rz_poly.cc

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#include <iostream>
#include "rz_poly.h"
 
using namespace std;
using namespace magfieldparam;
 
//_______________________________________________________________________________
rz_poly::rz_poly(int N) {
  int nz, nr = 0, nv, nt;
  poly_term v3;
 
  if (N < 2)
    N = 2;
  data.reserve(N);
 
  v3.coeff = 1.;
  v3.np[0] = 0;
  v3.np[1] = 1;
 
  data.push_back(poly_vect(1, v3));
 
  for (int m = 2; m <= N; ++m) {
    nz = m;
    nr = 0;
    nv = 0;
    v3.coeff = 1. / m;
    v3.np[0] = nr;
    v3.np[1] = nz;
 
    nt = (m + 2) / 2;
    poly_vect v3x(nt, v3);
 
    while (nz >= 2) {
      nz -= 2;
      nr += 2;
      nv += 1;
      v3x[nv].coeff = -v3x[nv - 1].coeff * (nz + 1) * (nz + 2) / (nr * nr);
      v3x[nv].np[0] = nr;
      v3x[nv].np[1] = nz;
    }
    data.push_back(v3x);
  }
  max_nr = nr + 1;
  max_nz = N + 1;
  r_pow = new double[max_nr];
  z_pow = new double[max_nz];
  fill(r_pow, r_pow + max_nr, 1.);
  fill(z_pow, z_pow + max_nz, 1.);
 
  n_active = data.size();
  is_off = new bool[n_active];
  fill(is_off, is_off + n_active, false);
}
 
//_______________________________________________________________________________
rz_poly::rz_poly(const rz_poly &S) {
  data = S.data;
  max_nr = S.max_nr;
  max_nz = S.max_nz;
  n_active = S.n_active;
 
  if (max_nr) {
    r_pow = new double[max_nr];
    copy(S.r_pow, S.r_pow + max_nr, r_pow);
  } else
    r_pow = nullptr;
 
  if (max_nz) {
    z_pow = new double[max_nz];
    copy(S.z_pow, S.z_pow + max_nz, z_pow);
  } else
    z_pow = nullptr;
 
  if (S.is_off) {
    is_off = new bool[data.size()];
    copy(S.is_off, S.is_off + data.size(), is_off);
  } else
    is_off = nullptr;
}
 
//_______________________________________________________________________________
rz_poly::~rz_poly() {
  if (is_off)
    delete[] is_off;
  if (r_pow)
    delete[] r_pow;
  if (z_pow)
    delete[] z_pow;
}
 
//_______________________________________________________________________________
void rz_poly::SetOFF(int npoly) {
  if ((npoly < 0) || (npoly >= (int)data.size()))
    return;
  if (is_off[npoly])
    return;
  is_off[npoly] = true;
  --n_active;
}
 
//_______________________________________________________________________________
void rz_poly::SetON(int npoly) {
  if ((npoly < 0) || (npoly >= (int)data.size()))
    return;
  if (is_off[npoly]) {
    is_off[npoly] = false;
    ++n_active;
  }
}
 
//_______________________________________________________________________________
void rz_poly::Print() {
  if (data.empty()) {
    cout << "The \"rz_poly\" object is NOT initialized!" << endl;
    return;
  }
 
  for (unsigned int ip = 0; ip < data.size(); ++ip) {
    cout << "Polynomial " << ip << " (size=" << data[ip].size() << ", status=";
    if (is_off[ip])
      cout << "OFF):" << endl;
    else
      cout << "ON):" << endl;
    for (unsigned int it = 0; it < data[ip].size(); ++it) {
      cout << "\tnr=" << data[ip][it].np[0] << "\tnz=" << data[ip][it].np[1] << "\tcoeff=" << data[ip][it].coeff
           << endl;
    }
  }
}
 
//_______________________________________________________________________________
rz_poly rz_poly::Diff(int nvar, bool keep_empty) {
  //Return the derivative of original polynomial by variable nvar.
  //If keep_empty=true, resulting polynomial may contain zero basis terms,
  //otherwise the resulting polynomial will be compressed, so that corresponding
  //basis terms will be shifted relatively to the original polynomial.
  //
  poly_term v3;
  rz_poly p_out;
  p_out.data.reserve(data.size());
 
  bool *tmp_mask = new bool[data.size()];
  unsigned int ind_tmp = 0;
  int tmp_act = 0;
 
  for (unsigned int ip = 0; ip < data.size(); ++ip) {
    poly_vect v3x;
    v3x.reserve(data[ip].size());
    for (unsigned int it = 0; it < data[ip].size(); ++it) {
      v3 = data[ip][it];
      v3.coeff = data[ip][it].coeff * data[ip][it].np[nvar];
      if (v3.coeff != 0) {
        v3.np[nvar] = data[ip][it].np[nvar] - 1;
        v3x.push_back(v3);
      }
    }
    if (!v3x.empty() || keep_empty) {
      v3x.resize(v3x.size());
      p_out.data.push_back(v3x);
      tmp_mask[ind_tmp] = is_off[ip];
      ++ind_tmp;
      if (!is_off[ip])
        ++tmp_act;
    }
  }
 
  p_out.data.resize(p_out.data.size());
  p_out.max_nr = max_nr;
  p_out.max_nz = max_nz;
 
  if (nvar == 0)
    --p_out.max_nr;
  else
    --p_out.max_nz;
 
  p_out.r_pow = new double[p_out.max_nr];
  copy(r_pow, r_pow + p_out.max_nr, p_out.r_pow);
  p_out.z_pow = new double[p_out.max_nz];
  copy(z_pow, z_pow + p_out.max_nz, p_out.z_pow);
 
  p_out.n_active = tmp_act;
  p_out.is_off = new bool[p_out.data.size()];
  copy(tmp_mask, tmp_mask + p_out.data.size(), p_out.is_off);
 
  delete[] tmp_mask;
 
  return p_out;
}
 
//_______________________________________________________________________________
rz_poly rz_poly::Int(int nvar) {
  //Return the integral of original polynomial by variable nvar
  //
  rz_poly p_out;
  p_out.data = data;
  for (unsigned int ip = 0; ip < data.size(); ++ip) {
    for (unsigned int it = 0; it < data[ip].size(); ++it) {
      p_out.data[ip][it].coeff /= ++p_out.data[ip][it].np[nvar];
    }
  }
 
  p_out.max_nr = max_nr;
  p_out.max_nz = max_nz;
 
  if (nvar == 0)
    ++p_out.max_nr;
  else
    ++p_out.max_nz;
 
  p_out.r_pow = new double[p_out.max_nr];
  copy(r_pow, r_pow + max_nr, p_out.r_pow);
  p_out.z_pow = new double[p_out.max_nz];
  copy(z_pow, z_pow + max_nz, p_out.z_pow);
 
  if (nvar == 0)
    p_out.r_pow[max_nr] = p_out.r_pow[max_nr - 1] * r_pow[1];
  else
    p_out.z_pow[max_nz] = p_out.z_pow[max_nz - 1] * z_pow[1];
 
  p_out.n_active = n_active;
  p_out.is_off = new bool[data.size()];
  copy(is_off, is_off + data.size(), p_out.is_off);
 
  return p_out;
}
 
//_______________________________________________________________________________
rz_poly &rz_poly::operator*=(double C) {
  //Multiply the polynomial by a constant. Skips terms that are switched off
 
  for (unsigned int ip = 0; ip < data.size(); ++ip) {
    if (is_off[ip])
      continue;
    for (unsigned int it = 0; it < data[ip].size(); ++it) {
      data[ip][it].coeff *= C;
    }
  }
  return *this;
}
 
//_______________________________________________________________________________
rz_poly &rz_poly::operator*=(double *C) {
  //Multiply the polynomial by an array. Skips terms that are switched off
 
  for (unsigned int ip = 0; ip < data.size(); ++ip) {
    if (is_off[ip])
      continue;
    for (unsigned int it = 0; it < data[ip].size(); ++it) {
      data[ip][it].coeff *= *C;
    }
    ++C;
  }
  return *this;
}
 
//_______________________________________________________________________________
double rz_poly::GetSVal(double r, double z, const double *C) const {
  //Return value of a polynomial, ignoring terms, that are switched off
 
  if (r_pow == nullptr)
    return 0.;
 
  double term, rez = 0.;
  int ip, it;
 
  if (r != r_pow[1])
    for (ip = 1; ip < max_nr; ++ip)
      r_pow[ip] = r * r_pow[ip - 1];
  if (z != z_pow[1])
    for (ip = 1; ip < max_nz; ++ip)
      z_pow[ip] = z * z_pow[ip - 1];
 
  for (ip = 0; ip < (int)data.size(); ++ip) {
    if (is_off[ip])
      continue;
    term = 0.;
    for (it = 0; it < (int)data[ip].size(); ++it) {
      term += data[ip][it].coeff * r_pow[data[ip][it].np[0]] * z_pow[data[ip][it].np[1]];
    }
    rez += *C * term;
    ++C;
  }
 
  return rez;
}
 
//_______________________________________________________________________________
double *rz_poly::GetVVal(double r, double z, double *rez_out) {
  //return an array of doubleype with values of the basis functions in the point
  //(r,z). In a case if rez_out != 0, the rez_out array must be long enough to fit
  //in n_active elements. In a case if rez_out == 0, a new array of n_active length
  //is created; it is in user's responsibility to free the memory after all;
  //
  if (r_pow == nullptr)
    return nullptr;
 
  double term;
  int ip, it;
 
  double *rez;
  if (rez_out)
    rez = rez_out;
  else
    rez = new double[n_active];
 
  double *pnt = rez;
 
  if (r != r_pow[1])
    for (ip = 1; ip < max_nr; ++ip)
      r_pow[ip] = r * r_pow[ip - 1];
  if (z != z_pow[1])
    for (ip = 1; ip < max_nz; ++ip)
      z_pow[ip] = z * z_pow[ip - 1];
 
  for (ip = 0; ip < (int)data.size(); ++ip) {
    if (is_off[ip])
      continue;
    term = 0.;
    for (it = 0; it < (int)data[ip].size(); ++it) {
      term += data[ip][it].coeff * r_pow[data[ip][it].np[0]] * z_pow[data[ip][it].np[1]];
    }
    *pnt = term;
    ++pnt;
  }
 
  return rez;
}
 
//_______________________________________________________________________________
double *rz_poly::Expand(double *C) {
  //Take C[n_active] - reduced vector of coefficients and return pointer to
  //expanded vector of coefficients of the data.size() length. It is in user's
  //responsibility to free the memory after all;
  //
  double *rez = new double[data.size()];
  for (int ip = 0; ip < (int)data.size(); ++ip) {
    if (is_off[ip])
      rez[ip] = 0.;
    else {
      rez[ip] = *C;
      ++C;
    }
  }
  return rez;
}