FrequencyAxis#

Class representing frequency axis of calculations

Examples

The default type of the FrequencyAxis is complete. See the discussion

of the types in the TimeAxis documentation.

>>> wa = FrequencyAxis(0.0,100,0.05)
>>> ta = wa.get_TimeAxis()
>>> print(ta.length)
100

The type upper-half only refers to the corresponding TimeAxis. Everything about the FrequencyAxis remains the same as with complete.

>>> wa = FrequencyAxis(0.0, 100, 0.05, atype = "upper-half")
>>> ta = wa.get_TimeAxis()
>>> print(ta.length)
50

#>>> print(ta.step,2.0*numpy.pi/(100*wa.step))

>>> print(numpy.allclose(ta.step,2.0*numpy.pi/(100*wa.step)))
True

For complete, everything should work also for an odd number of points

>>> wa = FrequencyAxis(0.0,99,0.05)
>>> ta = wa.get_TimeAxis()
>>> print(ta.length)
99

But upper-half throws an exception, because by definition its number of points is 2*N, where N is an integer.

>>> wa = FrequencyAxis(0.0,99,0.05,atype="upper-half")
>>> ta = wa.get_TimeAxis()
Traceback (most recent call last):
...
quantarhei.exceptions.QuantarheiError: Cannot create upper-half TimeAxis from an odd number of points

Relation between TimeAxis and FrequencyAxis#

Complete FrequencyAxis and even number of points

>>> wa = FrequencyAxis(0.0,10,0.1,atype="complete")
>>> frequencies = [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]
>>> print(numpy.allclose(wa.data,frequencies))
True

>>> ta = wa.get_TimeAxis()
>>> times = 2.0*numpy.pi*numpy.fft.fftshift(numpy.fft.fftfreq(10,0.1))
>>> print(numpy.allclose(ta.data,times))
True

>>> print(numpy.allclose(ta.step,times[1]-times[0]))
True

>>> wb = ta.get_FrequencyAxis()
>>> print(numpy.allclose(wb.data,frequencies))
True

>>> tb = wb.get_TimeAxis()
>>> print(numpy.allclose(tb.data,times))
True

Complete FrequencyAxis and odd number of points

>>> wa = FrequencyAxis(0.0,11,0.1,atype="complete")
>>> frequencies = [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
>>> print(numpy.allclose(wa.data,frequencies))
True

>>> ta = wa.get_TimeAxis()
>>> times = 2.0*numpy.pi*numpy.fft.fftshift(numpy.fft.fftfreq(11,0.1))
>>> print(numpy.allclose(ta.data,times))
True

>>> print(numpy.allclose(ta.step,times[1]-times[0]))
True

>>> wb = ta.get_FrequencyAxis()
>>> print(numpy.allclose(wb.data,frequencies))
True

>>> tb = wb.get_TimeAxis()
>>> print(numpy.allclose(tb.data,times))
True

Upper-half FrequencyAxis and even number of points

>>> wa = FrequencyAxis(0.0,10,0.1,atype="upper-half")
>>> frequencies = [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]
>>> print(numpy.allclose(wa.data,frequencies))
True

>>> ta = wa.get_TimeAxis()
>>> times = 2.0*numpy.pi*numpy.fft.fftshift(numpy.fft.fftfreq(10,0.1))
>>> print(numpy.allclose(ta.data,times[5:10]))
True

>>> print(numpy.allclose(ta.step,times[1]-times[0]))
True

>>> wb = ta.get_FrequencyAxis()
>>> print(numpy.allclose(wb.data,frequencies))
True

>>> tb = wb.get_TimeAxis()
>>> print(numpy.allclose(tb.data,times[5:10]))
True

Class Details#

class quantarhei.core.frequency.FrequencyAxis(start: float = 0.0, length: int = 1, step: float = 1.0, atype: str = 'complete', time_start: float = 0.0)[source]#

Bases: ValueAxis, EnergyUnitsManaged

Frequency grid dual to a TimeAxis via the FFT.

Stores frequency values whose units are managed by the global Manager. Typically obtained by calling TimeAxis.get_FrequencyAxis() rather than constructed directly.

Parameters:

  • start (float) – First frequency value (internal units, i.e. rad/fs).

  • length (int) – Number of frequency points.

  • step (float) – Spacing between consecutive frequency values (rad/fs).

  • atype (str, optional) – Axis type: 'complete' (default) or 'upper-half'.

  • time_start (float, optional) – Time-domain start value of the corresponding TimeAxis. Default is 0.0.

Raises:

Exception – If atype is not 'complete' or 'upper-half'.

property data: Any#
property step: Any#
property start: Any#
copy() → FrequencyAxis[source]#

Returns a shallow copy of the self

get_TimeAxis() → TimeAxis[source]#

Returns the corresponding TimeAxis object