void bi::cov(const ExpGaussianPdf<V1, M1>& q, M2 Sigma) {
/* pre-condition */
BI_ASSERT(Sigma.size1() == q.size());
BI_ASSERT(Sigma.size2() == q.size());
Sigma = q.cov();
}
void bi::marginalise(const ExpGaussianPdf<V1, M1>& p1,
const ExpGaussianPdf<V2,M2>& p2, const M3 C,
const ExpGaussianPdf<V4, M4>& q2, ExpGaussianPdf<V5,M5>& p3) {
/* pre-conditions */
BI_ASSERT(q2.size() == p2.size());
BI_ASSERT(p3.size() == p1.size());
BI_ASSERT(C.size1() == p1.size() && C.size2() == p2.size());
typename sim_temp_vector<V1>::type z2(p2.size());
typename sim_temp_matrix<M1>::type K(p1.size(), p2.size());
typename sim_temp_matrix<M1>::type A1(p2.size(), p2.size());
typename sim_temp_matrix<M1>::type A2(p2.size(), p2.size());
/**
* Compute gain matrix:
*
* \f[\mathcal{K} = C_{\mathbf{x}_1,\mathbf{x}_2}\Sigma_2^{-1}\,.\f]
*/
symm(1.0, p2.prec(), C, 0.0, K, 'R', 'U');
/**
* Then result is given by \f$\mathcal{N}(\boldsymbol{\mu}',
* \Sigma')\f$, where:
*
* \f[\boldsymbol{\mu}' = \boldsymbol{\mu}_1 +
* \mathcal{K}(\boldsymbol{\mu}_3 - \boldsymbol{\mu}_2)\,,\f]
*/
z2 = q2.mean();
axpy(-1.0, p2.mean(), z2);
p3.mean() = p1.mean();
gemv(1.0, K, z2, 1.0, p3.mean());
/**
* and:
*
* \f{eqnarray*}
* \Sigma' &=& \Sigma_1 + \mathcal{K}(\Sigma_3 -
* \Sigma_2)\mathcal{K}^T \\
* &=& \Sigma_1 + \mathcal{K}\Sigma_3\mathcal{K}^T -
* \mathcal{K}\Sigma_2\mathcal{K}^T\,.
* \f}
*/
p3.cov() = p1.cov();
A1 = K;
trmm(1.0, q2.std(), A1, 'R', 'U', 'T');
syrk(1.0, A1, 1.0, p3.cov(), 'U');
A2 = K;
trmm(1.0, p2.std(), A2, 'R', 'U', 'T');
syrk(-1.0, A2, 1.0, p3.cov(), 'U');
/* make sure correct log-variables set */
p3.setLogs(p2.getLogs());
p3.init(); // redo precalculations
}
void bi::mean(const M1 X, const V1 w, V2 mu) {
/* pre-conditions */
BI_ASSERT(X.size2() == mu.size());
BI_ASSERT(X.size1() == w.size());
typedef typename V1::value_type T;
T Wt = sum_reduce(w);
gemv(1.0/Wt, X, w, 0.0, mu, 'T');
}
inline void bi::mean(const InverseGammaPdf& q, V1 mu) {
/* pre-condition */
BI_ASSERT(mu.size() == q.size());
BI_ASSERT(q.shape() > 1.0);
real alpha = q.shape();
real beta = q.scale();
set_elements(mu, alpha*std::pow(beta, 2));
}
void bi::cov(const M1 X, const V1 mu, M2 Sigma) {
/* pre-conditions */
BI_ASSERT(X.size2() == mu.size());
BI_ASSERT(Sigma.size1() == mu.size() && Sigma.size2() == mu.size());
const int N = X.size1();
typename sim_temp_matrix<M2>::type Y(X.size1(), X.size2());
Y = X;
sub_rows(Y, mu);
syrk(1.0/(N - 1.0), Y, 0.0, Sigma, 'U', 'T');
}
void bi::cov(const GammaPdf& q, M1 Sigma) {
/* pre-condition */
BI_ASSERT(Sigma.size1() == q.size());
BI_ASSERT(Sigma.size2() == q.size());
real alpha = q.shape();
real beta = q.scale();
real sigma = alpha*std::pow(beta, 2);
Sigma.clear();
set_elements(diagonal(Sigma), sigma);
}
void bi::var(const M1 X, const V1 mu, V2 sigma) {
/* pre-conditions */
BI_ASSERT(X.size2() == mu.size());
BI_ASSERT(sigma.size() == mu.size());
const int N = X.size1();
typename sim_temp_matrix<M1>::type Z(X.size2(), X.size1());
Z = X;
sub_rows(Z, mu);
dot_columns(Z, sigma);
scal(1.0/(N - 1.0), sigma);
}
void bi::cov(const InverseGammaPdf& q, M1 Sigma) {
/* pre-condition */
BI_ASSERT(Sigma.size1() == q.size());
BI_ASSERT(Sigma.size2() == q.size());
BI_ASSERT(q.shape() > 2.0);
real alpha = q.shape();
real beta = q.scale();
real sigma = std::pow(beta, 2)/(std::pow(alpha - 1.0, 2)*(alpha - 2.0));
Sigma.clear();
set_elements(diagonal(Sigma), sigma);
}
void bi::cross(const M1 X, const M2 Y, const V1 muX, const V2 muY,
M3 SigmaXY) {
/* pre-conditions */
BI_ASSERT(X.size2() == muX.size());
BI_ASSERT(Y.size2() == muY.size());
BI_ASSERT(X.size1() == Y.size1());
BI_ASSERT(SigmaXY.size1() == muX.size() && SigmaXY.size2() == muY.size());
const int N = X.size1();
gemm(1.0/(N - 1.0), X, Y, 0.0, SigmaXY, 'T', 'N');
ger(-N/(N - 1.0), muX, muY, SigmaXY);
}
void bi::cov(const UniformPdf<V1>& q, M1 Sigma) {
/* pre-condition */
BI_ASSERT(Sigma.size1() == q.size());
BI_ASSERT(Sigma.size2() == q.size());
temp_host_vector<real>::type diff(q.size());
diff = q.upper();
sub_elements(diff, q.lower(), diff);
sq_elements(diff, diff);
Sigma.clear();
axpy(1.0/12.0, diff, diagonal(Sigma));
}
void bi::mean(const UniformPdf<V1>& q, V2 mu) {
/* pre-condition */
BI_ASSERT(q.size() == mu.size());
axpy(0.5, q.lower(), mu, true);
axpy(0.5, q.upper(), mu);
}
bi::Resampler::Resampler(const double essRel) :
essRel(essRel), maxLogWeight(0.0) {
/* pre-condition */
BI_ASSERT(essRel >= 0.0 && essRel <= 1.0);
//
}
void bi::condition(const ExpGaussianPdf<V1, M1>& p1, const ExpGaussianPdf<V2,
M2>& p2, const M3 C, const V3 x2, ExpGaussianPdf<V4, M4>& p3) {
/* pre-condition */
BI_ASSERT(x2.size() == p2.size());
BI_ASSERT(p3.size() == p1.size());
BI_ASSERT(C.size1() == p1.size() && C.size2() == p2.size());
typename sim_temp_vector<V1>::type z2(p2.size());
typename sim_temp_matrix<M1>::type K(p1.size(), p2.size());
/**
* Compute gain matrix:
*
* \f[\mathcal{K} = C_{\mathbf{x}_1,\mathbf{x}_2}\Sigma_2^{-1}\,.\f]
*/
symm(1.0, p2.prec(), C, 0.0, K, 'R', 'U');
/**
* Then result is given by \f$\mathcal{N}(\boldsymbol{\mu}',
* \Sigma')\f$, where:
*
* \f[\boldsymbol{\mu}' = \boldsymbol{\mu}_1 + \mathcal{K}(\mathbf{x}_2 -
* \boldsymbol{\mu}_2)\,,\f]
*/
z2 = x2;
log_vector(z2, p2.getLogs());
axpy(-1.0, p2.mean(), z2);
p3.mean() = p1.mean();
gemv(1.0, K, z2, 1.0, p3.mean());
/**
* and:
*
* \f{eqnarray*}
* \Sigma' &=& \Sigma_1 - \mathcal{K}C_{\mathbf{x}_1,\mathbf{x}_2}^T \\
* &=& \Sigma_1 - C_{\mathbf{x}_1,\mathbf{x}_2}\Sigma_2^{-1}
* C_{\mathbf{x}_1,\mathbf{x}_2}^T\,.\f}
*/
K = C;
trsm(1.0, p2.std(), K, 'R', 'U');
p3.cov() = p1.cov();
syrk(-1.0, K, 1.0, p3.cov(), 'U');
/* update log-variables and precalculations */
p3.setLogs(p1.getLogs());
p3.init();
}
void h_ode_set_safe(const real safein) {
/* pre-condition */
BI_ASSERT(safein > BI_REAL(0.001) && safein < BI_REAL(1.0));
h_safe = safein;
h_safe1 = BI_REAL(1.0) / safein;
h_logsafe = bi::log(safein);
}
inline T1 bi::inverse_gamma(R& rng, const T1 alpha, const T1 beta) {
/* pre-condition */
BI_ASSERT(alpha > static_cast<T1>(0.0) && beta > static_cast<T1>(0.0));
const T1 x = rng.gamma(alpha, static_cast<T1>(1.0)/beta);
return static_cast<T1>(1.0)/x;
}
void h_ode_set_beta(const real betain) {
/* pre-condition */
BI_ASSERT(betain >= 0.0 && betain <= BI_REAL(0.2));
h_beta = betain;
h_expo1 = BI_REAL(0.2) - betain*BI_REAL(0.75);
h_expo = BI_REAL(0.5)*(BI_REAL(0.2) - betain*BI_REAL(0.75));
}
inline T1 bi::beta(R& rng, const T1 alpha, const T1 beta) {
/* pre-condition */
BI_ASSERT(alpha > static_cast<T1>(0.0) && beta > static_cast<T1>(0.0));
const T1 x = rng.gamma(alpha, static_cast<T1>(1.0));
const T1 y = rng.gamma(beta, static_cast<T1>(1.0));
return x / (x + y);
}
inline void bi::mean(const GammaPdf& q, V1 mu) {
/* pre-condition */
BI_ASSERT(mu.size() == q.size());
real alpha = q.shape();
real beta = q.scale();
set_elements(mu, alpha*beta);
}
void bi::mean(const M1 X, V1 mu) {
/* pre-condition */
BI_ASSERT(X.size2() == mu.size());
const int N = X.size1();
typename sim_temp_vector<V1>::type w(N);
set_elements(w, 1.0);
gemv(1.0/N, X, w, 0.0, mu, 'T');
}
void bi::cov(const M1 X, const V1 w, const V2 mu, M2 Sigma) {
/* pre-conditions */
BI_ASSERT(X.size2() == mu.size());
BI_ASSERT(X.size1() == w.size());
BI_ASSERT(Sigma.size1() == mu.size() && Sigma.size2() == mu.size());
typedef typename V1::value_type T;
typename sim_temp_matrix<M2>::type Y(X.size1(), X.size2());
typename sim_temp_matrix<M2>::type Z(X.size1(), X.size2());
typename sim_temp_vector<V2>::type v(w.size());
T Wt = sum_reduce(w);
Y = X;
sub_rows(Y, mu);
sqrt_elements(w, v);
gdmm(1.0, v, Y, 0.0, Z);
syrk(1.0/Wt, Z, 0.0, Sigma, 'U', 'T');
// alternative weight: 1.0/(Wt - W2t/Wt)
}
void bi::distance(const M1 X, const real h, M2 D) {
/* pre-conditions */
BI_ASSERT(D.size1() == D.size2());
BI_ASSERT(D.size1() == X.size1());
BI_ASSERT(!M2::on_device);
typedef typename M1::value_type T1;
FastGaussianKernel K(X.size2(), h);
typename temp_host_vector<T1>::type d(X.size2());
int i, j;
for (j = 0; j < D.size2(); ++j) {
for (i = 0; i <= j; ++i) {
d = row(X, i);
axpy(-1.0, row(X, j), d);
D(i, j) = K(dot(d));
}
}
}
void bi::hist(const V1 x, const V2 w, V3 c, V4 h) {
/* pre-condition */
BI_ASSERT(x.size() == w.size());
BI_ASSERT(c.size() == h.size());
BI_ASSERT(!V3::on_device);
BI_ASSERT(!V4::on_device);
typedef typename V1::value_type T1;
typedef typename V2::value_type T2;
const int P = x.size();
const int B = c.size();
T1 mx, mn;
int i, j;
typename temp_host_vector<T1>::type xSorted(P);
typename temp_host_vector<T2>::type wSorted(P);
xSorted = x;
wSorted = w;
bi::sort_by_key(xSorted, wSorted);
mn = xSorted[0];
mx = xSorted[xSorted.size() - 1];
/* compute bin right edges */
for (j = 0; j < B; ++j) {
c[j] = mn + (j + 1)*(mx - mn)/B;
}
/* compute bin heights */
h.clear();
for (i = 0, j = 0; i < P; ++i) {
if (xSorted[i] >= c[j] && j < B - 1) {
++j;
}
h[j] += wSorted[i];
}
/* compute bin centres */
for (j = B - 1; j > 0; --j) {
c[j] = 0.5*(c[j - 1] + c[j]);
}
c[0] = 0.5*(mn + c[0]);
}
void bi::var(const M1 X, const V1 w, const V2 mu, V3 sigma) {
/* pre-conditions */
BI_ASSERT(X.size2() == mu.size());
BI_ASSERT(X.size1() == w.size());
BI_ASSERT(sigma.size() == mu.size());
typedef typename V1::value_type T1;
typename sim_temp_matrix<M1>::type Z(X.size1(), X.size2());
typename sim_temp_matrix<M1>::type Y(X.size1(), X.size2());
typename sim_temp_vector<V2>::type v(w.size());
T1 Wt = sum_reduce(w);
Z = X;
sub_rows(Z, mu);
sqrt_elements(w, v);
gdmm(1.0, v, Z, 0.0, Y);
dot_columns(Y, sigma);
divscal_elements(sigma, Wt, sigma);
// alternative weight: 1.0/(Wt - W2t/Wt)
}
void bi::Cache::resize(const int size) {
/* pre-condition */
BI_ASSERT(size >= 0);
int oldSize = this->size();
valids.resize(size, true); // true is to preserve contents here
dirties.resize(size, true);
if (size > oldSize) {
set_elements(subrange(valids, oldSize, size - oldSize), false);
set_elements(subrange(dirties, oldSize, size - oldSize), false);
}
}
void bi::InputNetCDFBuffer::readTime(int ncVar, const long start,
size_t* const len, real* const t) {
/* pre-condition */
BI_ASSERT(start >= 0);
BI_ASSERT(len != NULL);
BI_ASSERT(t != NULL);
std::vector<size_t> offsets(2), counts(2);
std::vector<int> dimids = nc_inq_vardimid(ncid, ncVar);
real tnxt;
int j = 0;
size_t T;
if (nsDim >= 0 && dimids[j] == nsDim) {
/* optional ns dimension */
offsets[j] = ns;
counts[j] = 1;
++j;
}
BI_ASSERT(j < static_cast<int>(dimids.size()));
T = nc_inq_dimlen(ncid, dimids[j]);
offsets[j] = start;
counts[j] = 1;
//++j; // not here, need to hold ref to last offset
/* may be multiple records with same time, keep reading until time changes */
*len = 0;
*t = 0.0;
tnxt = 0.0;
while (*t == tnxt && offsets[j] < T) {
nc_get_vara(ncid, ncVar, offsets, counts, &tnxt);
if (*len == 0) {
*t = tnxt;
}
if (tnxt == *t) {
++offsets[j];
++(*len);
}
}
}
T1 bi::truncated_gaussian(R& rng, const T1 lower, const T1 upper, const T1 mu,
const T1 sigma) {
/* pre-conditions */
BI_ASSERT(upper >= lower);
T1 u;
if (upper == lower) {
u = upper;
} else do {
u = rng.gaussian(mu, sigma);
} while (u < lower || u > upper);
return u;
}
void bi::inverse_gamma_log_densities(const M1 Z, const T1 alpha, const T1 beta,
V1 p, const bool clear) {
/* pre-condition */
BI_ASSERT(Z.size1() == p.size());
op_elements(vec(Z), vec(Z), inverse_gamma_log_density_functor<T1>(alpha, beta));
if (clear) {
sum_columns(Z, p);
} else {
typename sim_temp_vector<V1>::type p1(p.size());
sum_columns(Z, p1);
add_elements(p, p1, p);
}
}
void bi::standardise(const ExpGaussianPdf<V1,M1>& p, M2 X) {
/* pre-condition */
BI_ASSERT(p.size() == X.size2());
typename sim_temp_vector<M2>::type mu(X.size2());
log_columns(X, p.getLogs());
mean(X, mu);
sub_rows(X, mu);
trsm(1.0, p.std(), X, 'R', 'U');
add_rows(X, mu);
sub_rows(X, p.mean());
exp_columns(X, p.getLogs());
}
void bi::gaussian_log_densities(const M1 Z, const T1 logZ, V1 p,
const bool clear) {
/* pre-condition */
BI_ASSERT(Z.size1() == p.size());
typedef typename V1::value_type T2;
if (clear) {
dot_rows(Z, p);
op_elements(p, p, gaussian_log_density_functor<T2>(logZ));
} else {
typename sim_temp_vector<V1>::type p1(p.size());
dot_rows(Z, p1);
op_elements(p1, p, p, gaussian_log_density_update_functor<T2>(logZ));
}
}
void bi::MultinomialResamplerHost::ancestors(Random& rng, const V1 lws, V2 as,
MultinomialPrecompute<ON_HOST>& pre)
throw (ParticleFilterDegeneratedException) {
typedef typename V1::value_type T1;
const int P = as.size();
const int lwsSize = lws.size();
T1 lW;
/* weights */
if (pre.W > 0) {
lW = bi::log(pre.W);
#pragma omp parallel
{
int Q = P/bi_omp_max_threads;
int start = bi_omp_tid*Q + bi::min(bi_omp_tid, P % bi_omp_max_threads); // min() handles leftovers
if (bi_omp_tid < P % bi_omp_max_threads) {
++Q; // pick up a leftover
}
int i, j = lwsSize;
T1 lMax = 0.0, lu;
for (i = Q; i > 0; --i) {
lMax += bi::log(rng.uniform<T1>())/i;
lu = lW + lMax;
while (j > 0 && lu < bi::log(pre.Ws(j - 1))) {
--j;
}
if (pre.sort) {
as(start + i - 1) = pre.ps(j);
} else {
as(start + i - 1) = j;
}
}
}
} else {
throw ParticleFilterDegeneratedException();
}
/* post-condition */
BI_ASSERT(max_reduce(as) < lws.size());
}