// This is core/vnl/vnl_real_npolynomial.cxx
//:
//  \file
//  \brief a degree n real polynomial
//  \author Marc Pollefeys, ESAT-VISICS, K.U.Leuven, 12-08-97
//
//  Implements a polynomial with N variables

#include <cassert>
#include <iostream>
#include <sstream>
#include <utility>

#include "vnl_real_npolynomial.h"

//: Constructor
// \verbatim
// coeffs = vnl_vector<double>(nterms)
// polyn = vnl_matrix<int>(nterms,nvar)
// Example: A*x^3 + B*x*y + C*y^2 + D*x*y^2
// nvar = 2;
// nterms = 4;
// coeffs = [A B C D]';
// polyn = [3 0]
//         [1 1]
//         [0 2]
//         [1 2];
// \endverbatim

vnl_real_npolynomial::vnl_real_npolynomial(vnl_vector<double> c, const vnl_matrix<unsigned int> & p)
  : coeffs_{ std::move(c) }
  , polyn_(p)
  , nvar_{ p.cols() }
  , nterms_{ p.rows() }
  , ideg_{ p.max_value() }
{
  assert(coeffs_.size() == polyn_.rows());
  simplify();
}

//: Combine terms with identical exponents (i.e., identical rows in polyn_).
// Remove terms with zero coefficient, also at the end of the vector.
void
vnl_real_npolynomial::simplify()
{
  for (unsigned int row1 = 0; row1 < nterms_; ++row1)
    for (unsigned int row2 = row1 + 1; row2 < nterms_; ++row2)
    {
      unsigned int col = 0;
      while (col < nvar_ && polyn_(row1, col) == polyn_(row2, col))
        ++col;
      if (col < nvar_)
        continue; // not all exponents are identical
      coeffs_(row1) += coeffs_(row2);
      coeffs_(row2) = 0;
    }
  while (nterms_ > 0 && coeffs_(nterms_ - 1) == 0)
    --nterms_;
  for (unsigned int row = 0; row < nterms_; ++row)
    if (coeffs_(row) == 0)
    {
      --nterms_; // decrement nterms, and move last element to vacant place:
      coeffs_(row) = coeffs_(nterms_);
      for (unsigned int i = 0; i < nvar_; ++i)
        polyn_(row, i) = polyn_(nterms_, i);
    }
  // Now physically remove those rows that became "invisible":
  if (nterms_ < polyn_.rows())
    this->set(coeffs_.extract(nterms_), polyn_.extract(nterms_, nvar_));
}

double
vnl_real_npolynomial::eval(const vnl_matrix<double> & xn)
{
  double s = 0;
  for (unsigned int i = 0; i < nterms_; i++)
  {
    double t = coeffs_(i);
    for (unsigned int j = 0; j < nvar_; j++)
      t *= xn(j, polyn_(i, j));
    s += t;
  }
  return s;
}

double
vnl_real_npolynomial::eval(const vnl_vector<double> & x)
{
  vnl_matrix<double> xn(nvar_, ideg_ + 1);

  for (unsigned int j = 0; j < nvar_; j++)
  {
    xn(j, 0) = 1;
    for (unsigned int i = 1; i < ideg_ + 1; i++)
      xn(j, i) = xn(j, i - 1) * x(j);
  }
  return eval(xn);
}

double
vnl_real_npolynomial::deval(const vnl_vector<double> & x, unsigned int var)
{
  return deriv(var).eval(x);
}

vnl_vector<double>
vnl_real_npolynomial::deval(const vnl_vector<double> & x)
{
  vnl_vector<double> dx(nvar_);

  for (unsigned int j = 0; j < nvar_; j++)
  {
    dx(j) = deriv(j).eval(x);
  }
  return dx;
}

vnl_real_npolynomial
vnl_real_npolynomial::deriv(unsigned int unk)
{
  vnl_vector<double> c(nterms_);
  vnl_matrix<unsigned int> p = polyn_;

  for (unsigned int i = 0; i < nterms_; i++)
  {
    if (polyn_(i, unk) > 0)
    {
      p(i, unk) = p(i, unk) - 1;
      c(i) = coeffs_(i) * polyn_(i, unk);
    }
    else
    {
      c(i) = coeffs_(i);
    }
  }

  return vnl_real_npolynomial(c, p);
}

void
vnl_real_npolynomial::set(const vnl_vector<double> & c, const vnl_matrix<unsigned int> & p)
{
  coeffs_ = c;
  polyn_ = p;
  nvar_ = p.cols();
  nterms_ = p.rows();
  ideg_ = p.max_value();
}

unsigned int
vnl_real_npolynomial::degree() const
{
  unsigned int d = 0;
  for (unsigned int i = 0; i < nterms_; i++)
  {
    unsigned int dt = 0;
    for (unsigned int j = 0; j < nvar_; j++)
      dt += polyn_(i, j);
    if (dt > d)
      d = dt;
  }
  return d;
}

std::vector<unsigned int>
vnl_real_npolynomial::degrees() const
{
  std::vector<unsigned int> d(nvar_);
  for (unsigned int j = 0; j < nvar_; ++j)
  {
    d[j] = 0;
    for (unsigned int i = 0; i < nterms_; ++i)
      if (polyn_(i, j) > d[j])
        d[j] = polyn_(i, j);
  }
  return d;
}

vnl_real_npolynomial
vnl_real_npolynomial::operator-() const
{
  vnl_vector<double> coef(nterms_);
  for (unsigned int i = 0; i < nterms_; ++i)
    coef(i) = -coeffs_(i);

  const vnl_matrix<unsigned int> poly = polyn_;

  return vnl_real_npolynomial(coef, poly);
}

vnl_real_npolynomial
vnl_real_npolynomial::operator+(const vnl_real_npolynomial & P) const
{
  assert(nvar_ == P.nvar_); // both polynomials must have the same variables

  vnl_vector<double> coef(nterms_ + P.nterms_);
  unsigned int i = 0;
  for (; i < nterms_; ++i)
    coef(i) = coeffs_(i);
  for (unsigned int j = 0; j < P.nterms_; ++i, ++j)
    coef(i) = P.coeffs_(j);

  vnl_matrix<unsigned int> poly(nterms_ + P.nterms_, nvar_);
  for (i = 0; i < nterms_; ++i)
    for (unsigned int k = 0; k < nvar_; ++k)
      poly(i, k) = polyn_(i, k);
  for (unsigned int j = 0; j < P.nterms_; ++i, ++j)
    for (unsigned int k = 0; k < nvar_; ++k)
      poly(i, k) = P.polyn_(j, k);

  return vnl_real_npolynomial(coef, poly);
}

vnl_real_npolynomial
vnl_real_npolynomial::operator+(double P) const
{
  vnl_vector<double> coef(nterms_ + 1);
  for (unsigned int i = 0; i < nterms_; ++i)
    coef(i) = coeffs_(i);
  coef(nterms_) = P;

  vnl_matrix<unsigned int> poly(nterms_ + 1, nvar_);
  for (unsigned int i = 0; i < nterms_; ++i)
    for (unsigned int k = 0; k < nvar_; ++k)
      poly(i, k) = polyn_(i, k);
  for (unsigned int k = 0; k < nvar_; ++k)
    poly(nterms_, k) = 0;

  return vnl_real_npolynomial(coef, poly);
}

vnl_real_npolynomial
vnl_real_npolynomial::operator-(const vnl_real_npolynomial & P) const
{
  assert(nvar_ == P.nvar_); // both polynomials must have the same variables

  vnl_vector<double> coef(nterms_ + P.nterms_);
  unsigned int i = 0;
  for (; i < nterms_; ++i)
    coef(i) = coeffs_(i);
  for (unsigned int j = 0; j < P.nterms_; ++i, ++j)
    coef(i) = -P.coeffs_(j);

  vnl_matrix<unsigned int> poly(nterms_ + P.nterms_, nvar_);
  for (i = 0; i < nterms_; ++i)
    for (unsigned int k = 0; k < nvar_; ++k)
      poly(i, k) = polyn_(i, k);
  for (unsigned int j = 0; j < P.nterms_; ++i, ++j)
    for (unsigned int k = 0; k < nvar_; ++k)
      poly(i, k) = P.polyn_(j, k);

  return vnl_real_npolynomial(coef, poly);
}

vnl_real_npolynomial
vnl_real_npolynomial::operator*(const vnl_real_npolynomial & P) const
{
  assert(nvar_ == P.nvar_); // both polynomials must have the same variables

  vnl_vector<double> coef(nterms_ * P.nterms_);
  unsigned int k = 0;
  for (unsigned int i = 0; i < nterms_; ++i)
    for (unsigned int j = 0; j < P.nterms_; ++j, ++k)
      coef(k) = coeffs_(i) * P.coeffs_(j);

  vnl_matrix<unsigned int> poly(nterms_ * P.nterms_, nvar_);
  k = 0;
  for (unsigned int i = 0; i < nterms_; ++i)
    for (unsigned int j = 0; j < P.nterms_; ++j, ++k)
      for (unsigned int l = 0; l < nvar_; ++l)
        poly(k, l) = polyn_(i, l) + P.polyn_(j, l);

  return vnl_real_npolynomial(coef, poly);
}

vnl_real_npolynomial
vnl_real_npolynomial::operator*(double P) const
{
  vnl_vector<double> coef(nterms_);
  for (unsigned int i = 0; i < nterms_; ++i)
    coef(i) = coeffs_(i) * P;

  const vnl_matrix<unsigned int> poly = polyn_;

  return vnl_real_npolynomial(coef, poly);
}

std::ostream &
operator<<(std::ostream & os, const vnl_real_npolynomial & P)
{
  return os << P.asString() << std::endl;
}
vnl_real_npolynomial &
vnl_real_npolynomial::operator+=(const vnl_real_npolynomial & rhs)
{
  *this = (*this) + rhs;
  return *this;
}
vnl_real_npolynomial &
vnl_real_npolynomial::operator-=(const vnl_real_npolynomial & rhs)
{
  *this = (*this) - rhs;
  return *this;
}
vnl_real_npolynomial &
vnl_real_npolynomial::operator*=(const vnl_real_npolynomial & rhs)
{
  *this = (*this) * rhs;
  return *this;
}
std::string
vnl_real_npolynomial::asString() const
{
  std::ostringstream os;
  if (nvar_ <= 3)
    for (unsigned int i = 0; i < nterms_; ++i)
    {
      if (i > 0)
        os << ' ';
      if (i > 0 && coeffs_(i) >= 0)
        os << "+ ";
      double abs_coef = coeffs_(i);
      if (coeffs_(i) < 0)
      {
        abs_coef = -abs_coef;
        os << "- ";
      }
      if (abs_coef != 1)
        os << abs_coef << ' ';
      unsigned int totaldeg = 0;
      if (nvar_ > 0 && polyn_(i, 0) > 0)
      {
        os << 'X';
        totaldeg += polyn_(i, 0);
      }
      if (nvar_ > 0 && polyn_(i, 0) > 1)
        os << '^' << polyn_(i, 0) << ' ';
      if (nvar_ > 1 && polyn_(i, 1) > 0)
      {
        os << 'Y';
        totaldeg += polyn_(i, 1);
      }
      if (nvar_ > 1 && polyn_(i, 1) > 1)
        os << '^' << polyn_(i, 1) << ' ';
      if (nvar_ > 2 && polyn_(i, 2) > 0)
      {
        os << 'Z';
        totaldeg += polyn_(i, 2);
      }
      if (nvar_ > 2 && polyn_(i, 2) > 1)
        os << '^' << polyn_(i, 2) << ' ';
      if (totaldeg == 0 && abs_coef == 1)
        os << abs_coef;
    }
  else
    for (unsigned int i = 0; i < nterms_; ++i)
    {
      if (i > 0)
        os << ' ';
      if (i > 0 && coeffs_(i) >= 0)
        os << "+ ";
      double abs_coef = coeffs_(i);
      if (coeffs_(i) < 0)
      {
        abs_coef = -abs_coef;
        os << "- ";
      }
      if (abs_coef != 1)
        os << abs_coef << ' ';
      unsigned int totaldeg = 0;
      for (unsigned int j = 0; j < nvar_; ++j)
      {
        if (polyn_(i, j) > 0)
          os << 'X' << j;
        if (polyn_(i, j) > 1)
          os << '^' << polyn_(i, j) << ' ';
        totaldeg += polyn_(i, j);
      }
      if (totaldeg == 0 && abs_coef == 1)
        os << abs_coef;
    }
  return os.str();
}
