Functions module
The functions module contains utility functions used by the model, as well as some high-level functions to handle it.
Sparse matrix operation module
This module supports operations and functions on the sparse tensors defined in
the QgsTensor objects.
- qgs.functions.sparse_mul.sparse_mul2(coo, value, vec)[source]
Sparse multiplication of a tensor with one vector: \(A_{i,j} = {\displaystyle \sum_{k=0}^{\mathrm{ndim}}} \, \mathcal{T}_{i,j,k} \, a_k\)
Warning
It is a Numba-jitted function, so it cannot take a
sparse.COOsparse tensor directly. The tensor coordinates list and values must be provided separately by the user.In principle, this will be solved later in sparse, see https://github.com/pydata/sparse/issues/378.
- Parameters
coo (ndarray(int)) – A 2D array of shape (n_elems, 3), a list of n_elems tensor coordinates corresponding to each value provided.
value (ndarray(float)) – A 1D array of shape (n_elems,), a list of value in the tensor
vec (ndarray(float)) – The vector \(a_k\) to contract the tensor with. Must be of shape (
ndim+ 1,).
- Returns
- Return type
- qgs.functions.sparse_mul.sparse_mul3(coo, value, vec_a, vec_b)[source]
Sparse multiplication of a tensor with two vectors: \(v_i = {\displaystyle \sum_{j,k=0}^{\mathrm{ndim}}} \, \mathcal{T}_{i,j,k} \, a_j \, b_k\)
Warning
It is a Numba-jitted function, so it cannot take a
sparse.COOsparse tensor directly. The tensor coordinates list and values must be provided separately by the user.In principle, this will be solved later in sparse, see https://github.com/pydata/sparse/issues/378.
- Parameters
coo (ndarray(int)) – A 2D array of shape (n_elems, 3), a list of n_elems tensor coordinates corresponding to each value provided.
value (ndarray(float)) – A 1D array of shape (n_elems,), a list of value in the tensor
vec_a (ndarray(float)) – The vector \(a_j\) to contract the tensor with. Must be of shape (
ndim+ 1,).vec_b (ndarray(float)) – The vector \(b_k\) to contract the tensor with. Must be of shape (
ndim+ 1,).
- Returns
The vector \(v_i\), of shape (
ndim+ 1,).- Return type
- qgs.functions.sparse_mul.sparse_mul4(coo, value, vec_a, vec_b, vec_c)[source]
Sparse multiplication of a rank-5 tensor with three vectors: \(A_{i, j} = {\displaystyle \sum_{k,l,m=0}^{\mathrm{ndim}}} \, \mathcal{T}_{i,j,k,l, m} \, a_k \, b_l \, c_m\)
Warning
It is a Numba-jitted function, so it cannot take a
sparse.COOsparse tensor directly. The tensor coordinates list and values must be provided separately by the user.In principle, this will be solved later in sparse, see https://github.com/pydata/sparse/issues/378.
- Parameters
coo (ndarray(int)) – A 2D array of shape (n_elems, 5), a list of n_elems tensor coordinates corresponding to each value provided.
value (ndarray(float)) – A 1D array of shape (n_elems,), a list of value in the tensor
vec_a (ndarray(float)) – The vector \(a_j\) to contract the tensor with. Must be of shape (
ndim+ 1,).vec_b (ndarray(float)) – The vector \(b_k\) to contract the tensor with. Must be of shape (
ndim+ 1,).vec_c (ndarray(float)) – The vector \(c_l\) to contract the tensor with. Must be of shape (
ndim+ 1,).
- Returns
- Return type
- qgs.functions.sparse_mul.sparse_mul5(coo, value, vec_a, vec_b, vec_c, vec_d)[source]
Sparse multiplication of a rank-5 tensor with four vectors: \(v_i = {\displaystyle \sum_{j,k,l,m=0}^{\mathrm{ndim}}} \, \mathcal{T}_{i,j,k,l,m} \, a_j \, b_k \, c_l \, d_m\)
Warning
It is a Numba-jitted function, so it cannot take a
sparse.COOsparse tensor directly. The tensor coordinates list and values must be provided separately by the user.In principle, this will be solved later in sparse, see https://github.com/pydata/sparse/issues/378.
- Parameters
coo (ndarray(int)) – A 2D array of shape (n_elems, 5), a list of n_elems tensor coordinates corresponding to each value provided.
value (ndarray(float)) – A 1D array of shape (n_elems,), a list of value in the tensor
vec_a (ndarray(float)) – The vector \(a_j\) to contract the tensor with. Must be of shape (
ndim+ 1,).vec_b (ndarray(float)) – The vector \(b_k\) to contract the tensor with. Must be of shape (
ndim+ 1,).vec_c (ndarray(float)) – The vector \(c_l\) to contract the tensor with. Must be of shape (
ndim+ 1,).vec_d (ndarray(float)) – The vector \(d_m\) to contract the tensor with. Must be of shape (
ndim+ 1,).
- Returns
The vector \(v_i\), of shape (
ndim+ 1,).- Return type
Tendencies definition module
This module provides functions to create the tendencies functions of the model, based on its parameters.
- qgs.functions.tendencies.create_atmo_thermo_tendencies(params, return_atmo_thermo_tensor=False)[source]
Returns a function which return a part of the atmospheric thermodynamic tendencies useful for computing the vertical wind.
- Parameters
- Returns
f (callable) – The numba-jitted tendencies function.
atmo_thermo_tensor (AtmoThermoTensor) – If return_atmo_thermo_tensor is True, the tendencies tensor of the system.
- qgs.functions.tendencies.create_tendencies(params, return_inner_products=False, return_qgtensor=False)[source]
Function to handle the inner products and tendencies tensors construction. Returns the tendencies function \(\boldsymbol{f}\) determining the model’s ordinary differential equations:
\[\dot{\boldsymbol{x}} = \boldsymbol{f}(\boldsymbol{x})\]which is for the model’s integration.
It returns also the linearized tendencies \(\boldsymbol{\mathrm{J}} \equiv \boldsymbol{\mathrm{D}f} = \frac{\partial \boldsymbol{f}}{\partial \boldsymbol{x}}\) (Jacobian matrix) which are used by the tangent linear model:
\[\dot{\boldsymbol{\delta x}} = \boldsymbol{\mathrm{J}}(\boldsymbol{x}) \cdot \boldsymbol{\delta x}\]- Parameters
- Returns
f (callable) – The numba-jitted tendencies function.
Df (callable) – The numba-jitted linearized tendencies function.
inner_products ((AtmosphericInnerProducts, OceanicInnerProducts)) – If return_inner_products is True, the inner products of the system.
qgtensor (QgsTensor) – If return_qgtensor is True, the tendencies tensor of the system.
Utility functions module
This module has some useful functions for the model.
- qgs.functions.util.normalize_matrix_columns(a)[source]
Numba-jitted function to normalize the columns of a 2D array to one.