gstools.field.generator¶

GStools subpackage providing generators for spatial random fields.

The following classes are provided

`RandMeth`(model[, mode_no, seed, verbose])	Randomization method for calculating isotropic spatial random fields.
`IncomprRandMeth`(model[, mean_velocity, …])	RandMeth for incompressible random vector fields.

class gstools.field.generator.RandMeth(model, mode_no=1000, seed=None, verbose=False, **kwargs)[source]¶

Bases: object

Randomization method for calculating isotropic spatial random fields.

Parameters:	model (`CovModel`) – Covariance model mode_no (`int`, optional) – Number of Fourier modes. Default: `1000` seed (`int` or `None`, optional) – The seed of the random number generator. If “None”, a random seed is used. Default: `None` verbose (`bool`, optional) – Be chatty during the generation. Default: `False` **kwargs – Placeholder for keyword-args

Notes

The Randomization method is used to generate isotropic spatial random fields characterized by a given covariance model. The calculation looks like:

$u\left(x\right)= \sqrt{\frac{\sigma^{2}}{N}}\cdot \sum_{i=1}^{N}\left( Z_{1,i}\cdot\cos\left(\left\langle k_{i},x\right\rangle \right)+ Z_{2,i}\cdot\sin\left(\left\langle k_{i},x\right\rangle \right) \right)$

where:

$N$ : fourier mode number

$Z_{j,i}$ : random samples from a normal distribution

$k_i$ : samples from the spectral density distribution of the covariance model

Attributes:	`mode_no` `int`: Number of modes in the randomization method. `model` `CovModel`: Covariance model of the spatial random field. `name` `str`: Name of the generator. `seed` `int`: Seed of the master RNG. `value_type` `str`: Type of the field values (scalar, vector). `verbose` `bool`: Verbosity of the generator.

Methods

`__call__`(x[, y, z, mesh_type])	Calculate the random modes for the randomization method.
`reset_seed`([seed])	Recalculate the random amplitudes and wave numbers with the given seed.
`update`([model, seed])	Update the model and the seed.

__call__(x, y=None, z=None, mesh_type='unstructured')[source]¶

Calculate the random modes for the randomization method.

This method calls the summate_* Cython methods, which are the heart of the randomization method.

Parameters:	x (`float`, `numpy.ndarray`) – The x components of the pos. tuple. y (`float`, `numpy.ndarray`, optional) – The y components of the pos. tuple. z (`float`, `numpy.ndarray`, optional) – The z components of the pos. tuple. mesh_type (`str`, optional) – ‘structured’ / ‘unstructured’
Returns:	the random modes
Return type:	`numpy.ndarray`

reset_seed(seed=nan)[source]¶

Recalculate the random amplitudes and wave numbers with the given seed.

Parameters:	seed (`int` or `None` or `numpy.nan`, optional) – the seed of the random number generator. If `None`, a random seed is used. If `numpy.nan`, the actual seed will be kept. Default: `numpy.nan`

Notes

Even if the given seed is the present one, modes will be recalculated.

update(model=None, seed=nan)[source]¶

Update the model and the seed.

If model and seed are not different, nothing will be done.

Parameters:	model (`CovModel` or `None`, optional) – covariance model. Default: `None` seed (`int` or `None` or `numpy.nan`, optional) – the seed of the random number generator. If `None`, a random seed is used. If `numpy.nan`, the actual seed will be kept. Default: `numpy.nan`

mode_no¶

Number of modes in the randomization method.

Type:	`int`

model¶

Covariance model of the spatial random field.

Type:	`CovModel`

name¶

Name of the generator.

Type:	`str`

seed¶

Seed of the master RNG.

Notes

If a new seed is given, the setter property not only saves the new seed, but also creates new random modes with the new seed.

Type:	`int`

value_type¶

Type of the field values (scalar, vector).

Type:	`str`

verbose¶

Verbosity of the generator.

Type:	`bool`

class gstools.field.generator.IncomprRandMeth(model, mean_velocity=1.0, mode_no=1000, seed=None, verbose=False, **kwargs)[source]¶

Bases: gstools.field.generator.RandMeth

RandMeth for incompressible random vector fields.

Parameters:

model (CovModel) – covariance model
mean_velocity (float, optional) – the mean velocity in x-direction
mode_no (int, optional) – number of Fourier modes. Default: 1000
seed (int or None, optional) – the seed of the random number generator. If “None”, a random seed is used. Default: None
verbose (bool, optional) – State if there should be output during the generation. Default: False
**kwargs – Placeholder for keyword-args

Notes

The Randomization method is used to generate isotropic spatial incompressible random vector fields characterized by a given covariance model. The equation is:

$u_i\left(x\right)= \bar{u_i} \delta_{i1} + \bar{u_i}\sqrt{\frac{\sigma^{2}}{N}}\cdot \sum_{j=1}^{N}p_i(k_{j})\left( Z_{1,j}\cdot\cos\left(\left\langle k_{j},x\right\rangle \right)+ Z_{2,j}\cdot\sin\left(\left\langle k_{j},x\right\rangle \right) \right)$

where:

$\bar u$ : mean velocity in $e_1$ direction

$N$ : fourier mode number

$Z_{k,j}$ : random samples from a normal distribution

$k_j$ : samples from the spectral density distribution of the covariance model

$p_i(k_j) = e_1 - \frac{k_i k_1}{k^2}$ : the projector ensuring the incompressibility

Attributes:	`mode_no` `int`: Number of modes in the randomization method. `model` `CovModel`: Covariance model of the spatial random field. `name` `str`: Name of the generator. `seed` `int`: Seed of the master RNG. `value_type` `str`: Type of the field values (scalar, vector). `verbose` `bool`: Verbosity of the generator.

Methods

`__call__`(x[, y, z, mesh_type])	Calculate the random modes for the randomization method.
`reset_seed`([seed])	Recalculate the random amplitudes and wave numbers with the given seed.
`update`([model, seed])	Update the model and the seed.

__call__(x, y=None, z=None, mesh_type='unstructured')[source]¶

Calculate the random modes for the randomization method.

This method calls the summate_incompr_* Cython methods, which are the heart of the randomization method. In this class the method contains a projector to ensure the incompressibility of the vector field.

Parameters:	x (`float`, `numpy.ndarray`) – the x components of the position tuple, the shape has to be (len(x), 1, 1) for 3d and accordingly shorter for lower dimensions y (`float`, `numpy.ndarray`, optional) – the y components of the pos. tuples. Default: `None` z (`float`, `numpy.ndarray`, optional) – the z components of the pos. tuple. Default: `None` mesh_type (`str`, optional) – ‘structured’ / ‘unstructured’
Returns:	the random modes
Return type:	`numpy.ndarray`

reset_seed(seed=nan)¶

Recalculate the random amplitudes and wave numbers with the given seed.

Parameters:	seed (`int` or `None` or `numpy.nan`, optional) – the seed of the random number generator. If `None`, a random seed is used. If `numpy.nan`, the actual seed will be kept. Default: `numpy.nan`

Notes

Even if the given seed is the present one, modes will be recalculated.

update(model=None, seed=nan)¶

Update the model and the seed.

If model and seed are not different, nothing will be done.

Parameters:	model (`CovModel` or `None`, optional) – covariance model. Default: `None` seed (`int` or `None` or `numpy.nan`, optional) – the seed of the random number generator. If `None`, a random seed is used. If `numpy.nan`, the actual seed will be kept. Default: `numpy.nan`

mode_no¶

Number of modes in the randomization method.

Type:	`int`

model¶

Covariance model of the spatial random field.

Type:	`CovModel`

name¶

Name of the generator.

Type:	`str`

seed¶

Seed of the master RNG.

Notes

If a new seed is given, the setter property not only saves the new seed, but also creates new random modes with the new seed.

Type:	`int`

value_type¶

Type of the field values (scalar, vector).

Type:	`str`

verbose¶

Verbosity of the generator.

Type:	`bool`