constrNMPy package

Submodules

constrNMPy.constrNMPy module

constrNMPy.constrNMPy.constrNM(func, x0, LB, UB, args=(), xtol=0.0001, ftol=0.0001, maxiter=None, maxfun=None, full_output=0, disp=0, retall=0, callback=None)

Constrained Nelder-Mead optimizer.

Transforms a constrained problem

Parameters:
  • func (function) – Objective function.
  • x0 (numpy.ndarray) – Initial guess.
  • LB (numpy.ndarray) – Lower bounds.
  • UB (numpy.ndarray) – Upper bounds.
Keyword Arguments:
 
  • args (tuple) – Extra arguments passed to func, i.e. func(x,*args).
  • xtol (float) – Absolute error in xopt between iterations that is acceptable for convergence.
  • ftol (float) – Absolute error in func(xopt) between iterations that is acceptable for convergence.
  • maxiter (int) – Maximum number of iterations to perform.
  • maxfun (int) – Maximum number of function evaluations to make.
  • full_output (bool) – Set to True if fopt and warnflag outputs are desired.
  • disp (bool) – Set to True to print convergence messages.
  • retall (bool) – Set to True to return list of solutions at each iteration.
  • callback (callable) – Called after each iteration, as callback(xk), where xk is the current parameter vector.
constrNMPy.constrNMPy.constrObjFunc(x, func, LB, UB, args)

Objective function when using Constrained Nelder-Mead.

Calls TransformX() to transform x into constrained version, then calls objective function func.

Parameters:
  • x (numpy.ndarray) – Input vector.
  • func (function) – Objective function.
  • LB (numpy.ndarray) – Lower bounds.
  • UB (numpy.ndarray) – Upper bounds.
Keyword Arguments:
 

args (tuple) – Extra arguments passed to func, i.e. func(x,*args).
Returns:

Return value of func(x,*args).
Return type:

float
constrNMPy.constrNMPy.getArrayDetailsString(l)

Returns string saying “Array of shape x”, where x is the shape of the array.

Parameters:l (numpy.ndarray) – Some array.
Returns:Printout of type and shape.
Return type:str
constrNMPy.constrNMPy.getListDetailsString(l)

Returns string saying “List of length x”, where x is the length of the list.

Parameters:l (list) – Some list.
Returns:Printout of type and length.
Return type:str
constrNMPy.constrNMPy.printAttr(name, attr, maxL=5)

Prints single attribute in the form attributeName = attributeValue.

If attributes are of type list or numpy.ndarray, will check if the size exceeds threshold. If so, will only print type and dimension of attribute.

Parameters:
  • name (str) – Name of attribute.
  • attr (any) – Attribute value.
Keyword Arguments:
 

maxL (int) – Maximum length threshold.
constrNMPy.constrNMPy.printDict(dic, maxL=5)

Prints all dictionary entries in the form key = value.

If attributes are of type list or numpy.ndarray, will check if the size exceeds threshold. If so, will only print type and dimension of attribute.

Parameters:dic (dict) – Dictionary to be printed.
Returns:True
Return type:bool
constrNMPy.constrNMPy.transformX(x, LB, UB, offset=1e-20)

Transforms x into constrained form, obeying upper bounds UB and lower bounds LB.

Note

Will add tiny offset to LB if LB[i]=0, to avoid singularities.

Idea taken from http://www.mathworks.com/matlabcentral/fileexchange/8277-fminsearchbnd–fminsearchcon

Parameters:
  • x (numpy.ndarray) – Input vector.
  • LB (numpy.ndarray) – Lower bounds.
  • UB (numpy.ndarray) – Upper bounds.
Keyword Arguments:
 

offset (float) – Small offset added to lower bound if LB=0.
Returns:

Transformed x-values.
Return type:

numpy.ndarray
constrNMPy.constrNMPy.transformX0(x0, LB, UB)

Transforms x0 into constrained form, obeying upper bounds UB and lower bounds LB.

Idea taken from http://www.mathworks.com/matlabcentral/fileexchange/8277-fminsearchbnd–fminsearchcon

Parameters:
  • x0 (numpy.ndarray) – Input vector.
  • LB (numpy.ndarray) – Lower bounds.
  • UB (numpy.ndarray) – Upper bounds.
Returns:

Transformed x-values.
Return type:

numpy.ndarray

constrNMPy.test_funcs module

constrNMPy.test_funcs.beales(x)

Beales function.

Beales function given by

\[f(x,y)=(1.5-x+xy)^2+(2.25-x+xy^2)^2+(2.625-x+xy^3)^2\]

See also https://en.wikipedia.org/wiki/Test_functions_for_optimization .

Parameters:x (numpy.ndarray) – 2-D input array.
Returns:f(x,y).
Return type:float
constrNMPy.test_funcs.rosenbrock(x)

rosenbrock function.

Rosenbrock function given by

\[f(x,y)=(1-x)^2+100(y-x^2)^2\]

See also https://en.wikipedia.org/wiki/Test_functions_for_optimization .

Parameters:x (numpy.ndarray) – 2-D input array.

Returns: float: f(x,y).

Module contents

constNMPy: A Python package for constrained Nelder-Mead optimization.