Sparse along one dimension, 2D{1,1} dataset

The following is an example 1 of a 2D{1,1} sparse dataset with two-dimensions, \(d=2\), and two, \(p=2\), sparse single-component dependent-variables, where the component is sparsely sampled along one dimension.

Let’s import the CSD model data-file.

import csdmpy as cp

filename = "https://osu.box.com/shared/static/1ltzzbdyeo5bn7xuxmdkxj3e4o1xvvjc.csdf"
sparse_1d = cp.load(filename)

There are two linear dimensions and two single-component sparse dependent variables. The tuple of the dimension and the dependent variable instances are

x = sparse_1d.dimensions
y = sparse_1d.dependent_variables

The coordinates, viewed only for the first ten coordinates, are

print(x[0].coordinates[:10])

Out:

[   0.  192.  384.  576.  768.  960. 1152. 1344. 1536. 1728.] us

print(x[1].coordinates[:10])

Out:

[   0.  192.  384.  576.  768.  960. 1152. 1344. 1536. 1728.] us

Converting the coordinates to ms.

x[0].to("ms")
x[1].to("ms")

Visualizing the dataset

import matplotlib.pyplot as plt

plt.contourf(
    x[0].coordinates.value,
    x[1].coordinates.value,
    y[0].components[0].real,
    cmap="gray_r",
)
plt.xlabel(x[0].axis_label)
plt.ylabel(x[1].axis_label)
plt.title(y[0].name)
plt.show()

Citation

1

Balsgart NM, Vosegaard T., Fast Forward Maximum entropy reconstruction of sparsely sampled data., J Magn Reson. 2012, 223, 164-169. doi: 10.1016/j.jmr.2012.07.002