#!/usr/bin/env python
# Copyright 2014-2019 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#
# Ref:
# J. Chem. Phys. 117, 7433
#


from functools import reduce
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.dft import rks
from pyscf.dft import numint
from pyscf.scf import cphf
from pyscf.grad import rks as rks_grad
from pyscf.grad import tdrhf


#
# Given Y = 0, TDDFT gradients (XAX+XBY+YBX+YAY)^1 turn to TDA gradients (XAX)^1
#
def grad_elec(td_grad, x_y, singlet=True, atmlst=None,
              max_memory=2000, verbose=logger.INFO):
    '''
    Electronic part of TDA, TDDFT nuclear gradients

    Args:
        td_grad : grad.tdrhf.Gradients or grad.tdrks.Gradients object.

        x_y : a two-element list of numpy arrays
            TDDFT X and Y amplitudes. If Y is set to 0, this function computes
            TDA energy gradients.
    '''
    log = logger.new_logger(td_grad, verbose)
    time0 = logger.process_clock(), logger.perf_counter()

    mol = td_grad.mol
    mf = td_grad.base._scf
    mo_coeff = mf.mo_coeff
    mo_energy = mf.mo_energy
    mo_occ = mf.mo_occ
    nao, nmo = mo_coeff.shape
    nocc = (mo_occ>0).sum()
    nvir = nmo - nocc
    x, y = x_y
    xpy = (x+y).reshape(nocc,nvir).T
    xmy = (x-y).reshape(nocc,nvir).T
    orbv = mo_coeff[:,nocc:]
    orbo = mo_coeff[:,:nocc]

    dvv = numpy.einsum('ai,bi->ab', xpy, xpy) + numpy.einsum('ai,bi->ab', xmy, xmy)
    doo =-numpy.einsum('ai,aj->ij', xpy, xpy) - numpy.einsum('ai,aj->ij', xmy, xmy)
    dmxpy = reduce(numpy.dot, (orbv, xpy, orbo.T))
    dmxmy = reduce(numpy.dot, (orbv, xmy, orbo.T))
    dmzoo = reduce(numpy.dot, (orbo, doo, orbo.T))
    dmzoo+= reduce(numpy.dot, (orbv, dvv, orbv.T))

    mem_now = lib.current_memory()[0]
    max_memory = max(2000, td_grad.max_memory*.9-mem_now)

    ni = mf._numint
    ni.libxc.test_deriv_order(mf.xc, 3, raise_error=True)
    omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, mol.spin)
    # dm0 = mf.make_rdm1(mo_coeff, mo_occ), but it is not used when computing
    # fxc since rho0 is passed to fxc function.
    rho0, vxc, fxc = ni.cache_xc_kernel(mf.mol, mf.grids, mf.xc,
                                        [mo_coeff]*2, [mo_occ*.5]*2, spin=1)
    f1vo, f1oo, vxc1, k1ao = \
            _contract_xc_kernel(td_grad, mf.xc, dmxpy,
                                dmzoo, True, True, singlet, max_memory)

    if ni.libxc.is_hybrid_xc(mf.xc):
        dm = (dmzoo, dmxpy+dmxpy.T, dmxmy-dmxmy.T)
        vj, vk = mf.get_jk(mol, dm, hermi=0)
        vk *= hyb
        if omega != 0:
            vk += mf.get_k(mol, dm, hermi=0, omega=omega) * (alpha-hyb)
        veff0doo = vj[0] * 2 - vk[0] + f1oo[0] + k1ao[0] * 2
        wvo = reduce(numpy.dot, (orbv.T, veff0doo, orbo)) * 2
        if singlet:
            veff = vj[1] * 2 - vk[1] + f1vo[0] * 2
        else:
            veff = -vk[1] + f1vo[0] * 2
        veff0mop = reduce(numpy.dot, (mo_coeff.T, veff, mo_coeff))
        wvo -= numpy.einsum('ki,ai->ak', veff0mop[:nocc,:nocc], xpy) * 2
        wvo += numpy.einsum('ac,ai->ci', veff0mop[nocc:,nocc:], xpy) * 2
        veff = -vk[2]
        veff0mom = reduce(numpy.dot, (mo_coeff.T, veff, mo_coeff))
        wvo -= numpy.einsum('ki,ai->ak', veff0mom[:nocc,:nocc], xmy) * 2
        wvo += numpy.einsum('ac,ai->ci', veff0mom[nocc:,nocc:], xmy) * 2
    else:
        vj = mf.get_j(mol, (dmzoo, dmxpy+dmxpy.T), hermi=1)
        veff0doo = vj[0] * 2 + f1oo[0] + k1ao[0] * 2
        wvo = reduce(numpy.dot, (orbv.T, veff0doo, orbo)) * 2
        if singlet:
            veff = vj[1] * 2 + f1vo[0] * 2
        else:
            veff = f1vo[0] * 2
        veff0mop = reduce(numpy.dot, (mo_coeff.T, veff, mo_coeff))
        wvo -= numpy.einsum('ki,ai->ak', veff0mop[:nocc,:nocc], xpy) * 2
        wvo += numpy.einsum('ac,ai->ci', veff0mop[nocc:,nocc:], xpy) * 2
        veff0mom = numpy.zeros((nmo,nmo))

    # set singlet=None, generate function for CPHF type response kernel
    vresp = mf.gen_response(singlet=None, hermi=1)
    def fvind(x):
        dm = reduce(numpy.dot, (orbv, x.reshape(nvir,nocc)*2, orbo.T))
        v1ao = vresp(dm+dm.T)
        return reduce(numpy.dot, (orbv.T, v1ao, orbo)).ravel()
    z1 = cphf.solve(fvind, mo_energy, mo_occ, wvo,
                    max_cycle=td_grad.cphf_max_cycle,
                    tol=td_grad.cphf_conv_tol)[0]
    z1 = z1.reshape(nvir,nocc)
    time1 = log.timer('Z-vector using CPHF solver', *time0)

    z1ao  = reduce(numpy.dot, (orbv, z1, orbo.T))
    veff = vresp(z1ao+z1ao.T)

    im0 = numpy.zeros((nmo,nmo))
    im0[:nocc,:nocc] = reduce(numpy.dot, (orbo.T, veff0doo+veff, orbo))
    im0[:nocc,:nocc]+= numpy.einsum('ak,ai->ki', veff0mop[nocc:,:nocc], xpy)
    im0[:nocc,:nocc]+= numpy.einsum('ak,ai->ki', veff0mom[nocc:,:nocc], xmy)
    im0[nocc:,nocc:] = numpy.einsum('ci,ai->ac', veff0mop[nocc:,:nocc], xpy)
    im0[nocc:,nocc:]+= numpy.einsum('ci,ai->ac', veff0mom[nocc:,:nocc], xmy)
    im0[nocc:,:nocc] = numpy.einsum('ki,ai->ak', veff0mop[:nocc,:nocc], xpy)*2
    im0[nocc:,:nocc]+= numpy.einsum('ki,ai->ak', veff0mom[:nocc,:nocc], xmy)*2

    zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
    zeta[nocc:,:nocc] = mo_energy[:nocc]
    zeta[:nocc,nocc:] = mo_energy[nocc:]
    dm1 = numpy.zeros((nmo,nmo))
    dm1[:nocc,:nocc] = doo
    dm1[nocc:,nocc:] = dvv
    dm1[nocc:,:nocc] = z1
    dm1[:nocc,:nocc] += numpy.eye(nocc)*2 # for ground state
    im0 = reduce(numpy.dot, (mo_coeff, im0+zeta*dm1, mo_coeff.T))

    # Initialize hcore_deriv with the underlying SCF object because some
    # extensions (e.g. QM/MM, solvent) modifies the SCF object only.
    mf_grad = td_grad.base._scf.nuc_grad_method()
    hcore_deriv = mf_grad.hcore_generator(mol)
    s1 = mf_grad.get_ovlp(mol)

    dmz1doo = z1ao + dmzoo
    oo0 = reduce(numpy.dot, (orbo, orbo.T))
    if ni.libxc.is_hybrid_xc(mf.xc):
        dm = (oo0, dmz1doo+dmz1doo.T, dmxpy+dmxpy.T, dmxmy-dmxmy.T)
        vj, vk = td_grad.get_jk(mol, dm)
        vk *= hyb
        if omega != 0:
            vk += td_grad.get_k(mol, dm, omega=omega) * (alpha-hyb)
        vj = vj.reshape(-1,3,nao,nao)
        vk = vk.reshape(-1,3,nao,nao)
        if singlet:
            veff1 = vj * 2 - vk
        else:
            veff1 = numpy.vstack((vj[:2]*2-vk[:2], -vk[2:]))
    else:
        vj = td_grad.get_j(mol, (oo0, dmz1doo+dmz1doo.T, dmxpy+dmxpy.T))
        vj = vj.reshape(-1,3,nao,nao)
        veff1 = numpy.zeros((4,3,nao,nao))
        if singlet:
            veff1[:3] = vj * 2
        else:
            veff1[:2] = vj[:2] * 2

    fxcz1 = _contract_xc_kernel(td_grad, mf.xc, z1ao, None,
                                False, False, True, max_memory)[0]

    veff1[0] += vxc1[1:]
    veff1[1] +=(f1oo[1:] + fxcz1[1:] + k1ao[1:]*2)*2 # *2 for dmz1doo+dmz1oo.T
    veff1[2] += f1vo[1:] * 2
    time1 = log.timer('2e AO integral derivatives', *time1)

    if atmlst is None:
        atmlst = range(mol.natm)
    offsetdic = mol.offset_nr_by_atom()
    de = numpy.zeros((len(atmlst),3))
    for k, ia in enumerate(atmlst):
        shl0, shl1, p0, p1 = offsetdic[ia]

        # Ground state gradients
        h1ao = hcore_deriv(ia)
        h1ao[:,p0:p1]   += veff1[0,:,p0:p1]
        h1ao[:,:,p0:p1] += veff1[0,:,p0:p1].transpose(0,2,1)
        # oo0*2 for doubly occupied orbitals
        e1  = numpy.einsum('xpq,pq->x', h1ao, oo0) * 2

        e1 += numpy.einsum('xpq,pq->x', h1ao, dmz1doo)
        e1 -= numpy.einsum('xpq,pq->x', s1[:,p0:p1], im0[p0:p1])
        e1 -= numpy.einsum('xqp,pq->x', s1[:,p0:p1], im0[:,p0:p1])

        e1 += numpy.einsum('xij,ij->x', veff1[1,:,p0:p1], oo0[p0:p1])
        e1 += numpy.einsum('xij,ij->x', veff1[2,:,p0:p1], dmxpy[p0:p1,:]) * 2
        e1 += numpy.einsum('xij,ij->x', veff1[3,:,p0:p1], dmxmy[p0:p1,:]) * 2
        e1 += numpy.einsum('xji,ij->x', veff1[2,:,p0:p1], dmxpy[:,p0:p1]) * 2
        e1 -= numpy.einsum('xji,ij->x', veff1[3,:,p0:p1], dmxmy[:,p0:p1]) * 2

        e1 += td_grad.extra_force(ia, locals())

        de[k] = e1

    log.timer('TDRKS nuclear gradients', *time0)
    return de


# dmvo, dmoo in AO-representation
# Note spin-trace is applied for fxc, kxc
#TODO: to include the response of grids
def _contract_xc_kernel(td_grad, xc_code, dmvo, dmoo=None, with_vxc=True,
                        with_kxc=True, singlet=True, max_memory=2000):
    mol = td_grad.mol
    mf = td_grad.base._scf
    grids = mf.grids

    ni = mf._numint
    xctype = ni._xc_type(xc_code)

    mo_coeff = mf.mo_coeff
    mo_occ = mf.mo_occ
    nao, nmo = mo_coeff.shape
    shls_slice = (0, mol.nbas)
    ao_loc = mol.ao_loc_nr()

    # dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
    dmvo = (dmvo + dmvo.T) * .5 # because K_{ia,jb} == K_{ia,bj}

    f1vo = numpy.zeros((4,nao,nao))  # 0th-order, d/dx, d/dy, d/dz
    deriv = 2
    if dmoo is not None:
        f1oo = numpy.zeros((4,nao,nao))
    else:
        f1oo = None
    if with_vxc:
        v1ao = numpy.zeros((4,nao,nao))
    else:
        v1ao = None
    if with_kxc:
        k1ao = numpy.zeros((4,nao,nao))
        deriv = 3
    else:
        k1ao = None

    if xctype == 'LDA':
        ao_deriv = 1
        if singlet:
            def lda_sum_(vmat, ao, wv, mask):
                aow = numint._scale_ao(ao[0], wv)
                for k in range(4):
                    vmat[k] += numint._dot_ao_ao(mol, ao[k], aow, mask, shls_slice, ao_loc)

            for ao, mask, weight, coords \
                    in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
                rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, xctype)
                vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]

                wfxc = fxc[0] * weight * 2  # *2 for alpha+beta
                rho1 = ni.eval_rho(mol, ao[0], dmvo, mask, xctype, hermi=1)
                lda_sum_(f1vo, ao, wfxc * rho1, mask)
                if dmoo is not None:
                    rho2 = ni.eval_rho(mol, ao[0], dmoo, mask, xctype, hermi=1)
                    lda_sum_(f1oo, ao, wfxc * rho2, mask)
                if with_vxc:
                    lda_sum_(v1ao, ao, vxc[0] * weight, mask)
                if with_kxc:
                    lda_sum_(k1ao, ao, kxc[0] * weight * rho1**2, mask)
            if with_kxc:  # for (rho1*2)^2, *2 for alpha+beta in singlet
                k1ao *= 4

        else:
            raise NotImplementedError('LDA triplet')

    elif xctype == 'GGA':
        if singlet:
            def gga_sum_(vmat, ao, wv, mask):
                aow = numint._scale_ao(ao[:4], wv[:4])
                tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
                vmat[0] += tmp + tmp.T
                rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
            ao_deriv = 2
            for ao, mask, weight, coords \
                    in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
                rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, xctype)
                vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]

                rho1 = ni.eval_rho(mol, ao, dmvo, mask, xctype, hermi=1) * 2  # *2 for alpha + beta
                wv = numint._rks_gga_wv1(rho, rho1, vxc, fxc, weight)
                gga_sum_(f1vo, ao, wv, mask)

                if dmoo is not None:
                    rho2 = ni.eval_rho(mol, ao, dmoo, mask, xctype, hermi=1) * 2
                    wv = numint._rks_gga_wv1(rho, rho2, vxc, fxc, weight)
                    gga_sum_(f1oo, ao, wv, mask)
                if with_vxc:
                    wv = numint._rks_gga_wv0(rho, vxc, weight)
                    gga_sum_(v1ao, ao, wv, mask)
                if with_kxc:
                    wv = numint._rks_gga_wv2(rho, rho1, fxc, kxc, weight)
                    gga_sum_(k1ao, ao, wv, mask)
                vxc = fxc = kxc = rho = rho1 = None

        else:
            raise NotImplementedError('GGA triplet')

    elif xctype == 'MGGA':
        if singlet:
            def mgga_sum_(vmat, ao, wv, mask):
                aow = numint._scale_ao(ao[:4], wv[:4])
                tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
                aow = numint._scale_ao(ao[1], wv[5], aow)
                tmp += numint._dot_ao_ao(mol, ao[1], aow, mask, shls_slice, ao_loc)
                aow = numint._scale_ao(ao[2], wv[5], aow)
                tmp += numint._dot_ao_ao(mol, ao[2], aow, mask, shls_slice, ao_loc)
                aow = numint._scale_ao(ao[3], wv[5], aow)
                tmp += numint._dot_ao_ao(mol, ao[3], aow, mask, shls_slice, ao_loc)
                vmat[0] += tmp + tmp.T

                rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv[:4], mask, ao_loc)
                rks_grad._tau_grad_dot_(vmat[1:], mol, ao, wv[5]*2, mask, ao_loc, True)

            ao_deriv = 2
            for ao, mask, weight, coords \
                    in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
                rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, xctype)
                vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]

                rho1 = ni.eval_rho(mol, ao, dmvo, mask, xctype, hermi=1) * 2  # *2 for alpha + beta
                wv = numint._rks_mgga_wv1(rho, rho1, vxc, fxc, weight)
                mgga_sum_(f1vo, ao, wv, mask)

                if dmoo is not None:
                    rho2 = ni.eval_rho(mol, ao, dmoo, mask, xctype, hermi=1) * 2
                    wv = numint._rks_mgga_wv1(rho, rho2, vxc, fxc, weight)
                    mgga_sum_(f1oo, ao, wv, mask)
                if with_vxc:
                    wv = numint._rks_mgga_wv0(rho, vxc, weight)
                    mgga_sum_(v1ao, ao, wv, mask)
                if with_kxc:
                    wv = numint._rks_mgga_wv2(rho, rho1, fxc, kxc, weight)
                    mgga_sum_(k1ao, ao, wv, mask)
                vxc = fxc = kxc = rho = rho1 = None
        else:
            raise NotImplementedError('MGGA triplet')

    elif xctype == 'HF':
        pass
    else:
        raise NotImplementedError(f'td-rks for functional {xc_code}')

    f1vo[1:] *= -1
    if f1oo is not None: f1oo[1:] *= -1
    if v1ao is not None: v1ao[1:] *= -1
    if k1ao is not None: k1ao[1:] *= -1
    return f1vo, f1oo, v1ao, k1ao


class Gradients(tdrhf.Gradients):
    @lib.with_doc(grad_elec.__doc__)
    def grad_elec(self, xy, singlet, atmlst=None):
        return grad_elec(self, xy, singlet, atmlst, self.max_memory, self.verbose)

Grad = Gradients

from pyscf import tdscf
tdscf.rks.TDA.Gradients = tdscf.rks.TDDFT.Gradients = lib.class_as_method(Gradients)
