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bradyrx/bootstrapping_efficiency.ipynb

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bootstrapping_efficiency.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Resampling Example\n",
"\n",
"---\n",
"\n",
"The goal here is to take a historical ensemble (like the CESM Large Ensemble) and resample its members with replacement. We reference an initialized forecast system with dimensions `init` and `lead` and create an \"uninitialized\" (or historical) ensemble with the same dimensions."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import xarray as xr\n",
"import numpy as np\n",
"%load_ext line_profiler"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/glade/u/home/rbrady/miniconda3/envs/analysis/lib/python3.6/site-packages/distributed/dashboard/core.py:72: UserWarning: \n",
"Port 8787 is already in use. \n",
"Perhaps you already have a cluster running?\n",
"Hosting the diagnostics dashboard on a random port instead.\n",
" warnings.warn(\"\\n\" + msg)\n"
]
}
],
"source": [
"from dask.distributed import Client\n",
"from ncar_jobqueue import NCARCluster\n",
"cluster = NCARCluster(cores=36, memory=\"100GB\", walltime=\"00:30:00\", processes=36) # Change this to SLURMCluster if on DAV/Casper\n",
"cluster.scale(36*4)\n",
"client = Client(cluster)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table style=\"border: 2px solid white;\">\n",
"<tr>\n",
"<td style=\"vertical-align: top; border: 0px solid white\">\n",
"<h3 style=\"text-align: left;\">Client</h3>\n",
"<ul style=\"text-align: left; list-style: none; margin: 0; padding: 0;\">\n",
" <li><b>Scheduler: </b>tcp://128.117.181.207:40475</li>\n",
" <li><b>Dashboard: </b><a href='https://jupyterhub.ucar.edu/dav/user/rbrady/proxy/38999/status' target='_blank'>https://jupyterhub.ucar.edu/dav/user/rbrady/proxy/38999/status</a>\n",
"</ul>\n",
"</td>\n",
"<td style=\"vertical-align: top; border: 0px solid white\">\n",
"<h3 style=\"text-align: left;\">Cluster</h3>\n",
"<ul style=\"text-align: left; list-style:none; margin: 0; padding: 0;\">\n",
" <li><b>Workers: </b>144</li>\n",
" <li><b>Cores: </b>144</li>\n",
" <li><b>Memory: </b>400.32 GB</li>\n",
"</ul>\n",
"</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<Client: 'tcp://128.117.181.207:40475' processes=144 threads=144, memory=400.32 GB>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"client"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create dummy data.\n",
"\n",
"Here we create dummy data for an initialized hindcast system and a historical ensemble.\n",
"\n",
"`init` : re-initialization dates for the forecasting system\n",
"\n",
"`lead` : lead years for the forecasting system\n",
"\n",
"`member` : ensemble members for the forecasting system and historical ensemble\n",
"\n",
"`time` : time for the historical ensemble"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"nlead = 10\n",
"nmember = 10\n",
"\n",
"init = np.arange(1950, 2000)\n",
"lead = np.arange(nlead) + 1\n",
"member = np.arange(nmember) + 1\n",
"time = np.arange(1900, 2020)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"hindcast = xr.DataArray(np.random.rand(len(init), nlead, nmember),\n",
" dims=['init', 'lead', 'member'],\n",
" coords=[init, lead, member]).rename('SST').to_dataset()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"historical = xr.DataArray(np.random.rand(len(time), nmember),\n",
" dims=['time', 'member'],\n",
" coords=[time, member]).rename('SST').to_dataset()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Resample with integer time\n",
"\n",
"Our base case is to use this resampling method with integer time for `init`/`time`. We actually got a slowdown when trying `da.random.choice` and by removing `.values` references. We are loading very small coordinate arrays (time, ensemble members, etc.) into memory with `.values`.\n",
"\n",
"The bottleneck here is clearly the list comprehension and `xarray` concatenation."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def resample(hind, hist):\n",
" \"\"\"\n",
" Resample with a replacement a historical simulation along the ensemble member axis.\n",
" \n",
" Args:\n",
" hind (xarray object): Initialized hindcast simulation.\n",
" hist (xarray object): Historical simulation with multiple ensemble members.\n",
" \"\"\"\n",
" nlead = hind.lead.size\n",
" nmember = hind.member.size\n",
"\n",
" # Resample members with replacement.\n",
" random_members = np.random.choice(hist.member.values, hind.member.size)\n",
" hist = hist.sel(member=random_members)\n",
" \n",
" resampled_hist = xr.concat(\n",
" [hist.sel(time=hind['init'] + lead) for lead in hind.lead.values], \n",
" 'lead',\n",
" coords='minimal', compat='override', data_vars='minimal')\n",
" del resampled_hist['time']\n",
" resampled_hist['member'] = hind['member']\n",
" resampled_hist['lead'] = hind['lead']\n",
" return resampled_hist"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Timer unit: 1e-06 s\n",
"\n",
"Total time: 0.030328 s\n",
"File: <ipython-input-9-3a536d8ea0b7>\n",
"Function: resample at line 1\n",
"\n",
"Line # Hits Time Per Hit % Time Line Contents\n",
"==============================================================\n",
" 1 def resample(hind, hist):\n",
" 2 \"\"\"\n",
" 3 Resample with a replacement a historical simulation along the ensemble member axis.\n",
" 4 \n",
" 5 Args:\n",
" 6 hind (xarray object): Initialized hindcast simulation.\n",
" 7 hist (xarray object): Historical simulation with multiple ensemble members.\n",
" 8 \"\"\"\n",
" 9 1 392.0 392.0 1.3 nlead = hind.lead.size\n",
" 10 1 260.0 260.0 0.9 nmember = hind.member.size\n",
" 11 \n",
" 12 # Resample members with replacement.\n",
" 13 1 532.0 532.0 1.8 random_members = np.random.choice(hist.member.values, hind.member.size)\n",
" 14 1 1992.0 1992.0 6.6 hist = hist.sel(member=random_members)\n",
" 15 \n",
" 16 1 2.0 2.0 0.0 resampled_hist = xr.concat(\n",
" 17 1 19991.0 19991.0 65.9 [hist.sel(time=hind['init'] + lead) for lead in hind.lead.values], \n",
" 18 1 2.0 2.0 0.0 'lead',\n",
" 19 1 5222.0 5222.0 17.2 coords='minimal', compat='override', data_vars='minimal')\n",
" 20 1 27.0 27.0 0.1 del resampled_hist['time']\n",
" 21 1 924.0 924.0 3.0 resampled_hist['member'] = hind['member']\n",
" 22 1 983.0 983.0 3.2 resampled_hist['lead'] = hind['lead']\n",
" 23 1 1.0 1.0 0.0 return resampled_hist"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%lprun -f resample resample(hindcast, historical).compute()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def bootstrap(hind, hist, N):\n",
" \"\"\"Resample N times. Typically this would be done in addition to computing some metric\n",
" (e.g. MSE) relative to observations.\"\"\"\n",
" return xr.concat([resample(hind, hist) for _ in range(N)], 'bootstrap')"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"hindcast = hindcast.chunk()\n",
"historical = historical.chunk()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With 500 iterations, it take ~8s to build the task graph and 1.8s to compute."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 7.66 s, sys: 159 ms, total: 7.82 s\n",
"Wall time: 7.74 s\n"
]
}
],
"source": [
"%time graph = bootstrap(hindcast, historical, 500)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
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" <thead>\n",
" <tr><td> </td><th> Array </th><th> Chunk </th></tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr><th> Bytes </th><td> 2.00 MB </td> <td> 4.00 kB </td></tr>\n",
" <tr><th> Shape </th><td> (500, 50, 10) </td> <td> (1, 50, 10) </td></tr>\n",
" <tr><th> Count </th><td> 2001 Tasks </td><td> 500 Chunks </td></tr>\n",
" <tr><th> Type </th><td> float64 </td><td> numpy.ndarray </td></tr>\n",
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"text/plain": [
"dask.array<concatenate, shape=(500, 50, 10), dtype=float64, chunksize=(1, 50, 10), chunktype=numpy.ndarray>"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"graph.SST.data"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 1.18 s, sys: 88.3 ms, total: 1.26 s\n",
"Wall time: 1.83 s\n"
]
},
{
"data": {
"text/html": [
"<pre>&lt;xarray.Dataset&gt;\n",
"Dimensions: (bootstrap: 500, init: 50, lead: 10, member: 10)\n",
"Coordinates:\n",
" * init (init) int64 1950 1951 1952 1953 1954 ... 1995 1996 1997 1998 1999\n",
" * member (member) int64 1 2 3 4 5 6 7 8 9 10\n",
" * lead (lead) int64 1 2 3 4 5 6 7 8 9 10\n",
"Dimensions without coordinates: bootstrap\n",
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],
"text/plain": [
"<xarray.Dataset>\n",
"Dimensions: (bootstrap: 500, init: 50, lead: 10, member: 10)\n",
"Coordinates:\n",
" * init (init) int64 1950 1951 1952 1953 1954 ... 1995 1996 1997 1998 1999\n",
" * member (member) int64 1 2 3 4 5 6 7 8 9 10\n",
" * lead (lead) int64 1 2 3 4 5 6 7 8 9 10\n",
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"Data variables:\n",
" SST (bootstrap, init, member) float64 0.3958 0.8863 ... 0.5499 0.06219"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%time graph.compute()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Resample with `cftime`\n",
"\n",
"The second major issue is that we need to use `cftime` for our prediction package, since we work with Perfect Model setups that have simulation years (e.g. 0030 or 4050) that cannot be used in `numpy`/`pandas` datetime. Further, it enables us to use climate model calendars. Most importantly, we need it for proper datetime alignment in complicated cases of multiple initializations per year and different lead time resolutions (monthly, daily, etc.)."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"hindcast['init'] = xr.cftime_range('1950', '1999', freq='AS')\n",
"historical['time'] = xr.cftime_range('1900', '2019', freq='AS')"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"def shift_cftime_index(xobj, n, freq):\n",
" \"\"\"\n",
" Uses CFTimeIndex.shift() to shift initializations forward\n",
" a given lead time `n`.\n",
" \n",
" Args:\n",
" xobj (xarray object): xarray object with CFTimeIndex\n",
" n (int): number of time steps to move forward\n",
" freq (str): datetime frequency\n",
" \"\"\"\n",
" time_index = xobj['init'].to_index()\n",
" return time_index.shift(n, freq)\n",
"\n",
"def preprocess(hind, hist, lead):\n",
" \"\"\"\n",
" Selects appropriate times from historical run at each lead\n",
" for resampling.\n",
" \"\"\"\n",
" lead_dates = shift_cftime_index(hind, int(lead), 'YS')\n",
" hist = hist.sel(time=lead_dates).rename({'time': 'init'})\n",
" hist['init'] = hind['init']\n",
" return hist\n",
"\n",
"def resample(hind, hist):\n",
" \"\"\"\n",
" Resample with a replacement a historical simulation along the ensemble member axis.\n",
" \n",
" Args:\n",
" hind (xarray object): Initialized hindcast simulation.\n",
" hist (xarray object): Historical simulation with multiple ensemble members.\n",
" \"\"\"\n",
" nlead = hind.lead.size\n",
" nmember = hind.member.size\n",
" \n",
" # Resample members with replacement.\n",
" random_members = np.random.choice(hist.member.values, hind.member.size)\n",
" hist = hist.sel(member=random_members)\n",
" \n",
" resampled_hist = xr.concat(\n",
" [preprocess(hind, hist, lead) for lead in hind.lead.values],\n",
" 'lead',\n",
" coords='minimal', compat='override', data_vars='minimal')\n",
" \n",
" resampled_hist['member'] = hind['member']\n",
" resampled_hist['lead'] = hind['lead']\n",
" return resampled_hist"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The bottleneck here is even moreso the list comprehension, but now it's being driven by a very sluggish `CFTimeIndex.shift()` function."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Timer unit: 1e-06 s\n",
"\n",
"Total time: 0.199773 s\n",
"File: <ipython-input-21-60851257da43>\n",
"Function: resample at line 24\n",
"\n",
"Line # Hits Time Per Hit % Time Line Contents\n",
"==============================================================\n",
" 24 def resample(hind, hist):\n",
" 25 \"\"\"\n",
" 26 Resample with a replacement a historical simulation along the ensemble member axis.\n",
" 27 \n",
" 28 Args:\n",
" 29 hind (xarray object): Initialized hindcast simulation.\n",
" 30 hist (xarray object): Historical simulation with multiple ensemble members.\n",
" 31 \"\"\"\n",
" 32 1 428.0 428.0 0.2 nlead = hind.lead.size\n",
" 33 1 299.0 299.0 0.1 nmember = hind.member.size\n",
" 34 \n",
" 35 # Resample members with replacement.\n",
" 36 1 580.0 580.0 0.3 random_members = np.random.choice(hist.member.values, hind.member.size)\n",
" 37 1 2192.0 2192.0 1.1 hist = hist.sel(member=random_members)\n",
" 38 \n",
" 39 1 3.0 3.0 0.0 resampled_hist = xr.concat(\n",
" 40 1 186798.0 186798.0 93.5 [preprocess(hind, hist, lead) for lead in hind.lead.values],\n",
" 41 1 1.0 1.0 0.0 'lead',\n",
" 42 1 7108.0 7108.0 3.6 coords='minimal', compat='override', data_vars='minimal')\n",
" 43 \n",
" 44 1 1079.0 1079.0 0.5 resampled_hist['member'] = hind['member']\n",
" 45 1 1284.0 1284.0 0.6 resampled_hist['lead'] = hind['lead']\n",
" 46 1 1.0 1.0 0.0 return resampled_hist"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%lprun -f resample resample(hindcast, historical).compute()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Timer unit: 1e-06 s\n",
"\n",
"Total time: 0.188117 s\n",
"File: <ipython-input-21-60851257da43>\n",
"Function: preprocess at line 14\n",
"\n",
"Line # Hits Time Per Hit % Time Line Contents\n",
"==============================================================\n",
" 14 def preprocess(hind, hist, lead):\n",
" 15 \"\"\"\n",
" 16 Selects appropriate times from historical run at each lead\n",
" 17 for resampling.\n",
" 18 \"\"\"\n",
" 19 10 154470.0 15447.0 82.1 lead_dates = shift_cftime_index(hind, int(lead), 'YS')\n",
" 20 10 21269.0 2126.9 11.3 hist = hist.sel(time=lead_dates).rename({'time': 'init'})\n",
" 21 10 12367.0 1236.7 6.6 hist['init'] = hind['init']\n",
" 22 10 11.0 1.1 0.0 return hist"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%lprun -f preprocess resample(hindcast, historical).compute()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now it takes over a minute to set up the graph, but only 2s to compute."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"def bootstrap(hind, hist, N):\n",
" return xr.concat([resample(hind, hist) for _ in range(N)], 'bootstrap')"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"hindcast = hindcast.chunk()\n",
"historical = historical.chunk()"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 1min 7s, sys: 3.64 s, total: 1min 11s\n",
"Wall time: 1min 8s\n"
]
}
],
"source": [
"%time graph = bootstrap(hindcast, historical, 500)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
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{
"name": "stdout",
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"text": [
"CPU times: user 1.27 s, sys: 116 ms, total: 1.39 s\n",
"Wall time: 2.27 s\n"
]
},
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