16.1.1.13. pysisyphus.optimizers package
16.1.1.13.1. Submodules
16.1.1.13.2. pysisyphus.optimizers.BFGS module
- class pysisyphus.optimizers.BFGS.BFGS(geometry, *args, update='bfgs', **kwargs)[source]
Bases:
Optimizer- damped_bfgs_update(s, y, mu_1=0.2)[source]
Damped BFGS update of inverse Hessian.
Potentially updates s. See Section 3.2 of [2], Eq. (30) - (33). There is a typo ;) It should be
H_{k+1} = V_k H_k V_k^T + ...
- instead of
H_{k+1} = V_k^T H_k V_k + ...
- double_damped_bfgs_update(s, y, mu_1=0.2, mu_2=0.2)[source]
Double damped BFGS update of inverse Hessian.
See [3]. Potentially updates s and y.
- property eye
16.1.1.13.3. pysisyphus.optimizers.BacktrackingOptimizer module
16.1.1.13.4. pysisyphus.optimizers.ConjugateGradient module
16.1.1.13.5. pysisyphus.optimizers.CubicNewton module
16.1.1.13.6. pysisyphus.optimizers.FIRE module
16.1.1.13.7. pysisyphus.optimizers.HessianOptimizer module
- class pysisyphus.optimizers.HessianOptimizer.HessianOptimizer(geometry, trust_radius=0.5, trust_update=True, trust_min=0.1, trust_max=1, max_energy_incr=None, hessian_update='bfgs', hessian_init='fischer', hessian_recalc=None, hessian_recalc_adapt=None, hessian_xtb=False, hessian_recalc_reset=False, small_eigval_thresh=1e-08, line_search=False, alpha0=1.0, max_micro_cycles=25, rfo_overlaps=False, **kwargs)[source]
Bases:
Optimizer- __init__(geometry, trust_radius=0.5, trust_update=True, trust_min=0.1, trust_max=1, max_energy_incr=None, hessian_update='bfgs', hessian_init='fischer', hessian_recalc=None, hessian_recalc_adapt=None, hessian_xtb=False, hessian_recalc_reset=False, small_eigval_thresh=1e-08, line_search=False, alpha0=1.0, max_micro_cycles=25, rfo_overlaps=False, **kwargs)[source]
Baseclass for optimizers utilizing Hessian information.
- Parameters
geometry (
Geometry) -- Geometry to be optimized.trust_radius (
float, default:0.5) -- Initial trust radius in whatever unit the optimization is carried out.trust_update (
bool, default:True) -- Whether to update the trust radius throughout the optimization.trust_min (
float, default:0.1) -- Minimum trust radius.trust_max (
float, default:1) -- Maximum trust radius.max_energy_incr (
Optional[float], default:None) -- Maximum allowed energy increased after a faulty step. Optimization is aborted when the threshold is exceeded.hessian_update (
Literal['none', None, False, 'bfgs', 'damped_bfgs', 'flowchart', 'bofill', 'ts_bfgs', 'ts_bfgs_org', 'ts_bfgs_rev'], default:'bfgs') -- Type of Hessian update. Defaults to BFGS for minimizations and Bofill for saddle point searches.hessian_init (
Literal['calc', 'unit', 'fischer', 'lindh', 'simple', 'swart', 'xtb', 'xtb1', 'xtbff'], default:'fischer') -- Type of initial model Hessian.hessian_recalc (
Optional[int], default:None) -- Recalculate exact Hessian every n-th cycle instead of updating it.hessian_recalc_adapt (
Optional[float], default:None) -- Use a more flexible scheme to determine Hessian recalculation. Undocumented.hessian_xtb (
bool, default:False) -- Recalculate the Hessian at the GFN2-XTB level of theory.hessian_recalc_reset (
bool, default:False) -- Whether to skip Hessian recalculation after reset. Undocumented.small_eigval_thresh (
float, default:1e-08) -- Threshold for small eigenvalues. Eigenvectors belonging to eigenvalues below this threshold are discardewd.line_search (
bool, default:False) -- Whether to carry out a line search. Not implemented by a subclassing optimizers.alpha0 (
float, default:1.0) -- Initial alpha for restricted-step (RS) procedure.max_micro_cycles (
int, default:25) -- Maximum number of RS iterations.rfo_overlaps (
bool, default:False) -- Enable mode-following in RS procedure.**kwargs -- Keyword arguments passed to the Optimizer baseclass.
- get_newton_step_on_trust(eigvals, eigvecs, gradient, transform=True)[source]
Step on trust-radius.
See Nocedal 4.3 Iterative solutions of the subproblem
- housekeeping()[source]
Calculate gradient and energy. Update trust radius and hessian if needed. Return energy, gradient and hessian for the current cycle.
- property prev_eigvec_max
- property prev_eigvec_min
- rfo_dict = {'max': (-1, 'max'), 'min': (0, 'min')}
16.1.1.13.8. pysisyphus.optimizers.LBFGS module
- class pysisyphus.optimizers.LBFGS.LBFGS(geometry, keep_last=7, beta=1, max_step=0.2, double_damp=True, gamma_mult=False, line_search=False, mu_reg=None, max_mu_reg_adaptions=10, control_step=True, **kwargs)[source]
Bases:
Optimizer- __init__(geometry, keep_last=7, beta=1, max_step=0.2, double_damp=True, gamma_mult=False, line_search=False, mu_reg=None, max_mu_reg_adaptions=10, control_step=True, **kwargs)[source]
Limited-memory BFGS optimizer.
See [1] Nocedal, Wright - Numerical Optimization, 2006 for a general discussion of LBFGS. See pysisyphus.optimizers.hessian_updates for the references related to double damping and pysisyphus.optimizers.closures for references related to regularized LBFGS.
- Parameters
geometry (
Geometry) -- Geometry to be optimized.keep_last (
int, default:7) -- History size. Keep last 'keep_last' steps and gradient differences.beta (
float, default:1) -- Force constant β in -(H + βI)⁻¹g.max_step (
float, default:0.2) -- Upper limit for the absolute component of the step vector in whatever unit the optimization is carried out.double_damp (
bool, default:True) -- Use double damping procedure to modify steps s and gradient differences y to ensure sy > 0.gamma_mult (
bool, default:False) -- Estimate β from previous cycle. Eq. (7.20) in [1]. See 'beta' argument.line_search (
bool, default:False) -- Enable implicit linesearches.mu_reg (
Optional[float], default:None) -- Initial guess for regularization constant in regularized LBFGS.max_mu_reg_adaptions (
int, default:10) -- Maximum number of trial steps in regularized LBFGS.control_step (
bool, default:True) -- Wheter to scale down the proposed step its biggest absolute component is equal to or below 'max_step'**kwargs -- Keyword arguments passed to the Optimizer baseclass.
16.1.1.13.9. pysisyphus.optimizers.LayerOpt module
- class pysisyphus.optimizers.LayerOpt.LayerOpt(geometry, layers=None, **kwargs)[source]
Bases:
Optimizer- property layer_num: int
- Return type
int
16.1.1.13.10. pysisyphus.optimizers.MicroOptimizer module
16.1.1.13.11. pysisyphus.optimizers.NCOptimizer module
- class pysisyphus.optimizers.NCOptimizer.NCOptimizer(geometry, *args, freeze_modes=None, **kwargs)[source]
Bases:
HessianOptimizer
16.1.1.13.12. pysisyphus.optimizers.Optimizer module
- class pysisyphus.optimizers.Optimizer.Optimizer(geometry, thresh='gau_loose', max_step=0.04, max_cycles=100, min_step_norm=1e-08, assert_min_step=True, rms_force=None, rms_force_only=False, max_force_only=False, converge_to_geom_rms_thresh=0.05, align=False, dump=False, dump_restart=False, prefix='', reparam_thresh=0.001, reparam_check_rms=True, reparam_when='after', overachieve_factor=0.0, restart_info=None, check_coord_diffs=True, coord_diff_thresh=0.01, fragments=None, monitor_frag_dists=0, out_dir='.', h5_fn='optimization.h5', h5_group_name='opt')[source]
Bases:
object- __init__(geometry, thresh='gau_loose', max_step=0.04, max_cycles=100, min_step_norm=1e-08, assert_min_step=True, rms_force=None, rms_force_only=False, max_force_only=False, converge_to_geom_rms_thresh=0.05, align=False, dump=False, dump_restart=False, prefix='', reparam_thresh=0.001, reparam_check_rms=True, reparam_when='after', overachieve_factor=0.0, restart_info=None, check_coord_diffs=True, coord_diff_thresh=0.01, fragments=None, monitor_frag_dists=0, out_dir='.', h5_fn='optimization.h5', h5_group_name='opt')[source]
Optimizer baseclass. Meant to be subclassed.
- Parameters
geometry (
Geometry) -- Geometry to be optimized.thresh (
Literal['gau_loose', 'gau', 'gau_tight', 'gau_vtight', 'baker', 'never'], default:'gau_loose') -- Convergence threshold.max_step (
float, default:0.04) -- Maximum absolute component of the allowed step vector. Utilized in optimizers that don't support a trust region or line search.max_cycles (
int, default:100) -- Maximum number of allowed optimization cycles.min_step_norm (
float, default:1e-08) -- Minimum norm of an allowed step. If the step norm drops below this value a ZeroStepLength-exception is raised. The unit depends on the coordinate system of the supplied geometry.assert_min_step (
bool, default:True) -- Flag that controls whether the norm of the proposed step is check for being too small.rms_force (
Optional[float], default:None) -- Root-mean-square of the force from which user-defined thresholds are derived. When 'rms_force' is given 'thresh' is ignored.rms_force_only (
bool, default:False) -- When set, convergence is signalled only based on rms(forces).max_force_only (
bool, default:False) -- When set, convergence is signalled only based on max(|forces|).converge_to_geom_rms_thresh (
float, default:0.05) -- Threshold for the RMSD with another geometry. When the RMSD drops below this threshold convergence is signalled. Only used with Growing Newton trajectories.align (
bool, default:False) -- Flag that controls whether the geometry is aligned in every step onto the coordinates of the previous step. Must not be used with internal coordinates.dump (
bool, default:False) -- Flag to control dumping/writing of optimization progress to the filesystemdump_restart (
bool, default:False) -- Flag to control whether restart information is dumped to the filesystem.prefix (
str, default:'') -- Short string that is prepended to several files created by the optimizer. Allows distinguishing several optimizations carried out in the same directory.reparam_thresh (
float, default:0.001) -- Controls the minimal allowed similarity between coordinates after two successive reparametrizations. Convergence is signalled if the coordinates did not change significantly.reparam_check_rms (
bool, default:True) -- Whether to check for (too) similar coordinates after reparametrization.reparam_when (
Optional[Literal['before', 'after']], default:'after') -- Reparametrize before or after calculating the step. Can also be turned off by setting it to None.overachieve_factor (
float, default:0.0) -- Signal convergence when max(forces) and rms(forces) fall below the chosen threshold, divided by this factor. Convergence of max(step) and rms(step) is ignored.restart_info -- Restart information. Undocumented.
check_coord_diffs (
bool, default:True) -- Whether coordinates of chain-of-sates images are checked for being too similar.coord_diff_thresh (
float, default:0.01) -- Unitless threshold for similary checking of COS image coordinates. The first image is assigned 0, the last image is assigned to 1.fragments (
Optional[Tuple], default:None) -- Tuple of lists containing atom indices, defining two fragments.monitor_frag_dists (
int, default:0) -- Monitor fragment distances for N cycles. The optimization is terminated when the interfragment distances falls below the initial value after N cycles.out_dir (
str, default:'.') -- String poiting to a directory where optimization progress is dumped.h5_fn (
str, default:'optimization.h5') -- Basename of the HDF5 file used for dumping.h5_group_name (
str, default:'opt') -- Groupname used for dumping of this optimization.
16.1.1.13.13. pysisyphus.optimizers.PreconLBFGS module
- class pysisyphus.optimizers.PreconLBFGS.PreconLBFGS(geometry, alpha_init=1.0, history=7, precon=True, precon_update=1, precon_getter_update=None, precon_kind='full', max_step_element=None, line_search='armijo', c_stab=None, **kwargs)[source]
Bases:
Optimizer- __init__(geometry, alpha_init=1.0, history=7, precon=True, precon_update=1, precon_getter_update=None, precon_kind='full', max_step_element=None, line_search='armijo', c_stab=None, **kwargs)[source]
Preconditioned limited-memory BFGS optimizer.
See pysisyphus.optimizers.precon for related references.
- Parameters
geometry (
Geometry) -- Geometry to be optimized.alpha_init (
float, default:1.0) -- Initial scaling factor for the first trial step in the excplicit line search.history (
int, default:7) -- History size. Keep last 'history' steps and gradient differences.precon (
bool, default:True) -- Wheter to use preconditioning or not.precon_update (
int, default:1) -- Recalculate preconditioner P in every n-th cycle with the same topology.precon_getter_update (
Optional[int], default:None) -- Recalculate topology for preconditioner P in every n-th cycle. It is usually sufficient to only determine the topology once at the beginning.precon_kind (
Literal['full', 'full_fast', 'bonds', 'bonds_bends'], default:'full') -- What types of primitive internal coordinates to consider in the preconditioner.max_step_element (
Optional[float], default:None) -- Maximum component of the absolute step vector when no line search is carried out.line_search (
Literal['armijo', 'armijo_fg', 'strong_wolfe', 'hz', None, False], default:'armijo') -- Whether to use explicit line searches and if so, which kind of line search.c_stab (
Optional[float], default:None) -- Regularization constant c in (H + cI)⁻¹ in atomic units.**kwargs -- Keyword arguments passed to the Optimizer baseclass.
16.1.1.13.14. pysisyphus.optimizers.PreconSteepestDescent module
- class pysisyphus.optimizers.PreconSteepestDescent.PreconSteepestDescent(geometry, alpha_init=0.5, **kwargs)[source]
Bases:
PreconLBFGS
16.1.1.13.15. pysisyphus.optimizers.QuickMin module
16.1.1.13.16. pysisyphus.optimizers.RFOptimizer module
- class pysisyphus.optimizers.RFOptimizer.RFOptimizer(geometry, line_search=True, gediis=False, gdiis=True, gdiis_thresh=0.0025, gediis_thresh=0.01, gdiis_test_direction=True, max_micro_cycles=0, adapt_step_func=False, **kwargs)[source]
Bases:
HessianOptimizer- __init__(geometry, line_search=True, gediis=False, gdiis=True, gdiis_thresh=0.0025, gediis_thresh=0.01, gdiis_test_direction=True, max_micro_cycles=0, adapt_step_func=False, **kwargs)[source]
Rational function Optimizer.
- Parameters
geometry (
Geometry) -- Geometry to be optimized.line_search (
bool, default:True) -- Whether to carry out implicit line searches.gediis (
bool, default:False) -- Whether to enable GEDIIS.gdiis (
bool, default:True) -- Whether to enable GDIIS.gdiis_thresh (
float, default:0.0025) -- Threshold for rms(forces) to enable GDIIS.gediis_thresh (
float, default:0.01) -- Threshold for rms(step) to enable GEDIIS.gdiis_test_direction (
bool, default:True) -- Whether to the overlap of the RFO step and the GDIIS step.max_micro_cycles (
int, default:0) -- Number of restricted-step microcycles. Disabled by default.adapt_step_func (
bool, default:False) -- Whether to switch between shifted Newton and RFO-steps.**kwargs -- Keyword arguments passed to the Optimizer/HessianOptimizer baseclass.
16.1.1.13.17. pysisyphus.optimizers.RSA module
- class pysisyphus.optimizers.RSA.RSA(geometry, trust_radius=0.5, trust_update=True, trust_min=0.1, trust_max=1, max_energy_incr=None, hessian_update='bfgs', hessian_init='fischer', hessian_recalc=None, hessian_recalc_adapt=None, hessian_xtb=False, hessian_recalc_reset=False, small_eigval_thresh=1e-08, line_search=False, alpha0=1.0, max_micro_cycles=25, rfo_overlaps=False, **kwargs)[source]
Bases:
HessianOptimizerThe Importance of Step Control in Optimization Methods, del Campo, 2009.
16.1.1.13.18. pysisyphus.optimizers.StabilizedQNMethod module
16.1.1.13.19. pysisyphus.optimizers.SteepestDescent module
16.1.1.13.20. pysisyphus.optimizers.StringOptimizer module
- class pysisyphus.optimizers.StringOptimizer.StringOptimizer(geometry, max_step=0.1, stop_in_when_full=- 1, keep_last=10, lbfgs_when_full=True, gamma_mult=False, double_damp=True, scale_step='global', **kwargs)[source]
Bases:
Optimizer
16.1.1.13.21. pysisyphus.optimizers.closures module
- pysisyphus.optimizers.closures.bfgs_multiply(s_list, y_list, vector, beta=1, P=None, logger=None, gamma_mult=True, mu_reg=None, inds=None, cur_size=None)[source]
Matrix-vector product H·v.
Multiplies given vector with inverse Hessian, obtained from repeated BFGS updates calculated from steps in 's_list' and gradient differences in 'y_list'.
Based on algorithm 7.4 Nocedal, Num. Opt., p. 178.
- pysisyphus.optimizers.closures.get_update_mu_reg(mu_min=0.001, gamma_1=0.1, gamma_2=5.0, eta_1=0.01, eta_2=0.9, logger=None)[source]
See 5.1 in [1]
- pysisyphus.optimizers.closures.lbfgs_closure(force_getter, M=10, beta=1, restrict_step=None)[source]
- pysisyphus.optimizers.closures.modified_broyden_closure(force_getter, M=5, beta=1, restrict_step=None)[source]
https://doi.org/10.1006/jcph.1996.0059 F corresponds to the residual gradient, so we after calling force_getter we multiply the force by -1 to get the gradient.
- pysisyphus.optimizers.closures.small_lbfgs_closure(history=5, gamma_mult=True)[source]
Compact LBFGS closure.
The returned function takes two arguments: forces and prev_step. forces are the forces at the current iterate and prev_step is the previous step that lead us to the current iterate. In this way step restriction/line search can be done outisde of the lbfgs function.
16.1.1.13.22. pysisyphus.optimizers.cls_map module
16.1.1.13.23. pysisyphus.optimizers.exceptions module
16.1.1.13.24. pysisyphus.optimizers.gdiis module
- class pysisyphus.optimizers.gdiis.DIISResult(coeffs, coords, forces, energy, N, type)
Bases:
tuple- N
Alias for field number 4
- coeffs
Alias for field number 0
- coords
Alias for field number 1
- energy
Alias for field number 3
- forces
Alias for field number 2
- type
Alias for field number 5
16.1.1.13.25. pysisyphus.optimizers.guess_hessians module
- pysisyphus.optimizers.guess_hessians.get_guess_hessian(geometry, hessian_init, int_gradient=None, cart_gradient=None, h5_fn=None)[source]
Obtain/calculate (model) Hessian.
For hessian_init="calc" the Hessian will be in the coord_type of the geometry, otherwise a Hessian in primitive internals will be returned.
- pysisyphus.optimizers.guess_hessians.improved_guess(geom, bond_func, bend_func, dihedral_func)[source]
- pysisyphus.optimizers.guess_hessians.lindh_guess(geom)[source]
Slightly modified Lindh model hessian as described in [1].
Instead of using the tabulated r_ref,ij values from [1] we will use the 'true' covalent radii as pyberny. The tabulated r_ref,ij value for two carbons (2nd period) is 2.87 Bohr. Carbons covalent radius is ~ 1.44 Bohr, so 2*1.44 Bohr = 2.88 Bohr which fits nicely with the tabulate value. If values for elements > 3rd are requested the alpha values for the 3rd period will be (re)used.
- pysisyphus.optimizers.guess_hessians.lindh_style_guess(geom, ks, rhos)[source]
Approximate force constants according to Lindh.[1]
Bonds: k_ij = k_r * rho_ij Bends: k_ijk = k_b * rho_ij * rho_jk Dihedrals: k_ijkl = k_d * rho_ij * rho_jk * rho_kl
16.1.1.13.26. pysisyphus.optimizers.hessian_updates module
- pysisyphus.optimizers.hessian_updates.double_damp(s, y, H=None, s_list=None, y_list=None, mu_1=0.2, mu_2=0.2, logger=None)[source]
Double damped step 's' and gradient differences 'y'.
H is the inverse Hessian! See [6]. Potentially updates s and y. y is only updated if mu_2 is not None.
- Parameters
s (np.array, shape (N, ), floats) -- Coordiante differences/step.
y (np.array, shape (N, ), floats) -- Gradient differences
H (np.array, shape (N, N), floats, optional) -- Inverse Hessian.
s_list (list of nd.array, shape (K, N), optional) -- List of K previous steps. If no H is supplied and prev_ys is given the matrix-vector product Hy will be calculated through the two-loop LBFGS-recursion.
y_list (list of nd.array, shape (K, N), optional) -- List of K previous gradient differences. See s_list.
mu_1 (float, optional) -- Parameter for 's' damping.
mu_2 (float, optional) -- Parameter for 'y' damping.
logger (logging.Logger, optional) -- Logger to be used.
- Returns
s (np.array, shape (N, ), floats) -- Damped coordiante differences/step.
y (np.array, shape (N, ), floats) -- Damped gradient differences
- pysisyphus.optimizers.hessian_updates.ts_bfgs_update_org(H, dx, dg)[source]
Do not use! Implemented as described in the 1998 bofill paper [8].
This does not seem to work too well.
- pysisyphus.optimizers.hessian_updates.ts_bfgs_update_revised(H, dx, dg)[source]
TS-BFGS update as described in [9].
Better than the original formula of Bofill, worse than the implementation in [7]. a is caluclated as described in the footnote 1 on page 38. Eq. (8) looks suspicious as it contains the inverse of a vector?! As also outlined in the paper abs(a) is used (|a| in the paper).
16.1.1.13.27. pysisyphus.optimizers.poly_fit module
- class pysisyphus.optimizers.poly_fit.FitResult(x, y, polys)
Bases:
tuple- polys
Alias for field number 2
- x
Alias for field number 0
- y
Alias for field number 1
- pysisyphus.optimizers.poly_fit.gen_solutions()[source]
Given two energies (e0, e1) and corresponding gradients (g0, g1) we can (try to) fit a quartic polynomial
f(x) = a0 + a1*x + a2*x**2 + a3*x**3 + a4*x**4
s.t. the constraint f''(x) >= 0, with the equality being fullfilled at only one point. There are five unknowns (a0 - a4) to be determined. Four equations can be derived from f(x) and its first derivative
f'(x) = a1 + 2*a2*x + 3*a3*x**2 + 4*a4*x**3 .
With (e0, g0) being given at x=0 and (e1, g1) being given at x=1 we can setup the following equations:
f (0) = a0 (1) f'(0) = a1 (2)
- using e0 and g0 at x=0, and
f (1) = a0 + a1 + a2 + a3 + a4 (3) f'(1) = a1 + 2*a2 + 3*a3 + 4*a4 . (4)
The missing last equation can be derived from the constraint. The second derivative of f(x) is
f''(x) = 2*a2 + 6*a3*x + 12*a4*x**2
and shall be positive except at one point where it is allowed to be 0, that its two roots (f''(x) = 0) must be degenerate. This is fullfilled when the discriminant D of the quadratic polynomial a*x**2 + b*x + c is zero.
D = b**2 – 4*a*c = 0
- With
a = 12*a4 b = 6*a3 c = 2*a2
- we get
0 = (6*a3)**2 - 4*12*a4*2*a2 0 = 36*a3**2 - 96*a4*a2 0 = 3*a3**2 - 8*a4*a2 (5) or a4 = 3/8 * a3**2 / a2
Using (1) - (5) we can solve the set of equations for a0 - a4.
- pysisyphus.optimizers.poly_fit.poly_line_search(cur_energy, prev_energy, cur_grad, prev_grad, prev_step, cubic_max_x=2.0, quartic_max_x=4.0, logger=None)[source]
Generate directional gradients by projecting them on the previous step.
16.1.1.13.28. pysisyphus.optimizers.precon module
- pysisyphus.optimizers.precon.get_lindh_k(atoms, coords3d, bonds=None, angles=None, torsions=None)[source]
16.1.1.13.29. pysisyphus.optimizers.restrict_step module
16.1.1.13.30. Module contents
- class pysisyphus.optimizers.CubicNewton(geometry, **kwargs)[source]
Bases:
HessianOptimizer