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"## Carry out a few single indivual steps of diffusion, \n",
"### and directly verify that the values satisfy the diffusion equation\n",
"\n",
"In this \"PART 1\", we'll be looking at a tiny system with just 10 bins, to easily inspect the numbers directly.\n",
"We'll use concentrations initialized to an upward-shifted sine wave with 1 cycle over the length system\n",
"\n",
"LAST REVISED: Nov. 28, 2022"
]
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"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"# Extend the sys.path variable, to contain the project's root directory\n",
"import set_path\n",
"set_path.add_ancestor_dir_to_syspath(3) # The number of levels to go up \n",
" # to reach the project's home, from the folder containing this notebook"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a945cbfa",
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"outputs": [],
"source": [
"from experiments.get_notebook_info import get_notebook_basename\n",
"\n",
"from src.life_1D.bio_sim_1d import BioSim1D\n",
"from src.modules.reactions.reaction_data import ReactionData as chem\n",
"from src.modules.movies.movies import MovieArray\n",
"from src.modules.numerical.numerical import Numerical as num\n",
"\n",
"import numpy as np\n",
"\n",
"import plotly.express as px\n",
"import plotly.graph_objects as go"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6207338f",
"metadata": {},
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"source": [
"# We'll be considering just 1 chemical species, \"A\"\n",
"diffusion_rate = 10.\n",
"\n",
"chem_data = chem(diffusion_rates=[diffusion_rate], names=[\"A\"])"
]
},
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"execution_count": 4,
"id": "087caa8d",
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"# Initialize the system with just a few bins\n",
"bio = BioSim1D(n_bins=10, chem_data=chem_data)"
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"# Initialize the concentrations to a sine wave with 1 cycle over the system\n",
"# (with a bias to always keep it > 0)\n",
"bio.inject_sine_conc(species_name=\"A\", frequency=1, amplitude=10, bias=50)"
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"SYSTEM SNAPSHOT at time 0:\n",
" A\n",
"0 50.000000\n",
"1 55.877853\n",
"2 59.510565\n",
"3 59.510565\n",
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""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = px.line(data_frame=bio.system_snapshot(), y=[\"A\"], \n",
" title= \"Initial System State (for the tiny system)\",\n",
" color_discrete_sequence = ['red'],\n",
" labels={\"value\":\"concentration\", \"variable\":\"Chemical\", \"index\":\"Bin number\"})\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "cc542145",
"metadata": {},
"outputs": [
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Show as heatmap\n",
"fig = px.imshow(bio.system_snapshot().T, \n",
" title= \"Initial System State (for the tiny system)\", \n",
" labels=dict(x=\"Bin number\", y=\"Chem. species\", color=\"Concentration\"),\n",
" text_auto=False, color_continuous_scale=\"gray_r\") \n",
"\n",
"fig.data[0].xgap=1\n",
"fig.data[0].ygap=1\n",
"\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"id": "259c41dd",
"metadata": {},
"source": [
"### Now do 4 rounds of single-step diffusion, to collect the system state at a total of 5 time points: \n",
"#### t0 (the initial state), plus t1, t2, t3 and t4"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "5051007a",
"metadata": {},
"outputs": [],
"source": [
"# All the system states will get collected in this object\n",
"history = MovieArray()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "8ec78ba5",
"metadata": {},
"outputs": [],
"source": [
"# Store the initial state\n",
"arr = bio.lookup_species(species_index=0, copy=True)\n",
"history.store(pars=bio.system_time, data_snapshot=arr, caption=f\"State at time {bio.system_time}\")"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7ed98602",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[50. , 55.87785252, 59.51056516, 59.51056516, 55.87785252,\n",
" 50. , 44.12214748, 40.48943484, 40.48943484, 44.12214748]])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Take a look at what got stored so far (a matrix whose only row is the initial state)\n",
"history.get_array()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "5b702362",
"metadata": {},
"outputs": [],
"source": [
"# Additional parameters of the simulation run (the diffusion rate got set earlier)\n",
"delta_t = 0.01\n",
"delta_x = 2 # Note that the number of bins also define the fraction of the sine wave cycle in each bin\n",
"algorithm = None # \"Explicit, with 3+1 stencil\""
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "b02af31b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0.01:\n",
"[[50.14694631 55.82172403 59.41974735 59.41974735 55.82172403 50.\n",
" 44.17827597 40.58025265 40.58025265 44.03132966]]\n",
"SYSTEM STATE at Time t = 0.02:\n",
"[[50.28881576 55.76980517 59.32979676 59.32979676 55.76613151 50.\n",
" 44.23386849 40.67020324 40.66652958 43.94505274]]\n",
"SYSTEM STATE at Time t = 0.03:\n",
"[[50.42584049 55.72178022 59.24079697 59.24070513 55.71106985 50.\n",
" 44.28893015 40.75920303 40.7485845 43.86308966]]\n",
"SYSTEM STATE at Time t = 0.04:\n",
"[[50.55823898 55.67735715 59.15281926 59.15246655 55.65653399 50.\n",
" 44.34346372 40.84718074 40.82671259 43.78522703]]\n"
]
}
],
"source": [
"# Do the 4 rounds of single-step diffusion; show the system state after each step, and accumulate all data\n",
"# in the history object\n",
"for _ in range(4):\n",
" bio.diffuse(time_step=delta_t, n_steps=1, delta_x=delta_x , algorithm=algorithm)\n",
" bio.describe_state(concise=True)\n",
"\n",
" arr = bio.lookup_species(species_index=0, copy=True)\n",
" history.store(pars=bio.system_time, data_snapshot=arr, caption=f\"State at time {bio.system_time}\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "8a14efb3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[50. , 55.87785252, 59.51056516, 59.51056516, 55.87785252,\n",
" 50. , 44.12214748, 40.48943484, 40.48943484, 44.12214748],\n",
" [50.14694631, 55.82172403, 59.41974735, 59.41974735, 55.82172403,\n",
" 50. , 44.17827597, 40.58025265, 40.58025265, 44.03132966],\n",
" [50.28881576, 55.76980517, 59.32979676, 59.32979676, 55.76613151,\n",
" 50. , 44.23386849, 40.67020324, 40.66652958, 43.94505274],\n",
" [50.42584049, 55.72178022, 59.24079697, 59.24070513, 55.71106985,\n",
" 50. , 44.28893015, 40.75920303, 40.7485845 , 43.86308966],\n",
" [50.55823898, 55.67735715, 59.15281926, 59.15246655, 55.65653399,\n",
" 50. , 44.34346372, 40.84718074, 40.82671259, 43.78522703]])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Now, let's examine the data collected at the 5 time points\n",
"all_history = history.get_array()\n",
"all_history"
]
},
{
"cell_type": "markdown",
"id": "cc72bb99",
"metadata": {},
"source": [
"#### Each row in the above matrix is a state snapshot at a different time:\n",
"first row is the initial state at time 0; the successive rows are at t1, t2, t3, t4"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "8e767eb3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([50.28881576, 55.76980517, 59.32979676, 59.32979676, 55.76613151,\n",
" 50. , 44.23386849, 40.67020324, 40.66652958, 43.94505274])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's consider the state, i.e. the concentration across the bins, at the midpoint in time (t2)\n",
"f_at_t2 = all_history[2]\n",
"f_at_t2"
]
},
{
"cell_type": "markdown",
"id": "06ceebe4",
"metadata": {},
"source": [
"If one compares the above state (at t2) with the initial state (the top row in the matrix), \n",
"one can see, for example, that the leftmost bin's concentration is increasing (\"pulled up\" by its neighbor to the right):\n",
"50. has now become 50.28881576\n",
"\n",
"The rightmost bin's concentration is decreasing (\"pulled down\" by its neighbor to the left):\n",
"44.12214748 has now become 43.94505274"
]
},
{
"cell_type": "markdown",
"id": "3a88a1ca",
"metadata": {},
"source": [
"## The diffusion equation states that the partial derivative of the concentration values with respect to time must equal the (diffusion rate) times (the 2nd partial derivative with respect to space).\n",
"Let's see if that is the case for the values at time t2! We are picking t2 because we need at least a value at the earlier time, and a value at the later time"
]
},
{
"cell_type": "markdown",
"id": "09a0d7f8",
"metadata": {},
"source": [
"## A. The 2nd partial derivative with respect to space"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "1d06fc6a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 2.74049471, 2.26024525, 0.8899979 , -0.89091631, -2.33244919,\n",
" -2.88306575, -2.33244919, -0.89183473, 0.81871237, 1.63926158])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# A simple-minded way of computing the 2nd spacial derivative is to use the Numpy gradient function TWICE across the x value\n",
"# (that function approximates the derivative using differences)\n",
"gradient_x_at_t2 = np.gradient(f_at_t2, delta_x) # Start with taking the first derivative\n",
"gradient_x_at_t2 # This will be the partial derivative of the concentration with respect to x, at time t2"
]
},
{
"cell_type": "markdown",
"id": "b7ebf78e",
"metadata": {},
"source": [
"For example, the 2nd entry in the above array of estimated derivatives, can be manually checked from the 1st and 3rd value in the function f_at_t2(x), as follows:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "cde2fff9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.2602452500000005"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(59.32979676 - 50.28881576) / (2*delta_x) # This way of numerically estimating derivatives is called \"Central Differences\""
]
},
{
"cell_type": "markdown",
"id": "5b79c68f",
"metadata": {},
"source": [
"#### Now take the derivative again, with the Numpy gradient function, to arrive at a coarse estimate of the 2nd derivative with respect to x:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "980650d1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.24012473, -0.4626242 , -0.78779039, -0.80561177, -0.49803736,\n",
" 0. , 0.49780776, 0.78779039, 0.63277408, 0.4102746 ])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"second_gradient_x_at_t2 = np.gradient(gradient_x_at_t2, delta_x)\n",
"second_gradient_x_at_t2"
]
},
{
"cell_type": "markdown",
"id": "be13f82c",
"metadata": {},
"source": [
"Note how the 2nd derivative is 0 at bin 5 (bins are numbered 0 thru 9): if you look at the earlier sine plot, x5 is the inflection point."
]
},
{
"cell_type": "markdown",
"id": "58d3cd8e",
"metadata": {},
"source": [
"### B. The partial derivative with respect to time\n",
"Now, let's look at how concentrations change with time. Let's first revisit the full history:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "86a5c102",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[50. , 55.87785252, 59.51056516, 59.51056516, 55.87785252,\n",
" 50. , 44.12214748, 40.48943484, 40.48943484, 44.12214748],\n",
" [50.14694631, 55.82172403, 59.41974735, 59.41974735, 55.82172403,\n",
" 50. , 44.17827597, 40.58025265, 40.58025265, 44.03132966],\n",
" [50.28881576, 55.76980517, 59.32979676, 59.32979676, 55.76613151,\n",
" 50. , 44.23386849, 40.67020324, 40.66652958, 43.94505274],\n",
" [50.42584049, 55.72178022, 59.24079697, 59.24070513, 55.71106985,\n",
" 50. , 44.28893015, 40.75920303, 40.7485845 , 43.86308966],\n",
" [50.55823898, 55.67735715, 59.15281926, 59.15246655, 55.65653399,\n",
" 50. , 44.34346372, 40.84718074, 40.82671259, 43.78522703]])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"all_history"
]
},
{
"cell_type": "markdown",
"id": "cace8215",
"metadata": {},
"source": [
"#### For simplicity, let's start by just inspecting how the values change over time at the *3rd bin* from the left, \n",
"i.e. the 3rd *column* (index 2 because counting starts at 0) of the above matrix:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "f1dc7ce4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([59.51056516, 59.41974735, 59.32979676, 59.24079697, 59.15281926])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f_of_t_at_x2 = all_history[ : , 2] # The column with index 2\n",
"f_of_t_at_x2"
]
},
{
"cell_type": "markdown",
"id": "2f372d89",
"metadata": {},
"source": [
"### The above a function of time \n",
"(we took an entry from each row - the rows being the system states at t0, t1, t2, t3, t4); let's look at its time derivative:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "21654172",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-9.0817816 , -9.03841995, -8.94751865, -8.84887524, -8.79777149])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gradient_t_at_x2 = np.gradient(f_of_t_at_x2, delta_t)\n",
"gradient_t_at_x2"
]
},
{
"cell_type": "markdown",
"id": "8fe73fb8",
"metadata": {},
"source": [
"### The above is the rate of change of the concentration, as the diffusion proceeds, at the position x2\n",
"At time t2, the midpoint in the simulation, the value is:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "270aaafa",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-8.947518648702157"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gradient_t_at_x2[2]"
]
},
{
"cell_type": "markdown",
"id": "3cf59301",
"metadata": {},
"source": [
"### C. All said and done, we have collected the time derivative and the 2nd spacial derivative, at the point (x2, t2).\n",
"Do those values satisfy the diffusion equation?? Does the time derivative indeed equal the (diffusion rate) x (the \n",
"2nd spacial derivative)? Let's see:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "9b64a095",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-8.947518648702157"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gradient_t_at_x2[2]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "e19fc288",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-7.877903914825475"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"diffusion_rate * second_gradient_x_at_t2[2]"
]
},
{
"cell_type": "markdown",
"id": "24121c37",
"metadata": {},
"source": [
"## D. The 2 value indeed roughly match - considering the coarseness of the large spacial grid, and the coarseness of estimating the derivatives numerically. \n",
"We have evidence that the diffusion equation may indeed be satisfied by the values we obtained from our diffusion algorithm, in the proximity of the point (x2, t2)"
]
},
{
"cell_type": "markdown",
"id": "86a00a96",
"metadata": {},
"source": [
"### E. Finally, instead of just scrutining the match at the point x2, let's do that for all the points in space at time t2,\n",
"WITH THE EXCEPTION of the outmost points (because the numeric estimation of the derivatives gets very crummy at the boundary).\n",
" \n",
"Let's first re-visit all the data once again:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "28225e05",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[50. , 55.87785252, 59.51056516, 59.51056516, 55.87785252,\n",
" 50. , 44.12214748, 40.48943484, 40.48943484, 44.12214748],\n",
" [50.14694631, 55.82172403, 59.41974735, 59.41974735, 55.82172403,\n",
" 50. , 44.17827597, 40.58025265, 40.58025265, 44.03132966],\n",
" [50.28881576, 55.76980517, 59.32979676, 59.32979676, 55.76613151,\n",
" 50. , 44.23386849, 40.67020324, 40.66652958, 43.94505274],\n",
" [50.42584049, 55.72178022, 59.24079697, 59.24070513, 55.71106985,\n",
" 50. , 44.28893015, 40.75920303, 40.7485845 , 43.86308966],\n",
" [50.55823898, 55.67735715, 59.15281926, 59.15246655, 55.65653399,\n",
" 50. , 44.34346372, 40.84718074, 40.82671259, 43.78522703]])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"all_history"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "380f8bf6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[14.69463131, -5.61284971, -9.0817816 , -9.0817816 , -5.61284971,\n",
" 0. , 5.61284971, 9.0817816 , 9.0817816 , -9.0817816 ],\n",
" [14.44078779, -5.40236784, -9.03841995, -9.03841995, -5.58605073,\n",
" 0. , 5.58605073, 9.03841995, 8.85473706, -8.85473706],\n",
" [13.9447089 , -4.99719025, -8.94751865, -8.95211072, -5.5327087 ,\n",
" 0. , 5.5327087 , 8.94751865, 8.41659228, -8.41200021],\n",
" [13.47116142, -4.62240099, -8.84887524, -8.86651087, -5.47987603,\n",
" 0. , 5.47976123, 8.84887524, 8.00915063, -7.99128539],\n",
" [13.23984932, -4.44230744, -8.79777149, -8.8238586 , -5.45358643,\n",
" 0. , 5.45335682, 8.79777149, 7.81280921, -7.7862629 ]])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The following is just an expanded version of what we did before for the time derivative; \n",
"# instead of just considering 1 column,\n",
"# like we did before, we're now repeating the computations along all columns\n",
"# (the computations are applied vertically, \"along axis 0\" in Numpy-speak)\n",
"gradient_t = np.apply_along_axis(np.gradient, 0, all_history, delta_t)\n",
"gradient_t"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "3278805e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([13.9447089 , -4.99719025, -8.94751865, -8.95211072, -5.5327087 ,\n",
" 0. , 5.5327087 , 8.94751865, 8.41659228, -8.41200021])"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Again, we focus on time t2 (the 3rd row), to stay away from the edges\n",
"gradient_t_at_t2 = gradient_t[2]\n",
"gradient_t_at_t2"
]
},
{
"cell_type": "markdown",
"id": "d03cb73c",
"metadata": {},
"source": [
"Note the value -8.94751865, 3rd from left : that's the single value we looked at before (at point x2)"
]
},
{
"cell_type": "markdown",
"id": "9bba1933",
"metadata": {},
"source": [
"#### Time to again check the match of the two sides of the diffusion equation"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "d1bde2cd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([13.9447089 , -4.99719025, -8.94751865, -8.95211072, -5.5327087 ,\n",
" 0. , 5.5327087 , 8.94751865, 8.41659228, -8.41200021])"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lhs = gradient_t_at_t2 # The LEFT-hand side of the diffusion equation, as a vector for all the spacial points at time t2\n",
"lhs"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "1daa4abd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-2.40124727, -4.62624201, -7.87790391, -8.05611773, -4.9803736 ,\n",
" 0. , 4.97807756, 7.87790391, 6.32774077, 4.10274602])"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rhs = diffusion_rate * second_gradient_x_at_t2 # The RIGHT-hand side of the diffusion equation, again as a vector\n",
"rhs"
]
},
{
"cell_type": "markdown",
"id": "b0df453b",
"metadata": {},
"source": [
"## The left-hand side and the right-hand side of the diffusion equation appear to generally agree, except at the boundary points, where our approximations are just too crummy"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "aa858793",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 16.34595617, -0.37094824, -1.06961473, -0.89599299,\n",
" -0.5523351 , 0. , 0.55463113, 1.06961473,\n",
" 2.08885151, -12.51474623])"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lhs - rhs"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "0649f714",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.8643581811669576"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Here we use a handy function to compare two equal-sized vectors,\n",
"# while opting to disregarding a specified number of entries at each edge.\n",
"# It returns the Euclidean distance (\"L2 norm\") of the shortened vectors\n",
"num.compare_vectors(lhs, rhs, trim_edges=1)"
]
},
{
"cell_type": "markdown",
"id": "3878d34e",
"metadata": {},
"source": [
"#### IMPORTANT: all values in this experiment are VERY coarse, because of the large effective delta_x (the tiny number of bins.)\n",
"In part2 (notebook \"validate_diffusion_2\"), much-better approximations will get looked at!"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3926f0e9",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}