import numpy as np
from scipy.linalg import inv
from sklearn.datasets import load_boston
from sklearn.kernel_ridge import KernelRidge as skKernelRidge
from sklearn.linear_model import Ridge as skRidge

class KernelRidge():
    def __init__(self, alpha=1.0):
        self.alpha = alpha

    """
    @staticmethod
    def _linear_kernel(X, Y):
        K = np.zeros((X.shape[0], Y.shape[0]))
        for i in range(X.shape[0]):
            for j in range(Y.shape[0]):
                K[i, j] = np.dot(X[i], Y[j])
        return K
    """

    @staticmethod
    def _linear_kernel(X, Y):
        K = np.dot(X, Y.T)
        return K

    def fit(self, X, y):
        A = self._linear_kernel(X, X) + np.diag(np.full(X.shape[0], self.alpha))
        self.dual_coef_ = np.dot(inv(A), y)
        self.X_fit_ = X
        return self

    def predict(self, X):
        K = self._linear_kernel(X, self.X_fit_)
        return np.dot(K, self.dual_coef_)

for alpha in [0.1, 1, 10]:
    X, y = load_boston(return_X_y = True)
    clf1 = KernelRidge(alpha=alpha).fit(X, y)
    clf2 = skKernelRidge(alpha=alpha).fit(X, y)
    assert np.allclose(clf1.dual_coef_, clf2.dual_coef_, atol=1e-5)
    assert np.allclose(clf1.X_fit_, clf2.X_fit_)
    pred1 = clf1.predict(X)
    pred2 = clf2.predict(X)
    assert np.allclose(pred1, pred2)

# KernelRidge kernel='linear' is equivalant to Ridge
X, y = load_boston(return_X_y = True)
X = X - X.mean(axis=0)
y = y - y.mean()
clf1 = skKernelRidge().fit(X, y)
clf2 = skRidge().fit(X, y)
assert np.allclose(np.dot(X.T, clf1.dual_coef_), clf2.coef_)
pred1 = clf1.predict(X)
pred2 = clf2.predict(X)
assert np.allclose(pred1, pred2)

class KernelRidge():
    def __init__(self, alpha=1.0, gamma=None):
        self.alpha = alpha
        self.gamma = gamma

    @staticmethod
    def _rbf_kernel(X, Y, gamma):
        if gamma is None:
            gamma = 1 / X.shape[1]
        K = np.zeros((X.shape[0], Y.shape[0]))
        for i in range(X.shape[0]):
            for j in range(Y.shape[0]):
                K[i, j] = np.exp(-gamma * np.sum(np.square(X[i] - Y[j])))
        return K

    def fit(self, X, y):
        A = self._rbf_kernel(X, X, self.gamma) + np.diag(np.full(X.shape[0], self.alpha))
        self.dual_coef_ = np.dot(inv(A), y)
        self.X_fit_ = X
        return self

    def predict(self, X):
        K = self._rbf_kernel(X, self.X_fit_, self.gamma)
        return np.dot(K, self.dual_coef_)

for gamma in [0.1, 1, 10, None]:
    X, y = load_boston(return_X_y = True)
    clf1 = KernelRidge(gamma=gamma).fit(X, y)
    clf2 = skKernelRidge(kernel='rbf', gamma=gamma).fit(X, y)
    assert np.allclose(clf1.dual_coef_, clf2.dual_coef_)
    assert np.allclose(clf1.X_fit_, clf2.X_fit_)
    pred1 = clf1.predict(X)
    pred2 = clf2.predict(X)
    assert np.allclose(pred1, pred2)