Implementation:Google deepmind Mujoco Engine Util Sparse

Knowledge Sources	Google_deepmind_Mujoco
Domains	Physics Simulation, Sparse Linear Algebra
Last Updated	2026-02-15 04:00 GMT

Overview

Implements sparse matrix and vector operations for MuJoCo's physics engine, using compressed sparse row (CSR) format with optional AVX SIMD acceleration.

Description

This file provides a comprehensive set of sparse linear algebra operations used in MuJoCo's constraint solver and dynamics pipeline. Key operations include sparse dot products (single-sparse and both-sparse variants), sparse matrix-vector multiplication with supernode support, dense-to-sparse and sparse-to-dense format conversions, sparse matrix addition and combination, sparse matrix transposition, supernode construction for performance optimization, and sparse M'*diag*M computation. The implementation dispatches to AVX-optimized versions when available. The sparse format uses CSR representation with rownnz (non-zeros per row), rowadr (row start addresses), and colind (column indices) arrays.

Usage

These functions are invoked during constraint Jacobian assembly, mass matrix operations, sparse Cholesky factorization, and anywhere the engine operates on large sparse matrices arising from the system topology.

Code Reference

Source Location

Repository: Google_deepmind_Mujoco
File: src/engine/engine_util_sparse.c
Lines: 1-1195

Key Functions

// Sparse dot products
void mju_dotSparseX3(mjtNum* res0, mjtNum* res1, mjtNum* res2,
                     const mjtNum* vec10, const mjtNum* vec11, const mjtNum* vec12,
                     const mjtNum* vec2, int nnz1, const int* ind1);
mjtNum mju_dotSparse2(const mjtNum* vec1, const int* ind1, int nnz1,
                      const mjtNum* vec2, const int* ind2, int nnz2);

// Format conversion
int mju_dense2sparse(mjtNum* res, const mjtNum* mat, int nr, int nc,
                     int* rownnz, int* rowadr, int* colind, int nnz);
void mju_sparse2dense(mjtNum* res, const mjtNum* mat, int nr, int nc,
                      const int* rownnz, const int* rowadr, const int* colind);

// Sparse matrix-vector
void mju_mulMatVecSparse(mjtNum* res, const mjtNum* mat, const mjtNum* vec,
                         int nr, const int* rownnz, const int* rowadr,
                         const int* colind, const int* rowsuper);

// Sparse matrix operations
void mju_transposeSparse(mjtNum* res, const mjtNum* mat, int nr, int nc, ...);
void mju_sqrMatTDSparse(mjtNum* res, const mjtNum* mat, const mjtNum* matT,
                        const mjtNum* diag, int nr, int nc, ...);
int mju_compressSparse(mjtNum* mat, int nr, int nc,
                       int* rownnz, int* rowadr, int* colind, mjtNum minval);

Import

#include "engine/engine_util_sparse.h"

I/O Contract

Inputs

Name	Type	Required	Description
mat	mjtNum*	Yes	Sparse matrix values in CSR format
vec	mjtNum*	Yes	Dense vector for matrix-vector operations
nr, nc	int	Yes	Number of rows and columns
rownnz	int*	Yes	Number of non-zeros per row
rowadr	int*	Yes	Starting address of each row in colind/mat arrays
colind	int*	Yes	Column indices of non-zero elements
rowsuper	int*	No	Supernode sizes for optimized matrix-vector multiply

Outputs

Name	Type	Description
res	mjtNum*	Result vector or matrix
return value	int/mjtNum	Number of non-zeros, or scalar dot product result

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