MonotonicDimensionΒΆ

Generalized ClassΒΆ

Dimension

DescriptionΒΆ

A monotonic dimension is a quantitative dimension where the coordinates along the dimension are explicitly defined and, unlike a LinearDimension, may not be derivable from the ordered array of indexes along the dimension. Let \(\mathbf{A}_k\) be an ordered set of strictly ascending or descending physical quantities and, \(o_k\), the origin offset along the \(k^{th}\) dimension, then the coordinates, \(\mathbf{X}_k\), and the absolute coordinates, \(\mathbf{X}_k^\mathrm{abs}\), along a monotonic dimension follow

()ΒΆ\[\begin{split}\begin{aligned} \mathbf{X}_k &= \mathbf{A}_k \text{ and}\\ \mathbf{X}_k^\mathrm{abs} &= \mathbf{X}_k + o_k \mathbf{1}, \end{aligned}\end{split}\]

respectively, where \(\mathbf{1}\) is an array of ones.

AttributesΒΆ

Name

Type

Description

coordinates

[ScalarQuantity, ScalarQuantity, … ]

A required array of strictly ascending or descending ScalarQuantity.

origin_offset

ScalarQuantity

An optional origin offset, \(o_k\), along the dimension. The default value is a physical quantity with zero numerical value.

quantity_name

String

An optional quantity name associated with the physical quantities describing the dimension.

period

ScalarQuantity

An optional period of the dimension. By default, the dimension is considered non-periodic.

reciprocal

ReciprocalDimension

An optional object with attributes required to describe the reciprocal dimension.

ExampleΒΆ

The following MonotonicDimension object,

{
    "type": "monotonic",
    "coordinates": ["1 Β΅s", "10 Β΅s", "100 Β΅s", "1 ms", "10 ms", "100 ms", "1 s", "10 s"]
}

will generate a dimension, where the coordinates \(\mathbf{X}_k\) are

["1 Β΅s", "10 Β΅s", "100 Β΅s", "1 ms", "10 ms", "100 ms", "1 s", "10 s"]