def id_to_svd(B, idx, proj): """ Convert ID to SVD. The SVD reconstruction of a matrix with skeleton matrix `B` and ID indices and coefficients `idx` and `proj`, respectively, is:: U, S, V = id_to_svd(B, idx, proj) A = numpy.dot(U, numpy.dot(numpy.diag(S), V.conj().T)) See also :func:`svd`. .. This function automatically detects the matrix data type and calls the appropriate backend. For details, see :func:`backend.idd_id2svd` and :func:`backend.idz_id2svd`. Parameters ---------- B : :class:`numpy.ndarray` Skeleton matrix. idx : :class:`numpy.ndarray` Column index array. proj : :class:`numpy.ndarray` Interpolation coefficients. Returns ------- U : :class:`numpy.ndarray` Left singular vectors. S : :class:`numpy.ndarray` Singular values. V : :class:`numpy.ndarray` Right singular vectors. """ if _is_real(B): U, V, S = backend.idd_id2svd(B, idx + 1, proj) else: U, V, S = backend.idz_id2svd(B, idx + 1, proj) return U, S, V