Dense Matrices
RXMesh provides a DenseMatrix class designed for working with large numerical data tied to the mesh. DenseMatrix are allocated on both host and device and they are compatible with cuBLAS (on the device) and Eigen (on the host).
Dense matrices are often constructed from mesh attributes, e.g., vertex coordinates or physical quantities. Attributes can be directly converted to dense matrices and vice versa (see Attributes).
For small matrix operations—e.g., working with 3×3 matrices for SVD—we recommend using the attribute interface's to_eigen and to_glm methods (also documented in Attributes). These are optimized for use within GPU kernels and avoid unnecessary memory transfers.
Example: Converting vertex coordinates into a dense matrix, doing computations, then writing them back:
RXMeshStatic rx("mesh.obj");
// Get vertex coordinates as attribute
std::shared_ptr<VertexAttribute<float>> x = rx.get_input_vertex_coordinates();
// Convert to (#vertices × 3) dense matrix
std::shared_ptr<DenseMatrix<float>> x_mat = x->to_matrix();
// Do something with x_mat
// ...
// Copy results back to attribute
x->from_matrix(x_mat.get());
Access into the dense matrix can be done using either an integer index or a mesh handle (e.g., VertexHandle), making it intuitive to pair matrix operations with mesh data. For the latter, make sure to use the constructor that takes RXMesh as first argument, i.e.,
RXMeshStatic rx("mesh.obj");
//Allocating a N x 3 matrix (where N is the number of vertices)
DenseMatrix<float> mat(rx, rx.get_num_vertices(), 3);
//...
//Now, we can access the matrix using handles
VertexHandle vh;
mat(vh, 0) = 1.f;
Construction
Use one of the following constructors based on whether the matrix is mesh-aware or standalone:
Tie matrix to mesh topology (row indices will align with mesh handles):
Generic matrix not associated with mesh handles:
User-managed memory:
Accessors
rows(), cols() – Get matrix dimensions
lead_dim() – Get the leading dimension (row)
operator()(row, col) – Access matrix element by indices
operator()(handle, col) – Access matrix element by mesh handle
col(col_id) – Slice out a specific column as a new DenseMatrix
col_data(ld_idx) – Raw pointer to the start of a column
data(location) – Raw pointer to matrix data on host or device
to_eigen() – Return an Eigen matrix view on host memory
bytes() – Total bytes used in allocation
Modifiers
reset(val, location) – Fill the matrix with a constant
fill_random(min, max) – Fill with random values
reshape(new_rows, new_cols) – Reinterpret storage without copy
multiply(scalar) – Multiply all elements by a scalar
swap(other_matrix) – Swap contents with another matrix
Linear Algebra Operations
These methods operate on the device memory and use cuBLAS:
dot(other, use_conjugate) – Dot product or element-wise inner product
norm2() – L2 norm of matrix
abs_sum() – Sum of absolute values
abs_min(), abs_max() – Element-wise extrema
axpy(X, alpha) – In-place Y = αX + Y
Memory Management
move(source, target) – Copy between host/device
release(location) – Free host or device memory
copy_from(src, source_flag, target_flag) – Deep copy with location control