▶ generate random variables and measure their statistical properties,
\n",
"
▶ compute and manipulate histograms,
\n",
"
▶ use special functions and physical constants,
\n",
"
▶ fit a set of data with a function,
\n",
"
▶ read and write data (text or figures).
\n",
"
"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "88363a16-e64c-467f-82b6-b72570ff7ce0",
"metadata": {},
"source": [
"I. Fourier transform\n",
"\n",
"1) Mathematical reminders\n",
"\n",
"You can also consult §IV.1.1 of the lectures notes for another presentation.\n",
"\n",
"a) Definitions and conventions\n",
"\n",
"The Fourier transform generalizes the Fourier series to non-periodic functions. \n",
"\n",
"Let $s(t)$ be a time-dependent signal (real or complex) and $\\tilde{s}(f)$ its Fourier transform: \n",
"$$\\displaystyle \\tilde{s}(f)=\\int_{-\\infty}^{+\\infty}\\mathrm{d}t\\,s(t)e^{-\\mathrm{i}2\\pi ft}.$$ \n",
"\n",
"The Fourier transform is invertible:\n",
"\n",
"$$\\displaystyle s(t)=\\int_{-\\infty}^{+\\infty}\\mathrm{d}f\\,\\tilde{s}(f)e^{\\mathrm{i}2\\pi ft}.$$\n",
"\n",
"In practice, we can never measure the entire signal, we only have a finite number of samples. In other words, the value of $s(t)$ is only known at a finite number $N$ of points regularly spaced by $\\delta t$ ($f_\\mathrm{s}=1/\\delta t$ is the sampling frequency). Thus, $s_k \\equiv s(t_k)$, with $t_k \\equiv k\\delta t$, and $k = 0, \\dots , N − 1$.\n",
"\n",
"Trying to apply the Fourier transform to such a signal (by approximating the integral by a Riemann sum) would yield:\n",
"$$\\tilde{s}(f)=\\delta ts_0e^{-\\mathrm{i}2\\pi f(0\\times \\delta t)}+\\delta ts_1e^{-\\mathrm{i}2\\pi f(\\delta t)}+\\dots \\delta ts_k e^{-\\mathrm{i}2\\pi f(k\\delta t)}+\\dots +\\delta ts_{N-1}e^{-\\mathrm{i}2\\pi f[(N-1)\\delta t]}=\\delta t\\sum_{k=0}^{N-1}s_ke^{-\\mathrm{i}2\\pi k f \\delta t}.$$\n",
"It is then obvious that $\\tilde{s}(f+f_\\mathrm{s})=\\tilde{s}(f+1/\\delta t)=\\tilde{s}(f)$. Said differently, because of the time sampling, the Fourier transform is now periodic of period equal to the sampling frequency $f_\\mathrm{s}$. Therefore, we can restrict ourselves to the frequency range $[-1/(2\\delta t),\\, 1/(2\\delta t)[$. We note that the maximum frequency we can probe is half the sampling frequency. The total frequency range that you can probe is inversely proportional to the time discretization: the smaller the time discretization, the larger the frequency range!\n",
"\n",
"Moreover, you cannot evaluate the above formula for any frequency $f\\in\\mathbb{R}$, because your signal is not infinitely long. Indeed, very loosely speaking, the Fourier transform $\\tilde{s}(f)$ measures the amount of oscillation of the signal at frequency $f$. Because the total duration of the signal is $N\\delta t$, you cannot detect oscillatory patterns of period larger than $N\\delta t$, and consequently you cannot probe frequencies smaller than $1/(N\\delta t)$ (except $f=0$ of course). In other words, the minimum strictly positive frequency you can probe (which corresponds to your frequency resolution) is inversely proportional to the total duration of the signal: the longer the signal, the thinner the frequency resolution! \n",
"\n",
"It turns out that you do not need to compute the $\\tilde{s}(f)$ for all frequencies $f\\in[-1/(2\\delta t),\\, -1/(N\\delta t)]\\times\\lbrace0\\rbrace\\times[1/(N\\delta t),\\,1/(2\\delta t)[$. You just need to evaluate the Fourier transform for $N$ discrete frequencies $$\n",
"f_n=\\begin{cases}\\displaystyle \\frac{n}{N\\delta t}\\quad \\text{for}\\quad n=0,\\dots,N/2-1,\\\\[0.8em]\n",
"\\displaystyle \\frac{n-N}{N\\delta t}\\quad \\text{for}\\quad n=N/2,..,N-1.\n",
"\\end{cases}$$\n",
"The value of the Fourier transform for these $N$ discrete frequencies is then given by the Discrete Fourier Transform (DFT):\n",
"$$\\tilde s_n=\\sum_{k=0}^{N-1}s_ke^{-\\mathrm{i}2\\pi kn/N}.$$\n",
"(We have removed the multiplicative factor if you compare with the previous equation.)\n",
"\n",
"The reason why we can restrict ourselves to these $N$ discrete frequencies is because the DFT is invertible, and that you can resconstruct the original signal from it:\n",
"$$s_k=\\dfrac{1}{N}\\sum_{n=0}^{N-1}\\tilde s_ne^{\\mathrm{i}2\\pi kn/N}.$$\n",
"This formula looks very similar to the inverse Fourier transform for infinitely-long time-continuous signals.\n",
"\n",
"b) Spectrum of a signal\n",
"\n",
"Because the DFT is a complex number, one usually considers the spectrum $\\vert\\tilde s(f)\\vert$ of a signal defined as the modulus of the DFT. The power spectrum is defined as the squared spectrum $\\mathcal{S}(f)=\\vert\\tilde s(f)\\vert^2$. Loosely speaking, the power spectrum is a strictly positive quantity which tells you the amount of \"energy\" in your signal at each frequency. This \"energy\" interpretation can be made more obvious thanks to the Plancherel-Parseval theorem:\n",
"$$\\sum_{k=0}^{N-1}\\vert s_k\\vert^2=\\frac{1}{N}\\sum_{n=0}^{N-1}\\vert\\tilde s_n\\vert^2.$$\n",
"\n",
"c) Aliasing\n",
"\n",
"As mentioned above, the time sampling of a continuous-time signal $s(t)$ results in a periodic Fourier transform of period $f_\\mathrm{s}$ (the sampling frequency). \n",
"\n",
"Consequently, the DFT is a good approximate of the Fourier transform $\\tilde{s}(f)$ of the original signal only if $\\tilde{s}(f)$ is periodic of period $f_\\mathrm{s}$. Obviously, this is verified if $\\tilde{s}(f)$ vanishes for $\\vert{f}\\vert>f_\\mathrm{s}/2$, or if the maximum frequency $f_\\mathrm{max}$ (in absolute value) in the Fourier transform of $s(t)$ is such that $f_\\mathrm{max} We recover the Nyquist-Shannon sampling theorem, which tells you that if you want to reconstruct a signal, you have to choose the sampling frequency such that it is twice larger than the maximum frequency in the spectrum of the signal you want to reconstruct.\n",
"\n",
"If the above condition is not verified, i.e., if the Fourier transform presents frequencies larger than $f_\\mathrm{s}/2$, then ghosts will appear in the DFT. This phenomenon is called aliasing. Frequencies $f>f_\\mathrm{s}/2$ will \"fold\" back in the range $[-f_\\mathrm{s}/2,\\, f_\\mathrm{s}/2[$ and will appear as ghosts of frequencies $\\pm f+pf_\\mathrm{s}$ with $p\\in\\mathbb{Z}$. In other words, frequencies above the Nyquist frequency pollute the spectrum obtained by DFT at lower frequencies, and the inverse DFT no longer allows the original discrete signal to be recovered.\n",
"\n",
"2) Calculation with NumPy\n",
"\n",
"a) The algorithm\n",
"\n",
"The algorithm used to compute DFTs in Python is called the Fast Fourier Transform (FFT) algorithm. Because this algorithm is heavily used to compute DFTs, people often talk about FFTs rather than DFTs.\n",
"\n",
"b) Implementation\n",
"\n",
"The calculation of the DFT of a signal is done via the function fft of the fft module in the NumPy package. The frequencies at which the DFT is calculated can be returned by the function fftfreq. The module fft has other functions which will not be discussed in this notebook, but you can consult the documentation for more information: https://numpy.org/doc/stable/reference/routines.fft.html\n",
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" Run the code below to understand how to compute Discrete Fourier Transforms in Python. Add appropriate comments when required.\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"dt = 0.1 # Time interval between two samples.\n",
"fc = 1. / dt # Sampling frequency.\n",
"f0 = 1. # Frequency of the signal.\n",
"T0 = 1. / f0 # Period of the signal.\n",
"t = np.arange(0., 2 * T0, dt) # Creates an array of time of total duration twice the period and of time discretization dt.\n",
"# This simulates the process of time sampling.\n",
"s = np.cos(2. * np.pi * f0 * t + np.pi / 12.) # Synthetic signal.\n",
"print(s)\n",
"\n",
"tilde_s = np.fft.fft(s) # Computes the DFT of s.\n",
"freq = np.fft.fftfreq(s.size, dt) # Computes the frequencies at which the DFT is evaluated. Two inputs: the number of samples,\n",
"# and the time discretization.\n",
"print(freq) # The frequencies are in a particular order: first the positive frequencies in increasing order, then the negative\n",
"# frequencies also in increasing order.\n",
"print(tilde_s) # The DFT is an array of complex numbers.\n",
"\n",
"plt.figure()\n",
"plt.plot(freq, np.abs(tilde_s)) # The DFT is an array of complex numbers so we need to take the modulus to plot it.\n",
"plt.xlabel('f')\n",
"plt.ylabel(r'$\\vert\\tilde{s}(f)\\vert$')\n",
"plt.title(r'Spectrum of $s(t)=\\cos(2\\pi t + \\pi/12)$')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "8e29eebb-ea0e-43a9-acfc-96ee540406c2",
"metadata": {},
"source": [
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" What is the value of the Discrete Fourier Transform for a cosine (or sine) function?\n",
"
\n",
"
\n",
"
\n",
"\n",
"
\n",
"
▶ The modulus of the DFT is equal to half the number of samples for a cosine (or sine) function when the frequency equals the frequency of the signal or its opposite, and otherwise it is equal to 0.
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tilde_s = np.fft.fftshift(np.fft.fft(s))\n",
"freq = np.fft.fftshift(np.fft.fftfreq(s.size, dt))\n",
"print(freq) # The function fftshift sorts the values of the array such that the frequencies are in increasing order.\n",
"print(tilde_s)\n",
"\n",
"plt.figure()\n",
"plt.plot(freq, np.abs(tilde_s))\n",
"plt.xlabel('f')\n",
"plt.ylabel(r'$\\vert\\tilde{s}(f)\\vert$')\n",
"plt.title(r'Spectrum of $s(t)=\\cos(2\\pi t + \\pi/12)$')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "542a243a-ea04-4ebd-b81b-0293667b780a",
"metadata": {},
"source": [
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" What is the interest of the function fftshift?\n",
"
\n",
"
\n",
"
\n",
"\n",
"
\n",
"
▶ This function sorts the array elements so that the frequencies are in increasing order: this is better to plot the spectrum afterwards (no line going from the right to the left in the plot);
\n",
"
▶ Be careful that the function must be applied to the array of frequencies and the array of the DFT.
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dt = 0.1\n",
"fc = 1. / dt\n",
"f0 = 1.\n",
"T0 = 1. / f0\n",
"t1 = np.arange(0., 2 * T0, dt) # Creates an array of time of total duration twice the period and of time discretization dt.\n",
"s1 = np.cos(2. * np.pi * f0 * t1 + np.pi / 12.)\n",
"t2 = np.arange(0., 2.3 * T0, dt) # Creates an array of time of total duration 2.3 times the period and of time discretization dt.\n",
"s2 = np.cos(2. * np.pi * f0 * t2 + np.pi / 12.)\n",
"\n",
"tilde_s1 = np.fft.fftshift(np.fft.fft(s1))\n",
"freq1 = np.fft.fftshift(np.fft.fftfreq(s1.size, dt))\n",
"tilde_s2 = np.fft.fftshift(np.fft.fft(s2))\n",
"freq2 = np.fft.fftshift(np.fft.fftfreq(s2.size, dt))\n",
"\n",
"plt.figure()\n",
"plt.plot(freq1, np.abs(tilde_s1), '-o', label='Total duration = 2 periods')\n",
"plt.plot(freq2, np.abs(tilde_s2), '-s', label='Total duration = 2.3 periods')\n",
"plt.xlabel('f')\n",
"plt.ylabel(r'$\\vert\\tilde{s}(f)\\vert$')\n",
"plt.title(r'Spectrum of $s(t)=\\cos(2\\pi t + \\pi/12)$')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c5cf62a3-c737-41d0-b1db-3fdce80f5384",
"metadata": {},
"source": [
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" What is the effect on the Discrete Fourier Transform of sampling a periodic function on a total duration which is not an integer multiple of its period?\n",
"
\n",
"
\n",
"
\n",
"\n",
"
\n",
"
▶ This enlarges the width of the peaks in the spectrum: in other words, you have a non-zero DFT for multiple frequencies close to the actual frequency of the signal.
\n",
" Can you rationalize the output of the above cell?\n",
"
\n",
"
\n",
"
\n",
"\n",
"
\n",
"
▶ If we were recording the sample with an infinitely small sampling time interval, we would observe 2 peaks of amplitude t.size/2=10 at frequencies $\\pm\\,f_0=\\pm1$, and 2 peaks of amplitude t.size/2*0.1=1 at frequencies $\\pm\\,f_1=\\pm 6$;
\n",
"
▶ However, because the sampling frequency is $f_\\mathrm{s}=10$, we can only measure the spectrum for frequencies in the range $[-f_\\mathrm{s}/2,\\,f_\\mathrm{s}/2[$, and we thus observe the aliasing phenomenon;
\n",
"
▶ This is why we observe ghost peaks at frequencies $\\pm f_\\mathrm{c}\\pm f_1=\\pm 4$.
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"alpha = 5.\n",
"t = np.linspace(-5., 5., 101)\n",
"s = np.exp(-alpha * t ** 2) # We compute the DFT of a Gaussian, which is not a periodic function.\n",
"tt = np.linspace(t[0], t[-1], 1001)\n",
"ss = np.exp(-alpha * tt ** 2)\n",
"\n",
"tilde_s = np.fft.fftshift(np.fft.fft(s))\n",
"tilde_s *= (t[1] - t[0]) # To go from the DFT to the Fourier transform, we multiply by the time sampling.\n",
"freq = np.fft.fftshift(np.fft.fftfreq(t.size, t[1] - t[0]))\n",
"\n",
"ff = np.linspace(freq[0], freq[-1], 1001) # We create an array of values of f in the same range to compute the analytical prediction.\n",
"tilde_ss = np.sqrt(np.pi / alpha) * np.exp(- ff ** 2 * np.pi ** 2 / alpha) # Analytical result for the Fourier transform of the Gaussian.\n",
"\n",
"plt.figure(figsize=(5, 10)) # figsize allows you to give the width and height of the figure in inches (1 inch = 2.54 cm).\n",
"plt.subplot(3, 1, 1)\n",
"plt.plot(t, s, '.', label='Samples')\n",
"plt.plot(tt, ss, '--', label='Analytical expression')\n",
"plt.xlabel('t')\n",
"plt.ylabel('s(t)')\n",
"plt.legend()\n",
"plt.subplot(3, 1, 2)\n",
"plt.plot(freq, np.absolute(tilde_s), '.', label='DFT')\n",
"plt.plot(ff, np.absolute(tilde_ss), '--', label='Analytical expression')\n",
"plt.legend()\n",
"plt.ylabel(r'$\\vert\\tilde{s}(f)\\vert$')\n",
"plt.subplot(3, 1, 3)\n",
"plt.plot(freq, np.absolute(tilde_s), '.', label='DFT')\n",
"plt.plot(ff, np.absolute(tilde_ss), '--', label='Analytical expression')\n",
"plt.yscale('log')\n",
"plt.legend()\n",
"plt.ylabel(r'$\\vert\\tilde{s}(f)\\vert$')\n",
"plt.xlabel('f')\n",
"plt.suptitle('Sampling and Fourier transform of a Gaussian')\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "3d6a18b1-58f4-478e-9af5-e0ec07b8d2a2",
"metadata": {},
"source": [
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" How does the result change with the number of samples?\n",
"
\n",
"
\n",
"
\n",
"\n",
"
\n",
"
▶ The result gets better when we increase the number of samples;
\n",
"
▶ This is obvious in real space: for small number of samples, the peak of the Gaussian is not well captured;
\n",
"
▶ The error in the Fourier transform is larger at large frequencies but decreases with the number of samples (visible in logarithmic scale).
\n",
"
"
]
},
{
"cell_type": "markdown",
"id": "d897c9f3-2bb1-43aa-bf57-e60febeefc08",
"metadata": {},
"source": [
"II. Random numbers\n",
"\n",
"1) Generate random numbers\n",
"\n",
"The NumPy package has a module random which allows you to draw random numbers from different probability distributions. You can look at the documentation for the full list of distributions available: https://numpy.org/doc/stable/reference/random/generator.html\n",
"\n",
"To be more precise, all the functions of this module are pseudo-random number generators because they create deterministic arrays of samples which follow approximately the target probability distribution. These arrays are created from an integer, called a seed.\n",
"\n",
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" Run the code below which illustrates how to draw random numbers with a target distribution in Python. Add appropriate comments when required.\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.random.normal(4., 2., 1000) # Draw 1000 samples from a Gaussian distribution of mean 4 and standard deviation 2.\n",
"plt.hist(x, bins=50, density=True)\n",
"plt.xlabel('x')\n",
"plt.ylabel('f(x)')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a890521a-68a8-4fc2-9816-e953116d6432",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.7003673 0.74275081 0.70928001 0.56674552 0.97778533 0.70633485\n",
" 0.24791576 0.15788335 0.69769852 0.71995667]\n",
"[0.25774443 0.34154678 0.96876117 0.6945071 0.46638326 0.7028127\n",
" 0.51178587 0.92874137 0.7397693 0.62243903]\n",
"[0.7003673 0.74275081 0.70928001 0.56674552 0.97778533 0.70633485\n",
" 0.24791576 0.15788335 0.69769852 0.71995667]\n"
]
}
],
"source": [
"np.random.seed(19680801) # Impose the seed value to 19680801.\n",
"x = np.random.random(10)\n",
"print(x)\n",
"y = np.random.random(10)\n",
"print(y)\n",
"np.random.seed(19680801)\n",
"z = np.random.random(10) # We have fixed the seed to the same value as in the beginning and so we generate the same random numbers.\n",
"# This is important when you have to debug a code which involves random numbers.\n",
"print(z)"
]
},
{
"cell_type": "markdown",
"id": "b1b5ecd7-7959-4204-b0ec-8320fd410fd0",
"metadata": {},
"source": [
"2) Compute statistical properties\n",
"\n",
"When we work with random numbers, we are often interested in their statistical properties, like their distribution, or more reasonably, their first cumulants. Some functions are present in NumPy (see TP3), while others can be found in the module stats of the SciPy package. (The module stats also has functions to generate random numbers but they are not covered in these lectures.) The SciPy package heavily relies on the NumPy package and thus allows you to manipulate arrays. For more details about the functions available in the stats module, you can look at the documentation: https://docs.scipy.org/doc/scipy/reference/stats.html\n",
"\n",
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" Run the code below which illustrates how to compute the statistical properties of random variables in Python. Add appropriate comments when required.\n",
"
\n",
"
\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f9f42af4-ba9b-4fce-b2ff-ba9d00d573d6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.02872494264848393\n",
"0.33616512070859494\n",
"0.5797974824959099\n",
"0.04152439104261407\n"
]
}
],
"source": [
"x = np.random.uniform(-1, 1, 1000) # Generate 1000 samples according to a uniform distribution between -1 and 1.\n",
"print(np.mean(x)) # Compute the mean of x (its theoretical value is 0 for a uniform distribution between -1 and 1).\n",
"print(np.var(x)) # Compute the variance of x (its theoretical value is 1/3 for a uniform distribution between -1 and 1).\n",
"print(np.std(x)) # Compute the standard deviation of x (its theoretical value is 1/sqrt(3) here).\n",
"print(np.median(x)) # Compute the median of the samples (the value at the center is the samples of x are stored in increasing order.\n",
"# It should be close to 0."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3073ede4-2703-4f78-886a-391ea9b87692",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(array([636, 241, 79, 26, 10, 4, 3, 0, 0, 1]), array([6.18199023e-04, 9.79791095e-01, 1.95896399e+00, 2.93813689e+00,\n",
" 3.91730978e+00, 4.89648268e+00, 5.87565558e+00, 6.85482847e+00,\n",
" 7.83400137e+00, 8.81317426e+00, 9.79234716e+00]))\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.random.exponential(1., 1000) # Generate 1000 samples according to an exponential distribution of parameter 1.\n",
"print(np.histogram(x)) # Returns two elements, the first one being the values of the histogram, and the second one the left extremities\n",
"# of the interval and the right extremity of the last interval (the construction is similar to the function hist in\n",
"# matplotlib.pyplot).\n",
"\n",
"histo, bin_edges = np.histogram(x)\n",
"plt.figure()\n",
"plt.bar(bin_edges[:-1], histo, bin_edges[1] - bin_edges[0], align='edge') # Draw vertical bars of left extremity given by the first\n",
"# argument, the height given by the second argument, the width given by the third argument, while align='edge' tells that the position we\n",
"# have given is indeed the left extremity of the rectangles.\n",
"plt.xlabel('x')\n",
"plt.ylabel('Histogram of x')\n",
"plt.title('Exponential distribution')\n",
"plt.show()\n",
"\n",
"plt.figure()\n",
"plt.hist(x)\n",
"plt.xlabel('x')\n",
"plt.ylabel('Histogram of x')\n",
"plt.title('Exponential distribution')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "807c5a60-298a-4311-afe1-24652cfd9cf2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[0.07602738 0.01773915]\n",
" [0.01773915 0.08708275]]\n",
"0.07526710170804016 0.0175617540824993 0.08621192364981844\n",
"[[1. 0.21801262]\n",
" [0.21801262 1. ]]\n",
"0.21801261644903142\n"
]
}
],
"source": [
"x = np.random.random(100)\n",
"y = np.random.random(100)\n",
"print(np.cov(x, y)) # Compute the covariance matrix of the random samples x and y.\n",
"# The diagonal elements of the matrix are the variance of each random variable, while the off-diagonal elements are the covariance, namely\n",
"# the mean of the product of the two variables minus the product of the means.\n",
"# Note the slight different with the direct calculation, which comes from a difference in the normalization, in the cov function, the\n",
"# sums involved in the variances and covariances are divided by N - 1 (with N the size of the samples).\n",
"print(np.var(x), np.mean((x - np.mean(x)) * (y - np.mean(y))), np.var(y))\n",
"\n",
"print(np.corrcoef(x, y)) # Computes the matrices of the Pearson correlation coefficient defined as P_{ij} = C_{ij}/sqrt(C_{ii}C_{jj}).\n",
"# By construction the diagonal elements are equal to 1, while the off-diagonal elements are the Pearson correlations of variables i and j.\n",
"print(np.mean((x - np.mean(x)) * (y - np.mean(y))) / np.sqrt(np.var(x) * np.var(y)))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "1eb4c4cc-f89c-4e96-bf69-12c85f940c8f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.03419108984091339\n",
"-0.24154651663955562\n"
]
}
],
"source": [
"import scipy.stats as stats\n",
"x = np.random.normal(size=1000) # By default, the mean is 0 and the variance is 1.\n",
"print(stats.skew(x)) # Compute the skewness of x, defined as the ratio between the third order cumulant and the power 1.5 of the variance.\n",
"# The exact result is 0.\n",
"print(stats.kurtosis(x)) # Compute the kurtosis of x, defined as the ratio between the fourth order cumulant and the squared variance minus 3.\n",
"# The exact result is 0."
]
},
{
"cell_type": "markdown",
"id": "7fc2623c-c151-4e12-80a0-dd5aa612f65c",
"metadata": {},
"source": [
"III. Special functions and physical constants\n",
"\n",
"1) Special functions\n",
"\n",
"The module Special of the package SciPy presents many special functions that you might need one day (in particular to model experimental or numerical data). Below are listed few examples but the full list is given in the online documentation: https://docs.scipy.org/doc/scipy/reference/special.html\n",
"\n",
"
\n",
"
▶ Airy functions, their derivatives and their zeros (very useful in Optics);
\n",
"
▶ Bessel, Hankel functions, their derivatives, integrals and their zeros (very useful in the context of wave propagation or diffraction involving circular or cylindrical geometries);
\n",
"
▶ Gamma function and other related functions (very useful in Statistical Physics or in High-Energy Physics);
\n",
"
▶ Error function and other related functions (very useful in Statistical Physics);
\n",
"
▶ Fresnel integrals (very useful in Optics);
\n",
"
▶ Many polynomial functions, e.g., Legendre, Laguerre, Hermite polynomials (very useful in Quantum Mechanics);
\n",
"
▶ etc.
\n",
"
\n",
"\n",
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" Run the code below which illustrates the use of several special functions in Python. Add appropriate comments when required.\n",
"
\n",
"
\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "5245e70a-6bcb-49f9-ac7f-efff1983ee1f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1 2 3 4 5 6 7 8 9]\n",
"[1.000e+00 1.000e+00 2.000e+00 6.000e+00 2.400e+01 1.200e+02 7.200e+02\n",
" 5.040e+03 4.032e+04]\n",
"[ 1 1 2 6 24 120 720 5040 40320]\n"
]
}
],
"source": [
"import scipy.special as spe\n",
"x = np.arange(1, 10)\n",
"print(x)\n",
"print(spe.gamma(x)) # Compute the gamma function of x.\n",
"y = np.ones_like(x, dtype=int)\n",
"for i in range(1, x.size):\n",
" y[i] = np.prod(x[:i])\n",
"print(y) # Because elements of x are integers gamma(x)=(x-1)!"
]
},
{
"cell_type": "markdown",
"id": "b1e679aa-87ee-4a6f-8b8d-c945e085f075",
"metadata": {},
"source": [
"2) Physical constants\n",
"\n",
"The module Constants of the package SciPy presents physical and mathematical constants, along with units that you might need one day (again to model experimental or numerical data). Below are listed few examples but the full list is given in the online documentation: https://docs.scipy.org/doc/scipy/reference/constants.html\n",
"\n",
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" Run the code below which illustrates the use of several physical constants in Python. Add appropriate comments when required.\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(-20, 20, 201)\n",
"zeros_j0 = spe.jn_zeros(0, 6) # Useful if you are interested in the vibrational modes in a cylindrical waveguide.\n",
"zeros_j1 = spe.jn_zeros(1, 6)\n",
"plt.figure()\n",
"plt.plot(x, spe.j0(x))\n",
"plt.plot(zeros_j0, np.zeros(zeros_j0.size), 'or', label=r'Zeros of $J_0$')\n",
"plt.plot(zeros_j1, spe.j0(zeros_j1), 'sg', label=r'Zeros of $J_1$') # -J1 is the derivative of J0.\n",
"plt.xlabel('x')\n",
"plt.ylabel(r'$J_0(x)$')\n",
"plt.title(r'Bessel function of the first kind $J_0$')\n",
"plt.grid()\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "ce79a55b-ec86-4cfb-80b6-2c7e002649b4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3424821031470642.0\n",
"9.1093837139e-31\n",
"1.0545718176461565e-34\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"omega = 2. * np.pi * constant.nu2lambda(550 * constant.nano) # Compute the angular frequency associated with a radiation of 550 nm.\n",
"print(omega)\n",
"m = constant.electron_mass # Mass of the electron in kg.\n",
"print(m)\n",
"hbar = constant.hbar # Reduced Planck constant.\n",
"print(hbar)\n",
"\n",
"\n",
"def eigenfunction_harmonic_oscillator(x, n): # Return the value of the nth eigenfunction of the quantum harmonic oscillator at position x.\n",
" return 1. / np.sqrt(2 ** n * spe.gamma(n + 1)) * \\\n",
" (m * omega / (np.pi * hbar)) ** 0.25 * \\\n",
" np.exp(- m * omega * x ** 2 / (2. * hbar)) * \\\n",
" spe.eval_hermite(n, np.sqrt(m * omega / hbar) * x)\n",
"\n",
"\n",
"plt.figure()\n",
"x = np.linspace(-10. * np.sqrt(hbar / (m * omega)), 10 * np.sqrt(hbar / (m * omega)), 201) # The typical width of the wavefunction is\n",
"# sqrt(hbar / (m * omega)), do dimensional analysis.\n",
"shift = 1e5\n",
"for i in range(5):\n",
" plt.plot(x * 1e9, eigenfunction_harmonic_oscillator(x, i) + i * shift, label='n=' + str(i)) # Plot the 5 first eigenfunctions.\n",
" # Shift them vertically for visibility. The abscissae are given in nm.\n",
" plt.plot(x * 1e9, np.full_like(x, i * shift), '--k') # Plot an horizontal line to indicate the ordinate origin of each eigenfunction.\n",
" plt.fill_between(x * 1e9, i * shift, eigenfunction_harmonic_oscillator(x, i) + i * shift, alpha=0.3) # Fill the area between\n",
" # the two sets of data given as arguments after the array of abscissae (here the baseline and the shifted eigenfunction).\n",
"plt.xlabel('x (nm)')\n",
"plt.ylabel(r'$\\psi_n(x)$ (m$^{-1/2}$)')\n",
"plt.legend()\n",
"plt.title('First eigenfunctions of the quantum harmonic oscillator \\n' + # \\n to go to line but does not work with r before the string.\n",
" r'of mass $m=$' + str(m) + ' kg \\n' +\n",
" r'and angular frequency $\\omega=$' + str(omega) + ' rad/s')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "807ea632-6aa4-4a67-bb95-fd0f8186764c",
"metadata": {},
"source": [
"IV. Curve fitting\n",
"\n",
"When you perform an experiment or a simulation, you may have the objective of validating a theoretical model. Said differently, you may want to confront the results from your experiment or simulation to the analytical prediction of the model. Usually, this comparison is done by analyzing if the data points (your results) follow a curve (the analytical prediction). The latter involves several adjustable parameters which are usually unknown. The value of these parameters may also be interesting in order to characterize your system.\n",
"\n",
"As a result, the procedure of trying to overimpose data points with a model, called curve fitting is crucial. The module Optimize of the package SciPy presents several functions for curve fitting. In these lectures, we only focus on the function curve_fit, but the others (least_squares in particular which gives more freedom) are described in the online documentation: https://docs.scipy.org/doc/scipy/reference/optimize.html\n",
"\n",
"We illustrate the procedure on the following example. An experiment consists in measuring the magnetic field in the center of a coil at a constant current intensity $I$. The laws of magnetostatics give that the magnetic field equals\n",
"$$B=\\dfrac{\\mu_0 NI}{\\sqrt{D^2+\\ell^2}},$$ with $D$ the diameter of the coil, $\\ell$ its length, and $N$ the number of turns. You are given the results of $B$ (with their uncertainties) measured thanks to a teslameter, and of $I$ (with their uncertainties) measured thanks to an amperemeter. In the experiment, the coil had a diameter $D=(9.2\\pm0.2)\\,\\mathrm{cm}$, a length $\\ell=(41.0\\pm0.2)\\,\\mathrm{cm}$ and a number of turns $N=120\\pm1$. The function $B(I)$ is therefore expected to be a linear function, of slope $a=\\mu_0N/\\sqrt{\\ell^2+D^2}$, with an expected value $a_\\mathrm{th}=(0.359\\pm0.005)\\, \\mathrm{mT/A}$, where the uncertainty is obtained via propagation of uncertainties\n",
"$$\\frac{u(a_\\mathrm{th})}{a_\\mathrm{th}}=\\frac{u(N)}{N}+\\frac{\\ell u(\\ell)+Du(D)}{\\ell^2+D^2}.$$\n",
"\n",
"The objective is to validate the model obtained from the law of magnetostatics theory, which involves approximations or assumptions that may not be verified experimentally (the magnetic field is not precisely measured at the center of the coil, there are residual magnetic fields in the room, etc.).\n",
"\n",
"
\n",
"
\n",
"
\n",
" \n",
"
\n",
"
\n",
" Run the code below to understand how to fit a curve to a set of data in Python. Add appropriate comments when required.\n",
"
\n",
"
\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "67218ca6-0cc9-4d51-b0e2-e6889a69fc19",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"I = np.array([1.10, 2.00, 2.99, 4.06, 5.03, 6.02, 7.00, 8.04, 9.02, 9.99]) # Intensity of the current in A.\n",
"uI = np.array([0.04, 0.04, 0.04, 0.05, 0.06, 0.06, 0.06, 0.07, 0.08, 0.08]) # Uncertainty on the intensity in A.\n",
"B = np.array([0.39, 0.64, 0.99, 1.30, 1.66, 1.98, 2.30, 2.64, 3.0, 3.3]) # Magnetic field in mT.\n",
"uB = np.array([0.07, 0.08, 0.10, 0.12, 0.13, 0.15, 0.17, 0.18, 0.2, 0.2]) # Uncertainty on the magnetic field in mT.\n",
"B *= 1e-3 # We convert the magnetic field in T (safer to avoid conversion mistakes).\n",
"uB *= 1e-3 # We convert the uncertainty on the magnetic field in T (safer to avoid conversion mistakes).\n",
"D = 9.2e-2 # Diameter of the coil in m.\n",
"uD = 0.2e-2 # Uncertainty on the diameter in m.\n",
"l = 0.410 # Lenght of the coil in m.\n",
"ul = 0.2e-2 # Uncertainty on the length in m.\n",
"N = 120 # Number of turns.\n",
"uN = 1 # Uncertainty on the number of turns.\n",
"\n",
"plt.figure()\n",
"plt.errorbar(I, B, uB, uI, linestyle='', label='Measurements') # Plot data with errorbars. Be careful that you must give first the\n",
"# errorbars on the ordinates, and then the errorbar on the abscissae.\n",
"plt.xlabel('I (A)')\n",
"plt.ylabel('B (T)')\n",
"plt.title('Magnetic field at the center of a coil')\n",
"plt.legend()\n",
"plt.axis([0, 10.1, 0, 3.5e-3])\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "25956efe-7b65-4fbd-8308-a4d7687b4b87",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(array([ 3.30565579e-04, -6.37482306e-06]), array([[ 5.30526773e-12, -2.93116268e-11],\n",
" [-2.93116268e-11, 2.05302288e-10]]))\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlUAAAHFCAYAAADbiAxsAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjMsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvZiW1igAAAAlwSFlzAAAPYQAAD2EBqD+naQAAd4dJREFUeJzt3XlcF9X+x/HXlx0UKUUFTRHNNbMMzLAUtRTRyjVtoyyXTM2Fuua+VW6V11suZJrWrdRbuLSQSqWkSbnklrbndgs0V1xZz++P7/X76yugoMCwvJ+PB486Z86c+cwcvnw/zpyZsRljDCIiIiJyTVysDkBERESkNFBSJSIiIlIAlFSJiIiIFAAlVSIiIiIFQEmViIiISAFQUiUiIiJSAJRUiYiIiBQAJVUiIiIiBUBJlYiIiEgBUFIlZcLixYux2WzYbDbWr1+fbbkxhhtvvBGbzUbr1q2LPL5rFRcXx8SJE3NcVqtWLXr37l0g20lLS2PAgAEEBgbi6urKrbfees3byOu669evz3X8rsaff/7JxIkT2bFjR57a7927l4kTJ7J///5sy1q3bk3jxo0LJK7iaO7cuSxevNjqMHI1duxYatasiZubG9ddd53V4eRJ69ats/2tsdlsuX6OpWRwszoAkaLk6+vLwoULs/0xS0hI4LfffsPX19eawK5RXFwcc+bMyfEP8ooVK6hQoUKBbGfevHm88cYbvP7664SEhFC+fPkC30ZR+fPPP5k0aRK1atVyJIeXs3fvXiZNmkTr1q2pVatWocdXnMydOxd/f/8CS84L0qpVq3jppZcYM2YMkZGReHp6Wh1SnsydO9fqEKQQKKmSMqVXr1689957zJkzxykJWLhwIWFhYaSkpFgYXeFo2rRpgfX1/fff4+3tzeDBgwttG1I2GGO4cOEC3t7e19TP999/D8CQIUOoUqVKQYRWJBo1amR1CFIIdPlPypSHHnoIgCVLljjqTp06RWxsLE8++WSO60yaNInmzZtTsWJFKlSowG233cbChQu59F3kqampPPvsswQEBODj40OrVq3Ytm1btstbFy9Frlu3jqeffhp/f38qVapEt27d+PPPP7Ntf9myZYSFhVGuXDnKly9PREQE27dvdyzv3bs3c+bMAXBc4rTZbI7LVDldXjt58iTPPvsstWvXxtPTkypVqtCxY0d+/PHHXI+dzWZjwYIFnD9/3rGNi5eEctpGSkoKzz33HMHBwXh4eFC9enWGDRvG2bNnc93GRT/++CMdOnTAx8cHf39/BgwYwOnTp6+4HsCvv/7KE088Qd26dfHx8aF69ercd9997N6929Fm/fr1NGvWDIAnnnjCsT+5XXpZvHgxDzzwAABt2rTJtv8XbdmyhZYtW+Lj40Pt2rWZNm0aWVlZBXZcAFavXs3dd9+Nn58fPj4+NGzYkKlTpzq12bp1K/fffz8VK1bEy8uLpk2b8p///CfbPuXl97BWrVrs2bOHhIQEx37//UxdXvfHZrMxePBgYmJiaNiwIZ6enrz99tu57mdWVhYzZsygQYMGjt/Rxx57jP/+979OsY0dOxaAqlWrXvHy2datW3nwwQepVasW3t7e1KpVi4ceeogDBw7kus7fpaamMnnyZBo2bIiXlxeVKlWiTZs2bNq0ydHmwoULjBo1yul4DBo0iJMnTzr1ldPlPykFjEgZsGjRIgOYLVu2mKioKHP77bc7ls2bN8+UK1fOpKSkmJtuusmEh4c7rdu7d2+zcOFCEx8fb+Lj480LL7xgvL29zaRJk5zaPfTQQ8bFxcWMHDnSrF271syaNcvUqFHD+Pn5mccffzxbLLVr1zbPPPOMWbNmjVmwYIG5/vrrTZs2bZz6fOmll4zNZjNPPvmk+eSTT8zy5ctNWFiYKVeunNmzZ48xxphff/3V9OjRwwAmMTHR8XPhwgVjjDFBQUFO27+4n+XKlTOTJ082a9asMbGxsWbo0KHmyy+/zPUYJiYmmo4dOxpvb2/HNo4cOZLjNs6ePWtuvfVW4+/vb2bOnGk+//xz869//cv4+fmZtm3bmqysLEfbS9dNTk42VapUMdWrVzeLFi0ycXFx5pFHHjE1a9Y0gFm3bl2uMRpjTEJCgnn22WfNhx9+aBISEsyKFStMly5djLe3t/nxxx+NMcacOnXKMQ5jx4517M+hQ4dy7PPIkSNmypQpBjBz5szJtv/h4eGmUqVKpm7duiYmJsbEx8ebgQMHGsC8/fbbV3VccrJgwQJjs9lM69atzfvvv28+//xzM3fuXDNw4EBHmy+//NJ4eHiYli1bmmXLlpnVq1eb3r17G8AsWrTI0S6vv4ffffedqV27tmnatKljv7/77rt87w9gqlevbpo0aWLef/998+WXX5rvv/8+133t37+/AczgwYPN6tWrTUxMjKlcubKpUaOG+euvvxyx9enTxwBm9erVlx1DY4z54IMPzPjx482KFStMQkKCWbp0qQkPDzeVK1d29Jmb9PR006ZNG+Pm5maee+45ExcXZz766CMzevRos2TJEmOMMVlZWSYiIsK4ubmZcePGmbVr15pXXnnFlCtXzjRt2tTxmTTG/jtz6d8awEyYMOGycUjxpqRKyoS/J1Xr1q0zgOMPerNmzUzv3r2NMSbHpOrvMjMzTXp6upk8ebKpVKmS40tjz549BjDPP/+8U/slS5YYIMek6u9fhMYYM2PGDAOYpKQkY4wxBw8eNG5ubuaZZ55xanf69GkTEBBgevbs6agbNGiQye3fSJcmLZMnTzaAiY+Pz3U/c/P444+bcuXKXXEbU6dONS4uLmbLli1O7T788EMDmLi4uFzXff75543NZjM7duxwWrddu3Z5SqoulZGRYdLS0kzdunXN8OHDHfVbtmzJlmhczgcffJDr9sPDww1gvv32W6f6Ro0amYiICEc5P8flUqdPnzYVKlQwd91112WTrwYNGpimTZua9PR0p/p7773XBAYGmszMTGNM3n8Pjcn9c5Gf/QGMn5+fOX78eK6xX/TDDz/kGNu3335rADN69GhH3YQJEwxwxaQoJxkZGebMmTOmXLly5l//+tdl277zzjsGMG+++WaubVavXm0AM2PGDKf6ZcuWGcDMnz/fUaekqnTS5T8pc8LDw6lTpw5vvfUWu3fvZsuWLble+gP48ssvueeee/Dz88PV1RV3d3fGjx/PsWPHOHLkCGCf6A7Qs2dPp3V79OiBm1vOUxfvv/9+p3KTJk0AHJci1qxZQ0ZGBo899hgZGRmOHy8vL8LDw6/6LrjPPvuMevXqcc8991zV+nnxySef0LhxY2699Van2CMiIq54B9+6deu46aabuOWWW5zqH3744TxtOyMjgylTptCoUSM8PDxwc3PDw8ODX375hR9++OFaduuyAgICuP32253qmjRp4nRp6VqOy6ZNm0hJSWHgwIHYbLYc2/z666/8+OOPPPLIIwBO2+jYsSNJSUn89NNPTutc6ffwcvK7P23btuX666+/Yr/r1q0DyHZJ+fbbb6dhw4Z88cUXV+wjJ2fOnOH555/nxhtvxM3NDTc3N8qXL8/Zs2ev+Lvx2Wef4eXldcW/FTnF/cADD1CuXLmrjltKDk1UlzLHZrPxxBNP8Nprr3HhwgXq1atHy5Ytc2y7efNm2rdvT+vWrXnzzTe54YYb8PDwYOXKlbz00kucP38egGPHjgH2eR1/5+bmRqVKlXLs+9L6i3ctXezz8OHDAI65P5dycbm6fxP99ddf1KxZ86rWzavDhw/z66+/4u7unuPyo0eP5rrusWPHCA4OzlYfEBCQp21HR0czZ84cnn/+ecLDw7n++utxcXGhb9++jmNbGHIaZ09PT6dtXstx+euvvwC44YYbcm1z8Xfmueee47nnnsvTNq70e3g5+d2fwMDAK/YJ//95yql9tWrV8jwH6lIPP/wwX3zxBePGjaNZs2ZUqFABm81Gx44dr7i/f/31F9WqVbvs5+7YsWO4ublRuXJlp3qbzUZAQIBjv6T0UlIlZVLv3r0ZP348MTExvPTSS7m2W7p0Ke7u7nzyySd4eXk56leuXOnU7uIX0+HDh6levbqjPiMj46r/kPr7+wPw4YcfEhQUdFV95KRy5cpOk30Lg7+/P97e3rz11lu5Ls9NpUqVSE5OzlafU11O3n33XR577DGmTJniVH/06FHLn2F0Lcfl4hf15cbu4vqjRo2iW7duObapX79+XsO9ovzuT25n2C518fOUlJSULYn8888/L3uccnPq1Ck++eQTJkyYwMiRIx31qampHD9+/IrrV65cmY0bN5KVlZVrYlWpUiUyMjL466+/nBIrYwzJycm5/gNJSg8lVVImVa9enX/84x/8+OOPPP7447m2s9lsuLm54erq6qg7f/48//73v53atWrVCrDfqXfbbbc56j/88EMyMjKuKsaIiAjc3Nz47bff6N69+2Xb/v3swpVuUY+MjGT8+PF8+eWXtG3b9qpiu5J7772XKVOmUKlSpRzPOl1OmzZtmDFjBjt37nS6BPj+++/naX2bzZbtWUWffvopf/zxBzfeeKOjLj9nZK6mfU6u5bi0aNECPz8/YmJiePDBB3NMUOrXr0/dunXZuXNntqTyWlx6xu2ia9mfy7n4e/nuu+86JSJbtmzhhx9+YMyYMfnu02azYYzJ9ruxYMECMjMzr7h+ZGQkS5YsYfHixbleArz77ruZMWMG7777LsOHD3fUx8bGcvbsWe6+++58xy0li5IqKbOmTZt2xTadOnVi5syZPPzww/Tv359jx47xyiuvZPvDfNNNN/HQQw/x6quv4urqStu2bdmzZw+vvvoqfn5+V3WprlatWkyePJkxY8bw+++/06FDB66//noOHz7M5s2bKVeuHJMmTQLg5ptvBmD69OlERkbi6upKkyZN8PDwyNbvsGHDWLZsGZ07d2bkyJHcfvvtnD9/noSEBO69917atGmT71hz2kZsbCytWrVi+PDhNGnShKysLA4ePMjatWt59tlnad68ea7rvvXWW3Tq1IkXX3yRqlWr8t577132cQ9/d++997J48WIaNGhAkyZN2LZtGy+//HK2Mx516tTB29ub9957j4YNG1K+fHmqVatGtWrVcuz34hPT58+fj6+vL15eXgQHB+d6ebegj0v58uV59dVX6du3L/fccw/9+vWjatWq/Prrr+zcuZPZs2cD8MYbbxAZGUlERAS9e/emevXqHD9+nB9++IHvvvuODz74IM/xXnTzzTezdOlSli1bRu3atfHy8uLmm2++pv25nPr169O/f39ef/11XFxciIyMZP/+/YwbN44aNWo4JSx5VaFCBVq1asXLL7+Mv78/tWrVIiEhgYULF+bpDOZDDz3EokWLGDBgAD/99BNt2rQhKyuLb7/9loYNG/Lggw/Srl07IiIieP7550lJSeHOO+9k165dTJgwgaZNmxIVFZXvuKWEsXqmvEhR+Pvdf5eT011Ob731lqlfv77x9PQ0tWvXNlOnTjULFy40gNm3b5+j3YULF0x0dLSpUqWK8fLyMnfccYdJTEw0fn5+Tned5RbLxbsSL727bOXKlaZNmzamQoUKxtPT0wQFBZkePXqYzz//3NEmNTXV9O3b11SuXNnYbDan2C69u84YY06cOGGGDh1qatasadzd3U2VKlVMp06dHI8cyE1e7/4zxpgzZ86YsWPHmvr16xsPDw/j5+dnbr75ZjN8+HCTnJx82XX37t1r2rVrZ7y8vEzFihVNnz59zKpVq/J099+JEydMnz59TJUqVYyPj4+56667zIYNG3K822rJkiWmQYMGxt3dPU93Xs2aNcsEBwcbV1dXpzsHw8PDzU033ZSt/eOPP26CgoKu6rjkJi4uzoSHh5ty5coZHx8f06hRIzN9+nSnNjt37jQ9e/Y0VapUMe7u7iYgIMC0bdvWxMTEONrk5/dw//79pn379sbX19cATvuU1/0BzKBBg664fxdlZmaa6dOnm3r16hl3d3fj7+9vHn300WyPTMjP3X///e9/Tffu3c31119vfH19TYcOHcz333+f4+9gTs6fP2/Gjx9v6tatazw8PEylSpVM27ZtzaZNm5zaPP/88yYoKMi4u7ubwMBA8/TTT5sTJ0449aW7/0onmzGXPMFQRArMpk2buPPOO3nvvffyfPeaiIiUTEqqRApIfHw8iYmJhISE4O3tzc6dO5k2bRp+fn7s2rXLaaK7iIiUPppTJVJAKlSowNq1a5k1axanT5/G39+fyMhIpk6dqoRKRKQM0JkqERERkQJg+RPV586dS3BwMF5eXoSEhLBhw4bLtk9ISCAkJAQvLy9q165NTExMtjaxsbE0atQIT09PGjVqxIoVK5yWz5s3jyZNmlChQgUqVKhAWFgYn332mVOb3r17O72c1mazcccdd1z7DouIiEipZGlStWzZMoYNG8aYMWPYvn07LVu2JDIykoMHD+bYft++fXTs2JGWLVuyfft2Ro8ezZAhQ4iNjXW0SUxMpFevXkRFRbFz506ioqLo2bMn3377raPNDTfcwLRp09i6dStbt26lbdu2dO7cmT179jhtr0OHDiQlJTl+4uLiCudAiIiISIln6eW/5s2bc9tttzFv3jxHXcOGDenSpQtTp07N1v7555/no48+cnpH04ABA9i5cyeJiYkA9OrVi5SUFKczTxef77NkyZJcY6lYsSIvv/wyffr0Aexnqk6ePJntydkiIiIiObFsonpaWhrbtm1zel0AQPv27dm0aVOO6yQmJtK+fXunuoiICBYuXEh6ejru7u4kJiZmezBcREQEs2bNyrHPzMxMPvjgA86ePUtYWJjTsvXr11OlShWuu+46wsPDeemll6hSpUqu+5SamkpqaqqjnJWVxfHjx6lUqVKeX88gIiIi1jLGcPr06Su+7/FSliVVR48eJTMzM9sLaKtWrZrrO76Sk5NzbJ+RkcHRo0cJDAzMtc2lfe7evZuwsDAuXLhA+fLlWbFiBY0aNXIsj4yM5IEHHiAoKIh9+/Yxbtw42rZty7Zt27I9TfuiqVOnOp5wLSIiIiXboUOHLvsS80tZ/kiFS8/gGGMue1Ynp/aX1uelz/r167Njxw5OnjxJbGwsjz/+OAkJCY7EqlevXo62jRs3JjQ0lKCgID799NNcX1Q6atQooqOjHeVTp05Rs2ZNfv75ZypWrJjrPknhSk9PZ926dbRp0wZ3d3erwymzNA7Fh8aieNA4WO9cWgZ3zvgKgIThLahQzv74m9OnTxMcHIyvr2+++rMsqfL398fV1TXbGaQjR45kO9N0UUBAQI7t3dzcHO/fyq3NpX16eHg4Xq4aGhrKli1b+Ne//sUbb7yR47YDAwMJCgril19+yXWfPD09czyLVbFixXy9H0wKVnp6Oj4+PlSqVEl/uCykcSg+NBbFg8bBet5pGbh4+gBQsVJF/MrZX0h/cTzyO3XHsrv/PDw8CAkJIT4+3qk+Pj6eFi1a5LhOWFhYtvZr164lNDTUcQBya5NbnxcZY5zmQ13q2LFjHDp0iMDAwMv2IyIiImWTpZf/oqOjiYqKIjQ0lLCwMObPn8/BgwcZMGAAYL+c9scff/DOO+8A9jv9Zs+eTXR0NP369SMxMZGFCxc63dU3dOhQWrVqxfTp0+ncuTOrVq3i888/Z+PGjY42o0ePJjIykho1anD69GmWLl3K+vXrWb16NQBnzpxh4sSJdO/encDAQPbv38/o0aPx9/ena9euRXiEREREpKSwNKnq1asXx44dY/LkySQlJdG4cWPi4uIICgoCICkpyemZVcHBwcTFxTF8+HDmzJlDtWrVeO211+jevbujTYsWLVi6dCljx45l3Lhx1KlTh2XLltG8eXNHm8OHDxMVFUVSUhJ+fn40adKE1atX065dOwBcXV3ZvXs377zzDidPniQwMJA2bdqwbNmyfF9fFRERkbLB8onqAwcOZODAgTkuW7x4cba68PBwvvvuu8v22aNHD3r06JHr8oULF152fW9vb9asWXPZNgUpMzOT9PT0ItteWZOeno6bmxsXLlwgMzPT6nCKhIeHR75uAxYRkWtneVJVlhljSE5O5uTJk1aHUqoZYwgICODQoUNl5nlhLi4uBAcH4+HhYXUoIiJlhpIqC11MqKpUqYKPj0+Z+cIvallZWZw5c4by5cuXibM3WVlZ/PnnnyQlJVGzZk39XomIFBElVRbJzMx0JFR63ELhysrKIi0tDS8vrzKRVAFUrlyZP//8k4yMDN2qLSJSRMrGN0wxdHEOlY+Pj8WRSGl08bJfWZlDJiJSHCipspguzUhh0O+ViEjRU1IlIiIiUgCUVEmBad26NcOGDbuqdWvVqsWsWbMKNB4REZGipKRK8qV3797YbLZsP7/++ivLly/nhRdecLTNKVFavHgx1113XbZ+t2zZQv/+/Qs5ehERkcKju/8k3zp06MCiRYuc6ipXroyrq+tV91m5cuVrDcsSaWlpehaUiIgAOlMlV8HT05OAgACnH1dXV6fLf61bt+bAgQMMHz7ccTZr/fr1PPHEE5w6dcpRN3HiRCD7WS2bzcaCBQvo2rUrPj4+1K1bl48++sgpjo8++oi6devi7e1NmzZtePvtt7HZbJd9mOrJkyfp378/VatWxcvLi8aNG/PJJ58AMHHiRG699Van9rNmzaJWrVqOcu/evenSpQtTp06lWrVq1KtXj1GjRnHHHXdk21aTJk2YMGGCo7xo0SIaNmyIl5cXDRo0YO7cuVc+2CIiUmLoTFVxYgyknyv67br7QAHfLbZ8+XJuueUW+vfvT79+/QCoWLEis2bNYvz48fz0008AlC9fPtc+Jk2axIwZM3j55Zd5/fXXeeSRRzhw4AAVK1Zk//799OjRg6FDh9K3b1+2b9/Oc889d9mYsrKyiIyM5PTp07z77rvUqVOHvXv35vsM2xdffEGFChWIj4/HGAPAtGnT+O2336hTpw4Ae/bsYffu3Xz44YcAvPnmm0yYMIHZs2fTtGlTtm/fTr9+/ShXrhyPP/54vrYvIiLFk5Kq4iT9HEypVvTbHf0neJTLc/NPPvnEKRmKjIzkgw8+cGpTsWJFXF1d8fX1JSAgwFHv5+eHzWZzqstN7969eeihhwCYMmUKr7/+Ops3b6ZDhw7ExMRQv359Xn75ZQDq16/P999/z0svvZRrf59//jmbN2/mhx9+oF69egDUrl07z/t9Ubly5ViwYIHTZb8mTZrw/vvvM27cOADee+89mjVr5tjOCy+8wKuvvkq3bt0A+8vB9+7dyxtvvKGkSkSklFBSJfnWpk0b5s2b5yiXK5f3hCw/mjRp4rQNX19fjhw5AsBPP/1Es2bNnNrffvvtl+1v586d3HDDDY5E52rdfPPN2eZRPfLII7z11luMGzcOYwxLlixxXAr966+/OHToEH369HGctQPIyMjAz8/vmmIREZH8O5eW4fRf+/9n4u6ekdsqeaKkqjhx97GfNbJiu/lQrlw5brzxxkIK5v9d+noVm81GVlYWYH9J8qUPuLx4KS433t7el13u4uKSrY+LT77/u5ySyIcffpiRI0fy3Xffcf78eQ4dOsSDDz4I4Ij5zTffpHnz5k7rXcvkfhERuTqNxq8BwJ0Mhrut4IPMcMKmJziW7xrd8qr6VVJVnNhs+boMV9x5eHhke01KTnVXo0GDBsTFxTnVbd269bLr3Hzzzfz3v//l559/zvFsVeXKlUlOTnZK2Hbs2JGneG644QZatWrFe++9x/nz57nnnnuoWrUqAFWrVqV69er8/vvvPPLII3nqT0REClewLYlZ7nO4xeV37nTZwwNp4zHXeP+ekiopNLVq1eKrr77iwQcfxNPTE39/f2rVqsWZM2f44osvuOWWW/Dx8bmq9x8+9dRTzJw5k+eff54+ffqwY8cOFi9eDOT+ipbw8HBatWpF9+7dmTlzJjfeeCM//vgjNpuNDh060Lp1a/766y9mzJhBjx49WL16NZ999hkVKlTIU0yPPPIIEydOJC0tjX/+859OyyZOnMiQIUOoUKECkZGRpKamsnXrVk6cOEF0dHS+919ERK6SMfzU9TAen4/Dln6Ok6YcCzI6sun5NviV8wIg48LV3TSmRypIoZk8eTL79++nTp06judQtWjRggEDBtCrVy8qV67MjBkzrqrv4OBgPvzwQ5YvX06TJk2YN28eY8aMAeyPfMhNbGwszZo146GHHqJRo0aMGDHCceasYcOGzJ07lzlz5nDLLbewefPmK95R+HcPPPAAx44d49y5c3Tp0sVpWd++fVmwYAGLFy/m5ptvJjw8nMWLFxMcHJz/nRcRkatz9hgsexTPz4ZjSz9HZlBLOqROY3XW7fh4uOLj4YaPx9Wfb7KZK01EkauWkpKCn58fR48epVKlSk7LLly4wL59+wgODsbLy8uiCEuXl156iZiYGA4dOuRUn5WVRUpKChUqVMDFpWz8O6I4/n6lp6cTFxdHx44ds82Xk6KlsSgeNA5F7LcvYcXTcCYZXNzh7vGcCx1AownxAOwc1xa/cva5txe/v0+dOpXnqxWgy39Sgs2dO5dmzZpRqVIlvv76a15++WUGDx5sdVgiIlKcZKTCF5Mhcba97F8Pui+AwFsg7dru9ruUkiopsX755RdefPFFjh8/Ts2aNXn22WcZNWqU1WGJiEhxceRHiO0Lh3fby6F9oP2L4JH/ubx5oaRKSqx//vOf2SaEi4iIYAxsWQBrx0LGBfCpBJ3nQP3IQt2skioREREpPc78BasGwS/2Z1FR527oMg98qxb6ppVUiYiISOnw81pYNRDO/gWuntBuMtzeH4roJiUlVSIiIlKypZ+H+PGweb69XKWRfTJ61ZuKNAwlVSIiIlJyJe+2T0b/60d7ufnTcM9EcC/6x8koqRIREZGrci4tw/Eevb2TI67pwZn5lpUF386DzydCZhqUq2KfO1X3nqKL4RJKqko4S3+hRURErJCSBCufht/X2cv1IqHzbCjnb2lY+gYWERGRkuOHT+CjZ+D8cXDzhoiXIPRJyOW9r0WpbLyzQwpU7969sdlsDBgwINuygQMHYrPZ6N27d9EHVorYbDZWrlxpdRgiIsVH2ln4eCgse8SeUAU0gacSoFmfYpFQgZIquUo1atRg6dKlnD9/3lF34cIFlixZQs2aNS2M7MrS0tKsDkFERPLjz+3wRivYthiwwZ1Doe8XULm+1ZE5UVIlV+W2226jZs2aLF++3FG3fPlyatSoQdOmTR11xhhmzJhB7dq18fb25pZbbuHDDz90LM/MzKRPnz4EBwfj7e1N/fr1+de//uW0rfXr13P77bdTrlw5rrvuOu68804OHDgA2M+adenSxan9sGHDaN26taPctm1b/vGPf/Dss8/i7+9Pu3btANi7dy8dO3akfPnyVK1alaioKI4ePepYr3Xr1jzzzDMMGzaM66+/nqpVqzJ//nzOnj3LE088ga+vL3Xq1OGzzz5z2n5e+h0yZAgjRoygYsWKBAQEMHHiRMfyWrVqAdC1a1dsNpujvHPnTtq0aYOvry8VKlQgJCSErVu3XmGkRERKsKxM2PhPWHAPHPsVfKvBY6vsz59y87A6umyUVJUg59IycvzJ6/KC9sQTT7Bo0SJH+a233uLJJ590ajN27FgWLVrEvHnz2LNnD8OHD+fRRx8lISEBgKysLG644Qb+85//sHfvXsaPH8/o0aP5z3/+A0BGRgZdunQhPDycXbt2kZiYSP/+/bHl81Tv0qVLcXNz4+uvv+aNN94gKSmJ8PBwbr31VrZu3crq1as5fPgwPXv2dFrv7bffxt/fn82bN/PMM8/w9NNP88ADD9CiRQu+++47IiIiiIqK4ty5cwD56rdcuXJ8++23zJgxg8mTJxMfb39T+pYtWwBYtGgRSUlJjvIjjzzCDTfcwJYtW9i2bRsjR47Um+1FpPQ69V94p7P97r6sDGh4Pzz9NdQOtzqyXGmiegly8S6/3IS++EWO9fundSqMcIiKimLUqFHs378fm83G119/zdKlS1m/fj0AZ8+eZebMmXz55ZeEhYUBULt2bTZu3Mgbb7xBeHg47u7uTJo0ydFncHAwmzZt4j//+Q89e/YkJSWFU6dOce+991KnTh0AGjZsmO9Yg4ODmT59Oi7/e6ru+PHjue2225gyZYqjzVtvvUWNGjX4+eefqVevHgC33HILY8eOBWDUqFFMmzYNf39/+vXr5+hn3rx57Nq1izvuuIN58+blqd8mTZowYcIEAOrWrcvs2bP54osvaNeuHZUrVwbguuuuIyAgwNHPwYMH+cc//kGDBg0c64mIlEp7VtjnT104Be7lIHI6NH202Mydyo2SKrlq/v7+dOrUibfffhtjDJ06dcLf//9vZ927dy8XLlxwXG67KC0tzekSYUxMDAsWLODAgQOcP3+etLQ0br31VgAqVqxI7969iYiIoF27dtxzzz307NmTwMDAfMX69+0BbNu2jXXr1lG+fPlsbX/77Ten5OciV1dXKlWqxM033+yoq1rV/i6pI0eOXHW/AIGBgY4+chMdHU3fvn3597//zT333MMDDzzgSDRFREqF1NPw2fOw4z17udpt9iejVyoZf+uUVJUgeydHZKs7l5bhOEO1dezdRf6cqieffJLBgwcDMGfOHKdlWVlZAHz66adUr17daZmnpycA//nPfxg+fDivvvoqYWFh+Pr68vLLL/Ptt9862i5atIghQ4awevVqli1bxtixY4mPj+eOO+7AxcUFY4xT3+np6dni9PHxyRbbfffdx/Tp07O1/XvCdunlNZvN5lR38TLkxX29ln4v9pGbiRMn8vDDD/Ppp5/y2WefMWHCBJYuXUrXrl0vu56ISIlwaAss7wsn9gM2aPkstB4JriVnmoOSqhLkSgmTj4dbkSdVHTp0cNxNFxHhnPQ1atQIT09PDh48SHh4ztfAN2zYQIsWLRg4cKCj7rfffsvWrmnTpjRt2pRRo0YRFhbG+++/zx133EHlypX5/vvvndru2LHjinONbrvtNmJjY6lVqxZubgV3zAqqX3d3dzIzM7PV16tXj3r16jF8+HAeeughFi1apKRKREq2zAzYOBPWTwOTCX41oNt8CGpR6Jv28XDjlxfaExcXVyDfn5qoLtfE1dWVH374gR9++AFXV1enZb6+vjz33HMMHz6ct99+m99++43t27czZ84c3n77bQBuvPFGtm7dypo1a/j5558ZN26cY2I2wL59+xg1ahSJiYkcOHCAtWvX8vPPPzvmVbVt25atW7fyzjvv8MsvvzBhwoRsSVZOBg0axPHjx3nooYfYvHkzv//+O2vXruXJJ5/MMZnJq4Lqt1atWnzxxRckJydz4sQJzp8/z+DBg1m/fj0HDhzg66+/ZsuWLVc1v0xEpNg4sR8Wd4J1L9kTqsY9YMDGIkmoCoOSKrlmFSpUoEKFCjkue+GFFxg/fjxTp06lYcOGRERE8PHHHxMcHAzAgAED6NatG7169aJ58+YcO3bM6ayVj48PP/74I927d6devXr079+fwYMH89RTTwH2s2Pjxo1jxIgRNGvWjNOnT/PYY49dMeZq1arx9ddfk5mZSUREBI0bN2bo0KH4+fk5JrNfjYLq99VXXyU+Pt7xiApXV1eOHTvGY489Rr169ejZsyeRkZFOk/xFREqUnctg3l1w6Bvw8IVub0KPheB9ndWRXTWbuXRCihSYlJQU/Pz8OHr0KJUqVXJaduHCBfbt20dwcDBeXlf/Jm29++/KsrKySElJoUKFCteUMJUkBfX7VZDS09OJi4ujY8eOehSExTQWxUNpGIer+g46fxLinoPdH9jLNZrbL/ddX6vQ4rycnMbh4vf3qVOncj1pkBN9A4uIiEjROLAJlj8Fpw6CzdU+Ef2uaHAtHelI6diLMszHw63QnkMlIiJSIDLTIWE6bHgVTJb9rFS3BVCjmdWRFSglVSIiIlJ4jv0Gy/vBH9vs5Vseho4zwNPX2rgKgeUTTObOneuY9xESEsKGDRsu2z4hIYGQkBC8vLyoXbs2MTEx2drExsY6budv1KgRK1ascFo+b948mjRp4phgHRYWlu39bcYYJk6cSLVq1fD29qZ169bs2bPn2ndYRESkLDAGtr8LMS3tCZWXH/RYBF3nlcqECixOqpYtW8awYcMYM2YM27dvp2XLlkRGRnLw4MEc2+/bt4+OHTvSsmVLtm/fzujRoxkyZAixsbGONomJifTq1YuoqCh27txJVFQUPXv2dHqY5A033MC0adPYunUrW7dupW3btnTu3NkpaZoxYwYzZ85k9uzZbNmyhYCAANq1a8fp06cL9BjoPgEpDPq9EhFLnTsO/3kMVg2C9LMQdBc8vQkad7M6ssJlLHT77bebAQMGONU1aNDAjBw5Msf2I0aMMA0aNHCqe+qpp8wdd9zhKPfs2dN06NDBqU1ERIR58MEHLxvL9ddfbxYsWGCMMSYrK8sEBASYadOmOZZfuHDB+Pn5mZiYmCvv2P+cOnXKAObo0aPZlmVkZJi9e/fmuEwKVmZmpjlx4oTJzMy0OpQic/LkSbN3716TlpZmdSgOaWlpZuXKlcUqprJKY1E8lORxOJuabs6mppu/Tp83Qc9/YoKe/8T8dfq8OZuabs7/9IUxrzQwZkIFYyZVNGbDTGMyM6wOOVc5jcPF7+9Tp07lqy/L5lSlpaWxbds2Ro4c6VTfvn17Nm3alOM6iYmJtG/f3qkuIiKChQsXkp6ejru7O4mJiQwfPjxbm1mzZuXYZ2ZmJh988AFnz551vPR33759JCcnO23L09OT8PBwNm3a5HhG0qVSU1NJTU11lFNSUgD77Zo5vTrF19eXw4cPk5WVhY+Pj+OVJ1KwjDGkpaVx/vz5MnGMs7KyOHLkCF5eXhhjcvzds8LFOIpLPGWZxqJ4KMnj0Gj82mx1YS+u4Vm3/9Df9VOwGUzFOmR0eQMCb4XMLPtPMZTTOFztmFiWVB09epTMzEzHC2kvqlq1KsnJyTmuk5ycnGP7jIwMjh49SmBgYK5tLu1z9+7dhIWFceHCBcqXL8+KFSto1KiRYzsX17u0nwMHDuS6T1OnTs3xYYzr1q3L9u65i3x9fTl79myZeX6SFI309HT++usvdu3aZXUo2cTHx1sdgvyPxqJ4KJnj4Jw+1LH9wb/c59DYZT8A+yu15vvqj5C5/U/Y/qcF8eXf38fh3LlzV9WH5Xf/XXrmwBhz2bMJObW/tD4vfdavX58dO3Zw8uRJYmNjefzxx0lISHAkVlcT26hRo4iOjnaUU1JSqFGjBm3atMn28M+/y8zMJCMjQ/NgCklGRgabNm2iRYsWBfqev+Lq4kufi1uinp6eTnx8PO3atSuxDzosLTQWxUNJHofW92QAcC41g9mvjmes27t429LI8q7I+YhXqX7TfVS3OMa8ymkcLl5pyi/LvmH8/f1xdXXNdgbpyJEj2c4QXRQQEJBjezc3N0fSklubS/v08PDgxhtvBCA0NJQtW7bwr3/9izfeeIOAgADAfsYqMDAwT7GB/RKhp6dntnp3d/fLfmBK2oeppElPTycjI4Py5cvrWBcDV/o8SNHRWBQPJXEc/Nzd4exRyn02iJfcVwOQGdwa164xlKsQePmVi6m/j8PVjodl/5T18PAgJCQk22nP+Ph4WrTI+UWKYWFh2dqvXbuW0NBQxwHIrU1ufV5kjHHMhwoODiYgIMCpn7S0NBISEq7Yj4iISKn36+cwrwVuv6wm1bjxQvqjpD74AZTQhKqgWHotJDo6mqioKEJDQwkLC2P+/PkcPHiQAQMGAPbLaX/88QfvvPMOYH/57uzZs4mOjqZfv34kJiaycOFClixZ4uhz6NChtGrViunTp9O5c2dWrVrF559/zsaNGx1tRo8eTWRkJDVq1OD06dMsXbqU9evXs3q1Pdu22WwMGzaMKVOmULduXerWrcuUKVPw8fHh4YcfLsIjJCIiUoykX4AvJsE3cwHI8q9Plz9684MJ4llb8ZpyYAVLk6pevXpx7NgxJk+eTFJSEo0bNyYuLo6goCAAkpKSnJ5ZFRwcTFxcHMOHD2fOnDlUq1aN1157je7duzvatGjRgqVLlzJ27FjGjRtHnTp1WLZsGc2bN3e0OXz4MFFRUSQlJeHn50eTJk1YvXo17dq1c7QZMWIE58+fZ+DAgZw4cYLmzZuzdu1afH1L5wPLRERELuvwHojtB0f+90zH2/tzIXw8P7zwlbVxFSOWz9odOHAgAwcOzHHZ4sWLs9WFh4fz3XffXbbPHj160KNHj1yXL1y48Ipx2Ww2Jk6cyMSJE6/YVkREpNQyBr59A+LHQ2YqlKsMnedCvfaQlmF1dMWK5UmViIiIFFOnD8OqgfY5VAB120PnOVC+irVxFVNKqkRERCS7nz6zv2bm3DFw84L2L0KzvlAGHqJ8tZRUiYiIyP9LOwdrx8LW/02VqdoYui+AKg2tjasEUFIlIiIidkk7IbYvHP3ZXg4bDHePB7fsz2CU7JRUiYiIlHVZWZA4G76YDFnpUD4Aus6DOm2tjqxEUVIlIiJSlqX8CSsGwL4Ee7nBvXDfa1Au99erSc6UVImIiJRVe1fBx0Ph/Alw94EOU+G2xzUZ/SopqRIRESlrUs/A6pGw/d/2cuCt9sno/nUtDaukU1IlIiJSlvyxzT4Z/fjvgA3uGgatR4Obh9WRlXhKqkRERMqCrEzY+E9YPxWyMqBCdej6BgS3tDqyUkNJlYiISGl38iAsfwoObrKXb+oK9/4TvK+3Nq5SRkmViIhIabb7Q/gkGlJPgUd56PgK3PKgJqMXAiVVIiIiFknNhLrj1gKwd3IEPh4F+LV8IQXi/gG7ltrLNzSDbvOhYu2C24Y4UVIlIiJS2hz8Fpb3g5MHwOYCrUZAq3+Aq772C5OOroiISGmRmQFfvQxfzQCTBdfVhG5vQs07CmVzPh5u7J/WqVD6LomUVImIiJQGx/fB8v7w3832cpMHoeMM8PKzNq4yREmViIhISWYM7FwKcc9B2hnw9IN7Z8LNPayOrMxRUiUiIlJSnT9hv7Nvz3J7uWYL6PaG/bKfFDklVSIiIiXR/o32Z0+l/Bdc3KD1KLhrOLi4Wh1ZmaWkSkREpCTJSLM/FX3jPwFjf0RCtwVwQ4jVkZV5SqpERERKiqO/wvK+8Od2e7lpFHSYBp7lrY1LACVVIiIixZ8x8N07sHokpJ8Dr+vg/tegUWerI5O/UVIlIiJSnJ07Dh89Az9+Yi8Ht4IuMeBX3dq4JBslVSIiIsXVb+tg5dNwOglc3OHu8RA2GFxcrI5McqCkSkREpLjJSIUvJkPibHvZvx50XwCBt1gbl1yWkioREZHi5MiPENsXDu+2l0P7QPsXwcPH2rjkipRUiYiIFAfGwOY3Ye1YyLgAPpWg8xyoH2l1ZJJHSqpEREQsVolTeH7wMPy61l5R527oMg98q1obmOSLkioRERELtXbZwcvuMbj+mgKuntBuMtzeX5PRSyAlVSIiIkXsXFoG6edO0+S//6anRzwAGf4NSO/yJt43NLE4OrlaSoNFRESKWLcJb5I8syUNjtsTqrcyOnDTf0fScPYhiyOTa6EzVSIiIkUlKwu+nccqj/F42jL4y/jxXPoAErL0qITSQEmViIhIUUhJsj/I8/d1eNogvU571rvdT8LOigBsHXs3Ph76Wi7JdPlPRESksP3wCcxrAb+vAzdv6DQTer2H8azgaOLj4aakqoTT6ImIiBSWtLOwZjRsW2wvBzSB7guhcj1IT7c0NCl4SqpEREQKw5/b7U9GP/YrYIM7h0CbseDmYXVkUkiUVImIiBSkrEzY9Bp8+SJkZYBvNegaA7XDrY5MCpmSKhERkYJy6r+wYgDs32AvN7wf7vsX+FS0Ni4pEkqqRERECsKeFfDxULhwCtzLQeR0aPoo2GxWRyZFREmViIjItUg9DZ89Dzves5erh0C3N6FSHWvjkiKnpEpERORqHdoCy/vCif1gc4GWz0L48+DqbnVkYgHLn1M1d+5cgoOD8fLyIiQkhA0bNly2fUJCAiEhIXh5eVG7dm1iYmKytYmNjaVRo0Z4enrSqFEjVqxY4bR86tSpNGvWDF9fX6pUqUKXLl346aefnNr07t0bm83m9HPHHXdc+w6LiEjJl5kBCTPgrQh7QuVXA3p/Cm3HKqEqwyxNqpYtW8awYcMYM2YM27dvp2XLlkRGRnLw4MEc2+/bt4+OHTvSsmVLtm/fzujRoxkyZAixsbGONomJifTq1YuoqCh27txJVFQUPXv25Ntvv3W0SUhIYNCgQXzzzTfEx8eTkZFB+/btOXv2rNP2OnToQFJSkuMnLi6ucA6EiIiUHCcOwOJOsO4lMJnQuAcM2AhBLayOTCxm6eW/mTNn0qdPH/r27QvArFmzWLNmDfPmzWPq1KnZ2sfExFCzZk1mzZoFQMOGDdm6dSuvvPIK3bt3d/TRrl07Ro0aBcCoUaNISEhg1qxZLFmyBIDVq1c79bto0SKqVKnCtm3baNWqlaPe09OTgICAAt9vEREpoXb9Bz59FlJTwMMX7p0JTXpaHZUUE5adqUpLS2Pbtm20b9/eqb59+/Zs2rQpx3USExOztY+IiGDr1q2k/+/JtLm1ya1PgFOnTgFQsaLzLa/r16+nSpUq1KtXj379+nHkyJG87ZyIiJQu50/aH+S5vJ89oarRHJ7eqIRKnFh2puro0aNkZmZStWpVp/qqVauSnJyc4zrJyck5ts/IyODo0aMEBgbm2ia3Po0xREdHc9ddd9G4cWNHfWRkJA888ABBQUHs27ePcePG0bZtW7Zt24anp2eOfaWmppKamuoop6SkAJCenu5I+qToXTz2GgNraRyKD41F/tgOJuL60UBspw5hbK5ktfwHWXcOAxe3a3rVzKXHPz09nXSbucZoJb9y+jxc7WfD8rv/bJc8v8MYk63uSu0vrc9Pn4MHD2bXrl1s3LjRqb5Xr16O/2/cuDGhoaEEBQXx6aef0q1btxz7mjp1KpMmTcpWv27dOnx8fHLdJyka8fHxVocgaByKE43F5dlMBvWTVlLv8MfYMJz1qMK2WgM4cfpGWL22wLe3Zs1aPF0LvFvJo79/Hs6dO3dVfViWVPn7++Pq6prtDNKRI0eynWm6KCAgIMf2bm5uVKpU6bJtcurzmWee4aOPPuKrr77ihhtuuGy8gYGBBAUF8csvv+TaZtSoUURHRzvKKSkp1KhRgzZt2jjik6KXnp5OfHw87dq1w91dd+VYReNQfGgs8uD477iuGoDL4e8AyGryEB7tpxDm6Vtgm0hPT+eT1f//RR4R0R4fD8vPdZQ5OX0eLl5pyi/LRs/Dw4OQkBDi4+Pp2rWroz4+Pp7OnTvnuE5YWBgff/yxU93atWsJDQ11HIiwsDDi4+MZPny4U5sWLf7/rgxjDM888wwrVqxg/fr1BAcHXzHeY8eOcejQIQIDA3Nt4+npmeOlQXd3d/3hKgY0DsWDxqH40FjkwBj7QzzjRkD6WfDyg3tn4dK4W6FPQraPh5Iqq/z983C1nwtLRy86OpqoqChCQ0MJCwtj/vz5HDx4kAEDBgD2Mz9//PEH77zzDgADBgxg9uzZREdH069fPxITE1m4cKHjrj6AoUOH0qpVK6ZPn07nzp1ZtWoVn3/+udPlvUGDBvH++++zatUqfH19HWe2/Pz88Pb25syZM0ycOJHu3bsTGBjI/v37GT16NP7+/k4JoIiIFL1zaRk0Gr8GgL2TIwru7M654/DJMNi7yl4Ougu6vQF+l7+SIXKRpUlVr169OHbsGJMnTyYpKYnGjRsTFxdHUFAQAElJSU7PrAoODiYuLo7hw4czZ84cqlWrxmuvveZ4nAJAixYtWLp0KWPHjmXcuHHUqVOHZcuW0bx5c0ebefPmAdC6dWuneBYtWkTv3r1xdXVl9+7dvPPOO5w8eZLAwEDatGnDsmXL8PUtuFO/IiJSTOz7CpY/Baf/tE9AbzsWWgwBl8Kd5OTpCr+80F5nDEsJy88zDhw4kIEDB+a4bPHixdnqwsPD+e677y7bZ48ePejRo0euyy9Obs+Nt7c3a9asuWwbEREpBTLS4MsXYNPrgIFKN0L3BVCtqdWRSQlkeVIlIiJiib9+htg+kLzLXg7pDRFTwKOcpWFJyaWkSkREyhZjYOtbsGYMZJwH74rQeTY06GR1ZFLCKakSEZGy4+xRWDUYfv7MXq7dBrrMgwq539ktkldKqkREpGz49XNYORDOHAZXD7hnIjR/Glwse2OblDJKqkREpHRLvwBfTIJv5trLlRvYJ6MH3GxtXFLqKKkSEZHS6/AeiO0HR/bYy7f3h3aTwd3b2rikVFJSJSIipY8x8O0bED8eMlOhXGXoPBfqtbc6MinFlFSJiEjpcvowrBpon0MFULc9dJ4D5atYG5eUekqqRESk9PjpM1g1CM4dAzcvaP8iNOsLNpvVkUkZoKRKRERKvrRzsHYsbF1oL1e92T4ZvUoDa+OSMkVJlYiIlGxJOyG2Lxz92V4OGwx3jwc3T2vjkjJHSZWIiJRINrJw+2Y2rH8RstKhfAB0nQd12lodmpRRSqpERKTEqcpxXnWfh8eX/3tUQoN74b7XoFwlawOTMk1JlYiIlBjn0jLI+H4lazyf5zrbWYybN2ntp+LZrLcmo4vl9Gx+EREpGVLP8NHk7lT4qA/X2c6yKyuYtmdfpP7yKkqopFjQmSoRESn+/tgGsX150O13soyNeZn3MSujB+n6GpNiRL+NIiJSfGVlwsZ/wvqpkJVBVoXqpETO5uW3zwOwdezd+Hjoq0yKB/0miohI8XTyICx/Cg5uspdv6orLvf/Ew9UXWAOAj4ebkiopNvSbKCIixc/uD+GTaEg9BR7loeMrcMuD9rlTaRlWRyeSIyVVIiJSfFw4BXH/gF3L7OUbmkG3+VCxtrVxieSBkioRESkeDn4Dy/vZL/vZXKDVCGj1D3DVV5WUDPpNFRERa2VmwFcz4KuXwWTBdTWh2wKo2dzqyETyRUmViIhY5/g++9mp/26xl5s8CB1fBq8K1sYlchWUVImISNEzBnYuhbjnIO0MePrBvTPh5h5WRyZy1ZRUiYhI0Tp/Aj4ZDntW2MtBd0LXGPtlP5ESTEmViIgUnX0bYMVTkPIHuLhBm9Fw5zBwcbU6MpFrpqRKREQKX0YarJ8CG2cBBirWge5vQvUQqyMTKTBKqkREpHAd/QVi+0LSDnv5tscgYip4lrc0LJGCpqRKREQKhzHw3duwehSknwPv6+G+16DR/VZHJlIolFSJiEjBO3sMPh4CP35iLweH2yejV6hmbVwihUhJlYiIFKzfvoQVT8OZZHBxh3smwB2DwMXF6shECpWSKhERKRgZqfDFZEicbS/714fuCyCwibVxiRQRJVUiInLtjvxgn4x++Ht7uVlfaPcCePhYG5dIEVJSJSJSxpxLy2BoohtDE9eyd3IEPh7X8FVgDGxZAGvHQsYF8PGHznOgfoeCC/gSPh5u7J/WqdD6F7laSqpEROTqnDkCqwbBL2vt5Rvvgc5zwbeqtXGJWERJlYiI5N/Pa2HVQDj7F7h6QvsX4Pb+YLNZHZmIZZRUiYhI3qWfh/jxsHm+vVzlJvtk9KqNrI1LpBhQUiUiInmTvNs+Gf2vH+3lOwbB3ePB3cvauESKCSVVIiJyeVlZ8M1c+GISZKZB+arQZa59DpWIOCipEhGR3KUkwcqn4fd19nL9jnD/61DO39q4RIohJVUiIpKzHz6Bj56B88fBzRs6TIGQJzQZXSQXSqpERMRZ2llYMxq2LbaXA2+Bbgugcj1LwxIp7ix/EdPcuXMJDg7Gy8uLkJAQNmzYcNn2CQkJhISE4OXlRe3atYmJicnWJjY2lkaNGuHp6UmjRo1YsWKF0/KpU6fSrFkzfH19qVKlCl26dOGnn35yamOMYeLEiVSrVg1vb29at27Nnj17rn2HRUSKsz+3wxut/pdQ2eDOYdDncyVUInlgaVK1bNkyhg0bxpgxY9i+fTstW7YkMjKSgwcP5th+3759dOzYkZYtW7J9+3ZGjx7NkCFDiI2NdbRJTEykV69eREVFsXPnTqKioujZsyfffvuto01CQgKDBg3im2++IT4+noyMDNq3b8/Zs2cdbWbMmMHMmTOZPXs2W7ZsISAggHbt2nH69OnCOyAiIlbJyoQNM2HBPXDsV/CtBo9/BO0mgZuH1dGJlAzGQrfffrsZMGCAU12DBg3MyJEjc2w/YsQI06BBA6e6p556ytxxxx2Ocs+ePU2HDh2c2kRERJgHH3ww1ziOHDliAJOQkGCMMSYrK8sEBASYadOmOdpcuHDB+Pn5mZiYmLztnDHm1KlTBjBHjx7N8zpS8NLS0szKlStNWlqa1aGUaRqH4uPkmXMm6PlPTNDzn5izqenGnDxkzFsdjZlQwf6zLMqYs8esDrPU02eieMhpHC5+f586dSpffVl2piotLY1t27bRvn17p/r27duzadOmHNdJTEzM1j4iIoKtW7eSnp5+2Ta59Qlw6tQpACpWrAjYz4glJyc79ePp6Ul4ePhl+xERKWlc966EeS3gwEZwL2d/zcwDb4NPRatDEylxLJuofvToUTIzM6la1fkdUVWrViU5OTnHdZKTk3Nsn5GRwdGjRwkMDMy1TW59GmOIjo7mrrvuonHjxo7tXFzv0n4OHDiQ6z6lpqaSmprqKKekpACQnp7uSPqk6F089hoDa2kcio/09AzKcZ5J7m/jufIrALKq3UZm5xioWBsyMiyOsGzQZ6J4yGkcrnZMLL/7z3bJrbnGmGx1V2p/aX1++hw8eDC7du1i48aN1xzb1KlTmTRpUrb6devW4ePjk+t6UjTi4+OtDkHQOFgtNRMqnP6VOI8YglyOkIWNH6vcx69VumC++RH40eoQyxx9JoqHv4/DuXPnrqoPy5Iqf39/XF1ds51BOnLkSLYzRBcFBATk2N7NzY1KlSpdtk1OfT7zzDN89NFHfPXVV9xwww1O2wH7GavAwMA8xQYwatQooqOjHeWUlBRq1KhBmzZtHPFJ0UtPTyc+Pp527drh7u5udThllsahGMjK4PXJgxnithw3lyz+a/wZljaQrQcb8Eu/9ldeXwqUPhPFQ07jcPFKU35ZllR5eHgQEhJCfHw8Xbt2ddTHx8fTuXPnHNcJCwvj448/dqpbu3YtoaGhjgMRFhZGfHw8w4cPd2rTokULR9kYwzPPPMOKFStYv349wcHBTn0GBwcTEBBAfHw8TZs2BexzwBISEpg+fXqu++Tp6Ymnp2e2end3d31gigGNQ/GgcbDIif2wvD/R7vY7oVdk3sn49Cc4jf0susbEOvpMFA9/H4erHQ9LL/9FR0cTFRVFaGgoYWFhzJ8/n4MHDzJgwADAfubnjz/+4J133gFgwIABzJ49m+joaPr160diYiILFy5kyZIljj6HDh1Kq1atmD59Op07d2bVqlV8/vnnTpf3Bg0axPvvv8+qVavw9fV1nNny8/PD29sbm83GsGHDmDJlCnXr1qVu3bpMmTIFHx8fHn744SI8QiIi18gY2PUf+PRZSDuN8fTlZOspDF9lP3u+dezd+HhYPhNEpFSw9JPUq1cvjh07xuTJk0lKSqJx48bExcURFBQEQFJSktMzq4KDg4mLi2P48OHMmTOHatWq8dprr9G9e3dHmxYtWrB06VLGjh3LuHHjqFOnDsuWLaN58+aONvPmzQOgdevWTvEsWrSI3r17AzBixAjOnz/PwIEDOXHiBM2bN2ft2rX4+voW0tEQESlg50/ak6nvP7SXa9yBrdt8XDyqwKovAfDxcFNSJVJALP8kDRw4kIEDB+a4bPHixdnqwsPD+e677y7bZ48ePejRo0euyy9Obr8cm83GxIkTmThx4hXbiogUOwc2wfL+cOoQ2Fyh9Si4azi4usHZ81ZHJ1IqWZ5UiYhIAcpMh/XTYONMMFlwfTB0XwA3hFodmUipp6RKRKS0OPYbxPaFP/93Nv/WRyFyGnhq2oJIUVBSJSJS0hkD29+Fz56H9LPgdR3cNwtu6nqlNUWkACmpEhEpyc4dh4+Hwg8f2cu1WkLXN8CvurVxiZRBSqpEREqq3xNgxQA4/Se4uEPbsdDiGXBxtToykTLpqpKqQ4cOsX//fs6dO0flypW56aabcnzopYiIFIKMVPjyRdj0OmCgUl3o/iZUa2p1ZCJlWp6TqgMHDhATE8OSJUs4dOiQ02MJPDw8aNmyJf3796d79+64uLgUSrAiImXeXz/ZJ6Mn77KXQ56AiJfAo5y1cYkIecp+hg4dys0338wvv/zC5MmT2bNnD6dOnSItLY3k5GTi4uK46667GDduHE2aNGHLli2FHbeISNliDGxZCG+E2xMq74rw4Pv2CelKqESKhTydqfLw8OC3336jcuXK2ZZVqVKFtm3b0rZtWyZMmEBcXBwHDhygWbNmBR6siEiZdPYorBoMP39mL9dpC13mgW+AtXGJiJM8JVUvv/wyBw8exBiDzWa7bNuOHTsWSGAiIgL88jmsfBrOHgFXD7hnEjQfAJpmIVLs5HlOVXBwMElJSVSpUqUw4xEREYD0C/D5RPjW/q5SKje0Pxk9oLGlYYlI7vKcVOXlfXkiIlIADu+xT0Y/stdevv0paDcJ3L0LpHsfDzf+FZZBx44dcXfXk3VECoo+TSIixUVWFmx+A+InQGYqlKsCXeZC3XZWRyYieZCvpGrBggWUL1/+sm2GDBlyTQGJiJRJp5Nh5UD47Qt7uV4HuH82lM9+g5CIFE/5SqpiYmJwdc39Sb02m01JlYhIfv0YBx8NhnPHwM3L/typ0D5whRuDRKR4yVdStXXrVk1UFxEpKGnnYO0Y2PqWvVz1Zvtk9CoNrI1LRK5KnpOqKz1KQUSkLDiXlkGj8WsA2Ds5Ah+Pq5yamrTTPhn96M/2cthguHs8uOmVXyIlle7+ExEpSllZkPg6fPECZKVD+QDoGgN12lgdmYhcozwnVRMmTLjiJHUREbmMU3/AygGw7yt7ucG9cP/r4FPR2rhEpEDkKak6ePAgEyZMyHOnf/zxB9WrV7/qoERESp29q+CjIXDhJLj7QIdpcNtjmowuUork6T0HzZo1o3///mzevDnXNqdOneLNN9+kcePGLF++vMACFBEp0VLPwKpB8J/H7AlVtabw1AYIeVwJlUgpk6czVT/88ANTpkyhQ4cOuLu7ExoaSrVq1fDy8uLEiRPs3buXPXv2EBoayssvv0xkZGRhxy0iUvz9dxss7wvHfwds0DIaWo8CV3erIxORQpCnpKpixYq88sorvPjii8TFxbFhwwb279/P+fPn8ff355FHHiEiIoLGjfVOKhERsjJh40xYNxVMJlS4Abq9AbXusjoyESlE+boX2MvLi27dutGtW7fCikdEpGQ7eRCWPwUHN9nLN3WDe2eC9/XWxiUihU7v/hMRKSi7P4RPoiH1FHj4QqdXoEkvzZ0SKSOUVImIXKsLpyDuH7Brmb18w+3QbT5UDLY2LhEpUkqqRESuxcFvYHk/+2U/mwu0GgGt/gGu+vMqUtboUy8ikkfn0jI4l5YBgCuZsG4K5pt/YjNZcF1N6LYAaja3OEoRsYqSKhGRPLr4zr+atsPMcp+DT+Kv9gW3PASRM8CrgoXRiYjV8p1UHTt2jEqVKgFw6NAh3nzzTc6fP8/9999Py5YtCzxAEZHiw9DdZQOT3BdT3naBFOPDmPQneb3rS1YHJiLFQJ6Tqt27d3Pfffdx6NAh6taty9KlS+nQoQNnz57FxcWFf/7zn3z44Yd06dKlEMMVEbHI+RP82vQD3H5YCcC3WQ2o+9S7TK+syegiYpen19QAjBgxgptvvpmEhARat27NvffeS8eOHTl16hQnTpzgqaeeYtq0aYUZq4iINfZtgHl34vbDSoyLGzPSe/FQ2li8Kgfj46FZFCJil+e/Blu2bOHLL7+kSZMm3HrrrcyfP5+BAwfi4mLPy5555hnuuOOOQgtURKTIZaTBupfg638BBirWIfX+GObG/GV1ZCJSDOU5qTp+/DgBAQEAlC9fnnLlylGxYkXH8uuvv57Tp08XfIQiIlY4+gvE9oGknfbybY9BxFSybF7AGktDE5HiKV/nrW2XPBX40rKISIlnDHz3NqweBenn7K+Xue81aHS/ffn/HqkgInKpfCVVvXv3xtPTE4ALFy4wYMAAypUrB0BqamrBRyciUpTOHoOPh8CPn9jLweHQNQYqVLM2LhEpEfKcVD3++ONO5UcffTRbm8cee+zaIxIRscJvX8KKp+FMMri4wz0T4I5B4JLn+3lEpIzLc1K1aNGiwoxDRMQa6Rfgi8nwzRx72b8+dF8AgU2sjUtEShzdCywiZdeRHyC2Lxz+3l5u1hfavQAePtbGJSIlkpIqESl7jIHNb0L8OMi4AD7+0HkO1O9gdWQiUoIpqRKRsuXMEVg1CH5Zay/feA90ngu+Va2NS0RKPCVVIlJ2/LwGVg6Ec0fB1RPavwC39wc9HkZECoDlt7XMnTuX4OBgvLy8CAkJYcOGDZdtn5CQQEhICF5eXtSuXZuYmJhsbWJjY2nUqBGenp40atSIFStWOC3/6quvuO+++6hWrRo2m42VK1dm66N3797YbDanHz0xXqSESj8Pnz4H7/e0J1RVboL+66H5U0qoRKTAWJpULVu2jGHDhjFmzBi2b99Oy5YtiYyM5ODBgzm237dvHx07dqRly5Zs376d0aNHM2TIEGJjYx1tEhMT6dWrF1FRUezcuZOoqCh69uzJt99+62hz9uxZbrnlFmbPnn3Z+Dp06EBSUpLjJy4urmB2XESKTtIumN8atrxpL98xCPp9CVUbXVV3Ph5u7J/Wif3TOum9fyLixNK/CDNnzqRPnz707dsXgFmzZrFmzRrmzZvH1KlTs7WPiYmhZs2azJo1C4CGDRuydetWXnnlFbp37+7oo127dowaNQqAUaNGkZCQwKxZs1iyZAkAkZGRREZGXjE+T09Px6t5RKSEycqCb+bCF5MgMw3KV4Uuc+1zqERECoFlSVVaWhrbtm1j5MiRTvXt27dn06ZNOa6TmJhI+/btneoiIiJYuHAh6enpuLu7k5iYyPDhw7O1uZiI5cf69eupUqUK1113HeHh4bz00ktUqVIl1/apqalOT5ZPSUkBID09nfT09HxvXwrGxWOvMbBWkY7D6SRcPx6My74EALLqdiCz0ywo5w/6PdBnopjQOBQPOY3D1Y6JZUnV0aNHyczMpGpV5ztuqlatSnJyco7rJCcn59g+IyODo0ePEhgYmGub3PrMTWRkJA888ABBQUHs27ePcePG0bZtW7Zt2+Z4Vc+lpk6dyqRJk7LVr1u3Dh8fPffGavHx8VaHIBT+OASe3MqtBxfiknmWDJsH39/wMAfKtYGEzYW63ZJIn4niQeNQPPx9HM6dO3dVfVg+IeDSlzIbYy77ouac2l9an98+c9KrVy/H/zdu3JjQ0FCCgoL49NNP6datW47rjBo1iujoaEc5JSWFGjVq0KZNGypVqpSv7UvBSU9PJz4+nnbt2uHu7m51OGVWoY9D2llc48fisu/fAJiAJpjOb3CTf11uKvitlWj6TBQPGofiIadxuHilKb8sS6r8/f1xdXXNdgbpyJEj2c40XRQQEJBjezc3N0fSklub3PrMq8DAQIKCgvjll19ybePp6ZnjWSx3d3d9YIoBjUPxUCjj8Md3sLwfHPsVsMGdQ7G1GYO7m0fBbqeU0WeieNA4FA9/H4erHQ/L7v7z8PAgJCQk22nP+Ph4WrRokeM6YWFh2dqvXbuW0NBQxwHIrU1ufebVsWPHOHToEIGBgdfUj4gUoKxM2PAqLGxnT6h8q8HjH0G7SaCESkSKmKWX/6Kjo4mKiiI0NJSwsDDmz5/PwYMHGTBgAGC/nPbHH3/wzjvvADBgwABmz55NdHQ0/fr1IzExkYULFzru6gMYOnQorVq1Yvr06XTu3JlVq1bx+eefs3HjRkebM2fO8OuvvzrK+/btY8eOHVSsWJGaNWty5swZJk6cSPfu3QkMDGT//v2MHj0af39/unbtWkRHR0Qu6+QhWPEUHPjaXm7UGe6dBT4VLQ1LRMouS5OqXr16cezYMSZPnkxSUhKNGzcmLi6OoKAgAJKSkpyeWRUcHExcXBzDhw9nzpw5VKtWjddee83xOAWAFi1asHTpUsaOHcu4ceOoU6cOy5Yto3nz5o42W7dupU2bNo7yxXlQjz/+OIsXL8bV1ZXdu3fzzjvvcPLkSQIDA2nTpg3Lli3D19e3sA+LiFzJ97Hw8XBIPQXu5aDjy3Drw3qQp4hYyvKJ6gMHDmTgwIE5Llu8eHG2uvDwcL777rvL9tmjRw969OiR6/LWrVs7JrjnxNvbmzVr1lx2GyJigQsp8NkI2Pm/s9PVQ6Dbm1CpjrVxiYhQDJIqEZE8ObTZPhn9xH6wuUDL5yB8BLhqgq+IFA9KqkSkeMvMsE9GT5gOJhP8akK3+RAUZnVkIiJOlFSJSJE6l5bBLePWArB3csTl3593fJ99Mvqh/7278+ae0OkV8PIrgkhFRPJHSZWIFD/GwK5l8OlzkHYaPCtAp1ehSU+rIxMRyZWSKhEpXs6fhE+j7Xf4AdS4w3657/ogS8MSEbkSJVUiUnzs/9p+ue/UIbC5QutRcNdwcNWfKhEp/vSXSkSsl5kO66fChpmAgeuDofsCuCHU6shERPJMSZWIWOvYbxDbF/783/Pnmj4KHaaBpx60KyIli5IqEbGIwXXHuxA/GtLPgtd1cN+/4KYuVgcmInJVlFSJSJG7jtNMdV+AZ9wWe0WtltD1DfCrbm1gIiLXQEmViBQp1wMbWO05kgDbCYyLO7a2Y6HFM+DianVoIiLXREmViBSNjFQa/bGE8ts/o7wNfssKpNoT7+IdpMnoIlI6uFgdgIiUAX/9hNviDtQ98hkA72Xczb1pL3G2UmPOpWVYHJyISMHQmSoRKTzGwNaFsGYMtowLpLr5MvhcP+Kz7GenQl/8AoD90zpZGaWISIFQUiUihePMX/DRYPh5NQBZtduwzqcr8Vv9LQ5MRKRw6PKfiBS8X+JhXgt7QuXqAR2mkfngMlLdryPx+XBHs61j72bv5AgLAxURKTg6UyUiBSf9PMRPgM1v2MuVG9qfjB7QGNLTAfDx+P+7/Hw83PDx0J8hESkd9NdMRArG4T32J6Mf2WsvNx8A90wEd29LwxIRKSpKqkTk2mRl2c9MxU+AzFQoVwW6zIW67ayOTESkSCmpEpGrdzoZVg6E3+x38VGvA9w/G8pXtjYuERELKKkSkavzY5z97r5zx8DNCyJegtA+YLNZHZmIiCWUVIlI/qSdg7VjYOtb9nLAzdB9IVSub21cIiIWU1IlInn35w77ZPRjv9jLLZ6BtuPAzdPSsEREigMlVSJyZVlZsOk1+PJFyEoH30DoMg/qtLE6MhGRYkNJlYhc3qk/YMVTsH+DvdzgXrj/dfCpaG1cIiLFjJIqEcndnpXw8VC4cBLcfSByOjSN0mR0EZEcKKkSkexST8NnI2HHu/ZytdvsT0avVMfauEREijElVSLi7L9b7ZPRT+wDbNAyGlqPAlf3Aunex8ON/dM6FUhfIiLFiZIqEbHLyoQNM2H9VDCZUOEG6DYfat1pdWQiIiWCkioRgZMHYXl/OJhoL9/UDe79J3hfZ2lYIiIliZIqkbJu1wfwaTSkpoCHL3R6BZr00mR0EZF8UlIlUlZdOAWfPge7/2Mv12huv9x3fS1LwxIRKamUVImURQcS7Zf7Th0EmyuEPw8tnwVX/UkQEbla+gsqUpZkpkPCDNjwCpgsuC7I/qiEGrdbHZmISImnpEqkrDj+O8T2gz+22su3PGx/mKdXBWvjEhEpJZRUiZR2xsCO9+GzEZB2Bjz94L5/QuPuVkcmIlKqKKkSKc3On4CPh8HelfZy0J3Q9Q24roaVUYmIlEpKqkSKuXNpGTQavwaAvZMj8PHI48d231ewYgCk/AEubtBmDNw5FFxcCzFaEZGyS0mVSGmTkQbrXoKv/wUYqFjHPhm9+m1WRyYiUqopqRIpTY7+ArF9IGmnvXzb49BhKniUszYuEZEyQEmVSGlgDGxbDKtHQcZ58L4e7n8dGt5ndWQiImWGkiqRku7sMfjoGfjpU3u5dmvoEgMVAi0NS0SkrHGxOoC5c+cSHByMl5cXISEhbNiw4bLtExISCAkJwcvLi9q1axMTE5OtTWxsLI0aNcLT05NGjRqxYsUKp+VfffUV9913H9WqVcNms7Fy5cpsfRhjmDhxItWqVcPb25vWrVuzZ8+ea9pXkQL36xcwL8yeULl6QPuX4NEVSqhERCxgaVK1bNkyhg0bxpgxY9i+fTstW7YkMjKSgwcP5th+3759dOzYkZYtW7J9+3ZGjx7NkCFDiI2NdbRJTEykV69eREVFsXPnTqKioujZsyfffvuto83Zs2e55ZZbmD17dq6xzZgxg5kzZzJ79my2bNlCQEAA7dq14/Tp0wV3AESuVvoFWD0a3u0GZw6Df33o+wW0GAwulv9bSUSkTLL0r+/MmTPp06cPffv2pWHDhsyaNYsaNWowb968HNvHxMRQs2ZNZs2aRcOGDenbty9PPvkkr7zyiqPNrFmzaNeuHaNGjaJBgwaMGjWKu+++m1mzZjnaREZG8uKLL9KtW7cct2OMYdasWYwZM4Zu3brRuHFj3n77bc6dO8f7779foMdAJN+O/AAL7oZv5tjLzfpB//UQ2MTSsEREyjrL5lSlpaWxbds2Ro4c6VTfvn17Nm3alOM6iYmJtG/f3qkuIiKChQsXkp6ejru7O4mJiQwfPjxbm78nVVeyb98+kpOTnbbl6elJeHg4mzZt4qmnnspxvdTUVFJTUx3llJQUANLT00lPT8/z9qVgXTz2JXUMTp29+DtlSP96Lmbji9gyUzHlKpPZ6V+Yuv/7PS3m+1fSx6E00VgUDxqH4iGncbjaMbEsqTp69CiZmZlUrVrVqb5q1aokJyfnuE5ycnKO7TMyMjh69CiBgYG5tsmtz9y2c3G9S/s5cOBArutNnTqVSZMmZatft24dPj4+ed6+FI74+HirQ7gqQxPd8OcUL7vH4Jdgf1TC4QpN2F6zH6m/ZMAvcRZHmD8ldRxKI41F8aBxKB7+Pg7nzp27qj4sv/vPZrM5lY0x2equ1P7S+vz2WVCxjRo1iujoaEc5JSWFGjVq0KZNGypVqpTv7UvBSE9PJz4+nnbt2uHu7m51OPm28tvpvOz+Bv62FFKNO24RL1AxtA93X8XvtJVK+jiUJhqL4kHjUDzkNA4XrzTll2VJlb+/P66urtnOIB05ciTbGaKLAgICcmzv5ubmSFpya5Nbn7ltB+xnrAID//8uqiv14+npiaenZ7Z6d3d3fWCKgRI3DunnYe04Fnm8CcAPWTUJePLfXF/rVkryi2ZK3DiUYhqL4kHjUDz8fRyudjwsm6ju4eFBSEhIttOe8fHxtGjRIsd1wsLCsrVfu3YtoaGhjgOQW5vc+sxJcHAwAQEBTv2kpaWRkJCQr35ErlrSLngjHLbYE6oFGZF0SZuMZ7XGFgcmIiK5sfTyX3R0NFFRUYSGhhIWFsb8+fM5ePAgAwYMAOyX0/744w/eeecdAAYMGMDs2bOJjo6mX79+JCYmsnDhQpYsWeLoc+jQobRq1Yrp06fTuXNnVq1axeeff87GjRsdbc6cOcOvv/7qKO/bt48dO3ZQsWJFatasic1mY9iwYUyZMoW6detSt25dpkyZgo+PDw8//HARHR0pk7Ky4Ju58MUkyEyD8gFcuHc2Ly5OszoyERG5AkuTql69enHs2DEmT55MUlISjRs3Ji4ujqCgIACSkpKcnlkVHBxMXFwcw4cPZ86cOVSrVo3XXnuN7t27O9q0aNGCpUuXMnbsWMaNG0edOnVYtmwZzZs3d7TZunUrbdq0cZQvzoN6/PHHWbx4MQAjRozg/PnzDBw4kBMnTtC8eXPWrl2Lr69vYR4SKctS/oSVT8Pv6+3l+p3g/tfJcvcD1lgZmYiI5IHlE9UHDhzIwIEDc1x2McH5u/DwcL777rvL9tmjRw969OiR6/LWrVs7JrjnxmazMXHiRCZOnHjZdiIF4oeP7a+aOX8C3H3sL0G+7XGw2SAtw+roREQkDyxPqkTKtNQzsGYUfGe/xE3grdB9AfjXtTQsERHJPyVVIlb5YxvE9oPjvwE2uGsYtB4Nbh5WRyYiIldBSZVIUcvKhK9nwbopkJUBFapD1zcguKXVkYmIyDVQUiVSlE4eghVPwYGv7eVGXeC+WeB9vZVRiYhIAVBSJVJUvo+Fj4dD6inwKA+RM+DWh+2T0UVEpMRTUiVS2C6kwGcjYOf/nqdWPRS6zYdKdfK0uo+HG/undSrEAEVEpCAoqRIpTIc2Q2xfOHkAbC7Q8jkIHwGueiWFiEhpo6RKpDBkZsCGVyBhBphMuK4mdHsTat5hdWQiIlJIlFSJFLTj+2B5f/jvZnu5SS/o+DJ4+Vkbl4iIFColVSIFxRjYtQw+fQ7SToNnBeg0E5o8YHVkIiJSBJRUiRSE8yfh02j7HX4ANcPsz566PsjSsEREpOgoqRK5Vvu/tj976tQhsLlCm1FwVzS4uFodmYiIFCElVSJXKzMd1k+FDTMBA9cH29/bd0Oo1ZGJiIgFlFSJXI1jv0FsH/hzu73c9FHoMA08fa2NS0RELKOkSiQ/jIHt/4bPnof0c+B1Hdz3L7ipi9WRiYiIxZRUieTVuePw8RD44WN7uVZL+2R0v+rWxiUiIsWCkiqRvPh9PawYAKeTwMUd7h4HYc+Ai4vVkYmISDGhpErkcjJS4csXYNPr9nKluvbJ6NVutTQsEREpfpRUieTmr5/sk9GTd9vLoU9C+5fAw8fauEREpFhSUiVyKWNgywJYOxYyLoBPJbh/NjToaHVkIiJSjCmpEvm7M3/BqkHwyxp7uc7d0GUu+AZYG5eIiBR7SqpELvolHlY+DWf/AldPaDcZbu+vyegiIpInSqpE0s9D/ATY/Ia9XKWRfTJ61ZusjUtEREoUJVVSqp1Ly6DR+LWAG63vycDP3d25weE9ENsXjuy1l5sPgHsmgrt3UYcqIiIlnJIqKZuysuDbGPh8AmSmQbkq9rlTddtZHZmIiJRQSqqk7DmdbJ879duX9nK9Dva7+8pXtjYuEREp0ZRUSdny46ewajCcPw5u3hDxIoT2AZvN6shERKSEU1IlZYI3F/BaOwJ2vmOvCLgZui+EyvWtDUxEREoNJVVS6t1k28dr7rPx3Jlkr2gxBNqOBTdPawMTEZFSRUmVlF5ZWZiNs1jhMQUPWyaZ5QJw7f4G1G5tdWQiIlIK6amGUjqd+gPeuZ9yX72Ahy2TzzKbEXJskhIqEREpNDpTJaXPnhXw8TC4cJKzxpOJGY/zQWY4oMnoIiJSeHSmSkqP1NOwchB80BsunIRqt5Hadz0fZLYGbCQ+H25tfCIiUqrpTJWUDv/dan8y+ol9gA1aPgutR+KVaQP2AeDj4WppiCIiUropqZKSLSsTNsyE9VPBZIJfDej6BtS60748M8Pa+EREpMxQUiUl14kDsOIpOJhoLzfuDp1mgvd1loYlIiJlk5IqKZl2fQCfRkNqCnj4QqdXoUlPPRldREQso6RKSpYLp+DTZ2H3B/ZyjebQbT5cX8vSsERERJRUSclxIBGW94dTB8HmCuHP2yeku+rXWERErKdvIyn+MtMhYTpseBVMFlwXBN0XQI3brY5MRETEQUmVFG/HfoPl/eCPbfbyLQ9D5HTwqpCn1X083PjlhfbExcXh46FfdxERKTz6lpHiyRjY8R7EjYD0s+DlB/f+036Hn4iISDFk+RPV586dS3BwMF5eXoSEhLBhw4bLtk9ISCAkJAQvLy9q165NTExMtjaxsbE0atQIT09PGjVqxIoVK/K93d69e2Oz2Zx+7rjjjmvbWcmbc8ftT0VfNcieUAXdBQO+VkIlIiLFmqVJ1bJlyxg2bBhjxoxh+/bttGzZksjISA4ePJhj+3379tGxY0datmzJ9u3bGT16NEOGDCE2NtbRJjExkV69ehEVFcXOnTuJioqiZ8+efPvtt/nebocOHUhKSnL8xMXFFc6BkP+37yuIuQv2rgQXN7h7Ajz+EVxXw+rIRERELsvSpGrmzJn06dOHvn370rBhQ2bNmkWNGjWYN29eju1jYmKoWbMms2bNomHDhvTt25cnn3ySV155xdFm1qxZtGvXjlGjRtGgQQNGjRrF3XffzaxZs/K9XU9PTwICAhw/FStWLJTjIEBGGsSPh7fvh5Q/oGId6BMPLaPBRa+XERGR4s+yOVVpaWls27aNkSNHOtW3b9+eTZs25bhOYmIi7du3d6qLiIhg4cKFpKen4+7uTmJiIsOHD8/W5mJSlZ/trl+/nipVqnDdddcRHh7OSy+9RJUqVXLdp9TUVFJTUx3llJQUANLT00lPT891vTLv6C+4rXoKW/IuALJujSKz3YvgUQ4K4LhdPPYaA2tpHIoPjUXxoHEoHnIah6sdE8uSqqNHj5KZmUnVqlWd6qtWrUpycnKO6yQnJ+fYPiMjg6NHjxIYGJhrm4t95nW7kZGRPPDAAwQFBbFv3z7GjRtH27Zt2bZtG56enjnGN3XqVCZNmpStft26dfj4+ORyJMowYwg6to7G/30fm0kjzbUcO2r2IckWCp8nFPjm4uPjC7xPyT+NQ/GhsSgeNA7Fw9/H4dy5c1fVh+V3/9kuea2IMSZb3ZXaX1qflz6v1KZXr16O/2/cuDGhoaEEBQXx6aef0q1btxxjGzVqFNHR0Y5ySkoKNWrUoE2bNlSqVCnXfSqTzh7F9dNhuBxaDUBWcDi2+2bT1DeQpgW8qfT0dOLj42nXrh3u7u4F3Lvklcah+NBYFA8ah+Ihp3G4eKUpvyxLqvz9/XF1dc12VurIkSPZziJdFBAQkGN7Nzc3R9KSW5uLfV7NdgECAwMJCgril19+ybWNp6dnjmex3N3d9YH5u1+/gJVPw5nD4OoB90zEpfnTuLgU7hQ/jUPxoHEoPjQWxYPGoXj4+zhc7XhYNlHdw8ODkJCQbKc94+PjadGiRY7rhIWFZWu/du1aQkNDHQcgtzYX+7ya7QIcO3aMQ4cOERgYmLcdlOzSL8DqUfBuN3tCVbkB9PsSwgZBISdUIiIihc3Sy3/R0dFERUURGhpKWFgY8+fP5+DBgwwYMACwX077448/eOeddwAYMGAAs2fPJjo6mn79+pGYmMjChQtZsmSJo8+hQ4fSqlUrpk+fTufOnVm1ahWff/45GzduzPN2z5w5w8SJE+nevTuBgYHs37+f0aNH4+/vT9euXYvwCBU/59IyaDR+DQB7J0fk/Snlh/dCbF84ssdevr0/tJsM7t6FFKmIiEjRsjSp6tWrF8eOHWPy5MkkJSXRuHFj4uLiCAoKAiApKcnp2VHBwcHExcUxfPhw5syZQ7Vq1Xjttdfo3v3/HwrZokULli5dytixYxk3bhx16tRh2bJlNG/ePM/bdXV1Zffu3bzzzjucPHmSwMBA2rRpw7Jly/D19S2io1NKGAOb58PacZCZCuUqQ+c5UC/C6shEREQKlOUT1QcOHMjAgQNzXLZ48eJsdeHh4Xz33XeX7bNHjx706NHjqrfr7e3NmjVrLru+5MHpw7BqIPz6ub18YzvoMhfK5/5YChERkZLK8qRKSqmfVttfM3PuKLh5QbsX4PZ+cJk7O0VEREoyJVVSsNLOQfw42LLAXq7aGLovgCoNrY1LRESkkCmpkoKTtMs+Gf3oT/Zy2GC4ezy45fywVBERkdJESZXky7m0DKf/9/Fwg6wsSJwNX0yGrHQoHwBd50GdthZGKiIiUrT0cCDJl9AXv3D+/5Q/4d9d7Jf8stKhfid4epMSKhERKXN0pkquWoTLZpg3CM6fAHcf6DAVbntck9FFRKRM0pkqyZetY+/GhwtMc5vPGx6z7AlV4K3w1FcQ0lsJlYiIlFk6UyX5Uu7MQT7xGE1tl2QMNmx3DYPWo8HNw+rQRERELKWkSvLF+AaQhQt/mopUfHQRXnVbWx2SiIhIsaCkSvLH3Yd+6c9yzPjyTdBdVkcjIiJSbCipknzbZwKtDkFERKTY0UR1ERERkQKgM1WSLz4ebuyf1snqMERERIodnakSERERKQBKqkREREQKgJIqERERkQKgpEpERESkACipEhERESkASqpERERECoCSKhEREZECoKRKREREpAAoqRIREREpAEqqRERERAqAkioRERGRAqCkSkRERKQAKKkSERERKQBKqkREREQKgJIqERERkQKgpEpERESkACipEhERESkASqpERERECoCSKhEREZECoKRKREREpAAoqRIREREpAEqqRERERAqAkioRERGRAqCkSkRERKQAKKkSERERKQBKqkREREQKgJIqERERkQKgpEpERESkAFieVM2dO5fg4GC8vLwICQlhw4YNl22fkJBASEgIXl5e1K5dm5iYmGxtYmNjadSoEZ6enjRq1IgVK1bke7vGGCZOnEi1atXw9vamdevW7Nmz59p2VkREREotS5OqZcuWMWzYMMaMGcP27dtp2bIlkZGRHDx4MMf2+/bto2PHjrRs2ZLt27czevRohgwZQmxsrKNNYmIivXr1Iioqip07dxIVFUXPnj359ttv87XdGTNmMHPmTGbPns2WLVsICAigXbt2nD59uvAOiIiIiJRcxkK33367GTBggFNdgwYNzMiRI3NsP2LECNOgQQOnuqeeesrccccdjnLPnj1Nhw4dnNpERESYBx98MM/bzcrKMgEBAWbatGmO5RcuXDB+fn4mJiYmz/t36tQpA5ijR4/meR0peGlpaWblypUmLS3N6lDKNI1D8aGxKB40DsVDTuNw8fv71KlT+erLsjNVaWlpbNu2jfbt2zvVt2/fnk2bNuW4TmJiYrb2ERERbN26lfT09Mu2udhnXra7b98+kpOTndp4enoSHh6ea2wiIiJStrlZteGjR4+SmZlJ1apVneqrVq1KcnJyjuskJyfn2D4jI4OjR48SGBiYa5uLfeZluxf/m1ObAwcO5LpPqamppKamOsqnTp0C4Pjx47muI4UvPT2dc+fOcezYMdzd3a0Op8zSOBQfGoviQeNQPOQ0Dhen+hhj8tWXZUnVRTabzalsjMlWd6X2l9bnpc+CavN3U6dOZdKkSdnq69Wrl+s6IiIiUjydPn0aPz+/PLe3LKny9/fH1dU121mpI0eOZDtDdFFAQECO7d3c3KhUqdJl21zsMy/bDQgIAOxnrAIDA/MUG8CoUaOIjo52lE+ePElQUBAHDx7M16BIwUpJSaFGjRocOnSIChUqWB1OmaVxKD40FsWDxqF4yGkcjDGcPn2aatWq5asvy5IqDw8PQkJCiI+Pp2vXro76+Ph4OnfunOM6YWFhfPzxx051a9euJTQ01HHKLiwsjPj4eIYPH+7UpkWLFnnebnBwMAEBAcTHx9O0aVPAPhcrISGB6dOn57pPnp6eeHp6Zqv38/PTB6YYqFChgsahGNA4FB8ai+JB41A8XDoOV3UypMCmz1+FpUuXGnd3d7Nw4UKzd+9eM2zYMFOuXDmzf/9+Y4wxI0eONFFRUY72v//+u/Hx8THDhw83e/fuNQsXLjTu7u7mww8/dLT5+uuvjaurq5k2bZr54YcfzLRp04ybm5v55ptv8rxdY4yZNm2a8fPzM8uXLze7d+82Dz30kAkMDDQpKSl53r+rvXtACpbGoXjQOBQfGoviQeNQPBTkOFg6p6pXr14cO3aMyZMnk5SUROPGjYmLiyMoKAiApKQkp2dHBQcHExcXx/Dhw5kzZw7VqlXjtddeo3v37o42LVq0YOnSpYwdO5Zx48ZRp04dli1bRvPmzfO8XYARI0Zw/vx5Bg4cyIkTJ2jevDlr167F19e3CI6MiIiIlDQ2Y/I5tV3yLDU1lalTpzJq1KgcLwtK0dA4FA8ah+JDY1E8aByKh4IcByVVIiIiIgXA8nf/iYiIiJQGSqpERERECoCSKhEREZECoKRKREREpAAoqSokc+fOJTg4GC8vL0JCQtiwYYPVIZU5U6dOpVmzZvj6+lKlShW6dOnCTz/9ZHVYZd7UqVOx2WwMGzbM6lDKnD/++INHH32USpUq4ePjw6233sq2bdusDqtMycjIYOzYsQQHB+Pt7U3t2rWZPHkyWVlZVodW6n311Vfcd999VKtWDZvNxsqVK52WG2OYOHEi1apVw9vbm9atW7Nnz558bUNJVSFYtmwZw4YNY8yYMWzfvp2WLVsSGRnp9MwtKXwJCQkMGjSIb775hvj4eDIyMmjfvj1nz561OrQya8uWLcyfP58mTZpYHUqZc+LECe68807c3d357LPP2Lt3L6+++irXXXed1aGVKdOnTycmJobZs2fzww8/MGPGDF5++WVef/11q0Mr9c6ePcstt9zC7Nmzc1w+Y8YMZs6cyezZs9myZQsBAQG0a9fO8XLlPLnmx4dKNrfffrsZMGCAU12DBg3MyJEjLYpIjDHmyJEjBjAJCQlWh1ImnT592tStW9fEx8eb8PBwM3ToUKtDKlOef/55c9ddd1kdRpnXqVMn8+STTzrVdevWzTz66KMWRVQ2AWbFihWOclZWlgkICDDTpk1z1F24cMH4+fmZmJiYPPerM1UFLC0tjW3bttG+fXun+vbt27Np0yaLohKAU6dOAVCxYkWLIymbBg0aRKdOnbjnnnusDqVM+uijjwgNDeWBBx6gSpUqNG3alDfffNPqsMqcu+66iy+++IKff/4ZgJ07d7Jx40Y6duxocWRl2759+0hOTnb67vb09CQ8PDxf392WvqamNDp69CiZmZlUrVrVqb5q1aokJydbFJUYY4iOjuauu+6icePGVodT5ixdupTvvvuOLVu2WB1KmfX7778zb948oqOjGT16NJs3b2bIkCF4enry2GOPWR1emfH8889z6tQpGjRogKurK5mZmbz00ks89NBDVodWpl38fs7pu/vAgQN57kdJVSGx2WxOZWNMtjopOoMHD2bXrl1s3LjR6lDKnEOHDjF06FDWrl2Ll5eX1eGUWVlZWYSGhjJlyhQAmjZtyp49e5g3b56SqiK0bNky3n33Xd5//31uuukmduzYwbBhw6hWrRqPP/641eGVedf63a2kqoD5+/vj6uqa7azUkSNHsmXAUjSeeeYZPvroI7766ituuOEGq8Mpc7Zt28aRI0cICQlx1GVmZvLVV18xe/ZsUlNTcXV1tTDCsiEwMJBGjRo51TVs2JDY2FiLIiqb/vGPfzBy5EgefPBBAG6++WYOHDjA1KlTlVRZKCAgALCfsQoMDHTU5/e7W3OqCpiHhwchISHEx8c71cfHx9OiRQuLoiqbjDEMHjyY5cuX8+WXXxIcHGx1SGXS3Xffze7du9mxY4fjJzQ0lEceeYQdO3YooSoid955Z7ZHivz8888EBQVZFFHZdO7cOVxcnL96XV1d9UgFiwUHBxMQEOD03Z2WlkZCQkK+vrt1pqoQREdHExUVRWhoKGFhYcyfP5+DBw8yYMAAq0MrUwYNGsT777/PqlWr8PX1dZw99PPzw9vb2+Loyg5fX99s89jKlStHpUqVNL+tCA0fPpwWLVowZcoUevbsyebNm5k/fz7z58+3OrQy5b777uOll16iZs2a3HTTTWzfvp2ZM2fy5JNPWh1aqXfmzBl+/fVXR3nfvn3s2LGDihUrUrNmTYYNG8aUKVOoW7cudevWZcqUKfj4+PDwww/nfSMFdXuiOJszZ44JCgoyHh4e5rbbbtNt/BYAcvxZtGiR1aGVeXqkgjU+/vhj07hxY+Pp6WkaNGhg5s+fb3VIZU5KSooZOnSoqVmzpvHy8jK1a9c2Y8aMMampqVaHVuqtW7cux++Exx9/3Bhjf6zChAkTTEBAgPH09DStWrUyu3fvztc2bMYYU1BZoIiIiEhZpTlVIiIiIgVASZWIiIhIAVBSJSIiIlIAlFSJiIiIFAAlVSIiIiIFQEmViIiISAFQUiUiIiJSAJRUiYiIiBQAJVUiIvkQFRXFlClT8rXOJ598QtOmTfV+N5FSTkmViAjQu3dvunTpctk2u3bt4tNPP+WZZ57Jtuz999/H1dU1x3d83nvvvdhsNt5///2CCldEiiElVSIieTR79mweeOABfH19sy176623GDFiBEuXLuXcuXPZlj/xxBO8/vrrRRGmiFhESZWISB5kZWXxwQcfcP/992dbtn//fjZt2sTIkSNp0KABH374YbY2999/P5s3b+b3338vinBFxAJKqkRE8mDXrl2cPHmS0NDQbMveeustOnXqhJ+fH48++igLFy7M1iYoKIgqVaqwYcOGoghXRCygpEpEJA/279+Pq6srVapUcarPyspi8eLFPProowA8+OCDJCYm8uuvv2bro3r16uzfv78owhURCyipEhHJg/Pnz+Pp6YnNZnOqX7t2LWfPniUyMhIAf39/2rdvz1tvvZWtD29v7xznW4lI6aCkSkQkD/z9/Tl37hxpaWlO9W+99RbHjx/Hx8cHNzc33NzciIuL4+233yYzM9Op7fHjx6lcuXJRhi0iRUhJlYhIHtx6660A7N2711F37NgxVq1axdKlS9mxY4fTz5kzZ/jss88cbS9cuMBvv/1G06ZNizp0ESkiblYHICJSElSuXJnbbruNjRs3OhKsf//731SqVIkHHngAFxfnf6Pee++9LFy4kHvvvReAb775Bk9PT8LCwoo6dBEpIjpTJSKSR/379+e9995zlN966y26du2aLaEC6N69O5988gmHDx8GYMmSJTzyyCP4+PgUWbwiUrRsxhhjdRAiIiXBhQsXqF+/PkuXLs3XGae//vqLBg0asHXrVoKDgwsxQhGxks5UiYjkkZeXF++88w5Hjx7N13r79u1j7ty5SqhESjmdqRIREREpADpTJSIiIlIAlFSJiIiIFAAlVSIiIiIFQEmViIiISAFQUiUiIiJSAJRUiYiIiBQAJVUiIiIiBUBJlYiIiEgBUFIlIiIiUgD+D+7a+jVoglQ9AAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Fitting procedure without considering the errorbars and without help to guess the adjustable parameters.\n",
"import scipy.optimize as opt\n",
"\n",
"\n",
"def affine_function(x, a, b): # Fitting function. The variation of B with I is linear, but to account for residual magnetic fields, we add\n",
" # an intercept. For the function curve_fit, the argument of the mathematical function must be the first argument of the Python function,\n",
" # and the adjustable parameters of the model must be separate other arguments of the Python function.\n",
" return a * x + b\n",
"\n",
"\n",
"print(opt.curve_fit(affine_function, I, B)) # The function returns two arrays, the first one is the array of best adjustable parameters\n",
"# (a,b), while the second argument is the covariant matrix of the fitting parameters (see later when we consider errorbars).\n",
"popt, pcov = opt.curve_fit(affine_function, I, B)\n",
"a = popt[0]\n",
"b = popt[1]\n",
"\n",
"plt.figure()\n",
"plt.errorbar(I, B, uB, uI, linestyle='', label='Measurements')\n",
"plt.plot(I, affine_function(I, a, b), label='Fitting curve')\n",
"plt.xlabel('I (A)')\n",
"plt.ylabel('B (T)')\n",
"plt.title('Magnetic field at the center of a coil')\n",
"plt.legend()\n",
"plt.axis([0, 10.1, 0, 3.5e-3])\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "ea4de1cd-8483-481f-bb61-de0c1fc6e89a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a= 0.00033056557786609943 T/A, a_th= 0.00035887237635885553 T/A\n",
"b= -6.3748172213222165e-06 T, b_th= 0 T\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Fitting procedure without considering the errorbars but with help to guess the adjustable parameters.\n",
"def affine_function(x, a, b):\n",
" return a * x + b\n",
"\n",
"\n",
"a_th = constant.mu_0 * N / np.sqrt(l ** 2 + D ** 2) # Expected value for the slope.\n",
"popt, pcov = opt.curve_fit(affine_function, I, B, p0=np.array([a_th, 0.])) # If we have rough estimates of the adjustable parameters,\n",
"# we can give them to the function: this is crucial if you try to fit a nonlinear function (less crucial for linear functions).\n",
"a = popt[0]\n",
"b = popt[1]\n",
"print('a=', a, 'T/A, a_th=', a_th, 'T/A') # The values of a and b look reasonable but without taking into account errorbars.\n",
"print('b=', b, 'T, b_th=', 0, 'T') # We cannot conclude on the validity of the model.\n",
"\n",
"plt.figure()\n",
"plt.errorbar(I, B, uB, uI, linestyle='', label='Measurements')\n",
"plt.plot(I, affine_function(I, a, b), label='Fitting curve')\n",
"plt.xlabel('I (A)')\n",
"plt.ylabel('B (T)')\n",
"plt.title('Magnetic field at the center of a coil')\n",
"plt.legend()\n",
"plt.axis([0, 10.1, 0, 3.5e-3])\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "1a57d375-d112-4085-92e7-15bd16377c18",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a=( 0.3278922062724227 +/- 0.014330540813255051 ) mT/A\n",
"a_th=( 0.35887237635885555 +/- 0.005031267517875478 ) mT/A\n",
"b=( 0.006891769518391891 +/- 0.062486775309015474 ) mT\n",
"b_th= 0 T\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Fitting procedure by considering the errorbars on the ordinates (here there are dominant so this is reasonable).\n",
"def affine_function(x, a, b):\n",
" return a * x + b\n",
"\n",
"\n",
"popt, pcov = opt.curve_fit(affine_function, I, B, sigma=uB, p0=np.array([a_th, 0.]), absolute_sigma=True)\n",
"# With the variable sigma, you can give the errorbars on the ordinates only. Besides, we add absolute_sigma=True to indicate that\n",
"# the absolute value of the errorbars are relevant, not only their relative value.\n",
"a = popt[0]\n",
"b = popt[1]\n",
"ua = np.sqrt(pcov[0, 0]) # In case you provide errorbars for your measurements, the covariance matrix has a precise meaning:\n",
"ub = np.sqrt(pcov[1, 1]) # its diagonal elements are the variance of each fitting variable\n",
"# (under some assumptions that will not be discussed here, the square root gives their uncertainty).\n",
"\n",
"ua_th = a_th * (uN / N + (l * ul + D * uD) / (l ** 2 + D ** 2)) # Uncertainty on the expected slope\n",
"# (obtained via propagation of uncertainties).\n",
"print('a=(', a * 1e3, '+/-', ua * 1e3, ') mT/A')\n",
"print('a_th=(', a_th * 1e3, '+/-', ua_th * 1e3, ') mT/A') # The values of a do not coincide despite the errorbars.\n",
"print('b=(', b * 1e3, '+/-', ub * 1e3, ') mT')\n",
"print('b_th= 0 T') # The linear model is justified because 0 is an acceptable value for the intercept.\n",
"\n",
"plt.figure()\n",
"plt.errorbar(I, B, uB, uI, linestyle='', label='Measurements')\n",
"plt.plot(I, affine_function(I, a, b), label='Fitting curve')\n",
"plt.xlabel('I (A)')\n",
"plt.ylabel('B (T)')\n",
"plt.title('Magnetic field at the center of a coil')\n",
"plt.legend()\n",
"plt.axis([0, 10.1, 0, 3.5e-3])\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "01c16074-54f0-4012-a976-df578a552381",
"metadata": {},
"source": [
"V. Importing and exporting data\n",
"\n",
"1) Importing data\n",
"\n",
"Experimental data or data obtained from a simulation are often obtained independently from the Python code you use to analyse your results. As a result, you should be able to import your data saved on your computer as a .txt or .csv file.\n",
"\n",
"If your data are stored in a file as $N$ columns, all having $M$ lines, then NumPy has two functions which allow you to import your data easily: loadtxt or genfromtxt. In these lecture notes, we focus on the function genfromtxt which gives more flexibility. Look at the online documentation to understand how to use it: https://numpy.org/doc/stable/reference/generated/numpy.genfromtxt.html\n",
"\n",
"2) Exporting data\n",
"\n",
"a) Exporting tables of data\n",
"\n",
"To save arrays of data with $N$ columns, all having $M$ lines, the function savetxt of the package NumPy can be used. This function gives you flexibility, in particular to add comments, change the delimiter between data, etc.). For more details, consult the online documentation: https://numpy.org/doc/stable/reference/generated/numpy.savetxt.html\n",
"\n",
"b) Saving figures\n",
"\n",
"To save figures, you can use the function savefig of the module Pyplot of the package Matplotlib. Many options can be customized, and you can consult the online documentation for more details: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.savefig.html"
]
},
{
"cell_type": "markdown",
"id": "5f651714-c763-47d2-ae04-6863347d1747",
"metadata": {},
"source": [
"VI. Exercises\n",
"\n",
"Exercise 1:\n",
"\n",
"We consider a random walker who takes steps of unit length along an axis. The walker starts at the origin $x = 0$ and the first step is chosen at random to the right or to the left with probability $1/2$ in each case. If the first step is to the right, the position after this first step is $x = +1$. The next step is then chosen, again with probability $1/2$ for each direction. This process is then repeated.\n",
"\n",
"1) Draw the curve representing the position of the walker as a function of the number of steps. As we can consider that there is one step per unit of time, this is equivalent to plotting the position versus time.\n",
"\n",
"2) Draw the curve which represents the square of the walker's distance from the origin as a function of time.\n",
"\n",
"3) Now consider that there are 500 walkers. Plot on the same graph the curves which represent the square of the walkers distance from the origin as a function of time for all walkers. Represent also the curve which represents the average of the square of the distance of the walkers from the origin (called the Mean-Squared Displacement or MSD) as a function of time. You must plot the curves for all walkers in black and a small opacity, and the average in red.\n",
"\n",
"4) The MSD $\\Delta^2$ varies linearly with time $\\Delta^2=2Dt$, with $D$ the diffusion coefficient of the walker. Perform a linear fit of the MSD and compare the estimated value of $D$ with the theoretical prediction $D=1/2$.\n",
"\n",
"5) Plot the result of the fit and the MSD on a new graph. The graph must indicate the value of $D$ obtained from the fitting procedure, and also the Pearson correlation coefficient of the MSD and the number of steps (to confirm the linear dependency). If you do not remember the mathematical definition of the Pearson correlation coefficient, look on Wikipedia.\n",
"\n",
"6) Save the result of the MSD and of the fit in a .txt file called MSD_Brownian.txt. The structure of the file is indicated below, the first line must explicitely indicate the content of each column, and the different columns must be separated by a 7 spaces:\n",
"#Number of steps MSD Linear fit"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "27e82f44-15e8-4a8a-996b-a7fb5d46aa18",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 2000 # Number of steps\n",
"kicks = np.random.choice(np.array([-1, 1]), size=n) # Array with entries +1 (right kick) or -1 (left kick) with probability 1/2\n",
"# for each entry.\n",
"x = np.cumsum(kicks) # At a given time, the position is the sum of positive kicks - the sum of negative kicks.\n",
"x = np.concatenate((np.array([0]), x)) # We add the initial position, which is x = 0.\n",
"plt.figure()\n",
"plt.plot(x)\n",
"plt.xlabel('Number of steps')\n",
"plt.ylabel('x')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "ac814b8c-e2e6-4612-b779-6c29e7b4c592",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(x ** 2)\n",
"plt.xlabel('Number of steps')\n",
"plt.ylabel('Squared distance from the origin')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "df5d4881-8927-4a38-9243-c4dfc665fcca",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nwalker = 500 # Number of walkers\n",
"kicks = np.random.choice(np.array([-1, 1]), size=(n, nwalker)) # Array of n rows and nwalker columns.\n",
"x = np.cumsum(kicks, axis=0) # Each column corresponds to the trajectory of 1 walker.\n",
"x = np.vstack((np.zeros(nwalker), x)) # We add the initial position for all walkers.\n",
"MSD = np.mean(x ** 2, axis=1) # We compute the MSD by averaging over all walkers (average over the columns on each row).\n",
"plt.figure()\n",
"plt.plot(x ** 2, 'k', alpha=0.3) # Each column corresponds to the trajectory of 1 walker, so the function plot plots every column\n",
"# separately.\n",
"plt.plot(MSD, 'r', label='Average')\n",
"plt.grid()\n",
"plt.xlabel('Number of steps')\n",
"plt.ylabel('Squared distance from the origin')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "da8408ef-748c-4dfd-9682-4298f8c92107",
"metadata": {},
"outputs": [],
"source": [
"def linear(x, a):\n",
" return 2. * a * x\n",
"\n",
"\n",
"steps = np.arange(n + 1)\n",
"popt, pcov = opt.curve_fit(linear, steps, MSD, p0=np.array([0.5])) # We use the theoretical result as guess.\n",
"D = popt[0] # Extract the diffusion constant."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "7ed3c4f0-06d9-4394-89eb-d34c6808e95a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"linear_fit = linear(steps, D) # Best fit.\n",
"pearson_correlation = np.corrcoef(steps, MSD)[1, 0] # Compute the Pearson correlation (symmetric) matrix between the two variables\n",
"# (Look on the webpage). The diagonal elements are equal to 1 by construction, and here we are only interested in the off-diagonal element.\n",
"plt.figure()\n",
"plt.plot(steps, MSD, 'r', label='MSD (r=' + str(pearson_correlation) + ')')\n",
"plt.plot(steps, linear_fit, 'b--', label='Linear fit (D=' + str(D) + ')')\n",
"plt.grid()\n",
"plt.title('Linear fit of the MSD')\n",
"plt.xlabel('Number of steps')\n",
"plt.ylabel('Squared distance from the origin')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "38a812f8-cf7b-4705-9769-502be0cd6ed2",
"metadata": {},
"outputs": [],
"source": [
"np.savetxt('MSD_Brownian.txt', np.vstack((steps, MSD, linear_fit)).T, header='Number of steps MSD Linear fit', delimiter=' ')"
]
},
{
"cell_type": "markdown",
"id": "0a55ec5a-46b3-4cde-acab-622e939fad0d",
"metadata": {},
"source": [
"Exercise 2:\n",
"\n",
"Write a program which performs the following tasks:\n",
"\n",
"1) Open the file signal3.txt which contains the time series of a signal $s(t)$ (the first column gives the abscissae, the second column gives the ordinates).\n",
"\n",
"2) Plot the signal $s(t)$.\n",
"\n",
"3) Compute the DFT $\\tilde{s}(f)$ of this signal.\n",
"\n",
"4) Plot the power spectrum $\\mathcal{S}(f)=\\vert\\tilde{s}(f)\\vert^2$ of the signal. What should be done to eliminate the maximum at zero frequency?\n",
"\n",
"5) Measure the three characteristic strictly positive frequencies of the signal. This question does not require any advanced function available in scipy.optimize or scipy.signal. What is the value of the spectrum for these frequencies?\n",
"\n",
"6) Mark the locations of the characteristic frequencies on the plot of the spectrum and allow them to be distinguishable. Save the plot as a .pdf file."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "81a47467-9671-47e5-a22b-54ce34c69b8d",
"metadata": {},
"outputs": [],
"source": [
"signal = np.genfromtxt('signal3.txt', delimiter=',', skip_header=1) # Indicate the delimiter (,) and that the first line must be skipped.\n",
"t = signal[:, 0] # The first column gives the time (abscissae).\n",
"s = signal[:, 1] # The second column gives the values of the signal (ordinates)."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "df415e7b-e629-4e9b-8d32-eb37a5d39c89",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(t, s)\n",
"plt.xlabel('t')\n",
"plt.ylabel('s(t)')\n",
"plt.title('Signal')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "2fd63105-dfeb-4a0f-83d8-315744a6e3f1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"FT_s = np.fft.fftshift(np.fft.fft(s)) # The fftshift command allows you to put the zero frequency in the middle of the interval.\n",
"freq = np.fft.fftshift(np.fft.fftfreq(s.size, t[1] - t[0]))\n",
"spectrum = np.abs(FT_s) ** 2 # Compute the spectrum as the squared modulus of the Fourier transform.\n",
"plt.figure()\n",
"plt.plot(freq, spectrum)\n",
"plt.yscale('log')\n",
"plt.xlabel('f')\n",
"plt.ylabel(r'$\\mathcal{S}(f)$')\n",
"plt.grid()\n",
"plt.title('Spectrum of the signal')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "a072d8f0-9908-4050-af1c-d310d6ff2893",
"metadata": {},
"outputs": [],
"source": [
"FT_reduced_s = np.fft.fftshift(np.fft.fft(s - np.mean(s))) # To remove the peak at 0 frequency, we have to substract the mean to\n",
"# the signal.\n",
"spectrum_reduced = np.abs(FT_reduced_s) ** 2"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "f58cb5f4-4ab0-40bc-aae4-093fb5ed5a5a",
"metadata": {},
"outputs": [],
"source": [
"max_freq = np.zeros(3) # Array of frequencies where the spectrum is maximum.\n",
"max_spectrum = np.zeros(3) # Array of local maxima of the spectrum.\n",
"spectrum_copy = np.copy(spectrum_reduced) # To avoid modifying the spectrum.\n",
"for i in range(3):\n",
" j = np.argmax(spectrum_copy[s.size // 2:])\n",
" j += s.size // 2 # The argmax command finds the maximum of the array given but its first element (position 0) is the s.size // 2 th\n",
" # element of the original array.\n",
" max_freq[i] = freq[j]\n",
" max_spectrum[i] = spectrum_copy[j]\n",
" spectrum_copy[j] = 0."
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "a1f46d4f-96ae-477e-bd64-b0f640b8f25d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(freq, spectrum_reduced, label='Spectrum')\n",
"plt.plot(np.tile(max_freq, (1, 2)).reshape((2, 3)), np.vstack((np.zeros(3), max_spectrum)), '--',\n",
" label='f=' + np.asarray(max_freq, dtype=str)) # To write the labels, we convert the frequency array into an array of strings.\n",
"# We create 2D arrays.\n",
"# For the abscissae, each column has its two entries equal to one characteristic frequency, and the characteristic frequency changes from\n",
"# one column to the next.\n",
"# For the ordinates, each column has two values, which are 0 and the value of the spectrum at the corresponding characteristic frequency.\n",
"# It will result in three plots corresponding to vertical lines from 0 to the maximum of the spectrum.\n",
"plt.yscale('log')\n",
"plt.xlabel('f')\n",
"plt.ylabel(r'$\\mathcal{S}(f)$')\n",
"plt.ylim(1e-6, 1e6)\n",
"plt.grid()\n",
"plt.legend()\n",
"plt.title('Power spectrum of the signal')\n",
"plt.savefig('spectrum_signal.pdf')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "8ed5444b-7ecf-4d55-a119-1002a8615579",
"metadata": {},
"source": [
"Exercise 3:\n",
"\n",
"Write a program which performs the following tasks.\n",
"\n",
"1) Generate $n=100\\, 000$ independent samples of a random variable $X$ drawn from a Gaussian distribution of mean $\\mu=3$ and standard deviation $\\sigma=5$. Verify that the values of the mean and of the variance are close to their expectations.\n",
"\n",
"2) Compute and plot the probability density function of $X$ (do not use the function matplotlib.pyplot.hist). Plot on the same graph the analytical prediction. We recall that the probability density function of a Gaussian random variable is given by\n",
"$$f(x)=\\dfrac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left[-\\dfrac{(x-\\mu)^2}{2\\sigma^2}\\right].$$\n",
"\n",
"3) The cumulative distribution function (CDF) of a random variable is defined as $P(X\\leq x) = \\displaystyle \\int_{-\\infty}^{x}\\mathrm{d}y\\,f(y)$. Compute the CDF from the histogram.\n",
"\n",
"4) Plot on the same graph the CDF computed from the histogram and its analytical expression. We recall that for a Gaussian distribution, the cumulative distribution function (CDF) reads $$P(X\\leq x) = \\dfrac{1}{2}\\left[1+\\mathrm{erf}\\left(\\dfrac{x-\\mu}{\\sqrt{2\\sigma^2}}\\right)\\right],$$ where $\\mathrm{erf}(x)=\\displaystyle\\frac{2}{\\sqrt{\\pi}}\\int_0^x\\mathrm{d}y\\,e^{-y^2}$ is the error function."
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "3ac2b05a-b173-4f22-98e9-674104e0d19c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.9934922108955835\n",
"25.036699731007694\n"
]
}
],
"source": [
"mu = 3.\n",
"sigma = 5.\n",
"x = np.random.normal(mu, sigma, size=100000)\n",
"print(np.mean(x)) # Expected value = 3.\n",
"print(np.var(x)) # Expected value = 25."
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "2dc080c4-f8dc-46cc-8806-40aa4a6ea2bb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"histo, bin_edges = np.histogram(x, bins=100, density=True)\n",
"plt.bar(bin_edges[:-1], height=histo, width=bin_edges[1] - bin_edges[0], align='edge') # Draw bars where the position is given by the\n",
"# first argument, the height by the second argument, and the width by the third argument. The align='edge' means that the position we have\n",
"# given is the left position of the bar.\n",
"xx = np.linspace(bin_edges[0], bin_edges[-1], 1000,) # We create an array of equally spaced values in the range of the histogram\n",
"# to compute the Gaussian distribution.\n",
"density = 1. / np.sqrt(2. * np.pi * sigma ** 2) * np.exp(-(xx - mu) ** 2 / (2. * sigma ** 2))\n",
"plt.plot(xx, density, 'r-', label='exact')\n",
"plt.xlabel('x')\n",
"plt.ylabel('f(x)')\n",
"plt.grid()\n",
"plt.legend()\n",
"plt.title(r'Normal distribution of mean $\\mu=3$ and standard deviation $\\sigma = 5$')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "599ea623-f571-476d-98fa-5f014be42459",
"metadata": {},
"outputs": [],
"source": [
"cdf_histo = np.cumsum(histo) # We approximate the integral via the Riemann sum so we just have to perform a cumulative sum, and then to\n",
"# multiply by the width of each interval in the histogram.\n",
"cdf_histo *= (bin_edges[1] - bin_edges[0])"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "d82464dc-e4f8-4b0b-9c80-187aeabb8bd6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cdf = 0.5 * (1. + spe.erf((xx - mu) / np.sqrt(2. * sigma ** 2)))\n",
"plt.bar(bin_edges[:-1], height=cdf_histo, width=bin_edges[1] - bin_edges[0], align='edge')\n",
"plt.plot(xx, cdf, 'r-', label='exact')\n",
"plt.xlabel('x')\n",
"plt.ylabel(r'$P(X\\leq x)$')\n",
"plt.grid()\n",
"plt.legend()\n",
"plt.title(r'CDF for a Gaussian distribution of mean $\\mu=3$ and standard deviation $\\sigma = 5$')\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}