def _multicomplex(f, fx, x, h):
n = len(x)
cmplx_wrap = Bicomplex.__array_wrap__
partials = [
cmplx_wrap(f(Bicomplex(x + 1j * hi, 0))).imag
for hi in Jacobian._increments(n, h)
]
return np.array(partials)
def _multicomplex2(f, fx, x, h):
n = len(x)
increments = np.identity(n) * h
cmplx_wrap = Bicomplex.__array_wrap__
partials = [
cmplx_wrap(f(Bicomplex(x + 1j * hi, hi))).imag12
for hi in increments
]
return np.array(partials)
def _multicomplex2(f, fx, x, h):
"""Calculate Hessian with Bicomplex-step derivative approximation"""
n = len(x)
ee = np.diag(h)
hess = np.outer(h, h)
cmplx_wrap = Bicomplex.__array_wrap__
for i in range(n):
for j in range(i, n):
zph = Bicomplex(x + 1j * ee[i, :], ee[j, :])
hess[i, j] = cmplx_wrap(f(zph)).imag12 / hess[j, i]
hess[j, i] = hess[i, j]
return hess
def _multicomplex2(f, fx, x, h):
z = Bicomplex(x + 1j * h, h)
return Bicomplex.__array_wrap__(f(z)).imag12