import numpy as np

### Functions for you to fill in ###


def polynomial_kernel(X, Y, c, p):
    """
        Compute the polynomial kernel between two matrices X and Y::
            K(x, y) = (<x, y> + c)^p
        for each pair of rows x in X and y in Y.

        Args:
            X - (n, d) NumPy array (n datapoints each with d features)
            Y - (m, d) NumPy array (m datapoints each with d features)
            c - a coefficient to trade off high-order and low-order terms (scalar)
            p - the degree of the polynomial kernel

        Returns:
            kernel_matrix - (n, m) Numpy array containing the kernel matrix
    """
    # YOUR CODE HERE

    return (X@Y.T+c)**p


def rbf_kernel(X, Y, gamma):
    """
        Compute the Gaussian RBF kernel between two matrices X and Y::
            K(x, y) = exp(-gamma ||x-y||^2)
        for each pair of rows x in X and y in Y.

        Args:
            X - (n, d) NumPy array (n datapoints each with d features)
            Y - (m, d) NumPy array (m datapoints each with d features)
            gamma - the gamma parameter of gaussian function (scalar)

        Returns:
            kernel_matrix - (n, m) Numpy array containing the kernel matrix
    """
    # YOUR CODE HERE
    n, d = X.shape
    m = Y.shape[0]
    res = np.zeros((n, m))

    for i in range(n):
        for j in range(m):

            r = np.linalg.norm(X[i]-Y[j])
            res[i, j] = r
    res = -gamma*res**2
    res = np.exp(res)
    return res
    #raise NotImplementedError
