ExpFitClass< M > Class Template Reference

Collaboration diagram for ExpFitClass< M >:

Public Member Functions
void	Fit (std::vector< double > &r, std::vector< double > &u)
void	FitCusp (std::vector< double > &r, std::vector< double > &u, double cusp)
void	eval (double r, double &u)
void	eval (double r, double &u, double &du, double &d2u)

Private Attributes
TinyVector< double, M >	Coefs
TinyVector< double, M >	dCoefs
TinyVector< double, M >	d2Coefs
double	sign

Friends
class	ComplexExpFitClass< M >

Detailed Description

template<int M>
class qmcplusplus::ExpFitClass< M >

Definition at line 31 of file ExpFitClass.h.

Member Function Documentation

eval() [1/2]

void eval ( double  r, double &  u  )

inline

Definition at line 163 of file ExpFitClass.h.

References qmcplusplus::exp(), and sign().

{
  double r2j  = 1.0;
  double poly = 0.0;
  for (int j = 0; j < M; j++)
  {
    poly += Coefs[j] * r2j;
    r2j *= r;
  }
  u = sign * std::exp(poly);
}

eval() [2/2]

void eval ( double  r, double &  u, double &  du, double &  d2u  )

inline

Definition at line 176 of file ExpFitClass.h.

References qmcplusplus::exp(), and sign().

{
  double r2j = 1.0;
  double P = 0.0, dP = 0.0, d2P = 0.0;
  for (int j = 0; j < M; j++)
  {
    P   += Coefs[j] * r2j;
    dP  += dCoefs[j] * r2j;
    d2P += d2Coefs[j] * r2j;
    r2j *= r;
  }
  u   = sign * std::exp(P);
  du  = dP * u;
  d2u = (d2P + dP * dP) * u;
}

Fit()

void Fit ( std::vector< double > &  r, std::vector< double > &  u  )

inline

Definition at line 107 of file ExpFitClass.h.

References qmcplusplus::app_error(), qmcplusplus::det(), qmcplusplus::invert_matrix(), qmcplusplus::log(), qmcplusplus::Units::force::N, and sign().

Referenced by ComplexExpFitClass< M >::Fit().

{
  int N = r.size();
  sign  = u[0] < 0.0 ? -1.0 : 1.0;
  if (r.size() != u.size())
    app_error() << "Different number of rows of basis functions than"
                << " of data points in LinFit.  Exitting.\n";
  std::vector<TinyVector<double, M>> F(N);
  std::vector<double> log_u(N);
  for (int i = 0; i < N; i++)
  {
    log_u[i]   = std::log(sign * u[i]);
    double r2j = 1.0;
    for (int j = 0; j < M; j++)
    {
      F[i][j] = r2j;
      r2j *= r[i];
    }
  }
  // Next, construct alpha matrix
  Matrix<double> alpha(M, M), alphaInv(M, M);
  alpha = 0.0;
  for (int j = 0; j < M; j++)
    for (int k = 0; k < M; k++)
    {
      alpha(k, j) = 0.0;
      for (int i = 0; i < N; i++)
        alpha(k, j) += F[i][j] * F[i][k];
    }
  // Next, construct beta vector
  TinyVector<double, M> beta;
  beta = 0.0;
  for (int k = 0; k < M; k++)
    for (int i = 0; i < N; i++)
      beta[k] += log_u[i] * F[i][k];
  // Now, invert alpha
  for (int i = 0; i < M; i++)
    for (int j = 0; j < M; j++)
      alphaInv(i, j) = alpha(i, j);
  double det = invert_matrix(alphaInv);
  for (int i = 0; i < M; i++)
  {
    Coefs[i] = 0.0;
    for (int j = 0; j < M; j++)
      Coefs[i] += alphaInv(i, j) * beta[j];
  }
  dCoefs  = 0.0;
  d2Coefs = 0.0;
  for (int i = 0; i < M - 1; i++)
    dCoefs[i] = (double)(i + 1) * Coefs[i + 1];
  for (int i = 0; i < M - 2; i++)
    d2Coefs[i] = (double)(i + 1) * dCoefs[i + 1];
}

FitCusp()

void FitCusp ( std::vector< double > &  r, std::vector< double > &  u, double  cusp  )

inline

Definition at line 46 of file ExpFitClass.h.

References qmcplusplus::app_error(), qmcplusplus::det(), qmcplusplus::invert_matrix(), qmcplusplus::log(), qmcplusplus::Units::force::N, and sign().

Referenced by ComplexExpFitClass< M >::FitCusp().

{
  int N = r.size();
  sign  = u[0] < 0.0 ? -1.0 : 1.0;
  if (r.size() != u.size())
    app_error() << "Different number of rows of basis functions than"
                << " of data points in LinFit.  Exitting.\n";
  std::vector<TinyVector<double, M - 1>> F(N);
  std::vector<double> log_u(N);
  for (int i = 0; i < N; i++)
  {
    log_u[i]     = std::log(sign * u[i]) - cusp * r[i];
    double r2jp1 = r[i] * r[i];
    F[i][0]      = 1.0;
    for (int j = 1; j < M - 1; j++)
    {
      F[i][j] = r2jp1;
      r2jp1 *= r[i];
    }
  }
  // Next, construct alpha matrix
  Matrix<double> alpha(M - 1, M - 1), alphaInv(M - 1, M - 1);
  alpha = 0.0;
  for (int j = 0; j < M - 1; j++)
    for (int k = 0; k < M - 1; k++)
    {
      alpha(k, j) = 0.0;
      for (int i = 0; i < N; i++)
        alpha(k, j) += F[i][j] * F[i][k];
    }
  // Next, construct beta vector
  TinyVector<double, M - 1> beta;
  beta = 0.0;
  for (int k = 0; k < M - 1; k++)
    for (int i = 0; i < N; i++)
      beta[k] += log_u[i] * F[i][k];
  // Now, invert alpha
  for (int i = 0; i < M - 1; i++)
    for (int j = 0; j < M - 1; j++)
      alphaInv(i, j) = alpha(i, j);
  double det = invert_matrix(alphaInv);
  TinyVector<double, M - 1> c;
  for (int i = 0; i < M - 1; i++)
  {
    c[i] = 0.0;
    for (int j = 0; j < M - 1; j++)
      c[i] += alphaInv(i, j) * beta[j];
  }
  Coefs[0] = c[0];
  Coefs[1] = cusp;
  for (int i = 2; i < M; i++)
    Coefs[i] = c[i - 1];
  dCoefs  = 0.0;
  d2Coefs = 0.0;
  for (int i = 0; i < M - 1; i++)
    dCoefs[i] = (double)(i + 1) * Coefs[i + 1];
  for (int i = 0; i < M - 2; i++)
    d2Coefs[i] = (double)(i + 1) * dCoefs[i + 1];
}

Friends And Related Function Documentation

ComplexExpFitClass< M >

friend class ComplexExpFitClass< M >

friend

Definition at line 42 of file ExpFitClass.h.

Member Data Documentation

Coefs

TinyVector<double, M> Coefs

private

Definition at line 34 of file ExpFitClass.h.

Referenced by ComplexExpFitClass< M >::Fit(), and ComplexExpFitClass< M >::FitCusp().

d2Coefs

TinyVector<double, M> d2Coefs

private

Definition at line 34 of file ExpFitClass.h.

Referenced by ComplexExpFitClass< M >::Fit(), and ComplexExpFitClass< M >::FitCusp().

dCoefs

TinyVector<double, M> dCoefs

private

Definition at line 34 of file ExpFitClass.h.

Referenced by ComplexExpFitClass< M >::Fit(), and ComplexExpFitClass< M >::FitCusp().

sign

double sign

private

Definition at line 35 of file ExpFitClass.h.

Referenced by ComplexExpFitClass< M >::Fit(), and ComplexExpFitClass< M >::FitCusp().

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The documentation for this class was generated from the following file:

• /home/pk7/projects/qmc/for_cron_doxygen/qmcpack/src/Numerics/ExpFitClass.h