{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple walkthrough" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The heart of the DDM code (found in the `ddm_calc.py` file) is the computation of the image structure function. This is found by taking the average of the Fourier transforms of all image *differences*. By \"image differences,\" I mean the result of subtracting two images separated by a given lag time $\\Delta t$.\n", "\n", "To describe the process mathematically, we find the difference between images separated by some lag time $\\Delta t$:\n", "$$\\Delta I = I(x,y;t) - I(x,y;t + \\Delta t)$$\n", "\n", "For a given $\\Delta t$ all such image differences are calculated. We then Fourier transform each $\\Delta I$ and average all of the same $\\Delta t$.\n", "\n", "This results in the image structure function $D(q_x,q_y,\\Delta t)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importing the necessary modules" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Modules for plotting\n", "We use [matplotlib](https://matplotlib.org/) for creating figures and plots. Note that we use:\n", "```python\n", "%matplotlib inline\n", "```\n", "This sets the backend of matplotlib to `inline` which means the plots are included in the notebook. If you want the plots to also be interactive (e.g., having the ability to zoom, scroll, and save) then use:\n", "```python\n", "%matplotlib notebook\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Modules for numerical work\n", "Here, we import [numpy](https://numpy.org/) and [xarray](https://xarray.pydata.org/en/stable/). \n", "\n", "Note that `xarray` might not have come with your Anaconda Python distribution (or whichever other distribution you installed). If that is the case, you'll need to [install](https://xarray.pydata.org/en/stable/getting-started-guide/installing.html) this package. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np #numerical python used for working with arrays, mathematical operations\n", "import xarray as xr #package for labeling and adding metadata to multi-dimensional arrays" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Import the PyDDM package\n", "Make sure you append to `sys.path` the directory containing the [PyDDM](https://rmcgorty.github.io/PyDDM/) code. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import sys\n", "sys.path.append(\"../../PyDDM\") #must point to the PyDDM folder\n", "import ddm_analysis_and_fitting as ddm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initializing DDM_Analysis class and computing the DDM matrix\n", "The instance of the `DDM_Analysis` class we create will need, when initialized, metadata about the images to analyze and the analysis and fitting parameters. This can be done by using a [yaml](https://yaml.org/) file as shown in the following cell of code (there, the metadata is saved in the file \"*example_data_silica_beads.yml*\". But one can also initialize `DDM_Analysis` with a dictionary containing the necessary metadata. One way to create such a dictionary and then using it to initialize `DDM_Analysis` is shown below. \n", "```python\n", "import yaml\n", "ddm_analysis_parameters_str = \"\"\"\n", "DataDirectory: 'C:/Users/rmcgorty/Documents/GitHub/DDM-at-USD/ExampleData/'\n", "FileName: 'images_nobin_40x_128x128_8bit.tif'\n", "Metadata:\n", " pixel_size: 0.242 # size of pixel in um\n", " frame_rate: 41.7 #frames per second\n", "Analysis_parameters:\n", " number_lag_times: 40\n", " last_lag_time: 600\n", " binning: no \n", "Fitting_parameters:\n", " model: 'DDM Matrix - Single Exponential' \n", " Tau: [1.0, 0.001, 10]\n", " StretchingExp: [1.0, 0.5, 1.1]\n", " Amplitude: [1e2, 1, 1e6]\n", " Background: [2.5e4, 0, 1e7]\n", " Good_q_range: [5, 20]\n", " Auto_update_good_q_range: True\n", "\"\"\"\n", "parameters_as_dictionary = yaml.safe_load(ddm_analysis_parameters_str)\n", "ddm_calc = ddm.DDM_Analysis(parameters_as_dictionary)\n", "```" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Provided metadata: {'pixel_size': 0.242, 'frame_rate': 41.7}\n", "Image shape: 3000-by-128-by-128\n", "Number of frames to use for analysis: 3000\n", "Maximum lag time (in frames): 600\n", "Number of lag times to compute DDM matrix: 40\n" ] } ], "source": [ "#The yaml file `example_data_silica_beads.yml` contains the metadata and parameters above\n", "ddm_calc = ddm.DDM_Analysis(\"../../Examples/example_data_silica_beads.yml\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, with the method `calculate_DDM_matrix`, we compute the DDM matrix and some associated data. The data will be stored as an [xarray Dataset](https://xarray.pydata.org/en/stable/generated/xarray.Dataset.html) as an attribute to `ddm_calc` called `ddm_dataset`.\n", "\n", "**Note**: There are a few optional arguments we can pass to `calculate_DDM_matrix`. There is an optional argument `quiet` (*True* or *False*, *False* by default). Then we have some optional keyword arguments (all of which could also be specified in the YAML file). These are: `overlap_method` which sets the degree of overlap between image pairs when finding all image differences for a each lag time and is either *0*, *1*, *2*, or *3*, `background_method` which sets how to estimate the background parameter *B* and is either *0*, *1*, *2*, or *3*, and `number_lag_times`. If any of these three keyword arguments are set here, the value specified in the YAML file will be overwritten. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2022-02-10 13:11:37,747 - DDM Calculations - Running dt = 1...\n", "2022-02-10 13:11:44,311 - DDM Calculations - Running dt = 5...\n", "2022-02-10 13:11:48,710 - DDM Calculations - Running dt = 9...\n", "2022-02-10 13:11:52,546 - DDM Calculations - Running dt = 16...\n", "2022-02-10 13:11:55,853 - DDM Calculations - Running dt = 27...\n", "2022-02-10 13:11:59,025 - DDM Calculations - Running dt = 47...\n", "2022-02-10 13:12:02,002 - DDM Calculations - Running dt = 81...\n", "2022-02-10 13:12:04,828 - DDM Calculations - Running dt = 138...\n", "2022-02-10 13:12:07,484 - DDM Calculations - Running dt = 236...\n", "2022-02-10 13:12:09,998 - DDM Calculations - Running dt = 402...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "DDM matrix took 34.66797375679016 seconds to compute.\n", " Background estimate ± std is 211.17 ± 1.49\n" ] }, { "data": { "text/html": [ "
<xarray.Dataset>\n", "Dimensions: (lagtime: 40, q_y: 128, q_x: 128, q: 64, y: 128, x: 128, frames: 40)\n", "Coordinates:\n", " * lagtime (lagtime) float64 0.02398 0.04796 0.07194 ... 12.59 14.36\n", " framelag (frames) int32 1 2 3 4 5 6 7 ... 308 352 402 459 525 599\n", " * q_y (q_y) float64 -12.98 -12.78 -12.58 ... 12.37 12.58 12.78\n", " * q_x (q_x) float64 -12.98 -12.78 -12.58 ... 12.37 12.58 12.78\n", " * q (q) float64 0.0 0.2028 0.4057 0.6085 ... 12.37 12.58 12.78\n", " * y (y) int32 0 1 2 3 4 5 6 7 ... 121 122 123 124 125 126 127\n", " * x (x) int32 0 1 2 3 4 5 6 7 ... 121 122 123 124 125 126 127\n", "Dimensions without coordinates: frames\n", "Data variables:\n", " ddm_matrix_full (lagtime, q_y, q_x) float64 194.5 183.5 ... 192.0 196.8\n", " ddm_matrix (lagtime, q) float64 0.0 294.2 321.4 ... 207.8 201.1 200.4\n", " first_image (y, x) float64 128.0 149.0 173.0 ... 175.0 229.0 215.0\n", " avg_image_ft (q) float64 0.0 1.293e+05 5.225e+03 ... 105.3 104.7 105.3\n", " num_pairs_per_dt (lagtime) int32 2999 2998 2997 1498 1498 ... 20 17 15 13\n", " B float64 211.2\n", " B_std float64 1.491\n", " Amplitude (q) float64 -211.2 2.585e+05 1.024e+04 ... -1.699 -0.52\n", " ISF (lagtime, q) float64 0.0 0.9997 0.9892 ... -4.952 -19.73\n", "Attributes: (12/24)\n", " units: Intensity\n", " lagtime: sec\n", " q: μm$^{-1}$\n", " x: pixels\n", " y: pixels\n", " info: ddm_matrix is the averages of FFT difference ima...\n", " ... ...\n", " split_into_4_rois: no\n", " use_windowing_function: no\n", " binning: no\n", " bin_size: 2\n", " central_angle: no\n", " angle_range: no
array([ 0.023981, 0.047962, 0.071942, 0.095923, 0.119904, 0.143885,\n", " 0.167866, 0.191847, 0.215827, 0.263789, 0.28777 , 0.335731,\n", " 0.383693, 0.431655, 0.503597, 0.57554 , 0.647482, 0.743405,\n", " 0.863309, 0.983213, 1.127098, 1.294964, 1.486811, 1.702638,\n", " 1.942446, 2.206235, 2.541966, 2.901679, 3.309353, 3.788969,\n", " 4.316547, 4.940048, 5.659472, 6.450839, 7.386091, 8.441247,\n", " 9.640288, 11.007194, 12.589928, 14.364508])
array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 16,\n", " 18, 21, 24, 27, 31, 36, 41, 47, 54, 62, 71, 81, 92,\n", " 106, 121, 138, 158, 180, 206, 236, 269, 308, 352, 402, 459, 525,\n", " 599])
array([-12.981788, -12.778947, -12.576107, -12.373267, -12.170426, -11.967586,\n", " -11.764745, -11.561905, -11.359064, -11.156224, -10.953383, -10.750543,\n", " -10.547703, -10.344862, -10.142022, -9.939181, -9.736341, -9.5335 ,\n", " -9.33066 , -9.12782 , -8.924979, -8.722139, -8.519298, -8.316458,\n", " -8.113617, -7.910777, -7.707937, -7.505096, -7.302256, -7.099415,\n", " -6.896575, -6.693734, -6.490894, -6.288053, -6.085213, -5.882373,\n", " -5.679532, -5.476692, -5.273851, -5.071011, -4.86817 , -4.66533 ,\n", " -4.46249 , -4.259649, -4.056809, -3.853968, -3.651128, -3.448287,\n", " -3.245447, -3.042607, -2.839766, -2.636926, -2.434085, -2.231245,\n", " -2.028404, -1.825564, -1.622723, -1.419883, -1.217043, -1.014202,\n", " -0.811362, -0.608521, -0.405681, -0.20284 , 0. , 0.20284 ,\n", " 0.405681, 0.608521, 0.811362, 1.014202, 1.217043, 1.419883,\n", " 1.622723, 1.825564, 2.028404, 2.231245, 2.434085, 2.636926,\n", " 2.839766, 3.042607, 3.245447, 3.448287, 3.651128, 3.853968,\n", " 4.056809, 4.259649, 4.46249 , 4.66533 , 4.86817 , 5.071011,\n", " 5.273851, 5.476692, 5.679532, 5.882373, 6.085213, 6.288053,\n", " 6.490894, 6.693734, 6.896575, 7.099415, 7.302256, 7.505096,\n", " 7.707937, 7.910777, 8.113617, 8.316458, 8.519298, 8.722139,\n", " 8.924979, 9.12782 , 9.33066 , 9.5335 , 9.736341, 9.939181,\n", " 10.142022, 10.344862, 10.547703, 10.750543, 10.953383, 11.156224,\n", " 11.359064, 11.561905, 11.764745, 11.967586, 12.170426, 12.373267,\n", " 12.576107, 12.778947])
array([-12.981788, -12.778947, -12.576107, -12.373267, -12.170426, -11.967586,\n", " -11.764745, -11.561905, -11.359064, -11.156224, -10.953383, -10.750543,\n", " -10.547703, -10.344862, -10.142022, -9.939181, -9.736341, -9.5335 ,\n", " -9.33066 , -9.12782 , -8.924979, -8.722139, -8.519298, -8.316458,\n", " -8.113617, -7.910777, -7.707937, -7.505096, -7.302256, -7.099415,\n", " -6.896575, -6.693734, -6.490894, -6.288053, -6.085213, -5.882373,\n", " -5.679532, -5.476692, -5.273851, -5.071011, -4.86817 , -4.66533 ,\n", " -4.46249 , -4.259649, -4.056809, -3.853968, -3.651128, -3.448287,\n", " -3.245447, -3.042607, -2.839766, -2.636926, -2.434085, -2.231245,\n", " -2.028404, -1.825564, -1.622723, -1.419883, -1.217043, -1.014202,\n", " -0.811362, -0.608521, -0.405681, -0.20284 , 0. , 0.20284 ,\n", " 0.405681, 0.608521, 0.811362, 1.014202, 1.217043, 1.419883,\n", " 1.622723, 1.825564, 2.028404, 2.231245, 2.434085, 2.636926,\n", " 2.839766, 3.042607, 3.245447, 3.448287, 3.651128, 3.853968,\n", " 4.056809, 4.259649, 4.46249 , 4.66533 , 4.86817 , 5.071011,\n", " 5.273851, 5.476692, 5.679532, 5.882373, 6.085213, 6.288053,\n", " 6.490894, 6.693734, 6.896575, 7.099415, 7.302256, 7.505096,\n", " 7.707937, 7.910777, 8.113617, 8.316458, 8.519298, 8.722139,\n", " 8.924979, 9.12782 , 9.33066 , 9.5335 , 9.736341, 9.939181,\n", " 10.142022, 10.344862, 10.547703, 10.750543, 10.953383, 11.156224,\n", " 11.359064, 11.561905, 11.764745, 11.967586, 12.170426, 12.373267,\n", " 12.576107, 12.778947])
array([ 0. , 0.20284 , 0.405681, 0.608521, 0.811362, 1.014202,\n", " 1.217043, 1.419883, 1.622723, 1.825564, 2.028404, 2.231245,\n", " 2.434085, 2.636926, 2.839766, 3.042607, 3.245447, 3.448287,\n", " 3.651128, 3.853968, 4.056809, 4.259649, 4.46249 , 4.66533 ,\n", " 4.86817 , 5.071011, 5.273851, 5.476692, 5.679532, 5.882373,\n", " 6.085213, 6.288053, 6.490894, 6.693734, 6.896575, 7.099415,\n", " 7.302256, 7.505096, 7.707937, 7.910777, 8.113617, 8.316458,\n", " 8.519298, 8.722139, 8.924979, 9.12782 , 9.33066 , 9.5335 ,\n", " 9.736341, 9.939181, 10.142022, 10.344862, 10.547703, 10.750543,\n", " 10.953383, 11.156224, 11.359064, 11.561905, 11.764745, 11.967586,\n", " 12.170426, 12.373267, 12.576107, 12.778947])
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,\n", " 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,\n", " 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,\n", " 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55,\n", " 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69,\n", " 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83,\n", " 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97,\n", " 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n", " 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n", " 126, 127])
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,\n", " 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,\n", " 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,\n", " 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55,\n", " 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69,\n", " 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83,\n", " 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97,\n", " 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n", " 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n", " 126, 127])
array([[[194.53933642, 183.46865602, 189.88360447, ..., 185.13501835,\n", " 189.88360447, 183.46865602],\n", " [180.54977527, 184.19554752, 188.62431121, ..., 190.98754022,\n", " 197.43847912, 186.62178023],\n", " [192.70890797, 195.93098872, 189.09845247, ..., 190.12737145,\n", " 189.83523821, 192.21421257],\n", " ...,\n", " [178.74506797, 186.95925279, 189.9972449 , ..., 190.31796269,\n", " 193.86216905, 184.71498966],\n", " [192.70890797, 192.21421257, 189.83523821, ..., 194.82373533,\n", " 189.09845247, 195.93098872],\n", " [180.54977527, 186.62178023, 197.43847912, ..., 189.320714 ,\n", " 188.62431121, 184.19554752]],\n", "\n", " [[192.53678443, 184.98536047, 183.00178339, ..., 189.93758386,\n", " 183.00178339, 184.98536047],\n", " [182.22340665, 190.38208686, 185.90468391, ..., 188.79454507,\n", " 188.52514631, 188.48204681],\n", " [192.71415943, 196.71513926, 189.84504279, ..., 187.27424593,\n", " 187.74393152, 186.99244495],\n", "...\n", " [224.60947387, 108.81451286, 189.02957545, ..., 137.44506309,\n", " 348.30437843, 228.73579002],\n", " [216.96920343, 166.46373793, 174.79469182, ..., 166.69258334,\n", " 126.31953212, 140.52349943],\n", " [164.20961535, 169.57957548, 133.76022938, ..., 125.77861768,\n", " 159.69240297, 247.86589588]],\n", "\n", " [[ 75.33297495, 174.05006796, 155.35027909, ..., 233.98667431,\n", " 155.35027909, 174.05006796],\n", " [167.22701098, 196.84765156, 192.02546007, ..., 131.6447673 ,\n", " 119.41026107, 235.53961919],\n", " [132.75085561, 149.1865022 , 144.63052109, ..., 237.29431965,\n", " 217.6141243 , 128.83335999],\n", " ...,\n", " [244.06105601, 195.72999615, 198.70767797, ..., 346.86825864,\n", " 208.46454057, 182.9136883 ],\n", " [132.75085561, 128.83335999, 217.6141243 , ..., 137.87697986,\n", " 144.63052109, 149.1865022 ],\n", " [167.22701098, 235.53961919, 119.41026107, ..., 165.83630492,\n", " 192.02546007, 196.84765156]]])
array([[ 0. , 294.18943955, 321.41822078, ..., 192.93331805,\n", " 193.46556826, 192.76671589],\n", " [ 0. , 432.05714374, 490.9677582 , ..., 194.84772175,\n", " 195.06799833, 194.40459328],\n", " [ 0. , 535.36374381, 619.95883018, ..., 196.12616285,\n", " 196.21094092, 195.79399928],\n", " ...,\n", " [ 0. , 3966.56056507, 5791.89215548, ..., 205.00017796,\n", " 211.36062787, 212.61362392],\n", " [ 0. , 4167.1712352 , 5456.14848464, ..., 203.8398704 ,\n", " 205.38454854, 207.78696548],\n", " [ 0. , 3716.77402137, 6067.88205869, ..., 207.76466695,\n", " 201.06258553, 200.39635905]])
array([[128., 149., 173., ..., 178., 224., 255.],\n", " [164., 163., 166., ..., 182., 197., 255.],\n", " [208., 182., 175., ..., 178., 210., 255.],\n", " ...,\n", " [147., 162., 162., ..., 182., 196., 165.],\n", " [201., 214., 234., ..., 189., 174., 178.],\n", " [255., 255., 255., ..., 175., 229., 215.]])
array([0.00000000e+00, 1.29341509e+05, 5.22511731e+03, 5.86989569e+03,\n", " 8.50478146e+03, 9.68446541e+03, 9.99103750e+03, 1.03319622e+04,\n", " 1.00264087e+04, 1.08058729e+04, 1.16343568e+04, 1.38669622e+04,\n", " 1.68988722e+04, 1.98642184e+04, 2.11800678e+04, 2.14311022e+04,\n", " 2.06130601e+04, 1.80258072e+04, 1.42561639e+04, 1.04082328e+04,\n", " 7.27537584e+03, 4.68549415e+03, 2.88015028e+03, 1.77658315e+03,\n", " 1.06139768e+03, 6.83505113e+02, 4.97908069e+02, 4.18238638e+02,\n", " 3.38383278e+02, 2.72050227e+02, 2.35672326e+02, 2.24525405e+02,\n", " 2.03430129e+02, 1.78436880e+02, 1.65009527e+02, 1.49291391e+02,\n", " 1.41201296e+02, 1.33121051e+02, 1.29764821e+02, 1.28159612e+02,\n", " 1.24131175e+02, 1.24052104e+02, 1.21220015e+02, 1.19076951e+02,\n", " 1.17509287e+02, 1.15310101e+02, 1.15268069e+02, 1.12572652e+02,\n", " 1.11849673e+02, 1.11765243e+02, 1.10247178e+02, 1.09703002e+02,\n", " 1.08834403e+02, 1.09662333e+02, 1.08597899e+02, 1.07728419e+02,\n", " 1.07789289e+02, 1.06907057e+02, 1.07036538e+02, 1.05981891e+02,\n", " 1.05125261e+02, 1.05313067e+02, 1.04737380e+02, 1.05326832e+02])
array([2999, 2998, 2997, 1498, 1498, 1497, 998, 998, 997, 748, 747,\n", " 598, 498, 497, 426, 372, 331, 270, 247, 212, 185, 164,\n", " 140, 123, 109, 94, 81, 71, 63, 54, 47, 41, 35,\n", " 31, 27, 23, 20, 17, 15, 13])
array(211.17365621)
array(1.49105881)
array([-2.11173656e+02, 2.58471844e+05, 1.02390610e+04, 1.15286177e+04,\n", " 1.67983893e+04, 1.91577572e+04, 1.97709014e+04, 2.04527506e+04,\n", " 1.98416438e+04, 2.14005721e+04, 2.30575400e+04, 2.75227507e+04,\n", " 3.35865707e+04, 3.95172631e+04, 4.21489620e+04, 4.26510308e+04,\n", " 4.10149466e+04, 3.58404407e+04, 2.83011541e+04, 2.06052919e+04,\n", " 1.43395780e+04, 9.15981465e+03, 5.54912690e+03, 3.34199265e+03,\n", " 1.91162170e+03, 1.15583657e+03, 7.84642482e+02, 6.25303620e+02,\n", " 4.65592900e+02, 3.32926798e+02, 2.60170996e+02, 2.37877154e+02,\n", " 1.95686602e+02, 1.45700103e+02, 1.18845397e+02, 8.74091262e+01,\n", " 7.12289354e+01, 5.50684455e+01, 4.83559858e+01, 4.51455685e+01,\n", " 3.70886933e+01, 3.69305527e+01, 3.12663737e+01, 2.69802467e+01,\n", " 2.38449170e+01, 1.94465450e+01, 1.93624826e+01, 1.39716478e+01,\n", " 1.25256899e+01, 1.23568306e+01, 9.32069947e+00, 8.23234748e+00,\n", " 6.49514954e+00, 8.15100953e+00, 6.02214129e+00, 4.28318246e+00,\n", " 4.40492236e+00, 2.64045708e+00, 2.89942014e+00, 7.90126460e-01,\n", " -9.23134186e-01, -5.47522559e-01, -1.69889697e+00, -5.19992889e-01])
array([[ 0. , 0.99967882, 0.98923294, ..., -32.31431348,\n", " -9.42328539, -34.39844623],\n", " [ 0. , 0.99914543, 0.97267385, ..., -28.81782979,\n", " -8.48006746, -31.24863895],\n", " [ 0. , 0.99874574, 0.96007591, ..., -26.48287376,\n", " -7.80731178, -28.57666779],\n", " ...,\n", " [ 0. , 0.98547081, 0.45495798, ..., -10.27529479,\n", " 1.11005474, 3.76920654],\n", " [ 0. , 0.98469467, 0.48774845, ..., -12.39449068,\n", " -2.40756842, -5.51295585],\n", " [ 0. , 0.98643721, 0.42800337, ..., -5.22620786,\n", " -4.95155025, -19.7258549 ]])
\n", " | Initial guess | \n", "Minimum | \n", "Maximum | \n", "
---|---|---|---|
Amplitude | \n", "100.0 | \n", "1.000 | \n", "1000000.0 | \n", "
Tau | \n", "1.0 | \n", "0.001 | \n", "10.0 | \n", "
Background | \n", "25000.0 | \n", "0.000 | \n", "10000000.0 | \n", "
StretchingExp | \n", "1.0 | \n", "0.500 | \n", "1.1 | \n", "
q | Amplitude | Tau | Background | StretchingExp | |
---|---|---|---|---|---|
0 | \n", "0.000000 | \n", "1.000000 | \n", "10.000000 | \n", "0.000000 | \n", "1.100000 | \n", "
1 | \n", "0.202840 | \n", "5009.160959 | \n", "10.000000 | \n", "125.265537 | \n", "0.500000 | \n", "
2 | \n", "0.405681 | \n", "8482.808495 | \n", "10.000000 | \n", "0.000000 | \n", "0.525256 | \n", "
3 | \n", "0.608521 | \n", "10442.590957 | \n", "3.868067 | \n", "110.613248 | \n", "0.710762 | \n", "
4 | \n", "0.811362 | \n", "16595.852548 | \n", "2.556070 | \n", "83.269636 | \n", "0.811578 | \n", "
5 | \n", "1.014202 | \n", "18774.162108 | \n", "1.424364 | \n", "101.316228 | \n", "0.909133 | \n", "
6 | \n", "1.217043 | \n", "20126.206549 | \n", "1.035536 | \n", "37.943122 | \n", "0.911751 | \n", "
7 | \n", "1.419883 | \n", "20269.935277 | \n", "0.742219 | \n", "30.165661 | \n", "0.952913 | \n", "
8 | \n", "1.622723 | \n", "19408.933976 | \n", "0.552100 | \n", "0.000000 | \n", "0.955882 | \n", "
9 | \n", "1.825564 | \n", "21442.103307 | \n", "0.465083 | \n", "0.000000 | \n", "0.977973 | \n", "
10 | \n", "2.028404 | \n", "23388.120235 | \n", "0.396199 | \n", "0.000000 | \n", "0.968451 | \n", "
11 | \n", "2.231245 | \n", "27490.759703 | \n", "0.321218 | \n", "0.000000 | \n", "1.008676 | \n", "
12 | \n", "2.434085 | \n", "33464.835149 | \n", "0.290591 | \n", "0.000000 | \n", "1.014272 | \n", "
13 | \n", "2.636926 | \n", "39525.290291 | \n", "0.248451 | \n", "0.000000 | \n", "1.040113 | \n", "
14 | \n", "2.839766 | \n", "41793.934306 | \n", "0.213868 | \n", "0.000000 | \n", "1.030231 | \n", "
15 | \n", "3.042607 | \n", "42078.124470 | \n", "0.192926 | \n", "0.000000 | \n", "1.030781 | \n", "
16 | \n", "3.245447 | \n", "40768.461703 | \n", "0.172733 | \n", "0.000000 | \n", "1.045874 | \n", "
17 | \n", "3.448287 | \n", "35721.127412 | \n", "0.155423 | \n", "0.000000 | \n", "1.043916 | \n", "
18 | \n", "3.651128 | \n", "28431.332255 | \n", "0.142240 | \n", "0.000000 | \n", "1.043399 | \n", "
19 | \n", "3.853968 | \n", "20619.257623 | \n", "0.128071 | \n", "0.000000 | \n", "1.054034 | \n", "
20 | \n", "4.056809 | \n", "14370.154840 | \n", "0.121052 | \n", "0.000000 | \n", "1.035008 | \n", "
21 | \n", "4.259649 | \n", "9293.652992 | \n", "0.111708 | \n", "0.000000 | \n", "1.025896 | \n", "
22 | \n", "4.462490 | \n", "5662.007475 | \n", "0.102243 | \n", "0.000000 | \n", "1.008149 | \n", "
23 | \n", "4.665330 | \n", "3487.994425 | \n", "0.097775 | \n", "0.000000 | \n", "0.971809 | \n", "
24 | \n", "4.868170 | \n", "2077.865135 | \n", "0.090379 | \n", "0.000000 | \n", "0.913350 | \n", "
25 | \n", "5.071011 | \n", "1223.115625 | \n", "0.089518 | \n", "83.952238 | \n", "0.911770 | \n", "
26 | \n", "5.273851 | \n", "876.927434 | \n", "0.083446 | \n", "84.578516 | \n", "0.860156 | \n", "
27 | \n", "5.476692 | \n", "690.124583 | \n", "0.081228 | \n", "107.731737 | \n", "0.859201 | \n", "
28 | \n", "5.679532 | \n", "559.962532 | \n", "0.074982 | \n", "89.841197 | \n", "0.757985 | \n", "
29 | \n", "5.882373 | \n", "417.404173 | \n", "0.077395 | \n", "113.007189 | \n", "0.732307 | \n", "
30 | \n", "6.085213 | \n", "339.585926 | \n", "0.074093 | \n", "121.429878 | \n", "0.702539 | \n", "
31 | \n", "6.288053 | \n", "328.928162 | \n", "0.063312 | \n", "104.741958 | \n", "0.648010 | \n", "
32 | \n", "6.490894 | \n", "273.021363 | \n", "0.065949 | \n", "123.344201 | \n", "0.657741 | \n", "
33 | \n", "6.693734 | \n", "210.366431 | \n", "0.069732 | \n", "138.341989 | \n", "0.630490 | \n", "
34 | \n", "6.896575 | \n", "168.823091 | \n", "0.078894 | \n", "151.432022 | \n", "0.624047 | \n", "
35 | \n", "7.099415 | \n", "120.146768 | \n", "0.096006 | \n", "168.399637 | \n", "0.643459 | \n", "
36 | \n", "7.302256 | \n", "90.471468 | \n", "0.114569 | \n", "179.212366 | \n", "0.696849 | \n", "
37 | \n", "7.505096 | \n", "73.280303 | \n", "0.143625 | \n", "183.974447 | \n", "0.707400 | \n", "
38 | \n", "7.707937 | \n", "63.315036 | \n", "0.145241 | \n", "186.298290 | \n", "0.743781 | \n", "
39 | \n", "7.910777 | \n", "54.490768 | \n", "0.146684 | \n", "188.785276 | \n", "0.771679 | \n", "
40 | \n", "8.113617 | \n", "48.703834 | \n", "0.161850 | \n", "189.738060 | \n", "0.784964 | \n", "
41 | \n", "8.316458 | \n", "46.274244 | \n", "0.157325 | \n", "189.710146 | \n", "0.805431 | \n", "
42 | \n", "8.519298 | \n", "42.999737 | \n", "0.150650 | \n", "188.305785 | \n", "0.739396 | \n", "
43 | \n", "8.722139 | \n", "41.307921 | \n", "0.160369 | \n", "188.695165 | \n", "0.715729 | \n", "
44 | \n", "8.924979 | \n", "37.804395 | \n", "0.155632 | \n", "188.636134 | \n", "0.761223 | \n", "
45 | \n", "9.127820 | \n", "35.459070 | \n", "0.163358 | \n", "188.442035 | \n", "0.690826 | \n", "
46 | \n", "9.330660 | \n", "31.309845 | \n", "0.158481 | \n", "191.127615 | \n", "0.879080 | \n", "
47 | \n", "9.533500 | \n", "27.495879 | \n", "0.159557 | \n", "190.705808 | \n", "0.826357 | \n", "
48 | \n", "9.736341 | \n", "29.578351 | \n", "0.164955 | \n", "189.489710 | \n", "0.747781 | \n", "
49 | \n", "9.939181 | \n", "27.750185 | \n", "0.173154 | \n", "190.573335 | \n", "0.817289 | \n", "
50 | \n", "10.142022 | \n", "26.022042 | \n", "0.169798 | \n", "190.445764 | \n", "0.694703 | \n", "
51 | \n", "10.344862 | \n", "25.817798 | \n", "0.149565 | \n", "188.926426 | \n", "0.677988 | \n", "
52 | \n", "10.547703 | \n", "20.964509 | \n", "0.171498 | \n", "192.258742 | \n", "0.865291 | \n", "
53 | \n", "10.750543 | \n", "22.212659 | \n", "0.186064 | \n", "191.315356 | \n", "0.803059 | \n", "
54 | \n", "10.953383 | \n", "20.296560 | \n", "0.175117 | \n", "191.111831 | \n", "0.815027 | \n", "
55 | \n", "11.156224 | \n", "17.733487 | \n", "0.177052 | \n", "191.985542 | \n", "0.975116 | \n", "
56 | \n", "11.359064 | \n", "20.012534 | \n", "0.174850 | \n", "190.372072 | \n", "0.764394 | \n", "
57 | \n", "11.561905 | \n", "17.740871 | \n", "0.167563 | \n", "190.855691 | \n", "0.796393 | \n", "
58 | \n", "11.764745 | \n", "19.164617 | \n", "0.177914 | \n", "190.699793 | \n", "0.827180 | \n", "
59 | \n", "11.967586 | \n", "17.974918 | \n", "0.176198 | \n", "190.556119 | \n", "0.771980 | \n", "
60 | \n", "12.170426 | \n", "15.801139 | \n", "0.197665 | \n", "191.322769 | \n", "0.965799 | \n", "
61 | \n", "12.373267 | \n", "15.561198 | \n", "0.167777 | \n", "190.627761 | \n", "0.941686 | \n", "
62 | \n", "12.576107 | \n", "14.880392 | \n", "0.194683 | \n", "191.407404 | \n", "0.907700 | \n", "
63 | \n", "12.778947 | \n", "15.539401 | \n", "0.183432 | \n", "190.803455 | \n", "0.990262 | \n", "
<xarray.Dataset>\n", "Dimensions: (parameter: 4, q: 64, lagtime: 40)\n", "Coordinates:\n", " * parameter (parameter) <U13 'Amplitude' 'Tau' ... 'StretchingExp'\n", " * q (q) float64 0.0 0.2028 0.4057 0.6085 ... 12.37 12.58 12.78\n", " * lagtime (lagtime) float64 0.02398 0.04796 0.07194 ... 12.59 14.36\n", "Data variables:\n", " parameters (parameter, q) float64 1.0 5.009e+03 ... 0.9077 0.9903\n", " theory (lagtime, q) float64 0.001311 364.7 349.3 ... 206.3 206.3\n", " isf_data (lagtime, q) float64 0.0 0.9997 0.9892 ... -4.952 -19.73\n", " ddm_matrix_data (lagtime, q) float64 0.0 294.2 321.4 ... 207.8 201.1 200.4\n", " A (q) float64 -211.2 2.585e+05 1.024e+04 ... -1.699 -0.52\n", " B float64 211.2\n", "Attributes: (12/18)\n", " model: DDM Matrix - Single Exponential\n", " data_to_use: DDM Matrix\n", " initial_params_dict: ["{'n': 0, 'value': 100.0, 'limits': [1.0...\n", " effective_diffusion_coeff: 0.616760567419975\n", " tau_vs_q_slope: [-1.9799845]\n", " msd_alpha: [1.01010892]\n", " ... ...\n", " DataDirectory: C:/Users/rmcgorty/Documents/GitHub/PyDDM/...\n", " FileName: images_nobin_40x_128x128_8bit.tif\n", " pixel_size: 0.242\n", " frame_rate: 41.7\n", " BackgroundMethod: 0\n", " OverlapMethod: 2
array(['Amplitude', 'Tau', 'Background', 'StretchingExp'], dtype='<U13')
array([ 0. , 0.20284 , 0.405681, 0.608521, 0.811362, 1.014202,\n", " 1.217043, 1.419883, 1.622723, 1.825564, 2.028404, 2.231245,\n", " 2.434085, 2.636926, 2.839766, 3.042607, 3.245447, 3.448287,\n", " 3.651128, 3.853968, 4.056809, 4.259649, 4.46249 , 4.66533 ,\n", " 4.86817 , 5.071011, 5.273851, 5.476692, 5.679532, 5.882373,\n", " 6.085213, 6.288053, 6.490894, 6.693734, 6.896575, 7.099415,\n", " 7.302256, 7.505096, 7.707937, 7.910777, 8.113617, 8.316458,\n", " 8.519298, 8.722139, 8.924979, 9.12782 , 9.33066 , 9.5335 ,\n", " 9.736341, 9.939181, 10.142022, 10.344862, 10.547703, 10.750543,\n", " 10.953383, 11.156224, 11.359064, 11.561905, 11.764745, 11.967586,\n", " 12.170426, 12.373267, 12.576107, 12.778947])
array([ 0.023981, 0.047962, 0.071942, 0.095923, 0.119904, 0.143885,\n", " 0.167866, 0.191847, 0.215827, 0.263789, 0.28777 , 0.335731,\n", " 0.383693, 0.431655, 0.503597, 0.57554 , 0.647482, 0.743405,\n", " 0.863309, 0.983213, 1.127098, 1.294964, 1.486811, 1.702638,\n", " 1.942446, 2.206235, 2.541966, 2.901679, 3.309353, 3.788969,\n", " 4.316547, 4.940048, 5.659472, 6.450839, 7.386091, 8.441247,\n", " 9.640288, 11.007194, 12.589928, 14.364508])
array([[1.00000000e+00, 5.00916096e+03, 8.48280850e+03, 1.04425910e+04,\n", " 1.65958525e+04, 1.87741621e+04, 2.01262065e+04, 2.02699353e+04,\n", " 1.94089340e+04, 2.14421033e+04, 2.33881202e+04, 2.74907597e+04,\n", " 3.34648351e+04, 3.95252903e+04, 4.17939343e+04, 4.20781245e+04,\n", " 4.07684617e+04, 3.57211274e+04, 2.84313323e+04, 2.06192576e+04,\n", " 1.43701548e+04, 9.29365299e+03, 5.66200747e+03, 3.48799443e+03,\n", " 2.07786513e+03, 1.22311562e+03, 8.76927434e+02, 6.90124583e+02,\n", " 5.59962532e+02, 4.17404173e+02, 3.39585926e+02, 3.28928162e+02,\n", " 2.73021363e+02, 2.10366431e+02, 1.68823091e+02, 1.20146768e+02,\n", " 9.04714679e+01, 7.32803029e+01, 6.33150357e+01, 5.44907683e+01,\n", " 4.87038336e+01, 4.62742438e+01, 4.29997373e+01, 4.13079210e+01,\n", " 3.78043951e+01, 3.54590704e+01, 3.13098451e+01, 2.74958795e+01,\n", " 2.95783508e+01, 2.77501849e+01, 2.60220424e+01, 2.58177979e+01,\n", " 2.09645095e+01, 2.22126591e+01, 2.02965596e+01, 1.77334874e+01,\n", " 2.00125344e+01, 1.77408714e+01, 1.91646171e+01, 1.79749177e+01,\n", " 1.58011389e+01, 1.55611976e+01, 1.48803921e+01, 1.55394006e+01],\n", " [1.00000000e+01, 1.00000000e+01, 1.00000000e+01, 3.86806703e+00,\n", " 2.55607003e+00, 1.42436441e+00, 1.03553585e+00, 7.42218949e-01,\n", " 5.52099808e-01, 4.65083145e-01, 3.96199462e-01, 3.21218394e-01,\n", " 2.90591357e-01, 2.48450750e-01, 2.13867737e-01, 1.92925869e-01,\n", "...\n", " 1.89489710e+02, 1.90573335e+02, 1.90445764e+02, 1.88926426e+02,\n", " 1.92258742e+02, 1.91315356e+02, 1.91111831e+02, 1.91985542e+02,\n", " 1.90372072e+02, 1.90855691e+02, 1.90699793e+02, 1.90556119e+02,\n", " 1.91322769e+02, 1.90627761e+02, 1.91407404e+02, 1.90803455e+02],\n", " [1.10000000e+00, 5.00000000e-01, 5.25256250e-01, 7.10762423e-01,\n", " 8.11577597e-01, 9.09132603e-01, 9.11750806e-01, 9.52912612e-01,\n", " 9.55881909e-01, 9.77973210e-01, 9.68450925e-01, 1.00867592e+00,\n", " 1.01427194e+00, 1.04011253e+00, 1.03023058e+00, 1.03078082e+00,\n", " 1.04587435e+00, 1.04391625e+00, 1.04339937e+00, 1.05403372e+00,\n", " 1.03500754e+00, 1.02589585e+00, 1.00814937e+00, 9.71809223e-01,\n", " 9.13350170e-01, 9.11770109e-01, 8.60156008e-01, 8.59200914e-01,\n", " 7.57984830e-01, 7.32306884e-01, 7.02538757e-01, 6.48010499e-01,\n", " 6.57740648e-01, 6.30489631e-01, 6.24047453e-01, 6.43459316e-01,\n", " 6.96848874e-01, 7.07400213e-01, 7.43780605e-01, 7.71678627e-01,\n", " 7.84963506e-01, 8.05431476e-01, 7.39396254e-01, 7.15729270e-01,\n", " 7.61222935e-01, 6.90825910e-01, 8.79080214e-01, 8.26357425e-01,\n", " 7.47781032e-01, 8.17288832e-01, 6.94703179e-01, 6.77987575e-01,\n", " 8.65290831e-01, 8.03058811e-01, 8.15027059e-01, 9.75116037e-01,\n", " 7.64394075e-01, 7.96393191e-01, 8.27180284e-01, 7.71979700e-01,\n", " 9.65798637e-01, 9.41685954e-01, 9.07700392e-01, 9.90261864e-01]])
array([[1.31088782e-03, 3.64655869e+02, 3.49299499e+02, ...,\n", " 1.92929945e+02, 1.93473002e+02, 1.92743417e+02],\n", " [2.80784354e-03, 4.60431845e+02, 4.98126848e+02, ...,\n", " 1.94747318e+02, 1.95045541e+02, 1.94419819e+02],\n", " [4.38258463e-03, 5.32617276e+02, 6.11996774e+02, ...,\n", " 1.96271689e+02, 1.96363908e+02, 1.95882577e+02],\n", " ...,\n", " [6.70880118e-01, 3.38004449e+03, 5.51938876e+03, ...,\n", " 2.06188959e+02, 2.06287796e+02, 2.06342855e+02],\n", " [7.24267866e-01, 3.50338308e+03, 5.73872448e+03, ...,\n", " 2.06188959e+02, 2.06287796e+02, 2.06342855e+02],\n", " [7.74498650e-01, 3.62346204e+03, 5.95207817e+03, ...,\n", " 2.06188959e+02, 2.06287796e+02, 2.06342855e+02]])
array([[ 0. , 0.99967882, 0.98923294, ..., -32.31431348,\n", " -9.42328539, -34.39844623],\n", " [ 0. , 0.99914543, 0.97267385, ..., -28.81782979,\n", " -8.48006746, -31.24863895],\n", " [ 0. , 0.99874574, 0.96007591, ..., -26.48287376,\n", " -7.80731178, -28.57666779],\n", " ...,\n", " [ 0. , 0.98547081, 0.45495798, ..., -10.27529479,\n", " 1.11005474, 3.76920654],\n", " [ 0. , 0.98469467, 0.48774845, ..., -12.39449068,\n", " -2.40756842, -5.51295585],\n", " [ 0. , 0.98643721, 0.42800337, ..., -5.22620786,\n", " -4.95155025, -19.7258549 ]])
array([[ 0. , 294.18943955, 321.41822078, ..., 192.93331805,\n", " 193.46556826, 192.76671589],\n", " [ 0. , 432.05714374, 490.9677582 , ..., 194.84772175,\n", " 195.06799833, 194.40459328],\n", " [ 0. , 535.36374381, 619.95883018, ..., 196.12616285,\n", " 196.21094092, 195.79399928],\n", " ...,\n", " [ 0. , 3966.56056507, 5791.89215548, ..., 205.00017796,\n", " 211.36062787, 212.61362392],\n", " [ 0. , 4167.1712352 , 5456.14848464, ..., 203.8398704 ,\n", " 205.38454854, 207.78696548],\n", " [ 0. , 3716.77402137, 6067.88205869, ..., 207.76466695,\n", " 201.06258553, 200.39635905]])
array([-2.11173656e+02, 2.58471844e+05, 1.02390610e+04, 1.15286177e+04,\n", " 1.67983893e+04, 1.91577572e+04, 1.97709014e+04, 2.04527506e+04,\n", " 1.98416438e+04, 2.14005721e+04, 2.30575400e+04, 2.75227507e+04,\n", " 3.35865707e+04, 3.95172631e+04, 4.21489620e+04, 4.26510308e+04,\n", " 4.10149466e+04, 3.58404407e+04, 2.83011541e+04, 2.06052919e+04,\n", " 1.43395780e+04, 9.15981465e+03, 5.54912690e+03, 3.34199265e+03,\n", " 1.91162170e+03, 1.15583657e+03, 7.84642482e+02, 6.25303620e+02,\n", " 4.65592900e+02, 3.32926798e+02, 2.60170996e+02, 2.37877154e+02,\n", " 1.95686602e+02, 1.45700103e+02, 1.18845397e+02, 8.74091262e+01,\n", " 7.12289354e+01, 5.50684455e+01, 4.83559858e+01, 4.51455685e+01,\n", " 3.70886933e+01, 3.69305527e+01, 3.12663737e+01, 2.69802467e+01,\n", " 2.38449170e+01, 1.94465450e+01, 1.93624826e+01, 1.39716478e+01,\n", " 1.25256899e+01, 1.23568306e+01, 9.32069947e+00, 8.23234748e+00,\n", " 6.49514954e+00, 8.15100953e+00, 6.02214129e+00, 4.28318246e+00,\n", " 4.40492236e+00, 2.64045708e+00, 2.89942014e+00, 7.90126460e-01,\n", " -9.23134186e-01, -5.47522559e-01, -1.69889697e+00, -5.19992889e-01])
array(211.17365621)
\n", " | Initial guess | \n", "Minimum | \n", "Maximum | \n", "
---|---|---|---|
Tau | \n", "1.0 | \n", "0.001 | \n", "10.0 | \n", "
StretchingExp | \n", "1.0 | \n", "0.500 | \n", "1.1 | \n", "
<xarray.Dataset>\n", "Dimensions: (parameter: 2, q: 64, lagtime: 40)\n", "Coordinates:\n", " * parameter (parameter) <U13 'Tau' 'StretchingExp'\n", " * q (q) float64 0.0 0.2028 0.4057 0.6085 ... 12.37 12.58 12.78\n", " * lagtime (lagtime) float64 0.02398 0.04796 0.07194 ... 12.59 14.36\n", "Data variables:\n", " parameters (parameter, q) float64 0.001886 10.0 10.0 ... 1.1 1.093\n", " theory (lagtime, q) float64 4.761e-07 0.9987 0.9812 ... 0.0 0.0\n", " isf_data (lagtime, q) float64 0.0 0.9997 0.9892 ... -4.952 -19.73\n", " ddm_matrix_data (lagtime, q) float64 0.0 294.2 321.4 ... 207.8 201.1 200.4\n", " A (q) float64 -211.2 2.585e+05 1.024e+04 ... -1.699 -0.52\n", " B float64 211.2\n", "Attributes: (12/18)\n", " model: ISF - Single Exponential\n", " data_to_use: ISF\n", " initial_params_dict: ["{'n': 0, 'value': 1.0, 'limits': [0.001...\n", " effective_diffusion_coeff: 0.6044361168424172\n", " tau_vs_q_slope: [-1.97401294]\n", " msd_alpha: [1.01316459]\n", " ... ...\n", " DataDirectory: C:/Users/rmcgorty/Documents/GitHub/PyDDM/...\n", " FileName: images_nobin_40x_128x128_8bit.tif\n", " pixel_size: 0.242\n", " frame_rate: 41.7\n", " BackgroundMethod: 0\n", " OverlapMethod: 2
array(['Tau', 'StretchingExp'], dtype='<U13')
array([ 0. , 0.20284 , 0.405681, 0.608521, 0.811362, 1.014202,\n", " 1.217043, 1.419883, 1.622723, 1.825564, 2.028404, 2.231245,\n", " 2.434085, 2.636926, 2.839766, 3.042607, 3.245447, 3.448287,\n", " 3.651128, 3.853968, 4.056809, 4.259649, 4.46249 , 4.66533 ,\n", " 4.86817 , 5.071011, 5.273851, 5.476692, 5.679532, 5.882373,\n", " 6.085213, 6.288053, 6.490894, 6.693734, 6.896575, 7.099415,\n", " 7.302256, 7.505096, 7.707937, 7.910777, 8.113617, 8.316458,\n", " 8.519298, 8.722139, 8.924979, 9.12782 , 9.33066 , 9.5335 ,\n", " 9.736341, 9.939181, 10.142022, 10.344862, 10.547703, 10.750543,\n", " 10.953383, 11.156224, 11.359064, 11.561905, 11.764745, 11.967586,\n", " 12.170426, 12.373267, 12.576107, 12.778947])
array([ 0.023981, 0.047962, 0.071942, 0.095923, 0.119904, 0.143885,\n", " 0.167866, 0.191847, 0.215827, 0.263789, 0.28777 , 0.335731,\n", " 0.383693, 0.431655, 0.503597, 0.57554 , 0.647482, 0.743405,\n", " 0.863309, 0.983213, 1.127098, 1.294964, 1.486811, 1.702638,\n", " 1.942446, 2.206235, 2.541966, 2.901679, 3.309353, 3.788969,\n", " 4.316547, 4.940048, 5.659472, 6.450839, 7.386091, 8.441247,\n", " 9.640288, 11.007194, 12.589928, 14.364508])
array([[1.88589103e-03, 1.00000000e+01, 1.00000000e+01, 4.91794800e+00,\n", " 2.65628838e+00, 1.50327300e+00, 1.01994490e+00, 7.73490610e-01,\n", " 5.96273909e-01, 4.76451564e-01, 3.95261921e-01, 3.29426444e-01,\n", " 2.98344562e-01, 2.52353941e-01, 2.21023606e-01, 2.01537369e-01,\n", " 1.77734983e-01, 1.59432944e-01, 1.44271986e-01, 1.32113236e-01,\n", " 1.26393210e-01, 1.16714583e-01, 1.10908961e-01, 1.09684454e-01,\n", " 1.08269318e-01, 1.15043361e-01, 1.11857630e-01, 1.14807481e-01,\n", " 1.19359419e-01, 1.22539709e-01, 1.24224230e-01, 1.30311108e-01,\n", " 1.29868326e-01, 1.46928516e-01, 1.79917017e-01, 2.29897133e-01,\n", " 3.00841481e-01, 3.70318524e-01, 4.25745120e-01, 5.32776300e-01,\n", " 6.05123405e-01, 7.15176380e-01, 9.19222068e-01, 9.37440036e-01,\n", " 1.23116692e+00, 1.66636757e+00, 1.61883949e+00, 4.16763356e+00,\n", " 3.13511306e+00, 4.03316708e+00, 8.47590873e+00, 1.00000000e+01,\n", " 1.00000000e+01, 1.00000000e+01, 1.00000000e+01, 1.00000000e+01,\n", " 1.00000000e+01, 1.00000000e+01, 1.00000000e+01, 1.00000000e+01,\n", " 1.00000000e-03, 1.19234103e-03, 1.00005677e-03, 1.16635749e-03],\n", " [1.05319182e+00, 1.10000000e+00, 6.57192482e-01, 7.19198817e-01,\n", " 8.34029429e-01, 9.18452835e-01, 9.44371329e-01, 9.69649418e-01,\n", " 9.62634582e-01, 9.98357963e-01, 9.94382337e-01, 1.01920184e+00,\n", " 1.01976533e+00, 1.04708563e+00, 1.02648698e+00, 1.02019083e+00,\n", " 1.04248931e+00, 1.04339305e+00, 1.05283303e+00, 1.05848968e+00,\n", " 1.04109533e+00, 1.04954794e+00, 1.03737037e+00, 1.03106364e+00,\n", " 1.01864683e+00, 9.71396006e-01, 9.80075298e-01, 9.51053861e-01,\n", " 9.24786563e-01, 9.55424623e-01, 9.58598542e-01, 9.07784710e-01,\n", " 9.48445041e-01, 9.63368267e-01, 9.58958089e-01, 9.99925144e-01,\n", " 1.03313591e+00, 1.10000000e+00, 1.10000000e+00, 1.10000000e+00,\n", " 1.10000000e+00, 1.10000000e+00, 1.10000000e+00, 1.10000000e+00,\n", " 1.10000000e+00, 1.10000000e+00, 1.10000000e+00, 1.10000000e+00,\n", " 1.10000000e+00, 1.10000000e+00, 1.10000000e+00, 1.10000000e+00,\n", " 1.10000000e+00, 1.10000000e+00, 1.10000000e+00, 1.10000000e+00,\n", " 1.10000000e+00, 1.10000000e+00, 1.10000000e+00, 1.10000000e+00,\n", " 1.10000000e+00, 1.09262247e+00, 1.09999795e+00, 1.09332614e+00]])
array([[4.76121049e-07, 9.98689112e-01, 9.81208843e-01, ...,\n", " 2.92454151e-12, 4.91078571e-15, 1.44497734e-12],\n", " [7.59506876e-14, 9.97192156e-01, 9.70527228e-01, ...,\n", " 2.52673726e-25, 2.12987589e-31, 5.46062080e-26],\n", " [7.79395343e-21, 9.95617415e-01, 9.61702126e-01, ...,\n", " 4.91870075e-39, 1.22685721e-48, 4.41016073e-40],\n", " ...,\n", " [0.00000000e+00, 3.29119882e-01, 3.44694074e-01, ...,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n", " [0.00000000e+00, 2.75732134e-01, 3.12417562e-01, ...,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n", " [0.00000000e+00, 2.25501350e-01, 2.81187600e-01, ...,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]])
array([[ 0. , 0.99967882, 0.98923294, ..., -32.31431348,\n", " -9.42328539, -34.39844623],\n", " [ 0. , 0.99914543, 0.97267385, ..., -28.81782979,\n", " -8.48006746, -31.24863895],\n", " [ 0. , 0.99874574, 0.96007591, ..., -26.48287376,\n", " -7.80731178, -28.57666779],\n", " ...,\n", " [ 0. , 0.98547081, 0.45495798, ..., -10.27529479,\n", " 1.11005474, 3.76920654],\n", " [ 0. , 0.98469467, 0.48774845, ..., -12.39449068,\n", " -2.40756842, -5.51295585],\n", " [ 0. , 0.98643721, 0.42800337, ..., -5.22620786,\n", " -4.95155025, -19.7258549 ]])
array([[ 0. , 294.18943955, 321.41822078, ..., 192.93331805,\n", " 193.46556826, 192.76671589],\n", " [ 0. , 432.05714374, 490.9677582 , ..., 194.84772175,\n", " 195.06799833, 194.40459328],\n", " [ 0. , 535.36374381, 619.95883018, ..., 196.12616285,\n", " 196.21094092, 195.79399928],\n", " ...,\n", " [ 0. , 3966.56056507, 5791.89215548, ..., 205.00017796,\n", " 211.36062787, 212.61362392],\n", " [ 0. , 4167.1712352 , 5456.14848464, ..., 203.8398704 ,\n", " 205.38454854, 207.78696548],\n", " [ 0. , 3716.77402137, 6067.88205869, ..., 207.76466695,\n", " 201.06258553, 200.39635905]])
array([-2.11173656e+02, 2.58471844e+05, 1.02390610e+04, 1.15286177e+04,\n", " 1.67983893e+04, 1.91577572e+04, 1.97709014e+04, 2.04527506e+04,\n", " 1.98416438e+04, 2.14005721e+04, 2.30575400e+04, 2.75227507e+04,\n", " 3.35865707e+04, 3.95172631e+04, 4.21489620e+04, 4.26510308e+04,\n", " 4.10149466e+04, 3.58404407e+04, 2.83011541e+04, 2.06052919e+04,\n", " 1.43395780e+04, 9.15981465e+03, 5.54912690e+03, 3.34199265e+03,\n", " 1.91162170e+03, 1.15583657e+03, 7.84642482e+02, 6.25303620e+02,\n", " 4.65592900e+02, 3.32926798e+02, 2.60170996e+02, 2.37877154e+02,\n", " 1.95686602e+02, 1.45700103e+02, 1.18845397e+02, 8.74091262e+01,\n", " 7.12289354e+01, 5.50684455e+01, 4.83559858e+01, 4.51455685e+01,\n", " 3.70886933e+01, 3.69305527e+01, 3.12663737e+01, 2.69802467e+01,\n", " 2.38449170e+01, 1.94465450e+01, 1.93624826e+01, 1.39716478e+01,\n", " 1.25256899e+01, 1.23568306e+01, 9.32069947e+00, 8.23234748e+00,\n", " 6.49514954e+00, 8.15100953e+00, 6.02214129e+00, 4.28318246e+00,\n", " 4.40492236e+00, 2.64045708e+00, 2.89942014e+00, 7.90126460e-01,\n", " -9.23134186e-01, -5.47522559e-01, -1.69889697e+00, -5.19992889e-01])
array(211.17365621)