phasorpy.components#

Component analysis of phasor coordinates.

The phasorpy.components module provides functions to:

calculate fractions of two known components by projecting onto the line between the components (phasor_component_fraction())
calculate phasor coordinates of second component if only one is known (not implemented)
calculate fractions of multiple known components by using higher harmonic information (phasor_component_fit())
calculate fractions of two or three known components by resolving graphically with histogram (phasor_component_graphical())
blindly resolve fractions of multiple components by using harmonic information (phasor_component_blind(), not implemented)

phasorpy.components.phasor_component_fit(mean, real, imag, component_real, component_imag, /, **kwargs)[source]#

Return fractions of multiple components from phasor coordinates.

Component fractions are obtained from the least-squares solution of a linear matrix equation that relates phasor coordinates from one or multiple harmonics to component fractions according to [2].

Up to 2 * number harmonics + 1 components can be fit to multi-harmonic phasor coordinates, that is up to three components for single harmonic phasor coordinates.

Parameters:

mean (array_like) – Intensity of phasor coordinates.
real (array_like) – Real component of phasor coordinates. Harmonics, if any, must be in the first dimension.
imag (array_like) – Imaginary component of phasor coordinates. Harmonics, if any, must be in the first dimension.
component_real (array_like) – Real coordinates of components. Must be one or two-dimensional with harmonics in the first dimension.
component_imag (array_like) – Imaginary coordinates of components. Must be one or two-dimensional with harmonics in the first dimension.
**kwargs (optional) – Additional arguments passed to scipy.linalg.lstsq().

Returns:

fractions – Component fractions, one array per component. Fractions may not exactly add up to 1.0.

Return type:

tuple of ndarray

Raises:

ValueError – The array shapes of real and imag do not match. The array shapes of component_real and component_imag do not match. The number of harmonics in the components does not match the ones in the phasor coordinates. The system is underdetermined; the component matrix having more columns than rows.

See also

Component analysis, Multi-component fit

Notes

For now, calculation of fractions of components from different channels or frequencies is not supported. Only one set of components can be analyzed and is broadcast to all channels/frequencies.

The method builds a linear matrix equation, \(A\mathbf{x} = \mathbf{b}\), where \(A\) consists of the phasor coordinates of individual components, \(\mathbf{x}\) are the unknown fractions, and \(\mathbf{b}\) represents the measured phasor coordinates in the mixture. The least-squares solution of this linear matrix equation yields the fractions.

References

Example

>>> phasor_component_fit(
...     [1, 1, 1], [0.6, 0.5, 0.4], [0.4, 0.3, 0.2], [0.2, 0.9], [0.4, 0.3]
... )
(array([0.4644, 0.5356, 0.6068]), array([0.5559, 0.4441, 0.3322]))

phasorpy.components.phasor_component_fraction(real, imag, component_real, component_imag, /)[source]#

Return fraction of first of two components from phasor coordinates.

Return the relative distance (normalized by the distance between the two components) to the second component for each phasor coordinate projected onto the line between two components.

Parameters:

real (array_like) – Real component of phasor coordinates.
imag (array_like) – Imaginary component of phasor coordinates.
component_real (array_like, shape (2,)) – Real coordinates of first and second components.
component_imag (array_like, shape (2,)) – Imaginary coordinates of first and second components.

Returns:

fraction – Fractions of first component.

Return type:

ndarray

Raises:

ValueError – If the real or imaginary coordinates of the known components are not of size 2.

See also

Component analysis

Notes

The fraction of the second component is 1.0 - fraction.

For now, calculation of fraction of components from different channels or frequencies is not supported. Only one pair of components can be analyzed and will be broadcast to all channels/frequencies.

Examples

>>> phasor_component_fraction(
...     [0.6, 0.5, 0.4], [0.4, 0.3, 0.2], [0.2, 0.9], [0.4, 0.3]
... )
array([0.44, 0.56, 0.68])

phasorpy.components.phasor_component_graphical(real, imag, component_real, component_imag, /, *, radius=0.05, fractions=None)[source]#

Return fractions of two or three components from phasor coordinates.

The graphical method is based on moving circular cursors along the line between pairs of components and quantifying the phasors for each fraction.

Parameters:

real (array_like) – Real component of phasor coordinates.
imag (array_like) – Imaginary component of phasor coordinates.
component_real (array_like, shape (2,) or (3,)) – Real coordinates for two or three components.
component_imag (array_like, shape (2,) or (3,)) – Imaginary coordinates for two or three components.
radius (float, optional, default: 0.05) – Radius of cursor.
fractions (array_like or int, optional) – Number of equidistant fractions, or 1D array of fraction values. Fraction values must be in range [0.0, 1.0]. If an integer, numpy.linspace(0.0, 1.0, fractions) fraction values are used. If None (default), the number of fractions is determined from the longest distance between any pair of components and the radius of the cursor (see Notes below).

Returns:

counts – Counts along each line segment connecting components. Ordered 0-1 (2 components) or 0-1, 0-2, 1-2 (3 components).

Return type:

tuple of ndarray

Raises:

ValueError – The array shapes of real and imag, or component_real and component_imag do not match. The number of components is not 2 or 3. Fraction values are out of range [0.0, 1.0].