Implementation:Google deepmind Mujoco Engine Util Solve

Knowledge Sources	Google_deepmind_Mujoco
Domains	Physics Simulation, Numerical Solvers
Last Updated	2026-02-15 04:00 GMT

Overview

Implements numerical solver utilities for MuJoCo, including dense and sparse Cholesky factorization, LU factorization, band-dense solvers, eigenvalue decomposition, and box-constrained quadratic programming.

Description

This file provides the core linear system solvers used by MuJoCo's constraint solver and forward dynamics pipeline. It includes dense Cholesky factorization (mju_cholFactor) and solve (mju_cholSolve) with rank-one updates, sparse reverse-order Cholesky decomposition for tree-structured systems, band-dense Cholesky for banded matrices with dense border rows, LU factorization for tree-topology systems, eigenvalue decomposition of symmetric 3x3 matrices, QCQP (quadratically constrained quadratic programming) solvers in 2, 3, and n dimensions, and a box-constrained QP solver (mju_boxQP). The sparse Cholesky includes both symbolic and numeric phases for efficient repeated factorization.

Usage

These solvers are invoked during forward dynamics for mass matrix factorization, constraint solving (Newton and CG methods), implicit integrators, and actuator limit computations.

Code Reference

Source Location

Repository: Google_deepmind_Mujoco
File: src/engine/engine_util_solve.c
Lines: 1-1566

Key Functions

// Dense Cholesky
int mju_cholFactor(mjtNum* mat, int n, mjtNum mindiag);
void mju_cholSolve(mjtNum* res, const mjtNum* mat, const mjtNum* vec, int n);
int mju_cholUpdate(mjtNum* mat, mjtNum* x, int n, int flg_plus);

// Sparse Cholesky
int mju_cholFactorSparse(mjtNum* mat, int n, mjtNum mindiag,
                         int* rownnz, const int* rowadr, int* colind, mjData* d);
int mju_cholFactorSymbolic(int* L_colind, int* L_rownnz, int* L_rowadr,
                           int* LT_colind, int* LT_rownnz, int* LT_rowadr, int* LT_map,
                           const int* rownnz, const int* rowadr, const int* colind,
                           int n, mjData* d);
int mju_cholFactorNumeric(mjtNum* L, int n, mjtNum mindiag, ...);

// Band-dense Cholesky
mjtNum mju_cholFactorBand(mjtNum* mat, int ntotal, int nband, int ndense,
                          mjtNum diagadd, mjtNum diagmul);
void mju_cholSolveBand(mjtNum* res, const mjtNum* mat, const mjtNum* vec,
                       int ntotal, int nband, int ndense);

// Box-constrained QP
int mju_boxQP(mjtNum* res, mjtNum* R, int* index,
              const mjtNum* H, const mjtNum* g, int n,
              const mjtNum* lower, const mjtNum* upper);

// Eigenvalue decomposition
int mju_eig3(mjtNum eigval[3], mjtNum eigvec[9], mjtNum quat[4], const mjtNum mat[9]);

Import

#include "engine/engine_util_solve.h"

I/O Contract

Inputs

Name	Type	Required	Description
mat	mjtNum*	Yes	Input matrix, overwritten with factored form in-place
n	int	Yes	Matrix dimension
mindiag	mjtNum	Yes	Minimum diagonal value for regularization
vec	mjtNum*	Yes	Right-hand side vector for solve operations
H, g	mjtNum*	Yes	Hessian and gradient for QP problems
lower, upper	mjtNum*	No	Box constraint bounds for QP

Outputs

Name	Type	Description
mat	mjtNum*	Factored matrix (L or LU), modified in-place
res	mjtNum*	Solution vector
return value	int	Rank of factorized matrix, or constraint status for QP

Related Pages

Page Connections

Double-click a node to navigate. Hold to expand connections.

Principle

Implementation

Heuristic

Environment