From e34898009a5795fcc2c748fa947957231b9e2345 Mon Sep 17 00:00:00 2001 From: baptiste Date: Sat, 14 Feb 2026 16:16:57 +0100 Subject: [PATCH 1/7] Fix some docstring issue in PEP and Wrapper --- PEPit/pep.py | 5 +++-- PEPit/wrapper.py | 22 ++++++++++++---------- 2 files changed, 15 insertions(+), 12 deletions(-) diff --git a/PEPit/pep.py b/PEPit/pep.py index 8fd32905..af6a5df4 100644 --- a/PEPit/pep.py +++ b/PEPit/pep.py @@ -44,10 +44,11 @@ class PEP(object): _list_of_psd_sent_to_wrapper (list): list of :class:`PSDMatrix` objects actually sent to the wrapper. objective (Expression): the expression to be maximized by the solver. - It is set by the method `solve`. And should not be updated otherwise. + It is set by the method `solve`. + And should not be updated otherwise. G_value (ndarray): the value of the Gram matrix G that the solver found. - F_value (ndarray): the value of the vector of :class:`Expression`s F that the solver found. + F_value (ndarray): the value of the vector of :class:`Expression` F that the solver found. residual (ndarray): the dual value found by the solver to the lmi constraints G >> 0. diff --git a/PEPit/wrapper.py b/PEPit/wrapper.py index 27697aa2..c75605fb 100644 --- a/PEPit/wrapper.py +++ b/PEPit/wrapper.py @@ -16,8 +16,9 @@ class Wrapper(object): Attributes: _list_of_constraints_sent_to_solver (list): list of :class:`Constraint` and :class:`PSDMatrix` objects - associated to the PEP. This list does not contain constraints - due to internal representation of the problem by the solver. + associated to the :class:`PEP`. + This list does not contain constraints due to internal + representation of the problem by the solver. optimal_F (numpy.array): Elements of F after solving. optimal_G (numpy.array): Gram matrix of the PEP after solving. objective (Expression): The objective expression that must be maximized. @@ -30,9 +31,9 @@ class Wrapper(object): solver_name (str): The name of the solver the wrapper interact with. verbose (int): Level of information details to print (Override the solver verbose parameter). - - 0: No verbose at all - - 1: PEPit information is printed but not solver's - - 2: Both PEPit and solver details are printed + - 0: No verbose at all. + - 1: PEPit information is printed but not solver's. + - 2: Both PEPit and solver details are printed. """ @@ -44,9 +45,9 @@ def __init__(self, verbose=1): Args: verbose (int): Level of information details to print (Override the solver verbose parameter). - - 0: No verbose at all - - 1: PEPit information is printed but not solver's - - 2: Both PEPit and solver details are printed + - 0: No verbose at all. + - 1: PEPit information is printed but not solver's. + - 2: Both PEPit and solver details are printed. """ # Initialize lists of constraints that are used to solve the SDP. @@ -131,8 +132,9 @@ def assign_dual_values(self): residual (ndarray): main dual PSD matrix (dual to the PSD constraint on the Gram matrix). Raises: - TypeError if the attribute `_list_of_constraints_sent_to_solver` of this object - is neither a :class:`Constraint` object, nor a :class:`PSDMatrix` one. + TypeError + if the attribute `_list_of_constraints_sent_to_solver` of this object is neither + a :class:`Constraint` object, nor a :class:`PSDMatrix` one. """ dual_values, residual = self._recover_dual_values() From 5ffb5f73656885c268dd9ce35b851917070411b8 Mon Sep 17 00:00:00 2001 From: baptiste Date: Sat, 14 Feb 2026 16:18:48 +0100 Subject: [PATCH 2/7] Update TOCs in notebooks and add "return to TOCs" buttons --- ressources/demo/PEPit_demo.ipynb | 175 +++++-- .../demo/PEPit_demo_extracting_a_proof.ipynb | 485 ++++++++---------- 2 files changed, 355 insertions(+), 305 deletions(-) diff --git a/ressources/demo/PEPit_demo.ipynb b/ressources/demo/PEPit_demo.ipynb index 83bcbd0a..bd66af38 100644 --- a/ressources/demo/PEPit_demo.ipynb +++ b/ressources/demo/PEPit_demo.ipynb @@ -36,15 +36,34 @@ "toc": true }, "source": [ - "

Table of Contents

\n", - "" + "\n", + "## Table of Contents\n", + "- [1 Installing PEPit](#1-Installing-PEPit)\n", + "- [2 How to obtain a worst-case guarantee for GD using PEPit](#2-How-to-obtain-a-worst-case-guarantee-for-GD-using-PEPit)\n", + " - [2.1 Imports](#2.1-Imports)\n", + " - [2.2 Initialization of PEPit](#2.2-Initialization-of-PEPit)\n", + " - [2.3 Choose parameters values](#2.3-Choose-parameters-values)\n", + " - [2.4 Specifying the problem class](#2.4-Specifying-the-problem-class)\n", + " - [2.5 Algorithm initialization](#2.5-Algorithm-initialization)\n", + " - [2.6 Algorithm implementation](#2.6-Algorithm-implementation)\n", + " - [2.7 Setting up a performance measure](#2.7-Setting-up-a-performance-measure)\n", + " - [2.8 Solving the PEP](#2.8-Solving-the-PEP)\n", + " - [2.9 Analytical upper bound comparison](#2.9-Comparing-to-the-an-(established)-analytical-upper-bound-(worst-case-guarantee)-provided-by-the-literature)\n", + " - [2.10 Conclusion](#2.10-Conclusion)\n", + "- [3 Comparison of analytical and numerical worst-case guarantees](#3-Comparison-of-analytical-(obtained-in-the-literature)-and-numerical-(obtained-by-PEPit)-worst-case-guarantees-on-4-more-advanced-methods)\n", + " - [3.1 Example 1: GD with fixed step size](#3.1-Example-1-:-Gradient-descent-with-fixed-step-size-in-contraction)\n", + " - [3.1.1 Worst-case guarantees as functions of the iteration count](#3.1.1-Worst-case-guarantees-as-functions-of-the-iteration-count)\n", + " - [3.1.2 Worst-case guarantees as functions of the step size](#3.1.2-Worst-case-guarantees-as-functions-of-the-step-size)\n", + " - [3.2 Example 2: Accelerated gradient method](#3.2-Example-2-:-An-accelerated-gradient-method-for-strongly-convex-objectives)\n", + " - [3.3 Example 3: Accelerated Douglas-Rachford splitting](#3.3-Example-3-:-An-accelerated-Douglas-Rachford-splitting)\n", + " - [3.4 Example 4: point-SAGA](#3.4-Example-4-:-point-SAGA)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Installing PEPit" + "## 1 Installing PEPit" ] }, { @@ -56,14 +75,21 @@ "outputs": [], "source": [ "# If PEPit is not installed yet, you can run this cell.\n", - "!pip install pepit;" + "!pip3 install pepit;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## How to obtain a worst-case guarantee for GD using PEPit" + "
↩ Back to TOC
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2 How to obtain a worst-case guarantee for GD using PEPit" ] }, { @@ -97,7 +123,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Imports.\n", + "### 2.1 Imports\n", "Before anything else, we have to import the PEP and the classes of functions of interest." ] }, @@ -118,7 +144,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Initialization of PEPit.\n", + "### 2.2 Initialization of PEPit\n", "Then, we initialize a PEP object. This object allows manipulating the forthcoming ingredients of the PEP, such as functions and iterates." ] }, @@ -139,7 +165,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Choose parameters values\n", + "### 2.3 Choose parameters values\n", "\n", "For the sake of the example, we pick some simple values for the problem class and algorithmic parameters, for which we perform the worst-case analysis below. " ] @@ -165,7 +191,7 @@ "tags": [] }, "source": [ - "### Specifying the problem class. \n", + "### 2.4 Specifying the problem class\n", "Next, we specify our assumptions on the **class of functions** containing the function to be optimized, and instantiate a corresponding object. Here, we consider an $L$-smooth convex function. \n", "\n", "
*Remark*: PEPit can handle various function classes [(documentation)](https://pepit.readthedocs.io/en/latest/api/functions_and_operators.html).\n", @@ -214,7 +240,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Algorithm initialization.\n", + "### 2.5 Algorithm initialization\n", "\n", "Third, we can instantiate the starting points for the two gradient methods that we will run, and specify an **initial condition** on those points. \n", "To this end, a starting point $x_0$ is introduced, and a bound on the initial distance between those points is specified as $\\|x_0-x_*\\|^2\\leqslant 1$.\n", @@ -242,7 +268,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Algorithm implementation.\n", + "### 2.6 Algorithm implementation\n", "\n", "In this fourth step, we specify the **algorithm** in a natural format. In this example, we simply use the iterates (which are PEPit objects) as if we had to implement gradient descent in practice using a simple loop. Gradient descent with fixed step size $\\gamma$ may be described as follows, for $t \\in \\{0,1, \\ldots, n-1\\}$\n", "\\begin{equation}\n", @@ -271,7 +297,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Setting up a performance measure.\n", + "### 2.7 Setting up a performance measure\n", "\n", "It is crucial for the worst-case analysis to specify the **performance metric** for which we wish to compute a worst-case performance. In this example, we wish to compute the worst-case value of $f(x_n)-f_*$, which we specify as follows. \n", "\n", @@ -295,7 +321,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Solving the PEP.\n", + "### 2.8 Solving the PEP\n", "\n", "The last natural stage in the process is to solve the corresponding PEP. This is done via the following line, which will ask PEPit to perform the modelling steps and to call an appropriate SDP solver (which should be installed beforehand) to perform the worst-case analysis.\n", "\n", @@ -313,19 +339,29 @@ "name": "stdout", "output_type": "stream", "text": [ - "(PEPit) Setting up the problem: size of the main PSD matrix: 7x7\n", - "(PEPit) Setting up the problem: performance measure is minimum of 1 element(s)\n", + "(PEPit) Setting up the problem: size of the Gram matrix: 7x7\n", + "(PEPit) Setting up the problem: performance measure is the minimum of 1 element(s)\n", "(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n", "(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n", "(PEPit) Setting up the problem: interpolation conditions for 1 function(s)\n", - "\t\t function 1 : Adding 30 scalar constraint(s) ...\n", - "\t\t function 1 : 30 scalar constraint(s) added\n", + "\t\t\tFunction 1 : Adding 30 scalar constraint(s) ...\n", + "\t\t\tFunction 1 : 30 scalar constraint(s) added\n", + "(PEPit) Setting up the problem: additional constraints for 0 function(s)\n", "(PEPit) Compiling SDP\n", "(PEPit) Calling SDP solver\n", - "(PEPit) Solver status: optimal (solver: SCS); optimal value: 0.16666634633090185\n", + "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: SCS); optimal value: 0.16666634632022087\n", "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -2.6e-07 < 0).\n", " Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n", - " In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n" + " In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n", + "(PEPit) Primal feasibility check:\n", + "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 2.6031562588658637e-07\n", + "\t\tAll the primal scalar constraints are verified up to an error of 6.94474186248295e-07\n", + "(PEPit) Dual feasibility check:\n", + "\t\tThe solver found a residual matrix that is positive semi-definite\n", + "\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n", + "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 3.3690239638641244e-06\n", + "(PEPit) Final upper bound (dual): 0.16666732807401075 and lower bound (primal example): 0.16666634632022087 \n", + "(PEPit) Duality gap: absolute: 9.817537898748618e-07 and relative: 5.8905340613190735e-06\n" ] } ], @@ -339,7 +375,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Comparing to the an (established) analytical upper bound (worst-case guarantee) provided by the literature.\n", + "### 2.9 Comparing to the an (established) analytical upper bound (worst-case guarantee) provided by the literature\n", "\n", "We can now compare to a **analytical value**, provided in [1, Theorem 1]. When $\\gamma \\leqslant \\frac{1}{L}$, the analytical value for the exact worst case guarantee can be found is:\n", "$$f(x_n)-f_* \\leqslant \\frac{L||x_0-x_\\star||^2}{4nL\\gamma+2}$$\n", @@ -361,7 +397,7 @@ "output_type": "stream", "text": [ "*** Worst-case performance of gradient descent with fixed step-sizes ***\n", - "\tPEPit guarantee:\t f(x_n)-f_* <= 0.166666 ||x_0 - x_*||^2\n", + "\tPEPit guarantee:\t f(x_n)-f_* <= 0.166667 ||x_0 - x_*||^2\n", "\tTheoretical guarantee:\t f(x_n)-f_* <= 0.166667 ||x_0 - x_*||^2\n" ] } @@ -381,7 +417,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Conclusion. \n", + "### 2.10 Conclusion\n", "For the parameters specified above, the worst-case guarantee obtained numerically by PEPit matches the analytical value of the best known (tight) worst-case guarantee.\n", "\n", "The following code is provided as one of the 50+ examples in the package, see [`GradientMethod`](https://pepit.readthedocs.io/en/latest/examples/a.html#gradient-descent). \n", @@ -400,21 +436,31 @@ "name": "stdout", "output_type": "stream", "text": [ - "(PEPit) Setting up the problem: size of the main PSD matrix: 7x7\n", - "(PEPit) Setting up the problem: performance measure is minimum of 1 element(s)\n", + "(PEPit) Setting up the problem: size of the Gram matrix: 7x7\n", + "(PEPit) Setting up the problem: performance measure is the minimum of 1 element(s)\n", "(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n", "(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n", "(PEPit) Setting up the problem: interpolation conditions for 1 function(s)\n", - "\t\t function 1 : Adding 30 scalar constraint(s) ...\n", - "\t\t function 1 : 30 scalar constraint(s) added\n", + "\t\t\tFunction 1 : Adding 30 scalar constraint(s) ...\n", + "\t\t\tFunction 1 : 30 scalar constraint(s) added\n", + "(PEPit) Setting up the problem: additional constraints for 0 function(s)\n", "(PEPit) Compiling SDP\n", "(PEPit) Calling SDP solver\n", - "(PEPit) Solver status: optimal (solver: SCS); optimal value: 0.16666634633090185\n", + "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: SCS); optimal value: 0.16666634632022087\n", "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -2.6e-07 < 0).\n", " Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n", " In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n", + "(PEPit) Primal feasibility check:\n", + "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 2.6031562588658637e-07\n", + "\t\tAll the primal scalar constraints are verified up to an error of 6.94474186248295e-07\n", + "(PEPit) Dual feasibility check:\n", + "\t\tThe solver found a residual matrix that is positive semi-definite\n", + "\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n", + "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 3.3690239638641244e-06\n", + "(PEPit) Final upper bound (dual): 0.16666732807401075 and lower bound (primal example): 0.16666634632022087 \n", + "(PEPit) Duality gap: absolute: 9.817537898748618e-07 and relative: 5.8905340613190735e-06\n", "*** Example file: worst-case performance of gradient descent with fixed step-sizes ***\n", - "\tPEPit guarantee:\t f(x_n)-f_* <= 0.166666 ||x_0 - x_*||^2\n", + "\tPEPit guarantee:\t f(x_n)-f_* <= 0.166667 ||x_0 - x_*||^2\n", "\tTheoretical guarantee:\t f(x_n)-f_* <= 0.166667 ||x_0 - x_*||^2\n" ] } @@ -428,7 +474,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Comparison of analytical (obtained in the literature) and numerical (obtained by PEPit) worst-case guarantees on 4 more advanced methods.\n", + "
↩ Back to TOC
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3 Comparison of analytical (obtained in the literature) and numerical (obtained by PEPit) worst-case guarantees on 4 more advanced methods\n", "\n", "In this section, we compare the worst-case guarantees obtained with PEPit and to reference worst-case guarantees for four algorithms:\n", "- **gradient descent** with fixed step size (in terms of contraction rate),\n", @@ -440,12 +493,12 @@ "\n", "\n", "\n", - "* [Example 1 : Gradient descent with fixed step size in contraction](#example1)\n", - " * [1.1 Worst-case guarantee as a function of the iteration count](#section_1_1)\n", - " * [1.2 Worst-case guarantee as a function of the step size](#section_1_2)\n", - "* [Example 2 : Accelerated gradient method for strongly convex objective](#example2)\n", - "* [Example 3 : Accelerated Douglas Rachford Splitting](#example3)\n", - "* [Example 4 : Point-SAGA](#example4)" + "- [3.1 Example 1: GD with fixed step size](#3.1-Example-1-:-Gradient-descent-with-fixed-step-size-in-contraction)\n", + " - [3.1.1 Worst-case guarantees as functions of the iteration count](#3.1.1-Worst-case-guarantees-as-functions-of-the-iteration-count)\n", + " - [3.1.2 Worst-case guarantees as functions of the step size](#3.1.2-Worst-case-guarantees-as-functions-of-the-step-size)\n", + "- [3.2 Example 2: Accelerated gradient method](#3.2-Example-2-:-An-accelerated-gradient-method-for-strongly-convex-objectives)\n", + "- [3.3 Example 3: Accelerated Douglas-Rachford splitting](#3.3-Example-3-:-An-accelerated-Douglas-Rachford-splitting)\n", + "- [3.4 Example 4: point-SAGA](#3.4-Example-4-:-point-SAGA)" ] }, { @@ -499,7 +552,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Example 1 : Gradient descent with fixed step size in contraction" + "### 3.1 Example 1 : Gradient descent with fixed step size in contraction" ] }, { @@ -563,7 +616,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### 1.1 Worst-case guarantees as functions of the iteration count " + "#### 3.1.1 Worst-case guarantees as functions of the iteration count" ] }, { @@ -607,7 +660,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -636,7 +689,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### 1.2 Worst-case guarantees as functions of the step size " + "#### 3.1.2 Worst-case guarantees as functions of the step size" ] }, { @@ -680,7 +733,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -708,7 +761,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Example 2 : An accelerated gradient method for strongly convex objectives" + "
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" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3.2 Example 2 : An accelerated gradient method for strongly convex objectives" ] }, { @@ -817,7 +877,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -846,7 +906,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Example 3 : An accelerated Douglas-Rachford splitting" + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3.3 Example 3 : An accelerated Douglas-Rachford splitting" ] }, { @@ -964,7 +1031,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -994,7 +1061,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Example 4 : point-SAGA" + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3.4 Example 4 : point-SAGA" ] }, { @@ -1109,12 +1183,12 @@ "cell_type": "code", "execution_count": 23, "metadata": { - "scrolled": true + "scrolled": false }, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -1138,6 +1212,13 @@ "\n", "plt.show()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] } ], "metadata": { diff --git a/ressources/demo/PEPit_demo_extracting_a_proof.ipynb b/ressources/demo/PEPit_demo_extracting_a_proof.ipynb index ac241f4a..ce6655e8 100644 --- a/ressources/demo/PEPit_demo_extracting_a_proof.ipynb +++ b/ressources/demo/PEPit_demo_extracting_a_proof.ipynb @@ -2,7 +2,6 @@ "cells": [ { "cell_type": "markdown", - "id": "b626da1d-95a1-4176-a342-eb66d647b602", "metadata": { "tags": [] }, @@ -12,7 +11,6 @@ }, { "cell_type": "markdown", - "id": "318ecadc-e8fa-4cb1-a23b-56c932c79e19", "metadata": {}, "source": [ "# PEPit : numerical examples of worst-case analyses" @@ -20,7 +18,6 @@ }, { "cell_type": "markdown", - "id": "79ac4037-2324-4b0e-b64b-f85038445479", "metadata": {}, "source": [ "This notebook provides:\n", @@ -33,7 +30,6 @@ }, { "cell_type": "markdown", - "id": "e5cf3c75-9a56-48ef-85b9-e6f77b3a972f", "metadata": {}, "source": [ "This notebook is organized as follows:\n", @@ -48,7 +44,6 @@ { "cell_type": "code", "execution_count": 1, - "id": "6ae4cd3b-b120-47b0-a37c-7d5a124bc0a6", "metadata": { "tags": [] }, @@ -65,7 +60,6 @@ { "cell_type": "code", "execution_count": 2, - "id": "89818bda-47bd-4929-831d-e05706b2a27c", "metadata": { "tags": [] }, @@ -77,15 +71,27 @@ }, { "cell_type": "markdown", - "id": "f8a4ca21-ced4-4621-a5e4-852648ba1e17", "metadata": {}, "source": [ - "## 1. Gradient descent, distance to a solution " + "\n", + "## Table of Contents\n", + "- [1. Gradient descent, distance to a solution](#example1)\n", + "- [2. Gradient descent, function value accuracy](#example2)\n", + "- [3. Function values: numerical proof simplification](#example3)\n", + "- [4. Using SymPy for the distance analysis](#example4)\n", + "- [5. Using SymPy for the function value accuracy analysis](#example5)\n", + "- [6. Using symbolic regression (PySR)](#example6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1 Gradient descent, distance to a solution " ] }, { "cell_type": "markdown", - "id": "7f4b3c2b-83ec-494d-8a28-cda5f12338be", "metadata": {}, "source": [ "We start by a direct attempt: fix class parameters $L,\\mu$ (chosen above) and experiment with different step size values $\\gamma$. Verify that the obtained convergence rate is indeed smaller than one only when $\\gamma\\in\\left(0,\\frac{2}{L}\\right)$. Further verify that it matches the very well-known $\\max\\{(1-\\gamma L)^2,(1-\\gamma\\mu)^2\\}$." @@ -94,7 +100,6 @@ { "cell_type": "code", "execution_count": 3, - "id": "26925393-8cef-46d8-b1a9-291aade9e3dd", "metadata": { "tags": [] }, @@ -132,8 +137,7 @@ }, { "cell_type": "code", - "execution_count": 56, - "id": "c75fc2b0-e4ba-474f-ab43-2df06335f21e", + "execution_count": 4, "metadata": { "tags": [] }, @@ -156,20 +160,21 @@ }, { "cell_type": "code", - "execution_count": 57, - "id": "7a219f3b-ed75-4420-8292-60ded8f09c9f", + "execution_count": 5, "metadata": { "tags": [] }, "outputs": [ { "data": { - "image/png": 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", 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\n", "text/plain": [ - "
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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -187,7 +192,6 @@ }, { "cell_type": "markdown", - "id": "6287eeba-2a4a-4837-b568-96d93876e594", "metadata": {}, "source": [ "One can admit that the match between PEPit's results and the known convergence rate is pretty good. For completeness, let us also extract the dual variables. The next lines examplify how to do this extraction for given values of the parameters, and we integrate it in a loop for plotting below." @@ -195,8 +199,7 @@ }, { "cell_type": "code", - "execution_count": 58, - "id": "0c2f805d-dd80-4f65-94fb-95e4b2d3e213", + "execution_count": 6, "metadata": { "tags": [] }, @@ -205,10 +208,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Constraint \"Constraint 3\" value: 1.0\n", - "Constraint \"Constraint 0\" value: 0.8100000006611664\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" value: 1.800009898700675\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" value: 1.800009898700675\n" + "Constraint \"Constraint 3\" value: 0.9999999999866084\n", + "Constraint \"Constraint 0\" value: 0.8100001805827125\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" value: 1.7999998617137993\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" value: 1.7999998617138078\n" ] } ], @@ -227,7 +230,6 @@ }, { "cell_type": "markdown", - "id": "6e8721b0-982f-4d87-9de2-2f3520d343c6", "metadata": {}, "source": [ "One can observe that the performance estimation problem is actually involving 4 constraints, 2 of which are of interest for us: the 3rd and 4th ones (that encode the fact the function is smooth and strongly convex). We can therefore extract their values in a loop, plot them, and expect their closed-forms to be nice. Perhaps one could even guess their values." @@ -235,8 +237,7 @@ }, { "cell_type": "code", - "execution_count": 59, - "id": "bed29990-e7b3-4ab8-809c-aa5b864bb251", + "execution_count": 7, "metadata": { "tags": [] }, @@ -263,7 +264,6 @@ }, { "cell_type": "markdown", - "id": "25b693b7-e7dc-46d8-ad85-1f4c448c72fd", "metadata": {}, "source": [ "Playing a bit with candidate expressions, one can guess a closed-form for the multipliers (which happen to be always equal): $\\lambda=2|\\gamma| \\rho(\\gamma)$ with $\\rho(\\gamma)=\\max\\{|1-\\gamma L|,|1-\\gamma\\mu|\\}$." @@ -271,20 +271,21 @@ }, { "cell_type": "code", - "execution_count": 63, - "id": "fd795ad6-d8c1-454e-b1be-ae4ff67167be", + "execution_count": 8, "metadata": { "tags": [] }, "outputs": [ { "data": { - "image/png": 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", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -303,7 +304,6 @@ }, { "cell_type": "markdown", - "id": "20b45983-2f73-4af7-8bed-95bfff0f7145", "metadata": {}, "source": [ "Section [4](#example4) below explores how to transform that into a formal mathematical proof (that include replacing the actual guessing game by formal mathematical steps). In the meantime, we explore a case where things are directly less convenient, that of function values. In fact, this slightly more complicated problem already show a typical feature appearing in computer-aided analyses: non-uniqueness of the proofs. This might seem like a good thing (in fact, it is, in many aspects), but it actually renders the formal translation and search more painful, as the numerical solvers actually generally do not provide the simplest proofs possible, but rather combinations of them and fail providing the *sparse* (and likely simpler) ones." @@ -311,15 +311,20 @@ }, { "cell_type": "markdown", - "id": "a9ef34d5-d122-43b7-b0ee-267fa4dcaf26", "metadata": {}, "source": [ - "## 2. Gradient descent, function value accuracy " + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2 Gradient descent, function value accuracy " ] }, { "cell_type": "markdown", - "id": "91bbca45-c600-423f-a3c5-192d785187e6", "metadata": {}, "source": [ "Let us start with the exact same exercise, but now by changing the specific quantity under our radar to function values. Practically speaking, this means changing both the performance metric and the initial condition in the previous code. Executing the code in the same fashion as before, we observe the exact same worst-case ratios." @@ -327,8 +332,7 @@ }, { "cell_type": "code", - "execution_count": 68, - "id": "1cdc2dd8-502d-4826-90b9-1b235c4e6a62", + "execution_count": 9, "metadata": { "tags": [] }, @@ -366,20 +370,21 @@ }, { "cell_type": "code", - "execution_count": 69, - "id": "67257b5a-9ef3-486f-a502-dbcaa9ce2095", + "execution_count": 10, "metadata": { "tags": [] }, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -411,7 +416,6 @@ }, { "cell_type": "markdown", - "id": "82530092-bd44-4d95-bc34-8fb54e072a24", "metadata": {}, "source": [ "However, a bad surprise appears when inspecting the problem: there are actually more constraints, and hence possibly more dual multipliers to be identified. We do not describe here the reason for this difference (more constraints, explained at length, e.g., in [this blog post](https://francisbach.com/computer-aided-analyses/) or this [habilitation thesis](https://hal.science/tel-04794552v2/file/HDR_ATaylor_V_HAL2.pdf)) and instead focus on the consequences." @@ -419,8 +423,7 @@ }, { "cell_type": "code", - "execution_count": 70, - "id": "5504126a-0d28-490c-8dd1-ae0094129ce1", + "execution_count": 11, "metadata": { "tags": [] }, @@ -429,14 +432,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Constraint \"Constraint 7\" value: 1.0\n", - "Constraint \"Constraint 0\" value: 0.8099999034654997\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" value: 0.04318494581205349\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" value: 0.14690493317815176\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" value: 3.7068368407529674e-05\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" value: 1.3215023299277147\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" value: 5.272685701848342e-05\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" value: 0.46835454902147894\n" + "Constraint \"Constraint 7\" value: 1.000000000000004\n", + "Constraint \"Constraint 0\" value: 0.8099999986909497\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" value: 0.07413167584202415\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" value: 0.11586832639046385\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" value: 1.1349094168952335e-09\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" value: 1.0428149257255546\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" value: 1.2819965105035798e-09\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" value: 0.1586832515672777\n" ] } ], @@ -455,7 +458,6 @@ }, { "cell_type": "markdown", - "id": "18c9181e-fcc8-4f1f-b328-779c215f418d", "metadata": {}, "source": [ "To get a clearer picture, let us plot all those values as a function of $\\gamma$ again." @@ -463,20 +465,21 @@ }, { "cell_type": "code", - "execution_count": 76, - "id": "dc980cbb-6b58-4584-8dd4-be686b280d39", + "execution_count": 12, "metadata": { "tags": [] }, "outputs": [ { "data": { - "image/png": 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", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -524,7 +527,6 @@ }, { "cell_type": "markdown", - "id": "b5d251da-e8f0-424d-8fc9-6bd14b6c4d0b", "metadata": {}, "source": [ "Well, guessing closed-forms appears like a much more challenging game now. The next section illustrates that one can actually simplify this picture simply by removing certain of the constraints (or equivalently by forcing their multipliers to be zero)." @@ -532,15 +534,20 @@ }, { "cell_type": "markdown", - "id": "5cb7f440-0d34-4b6f-a140-1536ba4a11b0", "metadata": {}, "source": [ - "## 3. Function values: numerical proof simplification " + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3 Function values: numerical proof simplification " ] }, { "cell_type": "markdown", - "id": "71459a17-1cd4-4ecf-9ae1-1198cd592dd6", "metadata": {}, "source": [ "The game for this section consists in forcing certain multipliers to be zero (deactivating constraints) while keeping the same optimal value. In other words, we search for possibly *sparse* proofs. For doing that, we must experiment with solve/resolve the PEP with different constraints patterns. In PEPit, this can be done through the *prepare_problem* command (instead of solve) as follows:" @@ -548,8 +555,7 @@ }, { "cell_type": "code", - "execution_count": 78, - "id": "075773e8-1fc9-4a45-ade8-a4c68b387649", + "execution_count": 13, "metadata": { "tags": [] }, @@ -603,7 +609,6 @@ }, { "cell_type": "markdown", - "id": "9beb6ee2-0153-4e48-ad45-106189dd8000", "metadata": {}, "source": [ "We can now interactively iterate between solving the problem and activating/deactivating constraints, and the goal is to identify a minimal number of constraints that allows recovering the same optimal problem value. Let us start by solving the original problem." @@ -611,8 +616,7 @@ }, { "cell_type": "code", - "execution_count": 80, - "id": "df117c5b-664a-4f11-a98c-8c9b16dcbffc", + "execution_count": 14, "metadata": { "tags": [] }, @@ -624,27 +628,24 @@ "(PEPit) Setting up the problem: size of the Gram matrix: 4x4\n", "(PEPit) Compiling SDP\n", "(PEPit) Calling SDP solver\n", - "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.809999909317056\n", - "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -6.17e-09 < 0).\n", - " Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n", - " In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n", + "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: SCS); optimal value: 0.8099999973549602\n", "(PEPit) Primal feasibility check:\n", - "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 6.172665013326517e-09\n", - "\t\tAll the primal scalar constraints are verified up to an error of 2.0330860467376866e-09\n", + "\t\tThe solver found a Gram matrix that is positive semi-definite\n", + "\t\tAll the primal scalar constraints are verified up to an error of 2.02780943356351e-08\n", "(PEPit) Dual feasibility check:\n", - "\t\tThe solver found a residual matrix that is positive semi-definite\n", + "\t\tThe solver found a residual matrix that is positive semi-definite up to an error of 2.7515637538840285e-16\n", "\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n", - "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 5.109620224846845e-08\n", - "(PEPit) Final upper bound (dual): 0.8099999034654997 and lower bound (primal example): 0.809999909317056 \n", - "(PEPit) Duality gap: absolute: -5.85155635057788e-09 and relative: -7.224144451462428e-09\n", - "Constraint \"Constraint 7\" value: 1.0\n", - "Constraint \"Constraint 0\" value: 0.8099999034654997\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" value: 0.04318494581205349\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" value: 0.14690493317815176\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" value: 3.7068368407529674e-05\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" value: 1.3215023299277147\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" value: 5.272685701848342e-05\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" value: 0.46835454902147894\n" + "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 5.729466262983668e-09\n", + "(PEPit) Final upper bound (dual): 0.8099999986909497 and lower bound (primal example): 0.8099999973549602 \n", + "(PEPit) Duality gap: absolute: 1.3359895412179412e-09 and relative: 1.649369809358753e-09\n", + "Constraint \"Constraint 7\" value: 1.000000000000004\n", + "Constraint \"Constraint 0\" value: 0.8099999986909497\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" value: 0.07413167584202415\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" value: 0.11586832639046385\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" value: 1.1349094168952335e-09\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" value: 1.0428149257255546\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" value: 1.2819965105035798e-09\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" value: 0.1586832515672777\n" ] } ], @@ -663,7 +664,6 @@ }, { "cell_type": "markdown", - "id": "5d66e74d-c59d-4c22-a9bd-360f2287c468", "metadata": {}, "source": [ "The corresponding optimal value matches what we would expect. Let us now deactivate some constraints and observe the result. We start with the first interpolation constraint (third constraint in the list) as follows:" @@ -671,8 +671,7 @@ }, { "cell_type": "code", - "execution_count": 84, - "id": "94a9548e-3451-4087-b186-0fd5d8283ccf", + "execution_count": 15, "metadata": { "tags": [] }, @@ -684,27 +683,27 @@ "(PEPit) Setting up the problem: size of the Gram matrix: 4x4\n", "(PEPit) Compiling SDP\n", "(PEPit) Calling SDP solver\n", - "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.809999956944149\n", - "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -4.02e-09 < 0).\n", + "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: SCS); optimal value: 0.8099959237526846\n", + "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -7.95e-06 < 0).\n", " Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n", " In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n", "(PEPit) Primal feasibility check:\n", - "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 4.022897991237727e-09\n", - "\t\tAll the primal scalar constraints are verified up to an error of 2.0330860467376866e-09\n", + "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 7.950263779793486e-06\n", + "\t\tAll the primal scalar constraints are verified up to an error of 2.02780943356351e-08\n", "(PEPit) Dual feasibility check:\n", - "\t\tThe solver found a residual matrix that is positive semi-definite\n", + "\t\tThe solver found a residual matrix that is positive semi-definite up to an error of 1.294938016578548e-16\n", "\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n", - "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 2.8795806151076664e-08\n", - "(PEPit) Final upper bound (dual): 0.8099999517743242 and lower bound (primal example): 0.809999956944149 \n", - "(PEPit) Duality gap: absolute: -5.169824790485222e-09 and relative: -6.382500080603945e-09\n", - "Constraint \"Constraint 7\" dual value: 1.0 [activated? True]\n", - "Constraint \"Constraint 0\" dual value: 0.8099999517743242 [activated? True]\n", + "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 3.4788703067185206e-06\n", + "(PEPit) Final upper bound (dual): 0.8100122825325423 and lower bound (primal example): 0.8099959237526846 \n", + "(PEPit) Duality gap: absolute: 1.6358779857728045e-05 and relative: 2.0196126150781544e-05\n", + "Constraint \"Constraint 7\" dual value: 0.9999999999994755 [activated? True]\n", + "Constraint \"Constraint 0\" dual value: 0.8100122825325423 [activated? True]\n", "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" dual value: 0.0 [activated? False]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" dual value: 0.1900739137692873 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" dual value: 3.0943424661018764e-05 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" dual value: 1.7099721331569564 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" dual value: 4.292931902870809e-05 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" dual value: 0.9000031248051895 [activated? True]\n" + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" dual value: 0.18999927669423558 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" dual value: 0.0 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" dual value: 1.710173729689888 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" dual value: 1.164825840095675e-05 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" dual value: 0.900161358121609 [activated? True]\n" ] } ], @@ -723,7 +722,6 @@ }, { "cell_type": "markdown", - "id": "d4e026bb-e7b6-4e20-9877-fc6084c4f726", "metadata": {}, "source": [ "Good surprise: the same numerical bound can be achieved without using the first interpolation constraint... let's try to be more aggressive and deactivate more constraints." @@ -731,8 +729,7 @@ }, { "cell_type": "code", - "execution_count": 85, - "id": "b494a370-ef9e-43da-992a-bc23bea97106", + "execution_count": 16, "metadata": { "tags": [] }, @@ -744,7 +741,7 @@ "(PEPit) Setting up the problem: size of the Gram matrix: 4x4\n", "(PEPit) Compiling SDP\n", "(PEPit) Calling SDP solver\n", - "(PEPit) Solver status: unbounded (wrapper:cvxpy, solver: MOSEK); optimal value: None\n", + "(PEPit) Solver status: unbounded (wrapper:cvxpy, solver: SCS); optimal value: None\n", "\u001b[96m(PEPit) Problem issue: PEPit didn't find any nontrivial worst-case guarantee. It seems that the optimal value of your problem is unbounded.\u001b[0m\n", "Constraint \"Constraint 7\" dual value: 0.0 [activated? True]\n", "Constraint \"Constraint 0\" dual value: 0.0 [activated? True]\n", @@ -774,7 +771,6 @@ }, { "cell_type": "markdown", - "id": "0575db5a-c37b-495f-a606-c85295267797", "metadata": {}, "source": [ "This was too much. We need to reactivate some." @@ -782,8 +778,7 @@ }, { "cell_type": "code", - "execution_count": 90, - "id": "ef737d1e-00e2-4619-8868-70814933e342", + "execution_count": 17, "metadata": { "tags": [] }, @@ -795,27 +790,27 @@ "(PEPit) Setting up the problem: size of the Gram matrix: 4x4\n", "(PEPit) Compiling SDP\n", "(PEPit) Calling SDP solver\n", - "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.8099999473346992\n", - "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -2.02e-09 < 0).\n", + "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: SCS); optimal value: 0.8099888053087226\n", + "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -8.97e-06 < 0).\n", " Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n", " In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n", "(PEPit) Primal feasibility check:\n", - "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 2.0161722580930193e-09\n", - "\t\tAll the primal scalar constraints are verified up to an error of 2.0330860467376866e-09\n", + "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 8.969189465201078e-06\n", + "\t\tAll the primal scalar constraints are verified up to an error of 2.02780943356351e-08\n", "(PEPit) Dual feasibility check:\n", "\t\tThe solver found a residual matrix that is positive semi-definite\n", "\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n", - "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 2.5852069649931475e-08\n", - "(PEPit) Final upper bound (dual): 0.809999941112574 and lower bound (primal example): 0.8099999473346992 \n", - "(PEPit) Duality gap: absolute: -6.222125148447333e-09 and relative: -7.681636485188925e-09\n", - "Constraint \"Constraint 7\" dual value: 1.0 [activated? True]\n", - "Constraint \"Constraint 0\" dual value: 0.809999941112574 [activated? True]\n", + "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 1.9538734712248873e-06\n", + "(PEPit) Final upper bound (dual): 0.8100061200137512 and lower bound (primal example): 0.8099888053087226 \n", + "(PEPit) Duality gap: absolute: 1.7314705028526056e-05 and relative: 2.1376474483405552e-05\n", + "Constraint \"Constraint 7\" dual value: 0.9999999999992356 [activated? True]\n", + "Constraint \"Constraint 0\" dual value: 0.8100061200137512 [activated? True]\n", "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" dual value: 0.0 [activated? False]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" dual value: 0.19005372641333823 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" dual value: 0.18999905903570885 [activated? True]\n", "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" dual value: 0.0 [activated? False]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" dual value: 1.7099956087838943 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" dual value: 5.3673990181861823e-05 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" dual value: 0.8999956676713203 [activated? True]\n" + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" dual value: 1.7102118672605662 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" dual value: 5.1790508283630655e-06 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" dual value: 0.9002057472465224 [activated? True]\n" ] } ], @@ -835,7 +830,6 @@ }, { "cell_type": "markdown", - "id": "57aa820f-9320-4593-a9a1-ed51ee40a7c1", "metadata": { "tags": [] }, @@ -845,8 +839,7 @@ }, { "cell_type": "code", - "execution_count": 97, - "id": "23a08913-26cd-4468-9b45-6ce855e1dc32", + "execution_count": 18, "metadata": { "tags": [] }, @@ -858,25 +851,25 @@ "(PEPit) Setting up the problem: size of the Gram matrix: 4x4\n", "(PEPit) Compiling SDP\n", "(PEPit) Calling SDP solver\n", - "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.8099999848815963\n", - "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -1.29e-09 < 0).\n", + "(PEPit) Solver status: optimal (wrapper:cvxpy, solver: SCS); optimal value: 0.8100000003376879\n", + "\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -6.16e-10 < 0).\n", " Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n", " In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n", "(PEPit) Primal feasibility check:\n", - "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 1.2887427659820522e-09\n", - "\t\tAll the primal scalar constraints are verified up to an error of 2.0330860467376866e-09\n", + "\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 6.157372501933532e-10\n", + "\t\tAll the primal scalar constraints are verified up to an error of 2.02780943356351e-08\n", "(PEPit) Dual feasibility check:\n", - "\t\tThe solver found a residual matrix that is positive semi-definite\n", + "\t\tThe solver found a residual matrix that is positive semi-definite up to an error of 3.214747989495667e-16\n", "\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n", - "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 6.333316023113211\n", - "(PEPit) Final upper bound (dual): 0.8099999812120227 and lower bound (primal example): 0.8099999848815963 \n", - "(PEPit) Duality gap: absolute: -3.669573644948798e-09 and relative: -4.530337917827501e-09\n", - "Constraint \"Constraint 7\" dual value: 0.0 [activated? True]\n", - "Constraint \"Constraint 0\" dual value: 0.0 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" dual value: 0.0 [activated? True]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" dual value: 0.0 [activated? True]\n", + "(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 1.6402668650411512e-09\n", + "(PEPit) Final upper bound (dual): 0.810000000152885 and lower bound (primal example): 0.8100000003376879 \n", + "(PEPit) Duality gap: absolute: -1.8480295072009767e-10 and relative: -2.2815179091735007e-10\n", + "Constraint \"Constraint 7\" dual value: 1.0000000000000062 [activated? True]\n", + "Constraint \"Constraint 0\" dual value: 0.810000000152885 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_1)\" dual value: 0.08999999992515632 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_0, Point_2)\" dual value: 0.09999999992196733 [activated? True]\n", "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_0)\" dual value: 0.0 [activated? False]\n", - "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" dual value: 0.0 [activated? True]\n", + "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_1, Point_2)\" dual value: 0.9000000000780398 [activated? True]\n", "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_0)\" dual value: 0.0 [activated? False]\n", "Constraint \"IC_Function_0_smoothness_strong_convexity(Point_2, Point_1)\" dual value: 0.0 [activated? False]\n" ] @@ -902,7 +895,6 @@ }, { "cell_type": "markdown", - "id": "a9baba97-8b1f-44b8-b166-9e69d94b3c23", "metadata": {}, "source": [ "Let us verify that this pattern of inequalities works throughout the whole range of step sizes $\\gamma$." @@ -910,8 +902,7 @@ }, { "cell_type": "code", - "execution_count": 4, - "id": "8c4fa25f-ee3e-4ad9-ad7c-9753296287a5", + "execution_count": 19, "metadata": { "tags": [] }, @@ -954,20 +945,21 @@ }, { "cell_type": "code", - "execution_count": 121, - "id": "7a6b2196-9e54-42f1-8754-55b99fd57f05", + "execution_count": 20, "metadata": { "tags": [] }, "outputs": [ { "data": { - "image/png": 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", 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hyRJo0ADz2yK70ymVJxzeuo/DlKQQxylbp6xbl+0xxURE2ovIDhGJFZHBGUyvIiKLRGSjiCwRkUCnad1EJMZ6dHNvcnVB6dJUXTKFO4c3vnCb0Kn/3EaXWw9wbPCbkJpqc0ClcreEracAqEo8Us19pwWDhxQTEfEFxgG3AaFAVxEJTddtFDDNGFMPGA68Zc1bEhgGNAEaA8NEpIS7sqt0fHzg5Zdh4UJOlanMi7zFLB6g0dv3saHJ47B3r90Jlcq14hIcf9KrEu/Wa0zAQ4oJjiIQa4yJN8acBWYCHdP1CQUWW89/d5reDvjVGHPIGHMY+BVo74bM6kratCEgahXLmgyiPhuIJYSmaz9iQs33Mb8stDudUrlPWhpVkiPpw8d0YJ5brzEBzykmFYHdTq+TrDZnUcDd1vPOQBERKZXJeQEQkQgRiRSRyOTk5BwJrq7guusI+fMzVg75mQgmcgZ/+hwfxUPtD/DvwNf0bC+lctK+fTQ+u5yP6UdEyW+hWDG3Lt5TiklmDARaich6oBWwB8jSTnhjzERjTLgxJrxMmTKuyKjS8/Ul4I0hTFgcwvRi/SjEcb7iQR55rz7ccgvs2WN3QqVyh/j4i8/dvFUCnlNM9gDOl2oGWm0XGGP2GmPuNsY0BIZYbUcyM6/yAK1b8+COYUQ2f4omrGIEQ2DZMmjQAH75xe50Snm/+Hjm054o6pEalHeLyRogRESCRSQ/0AWY49xBREqLyPm8LwJTrOe/AG1FpIR14L2t1aY8Tbly1Fo2iZWvLyLMxzHasDlwgIntv9XdXkpl07noBO5kLg1ZT0pQdbcv3yOKiTEmBXgCRxHYBswyxmwRkeEicpfV7WZgh4hEA+WAEda8h4DXcRSkNcBwq015Ih8fZOgQWLwYrruOz+nG40wk/L0ubGzymO72Uuoa7dp8jFTyEUgSBWoGuX35HlFMAIwx84wxNYwx1Ywx5wvFK8aYOdbz2caYEKvPY8aYM07zTjHGVLceehtAb9CqFWzYQNPmvtRhE9HUpMm6j5lUaxRmgW5YKpVV8TGOQ8jViHP7acHgQcVE5UFly1Jr2SRWvzKPXkzmNAFEHB/NQ7cd5N/nXtXdXkplQVySY/gUO64xAS0mym4+PhR87QU+XVKdL4o9ceFsr0bvP0hc04cgKcnuhEp5vuPHif/XcYZqVZ+dEBh4lRlynhYT5RlateLh6FeIbP4UddmIH+cov/Ynx9le8+bZnU4pz5aQcHG04LL/gq+v2yNoMVGe4/xur1cXME/uoBAn4eBBTtx+H8eefgXOnbM7oVKeyWno+apBabZE0GKiPIuPDwHDnqfKks+hQgUA+jGeRh88wrpGvWHXLpsDKuWB4uNZSTO2U5N69eyJoMVEeaaWLWHDBo61uZso6hNLCM02TeCjWh9hfpxz9fmVykvi4ynAWWoSjX+NyrZE0GKiPFeZMhT95RtWvf4bfeVjzlKAJ0+9w72dznGk74tw9qzdCZXyDHFxF5/bMJQKaDFRns7HB/+hAxm/vD6zSvWlKEf5jnto+EkEq+tHXDoekVJ51E8bK9OKJYyjny2nBYMWE+Utmjfnvh1vsP6WgYSzhkSCmbT9JmjYEGbPtjudUvZJTWXjP2VZSit2UgWCg22JocVEeY9Spaj620SWv7uKET4v8wFPwbFjcN990K8fnD5td0Kl3G/PHuJSgwCoWiQZihSxJYYWE+VdRCgw8EleWnUXhYLLAXCCgtz6cWeW1ekLO3bYHFApN4uPv3hacEX7jiNqMVHe6YYbYN06uPdePuApfuNWbo77lDfqfk3q51/anU4p94mLIw7HQfeqNfLZFkOLifJexYvDrFkM+iiIwb7vkoYvL597hXbdy/P3A0/BiRN2J1TK5c5E7ySJQHxIpUode3ZxgRYT5e1E8OsfwVtr27KgYi/KsJ9FtKH+rJf4tfYA2LjR7oRKudTOzf9i8KEyu/ALCbIthxYTlTvUr0+77R8Qdc/r3MIi9lOOdrsnsSH8MfjkEzDG7oRKuUT+pHj68xFdmGnbNSYAYvLof7Lw8HATGRlpdwzlAqlTp/HW4wkknAtkMo85Gu+9FyZNcuwaUyo3KV0aDh50PE9KgooVXbo4EVlrjAlP365bJirX8e3xKEM3PsCndcdeaNs8exs/1HgeVq+2MZlSOezo0YuFpEABuO4626Jku5iISGpOBFEqR9WqhaxeBX37cgp/7mcWnZMn8mSzSE6/+T6k2TOyqlI5Kj6eFTRjHQ05HVQLfOzbPsiJJUsOvIdSOS8gAMaPx/+bL4nw/wI/zvKR6U+zIa3Z0SoC9u+3O6FS2RMfTx8+oRHr2FKmla1RcqKY5M2DLspryL338PS2x1lR53GqEcsGGtJo+Rim1XgDFi2yO55S18zEOV2wGBpga5YsFxMRKSkiV90ayWw/pdwiKIjwdRNZ9/QXdGUGJyhMt6Nj6dsmBoYM0fvNK6+0f/N+TlCY4hymRKh9x0sgi8VERMoDC4ErlsDM9ks3T3sR2SEisSIyOIPplUXkdxFZLyIbRaSD1R4kIqdEZIP1+CQrP5PKQ/z8KDr6NaYvKM3kIk8TwEmashLefBNatYKdO+1OqFSWxG93DJ9SjTjbRgs+L0vFxBjzN/A/Y8zJnOh3noj4AuOA24BQoKuIhKbrNhSYZYxpCHQBxjtNizPGNLAefTL546g8Stq1pWf0YGJa9OJRpjkaV6xgS90umG+/szecUlkQv9Nxr/eqxNt6jQlkopiISA3n18aYo9npdxmNgVhjTLwx5iwwE+iYro8BilrPiwF7s/D+Sl2qfHkqLpmOvPUW+PqyhVBu+HcRd93rx4HuA+HUKbsTKnVlKSnEHXD8SaxKPAQF2RonM1smvUWkbw72y0hFYLfT6ySrzdmrwMMikgTMA550mhZs7f76Q0RaXG4hIhIhIpEiEpmcnHyNUVWu4eMDgwfDsmXsKXs9BTjDT9xJ/c+fYUloP9iyxe6ESl3e7t3EpwUBUK3YAShY0NY4mSkmB4E+IvKBiPQUkesv0+9QJvtdq67AZ8aYQKAD8IWI+AD7gMrW7q9ngRkiUjSjNzDGTDTGhBtjwsuUKZPD8ZTXataMtjs+JOr2l7iR5eylIrckTublBnNJ+XiSDsWiPFN8PJPoTSzVuLvWNrvTXL2YGGNGAr2BV4A44KbL9HsrM/0uYw9Qyel1oNXmrBcwy1rWSsAfKG2MOWOMOWi1r7WWXQOlsqJ4cSrPHc+S8dt42fdNAN5IGczN/Wqz685+cOSIvfmUSi8uDj9SqEY8pWqWtjtN5g7AG2P+MsYcNcb8YYwZm91+GVgDhIhIsIjkx3GAfU66PruA/wGISG0cxSRZRMpYB/ARkapACKA3BldZJ0K+vr0ZHtWRRUG9qMAe1tOQEz8vgQYNYMUKuxMqdVG80585mw++QxbO5hKRTJW+zPZzZoxJAZ4AfgG24Thra4uIDBeRu6xuz+E4LhMFfAV0N45RKlsCG0VkAzAb6GOMOZTVDEpdEBZG663jieo2mu/pTG22w86dmBYtOfPaSEjVEYSU/aLXn6A5f/ICI20/LRiydmrwlBzudwljzDxjTA1jTDVjzAir7RVjzBzr+VZjzI3GmPrWKcALrfZvjTFhVtv1xpi517J8pS4REEDpz0bRdvbjF0Yanpr2KI1evYPNzXrDnvR7YZVyr+0xvqykORupByEhdsfJUjHJ7NXsetW7yj3uuQeioki7sQXj6M8W6nDDmnF8UnM0Zo5+b1E2MYbYPY5rwqsT6127ucj8GFx66ovKXSpXxmfJYpYOnk9PpnCaAPqeGMU9Hc9xKGIwnD5td0KV1+zfT+xZxzlL1f33QKlSNgfSLROlMidfPgq9NZTJS6rxVYl+FOUo33M39Sf154+wfrB1q90JVV4SG0ss1QGoHngKPGAYxKwUkxdzuJ9S3qdVK7rEvM6GNoNoykqSqMRT8QNIa3SD406Oek2KcgfnYhLiGfc4zHQKY8zmnOynlNcqVYrghRNYOjaKl33fZDoP4XP6JEREwH33weHDdidUudzZHQnspAo+pBJUL8NrtN0uK6cGlxGRaiLilxP9lPJqIvg92Yfh6+8kLMyxi8EA/b9tzTchL8Hy5fbmU7na6ehdPMmHdONzCtQKtjsOAPmu1kFEHsdxNfsp4AhQUUSOAu8aYxKy2k+pXKVuXVizBp57jkUfRzOe/ow/CL1aTOaDF/+g0PAXIN9V/5splSVFd25iDFMdL6ovszeMRcxV9vGKyPXGmHXp2goB1xljYkUk1Rjje4V+FYwxMTmePJvCw8NNZGSk3TFULmK+/4GPH1rOs6fe4Az+1GAHX9V/m+t/HAZVqtgdT+UmJUpcHOJn3z4oX95tixaRtcaY8PTtmRmba10Gzc2MMbEZ9RORh0VkkIgMAjp5YiFRyhWkcyf6RT/NmkZ9CWMz0dSkadQnvF9rImlffW13PJVbHDrEuiPBrCGcEwXLQLlydicCsnbM5CsReV5EXuDS4d/Tq2iMedcY8y6OARuVyjsCA6m7+lPWvDqPfjKec+TnudMj+PDBFdCzJxw/bndC5e1iY3mZ12nMGn4t86BHnBYMmThmAhfuhDjeGLPMel3nCv1WiMjzQBqgI+OpvMfXl4BhzzOu3Sradoxg1P5HeIxPYepJx4H5GTMg/D97CZTKnNhYYmkEQPXqNmdxktktk4nAWgARaXmF038nAmuNMe8Aa84XH6XypKZN6Rj9Lku7fkIhHHew/jdmH683mcvpEe9BWprNAZU3StkRRwKOM7iq1itsc5qLMltMXgEmi8gXwA2Z7KdfvZQqVgyZMR2mTYPChXmG0byS9hpNhrZhS3MdMFJl3e6NhzlHfiqSRMHannNiR2aLyevADhyn0s/KgX5K5S2PPAIbNvB42J9UJ4aN1Cd89Ud8XHMM5ocf7U6nvEjsDsctEKoT61H7uTJbTJ43xrwK9AWG5UA/pfKeatW4Yf1E1g/6ih5M5TQB9DvxLp06w4HuA+HkSbsTKi8Qu7sA4IXFRET8jTEHAIwxJ4DHz7dfSz+l8jQ/Pwq/8wpTllTl65J9KcYR5tCRep8/S3KDWyEqyu6EypMdPUrc8bIAVPdNhIoV7c3jJDMXLc7HcffDrTiubA8CqgLTjTF/Ol20eMV+Lsp/zfSiRWW7Q4fY+fAQHp7/ICHEMIVekD8/jBwJTz0FPp4xgJ/yIOvWkdKoMbupRKEagZTd4f5znK75okVgM3AY2Av4AUuMMf0yKBCZ7aeUAihZkio/j+f3CTGMCxjkaDt7lk3PTmF7ywjHlc1KOYuLIx+pBJNI2Zol7E5zicwUk4PAvUA7IADH9SPZ6aeUOk+EfBE9CdiwEho14gQFuZ9ZXP/nWCaEjNK7OapLxToNPOJBx0sgc8OpjAR64zjtNw7HYI7OJJP9lFKXU6MGrFhB2tPPcQNrOEVB+px4j7s7pnCgxyA9OK8A2BN1gCas4knGel8xATDG/GWMOWqM+cMYMzbdNJ/M9FNKXUX+/BQZPZxpiysxo0R/inKUH+hMvc+e4ddaT8KGDXYnVDaL2ZbCXzRhHdd7ZzFxBxFpLyI7RCRWRAZnML2yiPwuIutFZKOIdHCa9qI13w4Raefe5ErlsNat6RoznKh2L3ATy9hHBdrunsywRj/Be3rlfF4Wu9NxmyhPOy0YPKSYWGN6jQNuA0KBriISmq7bUGCWMaYh0AUYb80bar0OA9oD4633U8p7lSpF0PyP+X1iLK/7DceXFELStsPAgdC2rV45nxedOEHs0dIAVPeJh8qVbQ50KY8oJkBjINYYE2+MOQvMBDqm62OA8/enLIbjrDGsfjONMWesm3DFWu+nlHcTIV/vHgzd0pVtdR/gYaY72hctYlPoA5jvvrc3n3Kv+PiL930ve8zjbrrmKcWkIrDb6XWS1ebsVeBhEUkC5nFxGPzMzAuAiESISKSIRCYnJ+dEbqVcLySEkLUz4aWXQITNhHHDsd+48x4//nnoWR3WPq+Ijb1YTII9b1enpxSTzOgKfGaMCQQ6AF+ISJbyG2MmGmPCjTHhZcqUcUlIpVzCzw9GjIDff2dP6QYEcIqfuYN6M15gXo2n4a+/7E6oXMzEOBWTsAI2p/kvTykme4BKTq8DrTZnvbAGjzTGrAT8gdKZnFep3KFVK9rFfMTGO4dyM7+zn3Lcvu9T+jeN5OQrIyE11e6EykXORifyOBPoygxK1PGcYVTO85RisgYIEZFgEcmP44D6nHR9dgH/AxCR2jiKSbLVr4uIFBCRYCAE0K9pKvcqXpxKP37Eos/38E6BofhxlvGmH+Gv38Xm8O6QmGh3QuUCBRJ38B4DmcFDHncmF3hIMTHGpABPAL/gGN9rljFmi4gMF5G7rG7PAb1FJAr4CuhuHLbg2GLZCiwA+htj9OuZyt1E8Hn0YQZt68Xq+o9Ti23spAr5N6yG+vXhyy/hKuPuKS/jwVe/QyYGesytdKBHlWukpHBy+CjWjZjPTWlLAcepj8kde1N26ttQwrPGcFLX4MwZovybcJIAwmQbRU/9AwXsOW6SnYEelVKeLF8+Cg4fzE0r3rnwjXUSvan549t8XX0ILF5sc0CVbQkJjOQFmrOS70v1sq2QXIkWE6VyiyZNYP16eOwxFnMLRyhBl0PjefR/SRwd8DKcOWN3QnWtYmOJoxoA1YM8cy++FhOlcpPChWHSJL76zp+PCw0kgJN8waPU/7AXy8L6wJYtdidU18L5GpPQ/DaHyZgWE6VyIenciT4xz7H+pgE0IpKdBNEqbjIv1p/H2fc+1PG9vMyhzXs5TEkK8y9l65S1O06GtJgolVtddx01l05ixei/eMn3bQTD/NRbMQMHQvv2Or6XF4ndfBpwDPAoIZ53JhdoMVEqdxMh/9P9GLHxTpZW78V0HqIAZ+HXXzlV5wbMN7PtTqgyITbBMXatJ44WfJ4WE6XygtBQbtwykbAX7gQRDND9yGg63F+Ivx94Co4dszuhupxz54g74BjjtjqxULWqzYEypteZKJXX/PEHux98gQZ7f+YQpSjFASaVGULnbx+GFi3sTqfSi4sjrXoIe6lAvvJlKL9vva1x9DoTpZRDq1ZU2voLm+5+lVtZyEFKc3fyBHq2jOXfZ4fB2bN2J1TOYmPxwRDIHsrXLGZ3msvSYqJUXlSsGBW+/ZAFMw4zNuB5/DnFVHpQf3Q3loc9rqcQexIPH0blPC0mSuVhPl0f4MnoAaxt0p+GrCOBqsyKbQiNGsEHH+gpxB7g2JbdhLOGHkzRYqKU8mCBgYSu+JRVo/7kXd/BjGSw42r5p58m5dbbICnJ7oR5WtzmU6wlnEjCoVo1u+NclhYTpRT4+JD/uScZGPUIBRvUBOAYRai/+H3G1viQtBkzbQ6Yd8XECuDZpwWDFhOllLOwMFi1Cl54ge+4h62E8dSpt2n3UCmSOvaHw4ftTpi3pKQQ/Y/joHsNoiEkxOZAl6fFRCl1qQIFYORIui/tyfdlIihNMr9xK3XnvMFX1YbCb7/ZnTDv2LmTmDTHdSUhxZIdY695KC0mSqmMtWhBp9hRbO76JncwlyOU4MHD4+h6azKHI16AkyftTpj7RUcTTQ0AagR59inbWkyUUpdXtCjlZoxmzrcpTCz8DIU4zky6smzSNmjYEFavtjth7hYTc7GY1PHM0YLP02KilLoqubszvWNeYEPrZ3mb57mLuRAdDc2bk/bSUL3Q0UVStsfyGJ/yADMpV6+c3XGuSIuJUipzypen+qIJPP9pzQv77iPTGlL/rQdYU6cHbNxoc8DcJ1/cDt5mMDPpitSsYXecK9JiopTKPBHo1Qs2bYKbb+ZNXmIzdWkW8zmvNvyRcyPegVTPvBOgV4qOvvi8hhYTpVRuExQEixYx/Z29POM7llTy8Vray9w49Ga23/AIxMXZndD7nT7NusSSLOdGjkpxjx0t+DyPKSYi0l5EdohIrIgMzmD6aBHZYD2iReSI07RUp2lz3BpcqbzKx4eAQU/w/ua2LKrVj0rsYg2Nabh+Mh+GfkzaJxMhj45KniPi43mb52nBcuaU6uE4ZduDeUQxERFfYBxwGxAKdBWRUOc+xphnjDENjDENgA+B75wmnzo/zRhzl7tyK6WAWrW4ZdNYNr00k0flC04TwMtnh/JP32Fw553w9992J/RO0dHE4LhIsUbVFJvDXJ1HFBOgMRBrjIk3xpwFZgIdr9C/K/CVW5Ippa4uXz6KjXiez9eE8l3FJ5lEb67jb/j5Z0xYHb2j4zUw0RdPCw6pF2BzmqvzlGJSEdjt9DrJavsPEakCBAOLnZr9RSRSRFaJSKfLLUREIqx+kcnJyTkQWyl1iUaN6BzzDvc9HXihafShR7nvfki+rx8cOWJfNi+zb8M/nKAwpThAyXqBV5/BZp5STLKiCzDbGON8ykgV685fDwJjRCTDoTWNMRONMeHGmPAyZcq4I6tSeU9AAIweDYsWcaJiDUYymG+5lzqzhzGn2jPw6692J/QKMVsc1+54+phc53lKMdkDVHJ6HWi1ZaQL6XZxGWP2WP/GA0uAhjkfUSmVJbfcQqHNq/mr80hasYT9lKPjoan0aruLYxED4cQJuxN6tOidjiveQ4jx+NOCwXOKyRogRESCRSQ/joLxn7OyRKQWUAJY6dRWQkQKWM9LAzcCW92SWil1ZcWLE/Td+yz+5hDvFxpKAU4zhV7Um/QES2pEwMqVV3+PvOjff4k/WgqAGj5xULmyzYGuziOKiTEmBXgC+AXYBswyxmwRkeEi4nx2VhdgpjGXnG9YG4gUkSjgd2CkMUaLiVIexOfeu3km7knWtR5IIyLZSRBD9/bF3HgTvPSSDseSXkwMb/ISe7mOiKq/Qb58die6KjF59Dzw8PBwExkZaXcMpfIWYzg3eRoj+++my9nPCcFxf/O0uvXx+XIa1Ktnc0AP8fXX0KWL4/ldd8GPP9qbx4mIrLWOUV/CI7ZMlFJ5hAh+j3Xj5ehHCLnZcYaSATpveo1XGs7l7OtvQ4rnX1Phcs7DqHjBwXfQYqKUskOVKrBoEXzwAX/lb8Fc7uT1tCE0feVWNjfqdukf0zwocf1h6rOBvoz3ioPvoMVEKWUXHx8YMIAmGyexpFZfgolnPdfTaOMU3gn7nNQPPoK0NLtT2mLH1lQ2Up/t1NItE6WUypSaNWm5aRxRL39LhM8kzlKAF1JG0PLphsQ07wY7d9qd0O2id/kD3nNaMGgxUUp5gnz5KDJ8EBPW3sD8oL5UYA8ruJFpq2tA3boweXLeGTTy4EFiTjkGAKnhlwgVKtibJ5O0mCilPEeDBrTfPobNT0/mRd5iKG/Av//CY4+R0uEu2LvX7oSu53Tf95CKJx33kPECWkyUUp6lQAFKjH6FN1e2pkCNIAAOUpKwBaOYHDISM31G7t5KiYm5OFpwTe8oJKDFRCnlqZo2hfXr4amn+JKHiaYmj50cy+0PF2fvHRGQSwdrPbM1jkSC8CGVqvWL2B0n07SYKKU8V8GCMGYMAxZ1YnrpAZTgEPPpQNi8d/iy2jDMt99d/T28zNkdCQxmJI8zgQKhGY5Z65G0mCilPJ7c0poH40ew+aGRdOBnjlCCR/4dz933Cv/c0w8OH7Y7Yo4pkriJEQxlPP295rRg0GKilPIWRYpQ4ct3+GmeL5OLP0cRjvEDndn0XTSEhcG8eXYnzD5jICbm4msvOS0YtJgopbyM3NaenvFD2Xz3MMbRjzYsgn374PbbOd29Dxw9anfEa7dvH8tPNOAPWnKseGUoVcruRJmmxUQp5X1KlKDyt6Pp90M7KFsWgD9oSdXPX+HH6s/Cb7/ZHPAaRUfzMq9zM3+wsmxHrzktGMDzxzV2o3PnzpGUlMTp06ftjuIR/P39CQwMxM/Pz+4oSmWsY0e48Ubo35+ps25jHxXodGAyj9w6jQ96PEeJsa9B4cJ2p8y86Ghi6ABASG3v+vPsXWldLCkpiSJFihAUFIR40TcCVzDGcPDgQZKSkggODrY7jlKXV7o0fP01UzrP4vpeLzL45Mt8waP8NnUvk34ewO1fPwo332x3ykw5sSWRPQTix1mqNChhd5ws0d1cTk6fPk2pUqXyfCEBEBFKlSqlW2nKa/h0uZ8B8U8T1WYgzfmTfVTgjv1T6NE6gaOPP+8VtwmOjXJkrE4svrW850wu0GLyH1pILtJ1obxOuXKELBzH0mk7eS/AcZvgn7mdsxOnQv36sGyZ3QmvKDrW8SfZmwZ4PE+LiVIqdxHB95EHeTa2HxtaPc1XdKUMByAujnMt/8fRfi/CyZN2p/yv1FSi9zmueK9BtFddYwJaTDyOr68vDRo0oE6dOtx3332ctD7059vPP0aOHAnAzTffTM2aNalfvz433ngjO3bsAKB58+YAJCYmMmPGDHt+GKXsVKECtX7/mP999igUKwbAWwymzsf9WBjSH/780+aA6ezcyc40x90naxT9B4p4z1AqoMXE4wQEBLBhwwY2b95M/vz5+eSTTy5pP/8YPHjwhXmmT59OVFQU3bp1Y9CgQQCsWLEC0GKi8jgR6NYNtmwhtf3tLKQtSVSi3d6p9L5pG8f6e9BWSkwME3icfyjL/WFb7E6TZVpMLkfEdY9MatGiBbGxsZnu37Jlywv9C1unQw4ePJhly5bRoEEDRo8enbV1oFRuUbEivvPmsmRiDG8VeJX8nOFTHqPO+L6es5USHY0AZUmmWGhFu9NkmccUExFpLyI7RCRWRAZnMH20iGywHtEicsRpWjcRibEe3dwa3EVSUlKYP38+devWBeDUqVOX7Ob6+uuv/zPP3LlzL/Q/b+TIkbRo0YINGzbwzDPPuCW7Uh5JhHy9ezA4phfrbhxAOGvYTeULWymnBzxv71aKlw6jcp5HXGciIr7AOOBWIAlYIyJzjDFbz/cxxjzj1P9JoKH1vCQwDAgHDLDWmtcrR347XzTAsWXSq1cv4OJurow89NBDBAQEEBQUxIcffuimpEp5qUqVCFv2CSsnTWXUgJ8ZduZFEqlCgQ97w4IfYOpUx4WQbrZ2TRrd2ER7FjAqxHtGCz7PI4oJ0BiINcbEA4jITKAjsPUy/bviKCAA7YBfjTGHrHl/BdoDX2UrkU0337lS0bic6dOnEx4e7ppASuVGIuSL6Mng23ZzV9cnKfznAgQgJoY9Nz1A4X6PUuzdoY4h8N1kW5wfW6hDGFu8csvEU3ZzVQR2O71Ostr+Q0SqAMHA4qzOmxcVKVKEf//91+4YSnmmSpUIXTaByp8Og6JFSUN4iC+pM74vC6o/4b7rUnbtYnWyY2ukJtFQzfu2TDylmGRFF2C2MSY1qzOKSISIRIpIZLKX3aUt/TET57O5rqRevXr4+vpSv359PQCvVEZEoFcv2LyZQ63v5RQBJFGJ2/ZNoVfLGI70Gezyq+fPTP6SGXQF4O6me8Hf36XLcwVP2c21B6jk9DrQastIF6B/unlvTjfvkoxmNMZMBCYChIeHe+RNpI8fP55he2pqxrVzyZIlV3wfPz8/Fi9enGEfpZSTSpUovehr/vz0M95/8mdeOfMSU+jJLxOSmPjjADrMfBRatcr55RrD3E/2cIhS1GcDDZ5ywTLcwFO2TNYAISISLCL5cRSMOek7iUgtoASw0qn5F6CtiJQQkRJAW6tNKaWyxjrj6/nYCDa0fIqmrGQPgdz+92Qev3k79O8Pl/nCd82WLWPqfsdIwT38ZzpGQvZCHlFMjDEpwBM4isA2YJYxZouIDBeRu5y6dgFmGnPx6Lh14P11HAVpDTD8/MF4pZS6JoGB1FryCcunxDDKfyj+nCKIRBg/HurUydH7pfwz/lsW0B4/zvLQAykQEJBj7+1OYmw6a8lu4eHhJjIy8pK2bdu2Ubt2bZsSeSZdJyrP27OH2EdeI+j3KeTDsbt5OTdS+5EbKPXhqxeGarkmx49jypVn/ckarKURvVf3hsaNcya3i4jIWmPMf04f9YgtE6WU8lgVK1J90QTyffEZlCjB35SjIz8S+sVgvq06CObPv/b3nj0bOXmC61lP79p/wg035Fhsd9NiopRSVyMCDz8MW7dytt1d1GUT+ynHvYcmcl+H4+x/4Ek4nPXrpFOmTLv4okcPr7pNb3paTJRSKrPKl6fy/Aks/mo/4wo9TyGOM5v7CJ01jBlVh2J+/M95Q5cXF8cTy+6nBUtZ7dPMUay8mBYTD1PY6X7V8+bNo0aNGuzcudPGREqpS4jg0+V++iUMYvMdL9KGXzlIaR46Mo5nO8XBgw/CgQNXfZtTn07nK7qynBYUvqkBXHed67O7kBYTD7Vo0SIGDBjA/PnzqVKlit1xlFLplSlD0NwPWfjdCT4t+gwlOMT9zIKvvoKwMJg9+/LzpqXx/aQDHKMYN/AXYQP+577cLqLF5AquNIr8xIkX+02cmCMjzl+wdOlSevfuzU8//UQ1a1iF7t27M2DAAJo3b07VqlWZbX1QjTEMGjSIOnXqULdu3QujCffv3585cxyb3J07d6Znz54ATJkyhSFDhpCYmEjt2rXp3bs3YWFhtG3bllOnTmVjbSmVN0nnTvRKeJldXQfTjFWOxv37GXvfUnbe1gf++ee/My1ezNSDdwLQo+AsuOMONyZ2DS0mHubMmTN06tSJH374gVq1al0ybd++fSxfvpyffvrpwnAq3333HRs2bCAqKorffvuNQYMGsW/fPlq0aMEya1yhPXv2sHWrY8zMZcuW0bJlSwBiYmLo378/W7ZsoXjx4nz77bdu/EmVykVKlqTwjInw009QsSILuZWnGEudBe8yvuoo0qZ9ecngsbvGzWUR/6MAp+nykC8UKGBj+JyhxeQKjLn8IyLiYr+IiCv3zQo/Pz+aN2/O5MmT/zOtU6dO+Pj4EBoayj/Wt53ly5fTtWtXfH19KVeuHK1atWLNmjUXisnWrVsJDQ2lXLly7Nu3j5UrV164pW9wcPCF4e4bNWpEYmLitawmpdR5t98OW7ZQ/8E63MNsjlOE/iffpXW3SsS0joDdu+HoUab9VAKDD534gRJ9u9idOkdoMfEwPj4+zJo1i7/++os333zzkmkFnL69XO1i04oVK3LkyBEWLFhAy5YtadGiBbNmzaJw4cIUse4t7fx+vr6+pKSk5OBPolQeVawY5aa/z+yFxZhdug/l+JultKLeH2MZFfIJKT16MyvlbgB6BP8B1hc6b6fFxAMVLFiQn3/+menTp2e4heKsRYsWfP3116SmppKcnMzSpUtpbF1B27RpU8aMGXOhmIwaNYoWLVq440dQSt16K/ckjGJr7zE8yuecJoBBZ0Yw8vsaLKMFU+lOmydqefW1Jc48ZdRglU7JkiUvbFWUKVPmsv06d+7MypUrqV+/PiLCO++8Q/ny5QFHoVm4cCHVq1enSpUqHDp0SIuJUu5UuDAlJ47k80eX06VLb17b04sn+IhiHKN7vunwyLt2J8wxOjaXEx2H6r90nSiVQ06dwrz6GjLqXUhLg+7dHbcI9jKXG5tLt0yUUsodAgKQt0dCzx6weTN06GB3ohylxUQppdypZk3HI5fRA/Dp5NXdfhnRdaGUyiwtJk78/f05ePCg/hHFUUgOHjyIvxfei1op5X66m8tJYGAgSUlJJCcn2x3FI/j7+xMYGGh3DKWUF9Bi4sTPz4/g4GC7YyillNfR3VxKKaWyTYuJUkqpbNNiopRSKtvy7BXwIpIMXOstDEsDV7+VmvtprqzRXFmjubImt+aqYoz5zxhPebaYZIeIRGY0nIDdNFfWaK6s0VxZk9dy6W4upZRS2abFRCmlVLZpMbk2E6/exRaaK2s0V9ZorqzJU7n0mIlSSqls0y0TpZRS2abFRCmlVLZpMXEiIu1FZIeIxIrI4AymFxCRr63pq0UkyGnai1b7DhFp5+Zcz4rIVhHZKCKLRKSK07RUEdlgPebkZK5MZusuIslOGR5zmtZNRGKsRzc35xrtlClaRI44TXPJOhORKSKyX0Q2X2a6iMhYK/NGEbneaZor19XVcj1k5dkkIitEpL7TtESrfYOIRGY0vwtz3SwiR51+V684Tbvi79/FuQY5ZdpsfZ5KWtNcub4qicjv1t+CLSLyVAZ9XPcZM8bow3HcyBeIA6oC+YEoIDRdn37AJ9bzLsDX1vNQq38BINh6H1835moNFLSe9z2fy3p93OZ11h34KIN5SwLx1r8lrOcl3JUrXf8ngSmuXmdAS+B6YPNlpncA5gMCNAVWu3pdZTJX8/PLA247n8t6nQiUtml93Qz8lN3ff07nStf3TmCxm9bXdcD11vMiQHQG/x9d9hnTLZOLGgOxxph4Y8xZYCbQMV2fjsDn1vPZwP9ERKz2mcaYM8aYBCDWej+35DLG/G6MOWm9XAW4a9z4zKyzy2kH/GqMOWSMOQz8CrS3KVdX4KscWvZlGWOWAoeu0KUjMM04rAKKi8h1uHZdXTWXMWaFtVxw4+crE+vrcrLzuczpXG75bAEYY/YZY9ZZz/8FtgEV03Vz2WdMi8lFFYHdTq+T+O8v4kIfY0wKcBQolcl5XZnLWS8c3zzO8xeRSBFZJSKdcihTVrPdY21SzxaRSlmc15W5sHYJBgOLnZpduc6u5HK5Xbmusir958sAC0VkrYhE2JCnmYhEich8EQmz2jxifYlIQRx/kL91anbL+hLHLviGwOp0k1z2GdP7meQiIvIwEA60cmquYozZIyJVgcUisskYE+fGWHOBr4wxZ0TkcRxbdre4cflX0wWYbYxJdWqze515JBFpjaOY3OTUfJO1rsoCv4rIduubuzusw/G7Oi4iHYAfgBA3LTsz7gT+NMY4b8W4fH2JSGEcBexpY8yxnHzvK9Etk4v2AJWcXgdabRn2EZF8QDHgYCbndWUuRKQNMAS4yxhz5ny7MWaP9W88sATHt5WcctVsxpiDTnk+BRpldl5X5nLShXS7IVy8zq7kcrldua4yRUTq4fj9dTTGHDzf7rSu9gPfk3O7d6/KGHPMGHPcej4P8BOR0njA+rJc6bPlkvUlIn44Csl0Y8x3GXRx3WfMFQeCvPGBYystHscuj/MH7cLS9enPpQfgZ1nPw7j0AHw8OXcAPjO5GuI44BiSrr0EUMB6XhqIIWcPRGYm23VOzzsDq6znJYEEK2MJ63lJd+Wy+tXCcUBU3LjOgrj8AeXbufTg6F+uXleZzFUZx3HA5unaCwFFnJ6vANq7MVf58787HH+Ud1nrLlO/f1flsqYXw3FcpZC71pf1s08Dxlyhj8s+Yzm2cnPDA8eZDtE4/jAPsdqG4/i2D+APfGP9x/oLqOo07xBrvh3AbW7O9RvwD7DBesyx2psDm6z/TJuAXjass7eALVaG34FaTvP2tNZlLNDDnbms168CI9PN57J1huNb6j7gHI590r2APkAfa7oA46zMm4BwN62rq+X6FDjs9PmKtNqrWuspyvodD3FzriecPlurcCp2Gf3+3ZXL6tMdx0k5zvO5en3dhOOYzEan31UHd33GdDgVpZRS2abHTJRSSmWbFhOllFLZpsVEKaVUtmkxUUoplW1aTJRSSmWbFhOllFLZpsVEKaVUtmkxUcoDiEiIda+L6tZrP+ueF5WuNq9SnkCLiVIewBgTA0zEMRQ4OK7unmOM2X35uZTyHDpqsFKeYzPQxrorXy+gic15lMo03TJRynNEAzVxjBk2yhhzwt44SmWejs2llIewhg/fi2MQvubGmDSbIymVabplopSHMMacA44Bg7WQKG+jxUQpz+IH/GF3CKWySouJUh7Cum/3TqP7npUX0mMmSimlsk23TJRSSmWbFhOllFLZpsVEKaVUtmkxUUoplW1aTJRSSmWbFhOllFLZpsVEKaVUtv0fyw1QVDDSP80AAAAASUVORK5CYII=\n", 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", 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\n", "text/plain": [ - "
" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -1060,7 +1053,6 @@ }, { "cell_type": "markdown", - "id": "e43af9f8-1de8-4e10-ba79-b8c4508fbef3", "metadata": {}, "source": [ "... much better! one can actually even fit; defining $\\rho(\\gamma)=\\max\\{|1-\\gamma L|,|1-\\gamma\\mu|\\}$, we find:\n", @@ -1074,20 +1066,21 @@ }, { "cell_type": "code", - "execution_count": 144, - "id": "23948925-8a27-4b84-86b2-0c71f1f62a7a", + "execution_count": 22, "metadata": { "tags": [] }, "outputs": [ { "data": { - "image/png": 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qsGxe8ZA4bFZ2A8D9/2Y1GySWJNewEzWXzVMzUBcBN7oBUlcg4BgAWYv73WLPDhFRY5E6iktwqy7DFQRx2bux+UFlV4A2GwD7/xMngZZdq5w3VJIs/hVdrVqWzXvEAe6vNnoz6QGTtQgo+x0I3G21vTm6rL+FRERNQSIRd3OWexl/2ryG1BZQdhIPQBzeUn1av3sKheIjNwoOiENfch9AIq08f/tpQGJbZbUYl81TFYXHgJz3gNarAGVHc9emWTDYISJqbDUtRVeEAkFJVR6wev/7iru1l533NZC38/597MVdqzVBjeor6O+CC2iXzVedG8Rl8w+e7FWAbS/gzhTAri/gNtvcNWo2DHaIiJqTxAZQPiQeVVXcq2Z+kM6y+XapAATD84VHYRjoAHrL5g2eNq+zbN5tDmA/oJEbSxaj8DCQtQCABIAU8I1/oAJdBjtERJZC5gbY9RYPXYIaKL8lBjU27cShK0UIgBGVefJ/AP54zLT7CSXiYwJKLwIOwwG7foYfgIIayP53ZQ+SIkScx0QthzofyHj+/gsBQIX4OuDkAxPwMNghIrJ0Eilg4yce1VF0BFq/I05s1vT2lN+q+z3+fAHInGG4QaLUBbgbp59X7qMzFBYq7izNZfOWK/MVoOy6fprzMw9MoANw6TmXnhOR9arzsnkZ0Ha3/qqx0lSg/Ca0y+brxMiyeafRgNyzkRtGdVZwALj5qH6aXX/A/7D+5PYWiEvPiYiolmXzWZXBT0UW4DTC8Hp1kTiElf1WHW9oZNm8XT/jwY66QFyZpggVn2tGja8iT9wFXJfEDvD+pMUHOqZisENE9KCRSMQARO5puGxel9ROfAK2Q5QYFJX9DtN6egD8MVpc3lx1g8TSG8DN+xOiZa2rnNcMi7XnsvmGyJp//3luOlqvABTB5qmPGXEYi8NYRER1oy4Cyq5WWTJ/ubJ3qCqpK+DyXGX+smuoXDGmAFBayw0lgE1A5dwgvWXzAQ9c74RJCvYDN6P10+wGAv4HrebfjcNYRETU+KR2gLKzeFRlbNm8zA3wWl2ZRygTJ8qWpgH33gMKD9ZyQ0F83EbZDRg8bT4kx/jwl6AGIGlxjz5oVBW5QMYU/TSJA+D9sdUEOqZisENERA1X3bJ5XRKbyp6Z/L3i3i9G9waqjQLIijO+QaLqS+DPfxp5tliH+8vmHerbwpYj81/3J5fr8FwFKNqZpz4WgMNYHMYiIjIPTU9Pyf0VYGU6vULlt6u/TuoOyNuIzyATSsQ0iUJcNi+ogbJL1V8rb2v8IavWsmw+fy/wx3D9NPshgN9+q+vV4TAWERFZPt2enqoq8sRgRvdxGpqvTk8A3h+JzyAru6n/6I28XTXfs/yWeBT+VOWETFy1FljTQ1otXMVfwJ0X9NOkjoD3FqsLdEzFYIeIiCyPzAmQVbNsXrg/sVkiAxSB4oH7k3GLEoGKO/W4YQVQ/ieQ/73xnp6/tgIFPxr2CFnSsvnCw4YbSXquFidzP+AY7BARUcshkYjP9KpO22/u9/Sk6k+WLk9Hrcvmy28Df4y8/6LKBolFJ4HiE4bXGCybN+PT5hUdxBVw6hzxtUMU4DKl5mseEAx2iIjIelTt6dHQWzZfJRDSPG3ePQ5oNdlwWX3+9+JGicZUZAFFWUDR8SondJbN2z8CuL/SuO3Ua1s+cHepuMJN3kZ8LbUD2nz4YK9K08Fgh4iIrF9dls3LvAAbX/FweEQ/z+XWlUFRnegsmxcEwPVl4z09ed8BFTmVD1qVta49QCm9KvY6AUDe10DmXKAiG/CIA9zmA7kfAbY9xRVqBIDBDhERPeg0y+arI6gBj6X6vUJl11HnZfOFCUCavf4GiZqHp2avAooTK/NKWxkfFlOEAkI5cPcNIGcd4PkukP9fca8ix8cBz/cARZBYhuuMev5DWC8uPefScyIiMpVQCpReqxzqqmnZvFssoGivP3RWdqVyonVdSWwBobjytTwIaLMecBxe/TVWjEvPiYiImpJEIT7zS9nR8Jzesvk0wHmc4fJ6oQIoSQFuhNf9nrqBDgA4/f2BDXRMxWCHiIioMVW3bF6XRAbIPQDHJ+rX0yNRAjKXBlf1QcFgh4iIyBzkbQDfePF7oQIoS9cf6tLMD6q6bN5hOOD1H3FojOqEwQ4REZG5SWTiBGNFEKpfNn8NkHsDthFcUm4iBjtERESWrKZl81QnFvewjA0bNiAoKAi2trbo2bMnjh49WmP+7du3o2vXrrC3t4e3tzeef/55ZGdnN1NtiYiIyNJZVLCzc+dOzJ49GwsXLsT58+cxYMAADBs2DOnp6UbzHzt2DBMnTsTkyZNx8eJFfP311/j5558xZQq3xyYiIiKRRQU7q1evxuTJkzFlyhSEhYVhzZo18PPzw8aNG43mP3nyJAIDAzFr1iwEBQWhf//+mDp1Ks6cOVPtPUpKSqBSqfQOIiIisl4WE+yUlpbi7NmziIqK0kuPiopCYmKi0Wv69euHP/74A3v27IEgCPjzzz+xa9cujBgxotr7LF++HC4uLtrDz8+vUdtBRERElsVigp27d++ioqICXl5eeuleXl64c+eO0Wv69euH7du3Y9y4cVAoFGjTpg1atWqFdevWVXuf2NhY5Obmao+bN282ajuIiIjIslhMsKMhqbKcThAEgzSN5ORkzJo1C4sXL8bZs2fx448/4vr165g2bVq15SuVSjg7O+sdREREZL0sZum5h4cHZDKZQS9OZmamQW+PxvLlyxEZGYn58+cDALp06QIHBwcMGDAAb731Fry9vZu83kRERGTZLKZnR6FQoGfPnkhISNBLT0hIQL9+/YxeU1hYCKlUvwkymQyA2CNEREREZDHBDgDMnTsXH330ET7++GOkpKRgzpw5SE9P1w5LxcbGYuLEidr8I0eOxLfffouNGzfi2rVrOH78OGbNmoVevXrBx8fHXM0gIiIiC2Ixw1gAMG7cOGRnZ2PJkiXIyMhA586dsWfPHgQEBAAAMjIy9Pbcee6555CXl4f169fjX//6F1q1aoVHHnkEK1asMFcTiIiIyMJIhAd8vEelUsHFxQW5ubmcrExERNRCmPL5bVHDWERERESNjcEOERERWTUGO0RERGTVGOwQERGRVWOwQ0RERFaNwQ4RERFZNQY7REREZNUY7BAREZFVY7BDREREVo3BDhEREVk1BjtERERk1RjsEBERkVVjsENERERWjcEOERERWTUGO0RERGTVGOwQERGRVWOwQ0RERFZNbu4KEBGR5aqoqEBZWZm5q0EPKIVCAam04f0yDHaIiMiAIAi4c+cO/vrrL3NXhR5gUqkUQUFBUCgUDSqHwQ4RERnQBDqenp6wt7eHRCIxd5XoAaNWq3H79m1kZGTA39+/Qb+DDHaIiEhPRUWFNtBxd3c3d3XoAda6dWvcvn0b5eXlsLGxqXc5nKBMRER6NHN07O3tzVwTetBphq8qKioaVA6DHSIiMopDV2RujfU7yGCHiIiIrBqDHSIiIrJqDHaIiIjIqjHYISIiq7Jo0SIolUo8/fTTDS4rOzsbnp6euHHjRsMrZkaDBg3C7NmzG6WsMWPGYPXq1Y1SVnORCIIgmLsS5qRSqeDi4oLc3Fw4OzubuzpERGZXXFyM69evIygoCLa2tuaujslUKhU+++wzzJgxA5cvX0ZwcHC9y5o3bx5ycnKwZcuWRqxh87t37x5sbGzg5OTU4LIuXLiAwYMH4/r1603+uVnT76Ipn9/s2SEiIqvi7OyMmJgYSKVS/Pbbb/Uup6ioCFu2bMGUKVMasXbNq7S0FADg5ubWKIEOAHTp0gWBgYHYvn17o5TXHBjsEBGR1SkvL4e9vT2SkpLqXcbevXshl8vRt29fvfRBgwZh1qxZWLBgAdzc3NCmTRu88cYbenkCAwOxZs0avbRu3bpp8w0aNAgzZ87E7Nmz4erqCi8vL2zevBkFBQV4/vnn4eTkhPbt22Pv3r16ZQiCgJUrV6Jdu3aws7ND165dsWvXLr26zZgxA3PnzoWHhweGDh2qTdcdxlKr1VixYgWCg4OhVCrh7++PZcuWac/v2rUL4eHhsLOzg7u7Ox599FEUFBRoz48aNQo7duww9Z/UbBjsEBGR1Vm0aBHy8/MbFOwcOXIEERERRs9t27YNDg4OOHXqFFauXIklS5YgISHBpPK3bdsGDw8PnD59GjNnzsT06dMxduxY9OvXD+fOnUN0dDQmTJiAwsJCvXZ98skn2LhxIy5evIg5c+bg2WefxeHDh/XKlcvlOH78ODZt2mT03rGxsVixYgXi4uKQnJyML774Al5eXgCAjIwMjB8/HjExMUhJScGhQ4cwevRo6M566dWrF06fPo2SkhKT2mwufFwEERHVrrAQuHSp+e/bsSNg4k7OZ8+exQcffIARI0YYBDtPPvkkDh06hCFDhuj1iBhz48YN+Pj4GD3XpUsXvP766wCAkJAQrF+/HgcOHND2pNRF165dsWjRIgBi8PH222/Dw8MDL7zwAgBg8eLF2LhxIy5cuIA+ffqgoKAAq1evxsGDB7W9Te3atcOxY8ewadMmDBw4EAAQHByMlStXVnvfvLw8rF27FuvXr8ekSZMAAO3bt0f//v0BiMFOeXk5Ro8ejYCAAABAeHi4Xhlt27ZFSUkJ7ty5o81jyRjsEBFR7S5dAnr2bP77nj0L9OhR5+xqtRpTp07FjBkz0Lt3bzzzzDMoLS3VPnZg1qxZiImJwbZt22otq6ioqNoJ2l26dNF77e3tjczMzDrXs2oZMpkM7u7uekGFpqdFU25ycjKKi4sNAqrS0lJ0795d+7q63iiNlJQUlJSUYMiQIUbPd+3aFUOGDEF4eDiio6MRFRWFMWPGwNXVVZvHzs4OAPR6nSwZgx0iIqpdx45i4GGO+5pg3bp1yMrKwpIlS5Ceno7y8nKkpqZqg4jBgwfj0KFDdSrLw8MDOTk5Rs9VfSilRCKBWq3WvpZKpai62FnzzLGaytBN0zwqQVOu5usPP/yAtm3b6l2rVCq13zs4OFTfKFQGKtWRyWRISEhAYmIi9u/fj3Xr1mHhwoU4deoUgoKCAIiruwDxQZ0tAYMdIiKqnb29ST0s5nDr1i3ExcVhx44dcHBwQEhICJRKJZKSkgyGYeqie/fu+Pzzz+tVl9atWyMjI0P7WqVS4fr16/UqS6NTp05QKpVIT0/XDlnVR0hICOzs7HDgwIFqV5pJJBJERkYiMjISixcvRkBAAOLj4zF37lwAQFJSEnx9feHh4VHvejQnBjtERGQVZs2ahWHDhmHEiBEAALlcjrCwsHpPUo6OjkZsbCxycnL0hnDq4pFHHsHWrVsxcuRIuLq6Ii4uDjKZrF710HBycsK8efMwZ84cqNVq9O/fHyqVComJiXB0dNTOv6mNra0tXnnlFSxYsAAKhQKRkZHIysrCxYsXMXnyZJw6dQoHDhxAVFQUPD09cerUKWRlZSEsLExbxtGjRxEVFdWg9jQnBjtERNTiff/99zh48CBSUlL00sPDw+sd7ISHhyMiIgJfffUVpk6datK1sbGxuHbtGh577DG4uLhg6dKlDe7ZAYClS5fC09MTy5cvx7Vr19CqVSv06NEDr732mknlxMXFQS6XY/Hixbh9+za8vb0xbdo0AOI+RUeOHMGaNWugUqkQEBCAd999F8OGDQMgbvQXHx+Pffv2Nbg9zYU7KHMHZSIiPS19B+XaHDp0COvXr691NRYA7NmzB/PmzUNSUhKkUu7WAgDvv/8+du/ejf379zf5vRprB2X27BAR0QMjOjoa586dQ0FBAXx9fREfH4+HH3642vzDhw/H5cuXcevWLfj5+TVjTS2XjY0N1q1bZ+5qmIQ9O+zZISLSY+09O9Ry8NlYRERERHXAYIeIiIisGoMdIiIismoMdoiIiMiqMdghIiIiq8Zgh4iIiKwagx0iIiKyagx2iIiIyKox2CEiIiKrxmCHiIiIrBqDHSIisiqLFi2CUqnE008/3eCysrOz4enpiRs3bjS8YmY0aNAgzJ49u1HKGjNmDFavXt0oZTUXPhuLz8YiItLT0p+NpVKp8Nlnn2HGjBm4fPkygoOD613WvHnzkJOTgy1btjRiDZvfvXv3YGNjAycnpwaXdeHCBQwePBjXr19v8s9NPhuLiIjICGdnZ8TExEAqleK3336rdzlFRUXYsmULpkyZ0oi1a16lpaUAADc3t0YJdACgS5cuCAwMxPbt2xulvObAYIeIiKxOeXk57O3tkZSUVO8y9u7dC7lcjr59++qlDxo0CLNmzcKCBQvg5uaGNm3a4I033tDLExgYiDVr1uildevWTZtv0KBBmDlzJmbPng1XV1d4eXlh8+bNKCgowPPPPw8nJye0b98ee/fu1StDEASsXLkS7dq1g52dHbp27Ypdu3bp1W3GjBmYO3cuPDw8MHToUG267jCWWq3GihUrEBwcDKVSCX9/fyxbtkx7fteuXQgPD4ednR3c3d3x6KOPoqCgQHt+1KhR2LFjh6n/pGbDYIeIiKzOokWLkJ+f36Bg58iRI4iIiDB6btu2bXBwcMCpU6ewcuVKLFmyBAkJCSaVv23bNnh4eOD06dOYOXMmpk+fjrFjx6Jfv344d+4coqOjMWHCBBQWFuq165NPPsHGjRtx8eJFzJkzB88++ywOHz6sV65cLsfx48exadMmo/eOjY3FihUrEBcXh+TkZHzxxRfw8vICAGRkZGD8+PGIiYlBSkoKDh06hNGjR0N31kuvXr1w+vRplJSUmNRmc5GbuwJERGT5CguBS5ea/74dOwL29qZdc/bsWXzwwQcYMWKEXrBz8+ZNTJgwAZmZmZDL5YiLi8PYsWOrLefGjRvw8fExeq5Lly54/fXXAQAhISFYv349Dhw4oO1JqYuuXbti0aJFAMTg4+2334aHhwdeeOEFAMDixYuxceNGXLhwAX369EFBQQFWr16NgwcPanub2rVrh2PHjmHTpk0YOHAgACA4OBgrV66s9r55eXlYu3Yt1q9fj0mTJgEA2rdvj/79+wMQg53y8nKMHj0aAQEBAIDw8HC9Mtq2bYuSkhLcuXNHm8eSWVyws2HDBqxatQoZGRl46KGHsGbNGgwYMKDa/CUlJViyZAk+//xz3LlzB76+vli4cCFiYmKasdZERNbt0iWgZ8/mv+/Zs0CPHnXPr1arMXXqVMyYMQO9e/fGM888g9LSUigUCsjlcqxZswbdunVDZmYmevTogeHDh8PBwcFoWUVFRdVO0O7SpYvea29vb2RmZta9olXKkMlkcHd31wsqND0tmnKTk5NRXFxsEFCVlpaie/fu2tfV9UZppKSkoKSkBEOGDDF6vmvXrhgyZAjCw8MRHR2NqKgojBkzBq6urto8dnZ2AKDX62TJLCrY2blzJ2bPno0NGzYgMjISmzZtwrBhw5CcnAx/f3+j1zz11FP4888/sWXLFgQHByMzMxPl5eXNXHMiIuvWsaMYeJjjvqZYt24dsrKysGTJEqSnp6O8vBypqakIDw+Ht7c3vL29AQCenp5wc3PDvXv3qg12PDw8kJOTY/ScjY2N3muJRAK1Wq19LZVKUXWxc1lZWa1l6KZJJBIA0Jar+frDDz+gbdu2etcqlUrt99W1R0MTqFRHJpMhISEBiYmJ2L9/P9atW4eFCxfi1KlTCAoKAiCu7gKA1q1b11iWpbCoYGf16tWYPHmydub7mjVrsG/fPmzcuBHLly83yP/jjz/i8OHDuHbtGtzc3ACIk8JqUlJSojfGqFKpGq8BRERWyt7etB4Wc7h16xbi4uKwY8cOODg4ICQkBEqlEklJSQbDMGfOnIFarYafn1+15XXv3h2ff/55verSunVrZGRkaF+rVCpcv369XmVpdOrUCUqlEunp6dohq/oICQmBnZ0dDhw4UO1KM4lEgsjISERGRmLx4sUICAhAfHw85s6dCwBISkqCr68vPDw86l2P5mQxE5RLS0tx9uxZREVF6aVHRUUhMTHR6DX//e9/ERERgZUrV6Jt27YIDQ3FvHnzUFRUVO19li9fDhcXF+1R0y86ERG1HLNmzcKwYcMwYsQIAIBcLkdYWJjBJOXs7GxMnDgRmzdvrrG86OhoXLx4sdrenZo88sgj+Oyzz3D06FEkJSVh0qRJkMlkJpejy8nJCfPmzcOcOXOwbds2XL16FefPn8f777+Pbdu21bkcW1tbvPLKK1iwYAE+/fRTXL16FSdPntTuJXTq1Cn8+9//xpkzZ5Ceno5vv/0WWVlZCAsL05Zx9OhRg89rS2YxPTt3795FRUWFdoxSw8vLC3fu3DF6zbVr13Ds2DHY2toiPj4ed+/exUsvvYR79+7h448/NnpNbGysNjIFxGibAQ8RUcv2/fff4+DBg0hJSdFLDw8P1wt2SkpK8OSTTyI2Nhb9+vWrsczw8HBERETgq6++wtSpU02qT2xsLK5du4bHHnsMLi4uWLp0aYN7dgBg6dKl8PT0xPLly3Ht2jW0atUKPXr0wGuvvWZSOXFxcZDL5Vi8eDFu374Nb29vTJs2DYC4T9GRI0ewZs0aqFQqBAQE4N1338WwYcMAiBv9xcfHY9++fQ1uT3OxmB2Ub9++jbZt2yIxMVFvT4Nly5bhs88+wyUjywCioqJw9OhR3LlzBy4uLgCAb7/9FmPGjEFBQUGt45IAd1AmIqqqpe+gXB1BEPD000+jQ4cOBvviVGfPnj2YN28ekpKSIJVazGCIWb3//vvYvXs39u/f3+T3srodlD08PCCTyQx6cTIzMw16ezS8vb3Rtm1bbaADAGFhYRAEAX/88UeT1peIiFqW48ePY+fOnfjuu+/QrVs3dOvWrdYdlocPH46pU6fi1q1bzVRLy2djY4N169aZuxomsZhhLIVCgZ49eyIhIQFPPvmkNj0hIQGPP/640WsiIyPx9ddfIz8/H46OjgCAtLQ0SKVS+Pr6Nku9iYioZejfv7/eiqm6evnll5ugNi3Xiy++aO4qmMxienYAYO7cufjoo4/w8ccfIyUlBXPmzEF6erp2HDE2NhYTJ07U5n/66afh7u6O559/HsnJyThy5Ajmz5+PmJiYOg1hERERkfWzmJ4dABg3bhyys7OxZMkSZGRkoHPnztizZ492d8aMjAykp6dr8zs6OiIhIQEzZ85EREQE3N3d8dRTT+Gtt94yVxOIiIjIwljMBGVz4QRlIiJ91jpBmVoeq5ugTERERNQUGOwQERGRVWOwQ0RERFaNwQ4RERFZNQY7REREZNUY7BAREZFVY7BDREREVo3BDhERWZVFixZBqVTi6aefbnBZ2dnZ8PT0xI0bNxpeMTMaNGgQZs+e3ShljRkzBqtXr26UspoLNxXkpoJERHpa+qaCKpUKn332GWbMmIHLly8jODi43mXNmzcPOTk52LJlSyPWsPndu3cPNjY2cHJyanBZFy5cwODBg3H9+vUm/9zkpoJERERGODs7IyYmBlKptNanmtekqKgIW7ZswZQpUxqxds2rtLQUAODm5tYogQ4AdOnSBYGBgdi+fXujlNccGOwQEZHVKS8vh729PZKSkupdxt69eyGXy9G3b1+99EGDBmHWrFlYsGAB3Nzc0KZNG7zxxht6eQIDA7FmzRq9tG7dumnzDRo0CDNnzsTs2bPh6uoKLy8vbN68GQUFBXj++efh5OSE9u3bY+/evXplCIKAlStXol27drCzs0PXrl2xa9cuvbrNmDEDc+fOhYeHB4YOHapN1x3GUqvVWLFiBYKDg6FUKuHv749ly5Zpz+/atQvh4eGws7ODu7s7Hn30URQUFGjPjxo1Cjt27DD1n9RsGOwQEZHVWbRoEfLz8xsU7Bw5cgQRERFGz23btg0ODg44deoUVq5ciSVLliAhIcGk8rdt2wYPDw+cPn0aM2fOxPTp0zF27Fj069cP586dQ3R0NCZMmIDCwkK9dn3yySfYuHEjLl68iDlz5uDZZ5/F4cOH9cqVy+U4fvw4Nm3aZPTesbGxWLFiBeLi4pCcnIwvvvgCXl5eAMSHbo8fPx4xMTFISUnBoUOHMHr0aOjOeunVqxdOnz6NkpISk9psLhb11HMiIrJQ6kKg9FLz31fREZDam3TJ2bNn8cEHH2DEiBFGg53CwkKEhYVh7NixeOedd6ot58aNG/Dx8TF6rkuXLnj99dcBACEhIVi/fj0OHDig7Umpi65du2LRokUAxODj7bffhoeHB1544QUAwOLFi7Fx40ZcuHABffr0QUFBAVavXo2DBw9qe5vatWuHY8eOYdOmTRg4cCAAIDg4GCtXrqz2vnl5eVi7di3Wr1+PSZMmAQDat2+P/v37AxCDnfLycowePRoBAQEAgPDwcL0y2rZti5KSEty5c0ebx5I1KNgpKyvDnTt3UFhYiNatW8PNza2x6kVERJak9BJwo2fz3zfwLGDbo87Z1Wo1pk6dihkzZqB379545plnUFpaCoVCoc2zbNky9O7du9ayioqKqp2g3aVLF73X3t7eyMzMrHM9q5Yhk8ng7u6uF1Roelo05SYnJ6O4uNggoCotLUX37t21r6vrjdJISUlBSUkJhgwZYvR8165dMWTIEISHhyM6OhpRUVEYM2YMXF1dtXns7OwAQK/XyZKZHOzk5+dj+/bt2LFjh0EXlq+vL6KiovDiiy/i4YcfbtSKEhGRGSk6ioGHOe5rgnXr1iErKwtLlixBeno6ysvLkZqaqg0iLl++jEuXLmHkyJG1DnF5eHggJyfH6DkbGxu91xKJBGq1WvtaKpWi6mLnsrKyWsvQTZNIJACgLVfz9YcffkDbtm31rlUqldrvHRwcqm8UKgOV6shkMiQkJCAxMRH79+/HunXrsHDhQpw6dQpBQUEAxNVdANC6desay7IUJgU77733HpYtW4bAwECMGjUKr776Ktq2bQs7Ozvcu3cPSUlJOHr0KIYOHYo+ffpg3bp1CAkJaaq6ExFRc5Ham9TDYg63bt1CXFwcduzYAQcHB4SEhECpVCIpKUkb7MybNw+rVq1CYmJireV1794dn3/+eb3q0rp1a2RkZGhfq1QqXL9+vV5laXTq1AlKpRLp6enaIav6CAkJgZ2dHQ4cOFDtSjOJRILIyEhERkZi8eLFCAgIQHx8PObOnQsASEpKgq+vLzw8POpdj+ZkUrCTmJiIn376yWDsTqNXr16IiYnBBx98gC1btuDw4cMMdoiIqFnMmjULw4YNw4gRIwAAcrkcYWFh2h6c3bt3IzQ0FKGhoXUKdqKjoxEbG4ucnBy9IZy6eOSRR7B161aMHDkSrq6uiIuLg0wmM71ROpycnDBv3jzMmTMHarUa/fv3h0qlQmJiIhwdHbXzb2pja2uLV155BQsWLIBCoUBkZCSysrJw8eJFTJ48GadOncKBAwcQFRUFT09PnDp1CllZWQgLC9OWcfToUURFRTWoPc3JpGDn66+/1n7/6quvIi4uzmh3mVKpxEsvvdTw2hEREdXB999/j4MHDyIlJUUvPTw8XBvsnDx5El9++SW+/vpr5Ofno6ysDM7Ozli8eLHRMsPDwxEREYGvvvoKU6dONak+sbGxuHbtGh577DG4uLhg6dKlDe7ZAYClS5fC09MTy5cvx7Vr19CqVSv06NEDr732mknlxMXFQS6XY/Hixbh9+za8vb0xbdo0AOI+RUeOHMGaNWugUqkQEBCAd999F8OGDQMgbvQXHx+Pffv2Nbg9zaXeOyj36dMHv//+O9566y3ExMRoxxZbGu6gTESkr6XvoFwXW7duRVJSUo2rsQBgz549mDdvHpKSkiCVcrcWAHj//fexe/du7N+/v8nvZfYdlE+ePIlVq1bhzTffRI8ePfTW+BMREVmD4cOHY+rUqbh165a5q2IxbGxssG7dOnNXwyQNfjZWUVERVqxYgXfeeQdRUVF455130K5du8aqX5Njzw4Rkb4HoWeHWgaz9+xo2NnZ4Y033kBqaiocHBzQuXNnvPLKK0hKSkJFRUVDiyciIiJqkHpvKlhSUoLjx4/j0qVLSE1NRWpqKi5duoSSkhK88847WLVqFZRKJTp16oSzZ82wNwMRERERGhDsDB48GL/88gu6dOmC0NBQDBgwAJMnT9Yu6ysuLsYvv/yCCxcuNGZ9iYiIiExS72AnOzsbiYmJ6Natm9HzdnZ2GDx4MAYPHlzfWxARERE1WL2DndTU1MasBxEREVGT4KYBREREZNVMCnbS09NNKpz7EhAREZG5mRTsPPzww3jhhRdw+vTpavPk5ubiww8/ROfOnfHtt982uIJEREREDWHSnJ2UlBT8+9//xt/+9jfY2NggIiICPj4+sLW1RU5ODpKTk3Hx4kVERERg1apV2udoEBEREZmLST07bm5ueOedd3D79m1s3LgRoaGhuHv3Li5fvgwAeOaZZ3D27FkcP36cgQ4RERFZhHqtxrK1tcXo0aMxevToxq4PERERUaNq8GqstWvXAhCXoqvV6gZXiIiIqCEWLVoEpVKJp59+usFlZWdnw9PTEzdu3KhT/kGDBmH27NkNvm9D1VYPQRDw4osvws3NDRKJBL/88kuz1U1jzJgxWL16dbPcq9777Gh07twZADBnzhxcuXIFjo6OeOihh9C5c2d07twZI0aMaHAliYiI6mrBggXw9vbGjBkzsGTJEgQHB9e7rOXLl2PkyJEIDAxsvApagB9//BFbt27FoUOH0K5dO3h4eDR7HRYvXozBgwdjypQpTf4g7gb37AwZMgQAsGfPHqSlpeHQoUOYPn06XF1dkZCQ0OAKEhERmcLZ2RkxMTGQSqX47bff6l1OUVERtmzZgilTpjRi7SzD1atX4e3tjX79+qFNmzaQy+vX91FaWlrvOnTp0gWBgYHYvn17vcuoq0bfVNDZ2Rn9+vXDiy++iDVr1jR28UREZC5ZWfU/ioqqL/fuXePXNEB5eTns7e2RlJRU7zL27t0LuVyOvn376qWr1WqsWLECwcHBUCqV8Pf3x7Jly4yWUVJSglmzZsHT0xO2trbo378/fv75Z708u3btQnh4OOzs7ODu7o5HH30UBQUFAMThppUrV6Jdu3aws7ND165dsWvXLr3rCwoKMHHiRDg6OsLb2xvvvvtuje167rnnMHPmTKSnp0MikWh7repS10GDBmHGjBmYO3cuPDw8MHToUAwaNAgzZ87E7Nmz4erqCi8vL2zevBkFBQV4/vnn4eTkhPbt22Pv3r0GdRk1ahR27NhRY30bQ6MEO+Xl5bh48SJ27tyJuLg4PPnkk41RLBERWRJPz/ofH39cfblhYcavaYBFixYhPz+/QcHOkSNHEBERYZAeGxuLFStWIC4uDsnJyfjiiy/g5eVltIwFCxbgm2++wbZt23Du3DkEBwcjOjoa9+7dAwBkZGRg/PjxiImJQUpKCg4dOoTRo0dDEARtOz755BNs3LgRFy9exJw5c/Dss8/i8OHD2nvMnz8fP/30E+Lj47F//34cOnQIZ8+erbZda9euxZIlS+Dr64uMjAxtQFNbXTW2bdsGuVyO48ePY9OmTdo0Dw8PnD59GjNnzsT06dMxduxY9OvXD+fOnUN0dDQmTJiAwsJCvbJ69eqF06dPo6SkpLYfR8MIJrp69arw3XffCW+99Zbwj3/8Q+jcubOgUCgEqVQq2NraCt27dxcmTpxoarFmk5ubKwAQcnNzzV0VIiKLUFRUJCQnJwtFRUX6J4D6H+vXV39DDw/j19TTmTNnBIVCIYwYMULo1KmT3rknnnhCaNWqlfD3v/+91nIef/xxISYmRi9NpVIJSqVS+PDDD41eM3DgQOHll18WBEEQ8vPzBRsbG2H79u3a86WlpYKPj4+wcuVKQRAE4ezZswIA4caNGwZl5efnC7a2tkJiYqJe+uTJk4Xx48cLgiAIeXl5gkKhEL788kvt+ezsbMHOzk5bD2Pee+89ISAgQO9etdVV075u3boZtLl///7a1+Xl5YKDg4MwYcIEbVpGRoYAQDhx4oTetb/++mu17ReEGn4XBdM+v00apHv22WexY8cOSCQS2Nvbo6CgACNGjMDixYsRHh6OkJAQyGSyJgjJiIiIaqdWqzF16lTMmDEDvXv3xjPPPIPS0lIoFAoAwKxZsxATE4Nt27bVWlZRURFsbW310lJSUlBSUqKdr1qTq1evoqysDJGRkdo0Gxsb9OrVCykpKQCArl27YsiQIQgPD0d0dDSioqIwZswYuLq6Ijk5GcXFxRg6dKheuaWlpejevbv2HqWlpXpDbW5ubujQoQMAYPv27Zg6dar23N69ezFgwIB61VXDWG9Xly5dtN/LZDK4u7sjPDxcm6bp+crMzNS7zs7ODgAMenwam0nBzq5du7Bu3TrExMSgvLwcCxcuxKZNm9CxY0c89thjDHSIiMis1q1bh6ysLCxZsgTp6ekoLy9Hamqq9oN38ODBOHToUJ3K8vDwQE5Ojl6a5sO5LoT7Q1ESicQgXZMmk8mQkJCAxMRE7N+/H+vWrcPChQtx6tQp7XYuP/zwA9q2batXhlKp1LtHdUaNGoXevXtrX1ctx5S6ajg4OBhcb2Njo/daIpHopWnKqLpFjWaIrHXr1jW2o6FMmrMzf/58TJw4Eba2tnB0dMTatWtx/Phx/PTTT+jUqRN+/PHHpqonERGZW2Zm/Y+YmOrLTUkxfo2Jbt26hbi4OGzYsAEODg4ICQmBUqms97yd7t27Izk5WS8tJCQEdnZ2OHDgQK3XBwcHQ6FQ4NixY9q0srIynDlzBmFhYdo0iUSCyMhIvPnmmzh//jwUCgXi4+PRqVMnKJVKpKenIzg4WO/w8/PT3sPGxgYnT57UlpeTk4O0tDQAgJOTk9511QVrda1rY0tKSoKvr2+TL303qWdn6dKlBmk9e/bE6dOn8Z///Afjxo3DiBEjsHbt2iaP0oiIqJk11f/rjfRBN2vWLAwbNky7v5tcLkdYWFi9g53o6GjExsYiJycHrq6uAMQnCLzyyitYsGABFAoFIiMjkZWVhYsXL2Ly5Ml61zs4OGD69OmYP38+3Nzc4O/vj5UrV6KwsFCb99SpUzhw4ACioqLg6emJU6dOISsrC2FhYXBycsK8efMwZ84cqNVq9O/fHyqVComJiXB0dMSkSZPg6OiIyZMnY/78+XB3d4eXlxcWLlwIqdS09Ud1qWtTOHr0KKKiopqsfI0GbyoIiFHpyy+/jDFjxmDWrFno2LEjsrOzG6NoIiKiWn3//fc4ePCgwfyS8PDwegc74eHhiIiIwFdffaU37yUuLg5yuRyLFy/G7du34e3tjWnTphkt4+2334ZarcaECROQl5eHiIgI7Nu3Txs8OTs748iRI1izZg1UKhUCAgLw7rvvap8vuXTpUnh6emL58uW4du0aWrVqhR49euC1117T3mPVqlXIz8/HqFGj4OTkhH/961/Izc01ub211bWxFRcXIz4+Hvv27WuS8nVJhNoG/Orhhx9+aDE7J6tUKri4uCA3N7fJd3AkImoJiouLcf36dQQFBRlM0LUGhw4dwvr16w32qzFmz549mDdvHpKSkkzuLaGavf/++9i9ezf2799fbZ6afhdN+fxulJ6dqlpKoENERA+W6OhonDt3DgUFBfD19UV8fDwefvjhavMPHz4cly9fxq1bt7TzZKhx2NjYYN26dc1yrybp2WlJ2LNDRKTP2nt2qOVorJ4d9skRERGRVWOwQ0RERFaNwQ4RERFZNQY7REREZNUY7BAREZFVY7BDREREVo3BDhEREVk1BjtERERk1RjsEBERkVVjsENERERWzeKCnQ0bNmi3he7ZsyeOHj1ap+uOHz8OuVyObt26NW0FiYjIoi1atAhKpRJPP/10g8vKzs6Gp6cnbty4Uaf8gwYNwuzZsxt834aqrR6CIODFF1+Em5sbJBIJfvnll2arm8aYMWOwevXqZrmXRQU7O3fuxOzZs7Fw4UKcP38eAwYMwLBhw5Cenl7jdbm5uZg4cSKGDBnSTDUlIiJLtWDBAqxevRo7duzAlStXGlTW8uXLMXLkSAQGBjZO5SzEjz/+iK1bt+L7779HRkYGOnfu3Ox1WLx4MZYtWwaVStXk97KoYGf16tWYPHkypkyZgrCwMKxZswZ+fn7YuHFjjddNnToVTz/9NPr27dtMNSUiIkvl7OyMmJgYSKVS/Pbbb/Uup6ioCFu2bMGUKVMasXaW4erVq/D29ka/fv3Qpk0byOXyepVTWlpa7zp06dIFgYGB2L59e73LqCuLCXZKS0tx9uxZREVF6aVHRUUhMTGx2us++eQTXL16Fa+//nqd7lNSUgKVSqV3EBFR7bKy6n8UFVVf7t27xq9piPLyctjb2yMpKaneZezduxdyudzgD2m1Wo0VK1YgODgYSqUS/v7+WLZsmdEySkpKMGvWLHh6esLW1hb9+/fHzz//rJdn165dCA8Ph52dHdzd3fHoo4+ioKAAgDjctHLlSrRr1w52dnbo2rUrdu3apXd9QUEBJk6cCEdHR3h7e+Pdd9+tsV3PPfccZs6cifT0dEgkEm2vVV3qOmjQIMyYMQNz586Fh4cHhg4dikGDBmHmzJmYPXs2XF1d4eXlhc2bN6OgoADPP/88nJyc0L59e+zdu9egLqNGjcKOHTtqrG9jsJhg5+7du6ioqICXl5deupeXF+7cuWP0msuXL+PVV1/F9u3b6xyVLl++HC4uLtrDz8+vwXUnInoQeHrW//j44+rLDQszfk1DLFq0CPn5+Q0Kdo4cOYKIiAiD9NjYWKxYsQJxcXFITk7GF198YfDZpbFgwQJ888032LZtG86dO4fg4GBER0fj3r17AICMjAyMHz8eMTExSElJwaFDhzB69GgIgqBtxyeffIKNGzfi4sWLmDNnDp599lkcPnxYe4/58+fjp59+Qnx8PPbv349Dhw7h7Nmz1bZr7dq1WLJkCXx9fZGRkaENaGqrq8a2bdsgl8tx/PhxbNq0SZvm4eGB06dPY+bMmZg+fTrGjh2Lfv364dy5c4iOjsaECRNQWFioV1avXr1w+vRplJSU1PbjaBjBQty6dUsAICQmJuqlv/XWW0KHDh0M8peXlwsRERHCxo0btWmvv/660LVr1xrvU1xcLOTm5mqPmzdvCgCE3NzcRmkHEVFLV1RUJCQnJwtFRUV66UD9j/Xrq7+fh4fxa+rrzJkzgkKhEEaMGCF06tRJm56eni4MHDhQCAsLE8LDw4WvvvqqxnIef/xxISYmRi9NpVIJSqVS+PDDD41eM3DgQOHll18WBEEQ8vPzBRsbG2H79u3a86WlpYKPj4+wcuVKQRAE4ezZswIA4caNGwZl5efnC7a2tgafi5MnTxbGjx8vCIIg5OXlCQqFQvjyyy+157OzswU7OzttPYx57733hICAAL171VZXTfu6detm0Ob+/ftrX5eXlwsODg7ChAkTtGkZGRkCAOHEiRN61/7666/Vtl8Qqv9dFARByM3NrfPnd/0G6ZqAh4cHZDKZQS9OZmam0Yg5Ly8PZ86cwfnz5zFjxgwAYteiIAiQy+XYv38/HnnkEYPrlEollEpl0zSCiIjMSq1WY+rUqZgxYwZ69+6NZ555BqWlpVAoFJDL5VizZg26deuGzMxM9OjRA8OHD4eDg4PRsoqKimBra6uXlpKSgpKSkjotiLl69SrKysoQGRmpTbOxsUGvXr2QkpICAOjatSuGDBmC8PBwREdHIyoqCmPGjIGrqyuSk5NRXFyMoUOH6pVbWlqK7t27a+9RWlqqN9Tm5uaGDh06AAC2b9+OqVOnas/t3bsXAwYMqFddNYz1dnXp0kX7vUwmg7u7O8LDw7Vpms/xzMxMvevs7OwAwKDHp7FZTLCjUCjQs2dPJCQk4Mknn9SmJyQk4PHHHzfI7+zsbDDxbMOGDTh48CB27dqFoKCgJq8zERFZlnXr1iErKwtLlixBeno6ysvLkZqaivDwcHh7e8Pb2xsA4OnpCTc3N9y7d6/aYMfDwwM5OTl6aZoP57oQ7g9FSSQSg3RNmkwmQ0JCAhITE7F//36sW7cOCxcuxKlTp6BWqwEAP/zwA9q2batXhuaPds09qjNq1Cj07t1b+7pqOabUVcPYv5eNjY3ea4lEopemKUPTJg3NEFnr1q1rbEdDWUywAwBz587FhAkTEBERgb59+2Lz5s1IT0/HtGnTAIjjpLdu3cKnn34KqVRqsFROM6nKHEvoiIisXZU/yk3i6Fj9uZQUceCqoW7duoW4uDjs2LEDDg4OCAkJgVKpRFJSkl4vAwCcOXMGarW6xnmb3bt3x+eff66XFhISAjs7Oxw4cKDWVVrBwcFQKBQ4duyYds+fsrIynDlzRm8PHIlEgsjISERGRmLx4sUICAhAfHw8XnjhBSiVSqSnp2PgwIHV3sPGxgYnT56Ev78/ACAnJwdpaWkYOHAgnJyc4OTkVGM9TalrY0tKSoKvry88PDya7B6AhQU748aNQ3Z2NpYsWaJd979nzx4EBAQAECdy1bbnDhERNY2m+uO7sT7nZs2ahWHDhmHEiBEAALlcjrCwMINJytnZ2Zg4cSI++uijGsuLjo5GbGwscnJy4OrqCgCwtbXFK6+8ggULFkChUCAyMhJZWVm4ePEiJk+erHe9g4MDpk+fjvnz58PNzQ3+/v5YuXIlCgsLtXlPnTqFAwcOICoqCp6enjh16hSysrIQFhYGJycnzJs3D3PmzIFarUb//v2hUqmQmJgIR0dHTJo0CY6Ojpg8eTLmz58Pd3d3eHl5YeHChZBKTVt/VJe6NoWjR48arMJuChYV7ADASy+9hJdeesnoua1bt9Z47RtvvIE33nij8StFREQW7fvvv8fBgwcN5peEh4frBTslJSV48sknERsbi379+tVYZnh4OCIiIvDVV1/pzXuJi4uDXC7H4sWLcfv2bXh7e2tHIKp6++23oVarMWHCBOTl5SEiIgL79u3TBk/Ozs44cuQI1qxZA5VKhYCAALz77rsYNmwYAGDp0qXw9PTE8uXLce3aNbRq1Qo9evTAa6+9pr3HqlWrkJ+fj1GjRsHJyQn/+te/kJuba9o/YB3q2tiKi4sRHx+Pffv2NUn5uiRCbQN+Vk6lUsHFxQW5ublwdnY2d3WIiMyuuLgY169f1z66x1oIgoCnn34aHTp0qPMfxnv27MG8efOQlJRkcm8J1ez999/H7t27sX///mrz1PS7aMrnN39yRET0QDh+/Dh27tyJ7777Dt26dUO3bt1q3WF5+PDhmDp1Km7dutVMtXxw2NjYYN26dc1yL4sbxiIiImoK/fv3N1gNVBcvv/xyE9SGXnzxxWa7F3t2iIiIyKox2CEiIiKrxmCHiIiIrBqDHSIiIrJqDHaIiIjIqjHYISIiIqvGYIeIiIisGoMdIiIismoMdoiIiMiqMdghIiIiq8Zgh4iIrMqiRYugVCrx9NNPN7is7OxseHp64saNG3XKP2jQIMyePbvB922o2uohCAJefPFFuLm5QSKR4Jdffmm2ummMGTMGq1evbpZ7MdghIiKrsmDBAqxevRo7duzAlStXGlTW8uXLMXLkSAQGBjZO5SzEjz/+iK1bt+L7779HRkYGOnfu3Ox1WLx4MZYtWwaVStXk92KwQ0REVsXZ2RkxMTGQSqW1PtW8JkVFRdiyZQumTJnSiLWzDFevXoW3tzf69euHNm3aQC6v33PBS0tL612HLl26IDAwENu3b693GXXFYIeIiOqmPKv+h7qohnLvGr+mIVUtL4e9vT2SkpLqXcbevXshl8vRt29fvXS1Wo0VK1YgODgYSqUS/v7+WLZsmdEySkpKMGvWLHh6esLW1hb9+/fHzz//rJdn165dCA8Ph52dHdzd3fHoo4+ioKAAgDjctHLlSrRr1w52dnbo2rUrdu3apXd9QUEBJk6cCEdHR3h7e+Pdd9+tsV3PPfccZs6cifT0dEgkEm2vVV3qOmjQIMyYMQNz586Fh4cHhg4dikGDBmHmzJmYPXs2XF1d4eXlhc2bN6OgoADPP/88nJyc0L59e+zdu9egLqNGjcKOHTtqrG9jYLBDRER1c8Wz/kfux9WXez3M+DUNsGjRIuTn5zco2Dly5AgiIiIM0mNjY7FixQrExcUhOTkZX3zxBby8vIyWsWDBAnzzzTfYtm0bzp07h+DgYERHR+PevXsAgIyMDIwfPx4xMTFISUnBoUOHMHr0aAiCoG3HJ598go0bN+LixYuYM2cOnn32WRw+fFh7j/nz5+Onn35CfHw89u/fj0OHDuHs2bPVtmvt2rVYsmQJfH19kZGRoQ1oaqurxrZt2yCXy3H8+HFs2rRJm+bh4YHTp09j5syZmD59OsaOHYt+/frh3LlziI6OxoQJE1BYWKhXVq9evXD69GmUlJTU9uNoGOEBl5ubKwAQcnNzzV0VIiKLUFRUJCQnJwtFRUX6J1JQ/+Pe+upvmOZh/Jp6OnPmjKBQKIQRI0YInTp1MjhfUFAg+Pv7C//6179qLOfxxx8XYmJi9NJUKpWgVCqFDz/80Og1AwcOFF5++WVBEAQhPz9fsLGxEbZv3649X1paKvj4+AgrV64UBEEQzp49KwAQbty4YVBWfn6+YGtrKyQmJuqlT548WRg/frwgCIKQl5cnKBQK4csvv9Sez87OFuzs7LT1MOa9994TAgIC9O5VW1017evWrZtBm/v37699XV5eLjg4OAgTJkzQpmVkZAgAhBMnTuhd++uvv1bbfkGo4XdRMO3zmz07RERkNdRqNaZOnYoZM2Zg4sSJSEtLM5hXsmzZMvTu3bvWsoqKimBra6uXlpKSgpKSEgwZMqTW669evYqysjJERkZq02xsbNCrVy+kpKQAALp27YohQ4YgPDwcY8eOxYcffoicnBwAQHJyMoqLizF06FA4Ojpqj08//RRXr17V3qO0tFRvqM3NzQ0dOnQAAGzfvl3v2qNHj9a7rhrGeru6dOmi/V4mk8Hd3R3h4eHaNE3PV2Zmpt51dnZ2AGDQ49PY6jcjiYiIyAKtW7cOWVlZWLJkCdLT01FeXo7U1FTtB+/ly5dx6dIljBw5stYhLg8PD23goaH5cK4L4f5QlEQiMUjXpMlkMiQkJCAxMRH79+/HunXrsHDhQpw6dQpqtRoA8MMPP6Bt27Z6ZSiVSr17VGfUqFF6gV3Vckypq4aDg4PB9TY2NnqvJRKJXpqmDE2bNDRDZK1bt66xHQ3Fnh0iIqqb4Mz6Hy4x1ZcblGL8GhPdunULcXFx2LBhAxwcHBASEgKlUqkX1MybNw/Lly+vU3ndu3dHcnKyXlpISAjs7Oxw4MCBWq8PDg6GQqHAsWPHtGllZWU4c+YMwsLCtGkSiQSRkZF48803cf78eSgUCsTHx6NTp05QKpVIT09HcHCw3uHn56e9h42NDU6ePKktLycnB2lpaQAAJycnveuqC9bqWtfGlpSUBF9fX3h4eDTZPQD27BARUV3Jm+ivb3njfNDNmjULw4YNw4gRI8Ri5XKEhYVpg53du3cjNDQUoaGhSExMrLW86OhoxMbGIicnB66urgAAW1tbvPLKK1iwYAEUCgUiIyORlZWFixcvYvLkyXrXOzg4YPr06Zg/fz7c3Nzg7++PlStXorCwUJv31KlTOHDgAKKiouDp6YlTp04hKysLYWFhcHJywrx58zBnzhyo1Wr0798fKpUKiYmJcHR0xKRJk+Do6IjJkydj/vz5cHd3h5eXFxYuXAip1LS+jLrUtSkcPXoUUVFRTVa+BoMdIiJq8b7//nscPHjQYH5JeHi4Ntg5efIkvvzyS3z99dfIz89HWVkZnJ2dsXjxYqNlhoeHIyIiAl999RWmTp2qTY+Li4NcLsfixYtx+/ZteHt7Y9q0aUbLePvtt6FWqzFhwgTk5eUhIiIC+/bt0wZPzs7OOHLkCNasWQOVSoWAgAC8++67GDZsGABg6dKl8PT0xPLly3Ht2jW0atUKPXr0wGuvvaa9x6pVq5Cfn49Ro0bByckJ//rXv5Cbm2vyv2FtdW1sxcXFiI+Px759+5qkfF0SobYBPyunUqng4uKC3NxcODs7m7s6RERmV1xcjOvXryMoKMhggq612Lp1K5KSkvDOO+/UmG/Pnj2YN28ekpKSTO4toZq9//772L17N/bv319tnpp+F035/GbPDhERUTWGDx+Oy5cv49atW9p5MtQ4bGxssG7duma5F3t22LNDRKTnQejZoZahsXp22CdHREREVo3BDhEREVk1BjtERERk1RjsEBERkVVjsENEREY94OtXyAI01u8ggx0iItKjeaZRUz+ckag2moe4ymSyBpXDfXaIiEiPTCZDq1attE+otre3N3gYJFFTU6vVyMrKgr29PeTyhoUrDHaIiMhAmzZtAEAb8BCZg1Qqhb+/f4ODbQY7RERkQCKRwNvbG56enigrKzN3degBpVAoGuUxHQx2iIioWjKZrMHzJYjMjROUiYiIyKox2CEiIiKrxmCHiIiIrBqDHSIiIrJqDHaIiIjIqjHYISIiIqvGYIeIiIisGoMdIiIismoMdoiIiMiqMdghIiIiq8Zgh4iIiKwagx0iIiKyagx2iIiIyKox2CEiIiKrxmCHiIiIrBqDHSIiIrJqDHaIiIjIqjHYISIiIqvGYIeIiIismsUFOxs2bEBQUBBsbW3Rs2dPHD16tNq83377LYYOHYrWrVvD2dkZffv2xb59+5qxtkRERGTpLCrY2blzJ2bPno2FCxfi/PnzGDBgAIYNG4b09HSj+Y8cOYKhQ4diz549OHv2LAYPHoyRI0fi/PnzzVxzIiIislQSQRAEc1dCo3fv3ujRowc2btyoTQsLC8MTTzyB5cuX16mMhx56COPGjcPixYvrlF+lUsHFxQW5ublwdnauV72JiIioeZny+W0xPTulpaU4e/YsoqKi9NKjoqKQmJhYpzLUajXy8vLg5uZWbZ6SkhKoVCq9g4iIiKyXxQQ7d+/eRUVFBby8vPTSvby8cOfOnTqV8e6776KgoABPPfVUtXmWL18OFxcX7eHn59egehMREZFls5hgR0Mikei9FgTBIM2YHTt24I033sDOnTvh6elZbb7Y2Fjk5uZqj5s3bza4zkRERGS55OaugIaHhwdkMplBL05mZqZBb09VO3fuxOTJk/H111/j0UcfrTGvUqmEUqlscH2JiIioZbCYnh2FQoGePXsiISFBLz0hIQH9+vWr9rodO3bgueeewxdffIERI0Y0dTWJiIiohbGYnh0AmDt3LiZMmICIiAj07dsXmzdvRnp6OqZNmwZAHIK6desWPv30UwBioDNx4kSsXbsWffr00fYK2dnZwcXFxWztICIiagwFBcCVK0BaGnDtGuDjA4wbBygU5q5Zy2JRwc64ceOQnZ2NJUuWICMjA507d8aePXsQEBAAAMjIyNDbc2fTpk0oLy/HP//5T/zzn//Upk+aNAlbt25t7uoTERGZrLwcuHFDDGh0j9RU4I8/DPMvWwasXw/UMmuDdFjUPjvmwH12iIjIHP74QwxYrl4VAx5TTZ4MfPRR49erpTDl89uienaIiIhastxc4PJlsVdG00Mzbx7Qs2dlnvJy4PffgaQk8Xx9uxz8/Runzg8CBjtEREQmKCkR58/oDjdpvv/zT8P8NjaAl1dlnqtXgbIy8VwddlYBIAY2CoU4fwcAZDJg5UrA0RGYOVO8B1WPw1gcxiIiohqo1cCcOZXByo0bYpop2rcHQkMrjw4dxK8vvABonl/t5laZrnsEBwP29kBFBbBlC/Daa8CnnwJ79gAbNwJhYeIcnkGDGrvlls2Uz28GOwx2iIgeWHfvVgYxXboAPXoY5ikpEXtWMjPrd48RI4Dvvzd+7vRpMYgJCQE8POpWXkEB4OAgfn/+PPDPfwInTgDjxwPvvCMevXoB//hH/erbUnDODhER0X26y7erHvfuVeabMQPIzjbMY2pPjlQKBAVV9sz06VN93l69TG+PJtABgO7dgWPHxJ6eBQvEXqDiYnGYKywM6NrV9PKtEXt22LNDRGQ1DhwAfvtNfx6NseXbNbGxEYedQkIqh5X+9z/x0NWmjX4ezdG+vXn2wcnOFuuSnS2+7tYNOHXKevfkYc8OERFZHUEA7twRJ/dWtxJp0SLg5Mn6ld+uHbB/PxAQAMirfDq2bSuuqNIENCEhgKX9fXzgQGWgAwC//AL8+9/AG2+Yq0aWgz077NkhIrIoKpXh5nppaeKS7rw8YMIE4OOPxeXbVVdDnTgBFBaadj9NT063bsCOHU3SpGZRUgJERIhL2jXkcrF3x9hcpJaOE5RNwGCHiKj5VV2+rRvYGFu+rcvWVpzUq1m+bWsr9rSEhooTjg8fNn6dn59+z0yHDuJhrCfHbARBnEh05w6QkVH5NSMDyMoSGzF+PBAebvTyc+fEeUAVFZVp4eHAzz8D1vYMbA5jERGRRXvuOeDLL+t3rSAA771XOVfG11ecFAwAP/wAlJZWv3zbbASh+k11Fi0CEhIqgxtNFFed5cuB3r2BKVPEJVeOjtpTPXoACxcCS5ZUZv/tN2DpUuCttxqhHS0Ue3bYs0NE1CDGVjClpQHe3sCPP4p5Skv1e3J27BB7IerD1ha4fRtwdW28NtRbSYl+70tGhlg53dcZGeJzIT7/vPK68nKxpyYjA5g9Gzh6tH73d3IS/2F11q2Xloq9O7/+WplNJhPnMkVE1O82log9O0RE1KgKC8U5M7Ut39Z15Yq4x0xqKnD9euXybUfH2veUqbp8W3foSbcnp1l99JG4zls3oNGdEVyTAweA4cP1h6RM3ZnQGDc3g0lKCgWwbZsY2GieuVVRAUyaJAaY1jacVRcMdoiIqFqbN4vDHzdvmn5tYaE4evPEE/rLs9u0Ac6cEXsf2rQxPo+mXbsmWjJdVib2xNy+bfzo3h14+23D64qLgf/+13D9eV399ZfYoD59xEZ7e1ce8fHisqmq3N0r87ZpI0aJu3eLwZLGnTtAYCDwt7+Jw1ojRwI2NujaFYiLA15/vTJrcrK4Mmv58vo1oSXjMBaHsYjoASII4gRg3QnB9+6JjyHQpenJ+eAD8aivn382PnRSVgYUFTXR8u0TJ8SJKrduGQYztW2DHBwMjBlT2XOjuS4np2F1cnYWnxJqzK+/inXWDYA8PY13wZSXi8+J+PBDcVwqOVkMgD76SFx25eUlTtqZORNlReXoHSnH+fOVl0ulQGKiOOWnpeNqLBMw2CEia1R1+bbukZenn1ciETszbtyoXMZd3434qk4M7tlTb/6s6QRBbIwmcNF8bdMGeP5549c88wzwxRf1v2dgIODjIwYdPj6V3ycmil1dxiiVlYGKJn/Vo0uXuj/5sy7y8/X/cS9cANauFdflv/kmEB+P3/6xDD3jhuvNee7YURzOsrNrvKqYA4MdEzDYISJrcP48sGFDZUBz545p1ysUlUNIukNKrVoBnTpV5tNdvq37UMt6Ld8uKxN7T27dqjw0AY3u64ICw2t79hSXGOkGQJqvly6ZvtmOhoODGEQYc+wYsGuXYUDj4yP+QzVmIFNfggBMnw5s2iS+lsvx7/G/YeFnHfWyzZsHrFplhvo1Ik5QJiKyEmq12MuiGXKaOtV4UJGeLo5k1Nf27eLoTVWCIH6+h4SYuHxbpRIrrlYDnTsbz/Pcc/XvgTl7VpzwK5GIQz4+PpXbHLduXfko8eooFJW9NlUPtdr4DOj+/cXDkt29K66/1ygvx4KdPRHfIQNnUisDgsuXxUnLMpkZ6mgGDHaIiCxAdcu3L18W57ZotG8vLi2umk93zmpd6G7EpzmMkUiAv/9dJ0GtFlcS3bolBjPVfdX0jvzf/wE//VR5je5x4YJpldalVFaub7ex0T/3/ffiRCRNAGQsoHFzs4yemMbm4SH+wNau1SbJSwux7eYj6G5zGlKZFMXFwPz5D06gA3AYi8NYRNSscnPF/eOqBit1XcGs4ehouGneCy+I275oSKXi9BPd4SbNEJWfnwnLt9evF3cA1AQptW16p0suF4MK3WtkMnHOjUwmdknVlZubGLxoApiNG633KZcNoVaLK7M++UQv+RuHiXj421iMe70jsrPFZ2eZdaPFBuIwFhGRmZSXixN9fXyMf5BkZgJjx9a//JdeEhfbeHsbdkxcuSJOOdEENe3a6SzoKS2t7HVJ/EP8qnv4+YnjVboKCsRzx44Bx4/Xr8Ka7Y59fSsDFS8vMdD5+mvgqafESmp6YXQP3TQfH7E7imonlYoTqVUq4JtvtMl/L/gUmLQf27cdxUOPB2PRImD1ajPWsxmxZ4c9O0RkIs3Tt40NO129KnZiJCQAkZFiAKL7sMpLl8QVwqZydBR7ZF56Sfyj3aiUFHGm8s2blUGM5vvaHjjl6ioOf+gGQH/9ZXpFq3JzE/9RWrUyPFdYKB7u7tY5pGRuJSXA448bzl8KCMDmiccw7S1fHD4MDBhgnuo1FFdjmYDBDhFVx5Tl21W5uupvzdKqVWWPy549xoet5PLK5dvaTfjalSPU+Q7aFN+A5I+bYqT19NPGb7pgQcOW2PTsKfbwaHph/PzErxcvAjNm6OeVycTupbZtK/Pr9t74+oq9MS19fXNLV1gIREeLvXM6hI4dMdL5CC5lt8avv4q/ey1tZ2UOYxERNVBxsRig1PfPwfbtxV4YzRJuD4/KzospU8ShrtAQNULb5CHUKQMh8usIKrkEecZNsTfm6E3gi5vizGPdSgQEiI+xvnmzstdG8/1vvzWs0Xv3iiuZqgoKEueB6AY1mqEosmz29uKE7cGDobu7oOTSJex66G/wu3UY48c74vx54LPPgEGDzFfVpsSeHfbsEFk93eXbukdqKrB4sfjMIEDsrdE8/yk1FVi5sv7btYwZI05JMWrDBrHwW7cqH15UH1Kp2Hvi6yv2whQX1/44Azu7yvy6X319gUceadkzVql6WVniyrhLl7RJuXDGlFbfYNdfjwIQJ7P/9lsDN4FsRuzZIaIHUtXl25p5Mpcvi3GAMe+9Jy5aqbp8u3VrcaFPTcGOrVKNEJ8CdHC/i1C7PxAquYzQ4gsIzTkF99QCADpLq0tKKnthTpwAfv+9/g393/+Abt3EFU26m+788ovYEGOBjOa1pWx+R82rdWtxIln//trfvR0Yrw10ALG3ccECMRa3NuzZYc8OUYv3+OPilITqnr5dExcX8RmKusuzQ0LEmOCfE/PwweeOCHTLRahjBjrIryK0NAmhqjMIzT0NX/wBKar5L1QqFSumGWKqbYJwbWxtxWDFz098kFVgYMPKowfT5cvig7FycqCGBINwCEfxf3pZEhKARx+t5noLwgnKJmCwQ2R5ysvFPz51e2l69wYmTtTPd++eeG7SJPFrfTzk+xeSbrYyeu6vFZtg9+osKFFav8IHDhQ3wPH3rwxU/P3FIQXdnXhtbCp7Xqo7rHUTPGp+hw4BQ4cC5eW4inboYpOCwrLK/Yr8/cXhLEv/SGSwYwIGO0TmUfXp27rDTprl27oiI4ERI/Tz371r2j0dpQUIlVxBaEUyOiAVoUhDR/lV9LjylTjElJ4uRlnp6eKRlNSw4aZTp4BevQzT8/PF5cCaIMjT04Qd/ogawZYtwOHDgJMT3t8oxQxhnd7pF16o/pmnloLBjgkY7BA1n48/Bg4cqAxqalu+XZXu8m3d5dk/rL2MhZ+EAABsUIr2uIpQpBkcbXAHtfaNuLpWBiH29sBXX9WeX9NjU/Vr9+4tZ7YnPXgEAaiogHrk4xiS8CoOVehvuLNvHxAVZaa61QEnKBNRsyotBa5dEwMYGxtg2DDDPIIg7i+js6GrSRylhcjOsoVUrtMDIghAZiYcPH5CN7yMUKQhEDcgR4Vphb/3ntit7+en33efnQ2cOSMGLppDE8hovndyql+DiMxNIgHkckh37sDHEWMRfuVbFAgO2tOTJ4udmy4uZqxjI2GwQ0R1olaLK6WNDTtdvy6eB8RRG09P4xvxqVSm3dMV97TDTaHqNJS/ooYiN0t/qKm4GMEAguvTKDc3cd+ahx8GHnrI8Ly7uzimRmTNnJ0RtO8DvNPlDUzPr9yU8o8/gLlzxRGvlo7DWBzGIjKQmgqcPFnz07erI4EaAiQAJPD0rNxULzQUKDvxM+J2P6yX3xZFCMaVyqBG5/BAlW2GW7USJ/wGBIiHv7/41cVF3CNGl0wmTvrVzafbQ+PvzyEmIh3C8UREDSjE/xP0l2L98AMwfLiZKlUDDmMRUY2KisQ9Zdq1M37+00+Bf/+7fmULkOLgV1noPrQ1WsnzxV6Y338HbtzAZckNZCFRL6Dxw83ql29XtWmT+OBIg5sKwIoVYnCjCWx8fLjDL5EJJP5++Mh7HMJv90IeKoOHF14Qh7NcXc1YuQZisENkpSoqxBhDM9Ske6Sni7v+//FH5fJt3ePXxHwApvd6eOEOQpGGgFeXotX08/oPgJLLEeLjg7VIr1th7u6VPTiao1s343klEnE3NCKqvzNnEHD7BFZjLl7AR9rk27eB2bOBbdvMV7WG4jAWh7GoBbs/P9doQHP1qjhxuCa+rvn4I6cyqPH1FYebQipSsOlwmNFrHJGn7ZUJwWW94ScX3J+U88gj4hEYKAYpgYHiQyOlUnFCb0GB+FpzTverZriJQ0xEzW/ZMgiLFmEY9mIf/qZNlkgE/PabxOjUNnPhMBbRA+Ljj8WHStZXzMAreKi/O0JtriOkLBkOGVeA69eRfSkLh7DZ6DyaOi3f/tvfgPnzjZ+7eFF8iKStbf0rTkRN47XXILl0CR9+/gI6IwkquCAI17Ci8+d4qFMcUPu73yIx2CGyELrLt3WPK1fEXhqlsrInR3Pu+A9/AWhV73t2/+4NPPHdbvGFjY3YqxIUBPe+obh0pWv1XUNSqdgNFBho/PD1rf6mAQH1ri8RNTGJBPjwQ/glR2LNudk4gwiswCtw/K0ABavc4bDgn+auYb1wGIvDWNSMNMu3jQ076S7frmrCI7eQomqrt3xbIgG6+GTi11ueNd6zFXIMemg6IBXBuAKHf4wC/vlPICiocphJIypKfHhldcGMjU3D/0GIyDJduwb06AHk5mqTyqU2kJ84ZnxXcDPgMBaRhfnlF/H5TXVdvl1V0W+X0aVTMcb2vYHQ8hSE5p9Du4zjUN68Amf8hTLYIASX9YIZzffuyDbseJZIxBnKERH6z2jStX+/6RUlIuvQrp24LPPxx7VJcnUZCh8bC/uUc+ICghaEwQ5RPRUViUNMur00b72lP4Kj6clJPlOICxfs632vh7P2YMHhVeJ/MEFB4jHwCSAoCGlvPQKvW2cNl297egJBwUDQUDF/YGDlV39/cVyMiKg6o0aJqxxXrtQm2Welo/QfE6HY978W9Tw3BjtENah++baA9HTDiXrtS5NR0q6TNn9lT44tFChBKWoPMDTLt3WPiJE+wHaV0UcTeN+7B2T/X2UQpAlo7OsfXBERAQCWLRN3GD1yRJsk/3978f4TCfB5PhpPPmnGupmAc3Y4Z4d0qFRi70xaGpCWKojLt8vqvvpgIA7hinMPdHC8hVDJFYQUXUCHv04hVJ2CJ/AdkiGu29Rdvq079BSCy5XLt5VKMWhp1w547DHgpZeaoMVERLXIyBAfavvnn7iBAMTgY/yER+DhUoqLaQp41jxtsMnwqecmYLDz4MjLq+yZ6dNH7ACpqrBAgJOjGmrUb+fdadiAja6LxAClXTvxJve/3z9vP5QXTlcu35ZIxDEvTW+MJr/m+zZtWlQ3MRFZsZ9+wrUhL6CrcB75qOxh/vtoNb7eJYXEDCvSOUGZHlgGy7dTBaQllSDtsgQZ2ZVDSO89ewY9X4zQe5hlWkoFrl6XwBd/IB11Xx7ti5va3pmhXe8Cv9wzmi/qzQIgQycICgjgvBkiahkGD0bQ0hgMXZSAeIzWJn/zrRRffQWMG2fGutUBe3bYs9NiHTx4P1BJLkfahWKkXZbg+p92qFDX3hsyCD/hEAZDAjUCFbcRqr6E0PJkhCIN3+FxHMBQvfy6y7c1X0NwGSGy63AI8KjsyendG4iJaaomExGZj1qNP6Mm4KGjG5FdWvl56eYm7hXapk3zVoc9O2QV7t0TVzN5eBg/P2lkNv4odIf4a2zaowVsUIok76FoHyqDbai/GKi0bw+0i4TDnAt4+OjyyuXbLplwb98KkvaaPO2Ado+IX/38ADnfRkT0AJBK4fX9FmzYrcS4f1Qm37sHTJsGxMfDLMNZdcH/pcmsNMu301IFpJ3LR9qvhUhLkyD1lgOyixzwWtQZLN0bgdu3xaGm1EuC2IvzWwm8in7HHzBtrwcJ1AjA7whspcJDtxOM5nn+nQrghgPQPkoMaFryo36JiBqTrS2eGgfs+gb4+uvK5N27gS++AJ55xnxVqwmHsTiM1eQ0y7fTLqmR9vNfSD1XiLTLQNotB9xUuUBA9cNOA6THcFbWC4VlCgCAHGVoh2sIRRpsUKY3dqzLYPm24neEBpSgXUeF2JPTqROHm4iI6ikrC3joIQFZWZVdOa6u4nCWt3fz1IHDWGRRHgm6jiM3gwBIAbjdP+omS+2Opc5vI8S3GB3CpAjq6gyb0CCgfXt88HoGfv/+bGVA4/wnQgNKEBImR6uObcQhp/ZhQPvHxAdPWmr/KhFRC9O6NbBxowRjxlSm5eQAU//2O3b/EmBx/92yZ4c9OyZRqYDLKWVIS7yLtLP5SLtUgbSbdogIuoeNJ7sDEHty0tOB1KRSpJ3Mwb41KdhTOKhe93OCCrkVTpBIjbxzUlOBpKT7QU17oxvuERFR0xk/HvjyS/20bSsyMHFB03fvcJ8dEzDYMVRaCly7VIq045lIO5OHtJRypP1ui9S77rhTarxXpqvsNwSF2SLtlgOu/OWBUkEcdlKiGI8iAT9gZI33bIs/xAnB0qsI9biHUP9ihHaSI7C7K2z++SIfOklEZIGykzLwUBcp/hS8tGkusjxcvGKLtoFN+/82h7GoXlaOO4vN//PG9SIvqKEA4FvrNRo3KvzgdfE0hrjfxfQuhejQAQjt6QS/CC/E71Tih806y7fl1xDqfg+hASUIDZMhuIczHDsHAsEhQNtBgKx+G/oREVHzcu/sjU1/24Qn9k7VpuVWOOGFoWn4IS3UYoazGOxYuXuZ5Ug7nIG0U/eQ9lsJpOoKLEnoq5enrAy4nlyE9LNZuFrUs173yUUrfJbUA56dDNeJ/83vNrI674B7Nz9IQoIBr96cP0NEZCUe3zUBz3rvxueqyiek770Sik8WXUHMsmAz1qwSgx0rUJRfgStHM8R5NL8WIfWKDGkZTkhTtUG22hWA3/0D8JL8ibbTziPtYhnSflci9a4brhV5owJ26Ie6zXmRQI1A3ECozXWEuN1DB79ChHaUwslpmNH8DiE+cAgZ30itJSIii2Jvj7Xf+uPAo7eRAR8AQF8kIvKz14HYeMDRtH3QmgLn7LTAOTuJW1Lwxfp7SP3DAWl/eSK93Mek61vhHlpL7yHUKQMdvHIR2r4CoV1sUVZYhuh1j2nzeeEOQuXXEeqWhVDfQoSGShDawxHt+nrB9qH23H+GiIi0vp/wJcZ8/gTewiLMwXuQQQ1MmQJ8+GGT3I9zdlooQS0g89I9pB3OwM3kPDy9rq/RfBcPZ+H9X/6v3vfZs+Yy+s7qBUj0uxcLMlT4/HY8QrvZIyTSE626BwGtjNeBiIhI12OfjMH1lCfhffb7ysSPPgJGjgRGjTJfxWCBwc6GDRuwatUqZGRk4KGHHsKaNWswYMCAavMfPnwYc+fOxcWLF+Hj44MFCxZg2rRpzVhj0+Vl5OPyT3/cn0dTitTrCqRltUJagS9UcAfu7wrc/W9X8fsFFdLOFyAtTUDaLbEnx7ncxaT7yVGG9tLrCHW+g1DvPHgEhxidM+Pg7Yxndj3ZGE0kIqIHjVwO751rgG6HgPz8yvQpU4DffhP3OzMTiwp2du7cidmzZ2PDhg2IjIzEpk2bMGzYMCQnJ8Pf398g//Xr1zF8+HC88MIL+Pzzz3H8+HG89NJLaN26Nf7+97+boQX67l3NwfGtl5H6SxHSrkjFeTR5bZChbgOgY63Xj3pMjSvoDiWK0V5xEx3csvCPbqkI9C7C9P91NcjfVnILoY630cHrL4QGlSM0XInQPm4IHOAHmzahAEIbv5FEREQa7dsDa9cCkydXpmVlia//9z+zLU6xqDk7vXv3Ro8ePbBx40ZtWlhYGJ544gksX77cIP8rr7yC//73v0hJSdGmTZs2Db/++itOnDhRp3s25ZydA6vO4dEFPep9/crIeIx9qzv8+vpCpqyMSwW1gBdDDyGgbTlCO8kR2qsVggf5wjHQg6uciIjIvAQBGD0a+O47bVIRbHHtvd14aHZUo92mRc7ZKS0txdmzZ/Hqq6/qpUdFRSExMdHoNSdOnEBUlP4/XHR0NLZs2YKysjLYGNmIrqSkBCUlJdrXKpWqEWpv3NfrM+p1nRLFCFbcRFBvLwQOCjQ4L5FK8OGVwQ2sHRERUROQSIDNm4ETJ4A//8QpPIz/5z8ZC6YNMVuVLCbYuXv3LioqKuBVZUzPy8sLd+7cMXrNnTt3jOYvLy/H3bt34W3kaWTLly/Hm2++2XgVr0GHbnawSy9EEewNzkmgRqD8D4S6/IkQnwJ0CAVCuzsgtL8n/Pq0hUwZAiCkWepJRETUqFq3hrDlY3w99f/hF/u+eHi0P2xszbdhrMUEOxqSKsMwgiAYpNWW31i6RmxsLObOnat9rVKp4OfnV9/q1mjO7kfwvds5lFbIEOql0i7xDu3ngfYDfWHbyh+A4VwkIiKilk4yYjjGXIvCUwrzhxrmr8F9Hh4ekMlkBr04mZmZBr03Gm3atDGaXy6Xw93d3eg1SqUSSqWycSpdBwfu1X/ODhERUUsmtYBABwCk5q6AhkKhQM+ePZGQkKCXnpCQgH79+hm9pm/fvgb59+/fj4iICKPzdYiIiOjBYzHBDgDMnTsXH330ET7++GOkpKRgzpw5SE9P1+6bExsbi4kTJ2rzT5s2Db///jvmzp2LlJQUfPzxx9iyZQvmzZtnriYQERGRhbGM/qX7xo0bh+zsbCxZsgQZGRno3Lkz9uzZg4CAAABARkYG0tPTtfmDgoKwZ88ezJkzB++//z58fHzwn//8xyL22CEiIiLLYFH77JhDS3w2FhER0YPOlM9vixrGIiIiImpsDHaIiIjIqjHYISIiIqvGYIeIiIisGoMdIiIismoMdoiIiMiqMdghIiIiq8Zgh4iIiKwagx0iIiKyahb1uAhz0GwgrVKpzFwTIiIiqivN53ZdHgTxwAc7eXl5AAA/Pz8z14SIiIhMlZeXBxcXlxrzPPDPxlKr1bh9+zacnJwgkUgatWyVSgU/Pz/cvHnTKp+7Ze3tA6y/jWxfy2ftbWT7Wr6maqMgCMjLy4OPjw+k0ppn5TzwPTtSqRS+vr5Neg9nZ2er/SUGrL99gPW3ke1r+ay9jWxfy9cUbaytR0eDE5SJiIjIqjHYISIiIqvGYKcJKZVKvP7661AqleauSpOw9vYB1t9Gtq/ls/Y2sn0tnyW08YGfoExERETWjT07REREZNUY7BAREZFVY7BDREREVo3BDhEREVk1Bjsm2LBhA4KCgmBra4uePXvi6NGjNeY/fPgwevbsCVtbW7Rr1w4ffPCBQZ5vvvkGnTp1glKpRKdOnRAfH99U1a+VKe379ttvMXToULRu3RrOzs7o27cv9u3bp5dn69atkEgkBkdxcXFTN6VaprTx0KFDRut/6dIlvXwt9Wf43HPPGW3fQw89pM1jST/DI0eOYOTIkfDx8YFEIsF3331X6zUt7T1oahtb2vvQ1Pa1xPegqW1sSe/D5cuX4+GHH4aTkxM8PT3xxBNPIDU1tdbrLOF9yGCnjnbu3InZs2dj4cKFOH/+PAYMGIBhw4YhPT3daP7r169j+PDhGDBgAM6fP4/XXnsNs2bNwjfffKPNc+LECYwbNw4TJkzAr7/+igkTJuCpp57CqVOnmqtZWqa278iRIxg6dCj27NmDs2fPYvDgwRg5ciTOnz+vl8/Z2RkZGRl6h62tbXM0yYCpbdRITU3Vq39ISIj2XEv+Ga5du1avXTdv3oSbmxvGjh2rl89SfoYFBQXo2rUr1q9fX6f8Le09CJjexpb2PjS1fRot5T0ImN7GlvQ+PHz4MP75z3/i5MmTSEhIQHl5OaKiolBQUFDtNRbzPhSoTnr16iVMmzZNL61jx47Cq6++ajT/ggULhI4dO+qlTZ06VejTp4/29VNPPSX87W9/08sTHR0t/OMf/2ikWtedqe0zplOnTsKbb76pff3JJ58ILi4ujVXFBjO1jT/99JMAQMjJyam2TGv6GcbHxwsSiUS4ceOGNs3SfoYaAIT4+Pga87S092BVdWmjMZb+PtSoS/ta2nuwqvr8DFvS+zAzM1MAIBw+fLjaPJbyPmTPTh2Ulpbi7NmziIqK0kuPiopCYmKi0WtOnDhhkD86OhpnzpxBWVlZjXmqK7Op1Kd9VanVauTl5cHNzU0vPT8/HwEBAfD19cVjjz1m8Bdnc2lIG7t37w5vb28MGTIEP/30k945a/oZbtmyBY8++igCAgL00i3lZ2iqlvQebCyW/j6sr5bwHmwsLel9mJubCwAGv2+6LOV9yGCnDu7evYuKigp4eXnppXt5eeHOnTtGr7lz547R/OXl5bh7926Neaors6nUp31VvfvuuygoKMBTTz2lTevYsSO2bt2K//73v9ixYwdsbW0RGRmJy5cvN2r966I+bfT29sbmzZvxzTff4Ntvv0WHDh0wZMgQHDlyRJvHWn6GGRkZ2Lt3L6ZMmaKXbkk/Q1O1pPdgY7H096GpWtJ7sDG0pPehIAiYO3cu+vfvj86dO1ebz1Lehw/8U89NIZFI9F4LgmCQVlv+qummltmU6luXHTt24I033sDu3bvh6empTe/Tpw/69OmjfR0ZGYkePXpg3bp1+M9//tN4FTeBKW3s0KEDOnTooH3dt29f3Lx5E++88w7+7//+r15lNrX61mXr1q1o1aoVnnjiCb10S/wZmqKlvQcboiW9D+uqJb4HG6IlvQ9nzJiBCxcu4NixY7XmtYT3IXt26sDDwwMymcwgyszMzDSIRjXatGljNL9cLoe7u3uNeaors6nUp30aO3fuxOTJk/HVV1/h0UcfrTGvVCrFww8/bJa/RhrSRl19+vTRq781/AwFQcDHH3+MCRMmQKFQ1JjXnD9DU7Wk92BDtZT3YWOw1PdgQ7Wk9+HMmTPx3//+Fz/99BN8fX1rzGsp70MGO3WgUCjQs2dPJCQk6KUnJCSgX79+Rq/p27evQf79+/cjIiICNjY2NeaprsymUp/2AeJfks899xy++OILjBgxotb7CIKAX375Bd7e3g2us6nq28aqzp8/r1f/lv4zBMQVFleuXMHkyZNrvY85f4amaknvwYZoSe/DxmCp78GGagnvQ0EQMGPGDHz77bc4ePAggoKCar3GYt6HjTbV2cp9+eWXgo2NjbBlyxYhOTlZmD17tuDg4KCdMf/qq68KEyZM0Oa/du2aYG9vL8yZM0dITk4WtmzZItjY2Ai7du3S5jl+/Lggk8mEt99+W0hJSRHefvttQS6XCydPnrT49n3xxReCXC4X3n//fSEjI0N7/PXXX9o8b7zxhvDjjz8KV69eFc6fPy88//zzglwuF06dOtXs7RME09v43nvvCfHx8UJaWpqQlJQkvPrqqwIA4ZtvvtHmack/Q41nn31W6N27t9EyLelnmJeXJ5w/f144f/68AEBYvXq1cP78eeH3338XBKHlvwcFwfQ2trT3oanta2nvQUEwvY0aLeF9OH36dMHFxUU4dOiQ3u9bYWGhNo+lvg8Z7Jjg/fffFwICAgSFQiH06NFDb7ndpEmThIEDB+rlP3TokNC9e3dBoVAIgYGBwsaNGw3K/Prrr4UOHToINjY2QseOHfXexM3NlPYNHDhQAGBwTJo0SZtn9uzZgr+/v6BQKITWrVsLUVFRQmJiYjO2yJApbVyxYoXQvn17wdbWVnB1dRX69+8v/PDDDwZlttSfoSAIwl9//SXY2dkJmzdvNlqeJf0MNcuQq/uds4b3oKltbGnvQ1Pb1xLfg/X5PW0p70Nj7QIgfPLJJ9o8lvo+lNxvABEREZFV4pwdIiIismoMdoiIiMiqMdghIiIiq8Zgh4iIiKwagx0iIiKyagx2iIiIyKox2CEiIiKrxmCHiIiIrBqDHSIiIrJqDHaIiIjIqjHYISKrExoair59+6KoqEibJggC+vTpgwULFpixZkRkDgx2iMjq7Ny5E+fPn8fx48e1adu3b8f169exaNEiM9aMiMyBwQ4RWZ3u3buja9euuHTpEgCgsLAQsbGxWLp0KZydnc1cOyJqbgx2iMgqhYaGIjU1FQCwcuVKuLm5YfLkyWauFRGZg9zcFSAiagodOnTAkSNH8Mcff2DVqlX43//+B5lMZu5qEZEZsGeHiKySpmfn1VdfxdChQ/HII4+Yu0pEZCYSQRAEc1eCiKix/fLLL+jRowcUCgWSkpIQHBxs7ioRkZmwZ4eIrFJoaCgAYMaMGQx0iB5wDHaIyCoVFxdDEARMnDjR3FUhIjNjsENEVunXX3+FQqFAWFiYuatCRGbGYIeIrNKvv/6KTp06wcbGxtxVISIz4wRlIiIismrs2SEiIiKrxmCHiIiIrBqDHSIiIrJqDHaIiIjIqjHYISIiIqvGYIeIiIisGoMdIiIismoMdoiIiMiqMdghIiIiq8Zgh4iIiKza/wcXFiMstbIbXwAAAABJRU5ErkJggg==", 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\n", 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" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -1109,15 +1102,20 @@ }, { "cell_type": "markdown", - "id": "e4359eb1-7a58-4114-aef2-98a82b44c41f", "metadata": {}, "source": [ - "## 4. Using SymPy for the distance analysis " + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4 Using SymPy for the distance analysis " ] }, { "cell_type": "markdown", - "id": "304a0611-4e21-4664-b883-cf1de9377d9a", "metadata": {}, "source": [ "This section requires SymPy (!pip install sympy)" @@ -1125,8 +1123,7 @@ }, { "cell_type": "code", - "execution_count": 149, - "id": "46d553b6-3495-45fd-9b32-b0298d63fc8f", + "execution_count": 23, "metadata": { "tags": [] }, @@ -1142,7 +1139,7 @@ "[ (-L*lambda_1/2 + gamma*(L - mu) - lambda_2*mu/2)/(L - mu), (4*gamma**2*(-L + mu) + 2.0*lambda_1 + 2.0*lambda_2)/(4*(L - mu))]])" ] }, - "execution_count": 149, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -1187,8 +1184,7 @@ }, { "cell_type": "code", - "execution_count": 150, - "id": "ba73d008-d96f-4425-ae0f-ecb265a53601", + "execution_count": 24, "metadata": { "tags": [] }, @@ -1202,7 +1198,7 @@ "lambda_1 - lambda_2" ] }, - "execution_count": 150, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } @@ -1216,8 +1212,7 @@ }, { "cell_type": "code", - "execution_count": 151, - "id": "c95f8df2-1f84-43fb-80a7-405f12f3fa88", + "execution_count": 25, "metadata": { "tags": [] }, @@ -1225,15 +1220,15 @@ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{L \\lambda_{1} \\mu + \\left(L - \\mu\\right) \\left(\\rho - 1\\right)}{L - \\mu} & \\frac{- \\frac{L \\lambda_{1}}{2} + \\gamma \\left(L - \\mu\\right) - \\frac{\\lambda_{1} \\mu}{2}}{L - \\mu}\\\\\\frac{- \\frac{L \\lambda_{1}}{2} + \\gamma \\left(L - \\mu\\right) - \\frac{\\lambda_{1} \\mu}{2}}{L - \\mu} & \\frac{- L \\gamma^{2} + \\gamma^{2} \\mu + \\lambda_{1}}{L - \\mu}\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}\\frac{L \\lambda_{1} \\mu + \\left(L - \\mu\\right) \\left(\\rho - 1\\right)}{L - \\mu} & \\frac{- \\frac{L \\lambda_{1}}{2} + \\gamma \\left(L - \\mu\\right) - \\frac{\\lambda_{1} \\mu}{2}}{L - \\mu}\\\\\\frac{- \\frac{L \\lambda_{1}}{2} + \\gamma \\left(L - \\mu\\right) - \\frac{\\lambda_{1} \\mu}{2}}{L - \\mu} & \\frac{\\gamma^{2} \\left(- L + \\mu\\right) + \\lambda_{1}}{L - \\mu}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ (L*lambda_1*mu + (L - mu)*(rho - 1))/(L - mu), (-L*lambda_1/2 + gamma*(L - mu) - lambda_1*mu/2)/(L - mu)],\n", - "[(-L*lambda_1/2 + gamma*(L - mu) - lambda_1*mu/2)/(L - mu), (-L*gamma**2 + gamma**2*mu + lambda_1)/(L - mu)]])" + "[(-L*lambda_1/2 + gamma*(L - mu) - lambda_1*mu/2)/(L - mu), (gamma**2*(-L + mu) + lambda_1)/(L - mu)]])" ] }, - "execution_count": 151, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -1247,8 +1242,7 @@ }, { "cell_type": "code", - "execution_count": 153, - "id": "929299d6-c1d4-4fde-8360-ef593fd9be9b", + "execution_count": 26, "metadata": { "tags": [] }, @@ -1256,13 +1250,13 @@ { "data": { "text/latex": [ - "$\\displaystyle \\frac{\\lambda_{1} \\cdot \\left(4 L \\gamma^{2} \\mu - 4 L \\gamma + L \\lambda_{1} - 4 \\gamma \\mu - \\lambda_{1} \\mu + 4\\right)}{4 \\left(- L \\gamma^{2} + \\gamma^{2} \\mu + \\lambda_{1}\\right)}$" + "$\\displaystyle \\frac{\\lambda_{1} \\left(4 L \\gamma^{2} \\mu - 4 L \\gamma + L \\lambda_{1} - 4 \\gamma \\mu - \\lambda_{1} \\mu + 4\\right)}{4 \\left(- L \\gamma^{2} + \\gamma^{2} \\mu + \\lambda_{1}\\right)}$" ], "text/plain": [ "lambda_1*(4*L*gamma**2*mu - 4*L*gamma + L*lambda_1 - 4*gamma*mu - lambda_1*mu + 4)/(4*(-L*gamma**2 + gamma**2*mu + lambda_1))" ] }, - "execution_count": 153, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -1274,7 +1268,6 @@ }, { "cell_type": "markdown", - "id": "5863eb52-72f8-40b8-a472-13ac1a06e3ea", "metadata": {}, "source": [ "There are two possibilities for choosing $\\lambda_1$:\n", @@ -1287,8 +1280,7 @@ }, { "cell_type": "code", - "execution_count": 158, - "id": "82cd6e45-a792-4021-960b-c9fe02e4d4f5", + "execution_count": 27, "metadata": { "tags": [] }, @@ -1299,7 +1291,7 @@ "[2*gamma*(L*gamma - 1), 2*gamma*(-gamma*mu + 1)]" ] }, - "execution_count": 158, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -1312,7 +1304,6 @@ }, { "cell_type": "markdown", - "id": "9bd5f23e-1eac-4870-b9b4-5bdfa638aaba", "metadata": {}, "source": [ "The corresponding \"final\" expressions for that must be checked are therefore:" @@ -1320,8 +1311,7 @@ }, { "cell_type": "code", - "execution_count": 159, - "id": "7c9685dc-0cdb-4b2e-9eb0-67d47494b630", + "execution_count": 28, "metadata": { "tags": [] }, @@ -1332,7 +1322,7 @@ "[(L*gamma - 1)**2, (gamma*mu - 1)**2]" ] }, - "execution_count": 159, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -1346,7 +1336,6 @@ }, { "cell_type": "markdown", - "id": "1edb17da-6d63-4658-a961-05f9cd09df09", "metadata": {}, "source": [ "... and we are done!" @@ -1354,15 +1343,20 @@ }, { "cell_type": "markdown", - "id": "17d79ecf-2254-4eba-89ba-9270263485b0", "metadata": {}, "source": [ - "## 5. Using SymPy for the function value accuracy analysis " + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 5 Using SymPy for the function value accuracy analysis " ] }, { "cell_type": "markdown", - "id": "cbc80f5f-7e6f-4712-a040-d5967aeebdb9", "metadata": {}, "source": [ "... same game with the already-simplified LMI. But using a few shortcuts." @@ -1370,8 +1364,7 @@ }, { "cell_type": "code", - "execution_count": 173, - "id": "ec070ccd-4be9-48b1-a407-303030523631", + "execution_count": 29, "metadata": { "tags": [] }, @@ -1379,16 +1372,16 @@ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{L \\mu \\left(\\lambda_{1} + \\lambda_{2}\\right)}{2 \\left(L - \\mu\\right)} & \\frac{- L \\lambda_{1} - \\lambda_{2} \\mu}{2 \\left(L - \\mu\\right)} & - \\frac{L \\lambda_{2}}{2 L - 2 \\mu}\\\\\\frac{- L \\lambda_{1} - \\lambda_{2} \\mu}{2 \\left(L - \\mu\\right)} & \\frac{L \\lambda_{1} + \\lambda_{2} \\mu + \\lambda_{4} \\left(L - \\mu\\right)}{2 L \\left(L - \\mu\\right)} & \\frac{\\lambda_{2}}{2 \\left(L - \\mu\\right)}\\\\- \\frac{L \\lambda_{2}}{2 L - 2 \\mu} & \\frac{\\lambda_{2}}{2 \\left(L - \\mu\\right)} & \\frac{0.5 \\left(\\lambda_{2} + \\lambda_{4}\\right)}{L - \\mu}\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}\\frac{L \\mu \\left(\\lambda_{1} + \\lambda_{2}\\right)}{2 \\left(L - \\mu\\right)} & - \\frac{L \\lambda_{1} + \\lambda_{2} \\mu}{2 L - 2 \\mu} & - \\frac{L \\lambda_{2}}{2 L - 2 \\mu}\\\\- \\frac{L \\lambda_{1} + \\lambda_{2} \\mu}{2 L - 2 \\mu} & \\frac{L \\lambda_{1} + \\lambda_{2} \\mu + \\lambda_{4} \\left(L - \\mu\\right)}{2 L \\left(L - \\mu\\right)} & \\frac{\\lambda_{2}}{2 \\left(L - \\mu\\right)}\\\\- \\frac{L \\lambda_{2}}{2 L - 2 \\mu} & \\frac{\\lambda_{2}}{2 \\left(L - \\mu\\right)} & \\frac{0.5 \\left(\\lambda_{2} + \\lambda_{4}\\right)}{L - \\mu}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", - "[ L*mu*(lambda_1 + lambda_2)/(2*(L - mu)), (-L*lambda_1 - lambda_2*mu)/(2*(L - mu)), -L*lambda_2/(2*L - 2*mu)],\n", - "[(-L*lambda_1 - lambda_2*mu)/(2*(L - mu)), (L*lambda_1 + lambda_2*mu + lambda_4*(L - mu))/(2*L*(L - mu)), lambda_2/(2*(L - mu))],\n", + "[ L*mu*(lambda_1 + lambda_2)/(2*(L - mu)), -(L*lambda_1 + lambda_2*mu)/(2*L - 2*mu), -L*lambda_2/(2*L - 2*mu)],\n", + "[-(L*lambda_1 + lambda_2*mu)/(2*L - 2*mu), (L*lambda_1 + lambda_2*mu + lambda_4*(L - mu))/(2*L*(L - mu)), lambda_2/(2*(L - mu))],\n", "[ -L*lambda_2/(2*L - 2*mu), lambda_2/(2*(L - mu)), 0.5*(lambda_2 + lambda_4)/(L - mu)]])" ] }, - "execution_count": 173, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -1438,8 +1431,7 @@ }, { "cell_type": "code", - "execution_count": 188, - "id": "27cbfe9c-48fb-4e4d-a315-9f6f21b44268", + "execution_count": 30, "metadata": { "tags": [] }, @@ -1450,7 +1442,7 @@ "[lambda_1 - lambda_4 + rho**2, lambda_2 + lambda_4 - 1]" ] }, - "execution_count": 188, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -1465,8 +1457,7 @@ }, { "cell_type": "code", - "execution_count": 192, - "id": "cf51b9da-6147-4576-8786-d4685127c192", + "execution_count": 31, "metadata": { "tags": [] }, @@ -1474,16 +1465,16 @@ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{L \\mu \\left(1 - \\rho^{2}\\right)}{2 \\left(L - \\mu\\right)} & \\frac{- L \\lambda_{1} + \\mu \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)} & \\frac{L \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)}\\\\\\frac{- L \\lambda_{1} + \\mu \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)} & \\frac{L \\lambda_{1} - \\mu \\left(\\lambda_{1} + \\rho^{2} - 1\\right) + \\left(L - \\mu\\right) \\left(\\lambda_{1} + \\rho^{2}\\right)}{2 L \\left(L - \\mu\\right)} & \\frac{- \\lambda_{1} - \\rho^{2} + 1}{2 \\left(L - \\mu\\right)}\\\\\\frac{L \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)} & \\frac{- \\lambda_{1} - \\rho^{2} + 1}{2 \\left(L - \\mu\\right)} & \\frac{0.5}{L - \\mu}\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}- \\frac{L \\mu \\left(\\rho^{2} - 1\\right)}{2 L - 2 \\mu} & \\frac{- L \\lambda_{1} + \\mu \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)} & \\frac{L \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)}\\\\\\frac{- L \\lambda_{1} + \\mu \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)} & \\frac{L \\lambda_{1} - \\mu \\left(\\lambda_{1} + \\rho^{2} - 1\\right) + \\left(L - \\mu\\right) \\left(\\lambda_{1} + \\rho^{2}\\right)}{2 L \\left(L - \\mu\\right)} & \\frac{- \\lambda_{1} - \\rho^{2} + 1}{2 \\left(L - \\mu\\right)}\\\\\\frac{L \\left(\\lambda_{1} + \\rho^{2} - 1\\right)}{2 \\left(L - \\mu\\right)} & \\frac{- \\lambda_{1} - \\rho^{2} + 1}{2 \\left(L - \\mu\\right)} & \\frac{0.5}{L - \\mu}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", - "[ L*mu*(1 - rho**2)/(2*(L - mu)), (-L*lambda_1 + mu*(lambda_1 + rho**2 - 1))/(2*(L - mu)), L*(lambda_1 + rho**2 - 1)/(2*(L - mu))],\n", + "[ -L*mu*(rho**2 - 1)/(2*L - 2*mu), (-L*lambda_1 + mu*(lambda_1 + rho**2 - 1))/(2*(L - mu)), L*(lambda_1 + rho**2 - 1)/(2*(L - mu))],\n", "[(-L*lambda_1 + mu*(lambda_1 + rho**2 - 1))/(2*(L - mu)), (L*lambda_1 - mu*(lambda_1 + rho**2 - 1) + (L - mu)*(lambda_1 + rho**2))/(2*L*(L - mu)), (-lambda_1 - rho**2 + 1)/(2*(L - mu))],\n", "[ L*(lambda_1 + rho**2 - 1)/(2*(L - mu)), (-lambda_1 - rho**2 + 1)/(2*(L - mu)), 0.5/(L - mu)]])" ] }, - "execution_count": 192, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -1498,8 +1489,7 @@ }, { "cell_type": "code", - "execution_count": 193, - "id": "334f59d7-e6d6-4a2d-82ac-12472bdf90f9", + "execution_count": 32, "metadata": { "tags": [] }, @@ -1507,7 +1497,7 @@ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}\\frac{\\mu^{2} \\left(L - \\frac{\\mu}{2}\\right)}{L \\left(L - \\mu\\right)} & \\frac{- L^{3} \\lambda_{1} + \\mu \\left(L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}\\right)}{2 L^{2} \\left(L - \\mu\\right)} & \\frac{L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}}{2 L \\left(L - \\mu\\right)}\\\\\\frac{- L^{3} \\lambda_{1} + \\mu \\left(L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}\\right)}{2 L^{2} \\left(L - \\mu\\right)} & \\frac{L^{3} \\lambda_{1} - \\mu \\left(L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}\\right) + \\left(L - \\mu\\right) \\left(L^{2} \\lambda_{1} + \\left(L - \\mu\\right)^{2}\\right)}{2 L^{3} \\left(L - \\mu\\right)} & \\frac{L^{2} \\cdot \\left(1 - \\lambda_{1}\\right) - \\left(L - \\mu\\right)^{2}}{2 L^{2} \\left(L - \\mu\\right)}\\\\\\frac{L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}}{2 L \\left(L - \\mu\\right)} & \\frac{L^{2} \\cdot \\left(1 - \\lambda_{1}\\right) - \\left(L - \\mu\\right)^{2}}{2 L^{2} \\left(L - \\mu\\right)} & \\frac{0.5}{L - \\mu}\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}\\frac{\\mu^{2} \\left(L - \\frac{\\mu}{2}\\right)}{L \\left(L - \\mu\\right)} & \\frac{- L^{3} \\lambda_{1} + \\mu \\left(L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}\\right)}{2 L^{2} \\left(L - \\mu\\right)} & \\frac{L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}}{2 L \\left(L - \\mu\\right)}\\\\\\frac{- L^{3} \\lambda_{1} + \\mu \\left(L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}\\right)}{2 L^{2} \\left(L - \\mu\\right)} & \\frac{L^{3} \\lambda_{1} - \\mu \\left(L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}\\right) + \\left(L - \\mu\\right) \\left(L^{2} \\lambda_{1} + \\left(L - \\mu\\right)^{2}\\right)}{2 L^{3} \\left(L - \\mu\\right)} & \\frac{L^{2} \\left(1 - \\lambda_{1}\\right) - \\left(L - \\mu\\right)^{2}}{2 L^{2} \\left(L - \\mu\\right)}\\\\\\frac{L^{2} \\left(\\lambda_{1} - 1\\right) + \\left(L - \\mu\\right)^{2}}{2 L \\left(L - \\mu\\right)} & \\frac{L^{2} \\left(1 - \\lambda_{1}\\right) - \\left(L - \\mu\\right)^{2}}{2 L^{2} \\left(L - \\mu\\right)} & \\frac{0.5}{L - \\mu}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", @@ -1516,7 +1506,7 @@ "[ (L**2*(lambda_1 - 1) + (L - mu)**2)/(2*L*(L - mu)), (L**2*(1 - lambda_1) - (L - mu)**2)/(2*L**2*(L - mu)), 0.5/(L - mu)]])" ] }, - "execution_count": 193, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -1528,8 +1518,7 @@ }, { "cell_type": "code", - "execution_count": 194, - "id": "baa01841-1ac3-4c5f-ae26-9e22699117b7", + "execution_count": 33, "metadata": { "tags": [] }, @@ -1543,7 +1532,7 @@ "mu*(L - mu)/L**2" ] }, - "execution_count": 194, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -1555,8 +1544,7 @@ }, { "cell_type": "code", - "execution_count": 195, - "id": "ce0cbfc9-7549-48b1-af42-b74a1bad3f9e", + "execution_count": 34, "metadata": { "tags": [] }, @@ -1570,7 +1558,7 @@ "mu*(1 - mu/L)/L" ] }, - "execution_count": 195, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -1581,15 +1569,20 @@ }, { "cell_type": "markdown", - "id": "0a48916a-1e37-440f-8160-025489d53d32", "metadata": {}, "source": [ - "## 6. Using symbolic regression (PySR) " + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 6 Using symbolic regression (PySR) " ] }, { "cell_type": "markdown", - "id": "c90bea86", "metadata": {}, "source": [ "Up to this point, two complementary approaches have been used to obtain the Lagrange multipliers needed to reconstruct a proof:\n", @@ -1607,7 +1600,6 @@ }, { "cell_type": "markdown", - "id": "3ca45317", "metadata": {}, "source": [ "First, imagine that you do not know the closed form of $\\lambda_1(\\gamma)$ given at the end of Section 3. The next cell automatically learns the closed form of $\\lambda_1(\\gamma)$ using measurements from PEPit:" @@ -1615,18 +1607,9 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "1300c9e0-4d69-4183-a57e-00c5a1ccaa0b", + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Detected IPython. Loading juliacall extension. See https://juliapy.github.io/PythonCall.jl/stable/compat/#IPython\n" - ] - } - ], + "outputs": [], "source": [ "import numpy as np\n", "from pysr import PySRRegressor\n", @@ -1662,25 +1645,15 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "51806a09", + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1.0 - rho) * rho\n" - ] - } - ], + "outputs": [], "source": [ "print(model.get_best().equation)" ] }, { "cell_type": "markdown", - "id": "293091d7", "metadata": {}, "source": [ "This recovers the expression $\\lambda_1(\\gamma)= (1-\\rho(\\gamma))\\rho(\\gamma)$. This was a simple, univariate function, which is where symbolic regression works best.\n", @@ -1690,8 +1663,7 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "59855db5", + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -1734,34 +1706,31 @@ }, { "cell_type": "code", - "execution_count": 8, - "id": "d8f49ee1", + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "square(max(1.0000066 - (g * mu), (g * L) + -0.99999446))\n" - ] - } - ], + "outputs": [], "source": [ "print(model.get_best().equation)" ] }, { "cell_type": "markdown", - "id": "7e518abc", "metadata": {}, "source": [ "PySR was able to effectively learn this convergence rate, which is a function of 3 different variables. This did, however, require guiding it to use the max and square operators. In other problems, a larger number of operators should be used, which does decrease the speed of convergence of the heuristic. This is why this type of approach works best for problems with relatively simple closed forms. When it works, it can save a lot of time." ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] } ], "metadata": { "kernelspec": { - "display_name": "pepit", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -1775,7 +1744,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.14.2" + "version": "3.7.9" } }, "nbformat": 4, From 60e5bfcb5003adcd36e15f43087ff69f6aaa7a41 Mon Sep 17 00:00:00 2001 From: baptiste Date: Sat, 14 Feb 2026 16:18:54 +0100 Subject: [PATCH 3/7] Include Notebooks in doc, make all necessary modifications and refresh conf.py --- .gitignore | 1 + docs/requirements.txt | 2 +- docs/source/_static/custom.css | 27 +++++++ docs/source/conf.py | 135 +++++++++++++++++++-------------- docs/source/index.rst | 1 + docs/source/tutorials.rst | 9 +++ 6 files changed, 115 insertions(+), 60 deletions(-) create mode 100644 docs/source/_static/custom.css create mode 100644 docs/source/tutorials.rst diff --git a/.gitignore b/.gitignore index f7d2b80e..52ba1070 100644 --- a/.gitignore +++ b/.gitignore @@ -137,3 +137,4 @@ dmypy.json # Documentation docs/autodocgen-output docs/build +docs/source/notebooks_folder diff --git a/docs/requirements.txt b/docs/requirements.txt index 1c2ac5ab..81eebfe9 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -1,6 +1,6 @@ sphinx sphinx-autodocgen sphinx-rtd-theme -myst-parser +myst-nb easydev -r ../requirements.txt diff --git a/docs/source/_static/custom.css b/docs/source/_static/custom.css new file mode 100644 index 00000000..071dbbe5 --- /dev/null +++ b/docs/source/_static/custom.css @@ -0,0 +1,27 @@ +/* 1. Fix the double math numbering */ +/* This targets the MyST-generated label that floats above the equation */ +div.myst-math-label { + display: none !important; +} + +/* 2. Hide "1." from the main Title */ +/* This targets the auto-numbering span inside the H1 tag */ +h1 span.section-number { + display: none !important; +} + +/* 3. Layout Fixes */ +/* Ensures the actual MathJax number on the right has space */ +div.math { + overflow: visible !important; + width: 100%; +} + +/* 4. Kill the 'ghost' equation numbers generated by Sphinx/MyST */ +span.eqno { + display: none !important; + visibility: hidden !important; + position: absolute !important; /* Move it out of the layout flow */ + width: 0 !important; + height: 0 !important; +} diff --git a/docs/source/conf.py b/docs/source/conf.py index 593ccc8c..e8e5e1a8 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -1,24 +1,12 @@ -# Configuration file for the Sphinx documentation builder. -# -# This file only contains a selection of the most common options. For a full -# list see the documentation: -# https://www.sphinx-doc.org/en/master/usage/configuration.html - -# -- Path setup -------------------------------------------------------------- - -# If extensions (or modules to document with autodoc) are in another directory, -# add these directories to sys.path here. If the directory is relative to the -# documentation root, use os.path.abspath to make it absolute, like shown here. -# -# import os import os import sys +import shutil +import PEPit # The module you're documenting (assumes you've added the project root dir to sys.path) sys.path.insert(0, os.path.abspath('../..')) # -- Project information ----------------------------------------------------- - project = 'PEPit' copyright = '2021, PEPit Contributors' author = 'PEPit Contributors' @@ -32,7 +20,6 @@ # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = [ - # 'easydev.copybutton', 'sphinx.ext.autodoc', 'sphinx.ext.doctest', 'sphinx.ext.intersphinx', @@ -43,68 +30,98 @@ 'sphinx.ext.viewcode', 'sphinx.ext.napoleon', 'sphinx.ext.autosummary', - # 'sphinxcontrib_autodocgen', - 'myst_parser', + 'myst_nb', ] -napoleon_custom_sections = [('Returns', 'params_style'), - ('Attributes', 'params_style')] +source_suffix = { + '.rst': 'restructuredtext', + '.md': 'markdown', + '.ipynb': 'myst-nb', +} -import PEPit +exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store', '**.ipynb_checkpoints'] +templates_path = ['_templates'] + +# -- MyST & Notebook Settings ------------------------------------------------ +nb_execution_mode = "off" +myst_title_to_header = True +myst_heading_anchors = None # Set to None to avoid Jupyter TOC conflicts +myst_dmath_allow_labels = False # Disable MyST labels to stop double-numbering +myst_update_mathjax = False # Let MathJax 3 handle its own configuration +myst_dmath_double_inline = True + +myst_enable_extensions = [ + "dollarmath", + "amsmath", + "colon_fence", + "deflist", + "html_image", + "html_admonition", +] + +# -- MathJax 3 Settings ------------------------------------------------------ +mathjax3_config = { + 'tex': { + 'inlineMath': [['$', '$'], ['\\(', '\\)']], + 'displayMath': [['$$', '$$'], ['\\[', '\\]']], + 'processEscapes': True, + 'tags': 'ams', # AMS numbering (1), (2) on the right + 'useLabelIds': True + }, + 'options': { + 'processHtmlClass': 'tex2jax_process|mathjax_process|math|output_area', + } +} + +# -- HTML Output Settings --------------------------------------------------- +html_theme = 'sphinx_rtd_theme' +html_static_path = ['_static'] +html_secnumber_suffix = " " +# -- Napoleon settings ------------------------------------------------------- +napoleon_google_docstring = True +napoleon_numpy_docstring = True +napoleon_include_init_with_doc = False +napoleon_include_private_with_doc = False +napoleon_include_special_with_doc = False + +# -- Napoleon & Autodoc ----------------------------------------------------- +napoleon_custom_sections = [('Returns', 'params_style'), ('Attributes', 'params_style')] +autoclass_content = 'both' autodocgen_config = [{ 'modules': [PEPit], 'generated_source_dir': './autodocgen-output/', - # if module matches this then it and any of its submodules will be skipped + # Skips any module with "__" in the name or specific internal modules 'skip_module_regex': '(.*[.]__|myskippedmodule)', - # produce a text file containing a list of everything documented. you can use this in a test to notice - # when you've intentionally added/removed/changed a documented API + # Log file to track exactly what is being documented 'write_documented_items_output_file': 'autodocgen_documented_items.txt', - # customize autodoc on a per-module basis + # Custom options for specific classes if needed 'autodoc_options_decider': { - 'mymodule.FooBar': {'inherited-members': True}, + 'PEPit.FooBar': {'inherited-members': True}, }, - # choose a different title for specific modules, e.g. the toplevel one - 'module_title_decider': lambda modulename: 'API Reference' if modulename == 'mymodule' else modulename, + # Renames the top-level module to "API Reference" in the TOC + 'module_title_decider': lambda modulename: 'API Reference' if modulename == 'PEPit' else modulename, }] -autoclass_content = 'both' - -# Include or not the special methods -napoleon_include_special_with_doc = False +# -- Automated Notebook Copying --------------------------------------------- +current_dir = os.path.dirname(__file__) +nb_source = os.path.abspath(os.path.join(current_dir, '../../ressources/demo/')) +nb_dest = os.path.join(current_dir, 'notebooks_folder') -# Add any paths that contain templates here, relative to this directory. -templates_path = ['_templates'] +if os.path.exists(nb_dest): + shutil.rmtree(nb_dest) +os.makedirs(nb_dest) -# List of patterns, relative to source directory, that match files and -# directories to ignore when looking for source files. -# This pattern also affects html_static_path and html_extra_path. -exclude_patterns = [] +if os.path.exists(nb_source): + for file in os.listdir(nb_source): + if file.endswith('.ipynb'): + shutil.copy2(os.path.join(nb_source, file), os.path.join(nb_dest, file)) -# -- Options for HTML output ------------------------------------------------- -# The theme to use for HTML and HTML Help pages. See the documentation for -# a list of builtin themes. -# -html_theme = 'sphinx_rtd_theme' - -# # Make the copy paste possible for any example code in documentation -# import easydev -# -# jscopybutton_path = easydev.copybutton.get_copybutton_path() -# -# # if not os.path.isdir('_static'): -# # os.mkdir('_static') -# -# import shutil -# -# shutil.copy(jscopybutton_path, '_static') - -# Add any paths that contain custom static files (such as style sheets) here, -# relative to this directory. They are copied after the builtin static files, -# so a file named "default.css" will overwrite the builtin "default.css". -html_static_path = ['_static'] +# -- Setup Function --------------------------------------------------------- +def setup(app): + app.add_css_file('custom.css') diff --git a/docs/source/index.rst b/docs/source/index.rst index 612be826..e33106bb 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -14,6 +14,7 @@ Welcome to PEPit's documentation! quickstart api examples + tutorials whatsnew contributing diff --git a/docs/source/tutorials.rst b/docs/source/tutorials.rst new file mode 100644 index 00000000..f3e00b79 --- /dev/null +++ b/docs/source/tutorials.rst @@ -0,0 +1,9 @@ +Tutorials +========= + +.. toctree:: + :maxdepth: 1 + :caption: Contents: + + Finding worst-case guarantees + Extracting a proof From 823bde212ff17f89c152ec2d668ea57452c07ca4 Mon Sep 17 00:00:00 2001 From: baptiste Date: Sat, 14 Feb 2026 16:28:43 +0100 Subject: [PATCH 4/7] fix conf.py --- docs/source/conf.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/conf.py b/docs/source/conf.py index e8e5e1a8..774da6ab 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -1,10 +1,10 @@ import os import sys import shutil -import PEPit # The module you're documenting (assumes you've added the project root dir to sys.path) sys.path.insert(0, os.path.abspath('../..')) +import PEPit # -- Project information ----------------------------------------------------- project = 'PEPit' From 10e8c28146033a15e498efd5436be83b4ef50234 Mon Sep 17 00:00:00 2001 From: baptiste Date: Sat, 14 Feb 2026 23:58:41 +0100 Subject: [PATCH 5/7] fix conf.py --- docs/source/conf.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/conf.py b/docs/source/conf.py index 774da6ab..7b5d5f22 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -45,7 +45,7 @@ # -- MyST & Notebook Settings ------------------------------------------------ nb_execution_mode = "off" myst_title_to_header = True -myst_heading_anchors = None # Set to None to avoid Jupyter TOC conflicts +# myst_heading_anchors = None # Set to None to avoid Jupyter TOC conflicts myst_dmath_allow_labels = False # Disable MyST labels to stop double-numbering myst_update_mathjax = False # Let MathJax 3 handle its own configuration myst_dmath_double_inline = True From b4de0bad9bcc0094a35a8efcffd2ba7e504fa949 Mon Sep 17 00:00:00 2001 From: baptiste Date: Sun, 15 Feb 2026 00:16:08 +0100 Subject: [PATCH 6/7] fix css file --- docs/source/_static/custom.css | 10 ++-------- docs/source/conf.py | 1 - 2 files changed, 2 insertions(+), 9 deletions(-) diff --git a/docs/source/_static/custom.css b/docs/source/_static/custom.css index 071dbbe5..3bf934fc 100644 --- a/docs/source/_static/custom.css +++ b/docs/source/_static/custom.css @@ -4,20 +4,14 @@ div.myst-math-label { display: none !important; } -/* 2. Hide "1." from the main Title */ -/* This targets the auto-numbering span inside the H1 tag */ -h1 span.section-number { - display: none !important; -} - -/* 3. Layout Fixes */ +/* 2. Layout Fixes */ /* Ensures the actual MathJax number on the right has space */ div.math { overflow: visible !important; width: 100%; } -/* 4. Kill the 'ghost' equation numbers generated by Sphinx/MyST */ +/* 3. Kill the 'ghost' equation numbers generated by Sphinx/MyST */ span.eqno { display: none !important; visibility: hidden !important; diff --git a/docs/source/conf.py b/docs/source/conf.py index 7b5d5f22..fa639cb9 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -45,7 +45,6 @@ # -- MyST & Notebook Settings ------------------------------------------------ nb_execution_mode = "off" myst_title_to_header = True -# myst_heading_anchors = None # Set to None to avoid Jupyter TOC conflicts myst_dmath_allow_labels = False # Disable MyST labels to stop double-numbering myst_update_mathjax = False # Let MathJax 3 handle its own configuration myst_dmath_double_inline = True From f4e0be9ac07c58d2cc0eb9aaa549cee7cb620d91 Mon Sep 17 00:00:00 2001 From: baptiste Date: Sun, 15 Feb 2026 00:16:24 +0100 Subject: [PATCH 7/7] Fix typo in PEPit_demo.ipynb --- ressources/demo/PEPit_demo.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ressources/demo/PEPit_demo.ipynb b/ressources/demo/PEPit_demo.ipynb index bd66af38..d845153c 100644 --- a/ressources/demo/PEPit_demo.ipynb +++ b/ressources/demo/PEPit_demo.ipynb @@ -1123,7 +1123,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Thoeretical guarantee" + "#### Theoretical guarantee" ] }, {