If I use the runnable code from the linked question and substitute your definition of initial_guess:
mean_gauss_x = sum(x * data.reshape(201,201)) / sum(data.reshape(201,201))
sigma_gauss_x = np.sqrt(sum(data.reshape(201,201) * (x - mean_gauss_x)**2) / sum(data.reshape(201,201)))
mean_gauss_y = sum(y * data.reshape(201,201)) / sum(data.reshape(201,201))
sigma_gauss_y = np.sqrt(sum(data.reshape(201,201) * (y - mean_gauss_y)**2) / sum(data.reshape(201,201)))
initial_guess = (np.max(data), mean_gauss_x, mean_gauss_y, sigma_gauss_x, sigma_gauss_y,0,10)
Then
print(inital_guess)
yields
(13.0, array([...]), array([...]), array([...]), array([...]), 0, 10)
Notice that some of the values in initial_guess are arrays. The optimize.curve_fit function expects initial_guess to be a tuple of scalars. This is the source of the problem.
The error message
ValueError: setting an array element with a sequence
often arises when an array-like is supplied when a scalar value is expected. It is a hint that the source of the problem may have to do with an array having the wrong number of dimensions. For example, it might arise if you pass a 1D array to a function that expects a scalar.
Let's look at this piece of code taken from the linked question:
x = np.linspace(0, 200, 201)
y = np.linspace(0, 200, 201)
X, Y = np.meshgrid(x, y)
x and y are 1D arrays, while X and Y are 2D arrays. (I've capitalized all 2D arrays to help distinguish them from 1D arrays).
Now notice that Python sum and NumPy's sum method behave differently when applied to 2D arrays:
In [146]: sum(X)
Out[146]:
array([ 0., 201., 402., 603., 804., 1005., 1206., 1407.,
1608., 1809., 2010., 2211., 2412., 2613., 2814., 3015.,
...
38592., 38793., 38994., 39195., 39396., 39597., 39798., 39999.,
40200.])
In [147]: X.sum()
Out[147]: 4040100.0
The Python sum function is equivalent to
total = 0
for item in X:
total += item
Since X is a 2D array, the loop for item in X is iterating over the rows of X. Each item is therefore a 1D array representing a row of X. Thus, total ends up being a 1D array.
In contrast, X.sum() sums all the elements in X and returns a scalar.
Since initial_guess should be a tuple of scalars,
everywhere you use sum you should instead use the NumPy sum method. For example, replace
mean_gauss_x = sum(x * data) / sum(data)
with
mean_gauss_x = (X * DATA).sum() / (DATA.sum())
import numpy as np
import scipy.optimize as optimize
import matplotlib.pyplot as plt
# define model function and pass independant variables x and y as a list
def twoD_Gaussian(data, amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
X, Y = data
xo = float(xo)
yo = float(yo)
a = (np.cos(theta) ** 2) / (2 * sigma_x ** 2) + (np.sin(theta) ** 2) / (
2 * sigma_y ** 2
)
b = -(np.sin(2 * theta)) / (4 * sigma_x ** 2) + (np.sin(2 * theta)) / (
4 * sigma_y ** 2
)
c = (np.sin(theta) ** 2) / (2 * sigma_x ** 2) + (np.cos(theta) ** 2) / (
2 * sigma_y ** 2
)
g = offset + amplitude * np.exp(
-(a * ((X - xo) ** 2) + 2 * b * (X - xo) * (Y - yo) + c * ((Y - yo) ** 2))
)
return g.ravel()
# Create x and y indices
x = np.linspace(0, 200, 201)
y = np.linspace(0, 200, 201)
X, Y = np.meshgrid(x, y)
# create data
data = twoD_Gaussian((X, Y), 3, 100, 100, 20, 40, 0, 10)
data_noisy = data + 0.2 * np.random.normal(size=data.shape)
DATA = data.reshape(201, 201)
# add some noise to the data and try to fit the data generated beforehand
mean_gauss_x = (X * DATA).sum() / (DATA.sum())
sigma_gauss_x = np.sqrt((DATA * (X - mean_gauss_x) ** 2).sum() / (DATA.sum()))
mean_gauss_y = (Y * DATA).sum() / (DATA.sum())
sigma_gauss_y = np.sqrt((DATA * (Y - mean_gauss_y) ** 2).sum() / (DATA.sum()))
initial_guess = (
np.max(data),
mean_gauss_x,
mean_gauss_y,
sigma_gauss_x,
sigma_gauss_y,
0,
10,
)
print(initial_guess)
# (13.0, 100.00000000000001, 100.00000000000001, 57.106515650488404, 57.43620227324201, 0, 10)
# initial_guess = (3,100,100,20,40,0,10)
popt, pcov = optimize.curve_fit(twoD_Gaussian, (X, Y), data_noisy, p0=initial_guess)
data_fitted = twoD_Gaussian((X, Y), *popt)
fig, ax = plt.subplots(1, 1)
ax.imshow(
data_noisy.reshape(201, 201),
cmap=plt.cm.jet,
origin="bottom",
extent=(X.min(), X.max(), Y.min(), Y.max()),
)
ax.contour(X, Y, data_fitted.reshape(201, 201), 8, colors="w")
plt.show()
