def general(mydf, mo_coeffs, kpts=None, compact=True): 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 q = kptj - kpti coulG = mydf.weighted_coulG(q, False, mydf.gs) 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(mydf.gs, kptijkl[:2], q, max_memory=max_memory, aosym='s2'): vG = numpy.sqrt(coulG[p0:p1]) pqkR *= vG pqkI *= vG 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, 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, 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(mydf.gs, kptijkl[:2], q, max_memory=max_memory): buf = lib.transpose(pqkR + pqkI * 1j, out=buf) buf *= numpy.sqrt(coulG[p0:p1]).reshape(-1, 1) zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk, lkslice, sym) lib.dot(zij.T, zlk.conj(), 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(mydf.gs, kptijkl[:2], q, max_memory=max_memory*.5), mydf.pw_loop(mydf.gs,-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].reshape(-1, 1) lib.dot(zij.T, zkl, 1, eri_mo, 1) pqkR = pqkI = rskR = rskI = None return eri_mo
def general(mydf, mo_coeffs, kpts=None, compact=True): 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 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 abs(kptijkl).sum() < KPT_DIFF_TOL 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])) coulG = mydf.weighted_coulG(kptj-kpti, False, mydf.gs) ijR = ijI = klR = klI = buf = None for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mydf.gs, kptijkl[:2], max_memory=max_memory, aosym='s2'): vG = numpy.sqrt(coulG[p0:p1]) pqkR *= vG pqkI *= vG 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, 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, 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 (abs(kpti-kptl).sum() < KPT_DIFF_TOL) and (abs(kptj-kptk).sum() < KPT_DIFF_TOL): 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])) coulG = mydf.weighted_coulG(kptj-kpti, False, mydf.gs) zij = zlk = buf = None for pqkR, pqkI, p0, p1 \ in mydf.pw_loop(mydf.gs, kptijkl[:2], max_memory=max_memory): buf = lib.transpose(pqkR+pqkI*1j, out=buf) buf *= numpy.sqrt(coulG[p0:p1]).reshape(-1,1) zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk, lkslice, sym) lib.dot(zij.T, zlk.conj(), 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 coulG = mydf.weighted_coulG(kptj-kpti, False, mydf.gs) zij = zkl = buf = None for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \ lib.izip(mydf.pw_loop(mydf.gs, kptijkl[:2], max_memory=max_memory*.5), mydf.pw_loop(mydf.gs,-kptijkl[2:], 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].reshape(-1,1) lib.dot(zij.T, zkl, 1, eri_mo, 1) pqkR = pqkI = rskR = rskI = None return eri_mo
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 general(mydf, mo_coeffs, kpts=None, compact=True): 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 eri_mo = pwdf_ao2mo.general(mydf, mo_coeffs, kptijkl, compact) 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 abs(kptijkl).sum() < KPT_DIFF_TOL 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) sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and iden_coeffs(mo_coeffs[1], mo_coeffs[3])) if sym: eri_mo *= .5 # because we'll do +cc later ijR = klR = None for LpqR, LpqI, j3cR, j3cI in mydf.sr_loop(kptijkl[:2], max_memory, True): ijR, klR = _dtrans(LpqR, ijR, ijmosym, moij, ijslice, j3cR, klR, klmosym, mokl, klslice, False) lib.ddot(ijR.T, klR, 1, eri_mo, 1) if not sym: ijR, klR = _dtrans(j3cR, ijR, ijmosym, moij, ijslice, LpqR, klR, klmosym, mokl, klslice, False) lib.ddot(ijR.T, klR, 1, eri_mo, 1) LpqR = LpqI = j3cR = j3cI = None if sym: eri_mo = lib.transpose_sum(eri_mo, inplace=True) return eri_mo #################### # (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 (abs(kpti-kptl).sum() < KPT_DIFF_TOL) and (abs(kptj-kptk).sum() < KPT_DIFF_TOL): 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_lk = 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 LpqR, LpqI, j3cR, j3cI in mydf.sr_loop(kptijkl[:2], max_memory, False): bufL = LpqR+LpqI*1j bufj = j3cR+j3cI*1j zij, zlk = _ztrans(bufL, zij, moij, ijslice, bufj, zlk, molk, lkslice, False) lib.dot(zij.T, zlk.conj(), 1, eri_lk, 1) if not sym: zij, zlk = _ztrans(bufj, zij, moij, ijslice, bufL, zlk, molk, lkslice, False) lib.dot(zij.T, zlk.conj(), 1, eri_lk, 1) LpqR = LpqI = j3cR = j3cI = bufL = bufj = None if sym: eri_lk += lib.transpose(eri_lk).conj() nmok = mo_coeffs[2].shape[1] nmol = mo_coeffs[3].shape[1] eri_lk = lib.transpose(eri_lk.reshape(-1,nmol,nmok), axes=(0,2,1)) eri_mo += eri_lk.reshape(nij_pair,nlk_pair) return eri_mo #################### # 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: 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:] max_memory *= .5 zij = zkl = None for (LpqR, LpqI, jpqR, jpqI), (LrsR, LrsI, jrsR, jrsI) in \ lib.izip(mydf.sr_loop(kptijkl[:2], max_memory, False), mydf.sr_loop(kptijkl[2:], max_memory, False)): zij, zkl = _ztrans(LpqR+LpqI*1j, zij, moij, ijslice, jrsR+jrsI*1j, zkl, mokl, klslice, False) lib.dot(zij.T, zkl, 1, eri_mo, 1) zij, zkl = _ztrans(jpqR+jpqI*1j, zij, moij, ijslice, LrsR+LrsI*1j, zkl, mokl, klslice, False) lib.dot(zij.T, zkl, 1, eri_mo, 1) LpqR = LpqI = jpqR = jpqI = LrsR = LrsI = jrsR = jrsI = None return eri_mo