3.2.4. horton.correlatedwfn.stepsearch – Step search methods for orbital rotations

Optimize step length for orbital optimization (kappa) and rotate orbitals.

Works only with diagonal approximation to the Hessian which is stored as a OneIndex instance.

class horton.correlatedwfn.stepsearch.StepSearch(lf, **kw)

Bases: object

Arguments:

lf

A LinalgFactory instance

Keywords:

method:step search method used, one of trust-region (default), None, backtracking alpha:scaling factor for step, used in backtracking and None method (default 0.75) c1:parameter used in backtracking (default 1e-4) minalpha:minimum step length used in backracking (default 1e-6) maxiterouter:maximum number of step search steps (default 10) maxiterinner:maximum number of optimization steps in each step search step (used only in pcg, default 500) maxeta:upper bound for estimated vs actual change in trust-region (default 0.75) mineta:lower bound for estimated vs actual change in trust-region (default 0.25) upscale:scaling factor to increase trust radius in trust-region (default 2.0) downscale:scaling factor to decrease trust radius in trust-region and step length in backtracking (float) (default 0.25) trustradius:initial trust radius (default 0.75) maxtrustradius:maximum trust radius (default 0.75) threshold:trust-region optimization threshold, only used in pcg method of trust-region optimizer:optimizes step to boundary of trust radius. One of pcg, dogleg, ddl (default ddl)

__call__(obj, one, two, orb, **kwargs)

__init__(lf, **kw)

Arguments:

lf

A LinalgFactory instance

Keywords:

method:step search method used, one of trust-region (default), None, backtracking alpha:scaling factor for step, used in backtracking and None method (default 0.75) c1:parameter used in backtracking (default 1e-4) minalpha:minimum step length used in backracking (default 1e-6) maxiterouter:maximum number of step search steps (default 10) maxiterinner:maximum number of optimization steps in each step search step (used only in pcg, default 500) maxeta:upper bound for estimated vs actual change in trust-region (default 0.75) mineta:lower bound for estimated vs actual change in trust-region (default 0.25) upscale:scaling factor to increase trust radius in trust-region (default 2.0) downscale:scaling factor to decrease trust radius in trust-region and step length in backtracking (float) (default 0.25) trustradius:initial trust radius (default 0.75) maxtrustradius:maximum trust radius (default 0.75) threshold:trust-region optimization threshold, only used in pcg method of trust-region optimizer:optimizes step to boundary of trust radius. One of pcg, dogleg, ddl (default ddl)

update_alpha(new)

Update current scaling factor

update_trustradius(new)

Update current trastradius

class horton.correlatedwfn.stepsearch.RStepSearch(lf, **kw)

Bases: horton.correlatedwfn.stepsearch.StepSearch

Arguments:

lf

A LinalgFactory instance

Keywords:

method:step search method used, one of trust-region (default), None, backtracking alpha:scaling factor for step, used in backtracking and None method (default 0.75) c1:parameter used in backtracking (default 1e-4) minalpha:minimum step length used in backracking (default 1e-6) maxiterouter:maximum number of step search steps (default 10) maxiterinner:maximum number of optimization steps in each step search step (used only in pcg, default 500) maxeta:upper bound for estimated vs actual change in trust-region (default 0.75) mineta:lower bound for estimated vs actual change in trust-region (default 0.25) upscale:scaling factor to increase trust radius in trust-region (default 2.0) downscale:scaling factor to decrease trust radius in trust-region and step length in backtracking (float) (default 0.25) trustradius:initial trust radius (default 0.75) maxtrustradius:maximum trust radius (default 0.75) threshold:trust-region optimization threshold, only used in pcg method of trust-region optimizer:optimizes step to boundary of trust radius. One of pcg, dogleg, ddl (default ddl)

__call__(*args, **kwargs)

Optimize Newton-Rapshon step.

Arguments:

obj

A class instance containing the objective function.

one, two

One- and Two-electron integrals (TwoIndex and FourIndex/Cholesky instances)

orb

An Expansion instance. Contains the MO coefficients

Keywords:

__init__(lf, **kw)

Arguments:

lf

A LinalgFactory instance

Keywords:

method:step search method used, one of trust-region (default), None, backtracking alpha:scaling factor for step, used in backtracking and None method (default 0.75) c1:parameter used in backtracking (default 1e-4) minalpha:minimum step length used in backracking (default 1e-6) maxiterouter:maximum number of step search steps (default 10) maxiterinner:maximum number of optimization steps in each step search step (used only in pcg, default 500) maxeta:upper bound for estimated vs actual change in trust-region (default 0.75) mineta:lower bound for estimated vs actual change in trust-region (default 0.25) upscale:scaling factor to increase trust radius in trust-region (default 2.0) downscale:scaling factor to decrease trust radius in trust-region and step length in backtracking (float) (default 0.25) trustradius:initial trust radius (default 0.75) maxtrustradius:maximum trust radius (default 0.75) threshold:trust-region optimization threshold, only used in pcg method of trust-region optimizer:optimizes step to boundary of trust radius. One of pcg, dogleg, ddl (default ddl)

check_line_search_condition(cetot, petot, kappa, grad)

Check if Armijo condition is satisfied (e_tot(0+alpha*kappa)-e_tot(0) <= c1*alpha*(kappa,grad))

do_backtracking(obj, one, two, orb, **kwargs)

Backtracking line search.

Arguments:

obj

A class instance containing the objctive function.

one, two

One- and Two-electron integrals (TwoIndex and FourIndex/Cholesky instances)

orb

An Expansion instance. Contains the MO coefficients

Keywords:

kappa:Initial step size (OneIndex instance) gradient:Orbital gradient (OneIndex instance)

do_no_stepsearch(obj, one, two, orb, **kwargs)

Scale step size with factor self.alpha

Arguments:

obj

A class instance containing the objective function.

one, two

One- and Two-electron integrals (TwoIndex and FourIndex/Cholesky instances)

orb

An Expansion instance. Contains the MO coefficients

Keywords:

kappa:Initial step size (OneIndex instance)

do_trust_region(obj, one, two, orb, **kwargs)

Do trust-region optimization.

Arguments:

obj

A class instance containing the objective function.

one/two

One and Two-body Hamiltonian (TwoIndex and FourIndex/Cholesky instances)

orb

(Expansion instance) An MO expansion

Keywords:

kappa:Initial step size (OneIndex instance) gradient:Orbital gradient (OneIndex instance) hessian:Orbital Hessian (OneIndex instance)

update_alpha(new)

Update current scaling factor

update_trustradius(new)

Update current trastradius