Mujoco_WASM/sample/derivative.cc

// Copyright 2021 DeepMind Technologies Limited
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include "mujoco.h"
#include <stdlib.h>
#include <stdio.h>
#include <string.h>


// enable compilation with and without OpenMP support
#if defined(_OPENMP)
    #include <omp.h>
#else
    // omp timer replacement
    #include <chrono>
    double omp_get_wtime(void)
    {
        static std::chrono::system_clock::time_point _start = std::chrono::system_clock::now();
        std::chrono::duration<double> elapsed = std::chrono::system_clock::now() - _start;
        return elapsed.count();
    }

    // omp functions used below
    void omp_set_dynamic(int) {}
    void omp_set_num_threads(int) {}
    int omp_get_num_procs(void) {return 1;}
#endif


// gloval variables: internal
const int MAXTHREAD = 64;   // maximum number of threads allowed
const int MAXEPOCH = 100;   // maximum number of epochs
int isforward = 0;          // dynamics mode: forward or inverse
mjtNum* deriv = 0;          // dynamics derivatives (6*nv*nv):
                            //  dinv/dpos, dinv/dvel, dinv/dacc, dacc/dpos, dacc/dvel, dacc/dfrc


// global variables: user-defined, with defaults
int nthread = 0;            // number of parallel threads (default set later)
int niter = 30;             // fixed number of solver iterations for finite-differencing
int nwarmup = 3;            // center point repetitions to improve warmstart
int nepoch = 20;            // number of timing epochs
int nstep = 500;            // number of simulation steps per epoch
double eps = 1e-6;          // finite-difference epsilon


// worker function for parallel finite-difference computation of derivatives
void worker(const mjModel* m, const mjData* dmain, mjData* d, int id)
{
    int nv = m->nv;

    // allocate stack space for result at center
    mjMARKSTACK
    mjtNum* center = mj_stackAlloc(d, nv);
    mjtNum* warmstart = mj_stackAlloc(d, nv);

    // prepare static schedule: range of derivative columns to be computed by this thread
    int chunk = (m->nv + nthread-1) / nthread;
    int istart = id * chunk;
    int iend = mjMIN(istart + chunk, m->nv);

    // copy state and control from dmain to thread-specific d
    d->time = dmain->time;
    mju_copy(d->qpos, dmain->qpos, m->nq);
    mju_copy(d->qvel, dmain->qvel, m->nv);
    mju_copy(d->qacc, dmain->qacc, m->nv);
    mju_copy(d->qacc_warmstart, dmain->qacc_warmstart, m->nv);
    mju_copy(d->qfrc_applied, dmain->qfrc_applied, m->nv);
    mju_copy(d->xfrc_applied, dmain->xfrc_applied, 6*m->nbody);
    mju_copy(d->ctrl, dmain->ctrl, m->nu);

    // run full computation at center point (usually faster than copying dmain)
    if( isforward )
    {
        mj_forward(m, d);

        // extra solver iterations to improve warmstart (qacc) at center point
        for( int rep=1; rep<nwarmup; rep++ )
            mj_forwardSkip(m, d, mjSTAGE_VEL, 1);
    }
    else
        mj_inverse(m, d);

    // select output from forward or inverse dynamics
    mjtNum* output = (isforward ? d->qacc : d->qfrc_inverse);

    // save output for center point and warmstart (needed in forward only)
    mju_copy(center, output, nv);
    mju_copy(warmstart, d->qacc_warmstart, nv);

    // select target vector and original vector for force or acceleration derivative
    mjtNum* target = (isforward ? d->qfrc_applied : d->qacc);
    const mjtNum* original = (isforward ? dmain->qfrc_applied : dmain->qacc);

    // finite-difference over force or acceleration: skip = mjSTAGE_VEL
    for( int i=istart; i<iend; i++ )
    {
        // perturb selected target
        target[i] += eps;

        // evaluate dynamics, with center warmstart
        if( isforward )
        {
            mju_copy(d->qacc_warmstart, warmstart, m->nv);
            mj_forwardSkip(m, d, mjSTAGE_VEL, 1);
        }
        else
            mj_inverseSkip(m, d, mjSTAGE_VEL, 1);

        // undo perturbation
        target[i] = original[i];

        // compute column i of derivative 2
        for( int j=0; j<nv; j++ )
            deriv[(3*isforward+2)*nv*nv + i + j*nv] = (output[j] - center[j])/eps;
    }

    // finite-difference over velocity: skip = mjSTAGE_POS
    for( int i=istart; i<iend; i++ )
    {
        // perturb velocity
        d->qvel[i] += eps;

        // evaluate dynamics, with center warmstart
        if( isforward )
        {
            mju_copy(d->qacc_warmstart, warmstart, m->nv);
            mj_forwardSkip(m, d, mjSTAGE_POS, 1);
        }
        else
            mj_inverseSkip(m, d, mjSTAGE_POS, 1);

        // undo perturbation
        d->qvel[i] = dmain->qvel[i];

        // compute column i of derivative 1
        for( int j=0; j<nv; j++ )
            deriv[(3*isforward+1)*nv*nv + i + j*nv] = (output[j] - center[j])/eps;
    }

    // finite-difference over position: skip = mjSTAGE_NONE
    for( int i=istart; i<iend; i++ )
    {
        // get joint id for this dof
        int jid = m->dof_jntid[i];

        // get quaternion address and dof position within quaternion (-1: not in quaternion)
        int quatadr = -1, dofpos = 0;
        if( m->jnt_type[jid]==mjJNT_BALL )
        {
            quatadr = m->jnt_qposadr[jid];
            dofpos = i - m->jnt_dofadr[jid];
        }
        else if( m->jnt_type[jid]==mjJNT_FREE && i>=m->jnt_dofadr[jid]+3 )
        {
            quatadr = m->jnt_qposadr[jid] + 3;
            dofpos = i - m->jnt_dofadr[jid] - 3;
        }

        // apply quaternion or simple perturbation
        if( quatadr>=0 )
        {
            mjtNum angvel[3] = {0,0,0};
            angvel[dofpos] = eps;
            mju_quatIntegrate(d->qpos+quatadr, angvel, 1);
        }
        else
            d->qpos[m->jnt_qposadr[jid] + i - m->jnt_dofadr[jid]] += eps;

        // evaluate dynamics, with center warmstart
        if( isforward )
        {
            mju_copy(d->qacc_warmstart, warmstart, m->nv);
            mj_forwardSkip(m, d, mjSTAGE_NONE, 1);
        }
        else
            mj_inverseSkip(m, d, mjSTAGE_NONE, 1);

        // undo perturbation
        mju_copy(d->qpos, dmain->qpos, m->nq);

        // compute column i of derivative 0
        for( int j=0; j<nv; j++ )
            deriv[(3*isforward+0)*nv*nv + i + j*nv] = (output[j] - center[j])/eps;
    }

    mjFREESTACK
}


// compute relative L1 norm of residual
double relnorm(mjtNum* residual, mjtNum* base, int n)
{
    mjtNum L1res = 0, L1base = 0;
    for( int i=0; i<n; i++ )
    {
        L1res += mju_abs(residual[i]);
        L1base += mju_abs(base[i]);
    }

    return (double) mju_log10(mju_max(mjMINVAL,L1res/mju_max(mjMINVAL,L1base)));
}


// names of residuals for accuracy check
const char* accuracy[8] = {
    "G2*F2 - I ",
    "G2 - G2'  ",
    "G1 - G1'  ",
    "F2 - F2'  ",
    "G1 + G2*F1",
    "G0 + G2*F0",
    "F1 + F2*G1",
    "F0 + F2*G0"
};


// check accuracy of derivatives using known mathematical identities
void checkderiv(const mjModel* m, mjData* d, mjtNum error[7])
{
    int nv = m->nv;

    // allocate space
    mjMARKSTACK
    mjtNum* mat = mj_stackAlloc(d, nv*nv);

    // get pointers to derivative matrices
    mjtNum* G0 = deriv;                 // dinv/dpos
    mjtNum* G1 = deriv + nv*nv;         // dinv/dvel
    mjtNum* G2 = deriv + 2*nv*nv;       // dinv/dacc
    mjtNum* F0 = deriv + 3*nv*nv;       // dacc/dpos
    mjtNum* F1 = deriv + 4*nv*nv;       // dacc/dvel
    mjtNum* F2 = deriv + 5*nv*nv;       // dacc/dfrc

    // G2*F2 - I
    mju_mulMatMat(mat, G2, F2, nv, nv, nv);
    for( int i=0; i<nv; i++ )
        mat[i*(nv+1)] -= 1;
    error[0] = relnorm(mat, G2, nv*nv);

    // G2 - G2'
    mju_transpose(mat, G2, nv, nv);
    mju_sub(mat, mat, G2, nv*nv);
    error[1] = relnorm(mat, G2, nv*nv);

    // G1 - G1'
    mju_transpose(mat, G1, nv, nv);
    mju_sub(mat, mat, G1, nv*nv);
    error[2] = relnorm(mat, G1, nv*nv);

    // F2 - F2'
    mju_transpose(mat, F2, nv, nv);
    mju_sub(mat, mat, F2, nv*nv);
    error[3] = relnorm(mat, F2, nv*nv);

    // G1 + G2*F1
    mju_mulMatMat(mat, G2, F1, nv, nv, nv);
    mju_addTo(mat, G1, nv*nv);
    error[4] = relnorm(mat, G1, nv*nv);

    // G0 + G2*F0
    mju_mulMatMat(mat, G2, F0, nv, nv, nv);
    mju_addTo(mat, G0, nv*nv);
    error[5] = relnorm(mat, G0, nv*nv);

    // F1 + F2*G1
    mju_mulMatMat(mat, F2, G1, nv, nv, nv);
    mju_addTo(mat, F1, nv*nv);
    error[6] = relnorm(mat, F1, nv*nv);

    // F0 + F2*G0
    mju_mulMatMat(mat, F2, G0, nv, nv, nv);
    mju_addTo(mat, F0, nv*nv);
    error[7] = relnorm(mat, F0, nv*nv);

    mjFREESTACK
}


// main function
int main(int argc, char** argv)
{
    // print help if not enough arguments
    if( argc<2 )
    {
        printf("\n Arguments: modelfile [nthread niter nwarmup nepoch nstep eps]\n\n");
        return 1;
    }

    // default nthread = number of logical cores (usually optimal)
    nthread = omp_get_num_procs();

    // get numeric command-line arguments
    if( argc>2 )
        sscanf(argv[2], "%d", &nthread);
    if( argc>3 )
        sscanf(argv[3], "%d", &niter);
    if( argc>4 )
        sscanf(argv[4], "%d", &nwarmup);
    if( argc>5 )
        sscanf(argv[5], "%d", &nepoch);
    if( argc>6 )
        sscanf(argv[6], "%d", &nstep);
    if( argc>7 )
        sscanf(argv[7], "%lf", &eps);

    // check number of threads
    if( nthread<1 || nthread>MAXTHREAD )
    {
        printf("nthread must be between 1 and %d\n", MAXTHREAD);
        return 1;
    }

    // check number of epochs
    if( nepoch<1 || nepoch>MAXEPOCH )
    {
        printf("nepoch must be between 1 and %d\n", MAXEPOCH);
        return 1;
    }

    // load model
    mjModel* m = 0;
    if( strlen(argv[1])>4 && !strcmp(argv[1]+strlen(argv[1])-4, ".mjb") )
        m = mj_loadModel(argv[1], NULL);
    else
        m = mj_loadXML(argv[1], NULL, NULL, 0);
    if( !m )
    {
        printf("Could not load modelfile '%s'\n", argv[1]);
        return 1;
    }

    // print arguments
#if defined(_OPENMP)
    printf("\nnthread : %d (OpenMP)\n", nthread);
#else
    printf("\nnthread : %d (serial)\n", nthread);
#endif
    printf("niter   : %d\n", niter);
    printf("nwarmup : %d\n", nwarmup);
    printf("nepoch  : %d\n", nepoch);
    printf("nstep   : %d\n", nstep);
    printf("eps     : %g\n\n", eps);

    // make mjData: main, per-thread
    mjData* dmain = mj_makeData(m);
    mjData* d[MAXTHREAD];
    for( int n=0; n<nthread; n++ )
        d[n] = mj_makeData(m);

    // allocate derivatives
    deriv = (mjtNum*) mju_malloc(6*sizeof(mjtNum)*m->nv*m->nv);

    // set up OpenMP (if not enabled, this does nothing)
    omp_set_dynamic(0);
    omp_set_num_threads(nthread);

    // save solver options
    int save_iterations = m->opt.iterations;
    mjtNum save_tolerance = m->opt.tolerance;

    // allocate statistics
    int nefc = 0;
    double cputm[MAXEPOCH][2];
    mjtNum error[MAXEPOCH][8];

    // run epochs, collect statistics
    for( int epoch=0; epoch<nepoch; epoch++ )
    {
        // set solver options for main simulation
        m->opt.iterations = save_iterations;
        m->opt.tolerance = save_tolerance;

        // advance main simulation for nstep
        for( int i=0; i<nstep; i++ )
            mj_step(m, dmain);

        // count number of active constraints
        nefc += dmain->nefc;

        // set solver options for finite differences
        m->opt.iterations = niter;
        m->opt.tolerance = 0;

        // test forward and inverse
        for( isforward=0; isforward<2; isforward++ )
        {
            // start timer
            double starttm = omp_get_wtime();

            // run worker threads in parallel if OpenMP is enabled
            #pragma omp parallel for schedule(static)
            for( int n=0; n<nthread; n++ )
                worker(m, dmain, d[n], n);

            // record duration in ms
            cputm[epoch][isforward] = 1000*(omp_get_wtime() - starttm);
        }

        // check derivatives
        checkderiv(m,  d[0], error[epoch]);
    }

    // compute statistics
    double mcputm[2] = {0,0}, merror[8] = {0,0,0,0,0,0,0,0};
    for( int epoch=0; epoch<nepoch; epoch++ )
    {
        mcputm[0] += cputm[epoch][0];
        mcputm[1] += cputm[epoch][1];

        for( int ie=0; ie<8; ie++ )
            merror[ie] += error[epoch][ie];
    }

    // print sizes, timing, accuracy
    printf("sizes   : nv %d, nefc %d\n\n", m->nv, nefc/nepoch);
    printf("inverse : %.2f ms\n", mcputm[0]/nepoch);
    printf("forward : %.2f ms\n\n", mcputm[1]/nepoch);
    printf("accuracy: log10(residual L1 relnorm)\n");
    printf("------------------------------------\n");
    for( int ie=0; ie<8; ie++ )
        printf("  %s : %.2g\n", accuracy[ie], merror[ie]/nepoch);
    printf("\n");

    // shut down
    mju_free(deriv);
    mj_deleteData(dmain);
    for( int n=0; n<nthread; n++ )
        mj_deleteData(d[n]);
    mj_deleteModel(m);
    return 0;
}