Implementation:Google deepmind Mujoco Engine Util Solve Header
| Knowledge Sources | |
|---|---|
| Domains | Physics Simulation, Numerical Solvers |
| Last Updated | 2026-02-15 04:00 GMT |
Overview
Header file declaring the numerical solver utility API for MuJoCo, including dense, sparse, and band-dense Cholesky/LU solvers, eigenvalue decomposition, and quadratic programming functions.
Description
This header declares the full solver utility interface covering multiple factorization and solving strategies. The dense Cholesky group includes mju_cholFactor (returns rank), mju_cholSolve, and mju_cholUpdate (rank-one update). The sparse Cholesky group includes mju_cholFactorSparse (reverse-order factorization), mju_cholFactorSymbolic (symbolic phase computing L and L^T sparsity structures), mju_cholFactorNumeric (numeric phase with fixed pattern), mju_cholSolveSparse, and mju_cholUpdateSparse. The band-dense group includes mju_cholFactorBand (returns minimum diagonal), mju_cholSolveBand, mju_band2Dense, mju_dense2Band, mju_bandMulMatVec, and mju_bandDiag. Additional solvers include mju_factorLUSparse and mju_solveLUSparse for tree-topology systems, mju_eig3 for 3x3 symmetric eigendecomposition, mju_QCQP2/mju_QCQP3/mju_QCQP for quadratically-constrained QP, and mju_boxQP/mju_boxQPoption/mju_boxQPmalloc for box-constrained QP with configurable options.
Usage
Included by solver implementation files, the forward dynamics pipeline, and any code that needs to factorize or solve linear systems arising from the physics simulation.
Code Reference
Source Location
- Repository: Google_deepmind_Mujoco
- File: src/engine/engine_util_solve.h
- Lines: 1-148
Key Functions
// Dense Cholesky
MJAPI int mju_cholFactor(mjtNum* mat, int n, mjtNum mindiag);
MJAPI void mju_cholSolve(mjtNum* res, const mjtNum* mat, const mjtNum* vec, int n);
MJAPI int mju_cholUpdate(mjtNum* mat, mjtNum* x, int n, int flg_plus);
// Sparse Cholesky
MJAPI int mju_cholFactorSparse(mjtNum* mat, int n, mjtNum mindiag,
int* rownnz, const int* rowadr, int* colind, mjData* d);
MJAPI int mju_cholFactorSymbolic(int* L_colind, int* L_rownnz, int* L_rowadr, ...);
MJAPI int mju_cholFactorNumeric(mjtNum* L, int n, mjtNum mindiag, ...);
// Band-dense Cholesky
MJAPI mjtNum mju_cholFactorBand(mjtNum* mat, int ntotal, int nband, int ndense,
mjtNum diagadd, mjtNum diagmul);
MJAPI void mju_cholSolveBand(mjtNum* res, const mjtNum* mat, const mjtNum* vec,
int ntotal, int nband, int ndense);
// Eigenvalue decomposition
MJAPI int mju_eig3(mjtNum eigval[3], mjtNum eigvec[9], mjtNum quat[4], const mjtNum mat[9]);
// Quadratic programming
MJAPI int mju_QCQP2(mjtNum* res, const mjtNum* Ain, const mjtNum* bin, const mjtNum* d, mjtNum r);
MJAPI int mju_QCQP3(mjtNum* res, const mjtNum* Ain, const mjtNum* bin, const mjtNum* d, mjtNum r);
MJAPI int mju_boxQP(mjtNum* res, mjtNum* R, int* index,
const mjtNum* H, const mjtNum* g, int n,
const mjtNum* lower, const mjtNum* upper);
Import
#include "engine/engine_util_solve.h"
I/O Contract
Inputs
| Name | Type | Required | Description |
|---|---|---|---|
| mat | mjtNum* | Yes | Matrix to factorize (overwritten in-place) |
| n, ntotal | int | Yes | Matrix dimension |
| mindiag | mjtNum | Yes | Minimum diagonal for regularization |
| vec | mjtNum* | Yes | Right-hand side vector for solve |
| H, g | mjtNum* | Yes | Hessian and gradient for QP |
| lower, upper | mjtNum* | No | Box constraint bounds |
| d | mjData* | No | Data for workspace allocation in sparse solvers |
Outputs
| Name | Type | Description |
|---|---|---|
| mat, L | mjtNum* | Factored matrix (modified in-place) |
| res | mjtNum* | Solution vector |
| return value | int or mjtNum | Rank, minimum diagonal, or constraint status |