mirror of
https://github.com/triqs/dft_tools
synced 2024-10-31 19:23:45 +01:00
100 lines
3.7 KiB
Python
100 lines
3.7 KiB
Python
|
|
################################################################################
|
|
#
|
|
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
|
|
#
|
|
# Copyright (C) 2011 by M. Ferrero, O. Parcollet
|
|
#
|
|
# TRIQS is free software: you can redistribute it and/or modify it under the
|
|
# terms of the GNU General Public License as published by the Free Software
|
|
# Foundation, either version 3 of the License, or (at your option) any later
|
|
# version.
|
|
#
|
|
# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
|
|
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
|
|
# details.
|
|
#
|
|
# You should have received a copy of the GNU General Public License along with
|
|
# TRIQS. If not, see <http://www.gnu.org/licenses/>.
|
|
#
|
|
################################################################################
|
|
|
|
import pytriqs.utility.mpi as mpi
|
|
|
|
def dichotomy(function, x_init, y_value, precision_on_y, delta_x, max_loops = 1000, x_name="", y_name="", verbosity=1):
|
|
"""
|
|
Solver function(x) = y_value.
|
|
|
|
Arguments :
|
|
- function : function (real valued) to be solved by dichotomy
|
|
- x_init : Init value for x. On success, returns the new value of x
|
|
- y_value :
|
|
- precision_on_y : calculation stops for abs(f(x) - y_value)<precision
|
|
- max_loops : maximum number of loops before failure. Default is 1000
|
|
- x_name, y_name : name of the variable x, y for the report
|
|
- verbosity : verbosity level.
|
|
|
|
Returns :
|
|
- A tuple (x,y). x is the value found, y is f(x).
|
|
- (None,None) if the calculation failed.
|
|
|
|
"""
|
|
def sign(x):
|
|
if x>0.0 : return 1
|
|
if x<0.0 : return -1
|
|
return 0
|
|
|
|
mpi.report("Dichotomy adjustment of %(x_name)s to obtain %(y_name)s = %(y_value)f +/- %(precision_on_y)f"%locals() )
|
|
PR = " "
|
|
if x_name=="" or y_name=="" : verbosity = max(verbosity,1)
|
|
x=x_init;delta_x= abs(delta_x)
|
|
|
|
# First find the bounds
|
|
y1 = function(x)
|
|
eps = sign(y1-y_value)
|
|
x1=x;y2=y1;x2=x1
|
|
nbre_loop=0
|
|
while (nbre_loop<= max_loops) and (y2-y_value)*eps>0 and abs(y2-y_value)>precision_on_y :
|
|
nbre_loop +=1
|
|
x2 -= eps*delta_x
|
|
y2 = function(x2)
|
|
if x_name!="" and verbosity>2:
|
|
mpi.report("%(PR)s%(x_name)s = %(x2)f \n%(PR)s%(y_name)s = %(y2)f"%locals())
|
|
|
|
mpi.report("%(PR)s%(x1)f < %(x_name)s < %(x2)f"%locals())
|
|
mpi.report("%(PR)s%(y1)f < %(y_name)s < %(y2)f"%locals())
|
|
|
|
# Now mu is between mu1 and mu2
|
|
yfound = y2
|
|
# We found bounds. What if the next loop is never run ?
|
|
# i.e. x1 or x2 are close to the solution
|
|
# we have to know which one is the best ....
|
|
if abs(y1-y_value)< abs(y2-y_value) :
|
|
x=x1
|
|
else:
|
|
x=x2
|
|
|
|
#Now let's refine our mu....
|
|
while (nbre_loop<= max_loops) and (abs(yfound-y_value)>precision_on_y) :
|
|
nbre_loop +=1
|
|
x = x1 + (x2 - x1) * (y_value - y1)/(y2-y1)
|
|
yfound = function(x)
|
|
if (y1-y_value)*(yfound - y_value)>0 :
|
|
x1 = x; y1=yfound
|
|
else :
|
|
x2= x;y2=yfound;
|
|
if verbosity>2 :
|
|
mpi.report("%(PR)s%(x1)f < %(x_name)s < %(x2)f"%locals())
|
|
mpi.report("%(PR)s%(y1)f < %(y_name)s < %(y2)f"%locals())
|
|
if abs(yfound - y_value) < precision_on_y :
|
|
if verbosity>0:
|
|
mpi.report("%(PR)s%(x_name)s found in %(nbre_loop)d iterations : "%locals())
|
|
mpi.report("%(PR)s%(y_name)s = %(yfound)f;%(x_name)s = %(x)f"%locals())
|
|
return (x,yfound)
|
|
else :
|
|
if verbosity>0:
|
|
mpi.report("%(PR)sFAILURE to adjust %(x_name)s to the value %(y_value)f after %(nbre_loop)d iterations."%locals())
|
|
return (None,None)
|
|
|