Real gmm_objective(std::vector<VectorD> const& x,
Vector const& alphas, std::vector<VectorD> const& means, std::vector<VectorD> const& qs, std::vector<Vector> const& ls,
Real wishart_gamma, Real wishart_m)
{
size_t n = x.size();
size_t d = x[0].size();
size_t K = alphas.size();
// assert (K = rows means)
// assert (d = cols means)
// assert (K = rows qs)
// assert (d = cols qs)
// assert (K = rows ls)
// assert (auto di = (cardToInt d) in di*(di-1)/2 = cardToInt (cols ls))
double out = 0.0;
Vector tmp{ K };
for (size_t i = 0; i < n; ++i) {
for (size_t k = 0; k < K; ++k)
tmp[k] = alphas[k] + sum(qs[k]) - 0.5 * sumsq(Qtimesv(qs[k], ls[k], x[i] - means[k]));
out += logsumexp(tmp);
}
out -= n * logsumexp(alphas);
for (size_t k = 0; k < K; ++k)
out += sumsq(exp(qs[k])) + sumsq(ls[k]);
return out;
}
/*
* Display the shortest sums of squares for long integer "d1".
*
* Return the minimum number of summed squares required to represent "d1".
*/
int
findsq(long d1)
{
if (sumsq(d1, 1))
return 1;
if (sumsq(d1, 2))
return 2;
if (sumsq(d1, 3))
return 3;
if (sumsq(d1, 4))
return 4;
fprintf(stderr, "Whoops! Can't find the sum of four squares that equal %ld.\n", d1);
exit(EXIT_FAILURE);
}
SpdMatrix WMS::center_sumsq(const Vector &mu)const{
SpdMatrix ans = sumsq(); // sum wyy^T
ans.add_outer(mu, sumw()); // wyyT + w.mu.muT
ans -= as_symmetric(mu.outer(sum_, 2));
return ans;
}
int main()
{
std::uniform_real_distribution<Real> dist(0, 1);
auto rand = [&dist] { return dist(rng); };
Vec<Real> theta{ 26 };
size_t n_bones = 15;
size_t n_verts = 500;
fillrand(&theta, std::uniform_real_distribution<Real>(-1, 1));
Mat<Real, 3, N_VERTS> base_positions{ 3, n_verts };
for (int i = 0; i < n_verts; ++i)
fillrand(&base_positions[i], std::uniform_real_distribution<Real>(1, 10));
std::vector<Real4x4> base_relatives{ n_bones };
for (int i = 0; i < n_bones; ++i) {
Vec<Real, 3> rvec; fillrand(&rvec, std::uniform_real_distribution<Real>(-2, 2));
Vec<Real, 3> tvec; fillrand(&tvec, std::uniform_real_distribution<Real>(1, 2));
base_relatives[i] = Rt_to_transform(angle_axis_to_rotation_matrix(rvec), tvec);
}
std::vector<int> parents{
-1, 0, 1,
-1, 3, 4,
-1, 6, 7,
-1, 9, 10,
-1, 12, 13,
};
Mat<Real, N_VERTS, N_BONES> weights{ n_verts, n_bones };
for (int i = 0; i < n_verts; ++i)
for (int j = 0; j < n_bones; ++j) {
if (rand() < 4.0 / n_bones)
weights[j][i] = rand();
}
boost::timer::auto_cpu_timer t;
// Debug 150s
// Release 1s
double total = 0;
size_t N = 1000;
#ifdef _DEBUG
N = N / 10; // Debug is roughly this much slower than release -- multiply timings.
#endif
for (size_t count = 0; count < N; ++count) {
std::vector<Vec3<Real>> pose_params = to_pose_params(theta, n_bones);
Mat<Real, 3, N_VERTS> verts = get_skinned_vertex_positions(base_relatives, parents, base_positions, weights, pose_params);
total += sumsq(verts[1]);
}
std::cout << "total =" << total << ", time per call = " << t.elapsed().wall / double(N) / 1e6 << "ms" << std::endl;
return 0;
}
// Pre-condition: start <= end
// Post-condition: Returns the sum of the squares of the integers starting from
// start and ending at end.
int sumsq(int start, int end) {
// Base case were one value is being summed.
if (start == end)
return start*start;
// This is the recursive solution for larger cases.
return start*start + sumsq(start+1, end);
}
void experiment_normal::get_state(libbase::vector<double>& state) const
{
assert(count() == sum.size());
assert(count() == sumsq.size());
state.init(2 * count());
for (int i = 0; i < count(); i++)
{
state(i) = sum(i);
state(count() + i) = sumsq(i);
}
}
void SLLPS::draw() {
for (int i = 0; i < variance_samplers_.size(); ++i) {
Ptr<ZeroMeanGaussianModel> innovation_model = model_->innovation_model(i);
const auto suf = innovation_model->suf();
double sigsq = variance_samplers_[i].draw(
rng(), suf->n(), suf->sumsq());
innovation_model->set_sigsq(sigsq);
}
observation_coefficient_sampler_->draw_Beta();
model_->impose_identifiability_constraint();
}
WM::WishartModel(double pri_df, const SpdMatrix &PriVarEst)
: ParamPolicy(new UnivParams(pri_df), new SpdParams(PriVarEst*pri_df)),
DataPolicy(new WS(PriVarEst.nrow())),
PriorPolicy()
{
Chol chol(sumsq());
if (!chol.is_pos_def()) {
report_error("Sum of squares matrix must be positive definite in "
"WishartModel constructor");
}
}
void Qtimesv_test()
{
auto q = vec(0.1, -1.0, 0.3);
auto l = vec(5.0, -2.0, 7.1);
auto v = vec(1.4, -7.0, 3.1);
auto ans0 = exp(q[0]) * v[0];
auto ans1 = l[0] * v[0] + exp(q[1]) * v[1];
auto ans2 = l[1] * v[0] + l[2] * v[1] + exp(q[2]) * v[2];
auto ans = vec(ans0, ans1, ans2);
auto qv = Qtimesv(q, l, v);
auto nrm = sumsq(qv - ans);
assert(nrm < 0.0001);
}
void main()
{
long s;
int i;
for(i=11, s=0; i<=1000; i++)
{
if(palindrome(i)&&odd(i)&&sumsq(i))
{
s+=(long)i;
}
}
printf("\nSum=%ld", s);
}
void experiment_normal::estimate(libbase::vector<double>& estimate,
libbase::vector<double>& stderror) const
{
assert(count() == sum.size());
assert(count() == sumsq.size());
// estimate is the mean value
assert(get_samplecount() > 0);
estimate = sum / double(get_samplecount());
// standard error is sigma/sqrt(n)
stderror.init(count());
if (get_samplecount() > 1)
for (int i = 0; i < count(); i++)
stderror(i) = sqrt((sumsq(i) / double(get_samplecount()) - estimate(i)
* estimate(i)) / double(get_samplecount() - 1));
else
stderror = std::numeric_limits<double>::max();
}
int main() {
// Very basic, NOT comprensive, tests of the recursive methods.
int vals[4];
printf("7! = %d\n", fact(7));
printf("31^2 + 32^2 + ... + 200^2 = %d\n", sumsq(31, 200));
vals[0] = 37; vals[1] = 48; vals[2] = 56; vals[3] = 63;
printf("vals has %d Odd values.\n", ArrayOdd(vals, 4));
print_reverse("writethisbackwards", 18);
printf("\n");
printf("3^10 = %d\n", powerA(3,10));
printf("3^11 = %d\n", powerB(3,11));
if (Rbinary(33, vals, 0, 3) == -1)
printf("33 was not found in vals.\n");
dectobin(179);
printf("\n");
if (check("madamimadam", 11))
printf("madamimadam is a palindrome.\n");
printf("The 27th Fibonacci number is %d\n", fibonacci(27));
// Test of fast exponentiation vs. regular version
int start = time(0);
int ans1 = slowModPow(6874, 1000000000, 13713);
int end1 = time(0);
int ans2 = modPow(6874, 1000000000, 13713);
int end2 = time(0);
printf("ans1 = %d, ans2 = %d.\n", ans1, ans2);
printf("slowModExp took %d sec.\n", end1-start);
printf("modPow took %d sec.\n", end2-end1);
system("PAUSE");
return 0;
}
Real3x3 angle_axis_to_rotation_matrix(Real3 const& angle_axis)
{
auto n = sqrt(sumsq(angle_axis));
if (n < 0.0001)
return vec(
vec(1., 0., 0.),
vec(0., 1., 0.),
vec(0., 0., 1.)
);
Real x = angle_axis[0] / n;
Real y = angle_axis[1] / n;
Real z = angle_axis[2] / n;
Real s = sin(n);
Real c = cos(n);
return vec(
vec(x*x + (1. - x*x)*c, x*y*(1. - c) - z*s, x*z*(1. - c) + y*s),
vec(x*y*(1. - c) + z*s, y*y + (1. - y*y)*c, y*z*(1. - c) - x*s),
vec(x*z*(1. - c) - y*s, z*y*(1. - c) + x*s, z*z + (1. - z*z)*c));
}
SpdMatrix WishartModel::simdat(){ return rWish(nu(), sumsq()); }
double WishartModel::logp(const SpdMatrix &W) const{
return dWish(W, sumsq(), nu(), true); }
int dim()const {return sumsq().nrow();}
SpdMatrix WMS::var_hat()const{
if(sumw()==0) return sumsq()*0.0;
return center_sumsq()/sumw();
}