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massmatrix

massmatrix(V, F=None, type='voronoi')

FEM Mass matrix

Builds the finite elements mass matrix of a triangle mesh or polyline using a piecewise linear hat function basis.

Parameters:

Name Type Description Default
V (n,d) numpy array

vertex list of a polyline or triangle mesh

 required
F numpy int array, optional (default: None)

if None or (m,2), interpret input as ordered polyline; if (m,3) numpy int array, interpred as face index list of a triangle mesh

 None
type str, optional (default 'voronoi')

Type of mass matrix computation: 'voronoi' (default), 'full' or 'barycentric'

 'voronoi'

Returns:

Name Type Description
M (n,n) scipy sparse.csr_matrix

Mass matrix
See Also

massmatrix.

Notes

For a polyline, this is just the finite difference mass matrix.

Examples:

# Mesh in V,F
from gpytoolbox import massmatrix
M = massmatrix(V,F)
Source code in src/gpytoolbox/massmatrix.py 
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def massmatrix(V,F=None,type='voronoi'):
    """FEM Mass matrix

    Builds the finite elements mass matrix of a triangle mesh or polyline using
    a piecewise linear hat function basis.

    Parameters
    ----------
    V : (n,d) numpy array
        vertex list of a polyline or triangle mesh
    F : numpy int array, optional (default: None)
        if None or (m,2), interpret input as ordered polyline;
        if (m,3) numpy int array, interpred as face index list of a triangle
        mesh
    type : str, optional (default 'voronoi')
        Type of mass matrix computation: 'voronoi' (default), 'full' or 'barycentric'

    Returns
    -------
    M : (n,n) scipy sparse.csr_matrix
        Mass matrix

    See Also
    --------
    massmatrix.

    Notes
    -----
    For a polyline, this is just the finite difference mass matrix.

    Examples
    --------
    ```python
    # Mesh in V,F
    from gpytoolbox import massmatrix
    M = massmatrix(V,F)
    ```
    """

    # if you didn't pass an F then this is a ordered polyline
    if (F is None):
        F = edge_indices(V.shape[0])

    simplex_size = F.shape[1]
    # Option 1: simplex size is two
    if simplex_size==2:
        # Then this is just finite difference with varying edge lengths
        edge_lengths = np.linalg.norm(V[F[:,1],:] - V[F[:,0],:],axis=1)
        vals = np.concatenate((edge_lengths,edge_lengths))/2.
        I = np.concatenate((F[:,0],F[:,1]))
        M = csr_matrix((vals,(I,I)),shape=(V.shape[0],V.shape[0]))

    # Option 2: simplex size is three - use intrinsic function
    if simplex_size==3:
        l_sq = halfedge_lengths_squared(V,F)
        M = massmatrix_intrinsic(l_sq,F,n=V.shape[0],type=type)

    return M