papyri
{ } Raw JSON

bundles / scipy latest / scipy / optimize / _lbfgsb_py / fmin_l_bfgs_b

function

scipy.optimize._lbfgsb_py:fmin_l_bfgs_b

source: /scipy/optimize/_lbfgsb_py.py :94

Signature

def   fmin_l_bfgs_b ( func ,  x0 ,  fprime = None ,  args = () ,  approx_grad = 0 ,  bounds = None ,  m = 10 ,  factr = 10000000.0 ,  pgtol = 1e-05 ,  epsilon = 1e-08 ,  iprint = <object object at 0x0000> ,  maxfun = 15000 ,  maxiter = 15000 ,  disp = <object object at 0x0000> ,  callback = None ,  maxls = 20 )

Summary

Minimize a function func using the L-BFGS-B algorithm.

Parameters

func : callable f(x,*args)

Function to minimize.

x0 : ndarray

Initial guess.

fprime : callable fprime(x,*args), optional

The gradient of func. If None, then func returns the function value and the gradient (f, g = func(x, *args)), unless approx_grad is True in which case func returns only f.

args : sequence, optional

Arguments to pass to func and fprime.

approx_grad : bool, optional

Whether to approximate the gradient numerically (in which case func returns only the function value).

bounds : list, optional

(min, max) pairs for each element in x, defining the bounds on that parameter. Use None or +-inf for one of min or max when there is no bound in that direction.

m : int, optional

The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.)

factr : float, optional

The iteration stops when (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B.

pgtol : float, optional

The iteration will stop when max{|proj g_i | i = 1, ..., n} <= pgtol where proj g_i is the i-th component of the projected gradient.

epsilon : float, optional

Step size used when approx_grad is True, for numerically calculating the gradient

iprint : int, optional

Deprecated option that previously controlled the text printed on the screen during the problem solution. Now the code does not emit any output and this keyword has no function.

disp : int, optional

Deprecated option that previously controlled the text printed on the screen during the problem solution. Now the code does not emit any output and this keyword has no function.

maxfun : int, optional

Maximum number of function evaluations. Note that this function may violate the limit because of evaluating gradients by numerical differentiation.

maxiter : int, optional

Maximum number of iterations.

callback : callable, optional

Called after each iteration, as callback(xk), where xk is the current parameter vector.

maxls : int, optional

Maximum number of line search steps (per iteration). Default is 20.

Returns

x : array_like

Estimated position of the minimum.

f : float

Value of func at the minimum.

d : dict

Information dictionary.

  • d['warnflag'] is

    • 0 if converged,

    • 1 if too many function evaluations or too many iterations,

    • 2 if stopped for another reason, given in d['task']

  • d['grad'] is the gradient at the minimum (should be 0 ish)

  • d['funcalls'] is the number of function calls made.

  • d['nit'] is the number of iterations.

Notes

SciPy uses a C-translated and modified version of the Fortran code, L-BFGS-B v3.0 (released April 25, 2011, BSD-3 licensed). Original Fortran version was written by Ciyou Zhu, Richard Byrd, Jorge Nocedal and, Jose Luis Morales.

Examples

Solve a linear regression problem via `fmin_l_bfgs_b`. To do this, first we define an objective function ``f(m, b) = (y - y_model)**2``, where `y` describes the observations and `y_model` the prediction of the linear model as ``y_model = m*x + b``. The bounds for the parameters, ``m`` and ``b``, are arbitrarily chosen as ``(0,5)`` and ``(5,10)`` for this example. 
import numpy as np
from scipy.optimize import fmin_l_bfgs_b
X = np.arange(0, 10, 1)
M = 2
B = 3
Y = M * X + B
def func(parameters, *args):
    x = args[0]
    y = args[1]
    m, b = parameters
    y_model = m*x + b
    error = sum(np.power((y - y_model), 2))
    return error
✓
initial_values = np.array([0.0, 1.0])
✓
x_opt, f_opt, info = fmin_l_bfgs_b(func, x0=initial_values, args=(X, Y),
                                   approx_grad=True)
✓
x_opt, f_opt
✗
The optimized parameters in ``x_opt`` agree with the ground truth parameters ``m`` and ``b``. Next, let us perform a bound constrained optimization using the `bounds` parameter. 
bounds = [(0, 5), (5, 10)]
x_opt, f_op, info = fmin_l_bfgs_b(func, x0=initial_values, args=(X, Y),
                                  approx_grad=True, bounds=bounds)
✓
x_opt, f_opt
✗

See also

minimize

Interface to minimization algorithms for multivariate functions. See the 'L-BFGS-B' method in particular. Note that the ftol option is made available via that interface, while factr is provided via this interface, where factr is the factor multiplying the default machine floating-point precision to arrive at ftol: ftol = factr * numpy.finfo(float).eps.

Aliases

  • scipy.optimize.fmin_l_bfgs_b

Referenced by

This package