hysop.tools.spectral_utils module

class hysop.tools.spectral_utils.EnergyDumper(energy_parameter, io_params, fname, **kwds)

Bases: object

classmethod build_energy_parameter(do_compute, field, output_params, prefix)

classmethod do_compute_energy(*args)

update(simulation, wait_for)

class hysop.tools.spectral_utils.EnergyPlotter(energy_parameters, io_params, fname, fig_title=None, axes_shape=(1,), figsize=(15, 9), basex=10, basey=10, **kwds)

Bases: object

update(simulation, wait_for)

class hysop.tools.spectral_utils.SpectralTransformUtils

Bases: object

Class that contains userfull methods for SpectralTransform setup.

C2C_transforms = (FFT(1), IFFT(2))

C2R_transforms = (IRFFT(4),)

R2C_transforms = (RFFT(3),)

R2R_transforms = (DCT_I(5), DCT_II(6), DCT_III(7), DCT_IV(8), IDCT_I(13), IDCT_II(14), IDCT_III(15), IDCT_IV(16), DST_I(9), DST_II(10), DST_III(11), DST_IV(12), IDST_I(17), IDST_II(18), IDST_III(19), IDST_IV(20))

backward_transforms = (IFFT(2), IRFFT(4), IDST_I(17), IDST_II(18), IDST_III(19), IDST_IV(20), IDCT_I(13), IDCT_II(14), IDCT_III(15), IDCT_IV(16))

classmethod boundaries_to_extensions(boundaries)

Convert a BoundaryCondition pair tuple to a BoundaryExtension pair tuple.

classmethod boundaries_to_transforms(boundaries, transformed_axes)

Return a tuple of TransformType from a tuple of (left_boundaries, right_boundaries).

classmethod boundary_to_extension(boundary)

Convert a BoundaryCondition to a BoundaryExtension

classmethod compute_wave_numbers(transform, N, L, ftype)

Compute wave numbers of a given transform.

cosine_transforms = (DCT_I(5), DCT_II(6), DCT_III(7), DCT_IV(8), IDCT_I(13), IDCT_II(14), IDCT_III(15), IDCT_IV(16))

classmethod determine_input_dtype(output_dtype, *transforms)

Compute input data type from output data type and list of backward transforms.

classmethod determine_output_dtype(input_dtype, *transforms)

Compute output data type from input data type and list of forward transforms.

classmethod extension_to_transform(left_ext, right_ext, is_complex=False)

Convert a BoundaryExtension pair to a TransformType.

classmethod extensions_to_transforms(extensions, transformed_axes, is_complex=False)

Convert a BoundaryExtension pair tuple to a TransformType tuple.

forward_transforms = (FFT(1), RFFT(3), DST_I(9), DST_II(10), DST_III(11), DST_IV(12), DCT_I(5), DCT_II(6), DCT_III(7), DCT_IV(8))

classmethod generate_wave_number(transform, axis, exponent)

Create a new wavenumber. WaveNumbers are registered dummy symbols.

classmethod generate_wave_numbers(*transforms)

Generare a list of wave_numbers in transform order. Axis will match transform position.

classmethod get_conjugate_inverse_transforms(*transforms)

Get the conjugate inverse TransformType (ie. inverse for odd derivatives).

classmethod get_inverse_transforms(*transforms)

Get the inverse TransformType of a TransformType (for all input arguments).

classmethod get_transform_offsets(transform)

Return left and right transform offsets.

classmethod get_transform_resolution(resolution, *transforms)

classmethod is_C2C(transform)

classmethod is_C2R(transform)

classmethod is_R2C(transform)

classmethod is_R2R(transform)

classmethod is_backward(transform)

classmethod is_cosine(transform)

classmethod is_forward(transform)

classmethod is_none(transform)

classmethod is_sine(transform)

classmethod parse_expression(expr, replace_pows=True)

Extract all wave_numbers from expression. If replace_pow is set, all wave_numbers powers will have their own symbol and are replace in expression (this allows to precompute wavenumber powers).

Returns parsed expression and a set of spectral transforms and a set of contained wave_numbers.

sine_transforms = (DST_I(9), DST_II(10), DST_III(11), DST_IV(12), IDST_I(17), IDST_II(18), IDST_III(19), IDST_IV(20))

classmethod transforms_from_field(field, transformed_axes)

Create a tuple of transforms by extracting field boundary conditions. Note that transforms are returned in natural ordering (ie. contiguous X-axis last).

hysop.tools.spectral_utils.make_multivariate_polynomial(Xl, Xr, lboundaries, rboundaries, N, order)

Build a tensor product of polynomials satisfying boundary conditions on each axis.

lboundaries: np.ndarray of BoundaryCondition rboundaries: np.ndarray of BoundaryCondition other parameters: scalar or array_like of the same size as boundary arrays

All parameters are expanded to the size of the length of prescribed boundaries. See make_polynomial for more informations about parameters.

This method returns a tuple (P,Y) where:

P is a sympy expression representing a multivariate polynomials in variables Y = (y0, y1, …, yd)

P(Y) = P0(y0) * P1(y1) * … * Pd(yd)

*d = lboundaries.size-1 = rboundaries.size-1

*P0 is a polynomial of order N[0] that satisfies (lboundaries[0], rboundaries[0])

on domain [Xl[0], Xr[0]] up to order order[0].

*P1 is a polynomial of order N[1] that satisfies (lboundaries[1], rboundaries[1])

on domain [Xl[1], Xr[1]] up to order order[1].

.

. *Pd is a polynomial of order N[d] that satisfies (lboundaries[d], rboundaries[d])

on domain [Xl[d], Xr[d]] up to order order[d].

hysop.tools.spectral_utils.make_multivariate_trigonometric_polynomial(Xl, Xr, lboundaries, rboundaries, N)

Build a tensor product of trigonometric polynomials satisfying boundary conditions on each axis.

lboundaries: np.ndarray of BoundaryCondition rboundaries: np.ndarray of BoundaryCondition other parameters: scalar or array_like of the same size as boundary arrays

All parameters are expanded to the size of the length of prescribed boundaries. See make_trigonometric_polynomial for more informations about parameters.

This method returns a tuple (P,Y) where:

P is a sympy expression representing a multivariate trigonometric polynomials in variables Y = (y0, y1, …, yd)

P(Y) = P0(y0) * P1(y1) * … * Pd(yd)

*d = lboundaries.size-1 = rboundaries.size-1

*P0 is a trigonometric polynomial of order N[0] that satisfies (lboundaries[0], rboundaries[0])

on domain [Xl[0], Xr[0]].

*P1 is a trigonometric polynomial of order N[1] that satisfies (lboundaries[1], rboundaries[1])

on domain [Xl[1], Xr[1]].

.

. *Pd is a trigonometric polynomial of order N[d] that satisfies (lboundaries[d], rboundaries[d])

on domain [Xl[d], Xr[d]].

hysop.tools.spectral_utils.make_polynomial(Xl, Xr, lboundary, rboundary, N, order)

Build a polynom of order N-1 between on domain [Xl, Xr] that verifies prescribed left and right boundary conditions up to a certain order.

Conditions:

Xl < Xr order >= 2 N > 2*order > 4

Valid boundary conditions are:

(PERIODIC, PERIODIC) dPi/dxi(Xl) - dPi/dxi(Xr) = 0 (HDIRICHLET, HDIRICHLET) dPp/dxi(Xl) = dPp/dxi(Xr) = 0 for even derivatives (i%2==0) (HDIRICHLET, HNEUMANN) mix of the 2nd and 4th conditions (HNEUMANN, HDIRICHLET) mix of the 2nd and 4th conditions (HNEUMANN, HNEUMANN) dPi/dxi(Xl) = dPi/dxi(Xr) = 0 for odd derivatives (i%2==1)

Return (P, X) where P is a sympy expression that represent the polynomial and X is the corresponding sympy.Symbol.

hysop.tools.spectral_utils.make_trigonometric_polynomial(Xl, Xr, lboundary, rboundary, N)

Build a real trigonometric polynomial of order N-1 between on domain [Xl, Xr] that verifies prescribed left and right boundary conditions.

Conditions:

Xl < Xr N >= 1

Valid boundary conditions are:

(PERIODIC, PERIODIC) (HDIRICHLET, HDIRICHLET) (HDIRICHLET, HNEUMANN) (HNEUMANN, HDIRICHLET) (HNEUMANN, HNEUMANN)

Return (P, X) where P is a sympy expression that represent the polynomial and X is the corresponding sympy.Symbol.