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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def transform(self, X, mean=None, lenscale=None):
 """ Apply the spectral mixture component basis to X. Parameters X: ndarray (N, d) array of observations where N is the number of samples, and d is the dimensionality of X. mean: ndarray, optional array of shape (d,) frequency means (one for each dimension of X). If not input, this uses the value of the initial mean. lenscale: ndarray, optional array of shape (d,) length scales (one for each dimension of X). If not input, this uses the value of the initial length scale. Returns ------- ndarray: of shape (N, 4*nbases) where nbases is number of random bases to use, given in the constructor (to nearest larger two power). """

        mean = self._check_dim(X.shape[1], mean, paramind=0)
        lenscale = self._check_dim(X.shape[1], lenscale, paramind=1)

        VX = self._makeVX(X / lenscale)
        mX = X.dot(mean)[:, np.newaxis]
        Phi = np.hstack((np.cos(VX + mX), np.sin(VX + mX),
                         np.cos(VX - mX), np.sin(VX - mX))) / \
            np.sqrt(2 * self.n)

        return Phi