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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 check_angle_sampling(nvecs, angles):
 """ Returns a list of the index of elements of n which do not have adequate toy angle coverage. The criterion is that we must have at least one sample in each Nyquist box when we project the toy angles along the vector n. Parameters nvecs : array_like Array of integer vectors. angles : array_like Array of angles. Returns ------- failed_nvecs : :class:`numpy.ndarray` Array of all integer vectors that failed checks. Has shape (N,3). failures : :class:`numpy.ndarray` Array of flags that designate whether this failed needing a longer integration window (0) or finer sampling (1). """


    failed_nvecs = []
    failures = []

    for i, vec in enumerate(nvecs):
        # N = np.linalg.norm(vec)
        # X = np.dot(angles,vec)
        X = (angles*vec[:, None]).sum(axis=0)
        diff = float(np.abs(X.max() - X.min()))

        if diff < (2.*np.pi):
            warnings.warn("Need a longer integration window for mode {0}"
                          .format(vec))
            failed_nvecs.append(vec.tolist())
            # P.append(2.*np.pi - diff)
            failures.append(0)

        elif (diff/len(X)) > np.pi:
            warnings.warn("Need a finer sampling for mode {0}"
                          .format(str(vec)))
            failed_nvecs.append(vec.tolist())
            # P.append(np.pi - diff/len(X))
            failures.append(1)

    return np.array(failed_nvecs), np.array(failures)