Set DMT scalar field values as the Frobenius norm of the total derivative

Usage

dmt_set_f(dmt, field)

Arguments

dmt

A list containing the mesh data structures:

pts is a N x 2+M data table with columns X and Y containing the coordinates of cells and additional metadata.
tris is a F x 4 data table containing the X,Y coordinates of each triangle's centroid in the first two columns, and area and largest height of each triangle in the last two columns.
edges is a E x 14 data table with columns from_pt, to_pt, from_tri, to_tri, x0_pt, x1_pt, y0_pt, y1_pt, x0_tri, x1_tri, y0_tri, y1_tri, length_pt, length_tri. If only one triangle uses an edge, then the from_tri, x0_tri, and y0_tri fields will contain NaN values.
tri_to_pt is a F x N sparse matrix with value 1 at (i,j) if triangle i uses point j as a vertex.
udv_cells contains cell embeddings stored in embeddings (a N x D matrix with D-dimensional embeddings for each cell) and loadings (a G x D matrix with gene loadings for each latent variable).

field

A gradient field with the compressed representations pts_svd, tris_svd, edges_pts_svd, and edges_tris_svd. Each of these is a N x 6 matrix with the following columns for each location:

dx_grad,dy_grad: x,y directions of unit vector in the direction of greatest change (first singular vector).
dx_ortho,dy_ortho: x,y directions of unit vector orthogonal to the direction of greatest change (second singular vector).
len_grad,len_ortho: Magnitude of directional derivative in the gradient and orthogonal directions (singular values).

Value

dmt with the following additional attributes: dmt$pts$f, dmt$tris$f, dmt$edges$f_prim, and dmt$edges$f_dual