# Source code for pyscf.fci.rdm

#!/usr/bin/env python
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

'''FCI 1, 2, 3, 4-particle density matrices.

Note the 1-particle density matrix has the same convention as the mean-field
1-particle density matrix (see McWeeney's book Eq 5.4.20), which is
dm[p,q] = < q^+ p >
The contraction between 1-particle Hamiltonian and 1-pdm is
E = einsum('pq,qp', h1, 1pdm)
Different conventions are used in the high order density matrices:
dm[p,q,r,s,...] = < p^+ r^+ ... s q >
'''

import ctypes
import numpy
from pyscf import lib
from pyscf.fci import cistring

def reorder_rdm(rdm1, rdm2, inplace=False):
nmo = rdm1.shape[0]
if not inplace:
rdm2 = rdm2.copy()
for k in range(nmo):
rdm2[:,k,k,:] -= rdm1.T
#return rdm1, rdm2
rdm2 = lib.transpose_sum(rdm2.reshape(nmo*nmo,-1), inplace=True) * .5
return rdm1, rdm2.reshape(nmo,nmo,nmo,nmo)

# dm[p,q] = <|q^+ p|>
def make_rdm1_ms0(fname, cibra, ciket, norb, nelec, link_index=None):
assert(cibra is not None and ciket is not None)
cibra = numpy.asarray(cibra, order='C')
ciket = numpy.asarray(ciket, order='C')
neleca, nelecb = _unpack_nelec(nelec)
assert(neleca == nelecb)
assert(cibra.size == na**2)
assert(ciket.size == na**2)
rdm1 = numpy.empty((norb,norb))
fn = getattr(librdm, fname)
fn(rdm1.ctypes.data_as(ctypes.c_void_p),
cibra.ctypes.data_as(ctypes.c_void_p),
ciket.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(na),
return rdm1.T

# NOTE rdm1 in this function is calculated as rdm1[p,q] = <q^+ p>;
# rdm2 is calculated as <p^+ q r^+ s>. Call reorder_rdm to transform to the
# normal rdm2, which is  dm2[p,q,r,s] = <p^+ r^+ s q>.
# symm = 1: bra, ket symmetry
# symm = 2: particle permutation symmetry
def make_rdm12_ms0(fname, cibra, ciket, norb, nelec, link_index=None, symm=0):
neleca, nelecb = _unpack_nelec(nelec)
assert(neleca == nelecb)
return make_rdm12_spin1(fname, cibra, ciket, norb, nelec, link_index, symm)

make_rdm1 = make_rdm1_ms0
make_rdm12 = make_rdm12_ms0

###################################################
#
# nelec and link_index are tuples of (alpha,beta)
#
def make_rdm1_spin1(fname, cibra, ciket, norb, nelec, link_index=None):
assert(cibra is not None and ciket is not None)
cibra = numpy.asarray(cibra, order='C')
ciket = numpy.asarray(ciket, order='C')
neleca, nelecb = _unpack_nelec(nelec)
if neleca != nelecb:
else:
assert(cibra.size == na*nb)
assert(ciket.size == na*nb)
rdm1 = numpy.empty((norb,norb))
fn = getattr(librdm, fname)
fn(rdm1.ctypes.data_as(ctypes.c_void_p),
cibra.ctypes.data_as(ctypes.c_void_p),
ciket.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
return rdm1.T

# NOTE rdm1 in this function is calculated as rdm1[p,q] = <q^+ p>;
# rdm2 is calculated as <p^+ q r^+ s>. Call reorder_rdm to transform to the
# normal rdm2, which is  dm2[p,q,r,s] = <p^+ r^+ s q>.
# symm = 1: bra, ket symmetry
# symm = 2: particle permutation symmetry
def make_rdm12_spin1(fname, cibra, ciket, norb, nelec, link_index=None, symm=0):
assert(cibra is not None and ciket is not None)
cibra = numpy.asarray(cibra, order='C')
ciket = numpy.asarray(ciket, order='C')
neleca, nelecb = _unpack_nelec(nelec)
if neleca != nelecb:
else:
assert(cibra.size == na*nb)
assert(ciket.size == na*nb)
rdm1 = numpy.empty((norb,norb))
rdm2 = numpy.empty((norb,norb,norb,norb))
librdm.FCIrdm12_drv(getattr(librdm, fname),
rdm1.ctypes.data_as(ctypes.c_void_p),
rdm2.ctypes.data_as(ctypes.c_void_p),
cibra.ctypes.data_as(ctypes.c_void_p),
ciket.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(symm))
return rdm1.T, rdm2

##############################
#
# 3-particle and 4-particle density matrix for RHF-FCI wfn
#
# NOTE the dm3[p,q,r,s,t,u] is calculated as <p^+ q r^+ s t^+ u>
# call reorder_dm123 to transform dm3 to regular 3-pdm
[docs]def make_dm123(fname, cibra, ciket, norb, nelec): r'''Spin traced 1, 2 and 3-particle density matrices. .. note:: In this function, 2pdm[p,q,r,s] is :math:\langle p^\dagger q r^\dagger s\rangle; 3pdm[p,q,r,s,t,u] is :math:\langle p^\dagger q r^\dagger s t^\dagger u\rangle. After calling reorder_dm123, the 2pdm and 3pdm are transformed to the normal density matrices: 2pdm[p,r,q,s] = :math:\langle p^\dagger q^\dagger s r\rangle 3pdm[p,s,q,t,r,u] = :math:\langle p^\dagger q^\dagger r^\dagger u t s\rangle. ''' cibra = numpy.asarray(cibra, order='C') ciket = numpy.asarray(ciket, order='C') neleca, nelecb = _unpack_nelec(nelec) link_indexa = cistring.gen_linkstr_index(range(norb), neleca) link_indexb = cistring.gen_linkstr_index(range(norb), nelecb) na,nlinka = link_indexa.shape[:2] nb,nlinkb = link_indexb.shape[:2] assert(cibra.size == na*nb) assert(ciket.size == na*nb) rdm1 = numpy.empty((norb,)*2) rdm2 = numpy.empty((norb,)*4) rdm3 = numpy.empty((norb,)*6) librdm.FCIrdm3_drv(getattr(librdm, fname), rdm1.ctypes.data_as(ctypes.c_void_p), rdm2.ctypes.data_as(ctypes.c_void_p), rdm3.ctypes.data_as(ctypes.c_void_p), cibra.ctypes.data_as(ctypes.c_void_p), ciket.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(norb), ctypes.c_int(na), ctypes.c_int(nb), ctypes.c_int(nlinka), ctypes.c_int(nlinkb), link_indexa.ctypes.data_as(ctypes.c_void_p), link_indexb.ctypes.data_as(ctypes.c_void_p)) rdm3 = _complete_dm3_(rdm2, rdm3) return rdm1.T, rdm2, rdm3
def _complete_dm3_(dm2, dm3): # fci_4pdm.c assumed symmetry p >= r >= t for 3-pdm <p^+ q r^+ s t^+ u> # Using E^r_sE^p_q = E^p_qE^r_s - \delta_{qr}E^p_s + \delta_{ps}E^r_q to # complete the full 3-pdm def transpose01(ijk, i, j, k): jik = ijk.transpose(1,0,2) jik[:,j] -= dm2[i,:,k,:] jik[i,:] += dm2[j,:,k,:] dm3[j,:,i,:,k,:] = jik return jik def transpose12(ijk, i, j, k): ikj = ijk.transpose(0,2,1) ikj[:,:,k] -= dm2[i,:,j,:] ikj[:,j,:] += dm2[i,:,k,:] dm3[i,:,k,:,j,:] = ikj return ikj # ijk -> jik -> jki -> kji -> kij -> ikj norb = dm2.shape[0] for i in range(norb): for j in range(i+1): for k in range(j+1): tmp = transpose01(dm3[i,:,j,:,k,:].copy(), i, j, k) tmp = transpose12(tmp, j, i, k) tmp = transpose01(tmp, j, k, i) tmp = transpose12(tmp, k, j, i) tmp = transpose01(tmp, k, i, j) return dm3
[docs]def make_dm1234(fname, cibra, ciket, norb, nelec): r'''Spin traced 1, 2, 3 and 4-particle density matrices. .. note:: In this function, 2pdm[p,q,r,s] is :math:\langle p^\dagger q r^\dagger s\rangle; 3pdm[p,q,r,s,t,u] is :math:\langle p^\dagger q r^\dagger s t^\dagger u\rangle; 4pdm[p,q,r,s,t,u,v,w] is :math:\langle p^\dagger q r^\dagger s t^\dagger u v^\dagger w\rangle. After calling reorder_dm123, the 2pdm and 3pdm are transformed to the normal density matrices: 2pdm[p,r,q,s] = :math:\langle p^\dagger q^\dagger s r\rangle 3pdm[p,s,q,t,r,u] = :math:\langle p^\dagger q^\dagger r^\dagger u t s\rangle. 4pdm[p,t,q,u,r,v,s,w] = :math:\langle p^\dagger q^\dagger r^\dagger s^dagger w v u t\rangle. ''' cibra = numpy.asarray(cibra, order='C') ciket = numpy.asarray(ciket, order='C') neleca, nelecb = _unpack_nelec(nelec) link_indexa = cistring.gen_linkstr_index(range(norb), neleca) link_indexb = cistring.gen_linkstr_index(range(norb), nelecb) na,nlinka = link_indexa.shape[:2] nb,nlinkb = link_indexb.shape[:2] assert(cibra.size == na*nb) assert(ciket.size == na*nb) rdm1 = numpy.empty((norb,)*2) rdm2 = numpy.empty((norb,)*4) rdm3 = numpy.empty((norb,)*6) rdm4 = numpy.empty((norb,)*8) librdm.FCIrdm4_drv(getattr(librdm, fname), rdm1.ctypes.data_as(ctypes.c_void_p), rdm2.ctypes.data_as(ctypes.c_void_p), rdm3.ctypes.data_as(ctypes.c_void_p), rdm4.ctypes.data_as(ctypes.c_void_p), cibra.ctypes.data_as(ctypes.c_void_p), ciket.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(norb), ctypes.c_int(na), ctypes.c_int(nb), ctypes.c_int(nlinka), ctypes.c_int(nlinkb), link_indexa.ctypes.data_as(ctypes.c_void_p), link_indexb.ctypes.data_as(ctypes.c_void_p)) rdm3 = _complete_dm3_(rdm2, rdm3) rdm4 = _complete_dm4_(rdm3, rdm4) return rdm1.T, rdm2, rdm3, rdm4
def _complete_dm4_(dm3, dm4): # fci_4pdm.c assumed symmetry p >= r >= t >= v for 4-pdm <p^+ q r^+ s t^+ u v^+ w> # Using E^r_sE^p_q = E^p_qE^r_s - \delta_{qr}E^p_s + \delta_{ps}E^r_q to # complete the full 4-pdm def transpose01(ijkl, i, j, k, l): jikl = ijkl.transpose(1,0,2,3) jikl[:,j] -= dm3[i,:,k,:,l,:] jikl[i,:] += dm3[j,:,k,:,l,:] dm4[j,:,i,:,k,:,l,:] = jikl return jikl def transpose12(ijkl, i, j, k, l): ikjl = ijkl.transpose(0,2,1,3) ikjl[:,:,k] -= dm3[i,:,j,:,l,:] ikjl[:,j,:] += dm3[i,:,k,:,l,:] dm4[i,:,k,:,j,:,l,:] = ikjl return ikjl def transpose23(ijkl, i, j, k, l): ijlk = ijkl.transpose(0,1,3,2) ijlk[:,:,:,l] -= dm3[i,:,j,:,k,:] ijlk[:,:,k,:] += dm3[i,:,j,:,l,:] dm4[i,:,j,:,l,:,k,:] = ijlk return ijlk def chain(ijkl, i, j, k, l): tmp = transpose23(ijkl, i, j, k, l) tmp = transpose12(tmp, i, j, l, k) tmp = transpose23(tmp, i, l, j, k) tmp = transpose12(tmp, i, l, k, j) tmp = transpose23(tmp, i, k, l, j) return tmp # ijkl -> ijlk -> iljk -> ilkj -> iklj -> ikjl # -> jikl -> jilk -> jlik -> jlki -> jkli -> jkil #(ikjl)-> kijl -> kilj -> klij -> klji -> kjli -> kjil #(iljk)-> lijk -> likj -> lkij -> lkji -> ljki -> ljik norb = dm3.shape[0] for i in range(norb): for k in range(i+1): for j in range(k+1): for l in range(j+1): tmp = chain(dm4[i,:,j,:,k,:,l,:].copy(), i, j, k, l) tmp = transpose01(tmp, i, k, j, l) tmp = chain(tmp, k, i, j, l) tmp = transpose01(dm4[i,:,j,:,k,:,l,:].copy(), i, j, k, l) tmp = chain(tmp, j, i, k, l) tmp = transpose01(dm4[i,:,l,:,j,:,k,:].copy(), i, l, j, k) tmp = chain(tmp, l, i, j, k) return dm4 def reorder_dm12(rdm1, rdm2, inplace=True): return reorder_rdm(rdm1, rdm2, inplace) # <p^+ q r^+ s t^+ u> => <p^+ r^+ t^+ u s q> # rdm2[p,q,r,s] is <p^+ q r^+ s> def reorder_dm123(rdm1, rdm2, rdm3, inplace=True): rdm1, rdm2 = reorder_rdm(rdm1, rdm2, inplace) if not inplace: rdm3 = rdm3.copy() norb = rdm1.shape[0] for q in range(norb): rdm3[:,q,q,:,:,:] -= rdm2 rdm3[:,:,:,q,q,:] -= rdm2 rdm3[:,q,:,:,q,:] -= rdm2.transpose(0,2,3,1) for s in range(norb): rdm3[:,q,q,s,s,:] -= rdm1.T return rdm1, rdm2, rdm3 # <p^+ q r^+ s t^+ u w^+ v> => <p^+ r^+ t^+ w^+ v u s q> # rdm2, rdm3 are the (reordered) standard 2-pdm and 3-pdm def reorder_dm1234(rdm1, rdm2, rdm3, rdm4, inplace=True): rdm1, rdm2, rdm3 = reorder_dm123(rdm1, rdm2, rdm3, inplace) if not inplace: rdm4 = rdm4.copy() norb = rdm1.shape[0] for q in range(norb): rdm4[:,q,:,:,:,:,q,:] -= rdm3.transpose(0,2,3,4,5,1) rdm4[:,:,:,q,:,:,q,:] -= rdm3.transpose(0,1,2,4,5,3) rdm4[:,:,:,:,:,q,q,:] -= rdm3 rdm4[:,q,:,:,q,:,:,:] -= rdm3.transpose(0,2,3,1,4,5) rdm4[:,:,:,q,q,:,:,:] -= rdm3 rdm4[:,q,q,:,:,:,:,:] -= rdm3 for s in range(norb): rdm4[:,q,q,s,:,:,s,:] -= rdm2.transpose(0,2,3,1) rdm4[:,q,q,:,:,s,s,:] -= rdm2 rdm4[:,q,:,:,q,s,s,:] -= rdm2.transpose(0,2,3,1) rdm4[:,q,:,s,q,:,s,:] -= rdm2.transpose(0,2,1,3) rdm4[:,q,:,s,s,:,q,:] -= rdm2.transpose(0,2,3,1) rdm4[:,:,:,s,s,q,q,:] -= rdm2 rdm4[:,q,q,s,s,:,:,:] -= rdm2 for u in range(norb): rdm4[:,q,q,s,s,u,u,:] -= rdm1.T return rdm1, rdm2, rdm3, rdm4 def _unpack_nelec(nelec, spin=None): if spin is None: spin = 0 else: nelec = int(numpy.sum(nelec)) if isinstance(nelec, (int, numpy.number)): nelecb = (nelec-spin)//2 neleca = nelec - nelecb nelec = neleca, nelecb return nelec