void IntensityTransformer::Apply(cv::Mat &mat)
{
auto seed = GetSeed();
auto rng = m_rngs.pop_or_create([seed]() { return std::make_unique<std::mt19937>(seed); } );
// Using single precision as EigVal and EigVec matrices are single precision.
std::normal_distribution<float> d(0, (float)m_curStdDev);
cv::Mat alphas(1, 3, CV_32FC1);
assert(m_eigVal.rows == 1 && m_eigVec.cols == 3);
alphas.at<float>(0) = d(*rng) * m_eigVal.at<float>(0);
alphas.at<float>(1) = d(*rng) * m_eigVal.at<float>(1);
alphas.at<float>(2) = d(*rng) * m_eigVal.at<float>(2);
m_rngs.push(std::move(rng));
assert(m_eigVec.rows == 3 && m_eigVec.cols == 3);
cv::Mat shifts = m_eigVec * alphas.t();
// For multi-channel images data is in BGR format.
size_t cdst = mat.rows * mat.cols * mat.channels();
ElemType* pdstBase = reinterpret_cast<ElemType*>(mat.data);
for (ElemType* pdst = pdstBase; pdst < pdstBase + cdst;)
{
for (int c = 0; c < mat.channels(); c++)
{
float shift = shifts.at<float>(mat.channels() - c - 1);
*pdst = std::min(std::max(*pdst + shift, (ElemType)0), (ElemType)255);
pdst++;
}
}
}
Mat PcaModel::drawSample(float sigma /*= 1.0f*/)
{
std::normal_distribution<float> distribution(0.0f, sigma); // TODO: c'tor takes the stddev. Update all the documentation!!!
vector<float> alphas(getNumberOfPrincipalComponents());
for (auto& a : alphas) {
a = distribution(engine);
}
return drawSample(alphas);
/* without calling drawSample(alphas): (maybe if we add noise)
Mat alphas = Mat::zeros(getNumberOfPrincipalComponents(), 1, CV_32FC1);
for (int row=0; row < alphas.rows; ++row) {
alphas.at<float>(row, 0) = distribution(engine);
}
*/
/* with noise: (does the noise make sense in drawSample(vector<float> coefficients)?)
unsigned int vsize = mean.size();
vector epsilon = Utils::generateNormalVector(vectorSize) * sqrt(m_noiseVariance);
return m_mean + m_pcaBasisMatrix * coefficients + epsilon;
*/
}
void write_tasks(transport::repository<>& repo, transport::step_mpi<>* model)
{
const double M_P = 1.0;
const double m = 1E-5 * M_P;
const double c = 0.0018;
const double d = 0.022 * M_P;
const double phi0 = 14.84 * M_P;
const double phi_init = 16.5 * M_P;
const double N_init = 0.0;
const double N_pre = 6.0;
const double N_max = 50.1;
transport::parameters<> params(M_P, { m, c, d, phi0 }, model);
transport::initial_conditions<> ics("step", params, { phi_init }, N_init, N_pre);
transport::basic_range<> times(N_init, N_max, 100, transport::spacing::linear);
transport::basic_range<> ks(exp(7.0), exp(11.5), 1000, transport::spacing::log_bottom);
transport::basic_range<> alphas(0.0, 0.0, 0, transport::spacing::linear);
transport::basic_range<> betas(1.0/3.0, 1.0/3.0, 0, transport::spacing::linear);
// construct a threepf task
transport::threepf_alphabeta_task<> tk3("step.threepf", ics, times, ks, alphas, betas);
tk3.set_collect_initial_conditions(true).set_adaptive_ics_efolds(5.0);
transport::zeta_threepf_task<> ztk3("step.threepf-zeta", tk3);
repo.commit(ztk3);
}
/**
* Compute the search direction based on the current (inverse) Hessian
* approximation and given gradient.
*
* @param[out] pk The negative product of the inverse Hessian and gradient
* direction gk.
* @param[in] gk Gradient direction.
**/
inline void search_direction(VectorT &pk, const VectorT &gk) const {
std::vector<Scalar> alphas(_buf.size());
typename
boost::circular_buffer<UpdateT>::const_reverse_iterator buf_rit;
typename boost::circular_buffer<UpdateT>::const_iterator buf_it;
typename std::vector<Scalar>::const_iterator alpha_it;
typename std::vector<Scalar>::reverse_iterator alpha_rit;
pk.noalias() = -gk;
for (buf_rit = _buf.rbegin(), alpha_rit = alphas.rbegin();
buf_rit != _buf.rend();
buf_rit++, alpha_rit++) {
Scalar alpha;
const Scalar &rhoi(boost::get<0>(*buf_rit));
const VectorT &yi(boost::get<1>(*buf_rit));
const VectorT &si(boost::get<2>(*buf_rit));
alpha = rhoi * si.dot(pk);
pk -= alpha * yi;
*alpha_rit = alpha;
}
pk *= _gammak;
for (buf_it = _buf.begin(), alpha_it = alphas.begin();
buf_it != _buf.end();
buf_it++, alpha_it++) {
Scalar beta;
const Scalar &rhoi(boost::get<0>(*buf_it));
const VectorT &yi(boost::get<1>(*buf_it));
const VectorT &si(boost::get<2>(*buf_it));
beta = rhoi*yi.dot(pk);
pk += (*alpha_it - beta)*si;
}
}
Mat PcaModel::drawSample(vector<float> coefficients)
{
Mat alphas(coefficients);
Mat sqrtOfEigenvalues = eigenvalues.clone();
for (unsigned int i = 0; i < eigenvalues.rows; ++i) {
sqrtOfEigenvalues.at<float>(i) = std::sqrt(eigenvalues.at<float>(i));
}
//Mat smallBasis = pcaBasis(cv::Rect(0, 0, 55, 100));
//Mat smallMean = mean(cv::Rect(0, 0, 1, 100));
Mat modelSample = mean + pcaBasis * alphas.mul(sqrtOfEigenvalues); // Surr
//Mat modelSample = mean + pcaBasis * alphas; // Bsl .h5 old
return modelSample;
}
double bin_sugeno::operator()(const p_dna&d)
{
fuzzy::Function*y_function=fuzzy::function3(fuzzy::coord(0,0),
fuzzy::coord(0.5,1.0),
fuzzy::coord(1.0,0));
fuzzy::MyuFunctions mf={fuzzy::fvector(0),y_function};
const int x_count=m_cdata->x_count();
int i=0;
for(int k=0;k<m_numbers.size();++k)
for(int x=0;x<x_count;++x){
fuzzy::ExpFunction*ff=new fuzzy::ExpFunction(d->get(i),d->get(i+1));
mf.x_funcs.push_back(ff);
i+=2;
}
fuzzy::rule_vector rules=fuzzy::make_rules(*m_cdata,mf,m_numbers);
dvector errors; // ошибка на новых данных
for(int i=0;i<m_numbers.size();++i){
dvector alphas(m_numbers.size());
dvector y_1(m_numbers.size());
// считаем выход по каждому правилу для X из текущего набора
for(int j=0;j<rules.size();++j){
dvector myu_x(x_count);
for(int x=0;x<x_count;++x){
double x_value=(*m_cdata)[m_numbers[i]]->at(x);
myu_x[x]=rules[j](x_value,x);
}
alphas[i]=*std::min_element(myu_x.begin(),myu_x.end());
y_1[i]=rules[i].y();
}
// Собственно вывод. Алгоритм из черной книги
dvector up_mul=alphas*y_1;
double up=std::accumulate(up_mul.begin(),up_mul.end(),0.0);
double down=std::accumulate(alphas.begin(),alphas.end(),0.0);
double etalon=m_cdata->y_for_xp(m_numbers[i]);
double out=up/down; //Выход, для текущего набора
double delta=fabs(out-etalon);
errors.push_back(delta);
}
// Средняя ошибка.
return std::accumulate(errors.begin(),errors.end(),0.0)/errors.size();
}
void write_tasks(transport::repository<>& repo, transport::new_axion_mpi<>* model)
{
const double M_Planck = 1.0;
const double g = 1e-10;
const double f = M_Planck;
const double Lambda = std::pow(g, 1.0/4.0) * std::pow(25.0/(2*M_PI), 1.0/2.0) * M_Planck;
const double phi_init = 23.5 * M_Planck;
const double chi_init = f/2.0 - 0.001*M_Planck;
const double N_init = 0.0;
const double N_pre = 10.0;
const double N_max = 68.0;
transport::parameters<> params(M_Planck, { g, Lambda, f, M_PI }, model);
transport::initial_conditions<> ics("axion_cfs", params, { phi_init, chi_init }, N_init, N_pre);
transport::basic_range<> times(N_init, N_max, 500, transport::spacing::linear);
transport::basic_range<> ks(exp(5.0), exp(5.0), 0, transport::spacing::linear);
transport::basic_range<> alphas(0.0, 0.0, 0, transport::spacing::linear);
transport::basic_range<> beta_equi(1.0/3.0, 1.0/3.0, 0, transport::spacing::linear);
transport::basic_range<> beta_sq(0.95, 0.95, 0, transport::spacing::linear);
// construct a threepf task for the equilateral mode
transport::threepf_alphabeta_task<> tk3_equi("axion_cfs.equi.threepf", ics, times, ks, alphas, beta_equi);
tk3_equi.set_adaptive_ics_efolds(4.0);
tk3_equi.set_collect_initial_conditions(true);
transport::zeta_threepf_task<> ztk3_equi("axion_cfs.equi.threepf-zeta", tk3_equi);
ztk3_equi.set_paired(true);
// construct a threepf task for the squeezed mode
transport::threepf_alphabeta_task<> tk3_sq("axion_cfs.sq.threepf", ics, times, ks, alphas, beta_sq);
tk3_sq.set_adaptive_ics_efolds(4.0);
tk3_sq.set_collect_initial_conditions(true);
transport::zeta_threepf_task<> ztk3_sq("axion_cfs.sq.threepf-zeta", tk3_sq);
ztk3_sq.set_paired(true);
repo.commit(ztk3_equi);
repo.commit(ztk3_sq);
}
PlaneSet::PlaneSet(Material& in_material, int in_nnormal, double* in_normal, int in_noffset, double* in_offset)
:
TriangleSet(in_material,true, false/* true */),
nPlanes(max(in_nnormal, in_noffset)),
normal(in_nnormal, in_normal),
offset(in_noffset, in_offset)
{
/* We'll set up 4 triangles per plane, in case we need to render
a hexagon. Each triangle has 3 vertices (so 12 for the plane), and each vertex
gets 3 color components and 1 alpha component. */
ARRAY<int> colors(36*nPlanes);
ARRAY<double> alphas(12*nPlanes);
if (material.colors.getLength() > 1) {
material.colors.recycle(nPlanes);
for (int i=0; i<nPlanes; i++) {
Color color=material.colors.getColor(i);
for (int j=0; j<12; j++) {
colors.ptr[36*i+3*j+0] = color.getRedub();
colors.ptr[36*i+3*j+1] = color.getGreenub();
colors.ptr[36*i+3*j+2] = color.getBlueub();
alphas.ptr[12*i+j] = color.getAlphaf();
}
}
material.colors.set(12*nPlanes, colors.ptr, 12*nPlanes, alphas.ptr);
material.colorPerVertex(true, 12*nPlanes);
}
ARRAY<double> vertices(36*nPlanes),
normals(36*nPlanes);
for (int i=0; i<vertices.size(); i++)
vertices.ptr[i] = NA_REAL;
for (int i=0; i<nPlanes; i++)
for (int j=0; j<12; j++) {
normals.ptr[36*i+3*j+0] = normal.getRecycled(i).x;
normals.ptr[36*i+3*j+1] = normal.getRecycled(i).y;
normals.ptr[36*i+3*j+2] = normal.getRecycled(i).z;
}
initFaceSet(12*nPlanes, vertices.ptr, normals.ptr, NULL);
}
void assemble_cortical(const Geometry& geo, Matrix& mat, const Head2EEGMat& M, const std::string& domain_name, const unsigned gauss_order, double alpha, double beta, const std::string &filename)
{
// Following the article: M. Clerc, J. Kybic "Cortical mapping by Laplace–Cauchy transmission using a boundary element method".
// Assumptions:
// - domain_name: the domain containing the sources is an innermost domain (defined as the interior of only one interface (called Cortex)
// - Cortex interface is composed of one mesh only (no shared vertices)
// TODO check orders of MxM products for efficiency ... delete intermediate matrices
const Domain& SourceDomain = geo.domain(domain_name);
const Interface& Cortex = SourceDomain.begin()->interface();
const Mesh& cortex = Cortex.begin()->mesh();
// test the assumption
assert(SourceDomain.size() == 1);
assert(Cortex.size() == 1);
// shape of the new matrix:
unsigned Nl = geo.size()-geo.outermost_interface().nb_triangles()-Cortex.nb_vertices()-Cortex.nb_triangles();
unsigned Nc = geo.size()-geo.outermost_interface().nb_triangles();
std::fstream f(filename.c_str());
Matrix P;
if ( !f ) {
// build the HeadMat:
// The following is the same as assemble_HM except N_11, D_11 and S_11 are not computed.
SymMatrix mat_temp(Nc);
mat_temp.set(0.0);
double K = 1.0 / (4.0 * M_PI);
// We iterate over the meshes (or pair of domains) to fill the lower half of the HeadMat (since its symmetry)
for ( Geometry::const_iterator mit1 = geo.begin(); mit1 != geo.end(); ++mit1) {
for ( Geometry::const_iterator mit2 = geo.begin(); (mit2 != (mit1+1)); ++mit2) {
// if mit1 and mit2 communicate, i.e they are used for the definition of a common domain
const int orientation = geo.oriented(*mit1, *mit2); // equals 0, if they don't have any domains in common
// equals 1, if they are both oriented toward the same domain
// equals -1, if they are not
if ( orientation != 0) {
double Scoeff = orientation * geo.sigma_inv(*mit1, *mit2) * K;
double Dcoeff = - orientation * geo.indicator(*mit1, *mit2) * K;
double Ncoeff;
if ( !(mit1->outermost() || mit2->outermost()) && ( (*mit1 != *mit2)||( *mit1 != cortex) ) ) {
// Computing S block first because it's needed for the corresponding N block
operatorS(*mit1, *mit2, mat_temp, Scoeff, gauss_order);
Ncoeff = geo.sigma(*mit1, *mit2)/geo.sigma_inv(*mit1, *mit2);
} else {
Ncoeff = orientation * geo.sigma(*mit1, *mit2) * K;
}
if ( !mit1->outermost() && (( (*mit1 != *mit2)||( *mit1 != cortex) )) ) {
// Computing D block
operatorD(*mit1, *mit2, mat_temp, Dcoeff, gauss_order);
}
if ( ( *mit1 != *mit2 ) && ( !mit2->outermost() ) ) {
// Computing D* block
operatorD(*mit1, *mit2, mat_temp, Dcoeff, gauss_order, true);
}
// Computing N block
if ( (*mit1 != *mit2)||( *mit1 != cortex) ) {
operatorN(*mit1, *mit2, mat_temp, Ncoeff, gauss_order);
}
}
}
}
// Deflate the diagonal block (N33) of 'mat' : (in order to have a zero-mean potential for the outermost interface)
const Interface i = geo.outermost_interface();
unsigned i_first = (*i.begin()->mesh().vertex_begin())->index();
deflat(mat_temp, i, mat_temp(i_first, i_first) / (geo.outermost_interface().nb_vertices()));
mat = Matrix(Nl, Nc);
mat.set(0.0);
// copy mat_temp into mat except the lines for cortex vertices [i_vb_c, i_ve_c] and cortex triangles [i_tb_c, i_te_c].
unsigned iNl = 0;
unsigned i_vb_c = (*cortex.vertex_begin())->index();
unsigned i_ve_c = (*cortex.vertex_rbegin())->index();
unsigned i_tb_c = cortex.begin()->index();
unsigned i_te_c = cortex.rbegin()->index();
for ( unsigned i = 0; i < Nc; ++i) {
if ( !(i_vb_c<=i && i<=i_ve_c) && !(i_tb_c<=i && i<=i_te_c) ) {
mat.setlin(iNl, mat_temp.getlin(i));
++iNl;
}
}
// ** Construct P: the null-space projector **
Matrix W;
{
Matrix U, s;
mat.svd(U, s, W);
}
SparseMatrix S(Nc,Nc);
// we set S to 0 everywhere, except in the last part of the diag:
for ( unsigned i = Nl; i < Nc; ++i) {
S(i, i) = 1.0;
}
P = (W * S) * W.transpose(); // P is a projector: P^2 = P and mat*P*X = 0
if ( filename.length() != 0 ) {
std::cout << "Saving projector P (" << filename << ")." << std::endl;
P.save(filename);
}
} else {
std::cout << "Loading projector P (" << filename << ")." << std::endl;
P.load(filename);
}
// ** Get the gradient of P1&P0 elements on the meshes **
Matrix MM(M.transpose() * M);
SymMatrix RR(Nc, Nc); RR.set(0.);
for ( Geometry::const_iterator mit = geo.begin(); mit != geo.end(); ++mit) {
mit->gradient_norm2(RR);
}
// ** Choose Regularization parameter **
SparseMatrix alphas(Nc,Nc); // diagonal matrix
Matrix Z;
if ( alpha < 0 ) { // try an automatic method... TODO find better estimation
double nRR_v = RR.submat(0, geo.nb_vertices(), 0, geo.nb_vertices()).frobenius_norm();
alphas.set(0.);
alpha = MM.frobenius_norm() / (1.e3*nRR_v);
beta = alpha * 50000.;
for ( Vertices::const_iterator vit = geo.vertex_begin(); vit != geo.vertex_end(); ++vit) {
alphas(vit->index(), vit->index()) = alpha;
}
for ( Meshes::const_iterator mit = geo.begin(); mit != geo.end(); ++mit) {
if ( !mit->outermost() ) {
for ( Mesh::const_iterator tit = mit->begin(); tit != mit->end(); ++tit) {
alphas(tit->index(), tit->index()) = beta;
}
}
}
std::cout << "AUTOMATIC alphas = " << alpha << "\tbeta = " << beta << std::endl;
} else {
for ( Vertices::const_iterator vit = geo.vertex_begin(); vit != geo.vertex_end(); ++vit) {
alphas(vit->index(), vit->index()) = alpha;
}
for ( Meshes::const_iterator mit = geo.begin(); mit != geo.end(); ++mit) {
if ( !mit->outermost() ) {
for ( Mesh::const_iterator tit = mit->begin(); tit != mit->end(); ++tit) {
alphas(tit->index(), tit->index()) = beta;
}
}
}
std::cout << "alphas = " << alpha << "\tbeta = " << beta << std::endl;
}
Z = P.transpose() * (MM + alphas*RR) * P;
// ** PseudoInverse and return **
// X = P * { (M*P)' * (M*P) + (R*P)' * (R*P) }¡(-1) * (M*P)'m
// X = P * { P'*M'*M*P + P'*R'*R*P }¡(-1) * P'*M'm
// X = P * { P'*(MM + a*RR)*P }¡(-1) * P'*M'm
// X = P * Z¡(-1) * P' * M'm
Matrix rhs = P.transpose() * M.transpose();
mat = P * Z.pinverse() * rhs;
}
void TPZArtDiff::Bornhaus(int dim, TPZFMatrix<REAL> &jacinv, TPZVec<T> & sol, TPZVec<TPZDiffMatrix<T> > & Ai, TPZVec<TPZDiffMatrix<T> > & Tau){
#ifdef FASTESTDIFF
int i, j;
int nstate = Ai[0].Rows();
TPZDiffMatrix<T> RTM, RMi,
Y, Yi,
Temp, Temp2,
BornhausTau(nstate, nstate),
LambdaBornhaus;
T us, c;
TPZVec<REAL> alphas(dim,0.);
TPZEulerConsLaw::uRes(sol, us);
TPZEulerConsLaw::cSpeed(sol, 1.4, c);
RMMatrix(sol, us, fGamma, RTM, RMi);
BornhausTau.Redim(nstate, nstate);
for( i = 0; i < dim; i++)
{
for( j = 0; j < dim; j++)
alphas[j] = jacinv(i,j);
ContributeBornhaus(sol, us, c, fGamma, alphas, BornhausTau);
}
RTM. Multiply(BornhausTau, Temp);
Temp.Multiply(RMi, BornhausTau);
for( i = 0; i < dim;i++)
{
Ai[i].Multiply(BornhausTau, Tau[i]);
}
#else
int i, j;
int nstate = Ai[0].Rows();
TPZDiffMatrix<T> Rot, RotT,
Y, Yi,
M, Mi,
Temp, Temp2,
BornhausTau(nstate, nstate),
LambdaBornhaus;
T us, c;
TPZVec<REAL> alphas(dim,0.);
TPZEulerConsLaw::uRes(sol, us);
TPZEulerConsLaw::cSpeed(sol, 1.4, c);
RotMatrix(sol, us, Rot, RotT);
MMatrix(sol, us, fGamma, M, Mi);
for( i = 0; i < dim; i++)
{
for( j = 0; j < dim; j++)
alphas[j] = jacinv(i,j);
EigenSystemBornhaus(sol, us, c, fGamma, alphas,
Y, Yi, LambdaBornhaus);
Y. Multiply(LambdaBornhaus, Temp);
Temp.Multiply(Yi, Temp2);
BornhausTau.Add(Temp2);
}
RotT. Multiply(M, Temp);
Temp. Multiply(BornhausTau, Temp2);
Temp2. Multiply(Mi, Temp);
Temp. Multiply(Rot, BornhausTau);
BornhausTau.Inverse();
for( i = 0; i < dim;i++)
{
Ai[i].Multiply(BornhausTau, Tau[i]);
}
#endif
}
int main(int argc, char *argv[])
{
if (argc<2) {
cout << "\nUsage: " << argv[0] << " L [c=2 w=64 k=80 d=1]" << endl;
cout << " L is the number of levels\n";
cout << " optional c is number of columns in the key-switching matrices (default=2)\n";
cout << " optional w is Hamming weight of the secret key (default=64)\n";
cout << " optional k is the security parameter (default=80)\n";
cout << " optional d specifies GF(2^d) arithmetic (default=1, must be <=16)\n";
// cout << " k is the security parameter\n";
// cout << " m determines the ring mod Phi_m(X)" << endl;
cout << endl;
exit(0);
}
cout.unsetf(ios::floatfield);
cout.precision(4);
long L = atoi(argv[1]);
long c = 2;
long w = 64;
long k = 80;
long d = 1;
if (argc>2) c = atoi(argv[2]);
if (argc>3) w = atoi(argv[3]);
if (argc>4) k = atoi(argv[4]);
if (argc>5) d = atoi(argv[5]);
if (d>16) Error("d cannot be larger than 16\n");
cout << "\nTesting FHE with parameters L="<<L
<< ", c="<<c<<", w="<<w<<", k="<<k<<", d="<<d<< endl;
// get a lower-bound on the parameter N=phi(m):
// 1. Empirically, we use ~20-bit small primes in the modulus chain (the main
// constraints is that 2m must divide p-1 for every prime p). The first
// prime is larger, a 40-bit prime. (If this is a 32-bit machine then we
// use two 20-bit primes instead.)
// 2. With L levels, the largest modulus for "fresh ciphertexts" has size
// q0 ~ p0 * p^{L} ~ 2^{40+20L}
// 3. We break each ciphertext into upto c digits, do each digit is as large
// as D=2^{(40+20L)/c}
// 4. The added noise variance term from the key-switching operation is
// c*N*sigma^2*D^2, and this must be mod-switched down to w*N (so it is
// on part with the added noise from modulus-switching). Hence the ratio
// P that we use for mod-switching must satisfy c*N*sigma^2*D^2/P^2<w*N,
// or P > sqrt(c/w) * sigma * 2^{(40+20L)/c}
// 5. With this extra P factor, the key-switching matrices are defined
// relative to a modulus of size
// Q0 = q0*P ~ sqrt{c/w} sigma 2^{(40+20L)(1+1/c)}
// 6. To get k-bit security we need N>log(Q0/sigma)(k+110)/7.2, i.e. roughly
// N > (40+20L)(1+1/c)(k+110) / 7.2
long ptxtSpace = 2;
double cc = 1.0+(1.0/(double)c);
long N = (long) ceil((pSize*L+p0Size)*cc*(k+110)/7.2);
cout << " bounding phi(m) > " << N << endl;
#if 0 // A small m for debugging purposes
long m = 15;
#else
// pre-computed values of [phi(m),m,d]
long ms[][4] = {
//phi(m) m ord(2) c_m*1000
{ 1176, 1247, 28, 3736},
{ 1936, 2047, 11, 3870},
{ 2880, 3133, 24, 3254},
{ 4096, 4369, 16, 3422},
{ 5292, 5461, 14, 4160},
{ 5760, 8435, 24, 8935},
{ 8190, 8191, 13, 1273},
{10584, 16383, 14, 8358},
{10752, 11441, 48, 3607},
{12000, 13981, 20, 2467},
{11520, 15665, 24, 14916},
{14112, 18415, 28, 11278},
{15004, 15709, 22, 3867},
{15360, 20485, 24, 12767},
// {16384, 21845, 16, 12798},
{17208 ,21931, 24, 18387},
{18000, 18631, 25, 4208},
{18816, 24295, 28, 16360},
{19200, 21607, 40, 35633},
{21168, 27305, 28, 15407},
{23040, 23377, 48, 5292},
{24576, 24929, 48, 5612},
{27000, 32767, 15, 20021},
{31104, 31609, 71, 5149},
{42336, 42799, 21, 5952},
{46080, 53261, 24, 33409},
{49140, 57337, 39, 2608},
{51840, 59527, 72, 21128},
{61680, 61681, 40, 1273},
{65536, 65537, 32, 1273},
{75264, 82603, 56, 36484},
{84672, 92837, 56, 38520}
};
#if 0
for (long i = 0; i < 25; i++) {
long m = ms[i][1];
PAlgebra alg(m);
alg.printout();
cout << "\n";
// compute phi(m) directly
long phim = 0;
for (long j = 0; j < m; j++)
if (GCD(j, m) == 1) phim++;
if (phim != alg.phiM()) cout << "ERROR\n";
}
exit(0);
#endif
// find the first m satisfying phi(m)>=N and d | ord(2) in Z_m^*
long m = 0;
for (unsigned i=0; i<sizeof(ms)/sizeof(long[3]); i++)
if (ms[i][0]>=N && (ms[i][2] % d) == 0) {
m = ms[i][1];
c_m = 0.001 * (double) ms[i][3];
break;
}
if (m==0) Error("Cannot support this L,d combination");
#endif
// m = 257;
FHEcontext context(m);
#if 0
context.stdev = to_xdouble(0.5); // very low error
#endif
activeContext = &context; // Mark this as the "current" context
context.zMstar.printout();
cout << endl;
// Set the modulus chain
#if 1
// The first 1-2 primes of total p0size bits
#if (NTL_SP_NBITS > p0Size)
AddPrimesByNumber(context, 1, 1UL<<p0Size); // add a single prime
#else
AddPrimesByNumber(context, 2, 1UL<<(p0Size/2)); // add two primes
#endif
#endif
// The next L primes, as small as possible
AddPrimesByNumber(context, L);
ZZ productOfCtxtPrimes = context.productOfPrimes(context.ctxtPrimes);
double productSize = context.logOfProduct(context.ctxtPrimes);
// might as well test that the answer is roughly correct
cout << " context.logOfProduct(...)-log(context.productOfPrimes(...)) = "
<< productSize-log(productOfCtxtPrimes) << endl;
// calculate the size of the digits
context.digits.resize(c);
IndexSet s1;
#if 0
for (long i=0; i<c-1; i++) context.digits[i] = IndexSet(i,i);
context.digits[c-1] = context.ctxtPrimes / IndexSet(0,c-2);
AddPrimesByNumber(context, 2, 1, true);
#else
double sizeSoFar = 0.0;
double maxDigitSize = 0.0;
if (c>1) { // break ciphetext into a few digits
double dsize = productSize/c; // initial estimate
double target = dsize-(pSize/3.0);
long idx = context.ctxtPrimes.first();
for (long i=0; i<c-1; i++) { // compute next digit
IndexSet s;
while (idx <= context.ctxtPrimes.last() && sizeSoFar < target) {
s.insert(idx);
sizeSoFar += log((double)context.ithPrime(idx));
idx = context.ctxtPrimes.next(idx);
}
context.digits[i] = s;
s1.insert(s);
double thisDigitSize = context.logOfProduct(s);
if (maxDigitSize < thisDigitSize) maxDigitSize = thisDigitSize;
cout << " digit #"<<i+1<< " " <<s << ": size " << thisDigitSize << endl;
target += dsize;
}
IndexSet s = context.ctxtPrimes / s1; // all the remaining primes
context.digits[c-1] = s;
double thisDigitSize = context.logOfProduct(s);
if (maxDigitSize < thisDigitSize) maxDigitSize = thisDigitSize;
cout << " digit #"<<c<< " " <<s << ": size " << thisDigitSize << endl;
}
else {
maxDigitSize = context.logOfProduct(context.ctxtPrimes);
context.digits[0] = context.ctxtPrimes;
}
// Add primes to the chain for the P factor of key-switching
double sizeOfSpecialPrimes
= maxDigitSize + log(c/(double)w)/2 + log(context.stdev *2);
AddPrimesBySize(context, sizeOfSpecialPrimes, true);
#endif
cout << "* ctxtPrimes: " << context.ctxtPrimes
<< ", log(q0)=" << context.logOfProduct(context.ctxtPrimes) << endl;
cout << "* specialPrimes: " << context.specialPrimes
<< ", log(P)=" << context.logOfProduct(context.specialPrimes) << endl;
for (long i=0; i<context.numPrimes(); i++) {
cout << " modulus #" << i << " " << context.ithPrime(i) << endl;
}
cout << endl;
setTimersOn();
const ZZX& PhimX = context.zMstar.PhimX(); // The polynomial Phi_m(X)
long phim = context.zMstar.phiM(); // The integer phi(m)
FHESecKey secretKey(context);
const FHEPubKey& publicKey = secretKey;
#if 0 // Debug mode: use sk=1,2
DoubleCRT newSk(to_ZZX(2), context);
long id1 = secretKey.ImportSecKey(newSk, 64, ptxtSpace);
newSk -= 1;
long id2 = secretKey.ImportSecKey(newSk, 64, ptxtSpace);
#else
long id1 = secretKey.GenSecKey(w,ptxtSpace); // A Hamming-weight-w secret key
long id2 = secretKey.GenSecKey(w,ptxtSpace); // A second Hamming-weight-w secret key
#endif
ZZX zero = to_ZZX(0);
// Ctxt zeroCtxt(publicKey);
/******************************************************************/
/** TESTS BEGIN HERE ***/
/******************************************************************/
cout << "ptxtSpace = " << ptxtSpace << endl;
GF2X G; // G is the AES polynomial, G(X)= X^8 +X^4 +X^3 +X +1
SetCoeff(G,8); SetCoeff(G,4); SetCoeff(G,3); SetCoeff(G,1); SetCoeff(G,0);
GF2X X;
SetX(X);
#if 1
// code for rotations...
{
GF2X::HexOutput = 1;
const PAlgebra& al = context.zMstar;
const PAlgebraModTwo& al2 = context.modTwo;
long ngens = al.numOfGens();
long nslots = al.NSlots();
DoubleCRT tmp(context);
vector< vector< DoubleCRT > > maskTable;
maskTable.resize(ngens);
for (long i = 0; i < ngens; i++) {
if (i==0 && al.SameOrd(i)) continue;
long ord = al.OrderOf(i);
maskTable[i].resize(ord+1, tmp);
for (long j = 0; j <= ord; j++) {
// initialize the mask that is 1 whenever
// the ith coordinate is at least j
vector<GF2X> maps, alphas, betas;
al2.mapToSlots(maps, G); // Change G to X to get bits in the slots
alphas.resize(nslots);
for (long k = 0; k < nslots; k++)
if (coordinate(al, i, k) >= j)
alphas[k] = 1;
else alphas[k] = 0;
GF2X ptxt;
al2.embedInSlots(ptxt, alphas, maps);
// Sanity-check, make sure that encode/decode works as expected
al2.decodePlaintext(betas, ptxt, G, maps);
for (long k = 0; k < nslots; k++) {
if (alphas[k] != betas[k]) {
cout << " Mask computation failed, i="<<i<<", j="<<j<<"\n";
return 0;
}
}
maskTable[i][j] = to_ZZX(ptxt);
}
}
vector<GF2X> maps;
al2.mapToSlots(maps, G);
vector<GF2X> alphas(nslots);
for (long i=0; i < nslots; i++)
random(alphas[i], 8); // random degree-7 polynomial mod 2
for (long amt = 0; amt < 20; amt++) {
cout << ".";
GF2X ptxt;
al2.embedInSlots(ptxt, alphas, maps);
DoubleCRT pp(context);
pp = to_ZZX(ptxt);
rotate(pp, amt, maskTable);
GF2X ptxt1 = to_GF2X(to_ZZX(pp));
vector<GF2X> betas;
al2.decodePlaintext(betas, ptxt1, G, maps);
for (long i = 0; i < nslots; i++) {
if (alphas[i] != betas[(i+amt)%nslots]) {
cout << " amt="<<amt<<" oops\n";
return 0;
}
}
}
cout << "\n";
#if 0
long ord0 = al.OrderOf(0);
for (long i = 0; i < nslots; i++) {
cout << alphas[i] << " ";
if ((i+1) % (nslots/ord0) == 0) cout << "\n";
}
cout << "\n\n";
cout << betas.size() << "\n";
for (long i = 0; i < nslots; i++) {
cout << betas[i] << " ";
if ((i+1) % (nslots/ord0) == 0) cout << "\n";
}
#endif
return 0;
}
#endif
// an initial sanity check on noise estimates,
// comparing the estimated variance to the actual average
cout << "pk:"; checkCiphertext(publicKey.pubEncrKey, zero, secretKey);
ZZX ptxt[6]; // first four are plaintext, last two are constants
std::vector<Ctxt> ctxt(4, Ctxt(publicKey));
// Initialize the plaintext and constants to random 0-1 polynomials
for (size_t j=0; j<6; j++) {
ptxt[j].rep.SetLength(phim);
for (long i = 0; i < phim; i++)
ptxt[j].rep[i] = RandomBnd(ptxtSpace);
ptxt[j].normalize();
if (j<4) {
publicKey.Encrypt(ctxt[j], ptxt[j], ptxtSpace);
cout << "c"<<j<<":"; checkCiphertext(ctxt[j], ptxt[j], secretKey);
}
}
// perform upto 2L levels of computation, each level computing:
// 1. c0 += c1
// 2. c1 *= c2 // L1' = max(L1,L2)+1
// 3. c1.reLinearlize
// 4. c2 *= p4
// 5. c2.automorph(k) // k is the first generator of Zm^* /(2)
// 6. c2.reLinearlize
// 7. c3 += p5
// 8. c3 *= c0 // L3' = max(L3,L0,L1)+1
// 9. c2 *= c3 // L2' = max(L2,L0+1,L1+1,L3+1)+1
// 10. c0 *= c0 // L0' = max(L0,L1)+1
// 11. c0.reLinearlize
// 12. c2.reLinearlize
// 13. c3.reLinearlize
//
// The levels of the four ciphertexts behave as follows:
// 0, 0, 0, 0 => 1, 1, 2, 1 => 2, 3, 3, 2
// => 4, 4, 5, 4 => 5, 6, 6, 5
// => 7, 7, 8, 7 => 8,,9, 9, 10 => [...]
//
// We perform the same operations on the plaintext, and after each operation
// we check that decryption still works, and print the curretn modulus and
// noise estimate. We stop when we get the first decryption error, or when
// we reach 2L levels (which really should not happen).
zz_pContext zzpc;
zz_p::init(ptxtSpace);
zzpc.save();
const zz_pXModulus F = to_zz_pX(PhimX);
long g = context.zMstar.ZmStarGen(0); // the first generator in Zm*
zz_pX x2g(g, 1);
zz_pX p2;
// generate a key-switching matrix from s(X^g) to s(X)
secretKey.GenKeySWmatrix(/*powerOfS= */ 1,
/*powerOfX= */ g,
0, 0,
/*ptxtSpace=*/ ptxtSpace);
// generate a key-switching matrix from s^2 to s
secretKey.GenKeySWmatrix(/*powerOfS= */ 2,
/*powerOfX= */ 1,
0, 0,
/*ptxtSpace=*/ ptxtSpace);
// generate a key-switching matrix from s^3 to s
secretKey.GenKeySWmatrix(/*powerOfS= */ 3,
/*powerOfX= */ 1,
0, 0,
/*ptxtSpace=*/ ptxtSpace);
for (long lvl=0; lvl<2*L; lvl++) {
cout << "=======================================================\n";
ctxt[0] += ctxt[1];
ptxt[0] += ptxt[1];
PolyRed(ptxt[0], ptxtSpace, true);
cout << "c0+=c1: "; checkCiphertext(ctxt[0], ptxt[0], secretKey);
ctxt[1].multiplyBy(ctxt[2]);
ptxt[1] = (ptxt[1] * ptxt[2]) % PhimX;
PolyRed(ptxt[1], ptxtSpace, true);
cout << "c1*=c2: "; checkCiphertext(ctxt[1], ptxt[1], secretKey);
ctxt[2].multByConstant(ptxt[4]);
ptxt[2] = (ptxt[2] * ptxt[4]) % PhimX;
PolyRed(ptxt[2], ptxtSpace, true);
cout << "c2*=p4: "; checkCiphertext(ctxt[2], ptxt[2], secretKey);
ctxt[2] >>= g;
zzpc.restore();
p2 = to_zz_pX(ptxt[2]);
CompMod(p2, p2, x2g, F);
ptxt[2] = to_ZZX(p2);
cout << "c2>>="<<g<<":"; checkCiphertext(ctxt[2], ptxt[2], secretKey);
ctxt[2].reLinearize();
cout << "c2.relin:"; checkCiphertext(ctxt[2], ptxt[2], secretKey);
ctxt[3].addConstant(ptxt[5]);
ptxt[3] += ptxt[5];
PolyRed(ptxt[3], ptxtSpace, true);
cout << "c3+=p5: "; checkCiphertext(ctxt[3], ptxt[3], secretKey);
ctxt[3].multiplyBy(ctxt[0]);
ptxt[3] = (ptxt[3] * ptxt[0]) % PhimX;
PolyRed(ptxt[3], ptxtSpace, true);
cout << "c3*=c0: "; checkCiphertext(ctxt[3], ptxt[3], secretKey);
ctxt[0].square();
ptxt[0] = (ptxt[0] * ptxt[0]) % PhimX;
PolyRed(ptxt[0], ptxtSpace, true);
cout << "c0*=c0: "; checkCiphertext(ctxt[0], ptxt[0], secretKey);
ctxt[2].multiplyBy(ctxt[3]);
ptxt[2] = (ptxt[2] * ptxt[3]) % PhimX;
PolyRed(ptxt[2], ptxtSpace, true);
cout << "c2*=c3: "; checkCiphertext(ctxt[2], ptxt[2], secretKey);
}
/******************************************************************/
/** TESTS END HERE ***/
/******************************************************************/
cout << endl;
return 0;
}
SwaptionVolCube1::Cube
SwaptionVolCube1::sabrCalibration(const Cube& marketVolCube) const {
const std::vector<Time>& optionTimes = marketVolCube.optionTimes();
const std::vector<Time>& swapLengths = marketVolCube.swapLengths();
const std::vector<Date>& optionDates = marketVolCube.optionDates();
const std::vector<Period>& swapTenors = marketVolCube.swapTenors();
Matrix alphas(optionTimes.size(), swapLengths.size(),0.);
Matrix betas(alphas);
Matrix nus(alphas);
Matrix rhos(alphas);
Matrix forwards(alphas);
Matrix errors(alphas);
Matrix maxErrors(alphas);
Matrix endCriteria(alphas);
const std::vector<Matrix>& tmpMarketVolCube = marketVolCube.points();
std::vector<Real> strikes(strikeSpreads_.size());
std::vector<Real> volatilities(strikeSpreads_.size());
for (Size j=0; j<optionTimes.size(); j++) {
for (Size k=0; k<swapLengths.size(); k++) {
Rate atmForward = atmStrike(optionDates[j], swapTenors[k]);
strikes.clear();
volatilities.clear();
for (Size i=0; i<nStrikes_; i++){
Real strike = atmForward+strikeSpreads_[i];
if(strike>=MINSTRIKE) {
strikes.push_back(strike);
volatilities.push_back(tmpMarketVolCube[i][j][k]);
}
}
const std::vector<Real>& guess = parametersGuess_.operator()(
optionTimes[j], swapLengths[k]);
const boost::shared_ptr<SABRInterpolation> sabrInterpolation =
boost::shared_ptr<SABRInterpolation>(new
SABRInterpolation(strikes.begin(), strikes.end(),
volatilities.begin(),
optionTimes[j], atmForward,
guess[0], guess[1],
guess[2], guess[3],
isParameterFixed_[0],
isParameterFixed_[1],
isParameterFixed_[2],
isParameterFixed_[3],
vegaWeightedSmileFit_,
endCriteria_,
optMethod_,
errorAccept_,
useMaxError_,
maxGuesses_));
sabrInterpolation->update();
Real rmsError = sabrInterpolation->rmsError();
Real maxError = sabrInterpolation->maxError();
alphas [j][k] = sabrInterpolation->alpha();
betas [j][k] = sabrInterpolation->beta();
nus [j][k] = sabrInterpolation->nu();
rhos [j][k] = sabrInterpolation->rho();
forwards [j][k] = atmForward;
errors [j][k] = rmsError;
maxErrors [j][k] = maxError;
endCriteria[j][k] = sabrInterpolation->endCriteria();
QL_ENSURE(endCriteria[j][k]!=EndCriteria::MaxIterations,
"global swaptions calibration failed: "
"MaxIterations reached: " << "\n" <<
"option maturity = " << optionDates[j] << ", \n" <<
"swap tenor = " << swapTenors[k] << ", \n" <<
"error = " << io::rate(errors[j][k]) << ", \n" <<
"max error = " << io::rate(maxErrors[j][k]) << ", \n" <<
" alpha = " << alphas[j][k] << "n" <<
" beta = " << betas[j][k] << "\n" <<
" nu = " << nus[j][k] << "\n" <<
" rho = " << rhos[j][k] << "\n"
);
QL_ENSURE(useMaxError_ ? maxError : rmsError < maxErrorTolerance_,
"global swaptions calibration failed: "
"option tenor " << optionDates[j] <<
", swap tenor " << swapTenors[k] <<
(useMaxError_ ? ": max error " : ": error") <<
(useMaxError_ ? maxError : rmsError) <<
" alpha = " << alphas[j][k] << "n" <<
" beta = " << betas[j][k] << "\n" <<
" nu = " << nus[j][k] << "\n" <<
" rho = " << rhos[j][k] << "\n" <<
(useMaxError_ ? ": error" : ": max error ") <<
(useMaxError_ ? rmsError :maxError)
);
}
}
Cube sabrParametersCube(optionDates, swapTenors,
optionTimes, swapLengths, 8);
sabrParametersCube.setLayer(0, alphas);
sabrParametersCube.setLayer(1, betas);
sabrParametersCube.setLayer(2, nus);
sabrParametersCube.setLayer(3, rhos);
sabrParametersCube.setLayer(4, forwards);
sabrParametersCube.setLayer(5, errors);
sabrParametersCube.setLayer(6, maxErrors);
sabrParametersCube.setLayer(7, endCriteria);
return sabrParametersCube;
}
