issues: 1674818753

Is your feature request related to a problem?

Hi, I'm trying to use DataArray.curvefit to fit a bunch of data. Let's say the data dimensions are (x, experiment_index), and I'm trying to fit m * x + b, where m will be different for each experiment_index. I would like to supply an initial guess p0 to curvefit that depends on experiment_index, but it seems like this is not supported. Here's a minimal example:

```python import numpy as np import xarray as xr

x = xr.DataArray(coords=[("x", np.linspace(0, 10, 101))]).x i = xr.DataArray(coords=[("experiment_index", [1, 2, 3])]).experiment_index

data = 2.0 * i * x + 5

m_guess = 2 * i

data.curvefit( "x", lambda x, m, b: m * x + b, p0={"m": m_guess} # I would like to provide a guess for 'm' as a function of experiment_index ) ```

Describe the solution you'd like

I would like to be able to provide arrays as the values of p0, so that I can have different initial guesses for different slices of the data.

I suppose this could also be implemented for bounds.

Describe alternatives you've considered

I could wrap curvefit in a for-loop, for example

python result = [] for y in data.transpose("experiment_index", ...): result.append(y.curvefit( "x", lambda x, m, b: m * x + b, p0={"m": m_guess.sel(experiment_index=y.experiment_index).item()}, )) result = xr.concat(result, dim="experiment_index")

But this is quite cumbersome, especially for multidimensional data.

Additional context

The above example gives the error *** ValueError: setting an array element with a sequence. The requested array has an inhomogeneous shape after 1 dimensions. The detected shape was (2,) + inhomogeneous part. because curve_fit tries to do np.atleast_1d([m_guess, 1]), but it should be np.atleast_1d([m_guess[0], 1]).

~~The above example gives the error~~ ValueError: operands could not be broadcast together with shapes (3,) (101,) ~~which comes from scipy.curve_fit tying to compute m * x, where m is the DataArray m_guess, but x is a plain Numpy array, basically x.data.~~ - this applies for scipy 1.7.

This toy example of course works with just a scalar guess like p0={"m": 2}, but in my case the function is more complicated and fit might fail if the initial guess is too far off.

The initial guess is inserted into kwargs passed to curve_fit here: https://github.com/pydata/xarray/blob/c75ac8b7ab33be95f74d9e6f10b8173c68828751/xarray/core/dataset.py#L8659