discretize.operators.InnerProducts.get_edge_inner_product_surface_deriv#
- InnerProducts.get_edge_inner_product_surface_deriv(model, invert_model=False, invert_matrix=False, **kwargs)[source]#
Get a function handle to multiply a vector with derivative of edge inner product surface matrix (or its inverse).
Let \(\mathbf{M}(\mathbf{m})\) be the edge inner product surface matrix constructed with a set of diagnostic property parameters \(\mathbf{m}\) (or its inverse) defined on mesh faces. get_edge_inner_product_surface_deriv constructs a function handle
\[\mathbf{F}(\mathbf{u}) = \mathbf{u}^T \, \frac{\partial \mathbf{M}(\mathbf{m})}{\partial \mathbf{m}}\]which accepts any numpy.array \(\mathbf{u}\) of shape (n_edges,). That is, get_edge_inner_product_surface_deriv constructs a function handle for computing the dot product between a vector \(\mathbf{u}\) and the derivative of the edge inner product surface matrix (or its inverse) with respect to the property parameters. When computed, \(\mathbf{F}(\mathbf{u})\) returns a
scipy.sparse.csr_matrix
of shape (n_edges, n_param).The function handle can only be created for isotropic diagnostic properties.
- Parameters:
- model(
n_faces
, )numpy.ndarray
Parameters defining the diagnostic property values for every face in the mesh.
- invert_modelbool,
optional
The inverse of model is used as the diagnostic property.
- invert_matrixbool,
optional
Returns the inverse of the inner product surface matrix.
- model(
- Returns:
function
The function handle \(\mathbf{F}(\mathbf{u})\) which accepts a (
n_edges
)numpy.ndarray
\(\mathbf{u}\). The function returns a (n_edges
,n_params
)scipy.sparse.csr_matrix
.