Usage#

The basic usage of cmomy is to manipulate central moments.
We measure two quantities pretend quantities. The ‘energy’ and the ‘position’ of a thing. We’ll construct the average value for each record. Lets say 100 samples each.

import numpy as np
import xarray as xr

import cmomy

rng = cmomy.random.default_rng(seed=0)

nsamp = 100
energy = xr.DataArray(rng.random(nsamp), dims=["samp"])

position = xr.DataArray(rng.random((nsamp, 3)), dims=["samp", "dim"])

# weight associated with each sample and each record
w = xr.DataArray(rng.random(nsamp), dims=["samp"])

# average over the samples
ce = cmomy.xCentralMoments.from_vals(x=energy, w=w, dim="samp", mom=3)
cp = cmomy.xCentralMoments.from_vals(x=position, w=w, dim="samp", mom=3)

print("energy")
ce

energy

<xarray.DataArray (mom_0: 4)> Size: 32B
array([ 5.3105e+01,  5.5314e-01,  8.6378e-02, -5.7464e-03])
Dimensions without coordinates: mom_0

xCentralMoments

mom: 3

Info: (1)
mom_dims :
mom_0

<xarray.DataArray (mom_0: 4)> Size: 32B
array([ 5.3105e+01,  5.5314e-01,  8.6378e-02, -5.7464e-03])
Dimensions without coordinates: mom_0

xarray.DataArray

mom_0: 4

53.11 0.5531 0.08638 -0.005746

array([ 5.3105e+01,  5.5314e-01,  8.6378e-02, -5.7464e-03])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

print("position")
cp

position

<xarray.DataArray (dim: 3, mom_0: 4)> Size: 96B
array([[ 5.3105e+01,  5.2437e-01,  6.9091e-02, -5.5768e-04],
       [ 5.3105e+01,  4.9062e-01,  9.5523e-02,  2.2967e-03],
       [ 5.3105e+01,  5.6372e-01,  8.7545e-02, -8.3042e-03]])
Dimensions without coordinates: dim, mom_0

xCentralMoments

mom: 3
val_shape: 3

Info: (2)
mom_dims :
mom_0
val_dims :
dim

<xarray.DataArray (dim: 3, mom_0: 4)> Size: 96B
array([[ 5.3105e+01,  5.2437e-01,  6.9091e-02, -5.5768e-04],
       [ 5.3105e+01,  4.9062e-01,  9.5523e-02,  2.2967e-03],
       [ 5.3105e+01,  5.6372e-01,  8.7545e-02, -8.3042e-03]])
Dimensions without coordinates: dim, mom_0

xarray.DataArray

dim: 3
mom_0: 4

53.11 0.5244 0.06909 -0.0005577 ... 53.11 0.5637 0.08754 -0.008304

array([[ 5.3105e+01,  5.2437e-01,  6.9091e-02, -5.5768e-04],
       [ 5.3105e+01,  4.9062e-01,  9.5523e-02,  2.2967e-03],
       [ 5.3105e+01,  5.6372e-01,  8.7545e-02, -8.3042e-03]])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

Here, we’ve used the constructor cmomy.CentralMoments.from_vals(). There are a host of other constructors to create cmomy.CentralMoments object. Take a look at the docs for further info.

Basic attributes#

Notice that there are three shape parameters associated with a cmomy.CentralMoments object:

cmomy.CentralMoments.mom_shape : shape of the moments. For single variable, tuple (mom+1,). For comoments, (mom_0+1, mom_1+1)
cmomy.CentralMoments.val_shape: shape of the ‘values’ part of the data. For scalar data, val_shape = (). For vector data, this is the shape of the passed observation data.
cmomy.CentralMoments.shape: total shape of wrapped moments shape = val_shape + mom_shape

for name, c in {"energy": ce, "position": cp}.items():
    print(
        f"""
{name} shapes:
    mom_shape: {c.mom_shape}
    val_shape: {c.val_shape}
    shape    : {c.shape}
"""
    )

energy shapes:
    mom_shape: (4,)
    val_shape: ()
    shape    : (4,)


position shapes:
    mom_shape: (4,)
    val_shape: (3,)
    shape    : (3, 4)

To access the underlying data, use the cmomy.CentralMoments.to_numpy() method or cmomy.CentralMoments.values attribute. The structure is:

values[...,0]: total weight
values[...,1]: average/mean value
values[...,k>1]: kth central moment.

ce.to_numpy()

array([ 5.3105e+01,  5.5314e-01,  8.6378e-02, -5.7464e-03])

To access all the central moments (zeroth and first included), use the cmomy.CentralMoments.cmom() method.

ce.cmom()

<xarray.DataArray (mom_0: 4)> Size: 32B
array([ 1.    ,  0.    ,  0.0864, -0.0057])
Dimensions without coordinates: mom_0

xarray.DataArray

mom_0: 4

1.0 0.0 0.08638 -0.005746

array([ 1.    ,  0.    ,  0.0864, -0.0057])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

Likewise, the central moments can be converted to raw moments using the cmomy.CentralMoments.rmom() method. This uses the cmomy.convert module behind the scenes.

# <x**k>
ce.rmom()

<xarray.DataArray (mom_0: 4)> Size: 32B
array([1.    , 0.5531, 0.3923, 0.3068])
Dimensions without coordinates: mom_0

xarray.DataArray

mom_0: 4

1.0 0.5531 0.3923 0.3068
```
array([1.    , 0.5531, 0.3923, 0.3068])
```
Coordinates: (0)
Indexes: (0)
Attributes: (0)

Additionally, there are xarray.DataArray like attributes

ce.coords

Coordinates:
    *empty*

ce.attrs

{}

ce.sizes

Frozen({'mom_0': 4})

ce.dims

('mom_0',)

To access the underlying data use cmomy.xCentralMoments.to_dataarray() method or cmomy.xCentralMoments.values attribute to access the xarray.DataArray style data, or cmomy.xCentralMoments.to_numpy() method to access the underlying numpy.ndarray data.b

ce.to_dataarray()

<xarray.DataArray (mom_0: 4)> Size: 32B
array([ 5.3105e+01,  5.5314e-01,  8.6378e-02, -5.7464e-03])
Dimensions without coordinates: mom_0

xarray.DataArray

mom_0: 4

53.11 0.5531 0.08638 -0.005746

array([ 5.3105e+01,  5.5314e-01,  8.6378e-02, -5.7464e-03])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

ce.to_numpy()

array([ 5.3105e+01,  5.5314e-01,  8.6378e-02, -5.7464e-03])

Manipulating (co)moments#

So we have our averages. Cool. Not very special. But what if instead we repeat our experiment. Let’s say we did the experiment 10 times each time giving a single record. Then our data would look like

nsamp = 100
nrec = 10
energy = xr.DataArray(rng.random((nrec, nsamp)), dims=["rec", "samp"])
position = xr.DataArray(rng.random((nrec, nsamp, 3)), dims=["rec", "samp", "dim"])

# weight associated with each sample and each record
w = xr.DataArray(rng.random((nrec, nsamp)), dims=["rec", "samp"])

# average over the samples
ce = cmomy.xCentralMoments.from_vals(x=energy, w=w, dim="samp", mom=3)
cp = cmomy.xCentralMoments.from_vals(x=position, w=w, dim="samp", mom=3)

Consider just the energy. We suspect that there is some correlation between the experiments (they where done in rapid succession). So we’d like to consider two adjacent experiments as one experiment. For this, we can use the cmomy.xCentralMoments.block() method.

ce

<xarray.DataArray (rec: 10, mom_0: 4)> Size: 320B
array([[ 5.3064e+01,  4.7292e-01,  8.0077e-02,  6.5155e-03],
       [ 4.6744e+01,  4.7915e-01,  7.8450e-02,  1.8555e-03],
       [ 5.3254e+01,  5.0665e-01,  9.3529e-02,  2.1183e-03],
       [ 5.0303e+01,  5.3773e-01,  6.9736e-02, -6.0640e-03],
       [ 4.8231e+01,  5.2371e-01,  7.8316e-02, -3.9247e-03],
       [ 5.1988e+01,  4.4939e-01,  8.1112e-02,  3.2211e-03],
       [ 4.6908e+01,  4.9788e-01,  9.3582e-02, -4.0934e-03],
       [ 5.4791e+01,  4.8149e-01,  8.2545e-02,  8.0189e-04],
       [ 5.3189e+01,  4.6463e-01,  9.5055e-02,  3.3487e-03],
       [ 5.1267e+01,  5.4169e-01,  9.3554e-02, -4.9880e-03]])
Dimensions without coordinates: rec, mom_0

xCentralMoments

mom: 3
val_shape: 10

Info: (2)
mom_dims :
mom_0
val_dims :
rec

<xarray.DataArray (rec: 10, mom_0: 4)> Size: 320B
array([[ 5.3064e+01,  4.7292e-01,  8.0077e-02,  6.5155e-03],
       [ 4.6744e+01,  4.7915e-01,  7.8450e-02,  1.8555e-03],
       [ 5.3254e+01,  5.0665e-01,  9.3529e-02,  2.1183e-03],
       [ 5.0303e+01,  5.3773e-01,  6.9736e-02, -6.0640e-03],
       [ 4.8231e+01,  5.2371e-01,  7.8316e-02, -3.9247e-03],
       [ 5.1988e+01,  4.4939e-01,  8.1112e-02,  3.2211e-03],
       [ 4.6908e+01,  4.9788e-01,  9.3582e-02, -4.0934e-03],
       [ 5.4791e+01,  4.8149e-01,  8.2545e-02,  8.0189e-04],
       [ 5.3189e+01,  4.6463e-01,  9.5055e-02,  3.3487e-03],
       [ 5.1267e+01,  5.4169e-01,  9.3554e-02, -4.9880e-03]])
Dimensions without coordinates: rec, mom_0

xarray.DataArray

rec: 10
mom_0: 4

53.06 0.4729 0.08008 0.006516 46.74 ... 51.27 0.5417 0.09355 -0.004988

array([[ 5.3064e+01,  4.7292e-01,  8.0077e-02,  6.5155e-03],
       [ 4.6744e+01,  4.7915e-01,  7.8450e-02,  1.8555e-03],
       [ 5.3254e+01,  5.0665e-01,  9.3529e-02,  2.1183e-03],
       [ 5.0303e+01,  5.3773e-01,  6.9736e-02, -6.0640e-03],
       [ 4.8231e+01,  5.2371e-01,  7.8316e-02, -3.9247e-03],
       [ 5.1988e+01,  4.4939e-01,  8.1112e-02,  3.2211e-03],
       [ 4.6908e+01,  4.9788e-01,  9.3582e-02, -4.0934e-03],
       [ 5.4791e+01,  4.8149e-01,  8.2545e-02,  8.0189e-04],
       [ 5.3189e+01,  4.6463e-01,  9.5055e-02,  3.3487e-03],
       [ 5.1267e+01,  5.4169e-01,  9.3554e-02, -4.9880e-03]])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

ce.block(block_size=2, dim="rec")

<xarray.DataArray (rec: 5, mom_0: 4)> Size: 160B
array([[ 9.9808e+01,  4.7583e-01,  7.9325e-02,  4.3255e-03],
       [ 1.0356e+02,  5.2174e-01,  8.2213e-02, -2.4102e-03],
       [ 1.0022e+02,  4.8515e-01,  8.1146e-02, -3.6968e-04],
       [ 1.0170e+02,  4.8905e-01,  8.7702e-02, -1.3211e-03],
       [ 1.0446e+02,  5.0245e-01,  9.5802e-02, -8.2761e-04]])
Dimensions without coordinates: rec, mom_0

xCentralMoments

mom: 3
val_shape: 5

Info: (2)
mom_dims :
mom_0
val_dims :
rec

<xarray.DataArray (rec: 5, mom_0: 4)> Size: 160B
array([[ 9.9808e+01,  4.7583e-01,  7.9325e-02,  4.3255e-03],
       [ 1.0356e+02,  5.2174e-01,  8.2213e-02, -2.4102e-03],
       [ 1.0022e+02,  4.8515e-01,  8.1146e-02, -3.6968e-04],
       [ 1.0170e+02,  4.8905e-01,  8.7702e-02, -1.3211e-03],
       [ 1.0446e+02,  5.0245e-01,  9.5802e-02, -8.2761e-04]])
Dimensions without coordinates: rec, mom_0

xarray.DataArray

rec: 5
mom_0: 4

99.81 0.4758 0.07932 0.004325 103.6 ... 104.5 0.5025 0.0958 -0.0008276

array([[ 9.9808e+01,  4.7583e-01,  7.9325e-02,  4.3255e-03],
       [ 1.0356e+02,  5.2174e-01,  8.2213e-02, -2.4102e-03],
       [ 1.0022e+02,  4.8515e-01,  8.1146e-02, -3.6968e-04],
       [ 1.0170e+02,  4.8905e-01,  8.7702e-02, -1.3211e-03],
       [ 1.0446e+02,  5.0245e-01,  9.5802e-02, -8.2761e-04]])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

Instead, we can resample the already averaged data using cmomy.xCentralMoments.resample_and_reduce(). We produce a 20 new samples taken from the original (averaged) data.

ce_resamp = ce.resample_and_reduce(nrep=20, dim="rec")
ce_resamp

<xarray.DataArray (rep: 20, mom_0: 4)> Size: 640B
array([[ 4.9894e+02,  4.8483e-01,  8.4004e-02,  7.6615e-04],
       [ 5.0316e+02,  5.0209e-01,  8.0869e-02, -1.1553e-04],
       [ 5.1114e+02,  4.8697e-01,  8.6689e-02,  1.2299e-03],
       [ 5.2135e+02,  4.9141e-01,  8.4228e-02, -5.7084e-04],
       [ 5.0592e+02,  4.9809e-01,  8.5436e-02, -8.7446e-04],
       [ 5.1902e+02,  4.9260e-01,  8.5149e-02,  7.5026e-04],
       [ 5.0659e+02,  5.0687e-01,  8.3342e-02, -2.2954e-03],
       [ 5.0490e+02,  4.9669e-01,  8.6755e-02, -8.1764e-04],
       [ 5.1172e+02,  4.9714e-01,  8.1701e-02, -1.5562e-04],
       [ 5.1915e+02,  4.8611e-01,  9.0029e-02,  2.7399e-03],
       [ 5.1257e+02,  4.8789e-01,  8.3948e-02,  1.4324e-03],
       [ 5.0757e+02,  4.9311e-01,  8.1820e-02, -3.7571e-04],
       [ 4.9210e+02,  4.7666e-01,  8.3947e-02,  2.1234e-03],
       [ 5.2529e+02,  4.9417e-01,  8.4350e-02,  1.1154e-03],
       [ 4.9973e+02,  4.9879e-01,  8.9895e-02, -2.9911e-04],
       [ 5.0993e+02,  4.8937e-01,  8.6093e-02,  8.3597e-04],
       [ 5.0860e+02,  4.7908e-01,  8.5023e-02,  9.4369e-04],
       [ 5.0110e+02,  4.9114e-01,  8.4371e-02, -1.0724e-03],
       [ 5.2742e+02,  4.8909e-01,  8.5711e-02,  1.4218e-03],
       [ 4.9154e+02,  4.9741e-01,  8.1855e-02, -3.3717e-04]])
Dimensions without coordinates: rep, mom_0

xCentralMoments

mom: 3
val_shape: 20

Info: (2)
mom_dims :
mom_0
val_dims :
rep

<xarray.DataArray (rep: 20, mom_0: 4)> Size: 640B
array([[ 4.9894e+02,  4.8483e-01,  8.4004e-02,  7.6615e-04],
       [ 5.0316e+02,  5.0209e-01,  8.0869e-02, -1.1553e-04],
       [ 5.1114e+02,  4.8697e-01,  8.6689e-02,  1.2299e-03],
       [ 5.2135e+02,  4.9141e-01,  8.4228e-02, -5.7084e-04],
       [ 5.0592e+02,  4.9809e-01,  8.5436e-02, -8.7446e-04],
       [ 5.1902e+02,  4.9260e-01,  8.5149e-02,  7.5026e-04],
       [ 5.0659e+02,  5.0687e-01,  8.3342e-02, -2.2954e-03],
       [ 5.0490e+02,  4.9669e-01,  8.6755e-02, -8.1764e-04],
       [ 5.1172e+02,  4.9714e-01,  8.1701e-02, -1.5562e-04],
       [ 5.1915e+02,  4.8611e-01,  9.0029e-02,  2.7399e-03],
       [ 5.1257e+02,  4.8789e-01,  8.3948e-02,  1.4324e-03],
       [ 5.0757e+02,  4.9311e-01,  8.1820e-02, -3.7571e-04],
       [ 4.9210e+02,  4.7666e-01,  8.3947e-02,  2.1234e-03],
       [ 5.2529e+02,  4.9417e-01,  8.4350e-02,  1.1154e-03],
       [ 4.9973e+02,  4.9879e-01,  8.9895e-02, -2.9911e-04],
       [ 5.0993e+02,  4.8937e-01,  8.6093e-02,  8.3597e-04],
       [ 5.0860e+02,  4.7908e-01,  8.5023e-02,  9.4369e-04],
       [ 5.0110e+02,  4.9114e-01,  8.4371e-02, -1.0724e-03],
       [ 5.2742e+02,  4.8909e-01,  8.5711e-02,  1.4218e-03],
       [ 4.9154e+02,  4.9741e-01,  8.1855e-02, -3.3717e-04]])
Dimensions without coordinates: rep, mom_0

xarray.DataArray

rep: 20
mom_0: 4

498.9 0.4848 0.084 0.0007661 503.2 ... 491.5 0.4974 0.08186 -0.0003372

array([[ 4.9894e+02,  4.8483e-01,  8.4004e-02,  7.6615e-04],
       [ 5.0316e+02,  5.0209e-01,  8.0869e-02, -1.1553e-04],
       [ 5.1114e+02,  4.8697e-01,  8.6689e-02,  1.2299e-03],
       [ 5.2135e+02,  4.9141e-01,  8.4228e-02, -5.7084e-04],
       [ 5.0592e+02,  4.9809e-01,  8.5436e-02, -8.7446e-04],
       [ 5.1902e+02,  4.9260e-01,  8.5149e-02,  7.5026e-04],
       [ 5.0659e+02,  5.0687e-01,  8.3342e-02, -2.2954e-03],
       [ 5.0490e+02,  4.9669e-01,  8.6755e-02, -8.1764e-04],
       [ 5.1172e+02,  4.9714e-01,  8.1701e-02, -1.5562e-04],
       [ 5.1915e+02,  4.8611e-01,  9.0029e-02,  2.7399e-03],
       [ 5.1257e+02,  4.8789e-01,  8.3948e-02,  1.4324e-03],
       [ 5.0757e+02,  4.9311e-01,  8.1820e-02, -3.7571e-04],
       [ 4.9210e+02,  4.7666e-01,  8.3947e-02,  2.1234e-03],
       [ 5.2529e+02,  4.9417e-01,  8.4350e-02,  1.1154e-03],
       [ 4.9973e+02,  4.9879e-01,  8.9895e-02, -2.9911e-04],
       [ 5.0993e+02,  4.8937e-01,  8.6093e-02,  8.3597e-04],
       [ 5.0860e+02,  4.7908e-01,  8.5023e-02,  9.4369e-04],
       [ 5.0110e+02,  4.9114e-01,  8.4371e-02, -1.0724e-03],
       [ 5.2742e+02,  4.8909e-01,  8.5711e-02,  1.4218e-03],
       [ 4.9154e+02,  4.9741e-01,  8.1855e-02, -3.3717e-04]])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

This is different than the usual ‘resample values’. This is also available if the original data is available.

a = energy.stack(c=["rec", "samp"])

b = w.stack(c=["rec", "samp"])

# consider 'all' the data for this
out = cmomy.xCentralMoments.from_resample_vals(
    energy.stack(c=["rec", "samp"]),
    w=w.stack(c=["rec", "samp"]),
    dim="c",
    nrep=20,
    mom=3,
)
out

<xarray.DataArray (rep: 20, mom_0: 4)> Size: 640B
array([[ 5.0470e+02,  5.0732e-01,  8.3537e-02, -1.7364e-03],
       [ 5.1471e+02,  5.0032e-01,  8.5279e-02, -1.9318e-04],
       [ 5.1740e+02,  4.8807e-01,  8.1873e-02, -6.0608e-04],
       [ 5.2171e+02,  5.0050e-01,  8.3951e-02, -2.8801e-04],
       [ 5.1191e+02,  4.9601e-01,  8.5987e-02,  5.9479e-04],
       [ 4.9898e+02,  5.0192e-01,  8.6259e-02, -4.8733e-04],
       [ 5.0383e+02,  5.0676e-01,  8.4769e-02, -9.1195e-04],
       [ 5.3502e+02,  4.8362e-01,  8.1934e-02,  8.0303e-04],
       [ 4.9916e+02,  5.1223e-01,  8.6978e-02, -2.4868e-03],
       [ 5.1508e+02,  4.8799e-01,  8.1554e-02,  1.2730e-03],
       [ 5.0503e+02,  4.9609e-01,  8.7332e-02, -1.2149e-03],
       [ 5.0252e+02,  4.8657e-01,  8.4106e-02,  1.2529e-03],
       [ 5.0575e+02,  4.8867e-01,  8.9293e-02,  9.5625e-04],
       [ 5.0848e+02,  4.8416e-01,  8.4131e-02,  1.9068e-05],
       [ 5.0767e+02,  4.9133e-01,  8.2855e-02,  1.3108e-03],
       [ 5.2246e+02,  4.8245e-01,  8.5488e-02,  7.4083e-05],
       [ 5.1387e+02,  5.0965e-01,  8.5511e-02, -1.8175e-03],
       [ 5.2162e+02,  4.9756e-01,  8.8069e-02, -3.8196e-04],
       [ 5.0263e+02,  4.9969e-01,  8.5556e-02, -2.0398e-03],
       [ 5.0454e+02,  5.0938e-01,  8.2281e-02, -1.8049e-03]])
Dimensions without coordinates: rep, mom_0

xCentralMoments

mom: 3
val_shape: 20

Info: (2)
mom_dims :
mom_0
val_dims :
rep

<xarray.DataArray (rep: 20, mom_0: 4)> Size: 640B
array([[ 5.0470e+02,  5.0732e-01,  8.3537e-02, -1.7364e-03],
       [ 5.1471e+02,  5.0032e-01,  8.5279e-02, -1.9318e-04],
       [ 5.1740e+02,  4.8807e-01,  8.1873e-02, -6.0608e-04],
       [ 5.2171e+02,  5.0050e-01,  8.3951e-02, -2.8801e-04],
       [ 5.1191e+02,  4.9601e-01,  8.5987e-02,  5.9479e-04],
       [ 4.9898e+02,  5.0192e-01,  8.6259e-02, -4.8733e-04],
       [ 5.0383e+02,  5.0676e-01,  8.4769e-02, -9.1195e-04],
       [ 5.3502e+02,  4.8362e-01,  8.1934e-02,  8.0303e-04],
       [ 4.9916e+02,  5.1223e-01,  8.6978e-02, -2.4868e-03],
       [ 5.1508e+02,  4.8799e-01,  8.1554e-02,  1.2730e-03],
       [ 5.0503e+02,  4.9609e-01,  8.7332e-02, -1.2149e-03],
       [ 5.0252e+02,  4.8657e-01,  8.4106e-02,  1.2529e-03],
       [ 5.0575e+02,  4.8867e-01,  8.9293e-02,  9.5625e-04],
       [ 5.0848e+02,  4.8416e-01,  8.4131e-02,  1.9068e-05],
       [ 5.0767e+02,  4.9133e-01,  8.2855e-02,  1.3108e-03],
       [ 5.2246e+02,  4.8245e-01,  8.5488e-02,  7.4083e-05],
       [ 5.1387e+02,  5.0965e-01,  8.5511e-02, -1.8175e-03],
       [ 5.2162e+02,  4.9756e-01,  8.8069e-02, -3.8196e-04],
       [ 5.0263e+02,  4.9969e-01,  8.5556e-02, -2.0398e-03],
       [ 5.0454e+02,  5.0938e-01,  8.2281e-02, -1.8049e-03]])
Dimensions without coordinates: rep, mom_0

xarray.DataArray

rep: 20
mom_0: 4

504.7 0.5073 0.08354 -0.001736 ... 504.5 0.5094 0.08228 -0.001805

array([[ 5.0470e+02,  5.0732e-01,  8.3537e-02, -1.7364e-03],
       [ 5.1471e+02,  5.0032e-01,  8.5279e-02, -1.9318e-04],
       [ 5.1740e+02,  4.8807e-01,  8.1873e-02, -6.0608e-04],
       [ 5.2171e+02,  5.0050e-01,  8.3951e-02, -2.8801e-04],
       [ 5.1191e+02,  4.9601e-01,  8.5987e-02,  5.9479e-04],
       [ 4.9898e+02,  5.0192e-01,  8.6259e-02, -4.8733e-04],
       [ 5.0383e+02,  5.0676e-01,  8.4769e-02, -9.1195e-04],
       [ 5.3502e+02,  4.8362e-01,  8.1934e-02,  8.0303e-04],
       [ 4.9916e+02,  5.1223e-01,  8.6978e-02, -2.4868e-03],
       [ 5.1508e+02,  4.8799e-01,  8.1554e-02,  1.2730e-03],
       [ 5.0503e+02,  4.9609e-01,  8.7332e-02, -1.2149e-03],
       [ 5.0252e+02,  4.8657e-01,  8.4106e-02,  1.2529e-03],
       [ 5.0575e+02,  4.8867e-01,  8.9293e-02,  9.5625e-04],
       [ 5.0848e+02,  4.8416e-01,  8.4131e-02,  1.9068e-05],
       [ 5.0767e+02,  4.9133e-01,  8.2855e-02,  1.3108e-03],
       [ 5.2246e+02,  4.8245e-01,  8.5488e-02,  7.4083e-05],
       [ 5.1387e+02,  5.0965e-01,  8.5511e-02, -1.8175e-03],
       [ 5.2162e+02,  4.9756e-01,  8.8069e-02, -3.8196e-04],
       [ 5.0263e+02,  4.9969e-01,  8.5556e-02, -2.0398e-03],
       [ 5.0454e+02,  5.0938e-01,  8.2281e-02, -1.8049e-03]])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

We see that the deviation in the moments is similar using the two resampling methods:

out.to_dataarray().sel(mom_0=slice(1, None)).std("rep")

<xarray.DataArray (mom_0: 3)> Size: 24B
array([0.0093, 0.0021, 0.0012])
Dimensions without coordinates: mom_0

xarray.DataArray

mom_0: 3

0.00929 0.002098 0.001161
```
array([0.0093, 0.0021, 0.0012])
```
Coordinates: (0)
Indexes: (0)
Attributes: (0)

ce_resamp.to_dataarray().sel(mom_0=slice(1, None)).std("rep")

<xarray.DataArray (mom_0: 3)> Size: 24B
array([0.0072, 0.0024, 0.0012])
Dimensions without coordinates: mom_0

xarray.DataArray

mom_0: 3

0.007201 0.002359 0.001185
```
array([0.0072, 0.0024, 0.0012])
```
Coordinates: (0)
Indexes: (0)
Attributes: (0)

We can also reduce our original data across all the records using cmomy.xCentralMoments.reduce()

ce.reduce(dim="rec")

<xarray.DataArray (mom_0: 4)> Size: 32B
array([ 5.0974e+02,  4.9508e-01,  8.5572e-02, -6.5659e-05])
Dimensions without coordinates: mom_0

xCentralMoments

mom: 3

Info: (1)
mom_dims :
mom_0

<xarray.DataArray (mom_0: 4)> Size: 32B
array([ 5.0974e+02,  4.9508e-01,  8.5572e-02, -6.5659e-05])
Dimensions without coordinates: mom_0

xarray.DataArray

mom_0: 4

509.7 0.4951 0.08557 -6.566e-05

array([ 5.0974e+02,  4.9508e-01,  8.5572e-02, -6.5659e-05])

Coordinates: (0)
Indexes: (0)
Attributes: (0)

Usage

Contents

Usage#

Basic attributes#

Manipulating (co)moments#