waveformtools.integrate

Methods to integrate functions

Functions

`DriscollHealy2DInteg`(func, info)	Implementation of the Driscoll Healy 2D integration that exhibits near spectral convergence.
`DriscollHealy2DInteg_v2`(func, info)	Implementation of the Driscoll Healy 2D integration that exhibits near spectral convergence.
`GaussLegendre2DInteg`(func, info)	Evaulate the 2D surface integral using the Gauss-Legendre rule.
`MidPoint2DInteg`(func, info)	Evaulate the 2D surface integral using the midpoint rule.
`Simpson2DInteg`(func, info)	Implementation of Simpson's 2D integration scheme.
`TwoDIntegral`(func, grid_info[, int_method])	Integrate a function over a sphere.
`construct_ffi_omega_axis`(freq_axis, omega0, ...)	Construct an angular frequency axis for use with FFI
`fixed_frequency_integrator`(udata_time, delta_t)	Fixed frequency integrator as presented in Reisswig et.
`twod_time_integral`(times, twod_func_ts[, a, b])	Integrate a twoD array in time

waveformtools.integrate.DriscollHealy2DInteg(func, info)[source]

Implementation of the Driscoll Healy 2D integration that exhibits near spectral convergence.

Parameters:

funcfunction: The function to be integrated
NTheta, NPhiint: The number of grid points in the theta and phi directions. Note that NTheta must be even.
ht, hpfloat: The grid spacings.

Returns:

integfloat: The function f integrated over the sphere.

waveformtools.integrate.DriscollHealy2DInteg_v2(func, info)[source]

Implementation of the Driscoll Healy 2D integration that exhibits near spectral convergence.

Parameters:

funcfunction: The function to be integrated
NTheta, NPhiint: The number of grid points in the theta and phi directions. Note that NTheta must be even.
ht, hpfloat: The grid spacings.

Returns:

integfloat: The function f integrated over the sphere.

waveformtools.integrate.GaussLegendre2DInteg(func, info)[source]

Evaulate the 2D surface integral using the Gauss-Legendre rule.

Parameters:

func: ndarray: The data to be integrated
info: surface_grid_info: An instance of the surface grid info class containing information about the grid.
Returns
——-
integ: float: The function f integrated over the sphere.

waveformtools.integrate.MidPoint2DInteg(func, info)[source]

Evaulate the 2D surface integral using the midpoint rule.

Parameters:

func: ndarray: The data to be integrated
info: surface_grid_info: An instance of the surface grid info class containing information about the grid.
Returns
——-
integ: float: The function f integrated over the sphere.

waveformtools.integrate.Simpson2DInteg(func, info)[source]

Implementation of Simpson’s 2D integration scheme.

Parameters:

funcfunction: The function to be integrated
NTheta, NPhiint: The number of grid points in the theta and phi directions. Note that NTheta must be even.
ht, hpfloat: The grid spacings.

Returns:

integfloat: The function f integrated over the sphere.

waveformtools.integrate.TwoDIntegral(func, grid_info, int_method=None)[source]

Integrate a function over a sphere.

Parameters:

func: function: The function to be integrated
NTheta, NPhi: int: The number of grid points in the theta and phi directions. Note that NTheta must be even.
ht, hp: float: The grid spacings.
int_method: string: The method to use for the integration. Options are DH (Driscoll Healy), SP (Simpson’s), MP (Midpoint).

Returns:

integfloat: The function f integrated over the sphere.

waveformtools.integrate.construct_ffi_omega_axis(freq_axis, omega0, zero_index)[source]: Construct an angular frequency axis for use with FFI

waveformtools.integrate.fixed_frequency_integrator(udata_time, delta_t, utilde_conven=None, freq_axis=None, omega0='auto', order=1, zero_mode=0, omega_threshold_factor=10)[source]

Fixed frequency integrator as presented in Reisswig et. al.

Parameters:

udata_time: 1d array: The input data in time.
delta_t: float: The time stepping.
utilde_conven: 1d array, optional: The conventional FFT of the samples udata_time.
freq_axis: 1darray, optional: The frequency axis of the FFT. Must be supplied along with utilde_conven.
omega0: float, optional: The cutoff angular frequency in the integration. Must be lower than the starting angular frequency of the input waveform. All frequencies whose absolute value is below this value will be neglected. The default cutoff-value is 0.
order: int, optional: The number of times to integrate the integrand in time. Defaults to 1.
zero_mode: float, optional: The zero mode amplitude of the FFT required. Defaults to 0 i.e. the zero mode is removed.

Returns:

u_integ_n_time: 1d array: The input waveform in time-space, integrated in frequency space using FFI.
u_integ_integ_n: 1d array: The integrated u samples in Fourier space.

waveformtools.integrate.twod_time_integral(times, twod_func_ts, a=None, b=None)[source]: Integrate a twoD array in time