{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"\n",
"MetPy’s Choice of Unit Support:
A Descent into Madness
\n",
"
\n",
"14 July 2017\n",
"
\n",
"
\n",
"Ryan May (@dopplershift)\n",
"
\n",
"John Leeman (@geo_leeman)\n",
"
\n",
"UCAR/Unidata
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# MetPy\n",
"\n",
"- Community toolkit for solving meteorology and atmospheric science problems\n",
"- Plotting\n",
"- File Formats\n",
"- **Calculations**"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Units?\n",
"- Handling of physical quantities (aka. \"units\") important in scientific applications"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
">The MCO MIB has determined that the root cause for the loss of the MCO spacecraft was the failure to use metric units in the coding of a ground software file, “Small Forces,” used in trajectory models. Specifically, thruster performance data in English units instead of metric units was used in the software application code titled SM_FORCES (small forces)."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- To avoid these problems, part of MetPy's core architecture is the use of a unit library, Pint\n",
"- Simplifies documentation\n",
"- Eliminates manual auditing of units in calculation functions\n",
"- Supports data files with arbitrary units (e.g. netCDF) more easily"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Pint?\n",
"- Pure Python unit-handling library\n",
"- Wraps Python scalars, lists, or NumPy arrays\n",
"- Supports units using offsets (i.e. temperature)\n",
"- Alternatives:\n",
" - `astropy.units`\n",
" - `quantities`\n",
" - `cf_units`\n",
" - Many others"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Example usage"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"import astropy.units as aunits"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"64.56301588685112 degF"
],
"text/latex": [
"$64.56301588685112\\ \\mathrm{degF}$"
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import metpy.calc as mpcalc\n",
"from metpy.units import units\n",
"\n",
"temperature = 75 * units.degF\n",
"relative_humidity = 70 * units.percent\n",
"mpcalc.dewpoint_rh(temperature, relative_humidity).to('degF')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Without Pint"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"```python\n",
"from scipy.constants import convert_temperature\n",
"temperature = convert_temperature(75, 'F', 'C')\n",
"relative_humidity = 0.7\n",
"convert_temperature(mpcalc.dewpoint_rh(temperature,\n",
" relative_humidity), 'C', 'F')\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# The End\n",
"- Everything just works!"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"6.0560018454768532"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from metpy.constants import Rd\n",
"import numpy as np\n",
"\n",
"t_diff = (np.random.randn(10) * units.degC -\n",
" np.random.randn(10) * units.degC)\n",
"np.trapz(t_diff)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# The End--of sanity\n",
"- ~~Everything just works!~~"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- The only thing worse than not using a unit library..."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- ...is trying to use one with Python libraries expecting numpy arrays"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- Everything I show broken here is *also* broken for `astropy.units`"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# NumPy/SciPy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Let's start with concatenate"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3., 4.])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = np.array([3.])\n",
"b = np.array([4.])\n",
"np.concatenate((a, b))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- Now what about with units?"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3., 4.])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = np.array([3.]) * units.m\n",
"b = np.array([4.]) * units.m\n",
"np.concatenate((a, b))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- Units dropped because numpy creates a new array for storage\n",
"- No way for subclasses/array-like to declare how to make a new instance\n",
"- NumPy #4164"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Maybe calculating a gradient?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 10., 10., 10., 10., 10.])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"a = np.arange(5)\n",
"np.gradient(a, 0.1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"With units?"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"ename": "TypeError",
"evalue": "object of type 'float' has no len()",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0munits\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdegC\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgradient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.1\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0munits\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m~/miniconda3/envs/py36/lib/python3.6/site-packages/numpy/lib/function_base.py\u001b[0m in \u001b[0;36mgradient\u001b[0;34m(f, *varargs, **kwargs)\u001b[0m\n\u001b[1;32m 1692\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misscalar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdistances\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1693\u001b[0m \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1694\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdistances\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maxes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1695\u001b[0m raise ValueError(\"distances must be either scalars or match \"\n\u001b[1;32m 1696\u001b[0m \"the length of the corresponding dimension\")\n",
"\u001b[0;32m~/miniconda3/envs/py36/lib/python3.6/site-packages/pint/quantity.py\u001b[0m in \u001b[0;36m__len__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 1246\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1247\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__len__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1248\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_magnitude\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1249\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1250\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__iter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mTypeError\u001b[0m: object of type 'float' has no len()"
]
}
],
"source": [
"a = np.arange(5) * units.degC\n",
"np.gradient(a, 0.1 * units.m)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- `np.isscalar()` for a float with units attached returns `False`"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Interpolating: `numpy.interp()`"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"1.5"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.arange(5)\n",
"y = x\n",
"np.interp(1.5, x, y)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"With units?"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"ename": "ValueError",
"evalue": "object of too small depth for desired array",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0munits\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minterp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.5\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0munits\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m~/miniconda3/envs/py36/lib/python3.6/site-packages/numpy/lib/function_base.py\u001b[0m in \u001b[0;36minterp\u001b[0;34m(x, xp, fp, left, right, period)\u001b[0m\n\u001b[1;32m 2037\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0minterp_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2038\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2039\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0minterp_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2040\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2041\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mperiod\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: object of too small depth for desired array"
]
}
],
"source": [
"x = np.arange(5) * units.m\n",
"y = x\n",
"np.interp(1.5 * units.m, x, y)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- There's no way the average user is going to figure that out\n",
"- Disappears into C code, so not sure where the problem lies..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## What about using scipy optimization?\n",
"- Fixed point iteration `scipy.optimize.fixed_point`\n",
"- Uses other calculations that need units"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"from scipy.optimize import fixed_point\n",
"def step(p, p0, w, t):\n",
" td = dewpoint(vapor_pressure(p, w))\n",
" return (p0 * (td / t) ** (1. / kappa))\n",
"\n",
"fp = so.fixed_point(step, pressure,\n",
" args=(pressure, w, temperature))\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Nope, that doesn't work..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"```python\n",
"from scipy.optimize import fixed_point\n",
"def step(p, p0, w, t):\n",
" td = dewpoint(vapor_pressure(units.Quantity(p, pressure.units), w))\n",
" return (p0 * (td / t) ** (1. / kappa)).magnitude\n",
"\n",
"fp = so.fixed_point(step, pressure.magnitude,\n",
" args=(pressure.magnitude, w, temperature))\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- Need to drop units when going into scipy code..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- ...and reattach before going into MetPy code.\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Mitigation\n",
"- Drop units as necessary when calling functions...\n",
"- ...and reattach correct units on the way out\n",
"- Essentially subverting all of the unit-handling\n",
"- Not *so* bad if we're hiding inside calculation functions"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Matplotlib"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## `Plot()`\n",
"- Plotting with masked arrays in matplotlib\n",
"- Breaks up line nicely around missing points"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"First with units:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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vn7oOP/nDa3Hb5gFcOtSFH/7BNYinJHz0n17P6ubxVBovHpnCHZsHihbG1/V3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\nYCcIgmgx/i948UHevBMhLAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"temp_data = np.random.randn(50)\n",
"temp_units = temp_data * units.degC\n",
"t = np.linspace(0, 5, 50)\n",
"plt.plot(t, temp_units)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- Looks good"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Now masked arrays, no units:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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N4SFPATgDoAfA1wH8l6qttgytzR4MjC9n554o3o6by2m34e5rW/HM7wcxucz6+eVi0zCq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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"temp_masked = np.ma.masked_array(temp_data, mask=temp_data<0)\n",
"plt.plot(t, temp_masked)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"- Ok, that's fine"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Now what about masked *and* units?"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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4KVuqLFO9fQhfMIILk0HsrXELpNaYjaVftTfsC9VlpoyEg3sVFTvIJJ0uLXdj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\nB3fGGGtA/x8YO+l8/kPcXgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"temp_units_masked = temp_masked * units.degC\n",
"plt.plot(t, temp_units_masked)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"![\"No](\"no-idea.gif\")
\n",
"\n",
"\n",
" - I have no idea what's going on here
\n",
" - The filling is *not* the original values
\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `axhline()`/`axvline()`\n",
"- Horizontal/Vertical line spanning the entire axis\n",
"- Matplotlib has built-in support for unit conversions\n",
"- In theory, allows plotting data with one unit but request axes in another\n",
"- Let's see how this works"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"plt.axhline(0 * units.degC)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"```pytb\n",
"ValueError: Cannot compare Quantity and \n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- Problem is comparison between plotted value and plot limits\n",
"- Enabling Matplotlib's unit-conversion behavior doesn't help\n",
"- There is literally no code path through that allows the proper comparison with unit-ed values"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Mitigation\n",
"- Register with matplotlib's unit-handling..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- ...but use that to automatically drop units for every plotting function\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Xarray"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Xarray provides labeled axes for nd-grids\n",
"- Sort of works with units?"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/html": [
"array([1, 2, 3])Coordinates: * x (x) int64 1 2 3 meter"
],
"text/latex": [
"$array([1, 2, 3])Coordinates: * x (x) int64 1 2 3\\ \\mathrm{meter}$"
],
"text/plain": [
"\n",
"array([1, 2, 3])\n",
"Coordinates:\n",
" * x (x) int64 1 2 3, 'meter')>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import xarray as xr\n",
"data = xr.DataArray([1, 2, 3], dims=('x',), coords={'x':[1, 2, 3]})\n",
"units.m * data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Ok, but I'm not wild about meters being next to the coordinate values"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- Putting units to the right of the data looks more reasonable (to me):"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"array([1, 2, 3])\n",
"Coordinates:\n",
" * x (x) int64 1 2 3"
]
},
"execution_count": 15,
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"source": [
"data * units.m"
]
},
{
"cell_type": "markdown",
"metadata": {
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"source": [
"- Oh come on.\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- One way uses `pint.Quantity.__add__`\n",
"- The other `xarray.DataArray.__add__`\n",
"- I will **not** teach users that the order of multiplication matters"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# The end of the story\n",
"- This is the current state of things\n",
"- There is no happy ending here--I don't have any implemented solutions"
]
},
{
"cell_type": "markdown",
"metadata": {
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"slide_type": "subslide"
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},
"source": [
"- Core problems:\n",
" - `np.(as)array` == \"Please silently discard my units\"\n",
" - Uses:\n",
" - Convert lists/floats to array\n",
" - Make sure something supports math and slicing\n",
" - Enforce compatibility with numpy C-API\n",
" - Things that *should* be considered arrays aren't\n",
" - Other array-managing libraries need to know about your need for units\n",
" - `np.asanyarray` only helps for subclasses"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
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},
"source": [
"## Possible solutions\n",
"- NumPy's new `__array_ufunc__` support\n",
" - Available in numpy 1.13\n",
" - Improves overriding behavior for ufuncs\n",
" - Not how this plays out for operand order problem (like xarray example)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- NumPy Abstract Base Class(es) (ABCs)\n",
" - Allow other array-like classes to declare they implement certain interface\n",
" - Create separate ABCs for portions of numpy interface\n",
" - `numpy.asarray` can perform `isinstance` check with (one) ABC\n",
" - Will require downstream libraries to migrate away from `asarray` for other ABCs\n",
" - Not sure how this plays with composition between array-like libraries"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- Custom NumPy dtypes\n",
" - Modify NumPy C-level code to allow custom datatypes\n",
" - Encode units as part of datatype--then units don't drop\n",
" - Would *probably* solve all of the problems\n",
" - Most technically challenging"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "slide"
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},
"source": [
"# Concluding\n",
"- The user experience when trying to substitute for numpy arrays with a unit-ed array is pretty frustrating\n",
"- There **has** to be a way to make this work better\n",
"- I'm open to suggestions (besides removing our unit support)\n",
"- I'm not here to rag on anyone's work, this comes from a place of love..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- ...and immense frustration\n",
""
]
}
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