17.1.1.13. pysisyphus.optimizers package
17.1.1.13.1. Submodules
17.1.1.13.2. pysisyphus.optimizers.BFGS module
17.1.1.13.3. pysisyphus.optimizers.BacktrackingOptimizer module
17.1.1.13.4. pysisyphus.optimizers.ConjugateGradient module
17.1.1.13.5. pysisyphus.optimizers.CubicNewton module
17.1.1.13.6. pysisyphus.optimizers.FIRE module
17.1.1.13.7. pysisyphus.optimizers.HessianOptimizer module
17.1.1.13.8. pysisyphus.optimizers.LBFGS module
17.1.1.13.9. pysisyphus.optimizers.LayerOpt module
17.1.1.13.10. pysisyphus.optimizers.MicroOptimizer module
17.1.1.13.11. pysisyphus.optimizers.NCOptimizer module
17.1.1.13.12. pysisyphus.optimizers.Optimizer module
17.1.1.13.13. pysisyphus.optimizers.PreconLBFGS module
17.1.1.13.14. pysisyphus.optimizers.PreconSteepestDescent module
17.1.1.13.15. pysisyphus.optimizers.QuickMin module
17.1.1.13.16. pysisyphus.optimizers.RFOptimizer module
17.1.1.13.17. pysisyphus.optimizers.RSA module
17.1.1.13.18. pysisyphus.optimizers.StabilizedQNMethod module
17.1.1.13.19. pysisyphus.optimizers.SteepestDescent module
17.1.1.13.20. pysisyphus.optimizers.StringOptimizer module
17.1.1.13.21. 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.
17.1.1.13.22. pysisyphus.optimizers.cls_map module
17.1.1.13.23. pysisyphus.optimizers.exceptions module
17.1.1.13.24. pysisyphus.optimizers.gdiis module
- class pysisyphus.optimizers.gdiis.DIISResult(coeffs, coords, forces, energy, N, prefix)[source]
Bases:
object-
N:
int
-
coeffs:
ndarray
-
coords:
ndarray
-
energy:
float
-
forces:
ndarray
-
prefix:
str
- property type
-
N:
- pysisyphus.optimizers.gdiis.gdiis(err_vecs, coords, forces, ref_step, max_vecs=5, test_direction=True, logger=None)[source]
17.1.1.13.25. pysisyphus.optimizers.guess_hessians module
17.1.1.13.26. pysisyphus.optimizers.hessian_updates module
- pysisyphus.optimizers.hessian_updates.curvature_at_image(index, energies, coords)[source]
Curvate at given index for given reaction path.
Eq. (5) in [10]. Can be used to calculate the curvature at the HEI of in COS, to construct a suitable Hessian for a TS optimizatio.
- Parameters:
index (
int) -- Integer > 0. Index an image in energies & coords array.energies (
ndarray) -- 1d array of shape (nimages, ). Contains image energies.coords (
ndarray) -- 2d array of shape (nimages, ncoords). Contains the image coordinates, where the energies were calculated.
- Return type:
float
- pysisyphus.optimizers.hessian_updates.curvature_tangent_update(hessian, C, tangent)[source]
Introduce a direction with a certain curvature into the Hessian.
Can be used to construct a suitable starting Hessian for a TS optimization in a COS. See eq. (6) in [10].
- Parameters:
hessian (
ndarray) -- Cartesian Hessian of shape (3N, 3N), with N denoting the number of atoms.C (
float) -- Curvature.tangent (
ndarray) -- 1d array. Tanget vector of shape (3N, ) for which curvature C was calculated.
- Return type:
tuple[ndarray,str]- Returns:
dH -- Hessian update.
label -- Kind of update.
- 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).
17.1.1.13.27. 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.