diff --git a/pyci/__init__.py b/pyci/__init__.py index 241b08cb..015691b0 100644 --- a/pyci/__init__.py +++ b/pyci/__init__.py @@ -19,10 +19,10 @@ from pyci._pyci import secondquant_op, wavefunction, one_spin_wfn, two_spin_wfn from pyci._pyci import doci_wfn, fullci_wfn, genci_wfn, sparse_op from pyci._pyci import get_num_threads, set_num_threads, popcnt, ctz -from pyci._pyci import compute_overlap, compute_rdms, compute_transition_rdms +from pyci._pyci import compute_overlap, compute_rdms, compute_transition_rdms,compute_rdms_1234 from pyci._pyci import add_hci, compute_enpt2 -from pyci.utility import make_senzero_integrals, reduce_senzero_integrals, spinize_rdms +from pyci.utility import make_senzero_integrals, reduce_senzero_integrals, spinize_rdms,spinize_rdms_1234,spin_free_rdms from pyci.utility import odometer_one_spin, odometer_two_spin from pyci.excitation_ci import add_excitations diff --git a/pyci/include/pyci.h b/pyci/include/pyci.h index 881c2bb4..49159d03 100644 --- a/pyci/include/pyci.h +++ b/pyci/include/pyci.h @@ -221,6 +221,8 @@ void clearbit_det(const long, ulong *); void compute_rdms(const DOCIWfn &, const double *, double *, double *); +void compute_rdms_1234(const DOCIWfn &, const double *, double *, double *, double *, double *); + void compute_rdms(const FullCIWfn &, const double *, double *, double *); void compute_rdms(const GenCIWfn &, const double *, double *, double *); @@ -252,6 +254,8 @@ long py_ctz(const Array); pybind11::tuple py_compute_rdms_doci(const DOCIWfn &, const Array); +pybind11::tuple py_compute_rdms_1234_doci(const DOCIWfn &, const Array); + pybind11::tuple py_compute_rdms_fullci(const FullCIWfn &, const Array); pybind11::tuple py_compute_rdms_genci(const GenCIWfn &, const Array); diff --git a/pyci/src/binding.cpp b/pyci/src/binding.cpp index 93105420..d23ef2e5 100644 --- a/pyci/src/binding.cpp +++ b/pyci/src/binding.cpp @@ -1246,6 +1246,46 @@ For Generalized CI wave functions, ``rdm1`` and ``rdm2`` are the full 1-RDM and )""", py::arg("wfn"), py::arg("coeffs")); +m.def("compute_rdms_1234", &py_compute_rdms_1234_doci, R"""( +Compute the one-, two-, three-, and four-particle(not implemented yet) reduced density matrices (RDMs) of a wave function. + +Parameters +---------- +wfn : pyci.wavefunction + Wave function. +coeffs : numpy.ndarray + Coefficient vector. + +Returns +------- +For DOCI wave functions, this method returns two nbasis-by-nbasis matrices and two nbasis-by-nbasis-by-nbasis, + which include the unique seniority-zero and seniority-two terms from the full 2-RDMs: + +.. math:: + + D_0 = \left + +.. math:: + + D_2 = \left + +.. math:: + + D_3 = \left + +.. math:: + + D_4 = \left + + +Notes +----- +This method calculates all RDMs from 1-RDM to 4-RDM (so far implemented only to 3RDM) for a given DOCI wave function. + +)""", + py::arg("wfn"), py::arg("coeffs")); + + m.def("compute_rdms", &py_compute_rdms_fullci, py::arg("wfn"), py::arg("coeffs")); m.def("compute_rdms", &py_compute_rdms_genci, py::arg("wfn"), py::arg("coeffs")); diff --git a/pyci/src/rdm.cpp b/pyci/src/rdm.cpp index 44cc4c7d..357a9881 100644 --- a/pyci/src/rdm.cpp +++ b/pyci/src/rdm.cpp @@ -64,6 +64,95 @@ void compute_rdms(const DOCIWfn &wfn, const double *coeffs, double *d0, double * } } + +void compute_rdms_1234(const DOCIWfn &wfn, const double *coeffs, double *d0, double *d2, double *d3, double *d4) { + // prepare working vectors + AlignedVector v_det(wfn.nword); + AlignedVector v_occs(wfn.nocc_up); + AlignedVector v_virs(wfn.nvir_up); + ulong *det = &v_det[0]; + long *occs = &v_occs[0], *virs = &v_virs[0]; + // fill rdms with zeros + long i = wfn.nbasis * wfn.nbasis, j = 0; + while (j < i) { + d0[j] = 0; + d2[j++] = 0; + } + i = wfn.nbasis * wfn.nbasis * wfn.nbasis; + j = 0; + while (j < i) { + d3[j]=0; + d4[j++]=0; + } + // iterate over determinants + for (long idet = 0, jdet, mdet, k, l, m, n; idet < wfn.ndet; ++idet) { + double val1, val2; + // fill working vectors + wfn.copy_det(idet, det); + fill_occs(wfn.nword, det, occs); + fill_virs(wfn.nword, wfn.nbasis, det, virs); + // diagonal elements + val1 = coeffs[idet] * coeffs[idet]; + for (i = 0; i < wfn.nocc_up; ++i) { + k = occs[i]; + d0[k * (wfn.nbasis + 1)] += val1; + for (j = i + 1; j < wfn.nocc_up; ++j) { + l = occs[j]; + d2[wfn.nbasis * k + l] += val1; + d2[wfn.nbasis * l + k] += val1; + for (m= j + 1; m < wfn.nocc_up; ++m){ + n = occs[m]; + d3[(wfn.nbasis * wfn.nbasis) * k + wfn.nbasis * l + n] += val1; + d3[(wfn.nbasis * wfn.nbasis) * k + wfn.nbasis * n + l] += val1; + d3[(wfn.nbasis * wfn.nbasis) * l + wfn.nbasis * k + n] += val1; + d3[(wfn.nbasis * wfn.nbasis) * l + wfn.nbasis * n + k] += val1; + d3[(wfn.nbasis * wfn.nbasis) * n + wfn.nbasis * k + l] += val1; + d3[(wfn.nbasis * wfn.nbasis) * n + wfn.nbasis * l + k] += val1; + } + // pair excitation elements 3rdm j>i + for (m = 0; m < wfn.nvir_up; ++m) { + n = virs[m]; + excite_det(l, n, det); + mdet = wfn.index_det(det); + excite_det(n, l, det); + // check if excited determinant is in wfn + if (mdet > idet) { + val2 = coeffs[mdet] * coeffs[idet]; + d4[(wfn.nbasis * wfn.nbasis) * k + wfn.nbasis * l + n] += val2; + d4[(wfn.nbasis * wfn.nbasis) * k + wfn.nbasis * n + l] += val2; + } + } //pair excitation elements 3rdm i > j + for (m = 0; m < wfn.nvir_up; ++m) { + n = virs[m]; + excite_det(k, n, det); + mdet = wfn.index_det(det); + excite_det(n, k, det); + // check if excited determinant is in wfn + if (mdet > idet) { + val2 = coeffs[mdet] * coeffs[idet]; + d4[(wfn.nbasis * wfn.nbasis) * l + wfn.nbasis * k + n] += val2; + d4[(wfn.nbasis * wfn.nbasis) * l + wfn.nbasis * n + k] += val2; + } + } + + } + // pair excitation elements + for (j = 0; j < wfn.nvir_up; ++j) { + l = virs[j]; + excite_det(k, l, det); + jdet = wfn.index_det(det); + excite_det(l, k, det); + // check if excited determinant is in wfn + if (jdet > idet) { + val2 = coeffs[idet] * coeffs[jdet]; + d0[wfn.nbasis * k + l] += val2; + d0[wfn.nbasis * l + k] += val2; + } + } + } + } +} + void compute_rdms(const FullCIWfn &wfn, const double *coeffs, double *rdm1, double *rdm2) { long n1 = wfn.nbasis; long n2 = wfn.nbasis * wfn.nbasis; @@ -815,6 +904,19 @@ pybind11::tuple py_compute_rdms_doci(const DOCIWfn &wfn, const Array coe return pybind11::make_tuple(d0, d2); } +pybind11::tuple py_compute_rdms_1234_doci(const DOCIWfn &wfn, const Array coeffs) { + Array d0({wfn.nbasis, wfn.nbasis}); + Array d2({wfn.nbasis, wfn.nbasis}); + Array d3({wfn.nbasis, wfn.nbasis, wfn.nbasis}); + Array d4({wfn.nbasis, wfn.nbasis, wfn.nbasis}); + compute_rdms_1234(wfn, reinterpret_cast(coeffs.request().ptr), + reinterpret_cast(d0.request().ptr), + reinterpret_cast(d2.request().ptr), + reinterpret_cast(d3.request().ptr), + reinterpret_cast(d4.request().ptr)); + return pybind11::make_tuple(d0, d2, d3, d4); +} + pybind11::tuple py_compute_rdms_fullci(const FullCIWfn &wfn, const Array coeffs) { Array rdm1({static_cast(2), wfn.nbasis, wfn.nbasis}); Array rdm2({static_cast(3), wfn.nbasis, wfn.nbasis, wfn.nbasis, wfn.nbasis}); diff --git a/pyci/test/data/BH_sto-3g_eq.fcidump b/pyci/test/data/BH_sto-3g_eq.fcidump new file mode 100644 index 00000000..e8535bdd --- /dev/null +++ b/pyci/test/data/BH_sto-3g_eq.fcidump @@ -0,0 +1,194 @@ + &FCI NORB= 6,NELEC= 6,MS2=0, + ORBSYM=1,1,1,1,1,1, + ISYM=1, + &END + 2.890694185551886 1 1 1 1 + -0.2285478644008276 1 1 2 1 + 0.5953083364634656 1 1 2 2 + -0.2162016548582802 1 1 3 1 + 0.09104871057910127 1 1 3 2 + 0.6900652953132707 1 1 3 3 + 0.7419889025330183 1 1 4 4 + 0.7419889025330181 1 1 5 5 + 0.1413257075902383 1 1 6 1 + -0.1861902551212619 1 1 6 2 + 0.09008046930667073 1 1 6 3 + 0.6699597694264849 1 1 6 6 + -0.2285478644008276 2 1 1 1 + 0.02992401570960048 2 1 2 1 + -0.001146336251477235 2 1 2 2 + 0.02347037645652453 2 1 3 1 + -0.008237570230799412 2 1 3 2 + -0.01537296998854835 2 1 3 3 + -0.008814449236465278 2 1 4 4 + -0.008814449236465275 2 1 5 5 + -0.02314657520492044 2 1 6 1 + 0.003050017645768165 2 1 6 2 + -0.00419211917379873 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1 + -0.01533366994996728 6 3 3 2 + -0.08474684451134291 6 3 4 1 + 0.01380251877807095 6 3 4 3 + 0.0572597226318559 6 3 5 2 + 0.01720010942719272 6 3 5 4 + -0.03040828998749494 6 3 6 1 + 0.08826473242070912 6 3 6 3 + 0.0486414993890977 6 3 6 5 + 0.07102893902790244 6 4 1 1 + -0.03933516688000633 6 4 2 2 + -0.1074124027244903 6 4 3 1 + 0.02605010979246583 6 4 3 3 + -0.05740891566751927 6 4 4 2 + 0.0271815111949633 6 4 4 4 + -0.02707918220623886 6 4 5 1 + 0.05831038039821722 6 4 5 3 + -0.04198722662479192 6 4 5 5 + -0.02749406947280533 6 4 6 2 + 0.114158093843388 6 4 6 4 + 0.07645399389763961 6 4 6 6 + 0.1265883489266239 6 5 2 1 + 0.1015813908546368 6 5 3 2 + -0.04546449567905837 6 5 4 1 + 0.07460271379165258 6 5 4 3 + 0.03623646678909669 6 5 5 2 + -0.1045961073774792 6 5 5 4 + -0.0008704060307874548 6 5 6 1 + 0.04864149938909769 6 5 6 3 + 0.1378733942227017 6 5 6 5 + 0.3563217091402204 6 6 1 1 + 0.2830295621920237 6 6 2 2 + -0.07108492970990869 6 6 3 1 + 0.3121956089394763 6 6 3 3 + -0.06584844470332619 6 6 4 2 + 0.3169665388180512 6 6 4 4 + 0.00908736844753049 6 6 5 1 + 0.06924091763827081 6 6 5 3 + 0.2959042365247369 6 6 5 5 + 0.01073608413307035 6 6 6 2 + 0.07645399389763959 6 6 6 4 + 0.3834778853565485 6 6 6 6 + -1.696037966439943 1 1 0 0 + -1.538492256247005 2 2 0 0 + 0.1067870307836242 3 1 0 0 + -1.483885474763482 3 3 0 0 + 0.1468988929110372 4 2 0 0 + -1.386119822620544 4 4 0 0 + -0.05671979375364133 5 1 0 0 + -0.117268458518322 5 3 0 0 + -1.251984891232949 5 5 0 0 + -0.03775827634294857 6 2 0 0 + -0.1072466725959154 6 4 0 0 + -1.267956311081696 6 6 0 0 + 3.069227823336 0 0 0 0 diff --git a/pyci/test/test_routines.py b/pyci/test/test_routines.py index 538f5ac9..b833c578 100644 --- a/pyci/test/test_routines.py +++ b/pyci/test/test_routines.py @@ -133,6 +133,96 @@ def test_compute_rdms(filename, wfn_type, occs, energy): npt.assert_allclose(energy, es[0], rtol=0.0, atol=1.0e-9) +@pytest.mark.parametrize( + "filename, wfn_type, occs, energy", + [ + ("BH_sto-3g_eq", pyci.doci_wfn, (3, 3), -26.93841940211769), + ("h10_chain_1.4_STO-6G", pyci.doci_wfn, (5, 5), -9.84401083866329), + ("h6_sto_3g", pyci.doci_wfn, (3, 3), -5.877285606582455), + ], +) +def test_compute_rdms_1234(filename, wfn_type, occs, energy): + ham = pyci.secondquant_op(datafile("{0:s}.fcidump".format(filename))) + wfn = wfn_type(ham.nbasis, *occs) + wfn.add_all_dets() + op = pyci.sparse_op(ham, wfn) + es, cs = op.solve(n=1, tol=1.0e-6) + if not isinstance(wfn, pyci.doci_wfn): + raise TypeError('Wfn must be DOCI') + d0, d2, d3, d4= pyci.compute_rdms_1234(wfn, cs[0]) + npt.assert_allclose(np.trace(d0), wfn.nocc_up, rtol=0, atol=1.0e-9) + npt.assert_allclose(np.sum(d2), wfn.nocc_up * (wfn.nocc_up - 1), rtol=0, atol=1.0e-9) + k0, k2 = pyci.reduce_senzero_integrals(ham.h, ham.v, ham.w, wfn.nocc_up) + energy = ham.ecore + energy += np.einsum("ij,ij", k0, d0) + energy += np.einsum("ij,ij", k2, d2) + npt.assert_allclose(energy, es[0], rtol=0.0, atol=1.0e-9) + rdm1, rdm2, rdm3 = pyci.spinize_rdms_1234(d0, d2, d3 ,d4) + assert np.all(np.abs(rdm1 - rdm1.T) < 1e-5) + # # Test RDM2 is antisymmetric + # for i in range(0, wfn.nbasis * 2): + # for j in range(0, wfn.nbasis * 2): + # assert np.all(rdm2[i, j, :, :] + rdm2[i, j, :, :].T) < 1e-5 + # for k in range(0, wfn.nbasis * 2): + # for l in range(0, wfn.nbasis * 2): + # assert np.abs(rdm2[i, j, k, l] - rdm2[k, l, i, j]) < 1e-5 + # "Testing that non Antiysmmetric parts are all zeros." + for i in range(0, wfn.nbasis * 2): + assert np.all(np.abs(rdm2[i, i, :, :]) < 1e-5) + assert np.all(np.abs(rdm2[:, :, i, i]) < 1e-5) + + # # Test RDM3 is antisymmetric + # "Testing that non Antiysmmetric parts are all zeros." + for i in range(0, wfn.nbasis * 2): + assert np.all(np.abs(rdm3[i, i, i, :, :, :]) < 1e-5) + assert np.all(np.abs(rdm3[:, :, :, i, i, i]) < 1e-5) + assert np.all(np.abs(rdm3[i, i, :, :, :, :]) < 1e-5) + assert np.all(np.abs(rdm3[:, :, :, :, i, i]) < 1e-5) + assert np.all(np.abs(rdm3[i, :, i, :, :, :]) < 1e-5) + assert np.all(np.abs(rdm3[:, :, :, i, :, i]) < 1e-5) + #TEST COMPLETE 3RDM AND BLOCKS TRACES + aabaab=rdm3[:ham.nbasis, :ham.nbasis, ham.nbasis:, :ham.nbasis, :ham.nbasis, ham.nbasis:] + bbabba=rdm3[ham.nbasis:, ham.nbasis:, :ham.nbasis, ham.nbasis:, ham.nbasis:, :ham.nbasis] + aaaaaa=rdm3[:ham.nbasis, :ham.nbasis, :ham.nbasis, :ham.nbasis, :ham.nbasis, :ham.nbasis] + bbbbbb=rdm3[ham.nbasis:, ham.nbasis:, ham.nbasis:, ham.nbasis:, ham.nbasis:, ham.nbasis:] + npt.assert_allclose(np.einsum('ijkijk -> ', rdm3),(wfn.nocc_up * 2)*(wfn.nocc_up * 2 - 1) * (wfn.nocc_up * 2 - 2) ,rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('ijkijk -> ', aaaaaa),(wfn.nocc_up) * (wfn.nocc_up - 1) * (wfn.nocc_up - 2) , rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('ijkijk -> ', aabaab),(wfn.nocc_up) * (wfn.nocc_dn) * (wfn.nocc_up - 1) , rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('ijkijk -> ', bbbbbb),(wfn.nocc_dn) * (wfn.nocc_dn - 1) * (wfn.nocc_dn - 2) , rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('ijkijk -> ', bbabba),(wfn.nocc_up) * (wfn.nocc_dn) * (wfn.nocc_dn - 1) , rtol=0, atol=1.0e-9) + #TEST TRACING OVER TWO INDICES IN 3RDM REDUCES TO 2RDM + d2_block_aaaa = rdm2[:ham.nbasis, :ham.nbasis, :ham.nbasis, :ham.nbasis] + d2_block_bbbb = rdm2[ham.nbasis:, ham.nbasis:, ham.nbasis:, ham.nbasis:] + d2_block_abab = rdm2[:ham.nbasis, ham.nbasis:, :ham.nbasis, ham.nbasis:] + d2_block_baba = rdm2[ham.nbasis:, :ham.nbasis, ham.nbasis:, :ham.nbasis] + # All-alpha block + fac=(1.0 / (wfn.nocc_up - 2.0)) + npt.assert_allclose(np.einsum('ijmklm->ijkl ', aaaaaa) * fac,d2_block_aaaa, rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('imjkml->ijkl ', aaaaaa) * fac,d2_block_aaaa, rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('mijmkl->ijkl ', aaaaaa) * fac,d2_block_aaaa, rtol=0, atol=1.0e-9) + + fac=(1.0 / (wfn.nocc_up)) + npt.assert_allclose(np.einsum('ijmklm->ijkl ', aabaab) * fac,d2_block_aaaa, rtol=0, atol=1.0e-9) + + # All-beta block + fac=(1.0 / (wfn.nocc_dn - 2.0)) + npt.assert_allclose(np.einsum('ijmklm->ijkl ', bbbbbb) * fac,d2_block_bbbb, rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('imjkml->ijkl ', bbbbbb) * fac,d2_block_bbbb, rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('mijmkl->ijkl ', bbbbbb) * fac,d2_block_bbbb, rtol=0, atol=1.0e-9) + + fac=(1.0 / (wfn.nocc_dn)) + npt.assert_allclose(np.einsum('ijmklm->ijkl ', bbabba) * fac,d2_block_bbbb, rtol=0, atol=1.0e-9) + + #Mixed-spin blocks + fac=(1.0 / (wfn.nocc_up - 1.0)) + npt.assert_allclose(np.einsum('mijmkl->ijkl ', aabaab) * fac,d2_block_abab, rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('imjkml->ijkl ', aabaab) * fac,d2_block_abab, rtol=0, atol=1.0e-9) + + fac=(1.0 / (wfn.nocc_dn - 1.0)) + npt.assert_allclose(np.einsum('mijmkl->ijkl ', bbabba) * fac,d2_block_baba, rtol=0, atol=1.0e-9) + npt.assert_allclose(np.einsum('imjkml->ijkl ', bbabba) * fac,d2_block_baba, rtol=0, atol=1.0e-9) + + @pytest.mark.parametrize( "filename, wfn_type, occs, energy", [ diff --git a/pyci/utility.py b/pyci/utility.py index 1ecaff9c..af7330e1 100644 --- a/pyci/utility.py +++ b/pyci/utility.py @@ -91,7 +91,6 @@ def reduce_senzero_integrals(h, v, w, nocc): rw += w return rv, rw - def spinize_rdms(d1, d2): r""" Convert the DOCI matrices or FullCI RDM spin-blocks to full, generalized RDMs. @@ -151,6 +150,140 @@ def spinize_rdms(d1, d2): return rdm1, rdm2 +def spinize_rdms_1234(d1, d2, d3, d4): + r""" + Convert the DOCI matrices or FullCI RDM spin-blocks to full, generalized RDMs. + + Parameters + ---------- + .. math:: + d_0 = \left + .. math:: + d_2 = \left + .. math:: + d_3 = \left + .. math:: + d_4 = \left + Returns + ------- + rdm1 : numpy.ndarray + Generalized one-particle RDM. + rdm2 : numpy.ndarray + Generalized two-particle RDM. + rdm3 : numpy.ndarray + Generalized three-particle RDM. + """ + if d1.ndim != 2: + raise TypeError('wfn must be a DOCI') + nbasis = d1.shape[1] + nspin = nbasis * 2 + rdm1 = np.zeros((nspin, nspin), dtype=np.double) + rdm2 = np.zeros((nspin, nspin, nspin, nspin), dtype=np.double) + rdm3 = np.zeros((nspin, nspin, nspin, nspin,nspin,nspin), dtype=np.double) + aa = rdm1[:nbasis, :nbasis] + bb = rdm1[nbasis:, nbasis:] + aaaa = rdm2[:nbasis, :nbasis, :nbasis, :nbasis] + bbbb = rdm2[nbasis:, nbasis:, nbasis:, nbasis:] + abab = rdm2[:nbasis, nbasis:, :nbasis, nbasis:] + baba = rdm2[nbasis:, :nbasis, nbasis:, :nbasis] + abba = rdm2[:nbasis, nbasis:, nbasis:, :nbasis] + baab = rdm2[nbasis:, :nbasis, :nbasis, nbasis:] + aaaaaa = rdm3[:nbasis,:nbasis,:nbasis,:nbasis,:nbasis,:nbasis] + bbbbbb = rdm3[nbasis:,nbasis:,nbasis:,nbasis:,nbasis:,nbasis:] + bbabba = rdm3[nbasis:,nbasis:,:nbasis,nbasis:,nbasis:,:nbasis] + aabaab = rdm3[:nbasis,:nbasis,nbasis:,:nbasis,:nbasis,nbasis:] + for p in range(nbasis): + aa[p, p] = d1[p, p] + bb[p, p] = d1[p, p] + for q in range(nbasis): + abab[p, p, q, q] += d1[p, q] + baba[p, p, q, q] += d1[p, q] + aaaa[p, q, p, q] += d2[p, q] + bbbb[p, q, p, q] += d2[p, q] + abab[p, q, p, q] += d2[p, q] + baba[p, q, p, q] += d2[p, q] + bbabba[p, q, q, p, q, q] += 2.0 * d2[p, q] + aabaab[p, q, q, p, q, q] += 2.0 * d2[p, q] + for r in range(nbasis): + bbabba[p, q, q, p, r, r] += 2.0 * d4[p, q, r] + aabaab[p, q, q, p, r, r] += 2.0 * d4[p, q, r] + aaaaaa[p, q, r, p, q, r] += d3[p, q, r] + bbbbbb[p, q, r, p, q, r] += d3[p, q, r] + bbabba[p, q, r, p, q, r] += d3[p, q, r] + aabaab[p, q, r, p, q, r] += d3[p, q, r] + rdm2 -= np.transpose(rdm2, axes=(1, 0, 2, 3)) + rdm2 -= np.transpose(rdm2, axes=(0, 1, 3, 2)) + rdm2 *= 0.5 + rdm3 += np.einsum('ijklmn -> ijknlm', rdm3)+\ + np.einsum('ijklmn -> ijkmnl', rdm3) + rdm3 *= 1 + rdm3 -= np.einsum('ijklmn -> ijkmln', rdm3) + rdm3 += np.einsum('ijklmn -> kijlmn', rdm3)+\ + np.einsum('ijklmn -> jkilmn', rdm3) + aaaaaa *= 1/3 + bbbbbb *= 1/3 + rdm3 -= np.einsum('ijklmn -> jiklmn', rdm3) + rdm3 *= 0.5 + return rdm1, rdm2, rdm3 + +def spin_free_rdms(d1, d2, d3=None, d4=None): + r""" + + Wrapper of spinze_rdms function that sums over the spin degree of freedom + to obtain spinless rdms. + + Parameters + ---------- + d1 : numpy.ndarray + :math:`D_0` matrix or FullCI 1-RDM spin-blocks. + d2 : numpy.ndarray + :math:`D_2` matrix or FullCI 2-RDM spin-blocks. + d3 : numpy.ndarray + :math `D_3` matrix for 3-RDM spin-blocks + d4 : numpy.ndarray + :math `D_4` matrix for 3-RDM spin-blocks + + Returns + ------- + rdm1 : numpy.ndarray + Spin traced one-particle RDM. + rdm2 : numpy.ndarray + Spin traced two-particle RDM. + rdm3 : numpy.ndarray + Spin traced three-particle RDM. + """ + nbasis = d1.shape[1] + rdm1, rdm2, rdm3 = spinize_rdms_1234(d1, d2, d3, d4) + rdm1_sf = np.zeros((nbasis, nbasis), dtype=np.double) + rdm2_sf = np.zeros((nbasis, nbasis, nbasis, nbasis), dtype=np.double) + rdm3_sf = np.zeros((nbasis, nbasis, nbasis, nbasis, nbasis, nbasis), dtype=np.double) + aa = rdm1[:nbasis, :nbasis] + bb = rdm1[nbasis:, nbasis:] + aaaa = rdm2[:nbasis, :nbasis, :nbasis, :nbasis] + bbbb = rdm2[nbasis:, nbasis:, nbasis:, nbasis:] + abab = rdm2[:nbasis, nbasis:, :nbasis, nbasis:] + baba = rdm2[nbasis:, :nbasis, nbasis:, :nbasis] + if d1.ndim == 2: + # DOCI matrices + rdm3_sf=np.zeros((nbasis, nbasis, nbasis, nbasis,nbasis,nbasis), dtype=np.double) + aaaaaa= rdm3[:nbasis, :nbasis, :nbasis, :nbasis, :nbasis, :nbasis] + bbbbbb= rdm3[nbasis:, nbasis:, nbasis:, nbasis:, nbasis:, nbasis:] + bbabba= rdm3[nbasis:, nbasis:, :nbasis, nbasis:, nbasis:, :nbasis] + abbabb= rdm3[:nbasis, nbasis:, nbasis:, :nbasis, nbasis:, nbasis:] + babbab = rdm3[nbasis:, :nbasis, nbasis:, nbasis:, :nbasis, nbasis:] + aabaab = rdm3[:nbasis, :nbasis, nbasis:, :nbasis, :nbasis, nbasis:] + abaaba = rdm3[:nbasis, nbasis:, :nbasis, :nbasis, nbasis:, :nbasis] + baabaa = rdm3[nbasis:, :nbasis, :nbasis, nbasis:, :nbasis, :nbasis] + rdm1_sf = aa + bb + rdm2_sf = aaaa + abab+ baba+ bbbb + rdm3_sf = aaaaaa + bbbbbb + aabaab + abaaba + baabaa + bbabba + babbab + abbabb + return (rdm1_sf, rdm2_sf, rdm3_sf) + else: + # FullCI RDM spin-blocks + rdm1_sf = aa + bb + rdm2_sf = aaaa + abab + baba + bbbb + return (rdm1_sf, rdm2_sf) + def odometer_one_spin(wfn, cost, t, qmax): r""" Iterates over determinants of a one-spin wave function, adding those that satisfy