inline void f_harmonic(valarray<double> &r, valarray<double> &k, const int dim)
{
//constants
const double m = 1.0;
const double omega = 1.0;
//get number of particles
const int N_p = r.size() / (2 * dim);
//reset k vector
for (unsigned int i = 0; i < k.size(); i++)
{
k[i] = 0.0;
}
for (int d = 0; d < dim; d++)
{
for (int i = 0; i < N_p; i++)
{
k[(2 * i + 1)*dim + d] = (-1.) * m * omega * omega * r[i * 2 * dim + d];
k[i * 2 * dim + d] = r[(2 * i + 1) * dim + d] / m;
}
}
}
T norm(const valarray<T>& v, const unsigned p) {
T res = 0, scale = 0., absvi, ssq = 1., tmp;
if ( v.size() < 1 ) {
return static_cast<T>(0.);
}
else if ( v.size() == 1 ) {
return abs(v[0]);
}
else {
switch (p) {
case 0:
//for (size_t i = 0; i < v.size(); ++i) {
// if ( res < abs(v[i]) )
// res = abs(v[i]);
//}
//return res;
for (auto it = begin(v); it != end(v); ++it) {
if ( res < abs(*it) )
res = abs(*it);
}
return res;
//return MAX(abs(v.min()), abs(v.max()));
case 1:
for (size_t i = 0; i < v.size(); ++i) {
res += abs(v[i]);
}
return res;
//for ( auto it = begin(v); it != end(v); ++it)
// res += abs(*it);
//return res;
case 2:
for (size_t i = 0; i < v.size(); ++i) {
if ( v[i] != 0. ) {
absvi = abs(v[i]);
if ( scale < absvi ) {
tmp = scale/absvi;
ssq = 1. + ssq*tmp*tmp;
scale = absvi;
}
else {
tmp = absvi/scale;
ssq += tmp*tmp;
}
}
}
res = scale*sqrt(ssq);
return res;
default:
cerr << "error: utils:norm(vector): unsupported p-norm: p = " << p
<< endl;
exit(-1);
}
}
}
void SetUpCL(valarray<cl_float> & data, valarray<cl_float> & data_err, valarray<cl_float> & model, valarray<cl_float> & output)
{
unsigned int test_size = data.size();
assert(data_err.size() == test_size);
assert(model.size() == test_size);
assert(output.size() == test_size);
// Init OpenCL and the routine
cl = new COpenCL(CL_DEVICE_TYPE_GPU);
zero = new CRoutine_Zero(cl->GetDevice(), cl->GetContext(), cl->GetQueue());
zero->SetSourcePath(LIBOI_KERNEL_PATH);
zero->Init();
square = new CRoutine_Square(cl->GetDevice(), cl->GetContext(), cl->GetQueue());
square->SetSourcePath(LIBOI_KERNEL_PATH);
square->Init();
r = new CRoutine_Chi(cl->GetDevice(), cl->GetContext(), cl->GetQueue(), zero, square);
r->SetSourcePath(LIBOI_KERNEL_PATH);
r->Init(test_size);
// Make OpenCL buffers for the data, data_err, model, and output.
data_cl = clCreateBuffer(cl->GetContext(), CL_MEM_READ_WRITE, sizeof(cl_float) * test_size, NULL, NULL);
data_err_cl = clCreateBuffer(cl->GetContext(), CL_MEM_READ_WRITE, sizeof(cl_float) * test_size, NULL, NULL);
model_cl = clCreateBuffer(cl->GetContext(), CL_MEM_READ_WRITE, sizeof(cl_float) * test_size, NULL, NULL);
output_cl = clCreateBuffer(cl->GetContext(), CL_MEM_READ_WRITE, sizeof(cl_float) * test_size, NULL, NULL);
// Fill the input buffer
int err = CL_SUCCESS;
err = clEnqueueWriteBuffer(cl->GetQueue(), data_cl, CL_TRUE, 0, sizeof(cl_float) * test_size, &data[0], 0, NULL, NULL);
err = clEnqueueWriteBuffer(cl->GetQueue(), data_err_cl, CL_TRUE, 0, sizeof(cl_float) * test_size, &data_err[0], 0, NULL, NULL);
err = clEnqueueWriteBuffer(cl->GetQueue(), model_cl, CL_TRUE, 0, sizeof(cl_float) * test_size, &model[0], 0, NULL, NULL);
}
void apply_op(valarray<T>& lhs, valarray<T> const& x, valarray<T> const& y, Op op = Op{}) {
uint64_t size = std::min(x.size(), y.size());
size = std::min(size, lhs.size()); // probably not needed
for (uint64_t k = 0; k < size; k += 1) {
lhs[k] = op(x[k], y[k]);
}
}
void MakeChiZeroBuffers(valarray<cl_float> & data, valarray<cl_float> & data_err, valarray<cl_float> & model, valarray<cl_float> & output, unsigned int test_size)
{
unsigned int n = 2*test_size;
// Create buffers
data.resize(n);
data_err.resize(n);
model.resize(n);
output.resize(n);
valarray<cl_float2> temp = CModel::GenerateUVSpiral_CL(test_size);
// Set data = model to produce a zero chi result.
for(int i = 0; i < test_size; i++)
{
data[i] = temp[i].s0;
data[test_size + i] = temp[i].s1;
model[i] = temp[i].s0;
model[test_size + i] = temp[i].s1;
// 1% error on amplitudes, 10% error on phases
data_err[i] = amp_err * data[i];
data_err[test_size + i] = phi_err * data[i];
}
}
void report_distances(const valarray<double>& distances,
const string& name,
variables_map& args
)
{
if (not distances.size()) return;
bool show_mean = args.count("mean");
bool show_median = args.count("median");
bool show_minmax = args.count("minmax");
if (not show_mean and not show_median and not show_minmax)
show_median = true;
if (show_minmax)
cout<<" "<<name<<" in ["<<min(distances)<<", "<<max(distances)<<"]"<<endl;
if (show_mean){
cout<<" E "<<name<<" = "<<distances.sum()/distances.size();
cout<<" [+- "<<sqrt(Var(distances))<<"]"<<endl;
}
if (show_median) {
double P = args["CI"].as<double>();
pair<double,double> interval = central_confidence_interval(distances,P);
cout<<" "<<name<<" ~ "<<median(distances);
cout<<" ("<<interval.first<<", "<<interval.second<<")"<<endl;
}
}
void count_pair_distances::operator()(const SequenceTree& T)
{
if (not initialized) {
N = T.n_leaves();
names = T.get_leaf_labels();
m1.resize(N*(N-1)/2);
m2.resize(N*(N-1)/2);
m1 = 0;
m2 = 0;
initialized = true;
}
n_samples++;
// Theoretically, we could do this much faster, I think.
// vector<vector<int> > leaf_sets = partition_sets(T);
int k=0;
for(int i=0;i<N;i++)
for(int j=0;j<i;j++,k++)
{
double D = 0;
if (RF)
D = T.edges_distance(i,j);
else
D = T.distance(i,j);
m1[k] += D;
m2[k] += D*D;
}
}
static double compareAgainst(
const valarray<double> &z, // column vector
const valarray<double> &h, // column vector
const valarray<double> &Q, // symmetric matrix Q(x)
const valarray<double> &invQ // inverse of Q
)
{
const int n = z.size();
assert( Q.size() == n * n );
assert( h.size() == n );
//assert( hasPosDet( dmatQ ) );
valarray<double> Q2PI( n * n );
Q2PI = Q * 2.0 * PI;
// Compute det(Q2PI) = b * 2^c .
double b;
long c;
det( Q2PI, n, &b, &c );
// Compute log(det(Q2PI)).
double dTerm1 = log( b ) + c * log( 2.0 );
valarray<double> residual = z - h;
valarray<double> term2 = multiply( multiply( transpose( residual, n ), n, invQ, n ), n, residual, 1 );
double dTerm2 = term2[0];
return (dTerm1 + dTerm2) / 2.0;
}
// return dy/dx for each particular equation
valarray<double> dydx( const double x, const valarray<double>& y ) {
if ( y.size() != 4 ) throw;
valarray<double> tmpdydx(0.0,y.size());
try {
// slices would be easier, but oh well...
double z = y[0];
double p = y[1];
double zbar = y[2];
double pbar = y[3];
double zdot = ( 1 + z*zbar ) * ( pbar + (pbar*zbar)*z );
double pdot = 2 * zbar * ( p*pbar + (p*z)*(pbar*zbar) ) +
( 1 + z*zbar ) * ( (pbar*zbar)*z );
double zbardot = ( 1 + z*zbar ) * ( p + (p*z)*zbar );
double pbardot = 2 * z * ( p*pbar + (p*z)*(pbar*zbar) ) +
( 1 + z*zbar ) * ( (p*z)*zbar );
// recombine into tmpdydx... again, slices would be easier
tmpdydx[0] = zdot;
tmpdydx[1] = pdot;
tmpdydx[2] = zbardot;
tmpdydx[3] = pbardot;
}
catch(out_of_range) {
cerr << "oops" << endl;
exit(1);
}
return tmpdydx;
}
inline void rk4(valarray<double> &r, double h, double &t, const int dim, void (*f)(valarray<double> &, valarray<double> &, const int))
{
//define k, r_step, and temp arrays to hold eom evaluations
valarray<double> k(r.size());
valarray<double> r_step(r.size());
valarray<double> temp(r.size());
const double half_h = h / 2.;
//1st rk4 step
f(r, k, dim);
r_step = h * (1. / 6.) * k;
temp = r + half_h * k;
//2nd
f(temp, k, dim);
r_step += h * (1. / 3.) * k;
temp = r + half_h * k;
//3rd
f(temp, k, dim);
r_step += h * (1. / 3.) * k;
temp = r + h * k;
//4th
f(temp, k, dim);
//advance r in time
r += r_step + h * (1. / 6.) * k;
//advance time
t += h;
}
BroadEstepper1::BroadEstepper1(CanaryOptions& opts,
valarray<double> vals_in,
CanaryPrior & prior_in,
vector<int> & clusters_in)
: _opts(opts)
{
N = vals_in.size();
G = clusters_in.size();
_vals.resize(vals_in.size()); _vals = vals_in;
_prior = prior_in;
_cvec.resize(G); _cvec = clusters_in;
_prop.resize(G,1.0/G);
_mean.resize(G);
_var.resize(G);
for (unsigned int k=0; k<G; k++)
{
int cpos = _cvec[k];
// The algorithm converges to a cycle dependent on initial values. If it
// converged to a point - as it should - it would make sense to uncomment.
// _prop[k] = _prior.prop()[cpos];
_mean[k] = _prior.mean()[cpos];
_var[k] = _prior.var()[cpos];
}
_prob.ReSize(N,G);
_prob = 0.0;
update_prob();
}
double FullCovariance::calcLogdetFromCholesky( const valarray<double>& chol ) const
{
//------------------------------------------------------------
// Preliminaries.
//------------------------------------------------------------
int nChol = static_cast<int>(sqrt(static_cast<double>(chol.size())));
//------------------------------------------------------------
// Validate the current state (debug version only).
//------------------------------------------------------------
assert( chol.size() == nChol * nChol );
//------------------------------------------------------------
// Compute the logdet.
//------------------------------------------------------------
// Sum the logs of the diagonals.
double logsum = 0.0;
for ( int i = 0; i < nChol; i++ )
{
logsum += log( choleskyCached[i + i * nChol] );
}
// Return
// T 2 ---
// logdet( Chol Chol ) = log[ det( Chol ) ] = 2 > log( chol ) .
// --- ii
return 2.0 * logsum;
}
vector<double> convert(const valarray<double>& v1)
{
vector<double> v2(v1.size());
for(int i=0;i<v1.size();i++)
v2[i] = v1[i];
return v2;
}
double GradientProjection::computeSteepestDescentVector(
valarray<double> const &b,
valarray<double> const &x,
valarray<double> &g) const {
// find steepest descent direction
// g = 2 ( b - A x )
// where: A = denseQ + sparseQ
// g = 2 ( b - denseQ x) - 2 sparseQ x
//
// except the 2s don't matter because we compute
// the optimal stepsize anyway
COLA_ASSERT(x.size()==b.size() && b.size()==g.size());
g = b;
for (unsigned i=0; i<denseSize; i++) {
for (unsigned j=0; j<denseSize; j++) {
g[i] -= (*denseQ)[i*denseSize+j]*x[j];
}
}
// sparse part:
if(sparseQ) {
valarray<double> r(x.size());
sparseQ->rightMultiply(x,r);
g-=r;
}
return computeStepSize(g,g);
}
int drawCairo(const string& fname,
const valarray<double>& Xin, const valarray<double>& Yin,
const Hull& hull) {
#ifdef CAIRO_HAS_SVG_SURFACE
unsigned n=Xin.size();
assert(Yin.size()==n);
// normalise coords to range 0-1
valarray<double> X=Xin, Y=Yin;
X-=X.min();
Y-=Y.min();
X/=X.max();
Y/=Y.max();
Cairo::RefPtr<Cairo::SvgSurface> surface =
Cairo::SvgSurface::create(fname, width+2*border, height+2*border);
Cairo::RefPtr<Cairo::Context> cr = Cairo::Context::create(surface);
cr->save(); // save the state of the context
cr->set_source_rgba(0.0, 0.0, 0.0, 0.7);
// draw a circle at each coordinate
for(unsigned i=0;i<n;i++) {
dot(cr,xcoord(X[i]),ycoord(Y[i]));
}
cr->set_source_rgba(0.0, 0.0, 0.0, 0.3);
cr->move_to(xcoord(X[hull[0]]),ycoord(Y[hull[0]]));
for(unsigned i=1;i<hull.size();i++) {
cr->line_to(xcoord(X[hull[i]]),ycoord(Y[hull[i]]));
}
cr->line_to(xcoord(X[hull[0]]),ycoord(Y[hull[0]]));
cr->stroke();
cr->set_source_rgba(0.0, 0.0, 0.0, 1.);
for(vector<unsigned>::const_iterator i=hull.begin();i!=hull.end();++i) {
unsigned j=*i;
stringstream ss;
ss<<j;
printf("p[%d]=(%f,%f)\n",j,X[j],Y[j]);
cr->move_to(xcoord(X[j]),ycoord(Y[j]));
cr->show_text(ss.str());
cr->stroke();
}
cr->restore();
cr->show_page();
cout << "Wrote SVG file \"" << fname << "\"" << endl;
return 0;
#else
cout << "You must compile cairo with SVG support for this example to work."
<< endl;
return 1;
#endif
}
valarray<double> dirichlet(const valarray<double>& n)
{
valarray<double> x(n.size());
for(int i=0;i<n.size();i++)
x[i] = gamma(n[i],1.0);
x /= x.sum();
return x;
}
/// FIXME - this could be faster by a factor of 2 - we are sorting TWICE!
pair<double,double> confidence_interval(const valarray<double>& values,double P)
{
vector<double> values2(values.size());
for(int i=0;i<values.size();i++)
values2[i] = values[i];
return confidence_interval(values2,P);
}
valarray<int> iterate_zs(valarray<cmplx>& zs, const complex<float>& c,
size_t max_iters) {
valarray<int> ns(zs.size());
#pragma omp parallel for schedule(runtime)
for (size_t i = 0; i < zs.size(); i++)
ns[i] = iterate_z(zs[i], c, max_iters);
return ns;
}
/**
* generates a random set of n points in X and Y.
*/
void randTest(unsigned n, valarray<double>& X, valarray<double>& Y) {
X.resize(n);
Y.resize(n);
srand(time(NULL));
for(unsigned i=0;i<n;i++) {
X[i]=getRand(1.);
Y[i]=getRand(1.);
}
}
valarray<double> outer_prod(valarray<double> x, valarray<double> y) {
valarray<double> result(x.size()*y.size());
for(unsigned j = 0; j < x.size(); j++) {
for(unsigned i = 0; i < y.size(); i++) {
result[j*y.size() + i] = x[j]*y[i];
}
}
return result;
}
valarray<int> iterate_zs(valarray<cmplx>& zs, const complex<double>& c,
size_t max_iters) {
valarray<int> ns(zs.size());
#pragma omp parallel for default(none) shared(zs, c, max_iters, ns) \
schedule(runtime)
for (size_t i = 0; i < zs.size(); i++)
ns[i] = iterate_z(zs[i], c, max_iters);
return ns;
}
const valarray<double> multiply( const valarray<double>& X, int nColsX,
const valarray<double>& Y, int nColsY )
{
if( X.size() == 0 || Y.size() == 0 )
return valarray<double>(0);
//
// Row Major Matrices
//
// C = alpha * A * B + beta * C --- (1)
//
// A : m by k lda (stride) = k
// B : k by n ldb (stride) = n
// C : m by n ldc (stride) = n
//
//
// Column Major Matrices
//
// Z = alpha * X * Y + beta * C --- (2)
// Z = C^t
// = alpha * B^t * A^t + beta * C^t --- (3)
//
// X = B^t : n by k ldx (stride) = n
// Y = A^t : k by m ldy (stride) = k
// Z = C^t : n by m ldz (stride) = n
//
const int m = nColsY;
const int k = nColsX;
const int n = X.size() / k; assert( n*k == X.size() );
valarray<double> Z( n * m );
const double *pX = &X[0];
const double *pY = &Y[0];
double *pZ = &(Z[0]);
int lda = n;
int ldb = k;
int ldc = n;
cblas_dgemm( CblasColMajor,
CblasNoTrans,
CblasNoTrans,
n, // #rows of the first matrix
m, // #cols of the second matrix
k, // #cols of the first which is equal to the second matrix
ALPHA,
pX, // B^t
lda, // stride of B^t = #rows in B^t = #cols of B
pY, // A^t
ldb, // stride of A^t = #rows of A^t = #cols of A
BETA,
pZ, // C^t
ldc // stride of C^t = #rows of C^t = #cols of C
);
return Z;
}
double CMinimizerThread::ComputeChi2r(valarray<double> & chis, unsigned int n_params)
{
// Square the numerator, divide by the uncertainties
chis *= chis;
double chi2_sum = chis.sum();
// Now compute the sum dividied by (n_data - n_params - 1)
return chi2_sum / (chis.size() - n_params - 1);
}
valarray<cmplx> z_values(const valarray<float>& x_coords,
const valarray<float>& y_coords) {
valarray<cmplx> zs(x_coords.size()*y_coords.size());
size_t i {0};
for (auto y: y_coords)
for (auto x: x_coords) {
complex<float> z(x, y);
zs[i++] = z;
}
return zs;
}
vector<int> total_times(const valarray<bool>& v)
{
vector<int> total(v.size()+1);
total[0] = 0;
for(int i=0;i<v.size();i++) {
total[i+1] = total[i];
if (v[i]) total[i+1]++;
}
return total;
}
vector<int> regeneration_times(const valarray<bool>& v)
{
vector<int> times;
times.push_back(0);
for(int i=1;i<v.size();i++) {
if (v[i] and not v[i-1])
times.push_back(i);
}
times.push_back(v.size());
return times;
}
bool updateEigenSystem(unsigned max_tries, unsigned max_iters) {
if (max_iters==0) max_iters = 30 * p.n;
static double lastGoodMinimumEigenValue = 1.0;
/* Try to get a valid calculation */
for (unsigned tries = 0; tries < max_tries; ++tries) {
unsigned iters = eig( p.n, C, d, B, max_iters);
if (iters < max_iters)
{ // all is well
/* find largest/smallest eigenvalues */
double minEV = d.min();
double maxEV = d.max();
/* (MK Original comment was) :Limit Condition of C to dMaxSignifKond+1
* replaced dMaxSignifKond with 1./numeric_limits<double>::epsilon()
* */
if (maxEV * numeric_limits<double>::epsilon() > minEV) {
double tmp = maxEV * numeric_limits<double>::epsilon() - minEV;
minEV += tmp;
for (unsigned i=0;i<p.n;++i) {
C[i][i] += tmp;
d[i] += tmp;
}
} /* if */
lastGoodMinimumEigenValue = minEV;
d = sqrt(d);
//flgEigensysIsUptodate = 1;
//genOfEigensysUpdate = gen;
//clockeigensum += clock() - clockeigenbegin;
return true;
} /* if cIterEig < ... */
// numerical problems, ignore them and try again
/* Addition des letzten minEW auf die Diagonale von C */
/* Add the last known good eigen value to the diagonal of C */
double summand = lastGoodMinimumEigenValue * exp((double) tries);
for (unsigned i = 0; i < p.n; ++i)
C[i][i] += summand;
} /* for iEigenCalcVers */
return false;
}
/**
* Implementation of Graham's scan convex hull finding algorithm.
* X and Y give the horizontal and vertical positions of the pointset.
* The result is returned in hull as a list of indices referencing points in X and Y.
*/
void convex(valarray<double> const & X, valarray<double> const & Y, vector<unsigned> & h) {
unsigned n=X.size();
COLA_ASSERT(n==Y.size());
unsigned p0=0;
// find point p0 with min Y position, choose leftmost in case of tie.
// This is our "pivot" point
double minY=DBL_MAX,minX=DBL_MAX;
for(unsigned i=0;i<n;i++) {
if ( (Y[i] < minY) || ((Y[i] == minY) && (X[i] < minX)) )
{
p0=i;
minY=Y[i];
minX=X[i];
}
}
// sort remaining points by the angle line p0-p1 (p1 in points) makes
// with x-axis
vector<unsigned> points;
for(unsigned i=0;i<n;i++) {
if(i!=p0) points.push_back(i);
}
CounterClockwiseOrder order(p0,X,Y);
sort(points.begin(),points.end(),order);
// now we maintain a stack in h, adding points while each successive
// point is a "left turn", backtracking if we make a right turn.
h.clear();
h.push_back(p0);
h.push_back(points[0]);
for(unsigned i=1;i<points.size();i++) {
double o=crossProduct(
X[h[h.size()-2]],Y[h[h.size()-2]],
X[h[h.size()-1]],Y[h[h.size()-1]],
X[points[i]],Y[points[i]]);
if(o==0) {
h.pop_back();
h.push_back(points[i]);
} else if(o>0) {
h.push_back(points[i]);
} else {
while(o<=0 && h.size()>2) {
h.pop_back();
o=crossProduct(
X[h[h.size()-2]],Y[h[h.size()-2]],
X[h[h.size()-1]],Y[h[h.size()-1]],
X[points[i]],Y[points[i]]);
}
h.push_back(points[i]);
}
}
}
double quantile(const valarray<double>& values, double Q)
{
assert(0 <= Q and Q <= 1.0);
assert(values.size() > 0);
if (values.size() == 1)
return values[0];
// sort values
vector<double> values2(values.size());
for(int i=0;i<values.size();i++)
values2[i] = values[i];
return quantile(values2,Q);
}
log_double_t dirichlet_pdf(const valarray<double>& p,const valarray<double>& n)
{
assert(p.size() == n.size());
log_double_t Pr = 1;
for(int i=0; i<p.size(); i++)
Pr *= pow(log_double_t(p[i]),n[i]-1.0);
// This term is constant in p
Pr.log() += log_gamma(n.sum());
for(int i=0; i<p.size(); i++)
Pr.log() -= log_gamma(n[i]);
return Pr;
}