solve

xarray_einstats.linalg.solve(da, db, dims=None, **kwargs)

Wrap numpy.linalg.solve.

Usage examples of all arguments is available at the Intro to the linear algebra module page.

Parameters:

da, dbxarray.DataArray

dimssequence of hashable, optional

It can have either length 2 or 3. If length 2, both dimensions should have the same length and be present in da, and only one of them should also be present in db. If length 3, the first two elements behave the same; the third element is a dimension of arbitrary length which can only present in db.

From NumPy’s docstring, a has (..., M, M) shape and b has (M,) or (..., M, K). Here, b can be (..., M) this case is not limited to 1d, so dims with length two indicates the two dimensions of length M, with length 3 it is something like (M, M, K), which can be done thanks to named dimensions.

**kwargs

Passed to xarray.apply_ufunc

Returns:

xarray.DataArray

Examples

Dimension naming conventions are designed to ease inverse operation with xarray.dot.

The following example illustrates what this means and how to check that solve worked correctly

import xarray as xr
import numpy as np
from xarray_einstats.linalg import solve
from xarray_einstats.tutorial import generate_matrices_dataarray

matrices = generate_matrices_dataarray()
matrices

<xarray.DataArray (batch: 10, experiment: 3, dim: 4, dim2: 4)> Size: 4kB
0.0666 0.5816 0.6813 3.231 0.356 0.04923 ... 2.237 0.3365 0.6512 1.049 0.1507
Dimensions without coordinates: batch, experiment, dim, dim2

xarray.DataArray

• batch: 10
• experiment: 3
• dim: 4
• dim2: 4

• 0.0666 0.5816 0.6813 3.231 0.356 ... 2.237 0.3365 0.6512 1.049 0.1507

  array([[[[6.66015895e-02, 5.81641033e-01, 6.81278623e-01,
            3.23101857e+00],
           [3.55970742e-01, 4.92277206e-02, 1.42722673e+00,
            1.34248081e+00],
           [3.42609847e+00, 1.72028869e+00, 1.92399769e+00,
            2.10126761e-01],
           [1.80399352e-01, 5.22468421e-01, 1.37217067e+00,
            3.00578091e-01]],
  
          [[2.52704818e+00, 2.62386244e-01, 1.19000312e+00,
            2.58047179e+00],
           [7.55233680e-01, 4.48611905e+00, 1.56043558e+00,
            7.25958550e-02],
           [2.75486003e+00, 5.24243719e-02, 1.76903394e+00,
            7.11444689e-01],
           [4.24086894e-01, 1.53161527e+00, 3.01898378e-01,
            6.12508702e-01]],
  
          [[6.34942519e-01, 1.38132916e-01, 1.96754541e+00,
            5.73417721e-01],
  ...
           [4.41694443e-01, 2.48853646e+00, 6.46287779e-01,
            5.47439183e-01]],
  
          [[5.93873991e-02, 2.88225625e-01, 1.72458766e+00,
            1.00181691e+00],
           [2.95136286e+00, 1.40810936e+00, 7.31394970e-01,
            5.42560799e-02],
           [2.08476463e+00, 5.07645135e-01, 2.27059768e-01,
            1.80363555e-01],
           [6.08283310e-01, 8.46784363e-01, 1.32211641e-01,
            3.84583777e-02]],
  
          [[1.22448198e+00, 7.33052865e-02, 2.89624713e+00,
            2.01055833e-01],
           [1.11058326e+00, 3.18290050e-01, 5.49639945e-01,
            7.73674553e-02],
           [6.50517593e-01, 2.78183232e+00, 9.99172752e-01,
            2.23721543e+00],
           [3.36514454e-01, 6.51245953e-01, 1.04944305e+00,
            1.50660296e-01]]]])

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

b = matrices.std("dim2")  # dims (batch, experiment, dim)
y2 = solve(matrices, b, dims=("dim", "dim2"))  # dims (batch, experiment, dim2)
np.allclose(b, xr.dot(matrices, y2, dims="dim2"))

True