5.1.7.2. numdifftools.nd_scipy.Jacobian¶
- class Jacobian(fun, step=None, method='central', order=2, bounds=(-inf, inf), sparsity=None)[source]¶
Calculate Jacobian with finite difference approximation
- Parameters
- funfunction
function of one array fun(x, *args, **kwds)
- stepfloat, optional
Stepsize, if None, optimal stepsize is used, i.e., x * _EPS for method==`complex` x * _EPS**(1/2) for method==`forward` x * _EPS**(1/3) for method==`central`.
- method{‘central’, ‘complex’, ‘forward’}
defines the method used in the approximation.
Examples
>>> import numpy as np >>> import numdifftools.nd_scipy as nd
#(nonlinear least squares)
>>> xdata = np.arange(0,1,0.1) >>> ydata = 1+2*np.exp(0.75*xdata) >>> fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2 >>> np.allclose(fun([1, 2, 0.75]).shape, (10,)) True >>> dfun = nd.Jacobian(fun) >>> np.allclose(dfun([1, 2, 0.75]), np.zeros((10,3))) True
>>> fun2 = lambda x : x[0]*x[1]*x[2]**2 >>> dfun2 = nd.Jacobian(fun2) >>> np.allclose(dfun2([1.,2.,3.]), [[18., 9., 12.]]) True
>>> fun3 = lambda x : np.vstack((x[0]*x[1]*x[2]**2, x[0]*x[1]*x[2]))
TODO: The following does not work: der3 = nd.Jacobian(fun3)([1., 2., 3.]) np.allclose(der3, … [[18., 9., 12.], [6., 3., 2.]]) True np.allclose(nd.Jacobian(fun3)([4., 5., 6.]), … [[180., 144., 240.], [30., 24., 20.]]) True
np.allclose(nd.Jacobian(fun3)(np.array([[1.,2.,3.], [4., 5., 6.]]).T), … [[[ 18., 180.], … [ 9., 144.], … [ 12., 240.]], … [[ 6., 30.], … [ 3., 24.], … [ 2., 20.]]]) True
- __init__(fun, step=None, method='central', order=2, bounds=(-inf, inf), sparsity=None)¶
Methods
__init__
(fun[, step, method, order, bounds, ...])