pyFM.optimize.base_functions

Functions

LB_commutation(C, ev_sqdiff)

Compute the LB commutativity constraint

LB_commutation_grad(C, ev_sqdiff)

Compute the gradient of the LB commutativity constraint

descr_preservation(C, descr1_red, descr2_red)

Compute the descriptor preservation constraint

descr_preservation_grad(C, descr1_red, ...)

Compute the gradient of the descriptor preservation constraint

energy_func_std(C, descr_mu, lap_mu, ...)

Evaluation of the energy for standard FM computation

grad_energy_std(C, descr_mu, lap_mu, ...)

Evaluation of the gradient of the energy for standard FM computation

op_commutation(C, op1, op2)

Compute the operator commutativity constraint.

op_commutation_grad(C, op1, op2)

Compute the gradient of the operator commutativity constraint.

oplist_commutation(C, op_list)

Compute the operator commutativity constraint for a list of pairs of operators Can be used with a list of descriptor multiplication operator

oplist_commutation_grad(C, op_list)

Compute the gradient of the operator commutativity constraint for a list of pairs of operators Can be used with a list of descriptor multiplication operator
pyFM.optimize.base_functions.descr_preservation(C, descr1_red, descr2_red)

Compute the descriptor preservation constraint

Parameters:

  • C – (K2,K1) Functional map

  • descr1 – (K1,p) descriptors on first basis

  • descr2 – (K2,p) descriptros on second basis

Returns:

energy – descriptor preservation squared norm

Return type:

float

pyFM.optimize.base_functions.descr_preservation_grad(C, descr1_red, descr2_red)

Compute the gradient of the descriptor preservation constraint

Parameters:

  • C – (K2,K1) Functional map

  • descr1 – (K1,p) descriptors on first basis

  • descr2 – (K2,p) descriptros on second basis

Returns:

gradient – gradient of the descriptor preservation squared norm

Return type:

np.ndarray

pyFM.optimize.base_functions.LB_commutation(C, ev_sqdiff)

Compute the LB commutativity constraint

Parameters:

  • C – (K2,K1) Functional map

  • ev_sqdiff – (K2,K1) [normalized] matrix of squared eigenvalue differences

Returns:

energy – (float) LB commutativity squared norm

Return type:

float

pyFM.optimize.base_functions.LB_commutation_grad(C, ev_sqdiff)

Compute the gradient of the LB commutativity constraint

Parameters:

  • C – (K2,K1) Functional map

  • ev_sqdiff – (K2,K1) [normalized] matrix of squared eigenvalue differences

Returns:

gradient – (K2,K1) gradient of the LB commutativity squared norm

Return type:

np.ndarray

pyFM.optimize.base_functions.op_commutation(C, op1, op2)

Compute the operator commutativity constraint. Can be used with descriptor multiplication operator

Parameters:

  • C – (K2,K1) Functional map

  • op1 – (K1,K1) operator on first basis

  • op2 – (K2,K2) descriptros on second basis

Returns:

energy – (float) operator commutativity squared norm

Return type:

float

pyFM.optimize.base_functions.op_commutation_grad(C, op1, op2)

Compute the gradient of the operator commutativity constraint. Can be used with descriptor multiplication operator

Parameters:

  • C – (K2,K1) Functional map

  • op1 – (K1,K1) operator on first basis

  • op2 – (K2,K2) descriptros on second basis

Returns:

gardient – (K2,K1) gradient of the operator commutativity squared norm

Return type:

np.ndarray

pyFM.optimize.base_functions.oplist_commutation(C, op_list)

Compute the operator commutativity constraint for a list of pairs of operators Can be used with a list of descriptor multiplication operator

Parameters:

  • C – (K2,K1) Functional map

  • op_list – list of tuple( (K1,K1), (K2,K2) ) operators on first and second basis

Returns:

energy – (float) sum of operators commutativity squared norm

Return type:

float

pyFM.optimize.base_functions.oplist_commutation_grad(C, op_list)

Compute the gradient of the operator commutativity constraint for a list of pairs of operators Can be used with a list of descriptor multiplication operator

Parameters:

  • C – (K2,K1) Functional map

  • op_list – list of tuple( (K1,K1), (K2,K2) ) operators on first and second basis

Returns:

gradient – (K2,K1) gradient of the sum of operators commutativity squared norm

Return type:

np.ndarray

pyFM.optimize.base_functions.energy_func_std(C, descr_mu, lap_mu, descr_comm_mu, orient_mu, descr1_red, descr2_red, list_descr, orient_op, ev_sqdiff)

Evaluation of the energy for standard FM computation

Parameters:

C :

(K2*K1) or (K2,K1) Functional map

descr_mu :

scaling of the descriptor preservation term

lap_mu :

scaling of the laplacian commutativity term

descr_comm_mu :

scaling of the descriptor commutativity term

orient_mu :

scaling of the orientation preservation term

descr1 :

(K1,p) descriptors on first basis

descr2 :

(K2,p) descriptros on second basis

list_descr :
p-uple( (K1,K1), (K2,K2) ) operators on first and second basis

related to descriptors.

orient_op :
p-uple( (K1,K1), (K2,K2) ) operators on first and second basis

related to orientation preservation operators.

ev_sqdiff :

(K2,K1) [normalized] matrix of squared eigenvalue differences

returns:

energy – value of the energy

rtype:

float

pyFM.optimize.base_functions.grad_energy_std(C, descr_mu, lap_mu, descr_comm_mu, orient_mu, descr1_red, descr2_red, list_descr, orient_op, ev_sqdiff)

Evaluation of the gradient of the energy for standard FM computation

Parameters:

C :

(K2*K1) or (K2,K1) Functional map

descr_mu :

scaling of the descriptor preservation term

lap_mu :

scaling of the laplacian commutativity term

descr_comm_mu :

scaling of the descriptor commutativity term

orient_mu :

scaling of the orientation preservation term

descr1 :

(K1,p) descriptors on first basis

descr2 :

(K2,p) descriptros on second basis

list_descr :
p-uple( (K1,K1), (K2,K2) ) operators on first and second basis

related to descriptors.

orient_op :
p-uple( (K1,K1), (K2,K2) ) operators on first and second basis

related to orientation preservation operators.

ev_sqdiff :

(K2,K1) [normalized] matrix of squared eigenvalue differences

returns:

gradient – (K2*K1) - value of the energy

rtype:

float