BUG: GaussianProcessRegressor.predict inplace modifies input X, when passed via kernel

### Describe the bug

In line 425, 426 of /sklearn/gaussian_process/_gpr.py (inside the predict method) y_var is modified in place:

```
                # Compute variance of predictive distribution
                # Use einsum to avoid explicitly forming the large matrix
                # V^T @ V just to extract its diagonal afterward.
                y_var = self.kernel_.diag(X)
                y_var -= np.einsum("ij,ji->i", V.T, V)
```

If a kernel (e.g. a custom kernel) is used that returns X when diag(X) is called (X[:,0] == var == diag(X)) this leads to the modification of the original X vector.
So now X == y_var - np.einsum("ij,ji->i", V.T, V).

A simple but dirty fix for me is to always make and return a copy, when building a custom kernel: var = np.copy(X[:,0]).

But because this error is hard to find and debug, and the documentation does not state that one should make a copy, as well user expectation is that a method call won't modify the input, i suggest the following FIX:

# FIX

Just replace the in place modification : `y_var -= np.einsum("ij,ji->i", V.T, V)`

with creation of a new array: `y_var = y_var - np.einsum("ij,ji->i", V.T, V)`





### Steps/Code to Reproduce

```
import numpy as np

from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import Hyperparameter,  Kernel


min_x = 0
max_x = 50
std = 0.2
stop_time = 50

nr_plot_points = 20
number_of_train_points = 5

class MinT(Kernel):

    def __init__(self, sigma_0=1.0, sigma_0_bounds=(0.01, 10)):
        self.sigma_0 = sigma_0
        self.sigma_0_bounds = sigma_0_bounds

    @property
    def hyperparameter_sigma_0(self):
        return Hyperparameter("sigma_0", "numeric", self.sigma_0_bounds)

    def __call__(self, X, Y=None, eval_gradient=False):
        """Return the kernel k(X, Y) and optionally its gradient.

        Parameters
        ----------
        X : ndarray of shape (n_samples_X, n_features)
            Left argument of the returned kernel k(X, Y)

        Y : ndarray of shape (n_samples_Y, n_features), default=None
            Right argument of the returned kernel k(X, Y). If None, k(X, X)
            if evaluated instead.

        eval_gradient : bool, default=False
            Determines whether the gradient with respect to the log of
            the kernel hyperparameter is computed.
            Only supported when Y is None.

        Returns
        -------
        K : ndarray of shape (n_samples_X, n_samples_Y)
            Kernel k(X, Y)

        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims),\
                optional
            The gradient of the kernel k(X, X) with respect to the log of the
            hyperparameter of the kernel. Only returned when `eval_gradient`
            is True.
        """
        X = np.atleast_2d(X)
        ones_x = np.ones_like(X)
        if Y is None:
            Kc = X*ones_x.T
            Kr = ones_x * X.T
            Kcr = np.concatenate((Kc[...,None], Kr[...,None]), axis=-1)
            K = np.min(Kcr, axis=-1)
        else:
            if eval_gradient:
                raise ValueError("Gradient can only be evaluated when Y is None.")
            
            ones_y = np.ones_like(Y)
            Kc = X*ones_y.T
            Kr = ones_x * Y.T
            Kcr = np.concatenate((Kc[...,None], Kr[...,None]), axis=-1)
            K = np.min(Kcr, axis=-1)


        if eval_gradient:
            if not self.hyperparameter_sigma_0.fixed:
                K_gradient = np.empty((K.shape[0], K.shape[1], 1))
                K_gradient[..., 0] = self.sigma_0
                return K, K_gradient
            else:
                return K, np.empty((X.shape[0], X.shape[0], 0))
        else:
            return K

    def diag(self, X):
        """Returns the diagonal of the kernel k(X, X).

        The result of this method is identical to np.diag(self(X)); however,
        it can be evaluated more efficiently since only the diagonal is
        evaluated.

        Parameters
        ----------
        X : ndarray of shape (n_samples_X, n_features)
            Left argument of the returned kernel k(X, Y).

        Returns
        -------
        K_diag : ndarray of shape (n_samples_X,)
            Diagonal of kernel k(X, X).
        """
        return X[:,0] #np.copy(X[:,0])

    def is_stationary(self):
        """Returns whether the kernel is stationary."""
        return False

    def __repr__(self):
        return "{0}(sigma_0={1:.3g})".format(self.__class__.__name__, self.sigma_0)


rng = np.random.RandomState(None)


t_train = np.linspace(0, stop_time, num=number_of_train_points)
y_train =  rng.normal(0, t_train*std)

gpr_min_t = GaussianProcessRegressor(kernel=MinT(), random_state=None, n_restarts_optimizer=5)

gpr_min_t.fit(t_train.reshape(-1, 1), y_train)
x = np.linspace(min_x, max_x, nr_plot_points)
X = x.reshape(-1, 1)

X_copy = np.copy(X)

y_mean, y_std = gpr_min_t.predict(X, return_std=True)

assert np.all(X_copy == X)
```

### Expected Results

The assertion should hold: `assert np.all(X_copy == X)`

### Actual Results

You know: The assertion fails, because X is changed in place by sklearn code... and thus is now equal to:
`X = y_var - np.einsum("ij,ji->i", V.T, V)`

### Versions

```shell
System:
    python: 3.8.10 (default, Jun 22 2022, 20:18:18)  [GCC 9.4.0]
executable: .venv/bin/python
   machine: Linux-5.15.0-46-generic-x86_64-with-glibc2.29

Python dependencies:
      sklearn: 1.1.1
          pip: 22.2.1
   setuptools: 63.2.0
        numpy: 1.23.1
        scipy: 1.8.0
       Cython: None
       pandas: None
   matplotlib: 3.5.2
       joblib: 1.1.0
threadpoolctl: 3.1.0

Built with OpenMP: True

threadpoolctl info:
       user_api: openmp
   internal_api: openmp
         prefix: libgomp
       filepath: .venv/lib/python3.8/site-packages/scikit_learn.libs/libgomp-a34b3233.so.1.0.0
        version: None
    num_threads: 16

       user_api: blas
   internal_api: openblas
         prefix: libopenblas
       filepath: .venv/lib/python3.8/site-packages/numpy.libs/libopenblas64_p-r0-742d56dc.3.20.so
        version: 0.3.20
threading_layer: pthreads
   architecture: Zen
    num_threads: 16

       user_api: blas
   internal_api: openblas
         prefix: libopenblas
       filepath: .venv/lib/python3.8/site-packages/scipy.libs/libopenblasp-r0-8b9e111f.3.17.so
        version: 0.3.17
threading_layer: pthreads
   architecture: Zen
    num_threads: 16
```

COMMENT:
Feel free to submit a PR.

On Thu, 8 Sept 2022 at 08:51, Omar Salman ***@***.***> wrote:

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-- 
Guillaume Lemaitre
Scikit-learn @ Inria Foundation
https://glemaitre.github.io/

Labels: Bug