Vector4d compute_grad(Vector4d beta, VectorXd x, VectorXd y){
Vector4d grad;
ArrayXd tmp;
ArrayXd pred = model_fun(beta, x);
assert(x.size()==y.size());
// beta(0)
tmp = 1 / (1 + exp(-(x.array()-beta(2))/abs(beta(3))));
tmp *= pred - y.array();
grad(0) = tmp.sum() / x.size();
// beta(1)
tmp = 1 / (1 + exp(-(x.array()-beta(2))/abs(beta(3))));
tmp = 1 - tmp;
tmp *= pred - y.array();
grad(1) = tmp.sum() / x.size();
// beta(2)
tmp = -(beta(0)- beta(1)) * (exp((beta(2)-x.array())/abs(beta(3)))/abs(beta(3))) \
/ (1+exp((beta(2)-x.array())/abs(beta(3)))).pow(2);
tmp *= pred - y.array();
grad(2) = tmp.sum() / x.size();
// beta(3)
tmp = (beta(0) - beta(1)) * (beta(2)-x.array()).pow(2) * sgn(beta(3)) \
/ (abs(beta(3))*pow(beta(3), 2)*(1+exp((beta(2)-x.array())/abs(beta(3)))).pow(2));
tmp *= pred - y.array();
grad(3) = tmp.sum() / x.size();
return grad;
}
inline ArrayXd lm::Dplus(const ArrayXd& d) {
ArrayXd di(d.size());
double comp(d.maxCoeff() * threshold());
for (int j = 0; j < d.size(); ++j) di[j] = (d[j] < comp) ? 0. : 1./d[j];
m_r = (di != 0.).count();
return di;
}
//@{
double gammaDist::aic (const ArrayXd& y, const ArrayXd& n, const ArrayXd& mu,
const ArrayXd& wt, double dev) const {
double nn(wt.sum());
double disp(dev/nn);
double ans(0), invdisp(1./disp);
for (int i = 0; i < mu.size(); ++i)
ans += wt[i] * ::Rf_dgamma(y[i], invdisp, mu[i] * disp, true);
return -2. * ans + 2.;
}
double computeBinWidth(const MatrixXd& positions) {
// assumes first col of positions corresponds to dominant eigenvect
ArrayXd firstCol = positions.col(0).array();
firstCol -= firstCol.mean();
double SSE = firstCol.matrix().squaredNorm();
double variance = SSE / firstCol.size();
double std = sqrt(variance);
double targetBinsPerStd = (MAX_HASH_VALUE - HASH_VALUE_OFFSET) / TARGET_HASH_SPREAD_STDS;
return std / targetBinsPerStd;
}
VectorXd probutils::logsumexp (const MatrixXd& X)
{
const VectorXd mx = X.rowwise().maxCoeff(); // Get max of each row
// Perform the sum(exp(x - mx)) part
ArrayXd se = ((X.colwise() - mx).array().exp()).rowwise().sum();
// return total log(sum(exp(x))) - hoping for return value optimisation
return (se.log()).matrix() + mx;
}
ArrayXd GoSUM::CModelVariables::hcPoint2ModelPoint(const ArrayXd &x)
{
if ( x.size()!=mvs.size() ) throw "GoSUM::CModelVariables::hcPoint2ModelPoint error: wrong dimension";
int j,dim=int(x.size());
ArrayXd X(dim);
for ( j=0; j<dim; j++ )
{ X(j)=mvs[j].generateSampleValue(x(j)); }
return X;
}
void Functions::modeProfileSinc(RefArrayXd predictions, const RefArrayXd covariates,
const double centroid, const double height, const double resolution)
{
ArrayXd sincFunctionArgument = Functions::PI*(covariates - centroid)/resolution;
ArrayXd sincFunction = sincFunctionArgument.sin() / sincFunctionArgument;
// Multiply the profile by the height in the PSD
predictions = height*sincFunction.square();
}
void CMATLAB::matPut(string filename,const ArrayXd &X,string Xname)
{
MATFile *pmat=matOpen(filename,string("w"));
if (!pmat) throw "CMATLAB::exportTo error: matOpen failed";
mxArray *pa=mxCreateDoubleMatrix((int)X.size(),1);
if (!pa) throw "CMATLAB::exportTo error: mxCreateDoubleMatrix failed";
memcpy((void *)(mxGetPr(pa)), (void *)X.data(), X.size()*sizeof(double));
if (!matPutVariable(pmat,string("X"),pa)) throw "CMATLAB::exportTo error: matlab.matPutVariable failed";
mxDestroyArray(pa);
if (!matClose(pmat)) throw "CMATLAB::exportTo error: matlab.matClose failed";
}
AFI::AFI(const bool prompt) : SteadyState() {
if (prompt) cout << "Enter flip-angle (degrees): " << flush;
double inFlip;
QI::Read(cin, inFlip);
m_flip = ArrayXd::Ones(1) * inFlip * M_PI / 180.;
if (prompt) cout << "Enter TR1 & TR2 (seconds): " << flush;
ArrayXd temp;
QI::ReadArray(cin, temp);
if (temp.rows() != 2)
QI_EXCEPTION("Must enter 2 TR values.");
m_TR1 = temp[0]; m_TR2 = temp[1];
}
SSFPSimple::SSFPSimple(const ArrayXd &flip, const double TR, const ArrayXd &phi) :
SteadyState()
{
m_TR = TR;
m_flip = (flip * M_PI / 180.).replicate(phi.rows(), 1);
m_nphi = phi.size();
m_phi = ArrayXd::Zero(m_flip.size());
int start = 0;
for (int i = 0; i < phi.size(); i++) {
m_phi.segment(start, flip.size()).setConstant(phi[i] * M_PI / 180.);
start += flip.size();
}
}
void CMATLAB::matGet(string filename,ArrayXd &X,string Xname)
{
MATFile *pmat=matOpen(filename,string("r"));
if (!pmat) throw "CMATLAB::importFrom error: matlab.matOpen failed";
mxArray *pa=matGetVariable(pmat,Xname);
if (!pa) throw "CMATLAB::importFrom error: matlab.matGetVariable failed";
int N=mxGetNumberOfElements(pa);
if (N<=0) throw "CMATLAB::importFrom error: matlab.mxGetNumberOfElements failed";
X.resize(N);
memcpy((void *)(mxGetPr(pa)), (void *)X.data(), sizeof((double *)X.data()));
mxDestroyArray(pa);
if (!matClose(pmat)) throw "CMATLAB::importFrom error: matlab.matClose failed";
}
int gesdd(MatrixXd& A, ArrayXd& S, MatrixXd& Vt) {
int info, mone = -1, m = A.rows(), n = A.cols();
std::vector<int> iwork(8 * n);
double wrk;
if (m < n || S.size() != n || Vt.rows() != n || Vt.cols() != n)
throw std::invalid_argument("dimension mismatch in gesvd");
F77_CALL(dgesdd)("O", &m, &n, A.data(), &m, S.data(), A.data(),
&m, Vt.data(), &n, &wrk, &mone, &iwork[0], &info);
int lwork(wrk);
std::vector<double> work(lwork);
F77_CALL(dgesdd)("O", &m, &n, A.data(), &m, S.data(), A.data(),
&m, Vt.data(), &n, &work[0], &lwork, &iwork[0], &info);
return info;
}
NOMAD::Point CMADS::ArrayXd2NOMADPoint(const ArrayXd &x)
{
int i,n=int(x.size());
NOMAD::Point p(n);
for ( i=0; i<n; i++ ) p[i]=x(i);
return p;
}
void GoSUM::CModelVariables::setNTuple(const ArrayXd &X,int _at)
{
if ( X.size()!=mvs.size() ) throw "GoSUM::CModelVariables::setNTuple error: bad nTupe size";
int i,N=int(mvs.size());
for ( i=0; i<N; i++ ) mvs[i].setSampleValue(X(i),_at);
}
//@{
double negativeBinomialDist::aic (const ArrayXd& y, const ArrayXd& n, const ArrayXd& mu,
const ArrayXd& wt, double dev) const {
return 2. * (wt * (y + d_theta) * (mu + d_theta).log() -
y * mu.log() + (y + 1).unaryExpr(Lgamma<double>()) -
d_theta * std::log(d_theta) + lgamma(d_theta) -
(d_theta + y).unaryExpr(Lgamma<double>())).sum();
}
void CMT::HistogramNonlinearity::setParameters(const ArrayXd& parameters) {
if(parameters.size() != mHistogram.size())
throw Exception("Wrong number of parameters.");
for(int i = 0; i < mHistogram.size(); ++i)
mHistogram[i] = parameters[i];
}
double glmDist::aic(const ArrayXd& y, const ArrayXd& n, const ArrayXd& mu,
const ArrayXd& wt, double dev) const {
int nn = mu.size();
double ans =
::Rf_asReal(::Rf_eval(::Rf_lang6(as<SEXP>(d_aic),
as<SEXP>(NumericVector(y.data(), y.data() + nn)),
as<SEXP>(NumericVector(n.data(), n.data() + nn)),
as<SEXP>(NumericVector(mu.data(), mu.data() + nn)),
as<SEXP>(NumericVector(wt.data(), wt.data() + nn)),
PROTECT(::Rf_ScalarReal(dev))), d_rho));
UNPROTECT(1);
return ans;
}
Trajectory Trajectory::generateMinJerkTrajectory(const VectorXd& ts, const VectorXd& y_from, const VectorXd& y_to)
{
int n_time_steps = ts.size();
int n_dims = y_from.size();
MatrixXd ys(n_time_steps,n_dims), yds(n_time_steps,n_dims), ydds(n_time_steps,n_dims);
double D = ts[n_time_steps-1];
ArrayXd tss = (ts/D).array();
ArrayXd A = y_to.array()-y_from.array();
for (int i_dim=0; i_dim<n_dims; i_dim++)
{
// http://noisyaccumulation.blogspot.fr/2012/02/how-to-decompose-2d-trajectory-data.html
ys.col(i_dim) = y_from[i_dim] + A[i_dim]*( 6*tss.pow(5) -15*tss.pow(4) +10*tss.pow(3));
yds.col(i_dim) = (A[i_dim]/D)*( 30*tss.pow(4) -60*tss.pow(3) +30*tss.pow(2));
ydds.col(i_dim) = (A[i_dim]/(D*D))*(120*tss.pow(3) -180*tss.pow(2) +60*tss );
}
return Trajectory(ts,ys,yds,ydds);
}
const ArrayXd glmDist::devResid(const ArrayXd &y, const ArrayXd &mu, const ArrayXd &wt) const {
int n = mu.size();
return as<ArrayXd>(::Rf_eval(::Rf_lang4(as<SEXP>(d_devRes),
as<SEXP>(NumericVector(y.data(), y.data() + n)),
as<SEXP>(NumericVector(mu.data(), mu.data() + n)),
as<SEXP>(NumericVector(wt.data(), wt.data() + n))
), d_rho));
}
//@{
double binomialDist::aic (const ArrayXd& y, const ArrayXd& n, const ArrayXd& mu,
const ArrayXd& wt, double dev) const {
ArrayXd m((n > 1).any() ? n : wt);
ArrayXd yy((m * y).unaryExpr(Round<double>()));
m = m.unaryExpr(Round<double>());
double ans(0.);
for (int i=0; i < mu.size(); ++i)
ans += (m[i] <= 0. ? 0. : wt[i]/m[i]) * ::Rf_dbinom(yy[i], m[i], mu[i], true);
return (-2. * ans);
}
double Functions::logGaussLikelihood(const RefArrayXd observations, const RefArrayXd predictions, const RefArrayXd uncertainties)
{
if ((observations.size() != predictions.size()) || (observations.size() != uncertainties.size()))
{
cerr << "Array dimensions do not match. Quitting program." << endl;
exit(EXIT_FAILURE);
}
ArrayXd delta;
ArrayXd lambda0;
ArrayXd lambda;
delta = ((observations - predictions)*(observations - predictions)) / (uncertainties*uncertainties);
lambda0 = -1.*log(sqrt(2.*PI) * uncertainties);
lambda = lambda0 -0.5*delta;
return lambda.sum();
}
ArrayXd GoSUM::CModelVariables::expandNTuple(const ArrayXd &X) const
{
if ( X.size()!=mvs.size() ) throw "GoSUM::CModelVariables::expand error: wrong X size";
int i,j,k,N=int(mvs.size()),eN=expandedSize(),exsize;
ArrayXd eX=ArrayXd::Zero(eN);
for ( i=j=0; i<N; i++,j+=exsize )
{ exsize=mvs[i].expandedSize();
if ( exsize==1 ) { eX(j)=X(i); }
else { for ( k=0; k<exsize; k++ ) if (k==X(i)) { eX(j+k) = 1.; break; } } }
return eX;
}
void merPredD::updateXwts(const ArrayXd& sqrtXwt) {
if (d_Xwts.size() != sqrtXwt.size())
throw invalid_argument("updateXwts: dimension mismatch");
std::copy(sqrtXwt.data(), sqrtXwt.data() + sqrtXwt.size(), d_Xwts.data());
if (sqrtXwt.size() == d_V.rows()) { // W is diagonal
d_V = d_Xwts.asDiagonal() * d_X;
for (int j = 0; j < d_N; ++j)
for (MSpMatrixd::InnerIterator Utj(d_Ut, j), Ztj(d_Zt, j);
Utj && Ztj; ++Utj, ++Ztj)
Utj.valueRef() = Ztj.value() * d_Xwts.data()[j];
} else {
SpMatrixd W(d_V.rows(), sqrtXwt.size());
const double *pt = sqrtXwt.data();
W.reserve(sqrtXwt.size());
for (Index j = 0; j < W.cols(); ++j, ++pt) {
W.startVec(j);
W.insertBack(j % d_V.rows(), j) = *pt;
}
W.finalize();
d_V = W * d_X;
SpMatrixd Ut(d_Zt * W.adjoint());
if (Ut.cols() != d_Ut.cols())
throw std::runtime_error("Size mismatch in updateXwts");
// More complex code to handle the pruning of zeros
MVec(d_Ut.valuePtr(), d_Ut.nonZeros()).setZero();
for (int j = 0; j < d_Ut.outerSize(); ++j) {
MSpMatrixd::InnerIterator lhsIt(d_Ut, j);
for (SpMatrixd::InnerIterator rhsIt(Ut, j); rhsIt; ++rhsIt, ++lhsIt) {
Index k(rhsIt.index());
while (lhsIt && lhsIt.index() != k) ++lhsIt;
if (lhsIt.index() != k)
throw std::runtime_error("Pattern mismatch in updateXwts");
lhsIt.valueRef() = rhsIt.value();
}
}
}
d_VtV.setZero().selfadjointView<Eigen::Upper>().rankUpdate(d_V.adjoint());
updateL();
}
const ArrayXd binomialDist::devResid(const ArrayXd& y, const ArrayXd& mu, const ArrayXd& wt) const {
int debug=0;
if (debug) {
for (int i=0; i < mu.size(); ++i) {
double r = 2. * wt[i] * (Y_log_Y(y[i], mu[i]) + Y_log_Y(1. - y[i], 1. - mu[i]));
if (r!=r) {
// attempt to detect `nan` (needs cross-platform testing, but should compile
// everywhere whether or not it actually works)
Rcpp::Rcout << "(bD) " << "nan @ pos " << i << ": y= " << y[i]
<< "; mu=" << mu[i]
<< "; wt=" << wt[i]
<< "; 1-y=" << 1. - y[i]
<< "; 1-mu=" << 1. - mu[i]
<< "; ylogy=" << Y_log_Y(y[i], mu[i])
<< "; cylogy=" << Y_log_Y(1.-y[i], 1.-mu[i])
<< std::endl;
}
}
}
return 2. * wt * (Y_log_Y(y, mu) + Y_log_Y(1. - y, 1. - mu));
}
double MeanNormalLikelihood::logValue(RefArrayXd modelParameters)
{
unsigned long n = observations.size();
double lambda0;
double lambda;
ArrayXd argument;
ArrayXd predictions;
predictions.resize(n);
predictions.setZero();
model.predict(predictions, modelParameters);
argument = (observations - predictions);
argument = argument.square()*weights;
lambda0 = lgammal(n/2.) - log(2) - (n/2.)*log(Functions::PI) + 0.5*weights.log().sum();
lambda = lambda0 - (n/2.)*log(argument.sum());
return lambda;
}
void NestedSampler::setLogWeightOfPosteriorSample(ArrayXd newLogWeightOfPosteriorSample)
{
int Nsamples = newLogWeightOfPosteriorSample.size();
logWeightOfPosteriorSample.resize(Nsamples);
logWeightOfPosteriorSample = newLogWeightOfPosteriorSample;
}
const ArrayXd glmLink::muEta(const ArrayXd &eta) const {
return as<ArrayXd>(::Rf_eval(::Rf_lang2(as<SEXP>(d_muEta),
as<SEXP>(Rcpp::NumericVector(eta.data(),
eta.data() + eta.size()))
), d_rho));
}
const ArrayXd glmDist::variance(const ArrayXd &mu) const {
return as<ArrayXd>(::Rf_eval(::Rf_lang2(as<SEXP>(d_variance),
as<SEXP>(Rcpp::NumericVector(mu.data(),
mu.data() + mu.size()))
), d_rho));
}
MatrixXd NumInt::GuassLobattoQaudrature(const int &N) {
int N0=N;
double a=1.0; double b=1.0;
double a1=2.0; double b1 = 2.0;
if (N0>=1)
{
N0=N0-2;
}
// Build the pointers
int* _N = &N0;
double* _a=&a; double* _b=&b;
double* _a1=&a1; double* _b1=&b1;
// Initial Guess - Chebyshev-Gauss-Lobatto points
ArrayXd xu;
xu.setLinSpaced(N0+2,0.0,N0+1);
ArrayXd x=-cos(xu/(N0+1)*M_PI);
// Allocate space for points and weights
VectorXd z = VectorXd::Zero(x.size());
VectorXd w = VectorXd::Zero(x.size());
double x0,x1,del; double* _x0 = &x0; double* _x1 = &x1;
double deps = std::numeric_limits<double>::epsilon();
for (int k=0; k<=x.size()-1; k++)
{
x0=x(k);
del=2.0;
while (fabs(del) > deps)
{
// Polynomial Deflation: Exclude the already determined roots
VectorXd s1 = x.head(k);
VectorXd ones = VectorXd::Constant(s1.size(),1);
double s = (ones.cwiseQuotient((x0-s1.array()).matrix())).sum();
// Compute Jacobi polynomial p(a,b)
JacobiPolynomials J(_N,_a,_b,_x0,false);
VectorXd p = J.getJacobiPolynomials();
// Compute Jacobi polynomial p(a+1,b+1) for derivative dp(a,b)
JacobiPolynomials J1(_N,_a1,_b1,_x0,false);
VectorXd p1 = J1.getJacobiPolynomials();
VectorXd dp=VectorXd::Zero(p1.size()); dp(0)=0;
// Compute derivative of Jacobi polynomial p(a,b)
for (int j=0; j<=*_N-1; j++)
{
dp(j+1) = 0.5*(*_a+*_b+j+2)*p1(j);
}
//Gauss-Lobatto points are roots of (1-x^2)*dp, hence
double nom = (1-x0*x0)*p(N0); double dnom = -2*x0*p(N0)+(1-x0*x0)*dp(N0);
del = - nom/(dnom-nom*s);
x1 = x0+del;
x0=x1;
}
z(k)=x1;
double a2=0; double b2=0; int N1=N0+1;
double* _a2=&a2; double* _b2=&b2; int* _N1 = &N1;
JacobiPolynomials J(_N1,_a2,_b2,_x1,false);
VectorXd p = J.getJacobiPolynomials();
w(k) = 2.0/((N1)*(N1+1)*p(N1)*p(N1));
}
// Store
Matrix<double,Dynamic,Dynamic> zw(N0+2,2);
zw.col(0)=z;
zw.col(1)=w;
return zw;
}
MatrixXd NumInt::GuassQaudrature(const int& N, double& a, double& b) {
int N0=N-1;
const int N1 = N0+1;
const int N2 = N0+2;
VectorXd xu;
xu.setLinSpaced(N1,-1.0,1.0);
// Legendre-Gauss-Vandermonde Matrix
//Matrix<double,N1,N2> L = Matrix<double,N1,N2>::Zero();
MatrixXd L(N1,N2);
L = MatrixXd::Zero(N1,N2);
// Derivative of Legendre-Gauss-Vandermonde Matrix
//Matrix<double,N1,1> Lp = Matrix<double,N1,1>::Zero();
VectorXd Lp(N1);
Lp = VectorXd::Zero(N1);
VectorXd dum;
dum.setLinSpaced(N1,0.0,N0);
ArrayXd y;
y = cos((2*dum.array()+1)*M_PI/(2*N0+2))+(0.27/N1)*sin(M_PI*xu.array()*N0/N2);
double deps = std::numeric_limits<double>::epsilon();
//Initial Guess
//Array<double,N1,1> y0 = Array<double,N1,1>::Constant(2);
ArrayXd y0 = ArrayXd::Constant(N1,2);
while ((y-y0).abs().matrix().maxCoeff() > deps) {
// L.col(0) = Matrix<double,N1,1>::Constant(1);
L.col(0) = VectorXd::Constant(N1,1);
//Lp = Matrix<double,N1,1>::Zero();
Lp = VectorXd::Zero(N1);
L.col(1) = y;
for (int k=1; k!=N1; k++)
{
L.col(k+1) = ((2*k+1)*L.col(k).cwiseProduct(y.matrix())-k*L.col(k-1))/(k+1);
}
Lp = (N2)*(L.col(N0)-L.col(N1).cwiseProduct(y.matrix())).cwiseQuotient((1-y.square()).matrix());
y0 = y;
y = y0-(L.col(N1).cwiseQuotient(Lp)).array();
}
// Gauss Points
//Matrix<double,N1,1> z = ((a*(1-y)+b*(1+y))/2).matrix();
VectorXd z(N1);
z = ((a*(1-y)+b*(1+y))/2).matrix();
// Gauss Weights
//Matrix<double,N1,1> w;
VectorXd w(N1);
w = (b-a)/(((1-y.square()).matrix()).cwiseProduct(Lp.cwiseProduct(Lp))).array()*pow((double)N2/N1,2);
// Store
//Matrix<double,N1,2> zw;
Matrix<double,Dynamic,Dynamic> zw(N1,2);
zw.col(0)=z;
zw.col(1)=w;
return zw;
}
