qmctorch.wavefunction.jastrows.elec_elec.kernels.pade_jastrow_polynomial_kernel module

class qmctorch.wavefunction.jastrows.elec_elec.kernels.pade_jastrow_polynomial_kernel.PadeJastrowPolynomialKernel(*args: Any, **kwargs: Any)

Bases: JastrowKernelElectronElectronBase

Computes a polynomial Pade-Jastrow factor

\[B_{ij} = \frac{P_{ij}}{Q_{ij}}\]

with : .. math:

P_{ij} = a_1 r_{i,j} + a_2 r_{ij}^2 + ....

and :

Parameters:

• nup (int) – number of spin up electons

• ndow (int) – number of spin down electons

• order (int) – degree of the polynomial

• weight_a (torch.tensor, optional) – Value of the weight

• weight_b (torch.tensor, optional) – Value of the weight

• cuda (bool, optional) – Turns GPU ON/OFF. Defaults to False.

get_static_weight()

Get the matrix of static weights

Returns:

static weight (0.5 (0.25) for parallel(anti) spins

Return type:

torch.tensor

set_variational_weights(weight_a, weight_b)

Define the initial values of the variational weights.

Parameters:

• weight_a (torch.tensor or None) – Value of the weight

• weight_b (torch.tensor or None) – Value of the weight

forward(r)

Get the jastrow kernel.

\[B_{ij} = \frac{P_{ij}}{Q_{ij}}\]

Parameters:

r (torch.tensor) – matrix of the e-e distances Nbatch x Nelec x Nelec

Returns:

matrix of the jastrow kernels

Nbatch x Nelec x Nelec

Return type:

torch.tensor

compute_derivative(r, dr)

Get the elements of the derivative of the jastrow kernels wrt to the first electrons

The derivative is given by:

\[\text{out}_{k,i,j} = \frac{P'Q - PQ'}{Q^2}\]

with:

\[P_{ij} = a_1 r_{i,j} + a_2 r_{ij}^2 + .... Q_{ij} = 1 + b_1 r_{i,j} + b_2 r_{ij}^2 +\]

and :

\[P'_{ij} = a_1 dr + a_2 2 r dr + a_r 3 dr r^2 + .... Q'_{ij} = b_1 dr + b_2 2 r dr + b_r 3 dr r^2 + ....\]

Due to the properties of the derivative we have .. math:

\frac{d B_{ij}}{d k_i} =  \frac{d B_{ij}}{d k_j}  = -\frac{d B_{ji}{d k_i}

Parameters:

• r (torch.tensor) – matrix of the e-e distances Nbatch x Nelec x Nelec

• dr (torch.tensor) – matrix of the derivative of the e-e distances Nbatch x Ndim x Nelec x Nelec

Returns:

matrix fof the derivative of the jastrow elements

Nbatch x Ndim x Nelec x Nelec

Return type:

torch.tensor

compute_second_derivative(r, dr, d2r)

Get the elements of the pure 2nd derivative of the jastrow kernels wrt to the first electron

Due to the properties of the derivative we have .. math:

\frac{d B_{ij}}{d k_i} =  \frac{d B_{ij}}{d k_j}  = \frac{d B_{ji}{d k_i}

Parameters:

• r (torch.tensor) – matrix of the e-e distances Nbatch x Nelec x Nelec

• dr (torch.tensor) – matrix of the derivative of the e-e distances Nbatch x Ndim x Nelec x Nelec

• d2r (torch.tensor) –

  matrix of the 2nd derivative of

  the e-e distances

  Nbatch x Ndim x Nelec x Nelec

Returns:

matrix fof the pure 2nd derivative of

the jastrow elements Nbatch x Ndim x Nelec x Nelec

Return type:

torch.tensor