{ "cells": [ { "cell_type": "markdown", "id": "365dff92-0af6-48a8-af6b-abb09b39dea0", "metadata": {}, "source": [ "# Import relevant packages" ] }, { "cell_type": "code", "execution_count": 1, "id": "80015e92-9104-4663-aaa8-59caeab81e91", "metadata": { "tags": [] }, "outputs": [], "source": [ "from scipy.io import loadmat\n", "from scipy.special import erf\n", "from scipy.signal import welch\n", "\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['text.usetex'] = True\n", "\n", "import numpy as np\n", "\n", "from conv_kernels import pos_kernel, vel_kernel,acc_kernel" ] }, { "cell_type": "code", "execution_count": 2, "id": "7b9e998e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'/Users/cbrun/Documents/UFR/MASTER_TURBULENCE/TP/CEA/TP14_OSCILLATING_GRID'" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pwd" ] }, { "cell_type": "markdown", "id": "f55c4750-82dc-4e4c-9da6-c1ee657733c2", "metadata": {}, "source": [ "# Base parameters" ] }, { "cell_type": "code", "execution_count": 26, "id": "b566bc60-36d9-4296-9be4-7125882c744e", "metadata": { "tags": [] }, "outputs": [], "source": [ "fname = 'Tracking_Data_REF/tracks_run6V.mat'\n", "micrometers_per_pix = 10000/731\n", "frames_per_second = 7000" ] }, { "cell_type": "markdown", "id": "0a6c0d54-5cf0-40ef-bef1-63297dc41881", "metadata": {}, "source": [ "# Load data into a numpy 'record' objects" ] }, { "cell_type": "code", "execution_count": 27, "id": "3138d3ef-5003-4ac2-9820-2a500addf529", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(array([[25]], dtype=uint16), array([[ 1.],\n", " [ 2.],\n", " [ 3.],\n", " [ 4.],\n", " [ 5.],\n", " [ 6.],\n", " [ 7.],\n", " [ 8.],\n", " [ 9.],\n", " [10.],\n", " [11.],\n", " [12.],\n", " [13.],\n", " [14.],\n", " [15.],\n", " [16.],\n", " [17.],\n", " [18.],\n", " [19.],\n", " [20.],\n", " [21.],\n", " [22.],\n", " [23.],\n", " [24.],\n", " [25.]], dtype=float32), 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loadmat(fname)\n", "traj = data['traj'][0]\n", "#print(data)\n", "print(traj)\n", "n=len(traj)\n", "print(n)" ] }, { "cell_type": "markdown", "id": "64b9c2b4-304a-4927-ad1f-fdbbf35e9357", "metadata": {}, "source": [ "# Look at the shape of the longest trajectory" ] }, { "cell_type": "code", "execution_count": 28, "id": "b439d11f-4ef8-4f13-84e0-565922de9227", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ltraj = traj['L']\n", "idx = max(range(len(ltraj)), key=ltraj.__getitem__)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot (traj['x'][idx], traj['y'][idx])\n", "ax.set_xlabel ('x [pixel]')\n", "ax.set_ylabel ('y [pixel]')\n", "## Get smoother trajectories by convolving the trajectory \n", "## with a gaussian kernel of width 3 and 3 times larger support\n", "wd = 3\n", "pkern = pos_kernel (wd,3*wd)\n", "xsmooth = np.convolve (traj['x'][idx].ravel(), pkern, mode='valid')\n", "ysmooth = np.convolve (traj['y'][idx].ravel(), pkern, mode='valid')\n", "ax.plot (xsmooth, ysmooth)\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "eb8132f8-5f24-48fa-bbfc-c74bb4b685d5", "metadata": {}, "source": [ "# Shape of the smoothing kernel " ] }, { "cell_type": "code", "execution_count": 29, "id": "b1a2551e-c123-4ed8-898c-6f44c263c010", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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