# Source code for qutip.essolve

    __all__ = ['essolve', 'ode2es']

    import numpy as np
    import scipy.linalg as la
    import scipy.sparse as sp

    from qutip.qobj import Qobj, issuper, isket, isoper
    from qutip.eseries import eseries, estidy, esval
    from qutip.expect import expect
    from qutip.superoperator import liouvillian, mat2vec, vec2mat
    from qutip.solver import Result
    from qutip.operators import qzero

    # Only used for deprecation warnings.
    import functools
    import warnings

    def _deprecate(alternative):
        def decorated(f):
            message = (
                f"{f.__name__} is to be removed in QuTiP 5.0"
                f", consider swapping to {alternative}."
            )

            @functools.wraps(f)
            def out(*args, **kwargs):
                warnings.warn(message, DeprecationWarning, stacklevel=2)
                return f(*args, **kwargs)
            return out
        return decorated

    # -----------------------------------------------------------------------------
    # pass on to wavefunction solver or master equation solver depending on whether
    # any collapse operators were given.
    #

    @_deprecate("mesolve")
    def essolve(H, rho0, tlist, c_op_list, e_ops):
        """
        Evolution of a state vector or density matrix (`rho0`) for a given
        Hamiltonian (`H`) and set of collapse operators (`c_op_list`), by
        expressing the ODE as an exponential series. The output is either
        the state vector at arbitrary points in time (`tlist`), or the
        expectation values of the supplied operators (`e_ops`).

        .. deprecated:: 4.6.0
            :obj:`~essolve` will be removed in QuTiP 5.  Please use
            :obj:`~qutip.sesolve` or :obj:`~qutip.mesolve` for general-purpose
            integration of the Schroedinger/Lindblad master equation.
            This will likely be faster than :obj:`~essolve` for you.

        Parameters
        ----------
        H : qobj/function_type
            System Hamiltonian.

        rho0 : :class:`qutip.qobj`
            Initial state density matrix.

        tlist : list/array
            ``list`` of times for :math:`t`.

        c_op_list : list of :class:`qutip.qobj`
            ``list`` of :class:`qutip.qobj` collapse operators.

        e_ops : list of :class:`qutip.qobj`
            ``list`` of :class:`qutip.qobj` operators for which to evaluate
            expectation values.

        Returns
        -------
         expt_array : array
            Expectation values of wavefunctions/density matrices for the
            times specified in ``tlist``.

        .. note:: This solver does not support time-dependent Hamiltonians.

        """
        n_expt_op = len(e_ops)
        n_tsteps = len(tlist)

        # Calculate the Liouvillian
        if (c_op_list is None or len(c_op_list) == 0) and isket(rho0):
            L = H
        else:
            L = liouvillian(H, c_op_list)

        es = ode2es(L, rho0)

        # evaluate the expectation values
        if n_expt_op == 0:
            results = [Qobj()] * n_tsteps
        else:
            results = np.zeros([n_expt_op, n_tsteps], dtype=complex)

        for n, e in enumerate(e_ops):
            results[n, :] = expect(e, esval(es, tlist))

        data = Result()
        data.solver = "essolve"
        data.times = tlist
        data.expect = [np.real(results[n, :]) if e.isherm else results[n, :]
                       for n, e in enumerate(e_ops)]

        return data

    # -----------------------------------------------------------------------------
    #
    #

    @_deprecate("direct eigenstate and -value calculation")
    def ode2es(L, rho0):
        """Creates an exponential series that describes the time evolution for the
        initial density matrix (or state vector) `rho0`, given the Liouvillian
        (or Hamiltonian) `L`.

        .. deprecated:: 4.6.0
            :obj:`~ode2es` will be removed in QuTiP 5.  Please use
            :obj:`qutip.Qobj.eigenstates` to get the eigenstates and -values,
            and use :obj:`~qutip.QobjEvo` for general time-dependence.

        Parameters
        ----------
        L : qobj
            Liouvillian of the system.

        rho0 : qobj
            Initial state vector or density matrix.

        Returns
        -------
        eseries : :class:`qutip.eseries`
            ``eseries`` represention of the system dynamics.

        """
        if issuper(L):
            # check initial state
            if isket(rho0):
                # Got a wave function as initial state: convert to density matrix.
                rho0 = rho0 * rho0.dag()
            # check if state is below error threshold
            if abs(rho0.full()).sum() < 1e-10 + 1e-24:
                # enforce zero operator
                return eseries(qzero(rho0.dims[0]))
            w, v = L.eigenstates()
            v = np.hstack([ket.full() for ket in v])
            # w[i]   = eigenvalue i
            # v[:,i] = eigenvector i

            rlen = np.prod(rho0.shape)
            r0 = mat2vec(rho0.full())
            v0 = la.solve(v, r0)
            vv = v * sp.spdiags(v0.T, 0, rlen, rlen)

            out = None
            for i in range(rlen):
                qo = Qobj(vec2mat(vv[:, i]), dims=rho0.dims, shape=rho0.shape)
                if out:
                    out += eseries(qo, w[i])
                else:
                    out = eseries(qo, w[i])

        elif isoper(L):

            if not isket(rho0):
                raise TypeError('Second argument must be a ket if first' +
                                'is a Hamiltonian.')

            # check if state is below error threshold
            if abs(rho0.full()).sum() < 1e-5 + 1e-20:
                # enforce zero operator
                dims = rho0.dims
                return eseries(Qobj(sp.csr_matrix((dims[0][0], dims[1][0]),
                                                  dtype=complex)))

            w, v = L.eigenstates()
            v = np.hstack([ket.full() for ket in v])
            # w[i]   = eigenvalue i
            # v[:,i] = eigenvector i

            rlen = np.prod(rho0.shape)
            r0 = rho0.full()
            v0 = la.solve(v, r0)
            vv = v * sp.spdiags(v0.T, 0, rlen, rlen)

            out = None
            for i in range(rlen):
                qo = Qobj(np.array(vv[:, i]).T, dims=rho0.dims, shape=rho0.shape)
                if out:
                    out += eseries(qo, -1.0j * w[i])
                else:
                    out = eseries(qo, -1.0j * w[i])

        else:
            raise TypeError('First argument must be a Hamiltonian or Liouvillian.')

        return estidy(out)