem/lUAokYo5IMQl6KGW/j+6WWqt18HRgN/vxVmFVWF/wuydDhYOZ3bakO2R+/6yR1\nOGQUfa7HHd5jUddmaSOOVMK/ia86rDNv6BcpzIS0+J0mqTVNJOMx5FNqThIDRvpJ+vayVP+Q4bci\nU29oYDOfa0t1OGQspA3EGO3NaTDiMRRSCcr+TImfw0t02JtAMCPFo4hvATNj7HcYYzcZY2+OfO0f\nM8auMcZed//5Gb8+jxjPMJDxSZFxe5YypmbDemCYwvQrVV5rmsinEkgl1GxYDwSjljI2/H+hIrlk\nHEbcvxSmDsFfLMawmPGvhWFNg+wPABRz/il/NXedKW8zH9VSHfYmoM94bD8V5t8F8NUDvv4bnPOH\n3H/+nY+fR4yh5HP9muoXF4BgLmOpbrO0EUfGiPt2yKg2TRzLJhFXdJIY4KUw/Rv4UmuYSCbUzv4A\n/ip/dQ3uFwA+q6UDm6l76Q/w12Zerfyywq1FgWCGMUUR3wJmzvmzAOp+/TxiPgrpBGLM37Sv6s4l\nEY+hkE74Wr+mus0Af8djqz59zcNPRcZr9aVy9gfwV/mrNU0UFM/+AP5O4qw3TcTYUFhQFWeAFZWx\nTIMuCnMYksR/zxj7rwC8AuBXOOdb+7+BMfYNAN8AgHK5jPPnz4fwWHfSaDSEfXYQ5BLA25tXcD71\nydw/6+NqC9li7A77qGazNOvjvcsf4fz56tw/68qNNpbSTHmbJWwTm1ev4/z5O7b21Fz6uI0YoLzN\nmNnG5Y9bvvydNj7sIMm58jbrtzv4aPvOv+csvPtBB5m4rbzNzL0Oru/c+fechTc3usgZwLPP/sfb\nvq6azVrbXdzasXz5O73+rgkjBrz0/HO3HWhVs9lezUS92cMzzzwT2ME9CjYLOmD+TQD/FAB3f/3f\nAPw3+7+Jc/5NAN8EgEcffZSvra0F/FgHc/78eYj67CA4/up5ZIsLWFt7ZO6f1foPf4lPnbkPa2sP\n3vZ11Wx295vrSGaTWFt7bO6fZT7/Vzh36jjW1j5729dVs9m9m99Dp2djbe0Lc/+sf/rqeTxwVwFr\na5+77euq2ew7V1/B5WoLa2s/OffP+o23LuC+YgJra5+/7euq2ezf3vwBvnep5svf6bc2v4d7jD7W\n1p647euq2ez87lt4+/sf+fJ3+s7VV3CX2cTa2pdu/wzFbPZy9108d+0SvvSlL80d/P3bmz/A8a0q\nnnrqqdu+rprN3sFF/MUH7+LzT3wR2WQwYWUUbBZolwzO+Q3OeZ9zbgP4LQDzRyHExPg1HrvT66Np\n9pWvxwX8S2Fyzt2SDLVr1wD3hjSVsUyFn6Pr64qP3vXwtYylofbEOo9i1sBux4LVt+f+WTrtzb7N\nsduZf+JrvdlVut2jhy7jsQMNmBljJ0b++J8DePOw7yX8x6/aUl3qsAD/nPJe10Kvz7VwyqWs4cuF\nj77Nsd3uaXPI2G71wPn8o+tVH73rUcol3UEQ/bl/lk7BHwDs+DDxtdY0lb+8Bvg78EUn0QTwr8NU\nVPGzrdx3ALwA4AHG2EeMsV8A8C8YY28wxn4I4CkAf8+vzyOOxi+1VKeAuZhNYtuHfpK63MIHnCE5\n2y0Ttj1f8LfVMsG5+j1LAUf5M/s2WuZ8wZ9O2Z/FjD8tDDnn2GrpEsj4p/zpc8jwz2Yit4QkAAAg\nAElEQVTehVzVKfncXjSq+FZswjn/+QO+/C2/fj4xPUWf+pZW3WESyxo45WLWcNVhG0Z89vOkLj1L\nAcdmNgf2OhYWs7PfoPfaVulgs9LISPHcHO3gdBmMANw+JKe8kJ755+x2nOyPHu8zf9TSXt/Gdqun\nRcBcHNmb86JP6Y+/w5iiCk36U5hSLolOz0anN5+KNVSY1Vdk/Br1PAj+NLLZvC/LmiZN/oHRQGa+\ndaZTJqPk06hnnTJmfqml3t7W4TDr1yGjbfbR7vW1qmFWfTw2BcwK49dJWScH49dI8YHNdHhZ5vxd\nZ3TImBy9Mhn+BDI1Dcave/i1znTyAQObzXkwG+xNDWw2VJjVLsmggFlh/Nv4Jow4w0Ja7UligH8j\nxXVKlfumlmrllP1R/rTK/uT8sVlNo4OZbwKARpmMxYwBxnwUTTRYZ8lEDLlknEoyCHnx82VZyqo/\nSQzwV5HJJuNIG2pPEgN8VEtdp1yaow5aFvxSS/U6ZPislmqgyudTCSRijA4ZUxCPMSyk5+8wVdNo\nbwJ6jMemgFlhBvW4c7YU0mEstod3yNjxQfnTxWZ+3ZCuN00UswYSc1y2lIWiTzbTKfuTNuJIG7G5\nW6TVNcr+MMZ8CWR0OpgBbqvMeddZQ591BjgZIKphJqTFP0Wmq0WNJOBclAT8qC3V43Y0ACykDcR8\nSmHq4pCNeAyFVGL+valR9gdwB77M2eu11tAn+wN4fdLnf58xpkf2B/CnJatOmQzAG8ZECjMhKX6p\nWLo0XweAXDIOIz5/CrPe7GoT/MViDIsZP1KYekys8yjm5h/4olP2B/CmStLenAY/pkrWm10UM3pk\nfwB/Blh52Z/CHG0jZcKvuQ9RRo/VrylpI46MEfdFkdElkBmmMH2wmQZTsTz8cMrOOiObTUOt2dVi\n+pqHX2qpTnuz6MMkzlpDr4OZk8mY12ZdLOVSGmV//JksHGUoYFacpXwSN/e6M//3XauPva6lTcAM\nODVn89iMc65VSQYw/zoD3EyGJulLwF1nuz7YTKt1lpp7nekkAAA+2ayp12F2uZBCtdFFf47ppdrt\nzVwKO+3e3HMfogwFzIpz9ngemzcbM//33ilbp0Dm7Mp8NmuafZiWrdXL8uzxPC7OYTPbdsYV6xTI\nnD2ex8VbjfmcsmbK39njOVzdas3llHULZM4ez6HeNAf9p2dBR5t1LRvXttoz/wwnk6GRzVZyAICL\nt2b3A1GHAmbFqazM55R1ar7uUVnJ4+pWC21zNqesU89Sj9WVPGpzOOXtdg8218tmlXJ+LqesY/an\nslIA57M7Zc456pplfyrlAgDMJQLolv1ZXXFstnFzb+afodsho7Iy/zqLOhQwK865cgFdy8bVemum\n/16n5use58rzOWWdpq95nCt7DmY2m9U1Govt4QUy79+YzSnrmP2plPMAgI0bs62zRteC2dcr+1NZ\ncWz2/ox7s69h9mfVs9mM6wzQL2C+fzmHeIzN/D6TAQqYFWfVczAzBzL6qaWeg5lVXdDxkFGZc53V\nGvoMRvBYXZnTZhpmf04v5ZCIMR/2pj42O7GYRj6VwOaMgcx2ywTXLPuzmDFw10J65nXWtfpoaJb9\nSSZiOL2UnfkwKwMUMCvO6pzBX02z5usAcMpzyjNufJ3GYnvctTCfU9YxkFlIz+eUdTyYJRMxnF7O\nzb83NVLlGWNYXcnPLZro1FkEcESAWcsLdNybgFOWQSUZhLR4TnlzZgfTRdzts6sLA6c8r1qqoVOe\nNYVZdR3MskY2A+ZzyjquM8DJAM0cyGiYyQAcm836PqtqKJoAjti0ebMBe4b7P9ruzXIel2tNdC01\nO2VQwKwBlXIe78+hYpWyScRievSS9DhXzmNjZrW0i7QRQzapR8N6j3PlOVQs18GUNHPKlZUCNm7M\n6JQ1zGQATu335Vpzpk4ZNQ1r5QHnjsGtve5MPax1zP4Ajs1aZh/Xtqe/lKvz3rQ5cOlWU/SjBAIF\nzBrgpUlmPSnrtukB55b0h/XZ2lfp1rPUo7JSQLXRnWlQTr3ZxUI6AUOTSWIelXIe7d5sTrnuZn8W\n0vpkfwBHLbU58EF1eqesY0kGMN9dlrqGtfLA8C7LLNkMHS8xA6P3f9Qsy9DLO2lKpZxHp2fP6JT1\nuunr4TnlWU7KutpsHqes2/Q1j/mcsp7Zn3kumNYbppbZn0EgM0PJlHfI0C37M8/9Hx0vMQNOp4wY\nw8x3WaIOBcwaMGgrNMMi1q3/psfQKc9oM82cCzBfdxF9bTZ7azldsz9e+6pZSqbqmmZ/7l7MIJuM\nz+wDdMz+FLNJHC+kZrqXUW+aSMQYFjJ6HczSRhynlnJzteOLMnrtAE2prMzeI1e3Ec8eQ6c8g800\nDWTuKWaQS8ZnspmuAfNi1sBKITVjqlxPm6UScZyasX1VTVObxWJs5suSumZ/gNnvZdSbJkq5JBjT\nK/sDeBdMSWEmJGXglKd0ML2+jZ12T0sHM3DKpJZOjNcpY2anrKHNACebMXPArGH2B5jdKeu6NwHn\nXsZMNtNs/PoolZUCNm/sgfPp7v/o/j67XGvBtGzRj+I7FDBrgtO+arqX5VZLz/6bHrO0YmqZFtq9\nvrY2W10pTJ32tW2Oraap3UUsj3mc8rKuTnmlMJNTruu8zsp53NjtYqfdm+q/022U+CirK3k0zT6u\n73Sm+u+0XmcrBfRtjss19TplUMCsCZWVAjam7JSh49CSUc6VC7hSa03VU5JslsfNvS52WpM75d1O\nD5bNtWvy71EpO0754ymc8jD7o6/N+jafqlMG5xzVRlfbvTm8YDrdgbbW7Goc/M12/6fW6Gq9N4HZ\n7mVEHQqYNaFSzqNl9vHxzuSdMnTtv+mxujK9U9bdZt7LcvPW5C9LXXuWegzuGEzhYLzWffqWZHj3\nMia3Wcvso2vZ2gYy58reOps8a2bbHFstPcvygKHNpi0z07kk4+zxPBibrSNL1KGAWRNmufhHgcz0\nDqZOgQwATHVLWvtDxgyt5XTfm2eOO+2rZtmbutrsnmIGaSM2lQ/YaffQ1zj7U8olsZxPTrXOTMvG\nXsfS9n2WNuK471hWyRHZFDBrwsApT+NgGno2X/cYOGUKZCbmnmIGGWO6ThleGYuu62wWp6z7IWMW\np1zT3GaxmHMpl95n07E65QVT7+6PrusMmP5Sbt/m+LU/fgOvXtkK8KnmhwJmTXCccmqquqKNmw1k\nk3EUs3pufK+n5DSp8o2bezDiDOWFdIBPFl2GTnlym3k1lfcUM0E9VuSprBSmGl/vrcmTJX1tNu0F\n04HNjulrM2cU+/R7U+d15o2vn/RSrnfwvUdnm5UL+KDaRK8/2aXcN67t4DsvfTjTcLUwoYBZI6bt\n+nBhs4rHzywhrtkksVGmVWQubFbx8H0lpI14gE8Vbabt97q+WcWDJxa0myQ2SqWcx+YUTnl9s4b7\njmVxspQN+Mmiy7lyfiqnfGGziqVcEufcsiEdqZTzuL7TwV5nsku565tVZJNxfOZkMeAniy7nynns\ndS3c2O1O9P3rm1UkYgw/fvpYwE8WXSorefT6HFcm7JRxYbMKAPjC2aUgH2tuKGDWCKe13GRO+Wq9\nhcu1Fp5cXQ7hyaJLZSWPy9XmRO2r6k0Tb328iy9qbrNV1ynvTuCUW6aF71/ZxhcretussjK5U7b6\nNr53qYYndbdZOQ/Lnswpc86xvlnDE6vL2o0SH8W7YzDpgfbCZg2Pn1lCMqFvqLA65QXTC5tVPHJf\nCfmUXlP+Rpn2/s/6hiOaLEe8Hau+u0BDKuUCGl1rop6S3olPd6d8rlyANWFPyecvVsE58ITuNpvC\nKb/0QR1m38YTmh8yKuXJR2T/4KNtNLoWHWanuGD63o09VBtdspk3vn4Cm3201cIH1SbtzUGbtKNt\nttU08ebHO9rbbHXF6ZQxic3aZh+vXtmSItaggFkjBi/LCQKZ9c0qVgqpwX+jK6tTOJgLm1UU0gl8\n5p7FoB8r0gxay01os2Qihsfu1zd9CUy5NzdqYCz66cugmaZ91fqGIwDofpi991gWqURsIrXUE010\nz/4s5ZIoZY2J+lc/f7EGzkloyiTjOFnKTLTOXrosj2hCAbNGDNWF8YvYtjmev1jDk6vLYEzf9CUw\n4pQn2Pjrm1X8xJklJOJ6b6uTJccpT6KWrm/W8OgpvWu+AWea5rFcciKnvL55Cz92z6K2l3E9Msk4\n7i1NNr7+wmYVZ5ZzWl8sBYB4jOHs8cnuZaxv1kg0AcAYQ6VcmOxgtllFIZXAZ0/qLZoA7gTTCdbZ\nhc0qkvEYHpOg5ltvz64ZQ6c8fhG/fX0X9aap/SkZGHXK4212pdbE1XqbbIbJnfKtvS7eub4rhbIQ\nBqsr+SOdcqNr4bUPt7UvLfCY5IKpadl48YM67U2XSvnodWbbHBc2qySauHgX5o+6/7O+eQuPnyXR\nBHBsdulWE9YRl3Kf26jic6dKyCSjL5rQ/1XNqKzkj1T+vFQcBTIO58r5I1X5da/mm2wGwLHZUYHM\n8xcp5TvKubKzN8c55Rcv1WDZnNaZy2r5aKf82odbaJl9ep+5VFbyuLbdRrNrHfo973ziiCZkM4fK\nSh477R5u7R1+KffDWssRTchmAJx7GWbfxpV669DvqTYc0USWwywFzJpRKR99Ul7frKKykte2l/B+\nVleO7im5vlHF3Ytp3L+cC/HJokulXMC17TYaY5zy+kYVixkDP3o3pS8BJ4W527HGOuX1zSpSiRge\nOVUK8cmiS2XlaKe8vllFjAGPn9G75ttjdYJLuYOabwr+AAwv5Y7Lmj23eQsA2cxjkgumFyQTmihg\n1ozKSgF7HQs3D3HKnV4fL1H68jaGPSUPdsp9t+b7CUpfDlg9Ytwz507K9wtn9e7zPcokF/8ubFbx\n2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juKBIAMYywBIAvgOgS/0yhgdgKYqyN//sj9GjEZZc75dcAJEAGsCH6eSMIYOw3gYQAv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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r = 1 # generates undamped, nonexplosive cycles\n", "\n", "period = 10 # length of cycle in units of time\n", "phi = 2 * math.pi/period\n", "\n", "## Apply the reverse engineering function f\n", "\n", "rho1, rho2, a, b = f(r, phi)\n", "\n", "a = a.real # drop the imaginary part so that it is a valid input into y_nonstochastic\n", "b = b.real\n", "\n", "print(\"a, b =\", a, b)\n", "\n", "ytemp = y_nonstochastic(alpha=a, beta=b, y_0=20, y_1=30)\n", "plot_y(ytemp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "a, b = 0.6180339887498949 1.0\n", "Roots are complex with modulus less than one; therefore damped oscillations\n", "Roots are [ 0.80901699+0.58778525j 0.80901699-0.58778525j]\n", "Roots are complex\n", "Roots are less than one\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_19_1.png](_static/figures/sam_19_1.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interactive demonstration\n", "\n", "We'll use some widgets to show some of the consequences of parameters $(a,b)$ that are associated with complex conjugate roots of the characteristic polynomial. The widget will allow us to specify the amplitude and angle of the complex roots of the characteristic polynomial. (It will reverse engineer the $(a,b)$ that imply those roots.)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from ipywidgets import interact\n", "\n", "def choose_r_phi(r, phi):\n", " \n", " rho1, rho2, a, b = f(r, phi)\n", " a = a.real # drop the imaginary part so that it is a valid input into y_nonstochastic\n", " b = b.real\n", " ytemp = y_nonstochastic(alpha=a, beta=b, y_0=20, y_1=30)\n", " \n", " return plot_y(ytemp)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0b24e927953b4e2eb9420e3e5ca69d12", "version_major": 2, "version_minor": 0 }, "text/plain": [ "A Jupyter Widget" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "periodhighest = 20\n", "\n", "interact(choose_r_phi, r=(0, 1.5), phi=(math.pi/periodhighest, 10 * math.pi/periodhighest))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Digression: using sympy to find roots\n", "\n", "We can also use sympy to compute analytic formulas for the roots" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAAyBAMAAABhdUe6AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhBEmXarZt0i\nzbulB2H9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAFcklEQVRoBe2aT2gcVRzHfzuzs9nd2dgVFfyD\nzdJLLtJEK4ggdsBKT5LFk0XEKEIOHrKHag2lZTxVq9AIiqYiCXjwoMIi+P/fHgSlit0iPUiI2YPi\nTaM1xWDs+P7/2Xlv5k2s4oIPduc3vz/f32ff7s57swlMJL/CqA0vSZpw1YG7R40bggN3NeHqkcPG\nwOVccP+af/iF3dzeSYNc8EMLm5ruVOIyNrSarJPgxWUN3FU/FxyqOng3i2JHsVMauKt+UXC/syO4\nrCIN3Flfgs89HRnl9RmvzRqTHJw2fdDAnfUFuNepNKHcTxPo4GE6wc1j1dfBnfUF+OvQuFheMHzC\ndPA5N8x0llVfB3fWF+DXQ+UC+Lngj6eR3DxWfR3cWZ+DVzahuu0AbnhlTuB2fR3cWZ+Dj3VhvJsP\nXl5kmJM/tp2AeZJdXwN31+fgYQdmonxwb5qSeL1anzM5He36Gri7Pgd/cBB8APngIZvnsFfedgLm\nSXZ9Ddxdn4Pv/+JEZAQfe+7P07w7wNfMDGcbF6XXwbLqw8LEtytCwF2fgx8jtaarihDFxklx5us7\nAeQ/KGIG4zLolzuqLge/ljj9phoz2OeFL4yFyYxPhh3q+WXQDweqIANv/IadjaNbsRpM2YH8Rk6y\noM8rqrtT6dKR0hdlMgdZWfrw5EDNZeCVruq02vWYh+r8fRMEZ77jMcMxpS/KtOQs/cabAzWXf1RU\nn92+osdjD8Mj1BQErSxwXiaOokx4sJGl740P1Nxi4A+QUrTPK3+z7wcqwwnqPQxeeeJ5Vd1u8zI9\nI0Mf3iDgYo9ZDPwW3Afv80pJskF7coL7AINPwkPgHX+MhrKeeZmek6EfxBic7DHJqu0M/ipuQaYT\n7/NkP07QwuD1LpydvQlekWGbxctEPE/fAwyOe9NVm4HvkjeSSCpY/RCNjyNk0gD6DGyhEyBfYbLP\nozt3b21t9ca1tUW0dEUYvLQC89MfwUwPJ6tD15dlAKTxRq4+3ErAcW+6arvO+JlziMNvoSeyz5M7\ndzZ19wIGn2/Dqd47aNZRXvYYnvE8/aCFwUlvumq7gkdTEUANPWBon8cIbl9a+uUlOAqwilL2t9FT\n9hgGz9P3l5aWr4tpb8Crtis4zMQA5L5qaJ8nCXYDvAtlvJK9lw2No7KM5ebrlwZAewNetZ3BS32A\nOdxkaJ8nCS5BcAnuX8FffZSF0rOGLGNZ+fq7Bqw3unYVAK+ht4fcVw3t8wTB3uS0v/3UYaT5GnqE\nbzMgy0GU8Xiuvvfz1grtTVZtZcY/P/49V1GOjSM/RfjUv8AuKsdIUOwjVYIxMs2VVgVV3EHS1CdN\nX5Yxt4s+0N5k1ZbgwSJMzaqNqH0IPHLVDraA3lexfV6XpQY9WVOKsX3PvjvbAC1sqkPXF2Xc7aIP\npDddtSV4rQ2lptqJ2i8AXEmsc+BNI4Pu84z3SnA2wpkTSYKWghib6rDoC7eDPu1NV20JXupCDV8S\nhsYNAMsR9k1F5KLC9nm+4TXCo7K2Lk1mWfSF20Ff3WNK8PFNI/h6m4HPtPh9FSLJ3bmnuMGiL9wF\n9SU4ahWiK4dhfIo+smg57580xAq5LPrUXVBfA59vmTgq9E9Etc3zpmgRn1kfqLugvgb+vpEiXCRu\n//e+MVzAadYH6i6or4KPdYwQR6g3SGJj2N1p0Wfugvoq+AkjQ5W/nPWeMe7uNOsDdxfTV8DRHwO+\nMlDcBg1K/IwhWMRl0RfuYvoK+EGAZ9Mg6GeYKgX/LB0s5DHr49+RaNti+hK88dYe0+/6X+6ZfLkQ\nny3Zom9x21SEX4KPo5uorvALYz1J/hAnf8ew6FvcuZ0keG7qfyvhf/B/+/0Y5Rkf2X/7GNV/tPkL\nJmUnDeNVINwAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left [ \\frac{\\rho_{1}}{2} - \\frac{1}{2} \\sqrt{\\rho_{1}^{2} + 4 \\rho_{2}}, \\quad \\frac{\\rho_{1}}{2} + \\frac{1}{2} \\sqrt{\\rho_{1}^{2} + 4 \\rho_{2}}\\right ]$$" ], "text/plain": [ "⎡ ____________ ____________⎤\n", "⎢ ╱ 2 ╱ 2 ⎥\n", "⎢ρ₁ ╲╱ ρ₁ + 4⋅ρ₂ ρ₁ ╲╱ ρ₁ + 4⋅ρ₂ ⎥\n", "⎢── - ───────────────, ── + ───────────────⎥\n", "⎣2 2 2 2 ⎦" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy\n", "from sympy import Symbol, init_printing\n", "init_printing()\n", "\n", "r1 = Symbol(\"rho_1\")\n", "r2 = Symbol(\"rho_2\")\n", "z = Symbol(\"z\")\n", "\n", "sympy.solve(z**2 - r1*z - r2, z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
 $$\n", "\\left [ \\frac{\\rho_{1}}{2} - \\frac{1}{2} \\sqrt{\\rho_{1}^{2} + 4 \\rho_{2}},\n", "\\quad \\frac{\\rho_{1}}{2} + \\frac{1}{2} \\sqrt{\\rho_{1}^{2} + 4 \\rho_{2}}\\right ]\n", "$$\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAokAAAAyBAMAAADCa1yNAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left [ \\frac{\\alpha}{2} + \\frac{\\beta}{2} - \\frac{1}{2} \\sqrt{\\alpha^{2} + 2 \\alpha \\beta + \\beta^{2} - 4 \\beta}, \\quad \\frac{\\alpha}{2} + \\frac{\\beta}{2} + \\frac{1}{2} \\sqrt{\\alpha^{2} + 2 \\alpha \\beta + \\beta^{2} - 4 \\beta}\\right ]$$" ], "text/plain": [ "⎡ _______________________ _______________________⎤\n", "⎢ ╱ 2 2 ╱ 2 2 ⎥\n", "⎢α β ╲╱ α + 2⋅α⋅β + β - 4⋅β α β ╲╱ α + 2⋅α⋅β + β - 4⋅β ⎥\n", "⎢─ + ─ - ──────────────────────────, ─ + ─ + ──────────────────────────⎥\n", "⎣2 2 2 2 2 2 ⎦" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = Symbol(\"alpha\")\n", "b = Symbol(\"beta\")\n", "r1 = a + b\n", "r2 = -b\n", "\n", "sympy.solve(z**2 - r1*z - r2, z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
 $$\n", "\\left [ \\frac{\\alpha}{2} + \\frac{\\beta}{2} - \\frac{1}{2} \\sqrt{\\alpha^{2} +\n", "2 \\alpha \\beta + \\beta^{2} - 4 \\beta}, \\quad \\frac{\\alpha}{2} +\n", "\\frac{\\beta}{2} + \\frac{1}{2} \\sqrt{\\alpha^{2} + 2 \\alpha \\beta +\n", "\\beta^{2} - 4 \\beta}\\right ]\n", "$$\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stochastic shocks\n", "\n", "Now we’ll construct some code to simulate the stochastic version of the\n", "model that emerges when we add a random shock process to aggregate\n", "demand" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n", "[ 0.7236068 0.2763932]\n", "Roots are real\n", "Roots are less than one\n" ] }, { "data": { "image/png": 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MmHnNyzE4MrEQt26uwvM9s/D4g1k5B0JWMmp0okotg0y8fKQcR6sQI8QC9gJIcvASMDMM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\n77S/RMJpMMwOM7JjKT+5d0h6Mf3AzG6TtM3MfsfzVZUQ5xyBuQhUVZT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def y_stochastic(y_0=0, y_1=0, alpha=0.8, beta=0.2, gamma=10, n=100, sigma=5):\n", "\n", " \"\"\"This function takes parameters of a stochastic version of the model and proceeds to analyze\n", " the roots of the characteristic polynomial and also generate a simulation\"\"\"\n", "\n", " # Useful constants\n", " rho1 = alpha + beta\n", " rho2 = -beta\n", "\n", " # Categorize solution\n", " categorize_solution(rho1, rho2)\n", "\n", " # Find roots of polynomial\n", " roots = np.roots([1, -rho1, -rho2])\n", " print(roots)\n", "\n", " # Check if real or complex\n", " if all(isinstance(root, complex) for root in roots):\n", " print('Roots are complex')\n", " else:\n", " print('Roots are real')\n", "\n", " # Check if roots are less than one\n", " if all(abs(root) < 1 for root in roots):\n", " print('Roots are less than one')\n", " else:\n", " print('Roots are not less than one')\n", "\n", " # Generate shocks\n", " epsilon = np.random.normal(0, 1, n)\n", "\n", " # Define transition equation\n", " def transition(x, t): return rho1 * \\\n", " x[t - 1] + rho2 * x[t - 2] + gamma + sigma * epsilon[t]\n", "\n", " # Set initial conditions\n", " y_t = [y_0, y_1]\n", "\n", " # Generate y_t series\n", " for t in range(2, n):\n", " y_t.append(transition(y_t, t))\n", "\n", " return y_t\n", "\n", "plot_y(y_stochastic())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n", "[ 0.7236068 0.2763932]\n", "Roots are real\n", "Roots are less than one\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_27_1.png](_static/figures/sam_27_1.png) \n", "Let’s do a simulation in which there are shocks and the characteristic polynomial has complex roots" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a, b = 0.6285929690873979 0.9409000000000001\n", "Roots are complex with modulus less than one; therefore damped oscillations\n", "[ 0.78474648+0.57015169j 0.78474648-0.57015169j]\n", "Roots are complex\n", "Roots are less than one\n" ] }, { "data": { "image/png": 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/wsFUCHc3axYcEXGq69nBJ2QIsmdcOwGzgVMyao3mSI5ce3U+j/fdl9ixnv2h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\nc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r = .97\n", "\n", "period = 10 # length of cycle in units of time\n", "phi = 2 * math.pi/period\n", "\n", "### apply the reverse engineering function f\n", "\n", "rho1, rho2, a, b = f(r, phi)\n", "\n", "a = a.real # drop the imaginary part so that it is a valid input into y_nonstochastic\n", "b = b.real\n", "\n", "print(\"a, b = \", a, b)\n", "plot_y(y_stochastic(y_0=40, y_1 = 42, alpha=a, beta=b, sigma=2, n=100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "a, b = 0.6285929690873979 0.9409000000000001\n", "Roots are complex with modulus less than one; therefore damped oscillations\n", "[ 0.78474648+0.57015169j 0.78474648-0.57015169j]\n", "Roots are complex\n", "Roots are less than one\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_29_1.png](_static/figures/sam_29_1.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Government spending\n", "\n", "This function computes a response to either a permanent or one-off increase\n", "in government expenditures" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def y_stochastic_g(y_0=20,\n", " y_1=20,\n", " alpha=0.8,\n", " beta=0.2,\n", " gamma=10,\n", " n=100,\n", " sigma=2,\n", " g=0,\n", " g_t=0,\n", " duration='permanent'):\n", "\n", " \"\"\"This program computes a response to a permanent increase in government expenditures that occurs\n", " at time 20\"\"\"\n", "\n", " # Useful constants\n", " rho1 = alpha + beta\n", " rho2 = -beta\n", "\n", " # Categorize solution\n", " categorize_solution(rho1, rho2)\n", "\n", " # Find roots of polynomial\n", " roots = np.roots([1, -rho1, -rho2])\n", " print(roots)\n", "\n", " # Check if real or complex\n", " if all(isinstance(root, complex) for root in roots):\n", " print('Roots are complex')\n", " else:\n", " print('Roots are real')\n", "\n", " # Check if roots are less than one\n", " if all(abs(root) < 1 for root in roots):\n", " print('Roots are less than one')\n", " else:\n", " print('Roots are not less than one')\n", "\n", " # Generate shocks\n", " epsilon = np.random.normal(0, 1, n)\n", "\n", " def transition(x, t, g):\n", "\n", " # Non-stochastic - separated to avoid generating random series when not needed\n", " if sigma == 0:\n", " return rho1 * x[t - 1] + rho2 * x[t - 2] + gamma + g\n", "\n", " # Stochastic\n", " else:\n", " epsilon = np.random.normal(0, 1, n)\n", " return rho1 * x[t - 1] + rho2 * x[t - 2] + gamma + g + sigma * epsilon[t]\n", "\n", " # Create list and set initial conditions\n", " y_t = [y_0, y_1]\n", "\n", " # Generate y_t series\n", " for t in range(2, n):\n", "\n", " # No government spending\n", " if g == 0:\n", " y_t.append(transition(y_t, t))\n", "\n", " # Government spending (no shock)\n", " elif g != 0 and duration == None:\n", " y_t.append(transition(y_t, t))\n", "\n", " # Permanent government spending shock\n", " elif duration == 'permanent':\n", " if t < g_t:\n", " y_t.append(transition(y_t, t, g=0))\n", " else:\n", " y_t.append(transition(y_t, t, g=g))\n", "\n", " # One-off government spending shock\n", " elif duration == 'one-off':\n", " if t == g_t:\n", " y_t.append(transition(y_t, t, g=g))\n", " else:\n", " y_t.append(transition(y_t, t, g=0))\n", " return y_t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A permanent government spending shock can be simulated as follows" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n", "[ 0.7236068 0.2763932]\n", "Roots are real\n", "Roots are less than one\n" ] }, { "data": { "image/png": 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myR2LtnLlS+v4cc/xf9YdaXFyPkPDfTu1Sc1BLXOl41m5t4hNWaUOqK7zTNPk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\nWMEHrr3YF7GcgGocaxXHsc4Pxzo/HOv86C1jXfY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_y(y_stochastic_g(g=10, g_t=20, duration='permanent'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n", "[ 0.7236068 0.2763932]\n", "Roots are real\n", "Roots are less than one\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_31_1.png](_static/figures/sam_31_1.png) \n", "We can also see the response to a one time jump in government expenditures" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n", "[ 0.7236068 0.2763932]\n", "Roots are real\n", "Roots are less than one\n" ] }, { "data": { "image/png": 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SPrXA6wCAUMpsNpxPRVryJnf0DLHZEAAulPVdI9baNklt/ueHJd0wxXPGJH0g268NALhY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\nvE5vX1Gr65bVUMUGQow//QA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_y(y_stochastic_g(g=500, g_t=50, duration='one-off'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "Roots are real and absolute values are less than zero; therfore get smooth convergence to a steady state\n", "[ 0.7236068 0.2763932]\n", "Roots are real\n", "Roots are less than one\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_33_1.png](_static/figures/sam_33_1.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wrapping everything into a class\n", "\n", "Up to now we have written functions to do the work\n", "\n", "Now we’ll roll up our sleeves and write a Python class called Samuelson\n", "for the Samuleson model" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class Samuelson():\n", "\n", " r\"\"\"This class represents the Samuelson model, otherwise known as the\n", " multiple-accelerator model. The model combines the Keynesian multipler\n", " with the accelerator theory of investment.\n", "\n", " The path of output is governed by a linear second-order difference equation\n", "\n", " .. math::\n", "\n", " Y_t = + \\alpha (1 + \\beta) Y_{t-1} - \\alpha \\beta Y_{t-2}\n", "\n", " Parameters\n", " ----------\n", " y_0 : scalar\n", " Initial condition for Y_0\n", " y_1 : scalar\n", " Initial condition for Y_1\n", " alpha : scalar\n", " Marginal propensity to consume\n", " beta : scalar\n", " Accelerator coefficient\n", " n : int\n", " Number of iterations\n", " sigma : scalar\n", " Volatility parameter. Must be greater than or equal to 0. Set\n", " equal to 0 for non-stochastic model.\n", " g : scalar\n", " Government spending shock\n", " g_t : int\n", " Time at which government spending shock occurs. Must be specified\n", " when duration != None.\n", " duration : {None, 'permanent', 'one-off'}\n", " Specifies type of government spending shock. If none, government\n", " spending equal to g for all t.\n", "\n", " \"\"\"\n", "\n", " def __init__(self,\n", " y_0=100,\n", " y_1=50,\n", " alpha=1.3,\n", " beta=0.2,\n", " gamma=10,\n", " n=100,\n", " sigma=0,\n", " g=0,\n", " g_t=0,\n", " duration=None):\n", "\n", " self.y_0, self.y_1, self.alpha, self.beta = y_0, y_1, alpha, beta\n", " self.n, self.g, self.g_t, self.duration = n, g, g_t, duration\n", " self.gamma, self.sigma = gamma, sigma\n", " self.rho1 = alpha + beta\n", " self.rho2 = -beta\n", " self.roots = np.roots([1, -self.rho1, -self.rho2])\n", "\n", " def root_type(self):\n", " if all(isinstance(root, complex) for root in self.roots):\n", " return 'Complex conjugate'\n", " elif len(self.roots) > 1:\n", " return 'Double real'\n", " else:\n", " return 'Single real'\n", "\n", " def root_less_than_one(self):\n", " if all(abs(root) < 1 for root in self.roots):\n", " return True\n", "\n", " def solution_type(self):\n", " rho1, rho2 = self.rho1, self.rho2\n", " discriminant = rho1 ** 2 + 4 * rho2\n", " if rho2 >= 1 + rho1 or rho2 <= -1:\n", " return 'Explosive oscillations'\n", " elif rho1 + rho2 >= 1:\n", " return 'Explosive growth'\n", " elif discriminant < 0:\n", " return 'Damped oscillations'\n", " else:\n", " return 'Steady state'\n", "\n", " def _transition(self, x, t, g):\n", "\n", " # Non-stochastic - separated to avoid generating random series when not needed\n", " if self.sigma == 0:\n", " return self.rho1 * x[t - 1] + self.rho2 * x[t - 2] + self.gamma + g\n", "\n", " # Stochastic\n", " else:\n", " epsilon = np.random.normal(0, 1, self.n)\n", " return self.rho1 * x[t - 1] + self.rho2 * x[t - 2] + self.gamma + g + self.sigma * epsilon[t]\n", "\n", " def generate_series(self):\n", "\n", " # Create list and set initial conditions\n", " y_t = [self.y_0, self.y_1]\n", "\n", " # Generate y_t series\n", " for t in range(2, self.n):\n", "\n", " # No government spending\n", " if self.g == 0:\n", " y_t.append(self._transition(y_t, t))\n", "\n", " # Government spending (no shock)\n", " elif self.g != 0 and self.duration == None:\n", " y_t.append(self._transition(y_t, t))\n", "\n", " # Permanent government spending shock\n", " elif self.duration == 'permanent':\n", " if t < self.g_t:\n", " y_t.append(self._transition(y_t, t, g=0))\n", " else:\n", " y_t.append(self._transition(y_t, t, g=self.g))\n", "\n", " # One-off government spending shock\n", " elif self.duration == 'one-off':\n", " if t == self.g_t:\n", " y_t.append(self._transition(y_t, t, g=self.g))\n", " else:\n", " y_t.append(self._transition(y_t, t, g=0))\n", " return y_t\n", "\n", " def summary(self):\n", " print('Summary\\n' + '-' * 50)\n", " print('Root type: ' + self.root_type())\n", " print('Solution type: ' + self.solution_type())\n", " print('Roots: ' + str(self.roots))\n", "\n", " if self.root_less_than_one() == True:\n", " print('Absolute value of roots is less than one')\n", " else:\n", " print('Absolute value of roots is not less than one')\n", "\n", " if self.sigma > 0:\n", " print('Stochastic series with sigma = ' + str(self.sigma))\n", " else:\n", " print('Non-stochastic series')\n", "\n", " if self.g != 0:\n", " print('Government spending equal to ' + str(self.g))\n", "\n", " if self.duration != None:\n", " print(self.duration.capitalize() +\n", " ' government spending shock at t = ' + str(self.g_t))\n", "\n", " def plot(self):\n", " fig, ax = plt.subplots(figsize=(12, 8))\n", " ax.plot(self.generate_series())\n", " ax.set(xlabel='Iteration', xlim=(0, self.n))\n", " ax.set_ylabel('$Y_t$', rotation=0)\n", " ax.grid()\n", "\n", " # Add parameter values to plot\n", " paramstr = '$\\\\alpha=%.2f$\\n$\\\\beta=%.2f$\\n$\\\\gamma=%.2f$\\n$\\\\sigma=%.2f$\\n$\\\\rho_1=%.2f$\\n$\\\\rho_2=%.2f$'%(\n", " self.alpha, self.beta, self.gamma, self.sigma, self.rho1, self.rho2)\n", " props = dict(fc='white', pad=10, alpha=0.5)\n", " ax.text(0.87, 0.05, paramstr, transform=ax.transAxes,\n", " fontsize=12, bbox=props, va='bottom')\n", "\n", " return fig\n", "\n", " def param_plot(self):\n", "\n", " # Uses the param_plot() function defined earlier (it is then able\n", " # to be used standalone or as part of the model)\n", "\n", " fig = param_plot()\n", " ax = fig.gca()\n", "\n", " # Add lambda values to legend\n", " for i, root in enumerate(self.roots):\n", " if isinstance(root, complex):\n", " operator = ['+', ''] # Need to fill operator for positive as string is split apart\n", " label = r'$\\lambda_{0} = {1.real:.2f} {2} {1.imag:.2f}i$'.format(i+1, sam.roots[i], operator[i])\n", " else:\n", " label = r'$\\lambda_{0} = {1.real:.2f}$'.format(i+1, sam.roots[i])\n", " ax.scatter(0, 0, 0, label=label) # dummy to add to legend\n", "\n", " # Add rho pair to plot\n", " ax.scatter(self.rho1, self.rho2, 100, 'red', '+', label=r'$(\\ \\rho_1, \\ \\rho_2 \\ )$', zorder=5)\n", "\n", " plt.legend(fontsize=12, loc=3)\n", "\n", " return fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Illustration of Samuelson class\n", "\n", "Now we’ll put our Samuelson class to work on an example" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Summary\n", "--------------------------------------------------\n", "Root type: Complex conjugate\n", "Solution type: Damped oscillations\n", "Roots: [ 0.65+0.27838822j 0.65-0.27838822j]\n", "Absolute value of roots is less than one\n", "Stochastic series with sigma = 2\n", "Government spending equal to 10\n", "Permanent government spending shock at t = 20\n" ] } ], "source": [ "sam = Samuelson(alpha=0.8, beta=0.5, sigma=2, g=10, g_t=20, duration='permanent')\n", "sam.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "Summary\n", "---------------------------------------------------------\n", "Root type: Complex conjugate\n", "Solution type: Damped oscillations\n", "Roots: [ 0.65+0.27838822j 0.65-0.27838822j]\n", "Absolute value of roots is less than one\n", "Stochastic series with sigma = 2\n", "Government spending equal to 10\n", "Permanent government spending shock at t = 20\n", "\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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arGnR5mwcLTatGAZeZhc0sp1ATxfcMbQXvtp9Ck9O6I2eAfY5Nuxy4bqFq1KO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\n2X6Y4uKqXsWQwGhoaOj1fSHOpHtCfNF9Ib6E431RWVnJvn37Qt2NPqG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sam.plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_38_0.png](_static/figures/sam_38_0.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using the graph\n", "\n", "We’ll use our graph to show where the roots lie and how their location\n", "is consistent with the behavior of the path just graphed\n", "\n", "The red $+$ sign shows the location of the roots" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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D69atsXr16jJPhfrhhx/w3//+F02bNoWhoSEyMjIAVLxv/u233yBJEm7duiWfN3PmTEiS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sam.param_plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_40_0.png](_static/figures/sam_40_0.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the LinearStateSpace class\n", "\n", "It turns out that we can use the [QuantEcon.py](http://quantecon.org/python_index.html)\n", "[LinearStateSpace](https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/lss.py) class to do\n", "much of the work that we have done from scratch above\n", "\n", "Here is how we map the Samuelson model into an instance of a\n", "LinearStateSpace class" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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TUnE8fBiD1NRsQa7of1O5siImTGiG8+df48MH+j8v6K+//PDXX4/xyy+tsXBh\nW0Ey2Noa4u7dkeCcw9zcGTduvBUkh6xxcgqBiooCBgxoJHSUEunatS68vaORlZUrdBSJxjmHm1s4\nbGzOoGXL4zh//jVmzmyJZcs64OzZV9i2zU/oiKSAT5/ScPbsK4wb1wSqqkqC5ejSRQ+NGmkKUkSl\nrEMxSTl68OA9BgxwhYFBVdy4MQRVqgj3YAW+du5Ke8VQT08dt24Nxfbtlrh5MxzNmh3FuXOv6GwX\nISLk7v4OjAFdutQRNMf06SbIycnD4cPCLtQqSby9o7Bo0R3Y2hpg+3ZLQYYIfWNiUh2+vqPRqFFV\n9O17Hvv309XVn5GVlYvTp19iwIBGgr8+l5SVlR5SU7Px6BGtO1mUrKxcHDsWBBOTY+jR4yyCgj5j\n06bOiIychp07u2LDBnMMGWKIJUu86MqnBHFwCEJWVi6mTTMRNAdjDJMnN4eXVxRevSq8Ypx4UcdO\nwj19+hG9ep2Drq4qbt0aCm3tykJHKjM5OYb589vCz28MatdWw5Ahl9Cv3wWEhycKHY0QmeDu/g6t\nW9eAlpawzxNGRlro2rUuDhwIQG4urX2ZkJCB0aOvon59DRw92gvy8sK/9NaurQYvrxHo0UMf06ff\nwpIld5CXRyfaysLNLRzx8RlSMQzzmy5d9MAYqFNSCOcchw8/Q/36BzFhwg1wDhw92hNv307F0qUd\n/i2dzxjDkSM9YWhYFcOHX0ZUFM1ZFVpeHsf+/QGwsKiDpk11hI6D8eObQl6e4ciRoHI9rvCvLuS7\nQkLiYGNzFurqSrh9eyhq1pTuZQO+adasGh49GoNt2yzh6RmJJk0csHnzQ2Rn05AQQsoqNTULPj7v\nBZ1fV9CMGSZ49y4Z169X7KF+nHNMn34LMTGpcHLqAzU1ybmio6amhIsXB2HmzJbYvPkRhg+/jPR0\nWn+0tJycQqClVQk2NvpCRykxbe3KaNmyOhVQKSAuLh2DB1/ClCk3Ub++Bm7cGIzAwPEYP74ZlJX/\nuzqYmpoSLlwYgPT0HAwZcgmZmTkCpCbfuLmFIywsETNmtBQ6CgBAV7cK+vZtiKNHg8r1/S117CRU\nWNgXdOt2BvLyDO7uw1CvnmQudlpWCgpyWLCgLYKDJ8LGRh9LlnihTZsTuH8/WuhohEilu3ejkZ2d\nh65dJaNjN2BAI+jqqsLe3l/oKII6duw5Tp9+iXXrzNC+va7Qcf5DQUEOe/ZYY9s2S5w79wpdu56m\nOdClkJLZA0ctAAAgAElEQVSShYsXQzF0qBGUlOSFjlMqVlZ6uH//PTIyZKdDEhAQi169zuLEiefI\nySn5aIHbtyPQosUxXLnyBlu3dsm/ml2/2CHTxsbaOHq0F3x9YzB/vsfPxic/wd7eH9Wrq8DWtsjl\nswUxeXJzfPyYhqtXy2nRaVDHTiJFRSXD2vo0MjJycOvWUBgYVBU6ktjUrasOV9eBcHUdiC9fMmFm\n5oxp09yQkJAhdDRSCpxz3LkTicePab6GUNzd30FRUQ7m5rWFjgIAUFSUx5QpzXH9+lu8fVsxlzp5\n/ToBs2e7w9JSD7/+2k7oON/FGMOCBW1x9mx/BAR8gqmpEw2RL6FLl94gLS0Ho0YJV4GvrLp2rYvM\nzFw8ePBe6CgikZ6ejZEjr8DNLQLjxl2HkdFhHDwY+MMraZmZOVi40APdu5+BhoYSfH1HY+HCdqWq\nIzB4sCEWL24He/sAHDtWvsPuyFfv3iXhypUwTJ7cXKJOsPTqVR+6uqrlWkSFOnYSJjY2Fd26nUFc\nXAZu3BiM5s2rCR2pXAwY0AjBwROxYEEbHD78DMbGR3DhwmuhY5ESePQoBlZWp2BpeQpt257EsGGX\naM1CAbi7v0PHjrUErQRW2NSpLcAYw/79gUJHKXdZWbkYNeoKlJTkceJEb4mYV1ccW1tDeHoOx6dP\naVi40FPoOFLBySkEenpqMDcXtmBRWXTuXAfy8kxmhmMuW+aNkJB4XL8+GJcuDYK2dmXY2bmhUaPD\n2L37yX+GGQcHf0aHDo7Yvv0xZs5sCT+/sWjVqkaZjr1xY2dYWelh+vTbePr0oyh+HFIK35bSsrMT\nrmp8URQU5DBxYjNcv/623OZhSv4rTQWSkJABG5uz+WceBqFdO8kbtiNOVaooYds2K/j5jUWdOmoY\nOfIKLaIrwcLCvmDkyCto394RwcFx2L27K9as6YSrV8PQuPERzJ/vgbi4dKFjVgjx8el4+vSjxMyv\n+0ZPTx39+zfEoUPPKtzcrdWr78HP7yMOHbJBnTpqQscpsfbtdbFoUTucP/8ajx7FCB1HosXFpePm\nzXCMGGEs2NqyP0NdXRlt29aEh0ek0FF+2u3bEdi58wnmzGkFGxt99OvXEL6+o+HmNgT162vgl1/+\ngb7+QWzZ8hDJyVlwdY1FmzYn8f59Ci5fHoS9e7tBRUWxzMdXUJCDi0tf6OhUxuDBlxAfT6995enc\nuVewtq4HfX3Jm7Y0aVJz5OVxHD1aPldzqWMnIb526s4gJCQeFy4MgIWFntCRBNOyZXWcPdsPubkc\nGzf6Ch2HFBIXl4758z1gbHwEFy+GYsUKU4SGTsHs2a2xenUnvH49BePHN8WuXU/QqNEhbN36SKbm\ncEgiT89IcA6JmV9X0Jw5rREXlw4XlxdCRyk3Hh7v8OefDzF1agvY2hoKHafUFixoCx2dyli+/K7Q\nUSTa2bOvkJOTJ+hCyD+ra9e68PWNQUpKltBRyiwhIQMTJlyHsbEW/vjD4t/tjDF0764PL68RuHNn\nOFq2rI5ff/VCtWp7sXPnO1hZ6eHZswno27ehSHJUr66Ks2f7IyoqGaNHX6Uqs+Xky5cMhITEC77M\nz/c0bKiJrl3r4siRoHJ5TFDHTgJ8/pyGrl1PIzDwM86e7Y8ePeoLHUlw9etrYvLk5jh4MBARETTX\nQxKkp2fjzz990bDhIeza9QTjxzdFaOgUrF9vDnV15X/3q1WrCg4e7IGAgHHo2LEWFi++g8aNj8DF\n5QWtWygm7u7voKqqKJHFOays9NC0qTZ2735aIf7+cXHpGDv2GgwNtfDXX5ZCxykTNTUlLF/eAbdv\nR8DdPULoOBLL2TkERkZaaNmyutBRyqxr17rIycnD3bvSW7hs1qzb+PgxDSdO9P7uVTcLCz3cvDkE\nvr6jMXp0Y8yfXxdXr9qiRg3RVhvv0EEXu3Z1xY0b4di8+aFI2yZF+7YWo6lpLYGTfN/kyc3x9m1i\nuSwvQh07gcXGpqJr19MICYnDxYsD0a+faM4cyYLffusAxhjWr/cROkqF5+4eASOjI1i61BudO9dG\nYOB4HDzYA7VqVfnufZo1q4Zr1wbDzW0INDSUMXLkFVhYuNDVOzFwd38HC4s6EjVp/BvGGGbPboWn\nT2Nx/75sFGn4Hs45pk51Q2xsGpyd+0jUfMfSmjGjJfT01LB8uXeF6JCXVnR0Mry8ojBypLGgi83/\nrE6dakFRUU5q17Nzdg6Bs/MLrF7dEW3b1ix2//btdXH4cE/0719dbH+3adNM0LdvA2zd6kevd+XA\nxycGjAHt2hX/9xeKra0BqlatVC5FVGSiY3frVjiePJG+yaofPqTCyuo0QkO/4MoVW/TsSVfqCtLT\nU8f06SY4ejQIoaEJQsepkLKzc7F8uTe6dz8DVVVFeHgMw+XLtqVa/LN7d308fjwWe/da4+7daOza\n9USMiSue6OhkvHwZL5HDML8ZM6YJNDSUsXu3bP/tDx4MxIULr/HHHxZlLsIgKSpVUsCaNZ3w8OEH\nuLqGCh1H4pw69RKcQ6qHYQKAiooiOnasJZUFVKKikjFz5m2Ymupi6dIOQsf5F2MM8+e3RVxcOk6d\nqjhD0IXi4/MejRtrQ0NDufidBVKpkgLGjGmM8+dfi732gFR37Djn2LDBBzY2Z2FjcxYfPkjP2jvR\n0cno0sUFERFJuHbNFt261RM6kkRatqwDlJTksXbtA6GjVDjh4YmwsHDBpk2+mDy5Ofz8xsDSsmyd\nB3l5Ocyc2Qp9+jTAhg0++Pw5TcRpK65vb8gkrXBKQVWqKGHSpGY4d+413r9PETqOWLx58wXz5nnA\nxkYf8+a1ETqOSIwb1xTGxlpYseIucnNLviZYReDsHILWrWvA0FBL6Cg/zcpKD0+exOLLF+lZZigv\nj2PChOvIysrFiRO9oaAgWW9nraz00LixFvbseSp0FJnGOYev7weYmkreNITCpkxpgaysXJw8GSzW\n40jWf0IpZGfnws7ODStW3MWAAY2QkpIFOzs3qRgy8u5dErp0OYX371Nw48bgMr9Zrghq1lTFrFkt\n4egYjJCQOKHjVBhnzrxEy5bHERwcBxeXvjh4sIdIhpVt3myB1NRsrFtHHXVRcXd/By2tSjAxkex5\nPrNmtUJubh727ZPNBcvt7f2RnZ2HI0d6SGWFxKIoKMhh/XozBAfHif3NiDR5/ToBfn4fpf5q3Tdd\nu9ZFXh6Hl1eU0FFKbM+ep3B3f4e//rJCo0aSt9YvYwyzZrWCn99HPHxI1WXF5c2bL4iLS0eHDpLf\nsWvRohp69tQXewEVqezYJSdnoV+/Czh06BlWrDDFhQsD8McfFrh8+Q0cHCR7ccjw8ER06eKCT5/S\ncOvWUKlc+6a8/fpre6iqKmLNmvtCR5F5aWnZmDr1JoYNuwxjYy34+4/D8OGie/PSpIkOpk5tAXv7\nALx6FS+ydisqzjnc3b9Wd5P0zkTDhpro3bsB9u//8YLB0ig7OxcnTgSjX7+GqF1bepY2KInBgw3R\npk0NrF59X+b+bmX1rcLrsGFGAicRjQ4ddFG5soLUDMcMDv6MJUu80KdPA0ydKlnrlhU0blxTqKkp\n0VU7MfL1/dppluTCKQVdvz4E8+e3FesxpK5jFx2djM6dnXH7dgQOHeqB9evNwRjDL7+0hqWlHubN\n80B4uGRWUXzz5gssLFzw5Usm3N2HSc0DUWjVqqlg7tw2OH36JQIDPwkdR2YFBn5C27YncPjwMyxd\n2h7e3iNQv76myI+zZk0nVKokjyVLvETedkUTHZ2JqKhkWFtLx1DuOXNaITY2DWfOvBI6ikjduBGO\n2Ng0TJzYTOgoIscYw8aNnRERkYQDByreQvOFcc7h7BwCc/PaqFtXXeg4IqGsrAAzs9pwd5f8jl1W\nVi7Gjr2OKlUUcehQD4kuXKOmpoTx45vi1KmXiI2VnqlC0sTHJwaqqopo2lRb6CgSQ6o6ds+efYKp\nqRPevPmCq1dtMXly839vk5NjcHDoCQCYMOG6xK0f8vTpR1hYuCAtLQf//DOsRNWbyP9buLAtNDSU\nsWrVPaGjyKTLl9+gffuTSEjIhJvbUGzaZAFFRfFUWKxRQxXLlnWAq2so7tyR/oVxhfTkSRIAyZ5f\nV1D37vowNKwqc0VUHByCUL26Cnr21Bc6ilh0714PlpZ6WL/+gVSvdyYKz559RkhIvMwMw/ymf/+G\nCAr6DC8vyX1O5pzj11/v4MmTjzhwwAY1a4p2qQJxmDWrJbKycsulGmJF5OPzHu3a1YS8vFR1Z8RK\nan4Tt29HwNzcGXl5HN7eI4tc601fXwM7dljhzp0o7Nz5WICURbt69Q06d3aBvDyDp+cwqa+WJoSq\nVSth4cK2uHgxFH5+H4SOI1Py8jgWLfJEo0aaCAgYVy6FfObNa4M6ddSwaJGnxJ2EkSZPniSjTh01\nGBhI3hyTosjJfV364OHDDzIz7+TTpzRcvvwGY8c2EdvJEKExxrBpU2d8+pSOHTsk57VVCM7OIZCX\nZxg6VDaGYX4zeXJz6OqqYuXKexJZqyAvj+OXX/7Bzp1PMGdOKwwaZCB0pBIxNtaGtXVd7NsXgJwc\nKkAkSunp2fD3/yQVhVPKU7EdO8bYEcZYLGMsqMA2LcbYLcbY6/zPVfO3M8bYLsZYKGMskDHW+mcD\n5uTk4fDhZ+jV6xzq1VOHj8+oHy4GOnFiM/Tr1xDLlnkjOPjzzx7+p+3d+xT9+7vCyEgLPj6j0axZ\nNaEjSa25c1tDS6sSXbUTsStX3uDVqwSsXNkR1auXzxlQFRVFbNxoDj+/j//OVyGlk5fH8fRpMrp2\n1ZPo4UiFjR/fFFWqKGL3btmYd+LkFIKcnDxMmNBU6ChiZWpaC/37N8SWLY/EXq5bUnHO4eLyAt26\n1UO1aipCxxEpFRVF/PabKby8osQ6JLMs1VVzcvIwadIN7NnzFAsXtsXOnV3FkEx8Zs9uhcjIZFy+\n/EboKDLl6dNY5OTkSUXhlPJUkit2RwH0LLRtKQB3zrkBAPf87wGgFwCD/A87APalDZSQkIHr18Ow\ncuVddOt2GlWr7saUKTdhaakHb++R0NP78Zh2xhgOHrSBmpoSxo27juzs3NJGEInc3DzMn++B2bPd\n0adPA3h5Df/hYs6keOrqyliypD2uX3+L+/ejhY4jM7Zu9UO9euoYPNiwXI87enQTtG5dA8uWeSE9\nPbtcjy0LAgM/ISkpR2rm132jrq6MCROa4dSpF/j4UfrnnRw9+hxt29aoECftNmwwR3JyFv7886HQ\nUQTh4xOD8PAkmRuG+c2UKc2hp6eGFSvuiuWq3dGjQVBT24WNG32QlVWy92aZmTkYMeIyjh17jnXr\nzLBlSxepOpEFAH37NkTdumpUREXEvhVOoY7d/yq2Y8c59wJQuHzdAADH8r8+BmBgge3H+Vc+ADQZ\nY8X+xhMTczB16k00beoALa096N37PDZt8kVCQiYmTGgGF5e+uHbNtsSLD9aooYp9+7rj8eOP2LDB\np0T3EaXU1CwMHnwJO3Y8xty5rXHhwgCRlIonX8erV6+ugpUr6aqdKPj6xsDbOwrz5rUp93WA5OQY\ntm7tgnfvkmnR8jJwd48AAIlemPx7Zs9uhezsPKkvxuHvHwt//1hMmCB7RVOK0qxZNYwZ0wS7dz9F\ndHSy0HHKnbNzCJSV5aVmGGBpKSsrYNWqjvD1jcHVq2EibZtzjj//fAh5eYbffruLVq2O4+7dHy+v\nkJaWjQEDXHHu3Gvs2GGFlSs7Sl2nDvi6bMiMGS3xzz/vaNkmEfLxiUHdumrQ1aWLJgUplPF+NTjn\nMQDAOY9hjH0bG1kbQMGZt1H52/4zmYIxZoevV/UA1MHp08Fo0qQKJk+ujWbNVGFkpIrKlb/NV/iA\ne/dKN69KWxvo3l0L69c/gK7uFxgZlc8Qs7i4LCxfHorQ0DTMmaOHgQPl4O1N1f9EaehQbezd+w47\ndlxCy5bir0qWkpICT09PsR9HCGvWvIGqqjwMDb8I8jMyBnTqpIH16+/DyCgJmpqK5Z5BWp0+/Qq1\nayshNPQxQkOFTlN6bduqY9euh+jYMV3iFhcuqT173kFRkUFPL05mnyMK69VLHs7OuZg27RwWLdL/\n7n6y9ryZm8tx8uQztG+vhidPZHcdTn39PNSqpYz5829ARaWJyJZRefw4CS9exGPpUn2oqytg5853\n6NzZBX366MDOrg7U1f/37WhKSg5++y0UQUEpWLxYHyYmySJ9PJX349PYOBuKigzLl1/B3LnSNcpC\nUt258xaNG6vK1POMSHDOi/0AoA8gqMD3XwrdnpD/+SoA8wLb3QG0Ka59ff1GPDc3j4taQkI6r13b\nnhsbH+ZpaVkib7+wwMBYrqe3j6uq7uCXL4eK/XgVVXp6Nq9d256bmzvxvDzRP24K8/DwEPsxhBAW\nlsDl5LbyJUvuCJojJOQzl5ffymfNuiVoDmmSlJTJlZS28yFDjgkdpcwuXw7lwBbu4hIidJQyyczM\n4To6e/jQoReFjlLufvnFnTO2hfv5xXx3H1l73rx1K5wDW/iZMy+EjiJ2J04858AWfvbsS5G1OWiQ\nK9fR2cPT07M555ynpGTyxYs9ubz8Vl6t2h5+4sTzf1/PP31K5W3aHOcKCtv4qVPieX4Q4vE5btxV\nXqXKDp6YmFHux5Y1798nc2AL3779kdBRRA6AHy9B3+x7H2U9Tfrx2xDL/M+x+dujAOgV2K8OgPfF\nNaakJCeWxXU1NSvBwaEnXryIx+LFd0o8pru0cnPzcPBgIMzMnJGTkwcvrxHo27ehWI5FgEqVFPDb\nb6a4ezcaS5d6yXxVxWfPPuHatTCRz3nYseMJ5OUZ5sxpJdJ2S8vYWBvTpplg374AvHxJi5aXxPXr\nYcjKyoW5uXRUwyxKr1710aCBhtQWUbl6NQyfP6dXmGGYBa1d2wnVq6tg1ix3mX/+/cbZOQRqakro\n06eB0FHEbuRIYzRurIVVq+6VqdhJYZGRSbh4MRSTJzdHpUpfr8ypqiph8+YuePx4LBo00MTYsdfQ\nvfsZeHlFokuXU3j+PA4XLw7EsGGyM59x9uxWSEnJxvHjz4WOIvVoft33lbVjdwnA+PyvxwO4WGD7\nuPzqmKYAEnn+kE2hdO+uj9mzW2HvXn/o6OzF0KGXcPz4c3z6lCaS9v/55x1atz4BOzs3mJhUg6/v\naLRuTcsZiJudXQtMm2aCzZsfYdAgVyQny+baSvHx6bCxOYs+fc6jd+9zePv2i8jaPXz4GUaONEbt\n2moiafNnrF7dESoqirRoeQm5uoZCR6cymjWT3rkF8vJymDWrFe7di8bTpx+FjlNqDg5B0NVVhY2N\nvtBRyp2mZiVs2dIFvr4xOHxY9tfnyszMwblzrzFwYCNUriz7w8Xl5eWwdq0ZgoPjRFK1eP/+QHDO\nMX26yX9uMzGpjvv3R8Hevhv8/D6iS5dTiIxMxo0bg9G7t2x1otu100X79jWxd6+/RC4pIU18fWOg\nqCiHVq2+XyW/oirJcgfOAB4AMGKMRTHGJgP4A0B3xthrAN3zvweAawDCAIQCOAhgplhSl9KOHVa4\neHEgRowwxr170Rg//jpq1PgbZmZO2LTJF0FBn0r9T/b6dQIGDnSFtfVpJCZm4tSpvvDyGlFs1U4i\nGvLycrC374bdu7vi6tUwmJk5ITw8UehYIjd/vgc+fUrDkiXt4e0djaZNj2LLloc/Xe11//5ApKZm\nY+HCdiJK+nOqV1fF8uUdcPFiKPbufSqSs8SyKisrF1evhqF//4aQl5e+QgIFTZrUDCoqClJXLe7D\nh1RcuxaGsWObSO38wJ81ZkwTdO5cB0uXesn88gc3boQjMTFTZqthFmXwYEOYmFTDmjX3f2r9tczM\nHBw8GIh+/RpCX1+jyH3k5BimT2+JkJCJWLSoLTw8hqFLF70i95V2s2a1wosX8fjnH/EtKVER+PjE\noGXL6hXiREtplaQq5kjOuS7nXJFzXodzfphzHsc5t+acG+R/js/fl3POZ3HOG3LOm3PO/cT/IxRP\nXl4O/fs3woEDNoiKmg4/vzFYtaojMjNzsXy5N5o3P4YGDQ5i3Lhr2LPnCXx9Y5CRkVNkW1++ZGDR\nIk80beoAd/cIbNzYGSEhEzFsmLFUVmuSZowxzJ7dGtevD0ZkZDLatz9ZbJUtaXL16hscPx6MZcs6\n4I8/LBASMhHdu9fDr796oV27k2Ve4DkzMwe7dj2BjY0+WrSQnBLtc+e2RpcudTB7tjvat3eEt7fs\n/C1FycPjHZKSsjBwoPRX5tPUrIRx45rC0TFEZKMoyoOjYzByc3mFHIb5DWMMe/daIzExE8uWeQsd\nR6ycnUOgrV0Z3bpVnKIXcnIM69aZITT0y08NHTx79hViY9Mwa1bxQ/51datgyxZLtGlTs8zHk3TD\nhhlBR6ey1J3MkiS5uXl49OgDDcP8jgp3qlFOjqFNm5pYs8YMfn5jER09HQcO2KBly+q4dSsCc+b8\nA1NTR6ir70Lbticwc+YtODg8Q1DQJ+zb5w8Dg8PYvt0PY8c2watXk7FsWQc6YyCw7t314es7GlWr\nVkLXrqfh4CD9Q4MSEzMxbdotNG2qjRUrTAEAenrqcHUdiHPn+uPTp3SYmjril1/ckZSUWaq2nZxC\n8OFDKhYtaiuO6GVWubIiPDyGw9m5L2Jj02Bh4YLhwy8jIkL2rsT+DFfXUKiqKqJbN+lb5qAov/zS\nGpmZudi3L0DoKCXCOYeDQxA6dNBF48baQscRVPPm1TB3bmscOhT475wXWZOSkoVLl95g6FBDKCrK\nF38HGdKvX0O0a1cT69Y9KHONgr17/WFgULVCdYp/pFIlBUyd2gKXLr3Bu3dJQseRSs+fxyE1NRum\nptSxK0qF69gVVqtWFUyd2gIXLgzE+/fTERk5DefO9cfChW2hoaEMR8cQTJp0E82bH8OMGbfRpIk2\nHj8ei8OHe9LaGRLE0FALPj6j0aWLHiZNuomFCz2kejjfwoWeiIlJhYNDTygr/38ZaMYYbG0NERw8\nEbNmtcKePU/RpIkDLlx4XaJ2OefYts0PLVpUk8gXWsYYRowwxsuXk7BmTSdcvvwGxsYOWLXqLlJT\nSzaPUpbnLuTlcVy8GIqePfVl5oRS48ba6NWrPvbufYrMzKJHSkiSx48/4vnzOEycWHGv1hW0Zo0Z\ndHWrYObM21L9nPs9ly69QXp6ToUahvkNYwy//26OiIikMs2lfPr0Ix48eI+ZM1uKpUCetPo211Ba\nTmZJGh+frzUZ6Ypd0Sp8x64gxhjq1FGDra0hNm2ygLv7MCQkzEFIyEQcP94L167ZwtNzOFq1ouIo\nkqhq1Uq4fn0wZs9uhe3bH6N//wtITCzd1SxJ4OYWjsOHn2Hx4nZo167oJy4NDWXs3m2NBw9GQ1u7\nMmxtL2LcuGvFXr27eTMcz5/HYeHCthI9dFhFRRGrV3fCy5eTMGhQI6xf7wMjoyM4eTIY2dm5ePv2\nC9zdI3DwYCCWL/fGiBGX0aHDSVSrtheamrvh6Bgs9I8gFg8fxiAmJlXmFkhesKAtPn5Mg7Pzzxdq\nEDcHhyBUqqSA4cONhI4iEdTUlLBtmyWePPmI/ftl742qs3MI6tRRg7l5HaGjCKJ793owN6+N33/3\nQXp6dqnuu3evP1RUFDBhQlMxpZNOdeuqo3//hti3LwD370cLHUfq+PrGQFu7Mho21BQ6ikSijl0x\n5OQYjI21MXZsU/Tq1UCi3wwTQEFBDrt3W8Pevhvc3CIwf76H0JFKJSkpE1On3oSxsRbWrOlU7P4d\nOujCz28MVq/uCEfHELRqdfzfs1lF2br1EWrVqoIRI6Tj7LOenjqcnPri3r2R0NVVxdix16Cs/Bca\nNDiEbt3OwM7ODVu2PIKf30doaCjD1tYAzZrpYMyYa1i2TPaWwnB1DYWCgpzMVYuztq6L5s11sH27\nn0Rfcc3IyIGz8wsMGtQImpqVhI4jMYYPN0LXrnXx2293ERubKnQckQkPT8TNm+EYPtyowl5x+nbV\n7v37lFJdYUpIyICTUwjGjGlC/ytF2LDBHJqayujc2QUrVtz96YJoFYmPTwxMTXXp/fh3UMeOyKTp\n01tizJjGOH/+tVQM7/rm11+9EBWVAgeHnv+u91McRUV5rFljBi+vEcjN5TA3d8b69Q/+Myzq6dOP\ncHd/h7lzW0NJSbrminTqVBu+vmPg6NgHy5eb4vDhHvDwGIbw8KnIyJiH0NApcHMbiv37beDhMRzT\nppngjz8eYuBA11LPQZRUnHNcuPAalpZ6qFpVtt4oMcYwf34bPHv2WaKrxV26FIqEhIwKXTSlKN8K\nqaSmZsvMkiVpadkYNOgiKldWwMyZLYWOI6guXfTQrVs9bNrki5SUkg2Jd3AIQnp6TomKplRETZro\nwN9/HMaNa4ING3zQsaMTXryIEzqWxEtMzERISBwNw/wB6tgRmTVkiCESEzPh7i65bxQL+uefd9i/\nPwDz57eBqWmtUt/fzKw2AgLGY/hwY6xadQ+Wlqf+p/DItm1+qFJFEXZ2LUQZu9zIyTGMGtUYv/9u\njkmTmsPSsi7q1dOAvPz/Po0pKcnD3r4b9uyxxrVrYejUyQlhYaJZ/09IL17E49WrBAwa1EjoKGIx\nalRj1Kihgu3bJaKYcpGOHn2OOnXUYG0tG4VrRMnYWBsLFrTF0aPPce+edA8v45xj6lQ3BATEwsmp\nDxo0oCFfv/9ujs+f09Gr17lil7fIy+P4+29/mJvXlqjKy5JGXV0ZDg69cO5cf4SHJ6F16xPYu/ep\nRI9aENqjRx/AOahwyg9Qx47IrG7d6kFdXQlnz74SOkqxUlKyMHnyDRgYVMX69WZlbudrwZ8+OHGi\nNwICPsHE5DhcXF4gMjIJp069xJQpLSrEsBjGGGbNaoWbN4fg/ftUtG/vCE9P6ejgf8+3AjkDBshm\nx05Z+euVkWvX3krkmevo6GTcvBmOceOa/OdkAvlq5UpT6Omp5RdSkd43p3/99RhOTiFYt84Mffo0\nFNGpvDQAACAASURBVDqOROjQQRcuLn3x6NEHdOzohDdvvn+y7ObNt3jz5gtdrSshW1tDPHs2/t/l\nfnr3PoeYmBShY0mkb1NN2rWT3SUxfha9OhGZpaysgP79G8HVNVTix68vW+aNiIgkHDnSQyTVDseM\naQJ//3Fo0kQbI0deQZcup8A5x9y5rUWQVnpYW9fDw4ejUa1aZXTvfhb29v5CRyozV9dQtG9fE7Vr\nqwkdRWxmzGgJZWV57NjxROgo/3HyZDDy8ir22nXFUVVVwo4dVggM/IQLF2KFjlMmt29HYPHiO7C1\nNcDy5aZCx5Eow4YZw919GOLjM2Bq6ogHD4qez713rz9q1FCBra1sFXkSJ13dKrh2bTD27LGGp2cU\nmjc/VuJq1xWJr28MGjfWqhAnqMuKOnZEpg0ZYoiEhAx4eEQKHeW77tyJxJ49TzFnTmuRVl5r0EAT\nXl4jsGpVR0REJGH4cGPo62uIrH1p0ahRVfj4jIaNTT3MnHkbs2bdlviOfmFRUcl49OiDTCxK/iPV\nqqlg7NgmOH78OT5/lpwFy3Ny8rBvXwA6d64DA4OqQseRaIMGGaBHD304OETj7VvpGgL99u0XDB9+\nGcbGWjh6tFeFLZjyI2ZmtfHgwShoaCjDyuoUzp59+T+3v337BdeuhcHOroXUzeUW2reRJk+fjoW+\nvjpsbS9i3z7pPRkpapzz/MIppZ+qUpFQx47INBubeqhSRVFih2NmZeViypSbaNBAAxs3mou8fQUF\nOaxda4bQ0Mk4cKC7yNuXFhoayrh0aRAWLWqLv//2x9q1D4SOVCoXL4YCgMzOryto3rw2SE/Pwf79\ngUJH+Zer62uEhydh/vw2QkeReIwx/P13N8jJMQwY4FriYhtC+1YsJTeXw9V1INTUlISOJLEMDKri\nwYNRaN26BoYOvYytWx/9Oy/M3j4AcnIM06aZCJxSehkba+P+/VHo0UMfCxZ44tWr+DK14+8fi8mT\nb+DLlwwRJxRGWFgiPn9Op8IpxaCOHZFplSsrom/fhrhw4TVyciRv8VxHx2CEhn7B7t3WUFUV3xuJ\n+vU1xdq+NJCXl8OWLZbo168hjhx5JpGPh+9xdQ2FkZEWjI21hY4idk2b6qBHD33s2SM5C5Zv3/4Y\nDRpooH9/mm9VEg0aaGLVqgZ4/jwO48Zdl/hlRzjnmDz5JgIDP8HZuQ9dlS2BatVU4O4+FEOHGmLx\n4juYNes2UlKycPjwMwwaZCDTQ8bLg5KSPI4c+Vode/z466V+vYqPT8fAga44ciRIZirV+vrGAKDC\nKcWhjh2ReUOGGOLz53R4eUUJHeV/5OVxbN78CCYm1dCrV32h41QYEyc2Q0xMKtzcwoWOUiIJCRnw\n9IysEFfr/o+9+w6L6vj6AP4dFEHsoNh7V1Tsib0X7LFX7EY0auw9amLvJXaNBRsYsaHYew32Lih2\nY28gKmXePw684acgsG3u7p7P8/Cgy+69Z+HuvXdmzpyJNnBgGfz7bwg2bboV/5ON7NSpJzh16gkG\nDCjNRVMSoWzZNJgxoyp8fAIwYcJJ1eF818yZ/ti48SYmTqyM+vUta41IY0qe3BYbNzbCkCFlsWjR\nJZQosRqvX39Cnz7WvTyEoWTJkhILF9bC6dNPMW3a2QS/LjJSomPHXXjyJBiNG+fF0qWXcfSodqej\nJNTp00/g4JAURYumVx2KpvFVilm8+vVzw8Eh6TdzAVTbseMObt58jaFDy/FCmybUoEEepE+fHKtW\nXVUdSoL4+t5FeHikxc+vi6l27ZwoWtQJs2efU176e9Ysf6RNa4cuXbhoSmINGFAanTsXxfjxp/D3\n39pMh9+37x6GDTuKFi0KYPjwcqrDMTs2NgLTplXFwoW1cO/eexQp4oSqVbOrDstitGlTCK1aFcS4\ncSdx8WLCChJNmXIGu3YFYfbs6li/vgFy5UqNHj324tMnbWRA6OrMmacoWzYTkiblpsv38G+HWTwH\nB1s0aJAHW7YEfLNotypSSkydeha5cqVGq1YFVYdjVZIlS4L27Qtj27Y7eP36++sxaYGPTwCyZElp\nVeWdacHyMrh48TkOH1bX0xwU9BZbtgSgV68SSJnSulOZdSGEwOLFtfHDD5nRqdMuXLqkrUqZVCxl\nJ4oUccJff9XjDjY99O7tirNn22Pbtqb8ezSwhQtrwckpOTp23BVvevrBgw8wZswJtG1bCB4erkiR\nIhmWLKmD27ffYOLE0yaK2PA+fQrHhQvPuXBKAnDDjlmFFi0K4Nmzj5pZOPf48cc4deoJBg8uy71P\nCnTu7IIvXyKwYcNN1aF8V2hoGPz8gtCkSV6rq9DXvn1hZMiQHLNnn1MWw7x5F2BjI9C3L6/HpSs7\nu6TYsqUJ0qWzR5MmW/HihXaqnQ4YcAgREZHYurUpN9wNoHTpTMiXj+cnGpqTU3KsWFEXV6++xG+/\nxZ3W/ORJMNq23YmCBdNh6dI6/9/ArlMnFzp0KIIpU87i6tUXpgrboC5ceI6wsEgunJIAfEfJrIKb\nWx7Y2yfVTHXMqVPPIn365JzepYirqzNcXZ01n465f/8DfPwYjmbNrCcNM5q9PS1YvmPHHZ2rwunj\n3bvPWL78Mlq3Lohs2bgQhD4yZ04JH58m+PffELRsuV0Ty42cPfsU27ffwZAhZZE3b1rV4TD2XW5u\nedCjR3FMm3Y21g7qsLAItG69AyEhYdi8ufE3HRWzZ1dD2rR26NFjr2YylxIjunAKN+zip1fDTgjR\nXwhxVQhxTQgxIOqxcUKIx0KIi1FfboYJlTHdpUyZDPXr58bffwcor9B29eoL+PreRb9+peDgoP9i\n5Ew3nTsXhb//M033YPr4BCBNGjurnbMSvWD53LmmX7B8+fLLCA4O4yUODKRs2cxYsaIujhx5hP79\nD6oOB2PHnoCTU3L0789/X2YeZs6shly50sDdffc3y4iMHHkMx48/xtKldVCkyLfFRdKnd8Ds2dVx\n+vRTLFpkfmvjnT79BDlypEKWLClVh6J5OjfshBAuAHoAKAegBICGQojobuXZUkrXqK9dBoiTMb21\naFEAT54E4/TpJ0rjmDbtH6RIYcuVwxRr374wbG1tsGrVNdWhxCo8PBLbt99BgwZ5rHah34wZU6B9\n+8L466+reP48xGT7DQuLwNy551G1ajaULm09cxuNrX37Ihg6lCooqlx4+dixR9iz5x6GDy/H69Ux\ns5EqVTKsWlUPd+++xZAhR/7/cR+fAMyY4Q8PD1e0a1c4zte3b18YdevmwogRx/Dw4XtThGwwZ848\n5dG6BNJnxK4wgNNSyo9SynAARwA0M0xYjBlew4Z0g+ztrS4d88GD99iw4SZ69CgOR8fkyuJg1IPZ\nsGFerF17XROpYV87ceIxXr0KtaplDmIzcGAZhIVFokSJNdi48aZJqmT+/XcAHj78gEGDyhp9X9Zm\n0qTKcHPLjV9+OYh9++6ZfP9SSowefRyZMqWAhwd3rjHzUqVKdgwcWAaLF1/Cnj1BCAx8g86dd6Ns\n2UyYNavad18rhMCiRbUQGSnh4bFfecXhhLpx4xXu3XvPDbsE0qdhdxVAFSGEkxDCAYAbgOh8ob5C\niMtCiJVCCJ5JyzQhdWo71K2bC5s331aWjjlrlj8AYOBATv/Rgs6di+L584/w87unOpRvbN0aCDu7\nJKhXz7rXOCxaND1OnWqHrFlTom3bnahTZzMCAt4YbX9SSsyc+Q/y50+HBg14TTNDS5LEBuvXN0Sh\nQo5o2NAHmzaZtoDRgQMPcPToI4waVZ5T4ZlZ+uOPSihSxAldu+5B8+bbkSSJDby9G8HOLmm8r82d\nOy1+/70Sdu68C29vbS0BFZuPH8PQuvUOODklR9u2cY9Gsv8IfVrsQohuAPoACAZwHUAogCkAXgKQ\nAH4HkFlK2TWW1/YE0BMAMmTIUNrLy0vnOBhLqD17XmLKlHv4889CKFIkYbnawcHBSJlS/7zud+/C\n0abNZVSpkg4jRlj3zbpWhIdHolWry3BxSYkJE7QzMialRLt2V5A7d3JMmhR34RRDHZvmICJCYvv2\nF1ix4jG+fIlE+/aZ0bZtJiRLZtgaYFeufEC/frcwYEAONGnibNBtW5P4js0PH8IxenQgLl8ORp8+\n2dGiRUajxySlRJ8+N/HqVRjWrnUx+LHDzIe5nztv3w6Bh8dNRERITJ6cDz/8kPACQBEREh4eN/Di\nxResXu2CVKnibxCqMnVqEPbseYUpU/KjXLk0qsMxierVq5+TUpbReQNSSoN8AZgEwOOrx3IBuBrf\nawsUKCAZM4XXr0Olre1MOXjwoQS/5tChhD/3e8aNOyGB6fLq1RcG2R4zjIEDD0pb25nyxYsQ1aH8\nv0WLLkhguly16sp3n2eoY9OcPHnyQbZps0MC02W+fMvk3r1BBt1+s2ZbpaPjfBkS8sWg27U2CTk2\nQ0PD5E8/bZXAdDl48CEZERFp1Jh27AiUwHS5bNklo+6HaZ8lnDs3brwR7zUiLhcuPJNJksyQ3br5\nGTgqw1mx4rIEpsuxY4+rDsWkAPhLPdpj+lbFdI76ngPATwA2CCFiJsE2A6VsMqYJ6dLZo1atnNi8\n+bZJ88tDQr5g/vwLaNgwD4oW/bZiFVOnc2cXhIVFYv16baxpd/z4I/TrdxBubrnRoUMR1eFoTubM\nKbFhQ0Ps3dsCAFCnzma0bbsT//6rf3GVwMA32Lo1AL17u3KangnY2yeFl1cj9Onjihkz/NGp0y58\n+WKc+a6RkRJjxpxAnjxp4O5e1Cj7YMyUWrcuBHd33ZZMcnV1xuDBZbFixRX4+QUZODL9Xbr0HH36\nHECtWjkxduyPqsMxK/rmIfwthLgOYAeAPlLKNwCmCSGuCCEuA6gO4Fd9g2TMkFq0KIB7997j/Pln\nJtvnypVX8epVKIYNK2eyfbKEKVYsA0qXzoi//lLfB/Xo0Qe0aLEduXKlwbp1DZAkCaeKxaV27Vy4\ncqUzfvvtR2zZEoAyZdbi2rWXem1z7tzzSJrUhivWmlCSJDaYP78mJk2qjHXrbqBBgy14//6zwfez\nZcttXLz4HOPGVYCtrXVWmWUspt9++xFFizrhp5+2Yf/++6rD+X/v3n1Gixbb4ehoj3Xr3Pg6mEh6\n/baklJWllEWklCWklAeiHusopSwmpSwupWwspXxqmFAZM4wmTfIhSRJhssXKw8IiMHOmPypUyIJK\nlbKZZJ8scbp0ccHFi89x8eJzZTF8+hSO5s23ISQkDFu3NkHatPbKYjEX9vZJMW5cRZw92x4RERKV\nK2/EqVO6LWfy5s0nrFx5Be3aFUbmzOY798YcCSEwYkR5rFpVD4cOPUDVqpsMMgIbLSIiEmPHnkCh\nQo7fLQfPmDVJntwWBw+2Qv786dCw4Rb4+t5RHRKklOja1Q9BQe/g5dUIzs4pVIdkdrgZzKyOk1Ny\n1KxpunRML69buH//PY/WaVjbtoWQLFkSrFqlZtROSok+ffbj7Nl/sWaNW6wLzLK4lSjhjBMn2sLR\n0R61annplFq0dOklfPwYzguSK+Tu7oKdO39CQMAb/PjjOty69dog292w4SZu3HiNCRMqcu8/YzE4\nO6fAwYOt4OKSHs2abYOPT4DSeObMOYctWwIwbVpVVKyYVWks5orPcMwqtWhRAIGBb3H58guj7kdK\niWnT/kGRIk5o2DCvUffFdOfomBxNmuTFunU3jDbH53sWLryIlSuvYsyYH9CsWdxVMFnc8uRJi+PH\n2yJ//nRo1MgH69ffSNDrpJTYv/8+Zs8+h1q1cqJECa6EqVK9erlx6FArhISEoWrVjXj06INe2wsL\ni8C4cSdRokQGNG9ewEBRMmY5nJySY//+lihTJhNattyOjRvVzDc/efIxhg49imbN8nMHmx64Yces\nUtOm+WBjY/x0zG3bAnH58gsMGVIWNjbCqPti+unc2QUvX4Zi1667Jt3v0aMPMWDAITRsmAfjxlU0\n6b4tTaZMKXDkSBtUqJAF7dv7Yv7883E+V0qJAwfuo0qVjahd2xu2tkkweXJlE0bL4lK2bGYcOtQa\nISFhaNZsK0JDw3Te1po113Hnzlv8/nslPgczFoe0ae2xZ08LVKyYFe3b+2L1atNmr7x48RGtWu1A\nzpypsXJlXQjBn1VdccOOWaUMGRxQrVp2eHndMtpi5Y8ff0CPHnvh4pKe53WYgTp1ciFz5hQmLaLy\n8OF7tGy5A3nzpoWnZwO+8TSANGnssGdPCzRpkg/9+h3E2LHHv0m5Pnz4AapV24RatbwRFPQOf/5Z\nE4GB3VCmTCZFUbOvFS2aHp6eDeDv/wy9eu3TKW3+8+dwTJhwEuXKZULDhrzYPGPfkypVMuze3Rw1\nauRA585+WLr0kkn2GxERiQ4dduHly1Bs3tyY55friRt2zGp1714Mt2+/wfLllw2+7fDwSLRr54vQ\n0HB4ezdCsmRchU3rkia1QceOReDrexfPnhmucENcQkPD8NNP2xAaGo6tW5sgTRo7o+/TWtjbJ8Xm\nzY3RtasLfv/9NDw89iMiIhJHjz5E9eqbUL26FwID32L+/BoIDOwOD4+SsLPT7iK91qpJk3wYP74C\n1q69jjlzziX69cuXX8GDBx/wxx+VeASAsQRwcLDFjh3N4OaWG7167cO8eXFnPRjKiBHHsHfvPSxY\nUBOurpwKry9u2DGr1aZNIVSvnh3Dhh01+I38uHEncfToIyxaVAuFCjkZdNvMeDp3dkFEhMS6dQmb\nn6UrKSV6994Pf/9n8PR042PECJImtcHy5XUxdGhZLF58CXnzLkfVqptw8+ZrzJ1bA3fudEffvqVg\nb88NOi0bPfpHNGuWH4MHH0lUSXZv71sYPvwoqlTJhlq1choxQsYsi719Uvj4NEWzZvnRv/9BjBt3\nAmFhxpl7PnXqGUyf/g88PFzRrVsxo+zD2vAVjVktIQQWLaqN4sVXY/DgI1i71s0g292zJwiTJp1G\n164u6NiRF8I1J4ULO6F8+cxYtuwy+vcvpVMFPSkl+vY9gAMHHiAyUn7zFREhER4eiefPP2LcuApo\n3DifEd4JA+gzPnVqVWTMmAKLFl3E7NnV0atXcSRPzouPmwsbG4HVq+vjxx/XoVWrHfjnnw7Imzdt\nnM//8iUCgwcfxvz5F/DDD5mxbl0DHq1jLJGSJUuCTZsaoksXP4wffwqbNt3CrFnVUL++4VKaly69\nhOHDj6Ft20KYP78mf04NhEfsmFUrWNARw4aVhafndRw4oP8CnY8ff0CHDrtQpIgT5s+vaYAImakN\nGlQGN2++xtKluqXobt58GwsXXkS2bClRpkxG/PBDZlSqlBXVqmVHrVo5Ub9+bjRpkg/TplXBmDE/\nGjh6FpuBA8sgIKA7BgwozY06M5QqVTJs29YMANC06VYEB3+J9XkPHrxHlSobMX/+BQwYUBpHjrRB\ntmypTBkqYxbD1jYJ1q51w/btzRARIeHmtgVubn/j5s1Xem9706ab+PnnfXBzy43Vq+vz/HID4hE7\nZvVGjvwB69ffRO/e+3H5srvOqVnR8+o+fgyDt3djODjwDaQ5atGiAKpXz47Ro4+jVauCcHJKnuDX\nhoR8wcCBh+Hq6ow9e1rwmlmMGUjevGmxaVND1Kv3N9zdd8Pbu/H/3Azu3n0XHTrsQlhYJLy9G6FF\ni4IKo2XMMggh0KhRXtStmwsLFlzAhAmnUKzYanh4uOK3336Eo2PCr4/R/PyC0LHjLlSqlA3e3o1h\na8s1CAyJ7zqY1bO3T4pFi2ohIOANpk49q/N2/ptXVxuFC/OcKXMlhMC8eTXw7t1njB59PFGvnTTp\nDB49+oAFC2pyo44xA6tdOxemT6+KLVsCMHHiaQBUUW/06ONwc9uCbNlS4dy5jtyoY8zAkiVLEpX5\n0A3duhXDggUXkD//Cvz55wWEh0cmeDsnTjzGTz9tg4tLeuzY0Yw7wI2A7zwYA90wtG1bCJMmncHt\n268T/fq9e+/9/7y6Tp14Xp25c3HJgL59S2LJkks4f/5Zgl4TEPAGM2b4o2PHIqhYMauRI2TMOv36\na2l06FAEY8eewIoVV1CnzmZMnEjn3tOn2yF//nSqQ2TMYmXI4IDFi2vjwoVOcHV1Rt++B1C8+CrM\nnu2PBw/ef/e1ly49R4MGW5A9eyr4+TXnStBGwg07xqLMmlUdyZMnRe/e+xO1ZtKTJ8Ho0MGX59VZ\nmHHjKiB9+uT45ZcD8R4PUkr0738QdnZJMHVqFRNFyJj1EUJg6dLaKFMmI7p334OTJ59g5cq6WLGi\nHs+fZMxEihfPgP37W8LHpwns7JJi4MDDyJlzKcqX98T06Wdx9+7b/3l+QMAb1K27GalSJcO+fS3h\n7JxCUeSWjxt2jEXJlCkFJk+ujIMHH2D9+oSVu6d5dTsREsLz6ixN2rT2mDKlCk6efAJPz+vffe7O\nnXexe3cQxo2rgMyZU5ooQsasU/LktvDxaYru3YvhzJn26NKFy6QzZmpCCDRtmh8XLnRCQEA3TJlS\nGZGREkOHHkXevMtRqtQaTJp0GsePP0Lt2t6IiJDYt68FcuRIrTp0i8YNO8Zi6NWrBMqXz4yBAw/j\nzZtP333uw4fv0bPnXhw5wvPqLFXnzi4oVy4Thg49ivfvP8f6nE+fwtG//0EULuyIX34paeIIGbNO\n2bKlwrJldVG8eAbVoTBm9fLlS4dhw8rjn386IiioB2bMqAo7uyQYNeo4KlfeiNevP2HPnha8ZqsJ\ncMOOsRhsbAQWL66NV69CMXz40W9+Hhkp4ecXhCZNfJAr1zKsWnUVv/5amufVWSgbG4EFC2ri2bMQ\nTJhwKtbnTJ/+D4KC3mH+/Jpc3YsxxphVy5UrDQYNKotTp9rj4cNe+PPPmjh4sBVKlcqoOjSrwMsd\nMPYVV1dn9O9fCrNmnYO7OzXYXrz4iL/+uoolSy7h7t13cHZ2wLBh5dCzZ3HkypVGccTMmMqWzYyu\nXYth7tzz6Nat2P+MzN679w6TJp1By5YFULNmToVRMsYYY9qSLVsqeHhwJospccOOsViMH18RXl63\n0aPHXmTOLHHs2AV8+RKBqlWzYeLEyvjpp/xIloxHZ6zFpEmVsHnzbfTvfxB79rSAELR+1qBBh2Fj\nA8yYUU1tgIwxxhizenqlYgoh+gshrgohrgkhBkQ95iiE2CeECIj6zrWHmdlJmTIZ5s+vgevXX+H0\n6Xfo1as4rl3rjMOH26BNm0LcqLMyzs4pMGFCRezbdx9btwYCoCUutmwJwKhRP/BkcMYYY4wpp3PD\nTgjhAqAHgHIASgBoKITID2A4gANSyvwADkT9nzGz07Rpfpw71xHe3sUxb15NFCmSXnVITCEPD1e4\nuKTHr78ewrt3n9Gv30Hky5cWgwaVUR0aY4wxxpheI3aFAZyWUn6UUoYDOAKgGYAmAFZHPWc1gKb6\nhciYOqVKZUTy5Dw6x4CkSW0wf34N3L//HhUqrMetW68xd24N2NlxRjtjjDHG1NOnYXcVQBUhhJMQ\nwgGAG4DsADJKKZ8CQNR3Z/3DZIwx9apVy4HWrQvi+vVXaNQoL9zc8qgOiTHGGGMMACCklLq/WIhu\nAPoACAZwHUAogC5SyrQxnvNGSvnNPDshRE8APQEgQ4YMpb28vHSOgzFjCg4ORsqUvOg0Iy9ffsGK\nFY/h7p4FmTLZKY2Fj02mVXxsMi3j45NpVfXq1c9JKXWe46FXw+5/NiTEJACPAPQHUE1K+VQIkRnA\nYSllwe+9tmDBgvLWrVsGiYMxQzt8+DCqVaumOgzGvsHHJtMqPjaZlvHxybRKCKFXw07fqpjOUd9z\nAPgJwAYA2wG4Rz3FHcA2ffbBGGOMMcYYY+z79J31/7cQwglAGIA+Uso3QogpALyi0jQfAGipb5CM\nMcYYY4wxxuKmV8NOSlk5lsdeAaipz3YZY4wxxhhjjCWcXqmYjDHGGGOMMcbUM1jxFL2CEOIDAK6e\nwrQqPYCXqoNgLBZ8bDKt4mOTaRkfn0yrCkopU+n6Yq2srHtLnwowjBmTEMKfj0+mRXxsMq3iY5Np\nGR+fTKuEEP76vJ5TMRljjDHGGGPMzHHDjjHGGGOMMcbMnFYadktVB8DYd/DxybSKj02mVXxsMi3j\n45NplV7HpiaKpzDGGGOMMcYY051WRuwYY4wxxhhjjOmIG3aMMcYYY4wxZua4YccYY4wxxhhjZo4b\ndowxxhhjjDFm5rhhxxhjjCWCEOKaEKKakbY9WQgxQMfXnhVCFDV0TIwxxswDN+wYY4zpRQjRTgjh\nL4QIFkI8FULsFkJUUh2XIQgh7gkhasV8TEpZVEp52Aj7ygCgE4AlMR5LJYSYJIQIFEJ8EEIECSEW\nRD33azMATDB0XIwxxswDN+wYY4zpTAgxEMAcAJMAZASQA8BCAE1UxmWmOgPYJaUMBQAhRFoAxwAU\nAlBfSpkKQGUAtgByxvL67QCqCyEymyZcxhhjWsINO8YYYzoRQqQBjRD1kVJukVKGSCnDpJQ7pJRD\nop5TWAhxWAjxNiqFsXGM198TQgwWQlwWQrwTQmwSQtjH+PkwIcTjqJGqW0KImlGPSyFEvhjPWyWE\n+OOr7Q6J2m6IEGKFECJj1EjiByHEfiFEuhjPHSGEuC6EeCOE+Cs6BiHEWlBDdUfUaOTQGK+ppe/7\ni0V9AEdi/H82gNcAWkgpAwBASvlIStlLSun/9YullJ8AnANQ57t/OMYYYxaJG3aMMcZ09SMAewA+\nsf1QCGELYAeAvQCcAfwCYJ0QomCMp7UCUA9AbgDFQaNWiHpOXwBlo0aq6gK4l4jYmgOoDaAAgEYA\ndgMYCSA96NrXL8Zz20dtP2/U80cDgJSyI4AHABpJKVNKKacZ6v3FoRiAW1Hbzg6gI4BRUsrIRLzv\nGwBKJOL5jDHGLAQ37BhjjOnKCcBLKWV4HD//AUBKAFOklF+klAcB7ATQNsZz5kkpn0gpX4MaSa5R\nj0cAsANQRAhhK6W8J6W8k4jY5kspn0kpH4PSGc9IKS9IKT+DGqIlYzx3gZTyYVQME7+K73v0Kc8w\nrgAAIABJREFUeX+xSQvgQ9S/awF4IaU89b0AhBDVhRC5Yjz0IWo7jDHGrAw37BhjjOnqFYD0Qoik\ncfw8C4CHX4043QeQNcb//43x74+ghhKklIEABgAYB+C5EGKjECJLImJ7FuPfobH8P2WM/z/8Kr6E\n7kfn9xeHNwBSRf07I2i0MD5dAYgY/08F4G0CXscYY8zCcMOOMcaYrk4B+ASgaRw/fwIguxAi5rUm\nB4DHCdm4lHK9lLISqFCIBDA16kcfATjEeGqmxAQdi+xfxfckZhjfeZ1e7y8Wl0GpoAA16rJ+te3/\nETWfrxGAv4QQnaIeLgzgko77Z4wxZsa4YccYY0wnUsp3AMYC+FMI0VQI4SCEsBVC1BdCTANwBkAI\ngKFRj1cDNUQ2xrdtIURBIUQNIYQdqPEYCkrPBICLANoJIZIIIeoBqKrnW+kjhMgmhHAEzcPbFONn\nzwDkieN1Or+/OOzCf+9lZ9T3KUKI1FHbLxZVCCZDjOdckFJWk1KuifpdlQawT8f9M8YYM2PcsGOM\nMaYzKeUsAANBBUdegNIa+wLYKqX8AqAxqNrjS9AyCJ2klDcTsGk7AFOiXvcvqDjJyKif9Qc1oN6C\nCp9s1fNtrAcVQLkb9fVHjJ9NBjA6qurl4Jgv0vP9xWYNADchRHIp5XsANUAjeAGgtNeNAJ5JKV9E\nPT8fooqtRGkM4LCUMuaII2OMMSshpPxelgljjDFmuYQQ9wB0l1LuVx0LAAghJgF4LqWck4DnNgWQ\nK/q5QogzALpJKa8aOUzGGGMaFNeEd8YYY4yZmJRyZPzP+n+3AfwhhMglpRwgpSxvrLgYY4xpHzfs\nGGOMMTMkpbwOwEV1HIwxxrSBUzEZY4wxxhhjzMxx8RTGGGOMMcYYM3OaSMVMmzatzJcvn+owGItV\nSEgIUqRIoToMxr7BxybTKj42mZbx8cm06ty5cy+llBnif2bsNNGwy5gxI/z9/VWHwVisDh8+jGrV\nqqkOg7Fv8LHJtIqPTaZlfHwyrRJC3Nfn9fGmYgohVgohngshrsZ4zFEIsU8IERD1PV3U40IIMU8I\nESiEuCyEKKVPcIwxxhhjjDHG4peQOXarANT76rHhAA5IKfMDOBD1f4AWac0f9dUTwCLDhMkYY4wx\nxhhjLC7xNuyklEcBvP7q4SYAVkf9ezWApjEeXyPJaQBphRCZDRUsY4wxxhhjjLFv6TrHLqOU8ikA\nSCmfCiGcox7PCuBhjOc9inrs6dcbEEL0BI3qIUOGDDh8+LCOoTBmXMHBwXx8Mk3iY5NpFR+bJiIl\nUl+/jjRXruBJo0aI4IIgCcLHJ7NUhi6eImJ5LNaF8qSUSwEsBYCCBQtKnsTKtIonWTOt4mOTaRUf\nm0b28CGwdi2wejVw+zYAIO+5c8Du3UD69IqD0z4+Ppml0nUdu2fRKZZR359HPf4IQPYYz8sG4Inu\n4THGGGOMMXz8CHh6ArVrAzlzAqNGAZkyAStWAJs2AVevAlWqAI8eqY6UMaaIrg277QDco/7tDmBb\njMc7RVXH/AHAu+iUTcYYY4wxlkh37gDdulEjrmNH+v/YsfT9yBGga1egVSvAz48adZUqAYGBqqNm\njCkQbyqmEGIDgGoA0gshHgH4DcAUAF5CiG4AHgBoGfX0XQDcAAQC+AigixFiZowxxhizfFICrVsD\nN27Qd3d3oHJlwCaWfvmqVYFDh4C6dalxt2cPUKKE6WNmjCkTb8NOStk2jh/VjOW5EkAffYNijDHG\nGLN6x44B584BixcDvXrF//zSpek1deoA1aoBvr5AhQpGD5Mxpg26pmIyxhhjjDFjmjULcHKiFMyE\nKlwYOH6ciqjUrk0jd4wxq8ANO8YYY4wxrQkIALZvBzw8AAeHxL02Z05q3OXPDzRqBHh7GydGxpim\ncMOOMcYYY0xr5swBbG2pYaeLjBmBw4eBcuWANm2Av/82aHiMMe3hhh1jjDHGmJa8fg389RfQvj1V\nw9RV2rSUilm4MDB5suHiY4xpEjfsGGOMMca0ZMkSIDQU+PVX/beVIgUtiXDu3P8vZs4Ys0zcsGOM\nMcYY04ovX4D586myZbFihtlm69aAEMCGDYbZHmNMk7hhxxhjjDGmFRs3Ak+fAgMHGm6bWbPSOnfr\n19PaeIwxi8QNO8YYY4wxLZCSljgoWpRG7AypXTtKxbxwwbDbZYxpBjfsGGOMMca04OBB4NIlGq0T\nwrDbbt6cqmxyOiZjFosbdowxxhhjWjBrFuDsTKNrhuboCNStS6mekZGG3z5jTDlu2DHGGIudnx8w\naBDg4wO8eqU6GsYs240bwK5dQJ8+gL29cfbRrh3w6BEtXs4YszhJVQfAGGNMg168oJvAN29oFAEA\nihcHqlWjIgxVqgDp0ysNkTGLMmcONeh69zbePho3BhwcqIhKlSrG2w9jTAkesWOMMfatoUOBDx+o\n0MLx48DEiUDGjMDy5TRXJ0MGaugNHgyEhKiOljHz9uIFsGYN0KkTfbaMJUUKoEkTwNubllVgjFkU\nbtgxxhj7X8eOAatWURqmqytQsSIwciSwdy+N4J04QQ29zJmBmTOBsWNVR8yYeVu0CPj0CRgwwPj7\natsWeP0a2LfP+PtizBJISSPp5cpR8aHwcNURxYkbdowxxv4TFgZ4eAA5cgBjxnz782TJgAoVqKG3\nZw/Qsycwdy5w8aLpY2XMEnz6BPz5J+DmBhQubPz91a0LpEvH1TEZS6gxY4DFi2l+art2QMGC9P9P\nn1RH9g1u2LH/vH8PXLtGvfWcosGYdZo7F7h6FZg3j9K24jN5MlXb+/lnrrTHmC7WrQOeP6cRclNI\nlgxo0QLYuhX4+NE0+2TMXC1ZQhkq3btTw87Hh+aX9+4N5M4NTJtG988awQ07a/P+PbB2LfDHH0Cv\nXkD9+oCLC5AmDX25uNCE6tq1KeWKMWY9Hj4Exo0DGjWieTgJ4ehIxVXOnAGWLjVqeIxZHCmB2bOB\nEiWA6tVNt9+2bWlu7I4dptsnY+Zm507KYHFzo3RpGxugaVPg9Glac7JYMWDYMMpwGTWKOmgU44ad\nNXn7FqhRgyZnjxlDvQ7PnwP58gHu7tTrsGEDpYScPg1UqgQ8eKA6asaYqQwYQKNu8+Yl7nXt29O5\nZfhw4Nkz48TGmCU6dYoyZfr1M/yC5N9TpQqQJQunYzIWl7NngdatgZIlgU2bgKQxFhIQgjpi9u4F\n/vmHBkMmTwby5AGuXFEXM3i5A+sRHEw9DpcvA5s307+TJ4/7+YULA82aAT/+SOvqlChhulgZY6a3\naxewZQswaRKQK1fiXisEsHAhVckcOJBSyxhj8Vu9mpYfaNnStPtNkoRuWhcsoOycdOlMu3/GtOzO\nHaBhQ8DZmUbtUqaM+7llylCV2Zs3af754ME0/1wRHrGzBh8/UmrV2bPUO9e8+fcbdQD1RBw7Rjds\nlSsDBw6YJlbGmOmFhgK//AIUKqT7PJ+CBWnEbv16YP9+w8bHmCUKDQU2bqRrcqpUpt9/u3ZULGnL\nFtPvmzGtevECqFcPiIgA/PyATJkS9rpChSgbbu9ebtgxI/r8GfjpJ+DIEVojp3nzhL+2WDFKycyZ\nk+birV9vvDgZY+pMngzcvUtp2MmS6b6dESMotdvDQ5PVwhjTlG3baN57585q9l+6NH1eOR2TMfLx\nI9C4Mc03376dOiwTw8OD0jGHDKGGoQLcsLNkYWGUarFnDy0q3K5d4reRLRuN3FWsSPNopk6lyd6M\nMctw+zZ9rqPnyenD3p4mmAcEAFOmGCY+xizV6tVUdKFaNTX7F4LuCw4eBJ4+VRMDY1oREUGfhzNn\naDpBxYqJ34adHV37rlyhz7cC3LCzVBERQMeO1CO4YAHQtavu20qbloajW7emVKtfflHWE8EYMyAp\ngT59KDV7xgzDbLNWLbo4Tp4M3LplmG0yZmmePKGUrY4dqdKeKm3b0nnAy0tdDIxpwYABdM88Z07i\nstu+1qIF8MMPlJYZEmK4+BKIi6dYoshIoFs3quIzfTrduOnLzo5SMbNlA2bOBE6coBzkqlWpV0PF\n/ADGmH68vGg+3IIFCZ9HkBAzZwK+vpSWsn+/aav9WbIPH2g5in//pZvxyEj6/vW/S5Sg5WwM+Tdl\nhuXpSX8zd3e1cRQqRFX/1q8H+vdXGwtjqty6RdfBvn2pQq0+hKCO0kqVaCmgMWMME2MC6dVNJITo\nL4S4KoS4JoQYEPXYOCHEYyHExagvN8OEyhIkugd+9Wpg/HiqzmMoNjZ0sC5f/l8Pf/36VE2rXDlg\n6FC6mXv3znD7ZIwZR1gYVbAsXZoWFzekTJkoHeXgQa6QaUiTJv23ZuA//wAXLgCXLtGC8jdu0M3J\nzZvU+MuRg0aD/P1VR82+JiVdoytUAPLnVx0NjdqdPUuVABmzRp6edI87YoRhtlexItW3mDqVOuJM\nSOeGnRDCBUAPAOUAlADQUAgRfYaaLaV0jfraZYA4WUKNHAksXkwLJhqrl6BbN+DkSVoXb+9eSs+0\ns6Ph64YNacHi6GUSeD4eY9p04gSlg40YQaXPDa1nT6B8eWo8vnlj+O1bmwcPaCHrDh2AwECaxxjd\nkLt+ndZCu3qV/n37NjXWt24FypalmwwvL2rMM/X8/envpHq0Llrr1vR940a1cTCmgpTUsKtZk9Z2\nNJQpU6iA4bhxhttmAugzYlcYwGkp5UcpZTiAIwCaGSYsppPAQFpkvEsXmt9i7PSnFCloUcY//qAC\nK2/f0rIIo0cDL18CDRrQzy9eNG4cjLHE8/UFbG2BOnWMs30bG2DJEuD1a8oeYPoZOZLO6RMnxv/c\n/PlpkflHj6gx+O+/dPOeJw/dbLx6Zfx4WdxWr6ZCQ61aqY6E5MhByxqtW8edscz6nDwJ3LtHnWaG\nlD8/0Ls3sGwZdeSYiD4Nu6sAqgghnIQQDgDcAGSP+llfIcRlIcRKIQSvemkqU6bQjdqkSWrmtDg4\nUFW98eOp93juXEoVKlWKGpuPHpk+JsZY7Hx9aY6sMefHlihB1TaXL6eOH6Ybf3+66f71V7oJT6g0\naaggwO3b/5XuHjECyJ2b5mAz0/v8mZYXaNqUCpNpRfv2lM57/rzqSBgzLU9Pml7UzAhjU2PH0uLm\nw4YZfttxEFKP3hkhRDcAfQAEA7gOIBTAFAAvAUgAvwPILKX8piSjEKIngJ4AkCFDhtJeXJFJL3bP\nnqF8+/Z40rgxAvWd+GlASYODkcPTE9m2bIG0scHDVq3wsE0bRDg4qA4twYKDg5EyZUrVYTD2DV2P\nTfsnT/BD+/YI7NMHj1q0MEJk/0l5+zbK9OqFwN698UgrIxTmREq4DhgAhwcPcMbTExEpUui1uRRB\nQSgwcybSXLuGx02a4I6HByL1WbswDnzejF36I0fgMm4cLk+ditflyqkO5/8l/fABFZo3x5OGDTV1\nD2EsfHwyABBhYajQvDlelyuHG6NHG2Uf2TdsQN6lS3Fx1iy8LVky3udXr179nJSyjM47lFIa5AvA\nJAAeXz2WC8DV+F5boEAByfTUp4+UtrZSPnigOpLYBQVJ2bYt1WxzdpZy8WIpw8JUR5Ughw4dUh0C\nY7HS+dicN48+i7dvGzSeOFWpImXOnGbzmdcUHx/6Wy1caLhtfvki5eDBtN1SpaQMDDTctqPweTMO\njRpJmSWLlOHhqiP5VsuWUjo5Sfn5s+pIjI6PTyal/O/8umuX8fbx8aOUOXLQuTYiIt6nA/CXerTH\n9K2K6Rz1PQeAnwBsEEJkjvGUZqCUTWZMT59SqlPnzkD27PE+XYlcuaic8pkzlA70889UYMWEeceM\nsSi+vpT/b6qKfL/+Cty/T2sEsYQLC6Nqw4ULAz16GG67tra0FM727UBQEKXL//234bbPYvfsGRUV\n69DBOAWL9OXuTvMvd3HNO2YlPD2BDBmoHoSxJE9Oc6PPn6f7YCPTd1XMv4UQ1wHsANBHSvkGwDQh\nxBUhxGUA1QH8qm+QLB4zZgDh4VSdUuvKlQOOHKHqW/fu0fo5U6dS/Iwx4wsJAQ4fpgq2ptKoEc3r\nmjPHdPu0BIsXU/XL6dOBpEZYdrZRI7rZKFSIFtXt35/mgDHjWL8eiIjQTjXMr9WtC2TMSMVdGLN0\nb98CO3bQch/GOL/G1K4ddaCNGgWEhhp1V3o17KSUlaWURaSUJaSUB6Ie6yilLCalLC6lbCylfGqY\nUFmsXrygi3+7dlTxzBwIQRXarl2jG4vhw2khx5s3VUfGmOU7cIBu3hs0MN0+kyShRV+PH+d11RLq\n7VsqRFWjBuBmxOVgc+WiqsYDBlAlzcqVaRSPGd7q1bT8RJEiqiOJXdKkVETF15cqWzNmyTZvBr58\nMXw1zNhErwP94AGdZ425K6NunRnf7NnU+h85UnUkiefsDHh7U4WwgADA1ZUO/IgI1ZExZrl8fakS\nZuXKpt1v166037lzTbtfczVpEi0VMXOm8ascJ0tG15ItW6iCZqlSlDbPDOfiRVpMXqujddHc3SkF\neMMG1ZEwZlyenjQ1qIzudUoSpXp1Sqk38pQpbtiZszdvgAULgJYtKZXGHAkBtGlDo3f16gFDhtAN\n5+3bqiNjzPJISQ272rXpZt6UUqemxt3GjbQwOovbvXvUAO7UiTq8TKVZM0rNTJOG9v3pk+n2belW\nr6bPXJs2qiP5vuLF6Zhbs0Z1JIwZz/37NC2oQwfTLg+2dCll2BkRN+zM2fz5wIcPlLNr7jJlAnx8\nqAfl5k1a/2rJEtVRMWZZLl0CHj82bRpmTP360Yj8woVq9m8uRoyg9NWELEZuaHny0M3H7dvA77+b\nfv+WKCyM1iFs1AhwclIdTfzc3SllmoubMUsVXcTEyI0sFbhhZ64+fKBCBE2aUA+bJRCC8vuvXQOq\nVAF69wZOn1YdFWOWw9eXvhtzztb35MlD56zFi40+gdxsnTlDo5qDBwNZs6qJoU4durmfNo06A5h+\n/PxoPrzW0zCjtWtH8+24iAqzRFICa9cCFSuaT22KROCGnblauJBSMS1htO5rmTPT3LusWYFu3bhK\nG2OG4utL8wkyZVIXw4ABVFJ93Tp1MWiVlMCgQVSZcMgQtbHMmgU4OtI5mKsW62fVKppTXq+e6kgS\nxtkZqF+fMmh4zvv/ev+eliBJlw5o1YqLQZmjixeBGzdMUzRFAW7YmaOPH2lCfd26VGHLEqVOTb36\n168DkyerjoYx8/fyJY2Aq0rDjFalCs3hmTOHGjLsP1u2ACdOUApkqlRqY3F0pDnc587xMhX6ePWK\nSqq3b0/rB5oLd3eaC7t/v+pItCEykkZ5Chak5UcqVAD27KF7sJo1gb17+XxmLjw96bPYsqXqSIyC\nG3bmaNkySusYM0Z1JMbVoAFdDCdOBK5cUR0NY+Zt92668VDdsBOCRu2uXeObxpg+f6ZROhcXKjKj\nBS1aUOrsmDFAYKDqaMyTlxfNsTOXNMxoDRvSqBSnY1JBoUqVqKBQjhyULu3rCzx8SOnKN25QR3up\nUlRNlEe4tSs8nObXNWhgHvNddcANO3Pz6ROdSKpVo/xgSzdnDl1cunblkyVj+vD1pRS/0qVVR0KV\nATNm5JGgmObOpfXjZs2iwilaIATw559UzbFnTx6R0IWXF1WtNre58HZ29Dn18QHevVMdjRovXwK9\nelH6+p07wMqVwKlTQLly9PPUqakzJigIWLGC5g23awcUKECfG55HrD0HDwL//muxaZgAN+zMz6pV\nlB4xerTqSEwjfXqq/unvz+tfMaar8HBKG3Jzo4VSVbOzAzw8gF27gFu3VEej3rNnwB9/UNXE2rVV\nR/O/smal9UUPHaKbV5Zwz54BR49SypcpS6obirs7dSZ7e6uOxLTCw6lhVqAAHfP9+9N5qkuX2M+f\ndnbU+Xz9OjWEM2YE+valEW/uDNEWT09azkV15ooRaeAKzxIsLAyYMgX48UegRg3V0ZhOq1ZA48ac\nDsSYrk6eBN6+1dbF7OefaSRo3jzVkag3ejTdQM+YoTqS2HXvTlkigwfzGoSJsWULzc0y17k85crR\nnDJrSsc8doyyGvr2BUqWpKqws2cDadPG/1obG6BpUzrfTptGHVfbtxs/ZpYwISH0mWzZErC3Vx2N\n0XDDzlxISeX/798Hxo41z94/XQlBVUBtbYEePehCyRhLOF9f+vxoaTTI2Znm0K5aBbx+rToadS5e\npFGBX36hEQItEoLmdn/+DPTpw6MQCeXtTQ0jFxfVkehGCBq1O36cUhEt2ZMnlJ5XpQpVHPf2pjnA\nRYsmfltCAL/+Sn/3AQM4JVMrtm2jxp0Fp2EC3LAzH+PH08V/9GjzKZlsSFmzUiXQw4eB5ctVR8OY\nedm5E6hcmeaEaEn//lTl11o/01LSjZ+jo/aLYeXLR9ehrVuBv/9WHY32PX8OHDlivmmY0Tp2pPjX\nrFEdiXF8+UIj5QULUmNu9Gjg5k1Ko9Tn75Y0KU0juXePqmgy9Tw9qfhN5cqqIzEqbtiZg2XL6ILa\npQswYYLqaNTp1g2oXp0mKz96pDoaxszDvXs096NhQ9WRfKtECfpML1hgnetl+fjQzf/vvycs1Uu1\ngQOp8l/fvtY9ypoQ5p6GGS1bNirnv2aN5WXL7NtH56AhQyjV+No1+iw6OBhm+9Wq0VSSyZPpPMzU\nefaMlqRo314b88yNyLLfnSXYuZPmotSvDyxZYt49f/qKTgcKC6O0VE4HYix+vr70XUvz62Lq04fK\nhu/ZozoS0/r8measubhQirk5SJqUMkdevqRFmlncvL0ptbZYMdWR6M/dnRomx46pjsQw7t1D0d9+\nA+rUofuJnTtprcF8+Qy/rxkzqCExaJDht80SztubOg/bt1cdidFxw07Lzpyh3p5Spahksjktbmos\nefNS9bidO4FNm1RHwxJDSl6yQgVfX7ph0er8rUaNgAwZrK/iYszlDZImVR1Nwrm60vyhlSupsAT7\n1vPnNG3A3NMwozVrBqRMab5FVKSkteamTKGFxfPkgeOZM7RG7tWrxu30yp4dGDWKRnD37TPeftj3\nbd1Ky47oMmfSzHDDTqtu36bUqSxZ6MYsZUrVEWlH//5UreuXX+gCyrTl/XtanmLdOir006YNVRdL\nmZLKQJ88qTpC6xESQuv2aHW0DqDKmJ06UfW4Z89UR2MaWl7eICFGjaL1RYcNUx2JNvn4WEYaZrQU\nKei9eHvTOcUchIfTUhODB1OnVpEiwIgRNKdu3DicXbMGGDnSNNURBw2izrV+/Wj/zLTevKGU9yZN\nVEdiEtyw06Jnz6hAihCAnx9Vj2P/SZKEeouDg2lY3Rrn5mjN58+UTpY5M60RU7YsVZ6aOJEaeZkz\n0wLHTk50bJ8+rTpi63DwIP1ttDi/LqZu3ehGbO1a1ZGYxujRVClPq8sbxCdtWnoPe/bwKERsvL2B\n/PnNb1Hy73F3p2vuunWqI/m+p0+pHkGmTEDVqlTAJF8+qqz98CFdj8aOxWdT3lfZ2QFz5lBRFl7e\nxfR27aLrCzfsmBIfPtAiws+eUbqhMXK+LUHRonTC3r+fGg9MnehjdvlymmQ/dSr1WF+/ThUPAwPp\nxDp7Ni1ynDEjULcucPas6sgtX/Rof5UqqiP5vsKFaX3OFSssf+6sOSxvkBAeHkCuXFR4wtKKaujj\nxQs6z1lKGma0KlWA8uVppPnzZ9XRxO79e6pHsGkTXZO8vWk+6O7dNC8/WzZ1sTVoQB1s48dT45OZ\nzrZtdN9RvrzqSEyCG3ZaEhZGF4NLl2hOXblyqiPStm7dqBTzuHHAgQOqo7FOL15QVcMjR6hqmqcn\nFVVo2pRu1u3s/vf5WbPSTU/69DRx3d9fTdzWQEpq2NWuTemOWte9O/VonzqlOhLjibm8wdixqqPR\nj50dMGkSXa+0PopjSpaWhhlNCKrK/fChNufDhoXREgVXr9J8tjVr6P+pUqmO7D+zZ1MqJhceMp3P\nn6lh37ixxVfDjGYd79IcfP4MtGtHqS1Llmh7ToxWCAEsWkQNiHbtaIFRZjoPHgCVKlGJ6G3bqJGd\nENmyUeMuXTpqdJw/b9w4rdWVK7QsiLmcS1q1otFFS17TztyWN4hP69ZA6dI05+7TJ9XRaIO3N2Xa\nlCihOhLDq12bzvkTJ2pr0W0pKdV/3z5g6VLtrvWbLx+NcHt60qLvzPgOHaIUYitJwwQspWEXEWHe\n86w+fKCbr82bqUJat26qIzIfKVLQhTQ4GGjblqsumsr161Rd7NkzupgmtvGQIwedcFOnBmrVovQ0\nZli7dtF3Nze1cSRUypTUUPDyonOipQkLo576okXNZ3mD+NjY0OLLDx9Sary1e/nSMtMwowlBnRJP\nnlAHtFaMGwesWkXfu3ZVHEw8RoygSpm//GLe963mYutWuk+sWVN1JCZj3g27yEhKCciYkXL9160z\nv1z/589pEcvDh6mU8K+/qo7I/BQpQheZo0fNP73JHJw5A1SuTBelo0epB1cXuXLRcZ8yJTXuLl82\nZJTMz49K02fOrDqShOvenaruWeJSJmvXAnfuUMl1c1reID7Vq1PnwcSJwKtXqqNRy8eHzouWloYZ\nU7VqQI0atOi2FipkLl9OKaJdu5rH9T9FCmDmTOrMXLpUdTSWLTKSqi3Xq2ea6qcaYb4Nu/PngYoV\n6UagUCFq3HXoQBPwzWWORlAQvYcbNyiVrVMn1RGZrw4dqBd88uT/RiqY4e3dSz1fadNSKom+Vd9y\n56Ye7uTJabtXrxomTmv34QNw4oR2U5LiUr48ddRocQ6PPsLCqOFTurT5pMYmxtSpdMxZeyErb29a\na9XVVXUkxvX779Qp/eefauPYtQv4+Wc6zy1ebD6jpC1aUIfIqFE02s2Mw9+fCtVYURomYI4Nuzdv\ngL59qZz63bs0ynXsGFXYW7WK5pRUqEBrZ92/rzrauF2+THG+ekWVHS3xYm9qc+fSvIaOHWn+FzMs\nLy+q6pU3LzXq8uY1zHbz5qXGXbJk1BPMI3f6O3iQ0pLr1lUdSeIIQanop0/T3E1L4en1vQV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OYMj9ZF4YYdsy4NGwIZM1rWifHgQerFmzCBSnBfu0aNuK8NGEBpmCtX0jpb1ihJEiqs8u4dMHu2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\nUmobcL0x9j9prdfVbPMnoC8wWV/nIEqpecA8AFdX1z6rVq2qdxzCMhUcL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from quantecon import LinearStateSpace\n", "\n", "\"\"\" This script maps the Samuelson model in the the LinearStateSpace class\"\"\"\n", "alpha = 0.8\n", "beta = 0.9\n", "rho1 = alpha + beta\n", "rho2 = -beta\n", "gamma = 10\n", "sigma = 1\n", "g = 10\n", "n = 100\n", "\n", "A = [[1, 0, 0],\n", " [gamma + g, rho1, rho2],\n", " [0, 1, 0]]\n", "\n", "G = [[gamma + g, rho1, rho2], # this is Y_{t+1}\n", " [gamma, alpha, 0], # this is C_{t+1}\n", " [0, beta, -beta]] # this is I_{t+1}\n", "\n", "mu_0 = [1, 100, 100]\n", "C = np.zeros((3,1))\n", "C[1] = sigma # stochastic\n", "\n", "sam_t = LinearStateSpace(A, C, G, mu_0=mu_0)\n", "\n", "x, y = sam_t.simulate(ts_length=n)\n", "\n", "fig, axes = plt.subplots(3, 1, sharex=True, figsize=(15, 8))\n", "titles = ['Output ($Y_t$)', 'Consumption ($C_t$)', 'Investment ($I_t$)']\n", "colors = ['darkblue', 'red', 'purple']\n", "for ax, series, title, color in zip(axes, y, titles, colors):\n", " ax.plot(series, color=color)\n", " ax.set(title=title, xlim=(0, n))\n", " ax.grid()\n", "\n", "axes[-1].set_xlabel('Iteration')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_42_0.png](_static/figures/sam_42_0.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Other methods in the LinearStateSpace class\n", "\n", "Let’s plot **impulse response functions** for the instance of the\n", "Samuelson model using a method in the LinearStateSpace class" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGcAAAAUBAMAAABi2T6lAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n6owAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( 2, \\quad 6, \\quad 1\\right )$$" ], "text/plain": [ "(2, 6, 1)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "imres = sam_t.impulse_response()\n", "imres = np.asarray(imres)\n", "y1 = imres[:, :, 0]\n", "y2 = imres[:, :, 1]\n", "y1.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
 $$\n", "\\left ( 2, \\quad 6, \\quad 1\\right )\n", "$$\n", "\n", "
Now let’s compute the zeros of the characteristic polynomial by simply\n", "calculating the eigenvalues of $A$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.85+0.42130749j 0.85-0.42130749j 1.00+0.j ]\n" ] } ], "source": [ "A = np.asarray(A)\n", "w, v = np.linalg.eig(A)\n", "print(w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "[ 0.85+0.42130749j 0.85-0.42130749j 1.00+0.j ]\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inheriting methods from LinearStateSpace\n", "\n", "We could also create a subclass of LinearStateSpace (inheriting all its\n", "methods and attributes) to add more functions to use" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class SamuelsonLSS(LinearStateSpace):\n", "\n", " \"\"\"\n", " this subclass creates a Samuelson multiplier-accelerator model\n", " as a linear state space system\n", " \"\"\"\n", " def __init__(self,\n", " y_0=100,\n", " y_1=100,\n", " alpha=0.8,\n", " beta=0.9,\n", " gamma=10,\n", " sigma=1,\n", " g=10):\n", "\n", " self.alpha, self.beta = alpha, beta\n", " self.y_0, self.y_1, self.g = y_0, y_1, g\n", " self.gamma, self.sigma = gamma, sigma\n", "\n", " # Define intial conditions\n", " self.mu_0 = [1, y_0, y_1]\n", "\n", " self.rho1 = alpha + beta\n", " self.rho2 = -beta\n", "\n", " # Define transition matrix\n", " self.A = [[1, 0, 0],\n", " [gamma + g, self.rho1, self.rho2],\n", " [0, 1, 0]]\n", "\n", " # Define output matrix\n", " self.G = [[gamma + g, self.rho1, self.rho2], # this is Y_{t+1}\n", " [gamma, alpha, 0], # this is C_{t+1}\n", " [0, beta, -beta]] # this is I_{t+1}\n", "\n", " self.C = np.zeros((3, 1))\n", " self.C[1] = sigma # stochastic\n", "\n", " # Initialize LSS with parameters from Samuleson model\n", " LinearStateSpace.__init__(self, self.A, self.C, self.G, mu_0=self.mu_0)\n", "\n", " def plot_simulation(self, ts_length=100, stationary=True):\n", "\n", " # Temporarily store original parameters\n", " temp_mu = self.mu_0\n", " temp_Sigma = self.Sigma_0\n", "\n", " # Set distribution parameters equal to their stationary values for simulation\n", " if stationary == True:\n", " try:\n", " self.mu_x, self.mu_y, self.sigma_x, self.sigma_y = self.stationary_distributions()\n", " self.mu_0 = self.mu_y\n", " self.Sigma_0 = self.sigma_y\n", " # Exception where no convergence achieved when calculating stationary distributions\n", " except ValueError:\n", " print('Stationary distribution does not exist')\n", "\n", " x, y = self.simulate(ts_length)\n", "\n", " fig, axes = plt.subplots(3, 1, sharex=True, figsize=(15, 8))\n", " titles = ['Output ($Y_t$)', 'Consumption ($C_t$)', 'Investment ($I_t$)']\n", " colors = ['darkblue', 'red', 'purple']\n", " for ax, series, title, color in zip(axes, y, titles, colors):\n", " ax.plot(series, color=color)\n", " ax.set(title=title, xlim=(0, n))\n", " ax.grid()\n", "\n", " axes[-1].set_xlabel('Iteration')\n", "\n", " # Reset distribution parameters to their initial values\n", " self.mu_0 = temp_mu\n", " self.Sigma_0 = temp_Sigma\n", "\n", " return fig\n", "\n", " def plot_irf(self, j=5):\n", "\n", " x, y = self.impulse_response(j)\n", "\n", " # Reshape into 3 x j matrix for plotting purposes\n", " yimf = np.array(y).flatten().reshape(j+1, 3).T\n", "\n", " fig, axes = plt.subplots(3, 1, sharex=True, figsize=(15, 8))\n", " labels = ['$Y_t$', '$C_t$', '$I_t$']\n", " colors = ['darkblue', 'red', 'purple']\n", " for ax, series, label, color in zip(axes, yimf, labels, colors):\n", " ax.plot(series, color=color)\n", " ax.set(xlim=(0, j))\n", " ax.set_ylabel(label, rotation=0, fontsize=14, labelpad=10)\n", " ax.grid()\n", "\n", " axes[0].set_title('Impulse Response Functions')\n", " axes[-1].set_xlabel('Iteration')\n", "\n", " return fig\n", "\n", " def multipliers(self, j=5):\n", " x, y = self.impulse_response(j)\n", " return np.sum(np.array(y).flatten().reshape(j+1, 3), axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Illustrations\n", "\n", "Let’s show how we can use the SamuelsonLSS" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "samlss = SamuelsonLSS()" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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HxbrLS4gk5W1xcAetWmnBzEy0axCoqCjg559N8OTJNMye3RZ7996Dru5+/P77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V2FCsDYsaY1A3r6FJg3T+4Fzp//ZzCGnANLMcn28uWTzm3Xrsm+Zo0ayfqOPn1kxChVKlm3s3ix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\n/wOIidy2TmwXLgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samlss.plot_simulation(100, stationary=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_61_0.png](_static/figures/sam_61_0.png) " ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/quantecon/lss.py:173: RuntimeWarning: covariance is not positive-semidefinite.\n", " x0 = multivariate_normal(self.mu_0.flatten(), self.Sigma_0)\n" ] }, { "data": { "image/png": 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M03rhU1L+2iufmZlNVlY2mZnWvc8mK8uSlWXJzMzGGNffi6+vD76+xn3seu3j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\n6dPh0CE46yxYurR4ry8iIiIiJUq+k0Jr7TQgZ93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y4IsvIrPqaE7167sxWu+84yoiNmjg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samlss.plot_simulation(100, stationary=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_62_0.png](_static/figures/sam_62_0.png) " ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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127cPK1bXlr3++jLuuy+WiRN7MXhww7N+fWxsLDExMZ4PrBAtX76Xrl2nUbFi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\nW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e3apGFzzj3qnOvgnIvF108uds5NAD4BbvBvprYpnnDOfQdsNbN4/6qhwDrUd4r3vgWS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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samlss.plot_irf(100)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_63_0.png](_static/figures/sam_63_0.png) " ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 7.414389, 6.835896, 0.578493])" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samlss.multipliers()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "array([ 7.414389, 6.835896, 0.578493])\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pure multiplier model\n", "\n", "Let’s shut down the accelerator by setting $b=0$ to get a pure\n", "multiplier model\n", "\n", "- the absence of cycles gives an idea about why Samuelson included the\n", " accelerator " ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pure_multiplier = SamuelsonLSS(alpha=0.95, beta=0)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Stationary distribution does not exist\n" ] }, { "data": { "image/png": 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RwUpBUEREAGhr6+wxAUZ49sjwsbq61qhp7cPrmjWybZsPUftaiyw1NZnCwgxGjkwnFEqm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\n", "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pure_multiplier.plot_simulation()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "none\n", "Stationary distribution does not exist\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_67_1.png](_static/figures/sam_67_1.png) " ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pure_multiplier = SamuelsonLSS(alpha=0.8, beta=0)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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CLKHqUvX19fZNVST7piqZ/VOVyr6p3qycy0Q/APwjpfQKQETcDLwb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\nBvACcHy273bgSGA+sAb4OEBKaWlEfBt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"text/plain": [ "" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pure_multiplier.plot_simulation()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_69_0.png](_static/figures/sam_69_0.png) " ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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5817n+eezad68pbzwwjJeemk5Tz+9mJdfXsHatc0bHbdXrzoGDdqJQYN6lT43\nnN7ylp4MGNCTAQN6lE096d69toO+uSRJklQMhQ2REVELXAu8B1gAPBIRU1NKs8qanQ28llIaFRET\ngX8HTun4alUEEVEKgb04+OBd22zT3JxYvHgVL720gpdfXsFLL63gpZeW8+qrq1i4cP307LNLWLhw\nFUuXvrHZc+60Ux0DBvSgf/8e9O3bvdXUjT591i/36dONXr260atXHb16daN37w3nly5dx8qVa+nR\no5ba2ppq/IgkSZKkbVbYEAlMAOaklOYCRMRtwElAeYg8CbikNP9T4DsRESml1JGFasdRU7M+aO67\nb3277desaWLx4tUsWrSKJUveYMmS1aXPNzZaXrZsDcuWreHVV1eybNkali9fy7Jla3jjjaYtqHAm\nAN261dCzZx077VRHz5619OxZR8+edfToUUv37rWlzxp69Kjb4LN791q6dauhW7fy+doNluvqat78\nbJnWLwd1dTXU1tZQW9syH9TWZtta1resq6nJ5ls+W6/bcOLN7RG8ud57ViVJknYsRQ6RQ4H5ZcsL\ngEM31SaltC4ilgJvARZ2SIXq9Lp3r2XXXXuz6669t/oYa9c2sWzZGlauXMeKFWtZuXLtRvMrV65l\n5syn2H33PVi9eh2rVzexevU6Vq1at8HyG280sWZNE2+8kR2zZb78c+3a5jenNWu2JMDmpyVURkRZ\nuOTNz5b15e2y9ZTNb9y2JZ+21ab8s6VNSy0tnxuv21z7zS+3ta319tbbKm2zpdvb0l6YX7p0CQMG\nvNzOMbbtHNtDEf4m4R9GOtZrr73GwIGv5F2GtBH7pjqzIofItv4r3HqEsZI2RMQkYBJAfX09jY2N\n21yctK26d8+mAQOy5V137U2fPivLWgTQrTRtnZQSzc2wbl1i7dpmmpoSTU2UPsunrM26dc00N2eX\n/ba0y+az46xfXn/s5ua2P1u2p5RIKds3pWx7Srw5lS+3zDc3p1L90NwMkMrm17dradNyjvX7pLKf\nwfqp5Tjrl9f/nMq3lW0pO+6Gx2zrs+X/fjZev3Gb1tvLa229bnNaX3ixpftXIqurmddfX1pxHW0d\noyvoKt+zSJqamnj11cV5lyFtxL6pzqzIIXIBMLxseRjw4ibaLIiIOqA/sNH/WlNKU4ApAGPHjk0N\nDQ3VqFfaJo2Njdg3VVT2TxWVfVNFZd9UkUWcs037F/npHY8AoyNij4joDkwEprZqMxU4ozR/MvAb\n74eUJEl3qP4cAAAgAElEQVSSpOop7Ehk6R7Hc4F7yF7x8YOU0pMRcSkwPaU0FbgeuDEi5pCNQE7M\nr2JJkiRJ6vwKGyIBUkrTgGmt1l1cNr8a+FBH1yVJkiRJXVWRL2eVJEmSJBVMdLVbCCNiGTA77zqk\nNgzC19OouOyfKir7porKvqkiG5tS6ru1Oxf6ctYqmZ1SOjjvIqTWImK6fVNFZf9UUdk3VVT2TRVZ\nREzflv29nFWSJEmSVDFDpCRJkiSpYl0xRE7JuwBpE+ybKjL7p4rKvqmism+qyLapf3a5B+tIkiRJ\nkrZeVxyJlCRJkiRtJUOkJEmSJKlihkhJkiRJUsUMkZIkSZKkihkiJUmSJEkVM0RKkiRJkipmiJQk\nSZIkVcwQKUmSJEmqmCFSkiRJklQxQ6QkSZIkqWKGSEmSJElSxQyRkiRJkqSKGSIlSZIkSRUzREqS\nJEmSKmaIlCRJkiRVzBApSZIkSaqYIVKSJEmSVDFDpCRJkiSpYoZISZIkSVLF6vIuoKMNGDAgjRo1\nKu8ypI2sWLGC3r17512G1Cb7p4rKvqmism+qyGbMmLEwpVS/tft3uRA5ePBgpk+fnncZ0kYaGxtp\naGjIuwypTfZPFZV9U0Vl31SRRcTz27K/l7NKkiRJkipW6BAZEcdGxOyImBMRF7axffeIuC8iHo2I\nxyPi+DzqlCRJkqSuorAhMiJqgWuB44BxwKkRMa5Vsy8Ct6eUxgMTgf/s2ColSZIkqWspbIgEJgBz\nUkpzU0prgNuAk1q1SUC/0nx/4MX2Dlq3YsV2LVKSJEmSupIiP1hnKDC/bHkBcGirNpcA90bEp4De\nwNFtHSgiJgGTAPbu1o3GxsbtXau0zZYvX27fVGHZP1VU9k0VlX1TnVmRQ2S0sS61Wj4VuCGldGVE\nHAbcGBH7pJSaN9gppSnAFICDI1LDmDGw225VKVraWj7FTUVm/1RR2TdVVPZNdWZFvpx1ATC8bHkY\nG1+uejZwO0BK6SGgJzCo3SPfeuv2qVCSJEmSupgih8hHgNERsUdEdCd7cM7UVm1eAN4NEBFvJQuR\nr27uoE09e8JNN1WhXEmSJEnq/AobIlNK64BzgXuAp8iewvpkRFwaESeWmk0GPhYRjwG3AmemlFpf\n8rqBdf36wcyZ8Oc/V7N8SZIkSeqUinxPJCmlacC0VusuLpufBbx9S465tm9fWLQoG4287LLtU6gk\nSZIkdRGFHYmsllRbC8ceCzffDM3N7e8gSZIkSXpTlwuRAJx+OixYAA88kHclkiRJkrRD6Zoh8sQT\noU8fH7AjSZIkSVuoa4bIXr3ggx+En/wEVq/OuxpJkiRJ2mF0zRAJ2SWtr78Od92VdyWSJEmStMPo\nuiHyqKNgyBC48ca8K5EkSZKkHUbXDZG1tfCP/wjTpsHChXlXI0mSJEk7hK4bIiG7pHXduuzeSEmS\nJElSu7p2iNx/f9hnH5/SKkmSJEkV6tohMiIbjfz972Hu3LyrkSRJkqTC69ohErL7IgFuvjnfOiRJ\nkiRpB2CIHD4cGhqyp7SmlHc1kiRJklRohkjILmn9y1/gkUfyrkSSJEmSCs0QCfDBD0KPHj5gR5Ik\nSZLaYYgEGDAATjgBbrsN1q7NuxpJkiRJKixDZIvTT4dXX4Vf/SrvSiRJkiSpsAyRLY47Dnbe2Uta\nJUmSJGkzDJEtuneHU06Bn/0MFi7MuxpJkiRJKiRDZLlPfhJWr4b/+q+8K5EkSZKkQjJEltt77+yy\n1u98JwuTkiRJkqQNFDpERsSxETE7IuZExIWbaPPhiJgVEU9GxC3bfNLJk+GVV7w3UpIkSZLaUNgQ\nGRG1wLXAccA44NSIGNeqzWjgC8DbU0p7A+dv84nf9S7Yf3/41reguXmbDydJkiRJnUlhQyQwAZiT\nUpqbUloD3Aac1KrNx4BrU0qvAaSUXtnms0Zko5FPPQW//OU2H06SJEmSOpO6vAvYjKHA/LLlBcCh\nrdqMAYiI3wG1wCUppY2SX0RMAiYB1NfX09jYuNkTx6678rZBg1j5xS/yWK9eW/0FpC2xfPnydvum\nlBf7p4rKvqmism+qMytyiIw21qVWy3XAaKABGAY8GBH7pJSWbLBTSlOAKQBjx45NDQ0N7Z/9ggvo\n8fnP0zBgABxwwBYXL22pxsZGKuqbUg7snyoq+6aKyr6pzqzIl7MuAIaXLQ8DXmyjzf+mlNamlJ4D\nZpOFym03aRL06QNXXrldDidJkiRJnUGRQ+QjwOiI2CMiugMTgamt2vwcOAogIgaRXd46d7ucfcAA\nOPtsuO02WLBguxxSkiRJknZ0hQ2RKaV1wLnAPcBTwO0ppScj4tKIOLHU7B5gUUTMAu4DLkgpLdpu\nRXz609kTWq+5ZrsdUpIkSZJ2ZEW+J5KU0jRgWqt1F5fNJ+CzpWn722MP+OAHYcoU+NKXoG/fqpxG\nkiRJknYUhR2JLIzJk2HpUrj++rwrkSRJkqTcGSLbc+ih8I53wH/8B6xbl3c1kiRJkpQrQ2QlJk+G\n55+H//mfvCuRJEmSpFwZIitxwgkwahRccQWk1q+qlCRJkqSuwxBZidpa+Mxn4JFH4Le/zbsaSZIk\nScqNIbJSZ54JO+8MV16ZdyWSJEmSlBtDZKV69YJPfAKmToXZs/OuRpIkSZJyYYjcEueem4XJiy7K\nuxJJkiRJyoUhcksMHgyf/zzccQc8+GDe1UiSJElSh6tqiIyIAyLi5ohYEBGrI+K5iLgpIvar5nmr\navJkGDo0+2xuzrsaSZIkSepQVQuREXEmMB14AzgFGAOcUdr86Wqdt+p69YJvfCN7Uuutt+ZdjSRJ\nkiR1qKqEyIg4DLgOuCCldFZK6XcppRdSSg+klE4HLqjGeTvMaafBQQfBhRfCypV5VyNJkiRJHaZa\nI5FXAn9IKV3V1saU0uIqnbdj1NTAt74FCxbAVW1+RUmSJEnqlLZ7iIyI0cBhwLfbaTcyIk7a3ufv\nMO98J3zgA9mlrS+/nHc1kiRJktQhqjESeWDpc3o77Y4B9qnC+TvOv/87rFkDX/pS3pVIkiRJUoeo\nRojsVfpcvqkGEXEk8A3gzIiYGRH9q1BH9Y0aBZ/6FFx/PTz2WN7VSJIkSVLVVSNE/rn0eWRbGyOi\nV0rpfuBx4L0ppQNSSkurUEfH+OIXYeDA7JUfKeVdjSRJkiRV1XYPkSmlR4BpwLcj4syIGB0RoyLi\nwxHxK9Zf7joSmLe9z9/hBg6ESy6BX/8apk3LuxpJkiRJqqpqPZ31A8AVwGeBmcAjwOeBh4DpETEM\neDmlTjJ09/GPw5gx8LnPwdq1eVcjSZIkSVVTlRCZUnojpXR5Smm/lFLvlNLAlNJBKaWLU0qrgeHA\ni9U4dy66dYMrroCnn4YpU/KuRpIkSZKqplojke2ZBYyIiCciYt9NNYqIYyNidkTMiYgLN9Pu5IhI\nEXFwVaqtxPvfD+96F3z5y7BkSW5lSJIkSVI15RIiU0pLSyOT+6aUnmirTUTUAtcCxwHjgFMjYlwb\n7foC5wF/qGbN7YqAK6+ExYvhK1/JtRRJkiRJqpa8RiIrMQGYk1Kam1JaA9wGnNRGu38DLgdWd2Rx\nbTrggOz+yKuvhvvvz7saSZIkSdru6vIuYDOGAvPLlhcAh5Y3iIjxwPCU0l0R8blNHSgiJgGTAOrr\n62lsbNz+1ZbUnHACB995JzWnnML0665jXZ8+VTuXOpfly5dXtW9K28L+qaKyb6qo7JvqzIocIqON\ndW8+zTUiaoCrgDPbO1BKaQowBWDs2LGpoaFh+1S4KXfcAYcfzjtuuw1uuqm651Kn0djYSNX7prSV\n7J8qKvumisq+qc6syJezLiB7imuLYWz4RNe+wD5AY0TMA94GTM314TotJkzIHrBz881w6615VyNJ\nkiRJ202RQ+QjwOiI2CMiugMTgaktG0sP5xmUUhqZUhoJPAycmFKank+5rXzhC3DYYXDOOfDCC3lX\nI0mSJEnbRWFDZEppHXAucA/wFHB7SunJiLg0Ik7Mt7oK1NXBjTdCUxOccQY0N+ddkSRJkiRts8KG\nSICU0rSU0piU0p4ppa+V1l2cUpraRtuGwoxCtthzT7jmGmhshG99K+9qJEmSJGmbFTpEdgpnngkf\n+AD867/CY4/lXY0kSZIkbRNDZLVFwPe+B4MGwWmnwapVeVckSZIkSVvNENkRBg2C//5vePLJ7IE7\nkiRJkrSDMkR2lGOOgfPOg6uvhnvvzbsaSZIkSdoqhsiOdNllMG5cdp/kX/+adzWSJEmStMUMkR1p\np53g1lth2TI4/nh4/fW8K5IkSZKkLWKI7Gj77Qc//Wl2f+TJJ8PatXlXJEmSJEkVM0Tm4Zhj4Pvf\nh1/9CiZNgpTyrkiSJEmSKlKXdwFd1j/9Ezz/PHzlKzBiBFxySd4VSZIkSVK7DJF5+vKX4YUXsiC5\n++5w1ll5VyRJkiRJm2WIzFMEfO972ZNaJ02CoUOzS10lSZIkqaC8JzJv3brBT34C++yTPWjn0Ufz\nrkiSJEmSNskQWQT9+sG0aTBwILzvfdklrpIkSZJUQIbIothtN/jFL2DlSjjuOHjttbwrkiRJkqSN\nGCKLZO+94ec/hzlzoKEBXnop74okSZIkaQOGyKJpaIC77oJnn4W3vx3+8pe8K5IkSZKkNxkii+g9\n74H77oNly7IgOWNG3hVJkiRJEmCILK5DDoHf/hZ69cpGJ3/967wrkiRJkiRDZKGNHQu//z2MHAnH\nHw+33553RZIkSZK6OENk0e22GzzwAEyYABMnwrXX5l2RJEmSpC6s0CEyIo6NiNkRMSciLmxj+2cj\nYlZEPB4Rv46IEXnUWXUDB8K998IJJ8C558KXvwwp5V2VJEmSpC6osCEyImqBa4HjgHHAqRExrlWz\nR4GDU0r7AT8FLu/YKjvQTjvBHXfAWWfBpZfCP/8zrFqVd1WSJEmSupjChkhgAjAnpTQ3pbQGuA04\nqbxBSum+lNLK0uLDwLAOrrFj1dXBddfBF78IP/hB9vCdP/8576okSZIkdSF1eRewGUOB+WXLC4BD\nN9P+bOAXbW2IiEnAJID6+noaGxu3U4k5efe7Gdi3L2+97DJqDzqIZz/5SV484QSIyLsybYPly5fv\n+H1TnZb9U0Vl31RR2TfVmRU5RLaViNq8ETAiTgcOBo5sa3tKaQowBWDs2LGpoaFhO5WYo4YG+OhH\n4YwzGHPVVYx5/nn4/vdh553zrkxbqbGxkU7RN9Up2T9VVPZNFZV9U51ZkS9nXQAML1seBrzYulFE\nHA1cBJyYUnqjg2orhl13hV/8Ai6/HKZOhQMOyN4tKUmSJElVUuQQ+QgwOiL2iIjuwERganmDiBgP\nfI8sQL6SQ435q6mBCy7I3ifZvTsceWT24J2mprwrkyRJktQJFTZEppTWAecC9wBPAbenlJ6MiEsj\n4sRSs28CfYCfRMTMiJi6icN1foccAn/6E5x6avYKkHe9C2bPzrsqSZIkSZ1Mke+JJKU0DZjWat3F\nZfNHd3hRRdavH9x0E7z3vfCpT8E++8B558HFF0P//nlXJ0mSJKkTKOxIpLbBRz8KzzwDZ5wBV10F\nY8ZkrwRpbs67MkmSJEk7OENkZzV4cPZOyT/+EfbcE84+Gw49FB56KO/KJEmSJO3ADJGd3cEHw+9+\nl13m+uKLcPjh8JGPZPOSJEmStIUMkV1BBJx2WvagnS98AW6/PbvE9Utfgldfzbs6SZIkSTsQQ2RX\n0qcPfP3rMGsWHHssfPWrsPvucO658NxzeVcnSZIkaQdgiOyK9twTfvpTeOop+Md/hClTYPTobLTy\nscfyrk6SJElSgRkiu7K99oLrr4e5c+H882HqVDjgADjuOLj/fkgp7wolSZIkFYwhUjBsGFxxBbzw\nQnaJ64wZ0NAAEybAf/4nLF6cd4WSJEmSCsIQqfUGDoSLLoLnn8/C4xtvwCc/CUOGwIc+BHffDevW\n5V2lJEmSpBwZIrWxnXaCc87J7o/805/g4x+HxkZ4//uzUcvJk+GJJ/KuUpIkSVIODJHatAgYPx6u\nvhr++lf42c/gsMPgmmtgv/3gwAOzy19nzvT+SUmSJKmLMESqMt27w9//fRYkX3wxC5bdumXvmhw/\nPntVyDnnwLRpsGpV3tVKkiRJqhJDpLZcfT2cdx784Q/w0kvZE14POQRuvBHe9z54y1vgxBPh+9/P\n7q+UJEmS1GnU5V2AdnC77gpnnZVNq1dnrwa56y64885sAhg+HI44Yv301rdCjX+/kCRJknZEhkht\nPz17wjHHZNM118CsWXDfffDgg/Cb38Att2Ttdt4Z3vGOLFC+/e2w//7Qq1e+tUuSJEmqiCFS1REB\ne++dTeeemz1459lns0DZMk2dmrWtqYGxY7N7K8unnXfO9ztIkiRJ2oghUh0jAkaNyqZ/+qds3Usv\nwcMPw6OPZtMDD6wfrYTsYT3jx2eXv+61VxY0x47N3mcpSZIkKReGSOVnyBD4h3/Iphavvpq9MqQl\nWM6cCXffDevWrW9TX78+UI4dmwXTkSNhxIgsYEZ0+FeRJEmSugpDpIqlvh7e855sarF2LTz3HDz9\nNMyevX6aOjULneX69FkfKFs+d98ddtstC61DhkDv3h35jSRJkqROxRCp4uvWDcaMyabWXnsN5s7N\nXiUyb1722TL97newZMnG+/Ttuz5Qtky77AKDBm08DRwItbVV/4qSJEnSjqLQITIijgWuBmqB61JK\nl7Xa3gP4EXAQsAg4JaU0r6PrVI4GDoSDDsqmtrz+OrzwQnb/ZVvT9OnZ54oVbe8fkT3g5y1vgQED\nNj3175+F09ZTnz7ZyKevNJEkSVInUdgQGRG1wLXAe4AFwCMRMTWlNKus2dnAaymlURExEfh34JSO\nr1aF1a8f7LNPNm3OypWwaBEsXNj2tGgRLF2ajWy+8EL2uWRJ9m7M9kRkQbJPn+xVJi1T794bzI9e\nvDh7t2bPnpueevTIpu7dN/3ZrVs2tczX1XmfqCRJkrabwoZIYAIwJ6U0FyAibgNOAspD5EnAJaX5\nnwLfiYhIKaWOLFSdQEuYGz58y/ZbvToLl6+9BsuXw7Jlm55WrsxGPFeuXD+9/PKb8/VLlmTv1Vy1\nasMHCW0PdXUbhsq6ug3nW0+1tdm0qfmWqaZm08s1NRtPLesj1q9rbz5iw/nydZuaWtpA29tbr9/c\ncsv85tZV8tneuk0tV9JmS5fb0k6bgY8/3n6/3NY/VnTEHzu60h9Uush3HTBzZt4lSG2yb6ozK3KI\nHArML1teABy6qTYppXURsRR4C7CwvFFETAImAdTX19PY2FilktXlRWSjn/36bfGuy5cvp0+fPtlh\nmpqINWuoKU21pc9Ys4aadeuoWbt2w/m1a9d/NjUR69YR69ZRU/rcYL65Oftsatr8tHYt0dQEzc3Z\nPi3rm5vXr9vcfEobfjY3Eyllx4QNt/t3n8LbP+8CpE04IO8CpE2wb6ozK3KIbOtPqK3/pVlJG1JK\nU4ApAGPHjk0NDQ3bXJy0vTU2NtKl+2ZKUAqblMLlm+taz5eva2tqbl5/zNZT6/WbW26Z39y6Sj7b\nW7ep5UrabOlyW9prkxKPPvoo48eP3/pjbGsN20NX+mNFF/quM2fO5IAD/Oe6ise+qUI76qht2r3I\nIXIBUH5t4TDgxU20WRARdUB/YHHHlCdpu4pYfymsCmfpunXwjnfkXYa0kSUAXfkPcCos+6Y6syI/\nMvIRYHRE7BER3YGJwNRWbaYCZ5TmTwZ+4/2QkiRJklQ9hR2JLN3jeC5wD9krPn6QUnoyIi4FpqeU\npgLXAzdGxByyEciJ+VUsSZIkSZ1fYUMkQEppGjCt1bqLy+ZXAx/q6LokSZIkqauKrnb1Z0QsA2bn\nXYfUhkG0erKwVCD2TxWVfVNFZd9UkY1NKfXd2p0LPRJZJbNTSgfnXYTUWkRMt2+qqOyfKir7porK\nvqkii4jp27J/kR+sI0mSJEkqGEOkJEmSJKliXTFETsm7AGkT7JsqMvunisq+qaKyb6rItql/drkH\n60iSJEmStl5XHImUJEmSJG0lQ6QkSZIkqWKGSEmSJElSxQyRkiRJkqSKGSIlSZIkSRUzREqSJEmS\nKmaIlCRJkiRVzBApSZIkSaqYIVKSJEmSVDFDpCRJkiSpYoZISZIkSVLFDJGSJEmSpIoZIiVJkiRJ\nFTNESpIkSZIqZoiUJEmSJFXMEClJkiRJqpghUpIkSZJUMUOkJEmSJKlihkhJkiRJUsUMkZIkSZKk\nitXlXUBHGzBgQBo1alTeZUgbWbFiBb179867DKlN9k8VlX1TRWXfVJHNmDFjYUqpfmv373IhcvDg\nwUyfPj3vMqSNNDY20tDQkHcZUpvsnyoq+6aKyr6pIouI57dlfy9nlSRJkiRVzBApSZIkSaqYIVKS\nJEmSVDFDpCRJkiSpYoZISZIkSVLFDJGSJEmSpIoZIiVJkiRJFTNESpIkSZIqZoiUJEmSJFXMEClJ\nkqT/3969B9lZ13ccf38mEbyWm0ExwQY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"text/plain": [ "" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pure_multiplier.plot_irf(100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![_static/figures/sam_70_0.png](_static/figures/sam_70_0.png) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "In this lecture, we wrote functions and classes to represent non-stochastic and\n", "stochastic versions of the Samuelson (1939) multiplier-accelerator model, described\n", "in [[Sam39]](zreferences.ipynb#samuelson1939)\n", "\n", "We saw that different parameter values led to different output paths, which\n", "could either be stationary, explosive, or ocillating\n", "\n", "We also were able to represent the model using the [QuantEcon.py](http://quantecon.org/python_index.html)\n", "[LinearStateSpace](https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/lss.py) class" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 2 }