Source code for pyscf.fci.direct_spin0

#!/usr/bin/env python
# Copyright 2014-2021 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>
#

'''
FCI solver for Singlet state

Different FCI solvers are implemented to support different type of symmetry.
                    Symmetry
File                Point group   Spin singlet   Real hermitian*    Alpha/beta degeneracy
direct_spin0_symm   Yes           Yes            Yes                Yes
direct_spin1_symm   Yes           No             Yes                Yes
direct_spin0        No            Yes            Yes                Yes
direct_spin1        No            No             Yes                Yes
direct_uhf          No            No             Yes                No
direct_nosym        No            No             No**               Yes

*  Real hermitian Hamiltonian implies (ij|kl) = (ji|kl) = (ij|lk) = (ji|lk)
** Hamiltonian is real but not hermitian, (ij|kl) != (ji|kl) ...

direct_spin0 solver is specified for singlet state. However, calling this
solver sometimes ends up with the error "State not singlet x.xxxxxxe-06" due
to numerical issues. Calling direct_spin1 for singlet state is slightly
slower but more robust than direct_spin0 especially when combining to energy
penalty method (:func:`fix_spin_`)
'''

import ctypes
import numpy
from pyscf import lib
from pyscf import ao2mo
from pyscf.lib import logger
from pyscf.fci import cistring
from pyscf.fci import rdm
from pyscf.fci import direct_spin1
from pyscf.fci.spin_op import contract_ss

libfci = direct_spin1.libfci

[docs] @lib.with_doc(direct_spin1.contract_1e.__doc__) def contract_1e(f1e, fcivec, norb, nelec, link_index=None): fcivec = numpy.asarray(fcivec, order='C') link_index = direct_spin1._unpack(norb, nelec, link_index) if not isinstance(link_index, numpy.ndarray): # Handle computability. link_index should be (nparray, nparray) link_index = link_index[0] na, nlink = link_index.shape[:2] assert (fcivec.size == na**2) ci1 = numpy.empty_like(fcivec) f1e_tril = lib.pack_tril(f1e) libfci.FCIcontract_1e_spin0(f1e_tril.ctypes.data_as(ctypes.c_void_p), fcivec.ctypes.data_as(ctypes.c_void_p), ci1.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(norb), ctypes.c_int(na), ctypes.c_int(nlink), link_index.ctypes.data_as(ctypes.c_void_p)) # no *.5 because FCIcontract_2e_spin0 only compute half of the contraction ci1 = lib.transpose_sum(ci1, inplace=True).reshape(fcivec.shape) return ci1.view(direct_spin1.FCIvector)
# Note eri is NOT the 2e hamiltonian matrix, the 2e hamiltonian is # h2e = eri_{pq,rs} p^+ q r^+ s # = (pq|rs) p^+ r^+ s q - (pq|rs) \delta_{qr} p^+ s # so eri is defined as # eri_{pq,rs} = (pq|rs) - (1/Nelec) \sum_q (pq|qs) # to restore the symmetry between pq and rs, # eri_{pq,rs} = (pq|rs) - (.5/Nelec) [\sum_q (pq|qs) + \sum_p (pq|rp)] # Please refer to the treatment in direct_spin1.absorb_h1e # the input fcivec should be symmetrized
[docs] @lib.with_doc(direct_spin1.contract_2e.__doc__) def contract_2e(eri, fcivec, norb, nelec, link_index=None): fcivec = numpy.asarray(fcivec, order='C') eri = ao2mo.restore(4, eri, norb) lib.transpose_sum(eri, inplace=True) eri *= .5 link_index = direct_spin1._unpack(norb, nelec, link_index) if not isinstance(link_index, numpy.ndarray): # Handle computability. link_index should be (nparray, nparray) link_index = link_index[0] na, nlink = link_index.shape[:2] assert (fcivec.size == na**2) ci1 = numpy.empty((na,na)) libfci.FCIcontract_2e_spin0(eri.ctypes.data_as(ctypes.c_void_p), fcivec.ctypes.data_as(ctypes.c_void_p), ci1.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(norb), ctypes.c_int(na), ctypes.c_int(nlink), link_index.ctypes.data_as(ctypes.c_void_p)) # no *.5 because FCIcontract_2e_spin0 only compute half of the contraction ci1 = lib.transpose_sum(ci1, inplace=True).reshape(fcivec.shape) return ci1.view(direct_spin1.FCIvector)
absorb_h1e = direct_spin1.absorb_h1e
[docs] @lib.with_doc(direct_spin1.make_hdiag.__doc__) def make_hdiag(h1e, eri, norb, nelec, compress=False): hdiag = direct_spin1.make_hdiag(h1e, eri, norb, nelec) na = int(numpy.sqrt(hdiag.size)) # symmetrize hdiag to reduce numerical error hdiag = lib.transpose_sum(hdiag.reshape(na,na), inplace=True) * .5 return hdiag.ravel()
pspace = direct_spin1.pspace # be careful with single determinant initial guess. It may lead to the # eigvalue of first davidson iter being equal to hdiag
[docs] def kernel(h1e, eri, norb, nelec, ci0=None, level_shift=1e-3, tol=1e-10, lindep=1e-14, max_cycle=50, max_space=12, nroots=1, davidson_only=False, pspace_size=400, orbsym=None, wfnsym=None, ecore=0, **kwargs): e, c = direct_spin1._kfactory(FCISolver, h1e, eri, norb, nelec, ci0, level_shift, tol, lindep, max_cycle, max_space, nroots, davidson_only, pspace_size, ecore=ecore, **kwargs) return e, c
# dm[p,q] = <|q^+ p|>
[docs] @lib.with_doc(direct_spin1.make_rdm1.__doc__) def make_rdm1(fcivec, norb, nelec, link_index=None): rdm1 = rdm.make_rdm1('FCImake_rdm1a', fcivec, fcivec, norb, nelec, link_index) return rdm1 * 2
# alpha and beta 1pdm
[docs] @lib.with_doc(direct_spin1.make_rdm1s.__doc__) def make_rdm1s(fcivec, norb, nelec, link_index=None): rdm1 = rdm.make_rdm1('FCImake_rdm1a', fcivec, fcivec, norb, nelec, link_index) return rdm1, rdm1
# Chemist notation
[docs] @lib.with_doc(direct_spin1.make_rdm12.__doc__) def make_rdm12(fcivec, norb, nelec, link_index=None, reorder=True): #dm1, dm2 = rdm.make_rdm12('FCIrdm12kern_spin0', fcivec, fcivec, # norb, nelec, link_index, 1) # NOT use FCIrdm12kern_spin0 because for small system, the kernel may call # direct diagonalization, which may not fulfil fcivec = fcivet.T dm1, dm2 = rdm.make_rdm12('FCIrdm12kern_sf', fcivec, fcivec, norb, nelec, link_index, 1) if reorder: dm1, dm2 = rdm.reorder_rdm(dm1, dm2, True) return dm1, dm2
# dm[p,q] = <I|q^+ p|J>
[docs] @lib.with_doc(direct_spin1.trans_rdm1s.__doc__) def trans_rdm1s(cibra, ciket, norb, nelec, link_index=None): if link_index is None: if isinstance(nelec, (int, numpy.number)): neleca = nelec//2 else: neleca, nelecb = nelec assert (neleca == nelecb) link_index = cistring.gen_linkstr_index(range(norb), neleca) rdm1a = rdm.make_rdm1('FCItrans_rdm1a', cibra, ciket, norb, nelec, link_index) rdm1b = rdm.make_rdm1('FCItrans_rdm1b', cibra, ciket, norb, nelec, link_index) return rdm1a, rdm1b
[docs] @lib.with_doc(direct_spin1.trans_rdm1.__doc__) def trans_rdm1(cibra, ciket, norb, nelec, link_index=None): rdm1a, rdm1b = trans_rdm1s(cibra, ciket, norb, nelec, link_index) return rdm1a + rdm1b
# dm[p,q,r,s] = <I|p^+ q r^+ s|J>
[docs] @lib.with_doc(direct_spin1.trans_rdm12.__doc__) def trans_rdm12(cibra, ciket, norb, nelec, link_index=None, reorder=True): dm1, dm2 = rdm.make_rdm12('FCItdm12kern_sf', cibra, ciket, norb, nelec, link_index, 2) if reorder: dm1, dm2 = rdm.reorder_rdm(dm1, dm2, True) return dm1, dm2
[docs] def energy(h1e, eri, fcivec, norb, nelec, link_index=None): h2e = direct_spin1.absorb_h1e(h1e, eri, norb, nelec, .5) ci1 = contract_2e(h2e, fcivec, norb, nelec, link_index) return numpy.dot(fcivec.ravel(), ci1.ravel())
[docs] def get_init_guess(norb, nelec, nroots, hdiag): if isinstance(nelec, (int, numpy.number)): nelecb = nelec//2 neleca = nelec - nelecb else: neleca, nelecb = nelec na = cistring.num_strings(norb, neleca) nb = cistring.num_strings(norb, nelecb) init_strs = [] iroot = 0 for addr in numpy.argsort(hdiag): addra = addr // nb addrb = addr % nb if (addrb,addra) not in init_strs: # avoid initial guess linear dependency init_strs.append((addra,addrb)) iroot += 1 if iroot >= nroots: break ci0 = [] for addra,addrb in init_strs: x = numpy.zeros((na,nb)) if addra == addrb: x[addra,addrb] = 1 else: x[addra,addrb] = x[addrb,addra] = numpy.sqrt(.5) ci0.append(x.ravel().view(direct_spin1.FCIvector)) # Add noise ci0[0][0 ] += 1e-5 ci0[0][-1] -= 1e-5 return ci0
############################################################### # direct-CI driver ###############################################################
[docs] def kernel_ms0(fci, h1e, eri, norb, nelec, ci0=None, link_index=None, tol=None, lindep=None, max_cycle=None, max_space=None, nroots=None, davidson_only=None, pspace_size=None, hop=None, max_memory=None, verbose=None, ecore=0, **kwargs): if nroots is None: nroots = fci.nroots if davidson_only is None: davidson_only = fci.davidson_only if pspace_size is None: pspace_size = fci.pspace_size if max_memory is None: max_memory = fci.max_memory - lib.current_memory()[0] log = logger.new_logger(fci, verbose) nelec = direct_spin1._unpack_nelec(nelec, fci.spin) assert (0 <= nelec[0] <= norb and 0 <= nelec[1] <= norb) hdiag = fci.make_hdiag(h1e, eri, norb, nelec, compress=True) num_dets = hdiag.size pspace_size = min(num_dets, pspace_size) nroots = min(num_dets, nroots) na = cistring.num_strings(norb, nelec[0]) addr = [0] pw = pv = None if pspace_size > 0 and norb < 64: addr, h0 = fci.pspace(h1e, eri, norb, nelec, hdiag, pspace_size) pw, pv = fci.eig(h0) if getattr(fci, 'sym_allowed_idx', None): # Remove symmetry forbidden elements sym_idx = numpy.hstack(fci.sym_allowed_idx) civec_size = sym_idx.size else: sym_idx = None civec_size = num_dets if max_memory < num_dets*6*8e-6: log.warn('Not enough memory for FCI solver. ' 'The minimal requirement is %.0f MB', hdiag.size*60e-6) if pspace_size >= civec_size and ci0 is None and not davidson_only: e = [] civec = [] for i in range(pspace_size): c = numpy.empty(civec_size) c[addr] = pv[:,i] try: civec.append(_check_(c.reshape(na,na))) except ValueError: continue e.append(pw[i]) if len(civec) >= nroots: break if nroots == 1: return e[0]+ecore, civec[0] else: return numpy.array(e)+ecore, civec pw = pv = h0 = None if sym_idx is None: precond = fci.make_precond(hdiag) else: precond = fci.make_precond(hdiag[sym_idx]) h2e = fci.absorb_h1e(h1e, eri, norb, nelec, .5) if hop is None: cpu0 = [logger.process_clock(), logger.perf_counter()] def hop(c): hc = fci.contract_2e(h2e, c.reshape(na,na), norb, nelec, link_index) cpu0[:] = log.timer_debug1('contract_2e', *cpu0) return hc.ravel() def init_guess(): if callable(getattr(fci, 'get_init_guess', None)): return fci.get_init_guess(norb, nelec, nroots, hdiag) else: x0 = [] for i in range(nroots): x = numpy.zeros((na,na)) addra = addr[i] // na addrb = addr[i] % na if addra == addrb: x[addra,addrb] = 1 else: x[addra,addrb] = x[addrb,addra] = numpy.sqrt(.5) x0.append(x.ravel()) return x0 if ci0 is None: ci0 = init_guess # lazy initialization to reduce memory footprint elif not callable(ci0): if isinstance(ci0, numpy.ndarray): ci0 = [ci0.ravel()] else: ci0 = [x.ravel() for x in ci0] if sym_idx is not None and ci0[0].size != civec_size: ci0 = [x[sym_idx] for x in ci0] if len(ci0) < nroots: ci0.extend(init_guess()[len(ci0):]) if tol is None: tol = fci.conv_tol if lindep is None: lindep = fci.lindep if max_cycle is None: max_cycle = fci.max_cycle if max_space is None: max_space = fci.max_space tol_residual = getattr(fci, 'conv_tol_residual', None) with lib.with_omp_threads(fci.threads): e, c = fci.eig(hop, ci0, precond, tol=tol, lindep=lindep, max_cycle=max_cycle, max_space=max_space, nroots=nroots, max_memory=max_memory, verbose=log, follow_state=True, tol_residual=tol_residual, **kwargs) return e+ecore, c
def _check_(c): c = lib.transpose_sum(c, inplace=True) c *= .5 norm = numpy.linalg.norm(c) if abs(norm-1) > 1e-6: raise ValueError('State not singlet %g' % (norm - 1)) return c/norm
[docs] class FCISolver(direct_spin1.FCISolver): make_hdiag = staticmethod(make_hdiag)
[docs] def contract_1e(self, f1e, fcivec, norb, nelec, link_index=None, **kwargs): return contract_1e(f1e, fcivec, norb, nelec, link_index, **kwargs)
[docs] def contract_2e(self, eri, fcivec, norb, nelec, link_index=None, **kwargs): return contract_2e(eri, fcivec, norb, nelec, link_index, **kwargs)
[docs] def get_init_guess(self, norb, nelec, nroots, hdiag): return get_init_guess(norb, nelec, nroots, hdiag)
[docs] def kernel(self, h1e, eri, norb, nelec, ci0=None, tol=None, lindep=None, max_cycle=None, max_space=None, nroots=None, davidson_only=None, pspace_size=None, orbsym=None, wfnsym=None, ecore=0, **kwargs): if nroots is None: nroots = self.nroots if self.verbose >= logger.WARN: self.check_sanity() assert self.spin is None or self.spin == 0 self.norb = norb self.nelec = nelec link_index = direct_spin1._unpack(norb, nelec, None) e, c = kernel_ms0(self, h1e, eri, norb, nelec, ci0, link_index, tol, lindep, max_cycle, max_space, nroots, davidson_only, pspace_size, ecore=ecore, **kwargs) self.eci = e na = link_index[0].shape[0] if nroots > 1: self.ci = [ _check_(x.reshape(na,na)).view(direct_spin1.FCIvector) for x in c] else: self.ci = _check_(c.reshape(na,na)).view(direct_spin1.FCIvector) return self.eci, self.ci
[docs] def energy(self, h1e, eri, fcivec, norb, nelec, link_index=None): h2e = self.absorb_h1e(h1e, eri, norb, nelec, .5) ci1 = self.contract_2e(h2e, fcivec, norb, nelec, link_index) return numpy.dot(fcivec.reshape(-1), ci1.reshape(-1))
[docs] def make_rdm1s(self, fcivec, norb, nelec, link_index=None): return make_rdm1s(fcivec, norb, nelec, link_index)
[docs] def make_rdm1(self, fcivec, norb, nelec, link_index=None): return make_rdm1(fcivec, norb, nelec, link_index)
[docs] @lib.with_doc(make_rdm12.__doc__) def make_rdm12(self, fcivec, norb, nelec, link_index=None, reorder=True): return make_rdm12(fcivec, norb, nelec, link_index, reorder)
[docs] def trans_rdm1s(self, cibra, ciket, norb, nelec, link_index=None): return trans_rdm1s(cibra, ciket, norb, nelec, link_index)
[docs] def trans_rdm1(self, cibra, ciket, norb, nelec, link_index=None): return trans_rdm1(cibra, ciket, norb, nelec, link_index)
[docs] @lib.with_doc(trans_rdm12.__doc__) def trans_rdm12(self, cibra, ciket, norb, nelec, link_index=None, reorder=True): return trans_rdm12(cibra, ciket, norb, nelec, link_index, reorder)
[docs] def gen_linkstr(self, norb, nelec, tril=True, spin=None): if isinstance(nelec, (int, numpy.number)): neleca = nelec//2 else: neleca, nelecb = nelec assert (neleca == nelecb) if tril: link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca) else: link_index = cistring.gen_linkstr_index(range(norb), neleca) return link_index
FCI = FCISolver if __name__ == '__main__': from functools import reduce from pyscf import gto from pyscf import scf mol = gto.Mole() mol.verbose = 0 mol.output = None#"out_h2o" mol.atom = [ ['H', ( 1.,-1. , 0. )], ['H', ( 0.,-1. ,-1. )], ['H', ( 1.,-0.5 ,-1. )], ['H', ( 0.,-0.5 ,-1. )], ['H', ( 0.,-0.5 ,-0. )], ['H', ( 0.,-0. ,-1. )], ['H', ( 1.,-0.5 , 0. )], ['H', ( 0., 1. , 1. )], ] mol.basis = {'H': 'sto-3g'} mol.build() m = scf.RHF(mol) ehf = m.scf() cis = FCISolver(mol) norb = m.mo_coeff.shape[1] nelec = mol.nelectron h1e = reduce(numpy.dot, (m.mo_coeff.T, m.get_hcore(), m.mo_coeff)) eri = ao2mo.incore.general(m._eri, (m.mo_coeff,)*4, compact=False) e, c = cis.kernel(h1e, eri, norb, nelec) print(e - -15.9977886375) print('t',logger.process_clock())