void testIntegralAndDerivative() {
vector<Polynomial<CoefficientType>> polynomials;
int num_coefficients = 5;
int num_segments = 3;
typedef typename Polynomial<CoefficientType>::CoefficientsType CoefficientsType;
for (int i = 0; i < num_segments; ++i) {
CoefficientsType coefficients = CoefficientsType::Random(num_coefficients);
polynomials.push_back(Polynomial<CoefficientType>(coefficients));
}
// differentiate integral, get original back
PiecewisePolynomial<CoefficientType> piecewise(polynomials, generateSegmentTimes(num_segments));
PiecewisePolynomial<CoefficientType> piecewise_back = piecewise.integral().derivative();
if (!piecewise.isApprox(piecewise_back, 1e-10))
throw runtime_error("wrong");
// check value at start time
double value_at_t0 = uniform(generator);
PiecewisePolynomial<CoefficientType> integral = piecewise.integral(value_at_t0);
valuecheck(value_at_t0, integral.value(piecewise.getStartTime()), 1e-10);
// check continuity at knot points
for (int i = 0; i < piecewise.getNumberOfSegments() - 1; ++i) {
valuecheck(integral.getPolynomial(i).value(integral.getDuration(i)), integral.getPolynomial(i + 1).value(0.0));
}
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
string usage = "[coefs, objval] = nWaypointCubicSplinemex(ts, xs, xd0, xdf)";
if (nrhs != 4)
mexErrMsgIdAndTxt("Drake:nWaypointCubicSplinemex:WrongNumberOfInputs",
usage.c_str());
if (nlhs > 2)
mexErrMsgIdAndTxt("Drake:nWaypointCubicSplinemex:WrongNumberOfOutputs",
usage.c_str());
const std::vector<double> segment_times = matlabToStdVector<double>(prhs[0]);
MatrixXd xs = matlabToEigen<Dynamic, Dynamic>(prhs[1]);
auto xd0 = matlabToEigen<Dynamic, 1>(prhs[2]);
auto xdf = matlabToEigen<Dynamic, 1>(prhs[3]);
mwSize ndof = static_cast<mwSize>(xs.rows());
mwSize num_segments = static_cast<mwSize>(xs.cols()) - 1;
mwSize num_knots = num_segments - 1;
mwSize num_coeffs_per_segment = 4;
mwSize dims[] = {ndof, num_segments, num_coeffs_per_segment};
plhs[0] = mxCreateNumericArray(3, dims, mxDOUBLE_CLASS, mxREAL);
double objective_value = 0.0;
for (mwSize dof = 0; dof < ndof; dof++) {
VectorXd xi = xs.block(dof, 1, 1, num_knots).transpose();
PiecewisePolynomial<double> spline =
nWaypointCubicSpline(segment_times, xs(dof, 0), xd0[dof],
xs(dof, num_segments), xdf[dof], xi);
PiecewisePolynomial<double> acceleration_squared = spline.derivative(2);
acceleration_squared *= acceleration_squared;
PiecewisePolynomial<double> acceleration_squared_integral =
acceleration_squared.integral();
objective_value +=
acceleration_squared_integral.scalarValue(spline.getEndTime()) -
acceleration_squared_integral.scalarValue(spline.getStartTime());
for (mwSize segment_index = 0; segment_index < spline.getNumberOfSegments();
segment_index++) {
for (mwSize coefficient_index = 0;
coefficient_index < num_coeffs_per_segment; coefficient_index++) {
mwSize sub[] = {dof, segment_index,
num_coeffs_per_segment - coefficient_index -
1
}; // Matlab's reverse coefficient indexing...
*(mxGetPr(plhs[0]) + sub2ind(3, dims, sub)) =
spline.getPolynomial(static_cast<int>(segment_index))
.getCoefficients()[coefficient_index];
}
}
}
if (nlhs > 1) {
plhs[1] = mxCreateDoubleScalar(objective_value);
}
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
string usage =
"[coefs, ts, objective_value] = "
"nWaypointCubicSplineFreeKnotTimesmex.cpp(t0, tf, xs, xd0, xdf)";
if (nrhs != 5)
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfInputs",
usage.c_str());
if (nlhs < 2 || nlhs > 3)
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfOutputs",
usage.c_str());
double t0 = mxGetPrSafe(prhs[0])[0];
double tf = mxGetPrSafe(prhs[1])[0];
MatrixXd xs = matlabToEigen<Dynamic, Dynamic>(prhs[2]);
auto xd0 = matlabToEigen<Dynamic, 1>(prhs[3]);
auto xdf = matlabToEigen<Dynamic, 1>(prhs[4]);
mwSize ndof = static_cast<mwSize>(xs.rows());
mwSize num_segments = static_cast<mwSize>(xs.cols()) - 1;
mwSize num_knots = num_segments - 1;
if (num_knots >= 3)
mexWarnMsgTxt(
"More knots than two is likely to be super slow in a grid search!\n");
if (num_knots <= 0)
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:"
"NotEnoughKnotsToJustifyThisFunction",
usage.c_str());
mwSize num_coeffs_per_segment = 4;
mwSize dims[] = {ndof, num_segments, num_coeffs_per_segment};
plhs[0] = mxCreateNumericArray(3, dims, mxDOUBLE_CLASS, mxREAL);
std::vector<double> segment_times;
segment_times.resize(static_cast<size_t>(num_segments) + 1);
segment_times[0] = t0;
segment_times[static_cast<size_t>(num_segments)] = tf;
std::vector<double> best_segment_times = segment_times;
double t_step = (tf - t0) / GRID_STEPS;
double min_objective_value = numeric_limits<double>::infinity();
// assemble the knot point locations for input to nWaypointCubicSpline
MatrixXd xi = xs.block(0, 1, ndof, num_knots);
if (GRID_STEPS <= num_knots) {
// If we have have too few grid steps, then by pigeonhole it's
// impossible to give each a unique time in our grid search.
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:"
"TooManyKnotsForNumGridSteps",
usage.c_str());
}
std::vector<int> t_indices;
t_indices.reserve(num_knots);
for (mwSize i = 0; i < num_knots; i++) {
t_indices.push_back(i + 1); // assume knot point won't be the same time as
// the initial state, or previous knot point
}
while (t_indices[0] < (GRID_STEPS - static_cast<int>(num_knots) + 1)) {
for (mwSize i = 0; i < num_knots; i++)
segment_times[i + 1] = t0 + t_indices[i] * t_step;
bool valid_solution = true;
double objective_value = 0.0;
for (mwSize dof = 0; dof < ndof && valid_solution; dof++) {
try {
PiecewisePolynomial<double> spline = nWaypointCubicSpline(
segment_times, xs(dof, 0), xd0[dof], xs(dof, num_segments),
xdf[dof], xi.row(dof).transpose());
PiecewisePolynomial<double> acceleration_squared = spline.derivative(2);
acceleration_squared *= acceleration_squared;
PiecewisePolynomial<double> acceleration_squared_integral =
acceleration_squared.integral();
objective_value +=
acceleration_squared_integral.scalarValue(spline.getEndTime()) -
acceleration_squared_integral.scalarValue(spline.getStartTime());
} catch (ConstraintMatrixSingularError &) {
valid_solution = false;
}
}
if (valid_solution && objective_value < min_objective_value) {
best_segment_times = segment_times;
min_objective_value = objective_value;
}
// Advance grid search counter or terminate, counting from
// the latest t_index, and on overflow carrying to the
// next lowest t_index and resetting to the new value of that
// next lowest t_index. (since times must always be in order!)
t_indices[num_knots - 1]++;
// carry, except for the lowest place, which we
// use to detect doneness.
for (size_t i = num_knots - 1; i > 0; i--) {
if ((i == num_knots - 1 && t_indices[i] >= GRID_STEPS) ||
(i < num_knots - 1 && t_indices[i] >= t_indices[i + 1])) {
t_indices[i - 1]++;
t_indices[i] = t_indices[i - 1] + 1;
}
}
}
for (mwSize dof = 0; dof < ndof; dof++) {
PiecewisePolynomial<double> spline = nWaypointCubicSpline(
best_segment_times, xs(dof, 0), xd0[dof], xs(dof, num_segments),
xdf[dof], xi.row(dof).transpose());
for (mwSize segment_index = 0;
segment_index < static_cast<mwSize>(spline.getNumberOfSegments());
segment_index++) {
for (mwSize coefficient_index = 0;
coefficient_index < num_coeffs_per_segment; coefficient_index++) {
mwSize sub[] = {dof, segment_index,
num_coeffs_per_segment - coefficient_index -
1}; // Matlab's reverse coefficient indexing...
*(mxGetPr(plhs[0]) + sub2ind(3, dims, sub)) =
spline.getPolynomial(static_cast<int>(segment_index))
.GetCoefficients()[coefficient_index];
}
}
}
plhs[1] = stdVectorToMatlab(best_segment_times);
if (nlhs > 2) plhs[2] = mxCreateDoubleScalar(min_objective_value);
}
void mexFunction(int nlhs, mxArray *plhs[],int nrhs, const mxArray *prhs[]) {
string usage = "[coefs, ts, objective_value] = twoWaypointCubicSplineFreeKnotTimesmex.cpp(t0, tf, xs, xd0, xdf)";
if (nrhs != 5)
mexErrMsgIdAndTxt("Drake:twoWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfInputs", usage.c_str());
if (nlhs < 2 || nlhs > 3)
mexErrMsgIdAndTxt("Drake:twoWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfOutputs", usage.c_str());
double t0 = mxGetPrSafe(prhs[0])[0];
double tf = mxGetPrSafe(prhs[1])[0];
MatrixXd xs = matlabToEigen<Dynamic, Dynamic>(prhs[2]);
auto xd0 = matlabToEigen<Dynamic, 1>(prhs[3]);
auto xdf = matlabToEigen<Dynamic, 1>(prhs[4]);
mwSize ndof = static_cast<mwSize>(xs.rows());
mwSize num_segments = 3;
mwSize num_coeffs_per_segment = 4;
mwSize dims[] = {ndof, num_segments, num_coeffs_per_segment};
plhs[0] = mxCreateNumericArray(num_segments, dims, mxDOUBLE_CLASS, mxREAL);
std::vector<double> segment_times;
segment_times.resize(static_cast<size_t>(num_segments) + 1);
segment_times[0] = t0;
segment_times[static_cast<size_t>(num_segments)] = tf;
std::vector<double> best_segment_times = segment_times;
double t_step = (tf - t0) / GRID_STEPS;
double min_objective_value = numeric_limits<double>::infinity();
for (int t1_index = 0; t1_index < GRID_STEPS; t1_index++) {
segment_times[1] = t0 + t1_index * t_step;
for (int t2_index = t1_index; t2_index < GRID_STEPS; t2_index++) {
segment_times[2] = t0 + t2_index * t_step;
bool valid_solution = true;
double objective_value = 0.0;
for (int dof = 0; dof < ndof && valid_solution; dof++) {
try {
PiecewisePolynomial<double> spline = twoWaypointCubicSpline(segment_times, xs(dof, 0), xd0[dof], xs(dof, 3), xdf[dof], xs(dof, 1), xs(dof, 2));
PiecewisePolynomial<double> acceleration_squared = spline.derivative(2);
acceleration_squared *= acceleration_squared;
PiecewisePolynomial<double> acceleration_squared_integral = acceleration_squared.integral();
objective_value += acceleration_squared_integral.value(spline.getEndTime()) - acceleration_squared_integral.value(spline.getStartTime());
}
catch (ConstraintMatrixSingularError&) {
valid_solution = false;
}
}
if (valid_solution && objective_value < min_objective_value) {
best_segment_times[1] = segment_times[1];
best_segment_times[2] = segment_times[2];
min_objective_value = objective_value;
}
}
}
for (mwSize dof = 0; dof < ndof; dof++) {
PiecewisePolynomial<double> spline = twoWaypointCubicSpline(best_segment_times, xs(dof, 0), xd0[dof], xs(dof, 3), xdf[dof], xs(dof, 1), xs(dof, 2));
for (mwSize segment_index = 0; segment_index < spline.getNumberOfSegments(); segment_index++) {
for (mwSize coefficient_index = 0; coefficient_index < num_coeffs_per_segment; coefficient_index++) {
mwSize sub[] = {dof, segment_index, num_coeffs_per_segment - coefficient_index - 1}; // Matlab's reverse coefficient indexing...
*(mxGetPr(plhs[0]) + sub2ind(3, dims, sub)) = spline.getPolynomial(segment_index).getCoefficients()[coefficient_index];
}
}
}
plhs[1] = stdVectorToMatlab(best_segment_times);
if (nlhs > 2)
plhs[2] = mxCreateDoubleScalar(min_objective_value);
}