`TimeSpectrum`

class nexus.TimeSpectrum(experiment, time_length=200.0, time_step=0.2, max_detuning=400.0, electronic=False, time_data=[], intensity_data=[], scaling='auto', background=0.0, offset=0.0, distribution_points=1, fit_weight=1.0, bunch_spacing=inf, instrument=<nexus.clib.cnexus.DefaultInstrumentGaussian; proxy of <Swig Object of type 'Instrument *'> >, residual=<nexus.clib.cnexus.Sqrt; proxy of <Swig Object of type 'Residual *'> >, fft_window='auto', coherence=False, id='')

Bases: FitMeasurement

Constructor for the TimeSpectrum class. Class to calculate the time-dependent intensity of the experiment.

Parameters:

id (string) – User identifier.
experiment (Experiment) – Experiment
time_length (float) – Length of the calculation (nanoseconds).
time_step (float) – Step size of the calculation (nanoseconds).
max_detuning (float) – Maximum value of the energy detuning (Gamma). Set this value to speed up the calculation. If set to zero no maximum is applied. Also see fft_window.
electronic (bool) – If True electronic scattering is included.
time_data (list or ndarray) – Time data for fitting (nanoseconds).
intensity_data (list or ndarray) – Intensity data for fitting.
scaling (float or Var or string) – Intensity scaling factor for fitting. Default is auto.
background (float or Var or string) – Background for fitting. Default is 0.
offset (float or Var) –
Temporal offset of the model. Default is 0.

Added in version 1.1.0.
resolution (float or Var) –
Resolution value for convolution (nanoseconds). Corresponds to the APD resolution.

Removed in version 2.0.0.
instrument (Instrument) –
Instrument object with the implementation of a resolution function. Default is a Gaussian instrument function with FWHM = 0.5 ns.

Added in version 2.0.0.
distribution_points (int) – Number of points for thickness distributions in forward geometry and angular divergence in grazing geometry. Both distributions assume incoherent summation over the weighted contributions. Default is 1.
fit_weight (float) – Relative weight for the cost function in multi measurement fitting.
bunch_spacing (float) – Spacing of subsequent X-ray bunches in time (nanoseconds).
residual (Residual) – Implementation of the residual calculation used for fitting.
fft_window (string) –
A window function that is applied during the Fourier transformation from energy to time. This should be used when the max_detuning is not zero. Options are
- auto (default) - will pick a Hann window if max_detuning is not zero, no window otherwise.
- Hann
- Hamming
- Sine
- Welch
- Kaiser2 - \(\alpha = 2\)
- Kaiser25 - \(\alpha = 2.5\)
- Kaiser3 - \(\alpha = 3\)
- none
coherence (bool) –
Determines if the summation over the thickness and divergence distributions is performed coherently (True) or incoherently (False). Default is False.

Added in version 1.0.3.

id

User identifier.

Type:: string

experiment

Experiment

Type:: Experiment

time_length

Length of the calculation (nanoseconds).

Type:: float

time_step

Step size of the calculation (nanoseconds).

Type:: float

max_detuning

Maximum value of the energy detuning (Gamma). Set this value to speed up the calculation. If set to zero no maximum is applied. Also see fft_window.

Type:: float

electronic

If True electronic scattering is included.

Type:: bool

time_data

Time data for fitting (nanoseconds).

Type:: list

intensity_data

Intensity data for fitting.

Type:: list

data_size

Number of data points of experimental data.

Type:: int

scaling

Intensity scaling factor for fitting.

Type:: Var

background

Background for fitting.

Type:: Var

offset

Temporal offset of the model.

Added in version 1.1.0.

Type:: float or Var

resolution

Resolution value for convolution (nanoseconds). Corresponds to the APD resolution.

Removed in version 2.0.0.

Type:: Var

resolution_kernel

weight of the Gaussian resolution same step size as detuning.

Removed in version 2.0.0.

Type:: list

distribution_points

Number of points for thickness distributions in forward geometry and angular divergence in grazing geometry. Both distributions assume incoherent summation over the weighted contributions.

Type:: int

fit_weight

Relative weight for the cost function in multi measurement fitting.

Type:: float

bunch_spacing

Spacing of subsequent X-ray bunches in time (nanoseconds). instrument (Instrument): Instrument object.

Added in version 2.0.0.

Type:: float

residual

Implementation of the residual calculation used for fitting.

Type:: Residual

fft_window

A window function that is applied during the Fourier transformation from energy to time. This should be used when the max_detuning is not zero. Options are

auto (default) - will pick a Hann window if max_detuning is not zero, no window otherwise.
Hann
Hamming
Sine
Welch
Kaiser2 - \(\alpha = 2\)
Kaiser25 - \(\alpha = 2.5\)
Kaiser3 - \(\alpha = 3\)
none

Type:: string

coherence

Determines if the summation over the thickness and divergence distributions is performed coherently (True) or incoherently (False). Default is False.

Added in version 1.0.3.

Type:: bool

result

List of intensity values. It is the energy-integrated intensity per time in units of \(\Gamma /ns\).

Type:: list

Calculate()

Calculates the class method. Also callable via operator ().

Returns:: Time array of float values. ndarray: Intensity array of float values.
Return type:: ndarray

Cost()

Get the cost function of the measurement

\[cost = \frac{1}{n} \sum_i r(y_i, \hat{y}_i)\]

Added in version 2.0.0.

Returns:: cost function value.
Return type:: float

MeanSquaredError()

Get the mean squared error (MSE) of the measurement

\[cost = \frac{1}{n} \sum_i (y_i - \hat{y}_i)^2\]

Added in version 2.0.0.

Returns:: MSE value.
Return type:: float

Plot(data=True, residuals=True, datacolor='black', theorycolor='r', theorywidth=2, datalinestyle='none', datamarker='+', datamarkersize=2, datafillstyle='full', legend=True, errors=False, errorcap=2, name=None)

Plot the TimeSpectrum.

Added in version 1.0.3.

Changed in version 1.2.0.

Parameters:

data (bool) – Select if intensity_data should be plot.
residuals (bool) – Select if residuals from fit should be plot.
datacolor (string) – See matplotlib documentation.
theorycolor (string) – See matplotlib documentation.
theorywidth (float) – See matplotlib documentation.
datalinestyle (string) – See matplotlib documentation.
datamarker (string) – See matplotlib documentation.
datamarkersize (float) – See matplotlib documentation.
datafillstyle (string) – See matplotlib documentation.
legend (bool) – Select if legend should be plot when model and data are plot.
errors (bool) – Select if error bars should be plot.
errorcap (float) – See matplotlib documentation (capsize).
name (string) –
If given, the plot is saved under this name.

Added in version 1.2.0.

Velocity()

Returns the velocity detuning of the measurement in units of mm/s.

Returns:: Velocity detuning (mm/s).
Return type:: ndarray

TimeSpectrum

`TimeSpectrum`