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 <cstdio>
#include <cstring>

#include <mujoco/mujoco.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) {
    std::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) {
    std::sscanf(argv[2], "%d", &nthread);
  }
  if (argc>3) {
    std::sscanf(argv[3], "%d", &niter);
  }
  if (argc>4) {
    std::sscanf(argv[4], "%d", &nwarmup);
  }
  if (argc>5) {
    std::sscanf(argv[5], "%d", &nepoch);
  }
  if (argc>6) {
    std::sscanf(argv[6], "%d", &nstep);
  }
  if (argc>7) {
    std::sscanf(argv[7], "%lf", &eps);
  }

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

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

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

  // print arguments
#if defined(_OPENMP)
  std::printf("\nnthread : %d (OpenMP)\n", nthread);
#else
  std::printf("\nnthread : %d (serial)\n", nthread);
#endif
  std::printf("niter   : %d\n", niter);
  std::printf("nwarmup : %d\n", nwarmup);
  std::printf("nepoch  : %d\n", nepoch);
  std::printf("nstep   : %d\n", nstep);
  std::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
  std::printf("sizes   : nv %d, nefc %d\n\n", m->nv, nefc/nepoch);
  std::printf("inverse : %.2f ms\n", mcputm[0]/nepoch);
  std::printf("forward : %.2f ms\n\n", mcputm[1]/nepoch);
  std::printf("accuracy: log10(residual L1 relnorm)\n");
  std::printf("------------------------------------\n");
  for (int ie=0; ie<8; ie++) {
    std::printf("  %s : %.2g\n", accuracy[ie], merror[ie]/nepoch);
  }
  std::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;
}