def ao2mo(mydf, mo_coeffs, kpts): """ For ctf, this function needs to be used with caution, this function calls read on j3c twice, if other process does not explicitly perform ao2mo transformation, j3c needs to be read twice eg, if rank==0: eri = mydf.ao2mo(mo_coeffs, kpts) else: mydf.j3c.read([]) mydf.j3c.read([]) """ if mydf.j3c is None: mydf.build() log = Logger(mydf.stdout, mydf.verbose) cell = mydf.cell kptijkl = _format_kpts(kpts) kpti, kptj, kptk, kptl = kptijkl if isinstance(mo_coeffs, np.ndarray) and mo_coeffs.ndim == 2: mo_coeffs = (mo_coeffs,) * 4 if not _iskconserv(cell, kptijkl): log.warn('df_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return np.zeros([mo.shape[1] for mo in mo_coeffs]) ijid, ijdagger = get_member(kpti, kptj, mydf.kptij_lst) klid, kldagger = get_member(kptk, kptl, mydf.kptij_lst) aux_idx = np.arange(mydf.j3c.size).reshape(mydf.j3c.shape) nao, naux = mydf.j3c.shape[1], mydf.j3c.shape[-1] ijid = aux_idx[ijid].ravel() klid = aux_idx[klid].ravel() ijL = mydf.j3c.read(ijid).reshape(nao,nao,naux) if ijdagger: ijL = ijL.transpose(1,0,2).conj() klL = mydf.j3c.read(klid).reshape(nao,nao,naux) if kldagger: klL = klL.transpose(1,0,2).conj() pvL = np.dot(mo_coeffs[0].conj().T, ijL.transpose(1,0,2)) pqL = np.dot(mo_coeffs[1].T, pvL).transpose(1,0,2) pvL = ijL = None rvL = np.dot(mo_coeffs[2].conj().T, klL.transpose(1,0,2)) rLs = np.dot(mo_coeffs[3].T, rvL).transpose(1,2,0) rvL = klL = None eri = np.dot(pqL,rLs) return eri
def get_eri(mydf, kpts=None): """ For ctf, this function needs to be used with caution, this function calls read on j3c twice, if other process does not explicitly call this func, j3c still needs to be read twice eg, if rank==0: eri = mydf.get_eri(kpts) else: mydf.j3c.read([]) mydf.j3c.read([]) """ if mydf.j3c is None: mydf.build() log = Logger(mydf.stdout, mydf.verbose) cell = mydf.cell kptijkl = _format_kpts(kpts) kpti, kptj, kptk, kptl = kptijkl if not _iskconserv(cell, kptijkl): log.warn('df_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return np.zeros([mo.shape[1] for mo in mo_coeffs]) ijid, ijdagger = get_member(kpti, kptj, mydf.kptij_lst) klid, kldagger = get_member(kptk, kptl, mydf.kptij_lst) aux_idx = np.arange(mydf.j3c.size).reshape(mydf.j3c.shape) nao, naux = mydf.j3c.shape[1], mydf.j3c.shape[-1] ijid = aux_idx[ijid].ravel() klid = aux_idx[klid].ravel() ijL = mydf.j3c.read(ijid).reshape(nao,nao,naux) if ijdagger: ijL = ijL.transpose(1,0,2).conj() klL = mydf.j3c.read(klid).reshape(nao,nao,naux) if kldagger: klL = klL.transpose(1,0,2).conj() eri = np.dot(ijL,klL.transpose(0,2,1)) return eri
def get_eri(mydf, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_get_eri_compact', True)): if mydf._cderi is None: mydf.build() cell = mydf.cell nao = cell.nao_nr() kptijkl = _format_kpts(kpts) if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'df_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros((nao,nao,nao,nao)) kpti, kptj, kptk, kptl = kptijkl nao_pair = nao * (nao+1) // 2 max_memory = max(2000, mydf.max_memory-lib.current_memory()[0]-nao**4*16/1e6) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl): eriR = numpy.zeros((nao_pair,nao_pair)) for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, True): lib.ddot(LpqR.T, LpqR, sign, eriR, 1) LpqR = LpqI = None if not compact: eriR = ao2mo.restore(1, eriR, nao).reshape(nao**2,-1) return eriR elif is_zero(kpti-kptk) and is_zero(kptj-kptl): eriR = numpy.zeros((nao*nao,nao*nao)) eriI = numpy.zeros((nao*nao,nao*nao)) for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): zdotNN(LpqR.T, LpqI.T, LpqR, LpqI, sign, eriR, eriI, 1) LpqR = LpqI = None return eriR + eriI*1j #################### # (kpt) i == j == k == l != 0 # # (kpt) i == l && j == k && i != j && j != k => # both vbar and ovlp are zero. It corresponds to the exchange integral. # # complex integrals, N^4 elements elif is_zero(kpti-kptl) and is_zero(kptj-kptk): eriR = numpy.zeros((nao*nao,nao*nao)) eriI = numpy.zeros((nao*nao,nao*nao)) for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): zdotNC(LpqR.T, LpqI.T, LpqR, LpqI, sign, eriR, eriI, 1) LpqR = LpqI = None # transpose(0,1,3,2) because # j == k && i == l => # (L|ij).transpose(0,2,1).conj() = (L^*|ji) = (L^*|kl) => (M|kl) eri = lib.transpose((eriR+eriI*1j).reshape(-1,nao,nao), axes=(0,2,1)) return eri.reshape(nao**2,-1) #################### # aosym = s1, complex integrals # # kpti == kptj => kptl == kptk # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. # else: eriR = numpy.zeros((nao*nao,nao*nao)) eriI = numpy.zeros((nao*nao,nao*nao)) blksize = int(max_memory*.4e6/16/nao**2) for (LpqR, LpqI, sign), (LrsR, LrsI, sign1) in \ lib.izip(mydf.sr_loop(kptijkl[:2], max_memory, False, blksize), mydf.sr_loop(kptijkl[2:], max_memory, False, blksize)): zdotNN(LpqR.T, LpqI.T, LrsR, LrsI, sign, eriR, eriI, 1) LpqR = LpqI = LrsR = LrsI = None return eriR + eriI*1j
def general(mydf, mo_coeffs, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_general_compact', True)): warn_pbc2d_eri(mydf) if mydf._cderi is None: mydf.build() cell = mydf.cell kptijkl = _format_kpts(kpts) kpti, kptj, kptk, kptl = kptijkl if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2: mo_coeffs = (mo_coeffs,) * 4 if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'df_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros([mo.shape[1] for mo in mo_coeffs]) all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs) max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0])) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl) and all_real: ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1], compact) klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3], compact) eri_mo = numpy.zeros((nij_pair,nkl_pair)) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and iden_coeffs(mo_coeffs[1], mo_coeffs[3])) ijR = klR = None for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, True): ijR, klR = _dtrans(LpqR, ijR, ijmosym, moij, ijslice, LpqR, klR, klmosym, mokl, klslice, sym) lib.ddot(ijR.T, klR, sign, eri_mo, 1) LpqR = LpqI = None return eri_mo elif is_zero(kpti-kptk) and is_zero(kptj-kptl): mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:] eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and iden_coeffs(mo_coeffs[1], mo_coeffs[3])) zij = zkl = None for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): buf = LpqR+LpqI*1j zij, zkl = _ztrans(buf, zij, moij, ijslice, buf, zkl, mokl, klslice, sym) lib.dot(zij.T, zkl, sign, eri_mo, 1) LpqR = LpqI = buf = None return eri_mo #################### # (kpt) i == j == k == l != 0 # (kpt) i == l && j == k && i != j && j != k => # elif is_zero(kpti-kptl) and is_zero(kptj-kptk): mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:] eri_mo = numpy.zeros((nij_pair,nlk_pair), dtype=numpy.complex) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3]) and iden_coeffs(mo_coeffs[1], mo_coeffs[2])) zij = zlk = None for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): buf = LpqR+LpqI*1j zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk, lkslice, sym) lib.dot(zij.T, zlk.conj(), sign, eri_mo, 1) LpqR = LpqI = buf = None nmok = mo_coeffs[2].shape[1] nmol = mo_coeffs[3].shape[1] eri_mo = lib.transpose(eri_mo.reshape(-1,nmol,nmok), axes=(0,2,1)) return eri_mo.reshape(nij_pair,nlk_pair) #################### # aosym = s1, complex integrals # # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk # else: mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:] nao = mo_coeffs[0].shape[0] eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex) blksize = int(min(max_memory*.3e6/16/nij_pair, max_memory*.3e6/16/nkl_pair, max_memory*.3e6/16/nao**2)) zij = zkl = None for (LpqR, LpqI, sign), (LrsR, LrsI, sign1) in \ lib.izip(mydf.sr_loop(kptijkl[:2], max_memory, False, blksize), mydf.sr_loop(kptijkl[2:], max_memory, False, blksize)): zij, zkl = _ztrans(LpqR+LpqI*1j, zij, moij, ijslice, LrsR+LrsI*1j, zkl, mokl, klslice, False) lib.dot(zij.T, zkl, sign, eri_mo, 1) LpqR = LpqI = LrsR = LrsI = None return eri_mo
def get_eri(mydf, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_get_eri_compact', True)): cell = mydf.cell nao = cell.nao_nr() kptijkl = _format_kpts(kpts) if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'aft_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros((nao,nao,nao,nao)) kpti, kptj, kptk, kptl = kptijkl q = kptj - kpti mesh = mydf.mesh coulG = mydf.weighted_coulG(q, False, mesh) nao_pair = nao * (nao+1) // 2 max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .8) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl): eriR = numpy.zeros((nao_pair,nao_pair)) for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory, aosym='s2'): lib.ddot(pqkR*coulG[p0:p1], pqkR.T, 1, eriR, 1) lib.ddot(pqkI*coulG[p0:p1], pqkI.T, 1, eriR, 1) pqkR = pqkI = None if not compact: eriR = ao2mo.restore(1, eriR, nao).reshape(nao**2,-1) return eriR #################### # (kpt) i == j == k == l != 0 # (kpt) i == l && j == k && i != j && j != k => # # complex integrals, N^4 elements elif is_zero(kpti-kptl) and is_zero(kptj-kptk): eriR = numpy.zeros((nao**2,nao**2)) eriI = numpy.zeros((nao**2,nao**2)) for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory): # rho_pq(G+k_pq) * conj(rho_rs(G-k_rs)) zdotNC(pqkR*coulG[p0:p1], pqkI*coulG[p0:p1], pqkR.T, pqkI.T, 1, eriR, eriI, 1) pqkR = pqkI = None pqkR = pqkI = coulG = None # transpose(0,1,3,2) because # j == k && i == l => # (L|ij).transpose(0,2,1).conj() = (L^*|ji) = (L^*|kl) => (M|kl) # rho_rs(-G+k_rs) = conj(transpose(rho_sr(G+k_sr), (0,2,1))) eri = lib.transpose((eriR+eriI*1j).reshape(-1,nao,nao), axes=(0,2,1)) return eri.reshape(nao**2,-1) #################### # aosym = s1, complex integrals # # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk # else: eriR = numpy.zeros((nao**2,nao**2)) eriI = numpy.zeros((nao**2,nao**2)) # # (pq|rs) = \sum_G 4\pi rho_pq rho_rs / |G+k_{pq}|^2 # rho_pq = 1/N \sum_{Tp,Tq} \int exp(-i(G+k_{pq})*r) p(r-Tp) q(r-Tq) dr # = \sum_{Tq} exp(i k_q*Tq) \int exp(-i(G+k_{pq})*r) p(r) q(r-Tq) dr # Note the k-point wrap-around for rho_rs, which leads to G+k_{pq} in FT # rho_rs = 1/N \sum_{Tr,Ts} \int exp( i(G+k_{pq})*r) r(r-Tr) s(r-Ts) dr # = \sum_{Ts} exp(i k_s*Ts) \int exp( i(G+k_{pq})*r) r(r) s(r-Ts) dr # rho_pq can be directly evaluated by AFT (function pw_loop) # rho_pq = pw_loop(k_q, G+k_{pq}) # Assuming r(r) and s(r) are real functions, rho_rs is evaluated # rho_rs = 1/N \sum_{Tr,Ts} \int exp( i(G+k_{pq})*r) r(r-Tr) s(r-Ts) dr # = conj(\sum_{Ts} exp(-i k_s*Ts) \int exp(-i(G+k_{pq})*r) r(r) s(r-Ts) dr) # = conj( pw_loop(-k_s, G+k_{pq}) ) # # TODO: For complex AO function r(r) and s(r), pw_loop function needs to be # extended to include Gv vector in the arguments for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \ lib.izip(mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory*.5), mydf.pw_loop(mesh,-kptijkl[2:], q, max_memory=max_memory*.5)): pqkR *= coulG[p0:p1] pqkI *= coulG[p0:p1] zdotNC(pqkR, pqkI, rskR.T, rskI.T, 1, eriR, eriI, 1) pqkR = pqkI = rskR = rskI = None return (eriR+eriI*1j)
def general(mydf, mo_coeffs, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_general_compact', True)): warn_pbc2d_eri(mydf) cell = mydf.cell kptijkl = _format_kpts(kpts) kpti, kptj, kptk, kptl = kptijkl if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2: mo_coeffs = (mo_coeffs,) * 4 if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'aft_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros([mo.shape[1] for mo in mo_coeffs]) q = kptj - kpti mesh = mydf.mesh coulG = mydf.weighted_coulG(q, False, mesh) all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs) max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .5) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl) and all_real: ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1], compact) klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3], compact) eri_mo = numpy.zeros((nij_pair,nkl_pair)) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and iden_coeffs(mo_coeffs[1], mo_coeffs[3])) ijR = ijI = klR = klI = buf = None for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory, aosym='s2'): buf = lib.transpose(pqkR, out=buf) ijR, klR = _dtrans(buf, ijR, ijmosym, moij, ijslice, buf, klR, klmosym, mokl, klslice, sym) lib.ddot(ijR.T, klR*coulG[p0:p1,None], 1, eri_mo, 1) buf = lib.transpose(pqkI, out=buf) ijI, klI = _dtrans(buf, ijI, ijmosym, moij, ijslice, buf, klI, klmosym, mokl, klslice, sym) lib.ddot(ijI.T, klI*coulG[p0:p1,None], 1, eri_mo, 1) pqkR = pqkI = None return eri_mo #################### # (kpt) i == j == k == l != 0 # (kpt) i == l && j == k && i != j && j != k => # elif is_zero(kpti-kptl) and is_zero(kptj-kptk): mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:] eri_mo = numpy.zeros((nij_pair,nlk_pair), dtype=numpy.complex) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3]) and iden_coeffs(mo_coeffs[1], mo_coeffs[2])) zij = zlk = buf = None for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory): buf = lib.transpose(pqkR+pqkI*1j, out=buf) zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk, lkslice, sym) lib.dot(zij.T, zlk.conj()*coulG[p0:p1,None], 1, eri_mo, 1) pqkR = pqkI = None nmok = mo_coeffs[2].shape[1] nmol = mo_coeffs[3].shape[1] eri_mo = lib.transpose(eri_mo.reshape(-1,nmol,nmok), axes=(0,2,1)) return eri_mo.reshape(nij_pair,nlk_pair) #################### # aosym = s1, complex integrals # # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk # else: mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:] eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex) tao = [] ao_loc = None zij = zkl = buf = None for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \ lib.izip(mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory*.5), mydf.pw_loop(mesh,-kptijkl[2:], q, max_memory=max_memory*.5)): buf = lib.transpose(pqkR+pqkI*1j, out=buf) zij = _ao2mo.r_e2(buf, moij, ijslice, tao, ao_loc, out=zij) buf = lib.transpose(rskR-rskI*1j, out=buf) zkl = _ao2mo.r_e2(buf, mokl, klslice, tao, ao_loc, out=zkl) zij *= coulG[p0:p1,None] lib.dot(zij.T, zkl, 1, eri_mo, 1) pqkR = pqkI = rskR = rskI = None return eri_mo
def get_eri(mydf, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_get_eri_compact', True)): if mydf._cderi is None: mydf.build() cell = mydf.cell nao = cell.nao_nr() kptijkl = _format_kpts(kpts) if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'df_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros((nao,nao,nao,nao)) kpti, kptj, kptk, kptl = kptijkl nao_pair = nao * (nao+1) // 2 max_memory = max(2000, mydf.max_memory-lib.current_memory()[0]-nao**4*16/1e6) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl): eriR = numpy.zeros((nao_pair,nao_pair)) for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, True): lib.ddot(LpqR.T, LpqR, sign, eriR, 1) LpqR = LpqI = None if not compact: eriR = ao2mo.restore(1, eriR, nao).reshape(nao**2,-1) return eriR elif is_zero(kpti-kptk) and is_zero(kptj-kptl): eriR = numpy.zeros((nao*nao,nao*nao)) eriI = numpy.zeros((nao*nao,nao*nao)) for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): zdotNN(LpqR.T, LpqI.T, LpqR, LpqI, sign, eriR, eriI, 1) LpqR = LpqI = None return eriR + eriI*1j #################### # (kpt) i == j == k == l != 0 # # (kpt) i == l && j == k && i != j && j != k => # both vbar and ovlp are zero. It corresponds to the exchange integral. # # complex integrals, N^4 elements elif is_zero(kpti-kptl) and is_zero(kptj-kptk): eriR = numpy.zeros((nao*nao,nao*nao)) eriI = numpy.zeros((nao*nao,nao*nao)) for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): zdotNC(LpqR.T, LpqI.T, LpqR, LpqI, sign, eriR, eriI, 1) LpqR = LpqI = None # transpose(0,1,3,2) because # j == k && i == l => # (L|ij).transpose(0,2,1).conj() = (L^*|ji) = (L^*|kl) => (M|kl) eri = lib.transpose((eriR+eriI*1j).reshape(-1,nao,nao), axes=(0,2,1)) return eri.reshape(nao**2,-1) #################### # aosym = s1, complex integrals # # kpti == kptj => kptl == kptk # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. # else: eriR = numpy.zeros((nao*nao,nao*nao)) eriI = numpy.zeros((nao*nao,nao*nao)) blksize = int(max_memory*.4e6/16/nao**2) for (LpqR, LpqI, sign), (LrsR, LrsI, sign1) in \ lib.izip(mydf.sr_loop(kptijkl[:2], max_memory, False, blksize), mydf.sr_loop(kptijkl[2:], max_memory, False, blksize)): zdotNN(LpqR.T, LpqI.T, LrsR, LrsI, sign, eriR, eriI, 1) LpqR = LpqI = LrsR = LrsI = None return eriR + eriI*1j
def general(mydf, mo_coeffs, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_general_compact', True)): warn_pbc2d_eri(mydf) if mydf._cderi is None: mydf.build() cell = mydf.cell kptijkl = _format_kpts(kpts) kpti, kptj, kptk, kptl = kptijkl if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2: mo_coeffs = (mo_coeffs,) * 4 if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'df_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros([mo.shape[1] for mo in mo_coeffs]) all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs) max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0])) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl) and all_real: ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1], compact) klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3], compact) eri_mo = numpy.zeros((nij_pair,nkl_pair)) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and iden_coeffs(mo_coeffs[1], mo_coeffs[3])) ijR = klR = None for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, True): ijR, klR = _dtrans(LpqR, ijR, ijmosym, moij, ijslice, LpqR, klR, klmosym, mokl, klslice, sym) lib.ddot(ijR.T, klR, sign, eri_mo, 1) LpqR = LpqI = None return eri_mo elif is_zero(kpti-kptk) and is_zero(kptj-kptl): mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:] eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and iden_coeffs(mo_coeffs[1], mo_coeffs[3])) zij = zkl = None for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): buf = LpqR+LpqI*1j zij, zkl = _ztrans(buf, zij, moij, ijslice, buf, zkl, mokl, klslice, sym) lib.dot(zij.T, zkl, sign, eri_mo, 1) LpqR = LpqI = buf = None return eri_mo #################### # (kpt) i == j == k == l != 0 # (kpt) i == l && j == k && i != j && j != k => # elif is_zero(kpti-kptl) and is_zero(kptj-kptk): mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:] eri_mo = numpy.zeros((nij_pair,nlk_pair), dtype=numpy.complex) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3]) and iden_coeffs(mo_coeffs[1], mo_coeffs[2])) zij = zlk = None for LpqR, LpqI, sign in mydf.sr_loop(kptijkl[:2], max_memory, False): buf = LpqR+LpqI*1j zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk, lkslice, sym) lib.dot(zij.T, zlk.conj(), sign, eri_mo, 1) LpqR = LpqI = buf = None nmok = mo_coeffs[2].shape[1] nmol = mo_coeffs[3].shape[1] eri_mo = lib.transpose(eri_mo.reshape(-1,nmol,nmok), axes=(0,2,1)) return eri_mo.reshape(nij_pair,nlk_pair) #################### # aosym = s1, complex integrals # # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk # else: mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:] nao = mo_coeffs[0].shape[0] eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex) blksize = int(min(max_memory*.3e6/16/nij_pair, max_memory*.3e6/16/nkl_pair, max_memory*.3e6/16/nao**2)) zij = zkl = None for (LpqR, LpqI, sign), (LrsR, LrsI, sign1) in \ lib.izip(mydf.sr_loop(kptijkl[:2], max_memory, False, blksize), mydf.sr_loop(kptijkl[2:], max_memory, False, blksize)): zij, zkl = _ztrans(LpqR+LpqI*1j, zij, moij, ijslice, LrsR+LrsI*1j, zkl, mokl, klslice, False) lib.dot(zij.T, zkl, sign, eri_mo, 1) LpqR = LpqI = LrsR = LrsI = None return eri_mo
def get_eri(mydf, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_get_eri_compact', True)): cell = mydf.cell nao = cell.nao_nr() kptijkl = _format_kpts(kpts) if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'aft_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros((nao,nao,nao,nao)) kpti, kptj, kptk, kptl = kptijkl q = kptj - kpti mesh = mydf.mesh coulG = mydf.weighted_coulG(q, False, mesh) nao_pair = nao * (nao+1) // 2 max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .8) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl): eriR = numpy.zeros((nao_pair,nao_pair)) for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory, aosym='s2'): lib.ddot(pqkR*coulG[p0:p1], pqkR.T, 1, eriR, 1) lib.ddot(pqkI*coulG[p0:p1], pqkI.T, 1, eriR, 1) pqkR = pqkI = None if not compact: eriR = ao2mo.restore(1, eriR, nao).reshape(nao**2,-1) return eriR #################### # (kpt) i == j == k == l != 0 # (kpt) i == l && j == k && i != j && j != k => # # complex integrals, N^4 elements elif is_zero(kpti-kptl) and is_zero(kptj-kptk): eriR = numpy.zeros((nao**2,nao**2)) eriI = numpy.zeros((nao**2,nao**2)) for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory): # rho_pq(G+k_pq) * conj(rho_rs(G-k_rs)) zdotNC(pqkR*coulG[p0:p1], pqkI*coulG[p0:p1], pqkR.T, pqkI.T, 1, eriR, eriI, 1) pqkR = pqkI = None pqkR = pqkI = coulG = None # transpose(0,1,3,2) because # j == k && i == l => # (L|ij).transpose(0,2,1).conj() = (L^*|ji) = (L^*|kl) => (M|kl) # rho_rs(-G+k_rs) = conj(transpose(rho_sr(G+k_sr), (0,2,1))) eri = lib.transpose((eriR+eriI*1j).reshape(-1,nao,nao), axes=(0,2,1)) return eri.reshape(nao**2,-1) #################### # aosym = s1, complex integrals # # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk # else: eriR = numpy.zeros((nao**2,nao**2)) eriI = numpy.zeros((nao**2,nao**2)) # # (pq|rs) = \sum_G 4\pi rho_pq rho_rs / |G+k_{pq}|^2 # rho_pq = 1/N \sum_{Tp,Tq} \int exp(-i(G+k_{pq})*r) p(r-Tp) q(r-Tq) dr # = \sum_{Tq} exp(i k_q*Tq) \int exp(-i(G+k_{pq})*r) p(r) q(r-Tq) dr # Note the k-point wrap-around for rho_rs, which leads to G+k_{pq} in FT # rho_rs = 1/N \sum_{Tr,Ts} \int exp( i(G+k_{pq})*r) r(r-Tr) s(r-Ts) dr # = \sum_{Ts} exp(i k_s*Ts) \int exp( i(G+k_{pq})*r) r(r) s(r-Ts) dr # rho_pq can be directly evaluated by AFT (function pw_loop) # rho_pq = pw_loop(k_q, G+k_{pq}) # Assuming r(r) and s(r) are real functions, rho_rs is evaluated # rho_rs = 1/N \sum_{Tr,Ts} \int exp( i(G+k_{pq})*r) r(r-Tr) s(r-Ts) dr # = conj(\sum_{Ts} exp(-i k_s*Ts) \int exp(-i(G+k_{pq})*r) r(r) s(r-Ts) dr) # = conj( pw_loop(-k_s, G+k_{pq}) ) # # TODO: For complex AO function r(r) and s(r), pw_loop function needs to be # extended to include Gv vector in the arguments for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \ lib.izip(mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory*.5), mydf.pw_loop(mesh,-kptijkl[2:], q, max_memory=max_memory*.5)): pqkR *= coulG[p0:p1] pqkI *= coulG[p0:p1] zdotNC(pqkR, pqkI, rskR.T, rskI.T, 1, eriR, eriI, 1) pqkR = pqkI = rskR = rskI = None return (eriR+eriI*1j)
def general(mydf, mo_coeffs, kpts=None, compact=getattr(__config__, 'pbc_df_ao2mo_general_compact', True)): warn_pbc2d_eri(mydf) cell = mydf.cell kptijkl = _format_kpts(kpts) kpti, kptj, kptk, kptl = kptijkl if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2: mo_coeffs = (mo_coeffs,) * 4 if not _iskconserv(cell, kptijkl): lib.logger.warn(cell, 'aft_ao2mo: momentum conservation not found in ' 'the given k-points %s', kptijkl) return numpy.zeros([mo.shape[1] for mo in mo_coeffs]) q = kptj - kpti mesh = mydf.mesh coulG = mydf.weighted_coulG(q, False, mesh) all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs) max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .5) #################### # gamma point, the integral is real and with s4 symmetry if gamma_point(kptijkl) and all_real: ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1], compact) klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3], compact) eri_mo = numpy.zeros((nij_pair,nkl_pair)) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and iden_coeffs(mo_coeffs[1], mo_coeffs[3])) ijR = ijI = klR = klI = buf = None for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory, aosym='s2'): buf = lib.transpose(pqkR, out=buf) ijR, klR = _dtrans(buf, ijR, ijmosym, moij, ijslice, buf, klR, klmosym, mokl, klslice, sym) lib.ddot(ijR.T, klR*coulG[p0:p1,None], 1, eri_mo, 1) buf = lib.transpose(pqkI, out=buf) ijI, klI = _dtrans(buf, ijI, ijmosym, moij, ijslice, buf, klI, klmosym, mokl, klslice, sym) lib.ddot(ijI.T, klI*coulG[p0:p1,None], 1, eri_mo, 1) pqkR = pqkI = None return eri_mo #################### # (kpt) i == j == k == l != 0 # (kpt) i == l && j == k && i != j && j != k => # elif is_zero(kpti-kptl) and is_zero(kptj-kptk): mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:] eri_mo = numpy.zeros((nij_pair,nlk_pair), dtype=numpy.complex) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3]) and iden_coeffs(mo_coeffs[1], mo_coeffs[2])) zij = zlk = buf = None for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory): buf = lib.transpose(pqkR+pqkI*1j, out=buf) zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk, lkslice, sym) lib.dot(zij.T, zlk.conj()*coulG[p0:p1,None], 1, eri_mo, 1) pqkR = pqkI = None nmok = mo_coeffs[2].shape[1] nmol = mo_coeffs[3].shape[1] eri_mo = lib.transpose(eri_mo.reshape(-1,nmol,nmok), axes=(0,2,1)) return eri_mo.reshape(nij_pair,nlk_pair) #################### # aosym = s1, complex integrals # # If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave # vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition. # So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk # else: mo_coeffs = _mo_as_complex(mo_coeffs) nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:] nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:] eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex) tao = [] ao_loc = None zij = zkl = buf = None for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \ lib.izip(mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory*.5), mydf.pw_loop(mesh,-kptijkl[2:], q, max_memory=max_memory*.5)): buf = lib.transpose(pqkR+pqkI*1j, out=buf) zij = _ao2mo.r_e2(buf, moij, ijslice, tao, ao_loc, out=zij) buf = lib.transpose(rskR-rskI*1j, out=buf) zkl = _ao2mo.r_e2(buf, mokl, klslice, tao, ao_loc, out=zkl) zij *= coulG[p0:p1,None] lib.dot(zij.T, zkl, 1, eri_mo, 1) pqkR = pqkI = rskR = rskI = None return eri_mo