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