Tensors module

Module holding the model’s tendencies tensor encoding each of their additive terms.

qgs tensor module

This module computes and holds the tensors representing the tendencies of the model’s equations.

TODO: Add a list of the different tensor available

class qgs.tensors.qgtensor.QgsTensor(params=None, atmospheric_inner_products=None, oceanic_inner_products=None, ground_inner_products=None)[source]

Bases: object

qgs tendencies tensor class.

Parameters

params (None or QgParams, optional) – The models parameters to configure the tensor. None to initialize an empty tensor. Default to None.
atmospheric_inner_products (None or AtmosphericInnerProducts, optional) – The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.
oceanic_inner_products (None or OceanicInnerProducts, optional) – The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.
ground_inner_products (None or GroundInnerProducts, optional) – The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

params

The models parameters used to configure the tensor. None for an empty tensor.

Type: None or QgParams

atmospheric_inner_products

The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.

Type: None or AtmosphericInnerProducts

oceanic_inner_products

The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.

Type: None or OceanicInnerProducts

ground_inner_products

The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

Type: None or GroundInnerProducts

tensor

The tensor \(\mathcal{T}_{i,j,k}\) \(i\)-th components.

Type: sparse.COO(float)

jacobian_tensor

The jacobian tensor \(\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}\) \(i\)-th components.

Type: sparse.COO(float)

compute_tensor()[source]: Routine to compute the tensor.

static jacobian_from_tensor(tensor)[source]

Function to compute the Jacobian tensor.

Parameters: tensor (C00) – The qgs tensor.
Returns: The Jacobian tensor.
Return type: COO

load_from_file(filename, **kwargs)[source]

Function to load previously a saved tensor object with the method save_to_file().

Parameters

filename (str) – The file name where the tensor object was saved.
kwargs (dict) – Keyword arguments to pass to the pickle module method.

print_jacobian_tensor(tensor_name='')[source]

Routine to print the Jacobian tensor.

Parameters: tensor_name (str, optional) – Specify the name to print beside the values of the tensor. Default to QgsTensorJacobian.

print_jacobian_tensor_to_file(filename, tensor_name='')[source]

Routine to print the Jacobian tensor to a file.

Parameters

filename (str) – The filename where to print the tensor.
tensor_name (str, optional) – Specify the name to print beside the values of the tensor. Default to QgsTensorJacobian.

print_tensor(tensor_name='')[source]

Routine to print the tensor.

Parameters: tensor_name (str, optional) – Specify the name to print beside the values of the tensor. Default to QgsTensor.

print_tensor_to_file(filename, tensor_name='')[source]

Routine to print the tensor to a file.

Parameters

filename (str) – The filename where to print the tensor.
tensor_name (str, optional) – Specify the name to print beside the values of the tensor. Default to QgsTensor.

save_to_file(filename, **kwargs)[source]

Function to save the tensor object to a file with the pickle module.

Parameters

filename (str) – The file name where to save the tensor object.
kwargs (dict) – Keyword arguments to pass to the pickle module method.

static simplify_tensor(tensor)[source]

Routine that simplifies the component of a tensor \(\mathcal{T}\). For each index \(i\), it upper-triangularizes the tensor \(\mathcal{T}_{i,\ldots}\) for all the subsequent indices.

Parameters: tensor (COO) – The tensor to simplify.
Returns: The upper-triangularized tensor.
Return type: COO

class qgs.tensors.qgtensor.QgsTensorDynamicT(params=None, atmospheric_inner_products=None, oceanic_inner_products=None, ground_inner_products=None)[source]

Bases: QgsTensor

qgs dynamical temperature first order (linear) tendencies tensor class.

Parameters

params (None or QgParams, optional) – The models parameters to configure the tensor. None to initialize an empty tensor. Default to None.
atmospheric_inner_products (None or AtmosphericInnerProducts, optional) – The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.
oceanic_inner_products (None or OceanicInnerProducts, optional) – The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.
ground_inner_products (None or GroundInnerProducts, optional) – The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

params

The models parameters used to configure the tensor. None for an empty tensor.

Type: None or QgParams

atmospheric_inner_products

The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.

Type: None or AtmosphericInnerProducts

oceanic_inner_products

The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.

Type: None or OceanicInnerProducts

ground_inner_products

The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

Type: None or GroundInnerProducts

tensor

The tensor \(\mathcal{T}_{i,j,k}\) \(i\)-th components.

Type: sparse.COO(float)

jacobian_tensor

The jacobian tensor \(\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}\) \(i\)-th components.

Type: sparse.COO(float)

compute_tensor()[source]: Routine to compute the tensor.

class qgs.tensors.qgtensor.QgsTensorT4(params=None, atmospheric_inner_products=None, oceanic_inner_products=None, ground_inner_products=None)[source]

Bases: QgsTensorDynamicT

qgs \(T^4\) tendencies tensor class. Implies dynamical zeroth-order temperature.

Parameters

params (None or QgParams, optional) – The models parameters to configure the tensor. None to initialize an empty tensor. Default to None.
atmospheric_inner_products (None or AtmosphericInnerProducts, optional) – The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.
oceanic_inner_products (None or OceanicInnerProducts, optional) – The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.
ground_inner_products (None or GroundInnerProducts, optional) – The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

params

The models parameters used to configure the tensor. None for an empty tensor.

Type: None or QgParams

atmospheric_inner_products

The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.

Type: None or AtmosphericInnerProducts

oceanic_inner_products

The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.

Type: None or OceanicInnerProducts

ground_inner_products

The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

Type: None or GroundInnerProducts

tensor

The tensor \(\mathcal{T}_{i,j,k}\) \(i\)-th components.

Type: sparse.COO(float)

jacobian_tensor

The jacobian tensor \(\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}\) \(i\)-th components.

Type: sparse.COO(float)

qgs atmospheric thermodynamic tensor module

This module computes and holds the tensors representing the atmospheric thermodynamic tendencies of the model’s equations needed to compute the vertical wind velocity \(\omega\).

TODO: Add a list of the different tensor available

class qgs.tensors.atmo_thermo_tensor.AtmoThermoTensor(params=None, atmospheric_inner_products=None, oceanic_inner_products=None, ground_inner_products=None)[source]

Bases: QgsTensor

Atmospheric thermodynamic tendencies tensor class.

Parameters

params (None or QgParams, optional) – The models parameters to configure the tensor. None to initialize an empty tensor. Default to None.
atmospheric_inner_products (None or AtmosphericInnerProducts, optional) – The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.
oceanic_inner_products (None or OceanicInnerProducts, optional) – The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.
ground_inner_products (None or GroundInnerProducts, optional) – The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

params

The models parameters used to configure the tensor. None for an empty tensor.

Type: None or QgParams

atmospheric_inner_products

The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.

Type: None or AtmosphericInnerProducts

oceanic_inner_products

The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.

Type: None or OceanicInnerProducts

ground_inner_products

The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

Type: None or GroundInnerProducts

tensor

The tensor \(\mathcal{T}_{i,j,k}\) \(i\)-th components.

Type: sparse.COO(float)

jacobian_tensor

The jacobian tensor \(\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}\) \(i\)-th components.

Type: sparse.COO(float)

class qgs.tensors.atmo_thermo_tensor.AtmoThermoTensorDynamicT(params=None, atmospheric_inner_products=None, oceanic_inner_products=None, ground_inner_products=None)[source]

Bases: AtmoThermoTensor

Atmospheric thermodynamic dynamical temperature first order (linear) tendencies tensor class.

Parameters

params (None or QgParams, optional) – The models parameters to configure the tensor. None to initialize an empty tensor. Default to None.
atmospheric_inner_products (None or AtmosphericInnerProducts, optional) – The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.
oceanic_inner_products (None or OceanicInnerProducts, optional) – The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.
ground_inner_products (None or GroundInnerProducts, optional) – The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

params

The models parameters used to configure the tensor. None for an empty tensor.

Type: None or QgParams

atmospheric_inner_products

The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.

Type: None or AtmosphericInnerProducts

oceanic_inner_products

The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.

Type: None or OceanicInnerProducts

ground_inner_products

The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

Type: None or GroundInnerProducts

tensor

The tensor \(\mathcal{T}_{i,j,k}\) \(i\)-th components.

Type: sparse.COO(float)

jacobian_tensor

The jacobian tensor \(\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}\) \(i\)-th components.

Type: sparse.COO(float)

compute_tensor()[source]: Routine to compute the tensor.

class qgs.tensors.atmo_thermo_tensor.AtmoThermoTensorT4(params=None, atmospheric_inner_products=None, oceanic_inner_products=None, ground_inner_products=None)[source]

Bases: AtmoThermoTensorDynamicT

Atmospheric thermodynamic \(T^4\) tendencies tensor class. Implies dynamical zeroth-order temperature.

Parameters

params (None or QgParams, optional) – The models parameters to configure the tensor. None to initialize an empty tensor. Default to None.
atmospheric_inner_products (None or AtmosphericInnerProducts, optional) – The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.
oceanic_inner_products (None or OceanicInnerProducts, optional) – The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.
ground_inner_products (None or GroundInnerProducts, optional) – The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

params

The models parameters used to configure the tensor. None for an empty tensor.

Type: None or QgParams

atmospheric_inner_products

The inner products of the atmospheric basis functions on which the model’s PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. Default to None.

Type: None or AtmosphericInnerProducts

oceanic_inner_products

The inner products of the oceanic basis functions on which the model’s PDE oceanic equations are projected. If None, disable the oceanic tendencies. Default to None.

Type: None or OceanicInnerProducts

ground_inner_products

The inner products of the ground basis functions on which the model’s PDE ground equations are projected. If None, disable the ground tendencies. Default to None.

Type: None or GroundInnerProducts

tensor

The tensor \(\mathcal{T}_{i,j,k}\) \(i\)-th components.

Type: sparse.COO(float)

jacobian_tensor

The jacobian tensor \(\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}\) \(i\)-th components.

Type: sparse.COO(float)