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Commit 49b9b47e authored by Matevz, Sraml (sraml)'s avatar Matevz, Sraml (sraml)
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documentation LineSearchStrongWolfe and some changes

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nifty/minimization/line_searching/line_search_strong_wolfe.py
+ 111
− 17
View file @ 49b9b47e
......@@ -26,16 +26,17 @@ class LineSearchStrongWolfe(LineSearch):
Algorithm contains two stages. It begins whit a trial step length and it
keeps increasing the it until it finds an acceptable step length or an
interval. In the second stage the Zoom algorithm is performed which
decreases the size of the interval until an acceptable step length is found.
interval. If it does not satisfy the Wolfe conditions it performs the Zoom
algorithm (second stage). By interpolating it decreases the size of the
interval until an acceptable step length is found.
Parameters
----------
c1 : scalar
c1 : float
Parameter for Armijo condition rule. (Default: 1e-4)
c2 : scalar
c2 : float
Parameter for curvature condition rule. (Default: 0.9)
max_step_size : scalar
max_step_size : float
Maximum step allowed in to be made in the descent direction.
(Default: 50)
max_iterations : integer
......@@ -51,13 +52,12 @@ class LineSearchStrongWolfe(LineSearch):
Parameter for Armijo condition rule.
c2 : float
Parameter for curvature condition rule.
max_step_size : scalar
max_step_size : float
Maximum step allowed in to be made in the descent direction.
max_iterations : integer
Maximum number of iterations performed by the line search algorithm.
max_zoom_iterations : integer
Maximum number of iterations performed by the zoom algorithm.
"""
......@@ -77,8 +77,9 @@ class LineSearchStrongWolfe(LineSearch):
def perform_line_search(self, energy, pk, f_k_minus_1=None):
"""Performs the first stage of the algorithm.
Its starts with a trial step size and it keeps increasing it until it
satisfy the strong Wolf conditions.
It starts with a trial step size and it keeps increasing it until it
satisfy the strong Wolf conditions. It also performs the descent and
returns the optimal step length and the new enrgy.
Parameters
----------
......@@ -88,9 +89,18 @@ class LineSearchStrongWolfe(LineSearch):
pk : Field
Unit vector pointing into the search direction.
f_k_minus_1 : float
Value of the function (energy) which will be minimized at the k-1
Value of the fuction (which is being minimized) at the k-1
iteration of the line search procedure. (Default: None)
Returns
-------
alpha_star : float
The optimal step length in the descent direction.
phi_star : float
Value of the energy after the performed descent.
energy_star : Energy object
The new Energy object on the new position.
"""
self._set_line_energy(energy, pk, f_k_minus_1=f_k_minus_1)
......@@ -183,7 +193,47 @@ class LineSearchStrongWolfe(LineSearch):
def _zoom(self, alpha_lo, alpha_hi, phi_0, phiprime_0,
phi_lo, phiprime_lo, phi_hi, c1, c2):
"""Performs the second stage of the line search algorithm.
If the first stage was not successful then the Zoom algorithm tries to
find a suitable step length by using bisection, quadratic, cubic
interpolation.
Parameters
----------
alpha_lo : float
The lower boundary for the step length interval.
alph_hi : float
The upper boundary for the step length interval.
phi_0 : float
Value of the energy at the starting point of the line search
algorithm.
phiprime_0 : Field
Gradient at the starting point of the line search algorithm.
phi_lo : float
Value of the energy if we perform a step of length alpha_lo in
descent direction.
phiprime_lo : Field
Gradient at the nwe position if we perform a step of length
alpha_lo in descent direction.
phi_hi : float
Value of the energy if we perform a step of length alpha_hi in
descent direction.
c1 : float
Parameter for Armijo condition rule.
c2 : float
Parameter for curvature condition rule.
Returns
-------
alpha_star : float
The optimal step length in the descent direction.
phi_star : float
Value of the energy after the performed descent.
energy_star : Energy object
The new Energy object on the new position.
"""
max_iterations = self.max_zoom_iterations
# define the cubic and quadratic interpolant checks
cubic_delta = 0.2 # cubic
......@@ -254,12 +304,36 @@ class LineSearchStrongWolfe(LineSearch):
return alpha_star, phi_star, energy_star
def _cubicmin(self, a, fa, fpa, b, fb, c, fc):
"""
"""Estimating the minimum with cubic interpolation.
Finds the minimizer for a cubic polynomial that goes through the
points (a,fa), (b,fb), and (c,fc) with derivative at a of fpa.
points ( a,f(a) ), ( b,f(b) ), and ( c,f(c) ) with derivative at point a of fpa.
f(x) = A *(x-a)^3 + B*(x-a)^2 + C*(x-a) + D
If no minimizer can be found return None
Parameters
----------
a : float
Selected point.
fa : float
Value of polynomial at point a.
fpa : Field
Derivative at point a.
b : float
Selected point.
fb : float
Value of polynomial at point b.
c : float
Selected point.
fc : float
Value of polynomial at point c.
Returns
-------
xmin : float
Position of the approximated minimum.
"""
# f(x) = A *(x-a)^3 + B*(x-a)^2 + C*(x-a) + D
with np.errstate(divide='raise', over='raise', invalid='raise'):
try:
......@@ -285,9 +359,29 @@ class LineSearchStrongWolfe(LineSearch):
return xmin
def _quadmin(self, a, fa, fpa, b, fb):
"""
"""Estimating the minimum with quadratic interpolation.
Finds the minimizer for a quadratic polynomial that goes through
the points (a,fa), (b,fb) with derivative at a of fpa,
the points ( a,f(a) ), ( b,f(b) ) with derivative at point a of fpa.
f(x) = B*(x-a)^2 + C*(x-a) + D
Parameters
----------
a : float
Selected point.
fa : float
Value of polynomial at point a.
fpa : Field
Derivative at point a.
b : float
Selected point.
fb : float
Value of polynomial at point b.
Returns
-------
xmin : float
Position of the approximated minimum.
"""
# f(x) = B*(x-a)^2 + C*(x-a) + D
with np.errstate(divide='raise', over='raise', invalid='raise'):
......
nifty/minimization/quasi_newton_minimizer.py
+ 3
− 3
View file @ 49b9b47e
......@@ -40,7 +40,7 @@ class QuasiNewtonMinimizer(Loggable, object):
callback : function, *optional*
Function f(energy, iteration_number) specified by the user to print
iteration number and energy value at every iteration step. It accepts
a function(energy) and integer(iteration_number). (default: None)
an Energy object(energy) and integer(iteration_number). (default: None)
convergence_tolerance : scalar
Tolerance specifying convergence. (default: 1E-4)
convergence_level : integer
......@@ -63,7 +63,7 @@ class QuasiNewtonMinimizer(Loggable, object):
callback : function
Function f(energy, iteration_number) specified by the user to print
iteration number and energy value at every iteration step. It accepts
a function(energy) and integer(iteration_number).
an Energy object(energy) and integer(iteration_number).
Raises
------
......@@ -102,7 +102,7 @@ class QuasiNewtonMinimizer(Loggable, object):
Returns
-------
x : Field
energy : Energy object
Latest `energy` of the minimization.
convergence : integer
Latest convergence level indicating whether the minimization
......
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