LinearDimension¶
Description¶
A LinearDimension is where the coordinates along the dimension follow a linear relationship with the indexes, \(\mathbf{J}_k\), along the dimension. Let \(\Delta x_k\) be the increment, \(N_k \ge 1\), the number of points (counts), \(b_k\), the coordinates offset, and \(o_k\), the origin offset along the \(k^{th}\) dimension, then the corresponding coordinates along the dimension, \(\mathbf{X}_k\), are given as
and the absolute coordinates as,
Here, \(\mathbf{1}\) is an array of ones, and \(\mathbf{J}_k\) is the array of indexes along the \(k^\mathrm{th}\) dimension given as
The term, \(Z_k\), is an integer with a value of \(Z_k=0\) or \(\frac{T_k}{2}\) when the value of complex_fft attribute of the corresponding dimension object is false or true, respectively. Here, \(T_k=N_k\) and \(N_k-1\) for even and odd value of \(N_k\), respectively.
Note
When the value of the complex_fft attribute is true, and \(N_k\) is even, the dependent variable value corresponding to the index \(\pm N_k/2\) is an alias.
Attributes¶
Name |
Type |
Description |
---|---|---|
count |
Integer |
A required number of points, \(N_k\), along the dimension. |
increment |
A required increment, \(\Delta x_k\), along the dimension. |
|
coordinates_offset |
An optional coordinate, \(b_k\), corresponding to the zero of the indexes array, \(\bf{J}_k\). The default value is a physical quantity with zero numerical value. |
|
origin_offset |
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 |
An optional period of the dimension. By default, the dimension is considered non-periodic. |
|
complex_fft |
Boolean |
An optional boolean with default value as False. If true, the coordinates along the dimension are evaluated as the output of a complex fast Fourier transform (FFT) routine. See the description. |
reciprocal |
ReciprocalDimension |
An optional object with attributes required to describe the reciprocal dimension. |
Example¶
The following LinearDimension object,
{
"type": "linear",
"count": 10,
"increment": "2 µA",
"coordinates_offset": "0.1 µA"
}
will generate a dimension, where the coordinates \(\mathbf{X}_k\) are
[
"0.1 µA",
"2.1 µA",
"4.1 µA",
"6.1 µA",
"8.1 µA",
"10.1 µA",
"12.1 µA",
"14.1 µA",
"16.1 µA",
"18.1 µA"
]