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I found code for compute jacobian matrix from here and try it for non-linear system of equations.

import autograd.numpy as np
from autograd import jacobian

x = np.array([1,2], dtype=float)

def fs(x,y):
  return np.array([x + 2*y - 2, x**2 + 4*y**2 - 4])

jacobian_cost = jacobian(fs)

jacobian_cost(x[0],x[1])

But instead of outputting result like this

array([ 1.  2.]
 [ 2. 16.])

it outputting result like this

array([1., 2.])

I curious about whats wrong with this code, maybe i missing something.

tukulesia123
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1 Answers1

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You need to vectorize your function, and call it in a vectorized manner. So define

def fs(x):
    return np.stack([x[0,:]+ 2*x[1, :]-2, x[0, :]**2+4*x[1,:]**2-4])

and then call

x = np.array([[1.0, 2]])
output = jacobian(fs)(x)

But note that the autograd library is very outdated, doesn't have a very good documentation and is no longer maintained. I'd recommend using PyTorch or JAX instead.

flawr
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  • I'm very agree about 'autograd' are not have good documentation. It make me struggle bcs that. Moreover, I need jacobian for the broyden algorithm that I am currently making. Should I use JAX or Pytorch for jacobian? Btw i use numpy for my broyden algorithm. – tukulesia123 Oct 14 '22 at 10:02
  • I'm not very familiar with JAX, and I'd recommend using PyTorch for starting out, as it has a more extensive documentation and a very large community of users and therefore resources. It is compatible with numpy, but for most projects you can basically replace numpy with pytorch. – flawr Oct 14 '22 at 13:18