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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test of F12 matrix elements"
]
},
{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
"## Initialization"
]
},
{
"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val png_image : string -> unit = <fun>\n"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"- : unit = ()\n",
"Findlib has been successfully loaded. Additional directives:\n",
" #require \"package\";; to load a package\n",
" #list;; to list the available packages\n",
" #camlp4o;; to load camlp4 (standard syntax)\n",
" #camlp4r;; to load camlp4 (revised syntax)\n",
" #predicates \"p,q,...\";; to set these predicates\n",
" Topfind.reset();; to force that packages will be reloaded\n",
" #thread;; to enable threads\n",
"\n",
"- : unit = ()\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/scemama/qp2/external/opam/4.07.1/lib/bytes: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/base64: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/base64/base64.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamlcommon.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/result: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/result/result.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime/ppx_deriving_runtime.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime/ppx_deriving_yojson_runtime.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/unix.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/uuidm: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/uuidm/uuidm.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/easy-format: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/easy-format/easy_format.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/biniou: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/biniou/biniou.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/yojson: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/yojson/yojson.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/jupyter: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/jupyter.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook/jupyter_notebook.cma: loaded\n"
]
},
{
"data": {
"text/plain": [
"val png_image : string -> Jupyter_notebook.display_id = <fun>\n"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamlbytecomp.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamltoplevel.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/bigarray.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/lacaml: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/lacaml.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/top: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/top/lacaml_top.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/astring: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/astring/astring.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner/cmdliner.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/seq: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims/stdlib_shims.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/fmt: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_cli.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_tty.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/alcotest: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/alcotest/alcotest.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/str.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/zarith: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/zarith/zarith.cma: loaded\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/getopt: added to search path\n",
"/home/scemama/qp2/external/opam/4.07.1/lib/getopt/getopt.cma: loaded\n"
]
}
],
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"source": [
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"let png_image = print_endline ;;\n",
"\n",
"(* --------- *)\n",
"\n",
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"#cd \"/home/scemama/QCaml\";;\n",
"#use \"topfind\";;\n",
"#require \"jupyter.notebook\";;\n",
"\n",
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"let png_image name = \n",
" Jupyter_notebook.display_file ~base64:true \"image/png\" (\"Notebooks/images/\"^name)\n",
";;\n",
"\n",
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"#require \"lacaml.top\";;\n",
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"#require \"alcotest\";;\n",
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"#require \"str\";;\n",
"#require \"bigarray\";;\n",
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"#require \"zarith\";;\n",
"#require \"getopt\";;\n",
"#directory \"_build\";;\n",
"#directory \"_build/Basis\";;\n",
"#directory \"_build/CI\";;\n",
"#directory \"_build/MOBasis\";;\n",
"#directory \"_build/Nuclei\";;\n",
"#directory \"_build/Parallel\";;\n",
"#directory \"_build/Perturbation\";;\n",
"#directory \"_build/SCF\";;\n",
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"#directory \"_build/Utils\";;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"### Modules"
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]
},
{
"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
"outputs": [],
"source": [
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"#load \"Constants.cmo\";;\n",
"#load_rec \"Util.cma\";;\n",
"#load_rec \"Matrix.cmo\";;\n",
"#load_rec \"Simulation.cmo\";;\n",
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"#load_rec \"Spindeterminant.cmo\";;\n",
"#load_rec \"Determinant.cmo\";;\n",
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"#load_rec \"HartreeFock.cmo\";;\n",
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"#load_rec \"MOBasis.cmo\";;\n",
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"#load_rec \"F12CI.cmo\";;"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Printers"
]
},
{
"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val pp_mo : Format.formatter -> MOBasis.t -> unit = <fun>\n"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"#install_printer AngularMomentum.pp_string ;;\n",
"#install_printer Basis.pp ;;\n",
"#install_printer Charge.pp ;;\n",
"#install_printer Coordinate.pp ;;\n",
"#install_printer Vector.pp;;\n",
"#install_printer Matrix.pp;;\n",
"#install_printer Util.pp_float_2darray;;\n",
"#install_printer Util.pp_float_array;;\n",
"#install_printer Util.pp_matrix;;\n",
"#install_printer HartreeFock.pp ;;\n",
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"#install_printer Fock.pp ;;\n",
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"#install_printer MOClass.pp ;;\n",
"let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n",
"#install_printer pp_mo;;\n",
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"(*\n",
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"#install_printer DeterminantSpace.pp;;\n",
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"*)\n",
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"#install_printer SpindeterminantSpace.pp;;\n",
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"#install_printer Bitstring.pp;;\n",
"\n",
"(* --------- *)\n",
"\n",
"open Lacaml.D\n"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"## Run"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Simulation\n"
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]
},
{
"cell_type": "code",
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"execution_count": 23,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val basis_filename : string = \"/home/scemama/qp2/data/basis/6-31g\"\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val nuclei : Nuclei.t = [|(Element.N, 0.0000 0.0000 0.0000)|]\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val frozen_core : bool = true\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val multiplicity : int = 2\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val state : int = 1\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val basis : Basis.t =\n",
" \n",
" Atomic Basis set\n",
" ----------------\n",
"\n",
"-----------------------------------------------------------------------\n",
" # Angular Coordinates (Bohr) Exponents Coefficients\n",
" Momentum X Y Z\n",
"-----------------------------------------------------------------------\n",
" 1-3 S 0.0000 0.0000 0.0000 4.17351100e+03 1.83480000e-03\n",
" 6.27457900e+02 1.39950000e-02\n",
" 1.42902100e+02 6.85870000e-02\n",
" 4.02343300e+01 2.32241000e-01\n",
" 1.28202100e+01 4.69070000e-01\n",
" 4.39043700e+00 3.60455000e-01\n",
" \n",
" 1.16263580e+01 -1.14961000e-01\n",
" 2.71628000e+00 -1.69118000e-01\n",
" 7.72218000e-01 1.14585200e+00\n",
" \n",
" 2.12031300e-01 1.00000000e+00\n",
" \n",
" \n",
"-----------------------------------------------------------------------\n",
" 3-8 P 0.0000 0.0000 0.0000 1.16263580e+01 6.75800000e-02\n",
" 2.71628000e+00 3.23907000e-01\n",
" 7.72218000e-01 7.40895000e-01\n",
" \n",
" 2.12031300e-01 1.00000000e+00\n",
" \n",
" \n",
"-----------------------------------------------------------------------\n",
"\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val aux_basis : Basis.t =\n",
" \n",
" Atomic Basis set\n",
" ----------------\n",
"\n",
"-----------------------------------------------------------------------\n",
" # Angular Coordinates (Bohr) Exponents Coefficients\n",
" Momentum X Y Z\n",
"-----------------------------------------------------------------------\n",
" 1-6 S 0.0000 0.0000 0.0000 4.17351100e+03 1.83480000e-03\n",
" 6.27457900e+02 1.39950000e-02\n",
" 1.42902100e+02 6.85870000e-02\n",
" 4.02343300e+01 2.32241000e-01\n",
" 1.28202100e+01 4.69070000e-01\n",
" 4.39043700e+00 3.60455000e-01\n",
" \n",
" 1.16263580e+01 -1.14961000e-01\n",
" 2.71628000e+00 -1.69118000e-01\n",
" 7.72218000e-01 1.14585200e+00\n",
" \n",
" 2.12031300e-01 1.00000000e+00\n",
" \n",
" 9.04600000e+03 7.00000000e-04\n",
" 1.35700000e+03 5.38900000e-03\n",
" 3.09300000e+02 2.74060000e-02\n",
" 8.77300000e+01 1.03207000e-01\n",
" 2.85600000e+01 2.78723000e-01\n",
" 1.02100000e+01 4.48540000e-01\n",
" 3.83800000e+00 2.78238000e-01\n",
" 7.46600000e-01 1.54400000e-02\n",
" \n",
" 9.04600000e+03 -1.53000000e-04\n",
" 1.35700000e+03 -1.20800000e-03\n",
" 3.09300000e+02 -5.99200000e-03\n",
" 8.77300000e+01 -2.45440000e-02\n",
" 2.85600000e+01 -6.74590000e-02\n",
" 1.02100000e+01 -1.58078000e-01\n",
" 3.83800000e+00 -1.21831000e-01\n",
" 7.46600000e-01 5.49003000e-01\n",
" \n",
" 2.24800000e-01 1.00000000e+00\n",
" \n",
" \n",
"-----------------------------------------------------------------------\n",
" 3-14 P 0.0000 0.0000 0.0000 1.16263580e+01 6.75800000e-02\n",
" 2.71628000e+00 3.23907000e-01\n",
" 7.72218000e-01 7.40895000e-01\n",
" \n",
" 2.12031300e-01 1.00000000e+00\n",
" \n",
" 1.35500000e+01 3.99190000e-02\n",
" 2.91700000e+00 2.17169000e-01\n",
" 7.97300000e-01 5.10319000e-01\n",
" \n",
" 2.18500000e-01 1.00000000e+00\n",
" \n",
" \n",
"-----------------------------------------------------------------------\n",
" 19-24 D 0.0000 0.0000 0.0000 8.17000000e-01 1.00000000e+00\n",
" \n",
" \n",
"-----------------------------------------------------------------------\n",
"\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val f12 : F12factor.t =\n",
" {F12factor.expo_s = 1.;\n",
" gaussian =\n",
" {GaussianOperator.coef_g =\n",
" [ -0.314400 -0.303700 -0.168100 -0.098110 -0.060240 -0.037260 ];\n",
" expo_sg =\n",
" [ 0.220900 1.004000 3.622000 12.160000 45.870000 254.400000 ];\n",
" expo_sg_inv =\n",
" [ 4.526935 0.996016 0.276091 0.082237 0.021801 0.003931 ]}}\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val charge : int = 0\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val simulation : Simulation.t = <abstr>\n"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let basis_filename = \"/home/scemama/qp2/data/basis/6-31g\" \n",
"let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n",
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"let nuclei = Nuclei.of_zmt_string \"n\" \n",
"let frozen_core = true \n",
"let multiplicity = 2\n",
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"let state = 1\n",
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"\n",
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"let basis = Basis.of_nuclei_and_basis_filenames ~nuclei [basis_filename] \n",
"let aux_basis = Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filename :: []) \n",
"let f12 = F12factor.gaussian_geminal 1.0 \n",
"let charge = 0 \n",
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"\n",
"\n",
"let simulation =\n",
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" Simulation.make \n",
" ~f12 ~charge ~multiplicity ~nuclei\n",
" ~cartesian:true\n",
" basis\n"
]
},
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{
"cell_type": "code",
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"execution_count": 24,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val n_elec_alfa : int = 4\n",
"val n_elec_beta : int = 3\n",
"val n_elec : int = 7\n"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let n_elec_alfa, n_elec_beta, n_elec = \n",
" let e = Simulation.electrons simulation in\n",
" Electrons.(n_alfa e, n_beta e, n_elec e)"
]
},
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{
"cell_type": "markdown",
"metadata": {},
"source": [
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"### Hartree-Fock"
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]
},
{
"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"15 significant shell pairs computed in 0.005208 seconds\n",
"1\n",
"2\n",
"5\n",
"6\n",
"Computed ERIs in 0.026325 seconds\n",
"MOs =\n",
"\n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0.995805 -0.228629 -0 0 -0\n",
" 2 0.0207488 0.523688 2.54045E-16 1.78891E-15 -0\n",
" 3 0 -3.45043E-16 0.516899 5.11587E-15 0.306901\n",
" ... ... ... ... ...\n",
" 7 0 -0 0.381023 3.3482E-15 0.401251\n",
" 8 0 -6.37589E-16 -0.238604 0.273454 0.404641\n",
" 9 0 -6.8E-16 0.182264 0.357982 -0.309095\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 -0 0 0.0896964 4.08276E-15\n",
" 2 1.33506E-15 -3.60646E-15 -1.51213 -6.87142E-14\n",
" 3 -0.759946 0.656011 -2.25085E-15 -1.25628E-14\n",
" ... ... ... ...\n",
" 7 0.836375 -0.602939 2.17188E-15 1.39379E-14\n",
" 8 -0.523755 -0.608033 -2.87741E-14 0.655571\n",
" 9 0.400083 0.464461 -3.95033E-14 0.858218\n",
" \n"
]
},
{
"data": {
"text/plain": [
"val hf : HartreeFock.t = \n",
"======================================================================\n",
" Restricted Open-shell Hartree-Fock \n",
"======================================================================\n",
"\n",
" ------------------------------------------------------------\n",
" # HF energy Convergence HOMO-LUMO\n",
" ------------------------------------------------------------\n",
" 1 -52.57862719 9.9817e-01 0.0835\n",
" 2 -54.20380931 2.2021e-01 0.2639\n",
" 3 -54.23392256 5.7771e-02 0.2682\n",
" 4 -54.24023663 2.1083e-02 0.2680\n",
" 5 -54.24159726 8.9827e-03 0.2673\n",
" 6 -54.24188853 4.2281e-03 0.2669\n",
" 7 -54.24195106 1.9862e-03 0.2667\n",
" 8 -54.24196836 1.6000e-05 0.2665\n",
" 9 -54.24196836 1.6302e-06 0.2665\n",
" 10 -54.24196843 3.8429e-08 0.2665\n",
" ------------------------------------------------------------\n",
"\n",
"\n",
" ============================================================\n",
" One-electron energy -73.7477460896\n",
" Kinetic 54.1465371332\n",
" Potential -127.8942832228\n",
" -------------------------------------------------------- \n",
" Two-electron energy 19.5057776578\n",
" Coulomb 26.0005985081\n",
" Exchange -6.4948208503\n",
" -------------------------------------------------------- \n",
" HF HOMO -5.3102635644\n",
" HF LUMO 1.9421331121\n",
" HF LUMO-LUMO 7.2523966765\n",
" -------------------------------------------------------- \n",
" Electronic energy -54.2419684318\n",
" Nuclear repulsion 0.0000000000\n",
" Hartree-Fock energy -54.2419684318\n",
" ============================================================\n",
" \n",
"\n"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mo_basis : MOBasis.t =\n",
" Eigenvalues: -15.681404 -0.961606 -0.451178 -0.195149 0.040479 \n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0.995805 -0.228629 -0 0 -0\n",
" 2 0.0207488 0.523688 2.54045E-16 1.78891E-15 -0\n",
" 3 0 -3.45043E-16 0.516899 5.11587E-15 0.306901\n",
" ... ... ... ... ...\n",
" 7 0 -0 0.381023 3.3482E-15 0.401251\n",
" 8 0 -6.37589E-16 -0.238604 0.273454 0.404641\n",
" 9 0 -6.8E-16 0.182264 0.357982 -0.309095\n",
" \n",
" Eigenvalues: 0.908849 0.950925 0.975309 0.912008 \n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 -0 0 0.0896964 4.08276E-15\n",
" 2 1.33506E-15 -3.60646E-15 -1.51213 -6.87142E-14\n",
" 3 -0.759946 0.656011 -2.25085E-15 -1.25628E-14\n",
" ... ... ... ...\n",
" 7 0.836375 -0.602939 2.17188E-15 1.39379E-14\n",
" 8 -0.523755 -0.608033 -2.87741E-14 0.655571\n",
" 9 0.400083 0.464461 -3.95033E-14 0.858218\n",
" \n",
" \n"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let hf = HartreeFock.make ~guess:`Hcore ~max_scf:10 simulation ;;\n",
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"\n",
"let mo_basis = MOBasis.of_hartree_fock hf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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" FCI-F12"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notations:\n",
"\n",
"* $\\langle ij || kl \\rangle = \\int \\phi_i(r_1) \\phi_j(r_2) \\frac{1}{r_{12}} \\phi_k(r1) \\phi_l(r2) $ \n",
"* $\\left[ ij || kl \\right] = \\int \\phi_i(r_1) \\phi_j(r_2) f_{12} \\phi_k(r1) \\phi_l(r2) $ \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Common functions"
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]
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},
{
"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val f12 : F12factor.t =\n",
" {F12factor.expo_s = 1.;\n",
" gaussian =\n",
" {GaussianOperator.coef_g =\n",
" [ -0.314400 -0.303700 -0.168100 -0.098110 -0.060240 -0.037260 ];\n",
" expo_sg =\n",
" [ 0.220900 1.004000 3.622000 12.160000 45.870000 254.400000 ];\n",
" expo_sg_inv =\n",
" [ 4.526935 0.996016 0.276091 0.082237 0.021801 0.003931 ]}}\n"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mo_num : int = 9\n"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val pp_spindet : Format.formatter -> Spindeterminant.t -> unit = <fun>\n"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val pp_det : Format.formatter -> Determinant.t -> unit = <fun>\n"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let f12 = Util.of_some @@ Simulation.f12 simulation \n",
"\n",
"let mo_num = MOBasis.size mo_basis \n",
"\n",
"let pp_spindet = Spindeterminant.pp mo_num\n",
"\n",
"let pp_det = Determinant.pp mo_num\n",
"\n",
";;\n",
"\n",
"#install_printer pp_spindet ;;\n",
"#install_printer pp_det ;;\n",
"\n"
]
},
{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val simulation_aux : Simulation.t = <abstr>\n"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"66 significant shell pairs computed in 0.050789 seconds\n",
"1\n",
"2\n",
"5\n",
"6\n",
"9\n",
"10\n",
"11\n",
"12\n",
"15\n",
"18\n",
"Computed ERIs in 0.889029 seconds\n"
]
},
{
"data": {
"text/plain": [
"val aux_basis : MOBasis.t =\n",
" Eigenvalues: -15.681404 -0.961606 -0.451178 -0.195149 0.040479 \n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0.995805 -0.228629 -1.04121E-12 -1.20393E-11 -7.74166E-12\n",
" 2 0.0207488 0.523688 -3.08871E-13 -4.88506E-13 -3.2349E-13\n",
" 3 2.26649E-12 -2.08563E-12 0.516899 3.82452E-12 0.306901\n",
" ... ... ... ... ...\n",
" 22 0 0 0 0 -0\n",
" 23 0 0 0 0 -0\n",
" 24 0 0 0 0 -0\n",
" \n",
" Eigenvalues: 0.908849 0.950925 0.975309 0.912008 2.032635 \n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 -- -- 10 --\n",
" 1 -1.59863E-11 1.67271E-11 0.0896964 8.01274E-12 0\n",
" 2 7.28187E-13 -1.60327E-12 -1.51213 -2.11029E-13 0\n",
" 3 -0.759946 0.656011 -6.79771E-13 -6.65308E-12 0\n",
" ... ... ... ... ...\n",
" 22 -0 -0 0 0 0\n",
" 23 -0 -0 0 0 1\n",
" 24 -0 -0 0 0 0\n",
" \n",
" Eigenvalues: 2.209274 2.205946 2.198723 2.627905 18.044176 \n",
" -- 11 -- -- 12 -- -- 13 -- -- 14 -- -- 15 --\n",
" 1 4.4959E-10 -2.92245E-09 -6.60522E-10 7.27202 39.53\n",
" 2 -2.27871E-11 1.81557E-11 8.06971E-11 -19.3218 -84.1067\n",
" 3 -8.99756 -28.2245 -4.1365 -1.31641E-12 -1.85784E-10\n",
" ... ... ... ... ...\n",
" 22 -0 -0 2.75019E-14 0 0\n",
" 23 -0 -0 0 0 0\n",
" 24 -3.45546E-14 -7.00504E-14 0 0 0\n",
" \n",
" Eigenvalues: 31.400935 31.392955 31.387019 476.102993 2.036553 \n",
" -- 16 -- -- 17 -- -- 18 -- -- 19 -- -- 20 --\n",
" 1 -2.50732E-08 -1.36441E-09 1.64713E-08 416.882 -2.63792E-11\n",
" 2 5.37419E-10 -1.14011E-10 5.52992E-10 -1.46938 4.55954E-13\n",
" 3 -190.497 18.1424 30.0485 -1.1041E-08 -1.61968E-10\n",
" ... ... ... ... ...\n",
" 22 1.51034E-13 2.01121E-13 1.28118E-13 0 -0.128674\n",
" 23 -0 -0 -0 0 -0\n",
" 24 -7.82065E-13 -0 -0 0 0.923094\n",
" \n",
" Eigenvalues: 2.033307 2.036684 2.036990 \n",
" -- 21 -- -- 22 -- -- 23 --\n",
" 1 -5.67082E-11 1.56263E-12 3.6287E-10\n",
" 2 9.80094E-13 -2.68735E-14 -6.29775E-12\n",
" 3 -4.74932E-12 1.67489E-13 -0\n",
" ... ... ...\n",
" 22 0.986223 -0.103886 -0.00379526\n",
" 23 0 0 -0\n",
" 24 -0.383449 0.0293605 0.00152471\n",
" \n",
" \n"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val aux_num : int = 23\n"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let simulation_aux = \n",
" let charge = Charge.to_int @@ Simulation.charge simulation \n",
" and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation\n",
" and nuclei = Simulation.nuclei simulation\n",
" in\n",
" let general_basis = \n",
" Basis.general_basis @@ Simulation.basis simulation\n",
" in\n",
" GeneralBasis.combine [\n",
" general_basis ; GeneralBasis.read aux_basis_filename\n",
" ]\n",
" |> Basis.of_nuclei_and_general_basis nuclei\n",
" |> Simulation.make ~f12 ~charge ~multiplicity ~nuclei \n",
"\n",
"\n",
"let aux_basis = \n",
" MOBasis.of_mo_basis simulation_aux mo_basis\n",
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"\n",
"let aux_num = \n",
" MOBasis.size aux_basis\n"
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]
},
{
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"cell_type": "code",
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"execution_count": 28,
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"metadata": {},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"66 significant shell pairs computed in 0.842000 seconds\n",
"1\n",
"2\n",
"5\n",
"6\n",
"9\n",
"10\n",
"11\n",
"12\n",
"15\n",
"18\n",
"Computed ERIs in 17.257765 seconds\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"4-idx transformation \n",
"23 / 23\n",
"4-idx transformation \n",
"23 / 23\n"
]
}
],
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"source": [
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"let () = ignore @@ MOBasis.f12_ints aux_basis\n",
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"let () = ignore @@ MOBasis.two_e_ints aux_basis"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"## Integral-based functions"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"\\begin{equation}\n",
"\\langle I | \\hat{H} | J \\rangle = \\begin{cases}\n",
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"\\sum_i h_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n",
"h_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n",
"\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n",
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"\\end{cases}\n",
"\\end{equation}\n",
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"\n",
"\n",
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"\\begin{equation}\n",
"\\langle I | \\hat{F} | J \\rangle = \\begin{cases}\n",
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"\\sum_i f_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n",
"f_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n",
"\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n",
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"\\end{cases}\n",
"\\end{equation}"
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]
},
{
"cell_type": "code",
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"execution_count": 29,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val cancel_singles : bool = false\n"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mos_cabs : int list =\n",
" [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]\n"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mos_abs : int list =\n",
" [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21;\n",
" 22; 23]\n"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mos_in : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9]\n"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mos_a : Determinant.t -> int list = <fun>\n"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mos_b : Determinant.t -> int list = <fun>\n"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let cancel_singles = false \n",
"\n",
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"let mos_cabs = \n",
" Util.list_range (mo_num+1) aux_num\n",
" \n",
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"let mos_abs = \n",
" Util.list_range 1 aux_num\n",
" \n",
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"let mos_in = \n",
" Util.list_range 1 mo_num\n",
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"\n",
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"let mos_a k =\n",
" Determinant.alfa k\n",
" |> Spindeterminant.to_list\n",
" \n",
"let mos_b k =\n",
" Determinant.beta k\n",
" |> Spindeterminant.to_list\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### H integrals"
]
},
{
"cell_type": "code",
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"execution_count": 30,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val h_one : int -> int -> '_weak2 -> float = <fun>\n"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val h_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = <fun>\n"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let h_one =\n",
" let h = \n",
" MOBasis.one_e_ints aux_basis\n",
" in fun i j _ -> h.{i,j}\n",
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" \n",
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"let h_two = \n",
" let two_e_ints = MOBasis.two_e_ints aux_basis in\n",
" let h2 i j k l (s:Spin.t) (s':Spin.t) =\n",
" if s' <> s then\n",
" ERI.get_phys two_e_ints i j k l\n",
" else\n",
" (ERI.get_phys two_e_ints i j k l) -. \n",
" (ERI.get_phys two_e_ints i j l k)\n",
" in\n",
" h2\n",
"\n",
" \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### F12 integrals"
]
},
{
"cell_type": "code",
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"execution_count": 31,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val f_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = <fun>\n"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val f_one : 'a -> 'b -> 'c -> float = <fun>\n"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val f_one : int -> int -> '_weak2 -> float = <fun>\n"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let f_two = \n",
" let two_e_ints = MOBasis.f12_ints aux_basis in\n",
" let f2 i j k l (s:Spin.t) (s':Spin.t) =\n",
" if s' <> s then\n",
" 0.5 *. F12.get_phys two_e_ints i j k l\n",
" else\n",
" 0.5 *. (\n",
" (F12.get_phys two_e_ints i j k l) -. \n",
" (F12.get_phys two_e_ints i j l k) )\n",
" in\n",
" let f3 i j k l (s:Spin.t) (s':Spin.t) = \n",
" if (i=k && j<>l) || (j=l && i<>k) then\n",
" 0.\n",
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" else\n",
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" f2 i j k l s s'\n",
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" in\n",
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" if cancel_singles then f3 else f2\n",
"\n",
"let f_one = fun _ _ _ -> 0.\n",
"\n",
"(*\n",
"let f_two = h_two\n",
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"*)\n",
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"\n",
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"let f_one = h_one"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Determinant-based functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Integrals"
]
},
{
"cell_type": "code",
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"execution_count": 32,
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"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val f12_integrals :\n",
" 'a ->\n",
" (int -> int -> '_weak2 -> float) *\n",
" (int -> int -> int -> int -> Spin.t -> Spin.t -> float) * 'b option = <fun>\n"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val h_ij : MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n",
" <fun>\n"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val f_ij : 'a -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n",
" <fun>\n"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val hf_ij :\n",
" MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float list =\n",
" <fun>\n"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let f12_integrals mo_basis =\n",
" ( f_one, f_two, None )\n",
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"\n",
"let h_ij mo_basis ki kj =\n",
" let integrals =\n",
" List.map (fun f -> f mo_basis)\n",
" [ CI.h_integrals ]\n",
" in\n",
" CIMatrixElement.make integrals ki kj \n",
" |> List.hd\n",
"\n",
"\n",
"let f_ij mo_basis ki kj =\n",
" let integrals =\n",
" List.map (fun f -> f mo_basis)\n",
" [ f12_integrals ]\n",
" in\n",
" CIMatrixElement.make integrals ki kj \n",
" |> List.hd \n",
"\n",
"\n",
"let hf_ij mo_basis ki kj =\n",
" let integrals =\n",
" List.map (fun f -> f mo_basis)\n",
" [ CI.h_integrals ; f12_integrals ]\n",
" in\n",
" CIMatrixElement.make integrals ki kj\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Determinant space"
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]
},
{
"cell_type": "code",
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"execution_count": 33,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val is_a_double : DeterminantSpace.t -> Determinant.t -> bool = <fun>\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let is_a_double det_space =\n",
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" let mo_class = DeterminantSpace.mo_class det_space in\n",
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" let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n",
" let m l =\n",
" List.fold_left (fun accu i ->\n",
" let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
" ) (Bitstring.zero mo_num) l\n",
" in\n",
" let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
" fun k -> \n",
" let alfa =\n",
" Determinant.alfa k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let beta =\n",
" Determinant.beta k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let a = Bitstring.logand aux_mask alfa\n",
" and b = Bitstring.logand aux_mask beta\n",
" in\n",
" match Bitstring.popcount a + Bitstring.popcount b with\n",
" | 2 | 1 -> true\n",
" | 0 | _ -> false\n",
"\n"
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]
},
{
"cell_type": "code",
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"execution_count": 34,
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"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of determinants : 56 28 1568\n"
]
},
{
"data": {
"text/plain": [
"val in_space : DeterminantSpace.t = <abstr>\n"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of determinants : 1540 231 355740\n"
]
},
{
"data": {
"text/plain": [
"val aux_space : DeterminantSpace.t = <abstr>\n"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val det_space_in : unit -> Determinant.t Stream.t = <fun>\n"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val det_space_out : unit -> (Determinant.t * Determinant.t) Stream.t = <fun>\n"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let in_space = \n",
" DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num\n",
" \n",
"let aux_space = \n",
" DeterminantSpace.fci_of_mo_basis aux_basis ~frozen_core \n",
"\n",
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"let det_space_in () =\n",
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" DeterminantSpace.determinant_stream in_space\n",
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"\n",
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"let det_space_out () =\n",
" let s = \n",
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" DeterminantSpace.determinant_stream aux_space\n",
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" in\n",
" Stream.from (fun _ ->\n",
" try\n",
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" let is_a_double = is_a_double in_space in\n",
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" let rec result () =\n",
" let ki = Stream.next s in\n",
" if is_a_double ki then\n",
" Some (ki,ki)\n",
" else\n",
" result ()\n",
" in\n",
" result ()\n",
" with Stream.Failure -> None\n",
" )\n",
" "
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]
},
{
"cell_type": "code",
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"execution_count": 35,
2019-12-20 16:09:02 +01:00
"metadata": {
"scrolled": false
},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val ci : CI.t =\n",
" {CI.e_shift = -54.2419683633284677; det_space = <abstr>; m_H = <lazy>;\n",
" m_S2 = <lazy>; eigensystem = <lazy>; n_states = 1}\n"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1 0.0000000000 5.38465905e-01\n",
" 2 -0.0538262193 1.87217169e-01\n",
" 3 -0.0657011468 6.52524404e-02\n",
" 4 -0.0682884307 4.47790537e-02\n",
" 5 -0.0722202576 2.28670803e-02\n",
" 6 -0.0732730385 5.26351716e-03\n",
" 7 -0.0733234182 9.38250052e-04\n",
" 8 -0.0733249420 2.14671657e-04\n",
" 0 -0.0733250301 7.26676403e-05\n",
" 1 -0.0733250395 2.46738965e-05\n",
" 2 -0.0733250400 1.50948498e-05\n",
" 3 -0.0733250400 4.00236940e-06\n",
" 4 -0.0733250400 1.38596264e-06\n"
]
},
{
"data": {
"text/plain": [
"val ci_coef : Lacaml.D.Mat.t =\n",
" \n",
"\n",
" -- 1 --\n",
" 1 0.701258\n",
" 2 0\n",
" 3 0\n",
" ...\n",
" 1566 0\n",
" 1567 0\n",
" 1568 0\n",
" \n",
"val ci_energy : Lacaml.D.Vec.t =\n",
" R1 R2 R3 R5 R6 R7\n",
" -54.3153 -54.1549 -53.2726 ... -51.7367 -51.4918 -50.3061\n"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" 5 -0.0733250400 7.40047633e-07\n",
"\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let ci = CI.make ~n_states:state in_space\n",
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"\n",
"let ci_coef, ci_energy = Lazy.force ci.eigensystem \n",
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"\n",
"let _ = print_newline () \n"
2019-12-03 14:40:08 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
2019-12-03 12:25:31 +01:00
"source": [
"Permutation operator $p_{12}$ that generates a new determinant with electrons 1 and 2 swapped."
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"let p12 det_space =\n",
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" let mo_class = DeterminantSpace.mo_class det_space in\n",
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" let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n",
" let m l =\n",
" List.fold_left (fun accu i ->\n",
" let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
" ) (Bitstring.zero mo_num) l\n",
" in\n",
" let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
" let not_aux_mask =\n",
" Bitstring.(shift_left_one mo_num (mo_num-1) |> minus_one |> logxor aux_mask)\n",
" in\n",
" fun k ->\n",
" let alfa =\n",
" Determinant.alfa k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let beta =\n",
" Determinant.beta k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let a = Bitstring.logand aux_mask alfa\n",
" and b = Bitstring.logand aux_mask beta\n",
" in\n",
" match Bitstring.popcount a, Bitstring.popcount b with\n",
" | 2, 0 \n",
" | 0, 2 -> Some (Determinant.negate_phase k)\n",
" | 1, 1 -> Some (Determinant.of_spindeterminants\n",
" (Spindeterminant.of_bitstring @@\n",
" Bitstring.(logor b (logand not_aux_mask alfa)) )\n",
" (Spindeterminant.of_bitstring @@\n",
" Bitstring.(logor a (logand not_aux_mask beta))\n",
" ) )\n",
" | 1, 0 \n",
" | 0, 1 -> Some k\n",
" | _ -> None\n",
" \n",
" \n"
]
},
2019-12-03 14:40:08 +01:00
{
"cell_type": "markdown",
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"metadata": {},
"source": [
2019-12-03 14:40:08 +01:00
"## Matrices $\\langle I | H | \\alpha \\rangle$ and $\\langle I | F | \\alpha \\rangle$ "
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]
},
{
2019-12-03 14:40:08 +01:00
"cell_type": "code",
2020-02-05 12:15:47 +01:00
"execution_count": 36,
2020-01-06 19:43:55 +01:00
"metadata": {
2020-02-05 12:15:47 +01:00
"scrolled": true
2020-01-06 19:43:55 +01:00
},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val randomize : bool = false\n"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val out_list : (Determinant.t * Determinant.t) list =\n",
" [(phase:+1\n",
" a:+1 +++------+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +++------+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++-+-----+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++-+-----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-++-----+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-++-----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++--+----+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++--+----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-+-+----+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-+-+----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +--++----+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +--++----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++---+---+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++---+---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-+--+---+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-+--+---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +--+-+---+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +--+-+---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +---++---+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +---++---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++----+--+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++----+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-+---+--+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-+---+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +--+--+--+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +--+--+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +---+-+--+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +---+-+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +----++--+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +----++--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++-----+-+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++-----+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-+----+-+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-+----+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +--+---+-+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +--+---+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +---+--+-+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +---+--+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +----+-+-+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +----+-+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-----++-+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-----++-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++------++------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++------++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-+-----++------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-+-----++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +--+----++------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +--+----++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +---+---++------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +---+---++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +----+--++------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +----+--++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-----+-++------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-----+-++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +------+++------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +------+++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +++-------+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +++-------+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++-+------+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++-+------+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-++------+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-++------+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++--+-----+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++--+-----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-+-+-----+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-+-+-----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +--++-----+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +--++-----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++---+----+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 ++---+----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +-+--+----+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +-+--+----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +--+-+----+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +--+-+----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 +---++----+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
"a:+1 +---++----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
" a:+1 ++----+---+-----------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
",\n",
"phase:+1\n",
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");\n",
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" b:+1 +++-------------------------------------------------------------\n",
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"b:+1 +++-------------------------------------------------------------\n",
");\n",
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");\n",
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");\n",
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"b:+1 +++-------------------------------------------------------------\n",
");\n",
"(phase:+1\n",
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" b:+1 +++-------------------------------------------------------------\n",
",\n",
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");\n",
"(phase:+1\n",
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");\n",
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");\n",
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");\n",
"(phase:+1\n",
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");\n",
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");\n",
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");\n",
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");\n",
"(phase:+1\n",
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"b:+1 +++-------------------------------------------------------------\n",
");\n",
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");\n",
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");\n",
"(phase:+1\n",
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",\n",
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");\n",
"(phase:+1\n",
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");\n",
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");\n",
"(phase:+1\n",
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" b:+1 +++-------------------------------------------------------------\n",
", ...);\n",
"...]\n"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val in_list : Determinant.t list =\n",
" [phase:+1\n",
" a:+1 ++++------------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
";\n",
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";\n",
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";\n",
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";\n",
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";\n",
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"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++----+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+---+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++---+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+--+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+--+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++--+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-----+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+----+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++----+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+---+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+---+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++---+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++++------------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-+-----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"...]\n"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val det_a : Determinant.t array =\n",
" [|phase:+1\n",
" a:+1 +++------+------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++----+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++---+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++--+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-+-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----++-+------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++------++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-----++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+----++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+---++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+--++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+-++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +------+++------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-------+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+------+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++------+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++----+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+---+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+---+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+---+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+---+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++---+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----+--+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----+--+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---+--+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--+--+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-+--+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----++--+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++------+-+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-----+-+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+----+-+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+---+-+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+--+-+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+-+-+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +------++-+-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-------++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+------++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-----++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+----++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+---++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+--++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +------+-++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-------+++-----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--------+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-------+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-------+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+------+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+------+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++------+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+-----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+-----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+-----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++-----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++----+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----+---+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----+---+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---+---+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--+---+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-+---+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----++---+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++------+--+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-----+--+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+----+--+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+---+--+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+--+--+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+-+--+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +------++--+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-------+-+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+------+-+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-----+-+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+----+-+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+---+-+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+--+-+----------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
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"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---------+-+-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--------+-+-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-------+-+-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+------+-+-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+-----+-+-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +------+----+-+-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-------+---+-+-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----------++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----------++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---------++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--------++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-------++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+------++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +------+-----++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-------+----++-------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++------------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-----------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-----------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+----------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+----------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++----------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+---------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+---------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+---------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++---------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+--------+------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"...|]\n"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val det_I : Determinant.t array =\n",
" [|phase:+1\n",
" a:+1 ++++------------------------------------------------------------\n",
" b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-+-----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+++---------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++----+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+---+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++---+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+--+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+--+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++--+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+-+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+-+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+-+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++-+--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----++--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---++--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--++--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-++--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+++--------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-----+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+----+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++----+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+---+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+---+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++---+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+--+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+--+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+--+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++--+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+-+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+-+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+-+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+-+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++-+-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----++-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----++-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---++-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--++-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-++-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+++-------------------------------------------------------\n",
"b:+1 +++-------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++++------------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-+-----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+++---------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++----+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+---+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++---+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+--+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+--+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++--+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+-+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+-+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+-+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++-+--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----++--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---++--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--++--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-++--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+++--------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-----+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+----+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++----+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+---+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+---+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++---+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+--+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+--+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+--+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++--+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+-+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+-+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+-+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+-+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++-+-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----++-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----++-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---++-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--++-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-++-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+++-------------------------------------------------------\n",
"b:+1 ++-+------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++++------------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-+-----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+++---------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++----+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+---+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++---+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+--+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+--+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++--+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+-+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+-+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+-+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++-+--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----++--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---++--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--++--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-++--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+++--------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-----+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+----+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++----+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+---+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
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"a:+1 +-+-+---+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++---+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+--+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+--+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+--+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++--+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+-+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+-+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+-+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+-+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++-+-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----++-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----++-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---++-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--++-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-++-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+++-------------------------------------------------------\n",
"b:+1 +-++------------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++++------------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-+-----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+++---------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++----+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+---+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++---+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+--+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+--+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++--+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+-+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+-+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+-+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++-+--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----++--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---++--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--++--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-++--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+++--------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-----+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+----+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++----+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+---+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+---+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++---+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+--+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+--+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+--+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++--+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+-+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+-+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+-+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+-+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++-+-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----++-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----++-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---++-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--++-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-++-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+++-------------------------------------------------------\n",
"b:+1 ++--+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++++------------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-+-----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+++---------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++----+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+---+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++---+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+--+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+--+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++--+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++-+--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+++--------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-----+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+----+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++----+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+---+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+---+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++---+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---+--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--+--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-+--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---++--+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++----+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+---+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+--+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+-+-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----++-+-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-----++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+----++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+---++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +---+--++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +----+-++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-----+++-------------------------------------------------------\n",
"b:+1 +-+-+-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++++------------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++-+-----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-++-----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+++-----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++--+----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+-+----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++-+----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--++----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-++----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+++----------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +++---+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++-+--+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-++--+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++--+-+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+-+-+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--++-+---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 ++---++---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +-+--++---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"phase:+1\n",
"a:+1 +--+-++---------------------------------------------------------\n",
"b:+1 +--++-----------------------------------------------------------\n",
";\n",
"...|]\n"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
2019-12-03 14:40:08 +01:00
"source": [
2020-01-06 19:43:55 +01:00
"let randomize = false\n",
"\n",
2019-12-03 18:52:03 +01:00
"let out_list =\n",
2019-12-03 14:40:08 +01:00
" Util.stream_to_list (det_space_out ())\n",
" \n",
2019-12-03 18:52:03 +01:00
"let in_list =\n",
" Util.stream_to_list (det_space_in ())\n",
" \n",
"let det_a = Array.of_list out_list\n",
" |> Array.map (fun (i,_) -> i)\n",
2019-12-03 14:40:08 +01:00
"\n",
2020-01-06 19:43:55 +01:00
"let det_I =\n",
" if randomize then\n",
" let n = 123456789 in\n",
" in_list\n",
" |> List.map (fun k -> (Random.int n, k))\n",
" |> List.sort compare\n",
" |> List.map (fun (_,k) -> k)\n",
" |> Array.of_list\n",
" else\n",
" Array.of_list in_list\n"
2019-12-03 18:52:03 +01:00
]
},
{
2020-01-06 19:43:55 +01:00
"cell_type": "raw",
"metadata": {
"raw_mimetype": "text/markdown"
},
2019-12-03 18:52:03 +01:00
"source": [
2019-12-03 14:40:08 +01:00
"let m_H_aux, m_F_aux = \n",
" \n",
" let rec col_vecs_list accu_H accu_F = function\n",
" | [] -> \n",
" List.rev accu_H, \n",
" List.rev accu_F \n",
" | (ki, ki') :: rest when ki = ki' ->\n",
" begin\n",
2019-12-03 18:52:03 +01:00
" let h, f = \n",
" List.map (fun kj ->\n",
" match hf_ij aux_basis kj ki with\n",
" | [ a ; b ] -> a, b\n",
" | _ -> assert false ) in_list\n",
" |> List.split\n",
" in\n",
" let h = Vec.of_list h in\n",
" let f = Vec.of_list f in\n",
" scal 0.5 f; (* Specific to He singlet *)\n",
" col_vecs_list (h::accu_H) (f::accu_F) rest\n",
2019-12-03 14:40:08 +01:00
" end\n",
" | (ki, ki') :: rest ->\n",
" begin\n",
" assert false;\n",
" end\n",
" in\n",
" let h, f = \n",
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" col_vecs_list [] [] out_list\n",
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" in\n",
" Mat.of_col_vecs_list h,\n",
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" Mat.of_col_vecs_list f"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Function to generate all intermediate external determinants $|\\alpha \\rangle$ between $|I\\rangle$ and $|J\\rangle$, with a positive phase factor.\n",
"\n",
"* `exc` is the degree of excitation between $|I\\rangle$ and $|J\\rangle$\n",
"* `cabs` is the number of electrons in the CABS\n",
"* `l` is the degree of excitation between $|I\\rangle$ and $|\\alpha \\rangle$\n",
"* `r` is the degree of excitation between $|\\alpha \\rangle$ and $|J\\rangle$"
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]
},
{
"cell_type": "code",
2020-02-05 12:15:47 +01:00
"execution_count": 37,
2019-12-03 14:40:08 +01:00
"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val generate_alphas :\n",
" Determinant.t ->\n",
" Determinant.t -> int -> int -> int -> int -> Determinant.t list = <fun>\n"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val compute_HaaF :\n",
" CIMatrixElement.De.t ->\n",
" CIMatrixElement.De.t list -> CIMatrixElement.De.t -> float = <fun>\n"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let generate_alphas ki kj exc cabs l r =\n",
" (* Check input excitation degree *)\n",
" let d = Determinant.degree ki kj in\n",
" if d <> exc then\n",
" Printf.sprintf \"Invalid excitation degree. Expected %d and found %d.\" exc d\n",
" |> failwith;\n",
" \n",
" (* Generate single excitations *)\n",
" let all_singles ki =\n",
" let mos_a, mos_b = Determinant.to_lists ki in\n",
" [ List.map (fun hole -> \n",
" List.map (fun particle ->\n",
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" if hole = particle then None else\n",
" Some (Determinant.single_excitation Spin.Alfa hole particle ki)\n",
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" ) mos_abs\n",
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" ) mos_a\n",
" ;\n",
" List.map (fun hole -> \n",
" List.map (fun particle ->\n",
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" if hole = particle then None else\n",
" Some (Determinant.single_excitation Spin.Beta hole particle ki)\n",
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" ) mos_abs\n",
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" ) mos_b \n",
" ]\n",
" |> List.concat\n",
" |> List.concat\n",
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" |> Util.list_some\n",
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" |> List.filter (fun x -> Determinant.is_none x = false)\n",
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" |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
" in\n",
" \n",
" (* Generate double excitations *)\n",
" let all_doubles ki =\n",
" let mos_a, mos_b = Determinant.to_lists ki in\n",
" [ List.map (fun hole -> (* Alpha-Alpha *)\n",
" List.map (fun particle ->\n",
" List.map (fun hole' -> \n",
" List.map (fun particle' ->\n",
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" if hole = particle || hole' = particle' then None else\n",
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" if hole' > hole && particle' < particle then\n",
" Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n",
" else None\n",
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" ) mos_abs\n",
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" ) mos_a \n",
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" ) mos_abs\n",
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" ) mos_a\n",
" ; \n",
" List.map (fun hole -> (* Beta-Beta *)\n",
" List.map (fun particle ->\n",
" List.map (fun hole' -> \n",
" List.map (fun particle' ->\n",
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" if hole' > hole && particle' < particle && hole <> particle && hole' <> particle' then\n",
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" Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n",
" else None\n",
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" ) mos_abs\n",
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" ) mos_b \n",
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" ) mos_abs\n",
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" ) mos_b\n",
" ;\n",
" List.map (fun hole -> (* Alpha-Beta *)\n",
" List.map (fun particle ->\n",
" List.map (fun hole' -> \n",
" List.map (fun particle' ->\n",
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" if hole = particle || hole' = particle' then None else\n",
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" Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n",
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" ) mos_abs\n",
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" ) mos_b \n",
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" ) mos_abs\n",
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" ) mos_a\n",
" ]\n",
" |> List.concat\n",
" |> List.concat\n",
" |> List.concat\n",
" |> List.concat\n",
" |> Util.list_some\n",
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" |> List.filter (fun x -> Determinant.is_none x = false)\n",
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" |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
" in\n",
"\n",
" (* Generate left and right excitations *)\n",
" let al = \n",
" match l with\n",
" | 1 -> all_singles ki\n",
" | 2 -> all_doubles ki\n",
" | _ -> assert false\n",
" in\n",
" let ar = \n",
" match r with\n",
" | 1 -> all_singles kj\n",
" | 2 -> all_doubles kj\n",
" | _ -> assert false\n",
" in\n",
" \n",
" let mo_class = DeterminantSpace.mo_class in_space in\n",
" let m l =\n",
" List.fold_left (fun accu i ->\n",
" let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
" ) (Bitstring.zero mo_num) l\n",
" in\n",
" let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
" let good_cabs k = \n",
" let alfa =\n",
" Determinant.alfa k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let beta =\n",
" Determinant.beta k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let a = Bitstring.logand aux_mask alfa\n",
" and b = Bitstring.logand aux_mask beta\n",
" in\n",
" Bitstring.popcount a + Bitstring.popcount b = cabs\n",
" in\n",
" let good_lr k =\n",
" Determinant.degree ki k = l &&\n",
" Determinant.degree k kj = r \n",
" in\n",
"\n",
"\n",
" \n",
" (* Merge lists in a set of unique determinants *)\n",
" List.concat [ al; ar ]\n",
" |> List.sort_uniq compare\n",
" \n",
" (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n",
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" |> List.filter good_cabs \n",
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" \n",
" (* Filter out all determinants with incorrect excitation numbers *)\n",
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" |> List.filter good_lr \n",
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" \n",
" \n",
"let compute_HaaF ki alphas kj =\n",
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" List.fold_left (fun accu alpha -> accu\n",
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" +. h_ij aux_basis ki alpha\n",
" *. f_ij aux_basis alpha kj\n",
" ) 0. alphas\n"
]
},
{
"cell_type": "code",
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"execution_count": 38,
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"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val check :\n",
" int ->\n",
" (CIMatrixElement.De.t -> CIMatrixElement.De.t -> float) ->\n",
" int -> int -> int -> int -> unit = <fun>\n"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val sum : 'a list -> ('a -> float) -> float = <fun>\n"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let check n integral_value exc cabs lexc rexc =\n",
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" let cpudet, cpuint = ref 0., ref 0. in\n",
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" let det_list =\n",
" match n with\n",
" | 0 -> det_I\n",
" | n -> Array.sub det_I 0 n\n",
" in\n",
" let result =\n",
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" Printf.printf \"Checking ... \\n%!\";\n",
" let percent = ref 0 in\n",
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" let task (i,ki) =\n",
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" (let p = (10 * (i+1))/(Array.length det_list) in\n",
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" if p <> !percent then\n",
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" ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) ));\n",
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" Array.mapi (fun j kj -> \n",
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" if i > j || Determinant.degree ki kj <> exc then\n",
" (0,0,0.,0.)\n",
" else\n",
" begin\n",
" let alphas = generate_alphas ki kj exc cabs lexc rexc in\n",
" let det_value =\n",
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" let t0 = Unix.gettimeofday () in\n",
" let result = compute_HaaF ki alphas kj in\n",
" cpudet := !cpudet +. Unix.gettimeofday () -. t0;\n",
" result\n",
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" in\n",
" let int_value = \n",
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" let t0 = Unix.gettimeofday () in\n",
" let result = integral_value ki kj in\n",
" cpuint := !cpuint +. Unix.gettimeofday () -. t0;\n",
" result\n",
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" in\n",
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"(* Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value; *)\n",
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" (i,j,det_value,int_value)\n",
" end\n",
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" ) det_list\n",
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" in\n",
" det_list\n",
" |> Array.mapi (fun i ki -> (i,ki))\n",
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" |> Array.to_list\n",
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" |> Stream.of_list\n",
" |> Farm.run ~f:task\n",
" |> Util.stream_to_list\n",
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" |> Array.concat\n",
" in\n",
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" let i,j,d,v = \n",
" let rec aux k imax jmax emax dmax vmax = \n",
" if k = -1 then\n",
" imax, jmax, dmax, vmax\n",
" else\n",
" let i, j, d, v = result.(k) in\n",
" let e = abs_float (d -. v) in\n",
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" if e >= emax then\n",
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" aux (k-1) i j e d v\n",
" else\n",
" aux (k-1) imax jmax emax dmax vmax\n",
" in\n",
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" aux (Array.length result - 1) 0 0 0. 0. 0.\n",
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" in\n",
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" let error = abs_float (d -. v) in\n",
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" if error < epsilon_float then\n",
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" (*\n",
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" Printf.printf \"OK: %e\\n%!\" error\n",
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" *)\n",
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" Printf.printf \"OK: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n",
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" else\n",
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" Printf.printf \"Failed: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n",
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"\n",
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" \n",
"let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l"
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]
},
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{
"cell_type": "code",
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"execution_count": 39,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val array_3_init :\n",
" int ->\n",
" int ->\n",
" int ->\n",
" (int -> int -> int -> float) ->\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
" <fun>\n"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val array_4_init :\n",
" int ->\n",
" int ->\n",
" int ->\n",
" int ->\n",
" (int -> int -> int -> int -> float) ->\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
" <fun>\n"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val array_5_init :\n",
" int ->\n",
" int ->\n",
" int ->\n",
" int ->\n",
" int ->\n",
" (int -> int -> int -> int -> int -> float) ->\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
" <fun>\n"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let array_3_init d1 d2 d3 f =\n",
" let result = \n",
" Bigarray.(Array3.create Float64 fortran_layout) d1 d2 d3\n",
" in\n",
" for k=1 to d3 do\n",
" for j=1 to d2 do\n",
" for i=1 to d1 do\n",
" result.{i,j,k} <- f i j k\n",
" done\n",
" done\n",
" done;\n",
" result\n",
"\n",
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"\n",
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"let array_4_init d1 d2 d3 d4 f =\n",
" let result = \n",
" Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4 |]\n",
" in\n",
" for l=1 to d4 do\n",
" for k=1 to d3 do\n",
" for j=1 to d2 do\n",
" for i=1 to d1 do\n",
" result.{i,j,k,l} <- f i j k l\n",
" done\n",
" done\n",
" done\n",
" done;\n",
" result\n",
"\n",
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"\n",
"let array_5_init d1 d2 d3 d4 d5 f =\n",
" let result = \n",
" Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4;d5 |]\n",
" in\n",
" for m=1 to d5 do\n",
" for l=1 to d4 do\n",
" for k=1 to d3 do\n",
" for j=1 to d2 do\n",
" for i=1 to d1 do\n",
" result.{i,j,k,l,m} <- f i j k l m\n",
" done\n",
" done\n",
" done\n",
" done\n",
" done;\n",
" result\n",
"\n",
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"(* ----- *)"
]
},
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{
"cell_type": "markdown",
"metadata": {},
"source": [
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"******"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1. 0 1 11"
]
},
{
"cell_type": "code",
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"execution_count": 40,
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"metadata": {},
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"outputs": [
{
"data": {
"image/png": "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
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"- : Jupyter_notebook.display_id = <abstr>\n"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let _ = png_image \"0_1_11.png\""
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
"\n",
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"$\\sum_i \\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{i}$\n",
"\n",
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"\\begin{align}\n",
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"\\sum_{a} \\sum_{i}\n",
" \\left( h_{ia} +\n",
" \\sum_{j} \\langle i j || a j \\rangle +\n",
" \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n",
" \\left( f_{ai} +\n",
" \\sum_{j} \\left[ a j || i j \\right] + \n",
" \\sum_{\\bar{j}} \\left[ a \\bar{j} | i \\bar{j} \\right] \\right) + \\\\\n",
"\\sum_{\\bar{a}} \\sum_{\\bar{i}}\n",
" \\left( h_{ia} +\n",
" \\sum_{j} \\langle \\bar{i} j | \\bar{a} j \\rangle +\n",
" \\sum_{\\bar{j}} \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{j} \\rangle \\right) \n",
" \\left( f_{ai} +\n",
" \\sum_{j} \\left[ \\bar{a} j | \\bar{i} j \\right] + \n",
" \\sum_{\\bar{j}} \\left[ \\bar{a} \\bar{j} || \\bar{i} \\bar{j} \\right] \\right) \n",
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"\\end{align}"
]
},
{
"cell_type": "code",
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"execution_count": 41,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val integral_value : Determinant.t -> 'a -> float = <fun>\n"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking ... \n",
" - 10 %\n",
" - 20 %\n",
" - 30 %\n",
" - 40 %\n",
" - 50 %\n",
" - 60 %\n",
" - 70 %\n",
" - 80 %\n",
" - 90 %\n",
" - 100 %\n",
"Failed: (135, 135) | 2.284769e+00 2.284769e+00 | 1.776357e-15 | cpu : 2.160390 0.491860\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let integral_value ki kj = \n",
" (* Alpha-Beta *)\n",
" let s, s' = Spin.(Alfa, Beta) in \n",
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" let mos_a, mos_b = mos_a ki, mos_b ki in\n",
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" \n",
" sum mos_cabs (fun a ->\n",
" sum mos_a (fun i -> \n",
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" (h_one i a s +.\n",
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" sum mos_a (fun j -> h_two i j a j s s ) +.\n",
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" sum mos_b (fun j -> h_two i j a j s s')\n",
" ) *. \n",
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" (f_one a i s +.\n",
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" sum mos_a (fun j -> f_two a j i j s s ) +.\n",
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" sum mos_b (fun j -> f_two a j i j s s')\n",
" )\n",
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" )\n",
" +.\n",
" sum mos_b (fun i -> \n",
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" (h_one i a s' +.\n",
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" sum mos_b (fun j -> h_two i j a j s' s') +.\n",
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" sum mos_a (fun j -> h_two i j a j s' s )\n",
" ) *. \n",
" (f_one a i s' +.\n",
" sum mos_b (fun j -> f_two a j i j s' s') +.\n",
" sum mos_a (fun j -> f_two a j i j s' s )\n",
" )\n",
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" ) \n",
" ) \n",
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" \n",
"let _ =\n",
" check 0 integral_value 0 1 1 1\n",
" "
]
},
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{
"cell_type": "code",
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"execution_count": 42,
2019-12-20 16:09:02 +01:00
"metadata": {
"scrolled": false
},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val m_0111_1H_1F : Lacaml.D.vec =\n",
" R1 R2 R3 R7 R8 R9\n",
" 1.23163 0.512679 0.379158 ... 1.15717 0.783246 0.94134\n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_1H_2Fa : Lacaml.D.mat =\n",
" \n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0 9.54805E-05 0.000949414 0.00102124 0.000612123\n",
" 2 0.0157601 0 0.00387182 0.0040609 0.00288411\n",
" 3 0.0123451 0.00482411 0 0.00262065 0.00153994\n",
" ... ... ... ... ...\n",
" 7 0.0638665 0.0309407 0.0280828 0.0291155 0.0201909\n",
" 8 0.035099 0.00993291 0.0123105 0.0128627 0.0095454\n",
" 9 0.0546496 0.0268732 0.0249878 0.0209954 0.02047\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 0.00135039 0.00168769 -2.50132E-05 0.00127857\n",
" 2 0.00164244 0.00263016 -0.0049468 0.00145336\n",
" 3 -0.00786828 0.00262225 0.000307787 0.00154154\n",
" ... ... ... ...\n",
" 7 0.0210255 0 0.0169901 0.0199928\n",
" 8 0.0097481 0.0125132 0 0.00919583\n",
" 9 0.0187406 0.0232584 0.0154703 0\n",
" \n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_1H_2Fb : Lacaml.D.mat =\n",
" \n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0.00838947 0.000802512 0.000774268 0.000824527 0.000531664\n",
" 2 0.0167558 0.00284141 0.00289398 0.00311638 0.00181881\n",
" 3 0.0138217 0.00142914 0.000717031 0.00205097 0.00097096\n",
" ... ... ... ... ...\n",
" 7 0.0672127 0.0297099 0.0280681 0.029107 0.022267\n",
" 8 0.0361343 0.0135355 0.0127802 0.0133849 0.00974314\n",
" 9 0.0572555 0.0267995 0.0251558 0.0264006 0.020602\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 0.000838226 0.00108083 0.000590322 0.000787968\n",
" 2 0.00312393 0.0041991 0.00210452 0.00290152\n",
" 3 0.00156923 0.00296985 0.000876672 0.00188984\n",
" ... ... ... ...\n",
" 7 0.0206994 0.0254055 0.0187116 0.0196605\n",
" 8 0.00965382 0.0126909 0.00818378 0.00904916\n",
" 9 0.0183365 0.0228903 0.0168998 0.0166274\n",
" \n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_2Ha_1F : Lacaml.D.mat =\n",
" \n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0 0.00346355 -0.00957818 -0.0103791 -0.00586334\n",
" 2 -0.121634 0 -0.019873 -0.0209946 -0.0141534\n",
" 3 -0.115395 -0.0247239 0 -0.017339 -0.0100747\n",
" ... ... ... ... ...\n",
" 7 -0.405587 -0.140299 -0.129164 -0.134263 -0.0844326\n",
" 8 -0.207751 -0.0414479 -0.0574012 -0.0601297 -0.0438726\n",
" 9 -0.335499 -0.120993 -0.113422 -0.0875797 -0.091945\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 -0.0155848 -0.0192997 0.00228062 -0.0147839\n",
" 2 -0.0112498 -0.0169694 0.0224836 -0.0101282\n",
" 3 0.0322167 -0.0204013 -0.00423111 -0.013137\n",
" ... ... ... ...\n",
" 7 -0.106147 0 -0.0844097 -0.101048\n",
" 8 -0.0490936 -0.0626221 0 -0.0463651\n",
" 9 -0.0928575 -0.114335 -0.0760592 0\n",
" \n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_2Hb_1F : Lacaml.D.mat =\n",
" \n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 -0.267262 -0.0092275 -0.00385375 -0.00417671 -0.00235846\n",
" 2 -0.165952 -0.0180838 -0.0197588 -0.0214917 -0.0115557\n",
" 3 -0.149576 -0.0113644 -0.010116 -0.0155245 -0.00736965\n",
" ... ... ... ... ...\n",
" 7 -0.487134 -0.140774 -0.13287 -0.138318 -0.111128\n",
" 8 -0.253633 -0.0687529 -0.0664679 -0.0700869 -0.0486229\n",
" 9 -0.399565 -0.125537 -0.117439 -0.133629 -0.0946778\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 -0.00636217 -0.00785747 -0.00673128 -0.00603921\n",
" 2 -0.0272961 -0.0354992 -0.0184917 -0.0255632\n",
" 3 -0.0207391 -0.0252065 -0.0100414 -0.0170516\n",
" ... ... ... ...\n",
" 7 -0.111178 -0.151723 -0.0978176 -0.10573\n",
" 8 -0.0587109 -0.0765558 -0.0468344 -0.0550919\n",
" 9 -0.0962035 -0.118965 -0.0866369 -0.0978307\n",
" \n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_2Ha_2Fa :\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
" <abstr>\n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_2Hb_2Fa :\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
" <abstr>\n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_2Ha_2Fb :\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
" <abstr>\n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0111_2Hb_2Fb :\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
" <abstr>\n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val integral_value : Determinant.t -> 'a -> float = <fun>\n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking ... \n",
" - 10 %\n",
" - 20 %\n",
" - 30 %\n",
" - 40 %\n",
" - 50 %\n",
" - 60 %\n",
" - 70 %\n",
" - 80 %\n",
" - 90 %\n",
" - 100 %\n",
"Failed: (225, 225) | 2.333780e+00 2.333780e+00 | 1.776357e-15 | cpu : 2.156856 0.039502\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
2019-12-18 19:04:32 +01:00
"source": [
"let m_0111_1H_1F = \n",
" Vec.init mo_num (fun i -> \n",
" sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_one a i Spin.Alfa ))\n",
"\n",
" \n",
"let m_0111_1H_2Fa = \n",
" Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa ))\n",
"\n",
" \n",
"let m_0111_1H_2Fb = \n",
" Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta ))\n",
"\n",
"\n",
"let m_0111_2Ha_1F = \n",
" Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
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" h_two i j a j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa ))\n",
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"\n",
" \n",
"let m_0111_2Hb_1F = \n",
" Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
2020-01-07 16:45:14 +01:00
" h_two i j a j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa ))\n",
2019-12-18 19:04:32 +01:00
"\n",
"\n",
"let m_0111_2Ha_2Fa =\n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Alfa *.\n",
" f_two a k i k Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_0111_2Hb_2Fa =\n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Beta *.\n",
" f_two a k i k Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_0111_2Ha_2Fb =\n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Alfa *.\n",
" f_two a k i k Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_0111_2Hb_2Fb =\n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Beta *.\n",
" f_two a k i k Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
"\n",
"let integral_value ki kj = \n",
"\n",
" let mos_a, mos_b = mos_a ki, mos_b ki in\n",
" \n",
" sum mos_a (fun i ->\n",
" m_0111_1H_1F.{i} +. \n",
" sum mos_a (fun j ->\n",
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" m_0111_2Ha_1F.{i,j} +.\n",
" m_0111_1H_2Fa.{i,j} +.\n",
2019-12-18 19:04:32 +01:00
" sum mos_a (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n",
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" sum mos_b (fun k -> m_0111_2Ha_2Fb.{i,j,k})\n",
" ) +.\n",
2019-12-18 19:04:32 +01:00
" sum mos_b (fun j ->\n",
2020-01-07 16:45:14 +01:00
" m_0111_2Hb_1F.{i,j} +.\n",
" m_0111_1H_2Fb.{i,j} +.\n",
2019-12-18 19:04:32 +01:00
" sum mos_a (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n",
2020-01-07 16:45:14 +01:00
" sum mos_b (fun k -> m_0111_2Hb_2Fb.{i,j,k})\n",
" )\n",
2019-12-18 19:04:32 +01:00
" )\n",
" +.\n",
" sum mos_b (fun i ->\n",
" m_0111_1H_1F.{i} +. \n",
" sum mos_b (fun j ->\n",
2020-01-07 16:45:14 +01:00
" m_0111_2Ha_1F.{i,j} +.\n",
" m_0111_1H_2Fa.{i,j} +.\n",
2019-12-18 19:04:32 +01:00
" sum mos_b (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n",
2020-01-07 16:45:14 +01:00
" sum mos_a (fun k -> m_0111_2Ha_2Fb.{i,j,k})\n",
" ) +.\n",
2019-12-18 19:04:32 +01:00
" sum mos_a (fun j ->\n",
2020-01-07 16:45:14 +01:00
" m_0111_2Hb_1F.{i,j} +.\n",
" m_0111_1H_2Fb.{i,j} +.\n",
2019-12-18 19:04:32 +01:00
" sum mos_b (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n",
2020-01-07 16:45:14 +01:00
" sum mos_a (fun k -> m_0111_2Hb_2Fb.{i,j,k})\n",
" )\n",
2019-12-18 19:04:32 +01:00
" )\n",
" \n",
"let _ =\n",
" check 0 integral_value 0 1 1 1\n",
" "
]
},
2019-12-05 16:16:00 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. 0 1 22"
]
},
{
"cell_type": "code",
2020-02-05 12:15:47 +01:00
"execution_count": 43,
2019-12-05 16:16:00 +01:00
"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"image/png": "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
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"- : Jupyter_notebook.display_id = <abstr>\n"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
2019-12-05 16:16:00 +01:00
"source": [
2019-12-19 19:23:02 +01:00
"let _ = png_image \"0_1_22.png\""
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
"\n",
"$k$ : orbital indices of MOs unoccupied in $|I\\rangle$.\n",
"\n",
2019-12-09 19:37:58 +01:00
"$\\sum_i \\sum_a \\sum_j \\sum_k \\hat{T}_{ij}^{ak} \\hat{T}_{ak}^{ij}$\n",
"\n",
"\n",
2019-12-05 16:16:00 +01:00
"\\begin{align}\n",
"\\sum_{a} \\sum_{k} \\sum_{i} \\sum_{j<i}\n",
" \\langle i j || a k \\rangle \n",
" \\left[ a k || i j \\right] + \n",
"\\sum_{a} \\sum_{\\bar{k}} \\sum_{i} \\sum_{\\bar{j}}\n",
" \\langle i \\bar{j} | a \\bar{k} \\rangle \n",
" \\left[ a \\bar{k} | i \\bar{j} \\right] + \\\\\n",
"\\sum_{\\bar{a}} \\sum_{k} \\sum_{\\bar{i}} \\sum_{j}\n",
" \\langle \\bar{i} j | \\bar{a} k \\rangle \n",
" \\left[ \\bar{a} k | \\bar{i} j \\right] + \n",
"\\sum_{\\bar{a}} \\sum_{\\bar{k}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
" \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{k} \\rangle \n",
" \\left[ \\bar{a} \\bar{k} || \\bar{i} \\bar{j} \\right] \n",
"\\end{align}"
]
},
{
"cell_type": "code",
2020-02-05 12:15:47 +01:00
"execution_count": 44,
2019-12-05 16:16:00 +01:00
"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking ... \n",
" - 10 %\n",
" - 20 %\n",
" - 30 %\n",
" - 40 %\n",
" - 50 %\n",
" - 60 %\n",
" - 70 %\n",
" - 80 %\n",
" - 90 %\n",
" - 100 %\n",
"OK: (22, 22) | -3.896807e-02 -3.896807e-02 | 6.245005e-17 | cpu : 2.708850 0.154509\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
2019-12-05 16:16:00 +01:00
"source": [
"let integral_value ki kj = \n",
" (* mos unoccupied in both I and J *)\n",
" let mos_virt_a, mos_virt_b = \n",
" Array.init mo_num (fun i -> Some (i+1)) , \n",
" Array.init mo_num (fun i -> Some (i+1)) \n",
" in\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
" \n",
" let mos_virt_a, mos_virt_b = \n",
" Array.to_list mos_virt_a |> Util.list_some,\n",
" Array.to_list mos_virt_b |> Util.list_some\n",
" in\n",
" \n",
" (* Alpha-Beta *)\n",
" let s, s' = Spin.(Alfa, Beta) in\n",
2019-12-12 18:41:14 +01:00
" sum mos_cabs (fun a ->\n",
" sum (mos_b ki) (fun j -> \n",
" sum (mos_a ki) (fun i -> \n",
" sum mos_virt_b (fun k -> \n",
" h_two i j a k s s' *. f_two a k i j s s'\n",
" )))\n",
2019-12-05 16:16:00 +01:00
" +.\n",
2019-12-12 18:41:14 +01:00
" sum (mos_a ki) (fun j -> \n",
" sum (mos_b ki) (fun i -> \n",
" sum mos_virt_a (fun k -> \n",
" h_two i j a k s s' *. f_two a k i j s s'\n",
" )))) \n",
2019-12-05 16:16:00 +01:00
" +.\n",
" (* Alpha-Alpha / Beta-Beta *)\n",
" List.fold_left (fun accu (mos_virt,mos,s) -> \n",
" let s' = s in accu +.\n",
2019-12-12 18:41:14 +01:00
" sum mos (fun j -> \n",
" sum mos (fun i -> if i < j then 0. else\n",
" sum mos_virt (fun k -> \n",
" sum mos_cabs (fun a -> \n",
" h_two i j a k s s' *. f_two a k i j s s'\n",
" )))) \n",
" ) 0. [ (mos_virt_a,mos_a ki,Spin.Alfa) ; (mos_virt_b,mos_b ki,Spin.Beta)]\n",
2019-12-05 16:16:00 +01:00
" \n",
"let _ =\n",
2019-12-20 16:09:02 +01:00
" check 100 integral_value 0 1 2 2\n",
2019-12-05 16:16:00 +01:00
" "
]
},
2019-12-18 19:04:32 +01:00
{
"cell_type": "code",
2020-02-05 12:15:47 +01:00
"execution_count": 46,
2019-12-18 19:04:32 +01:00
"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val m_0122_Haa :\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
" <abstr>\n"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0122_Hab :\n",
" (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
" <abstr>\n"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking ... \n",
" - 10 %\n",
" - 20 %\n",
" - 30 %\n",
" - 40 %\n",
" - 50 %\n",
" - 60 %\n",
" - 70 %\n",
" - 80 %\n",
" - 90 %\n",
" - 100 %\n",
"OK: (22, 22) | -3.896807e-02 -3.896807e-02 | 6.938894e-17 | cpu : 2.688957 0.003098\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
2019-12-18 19:04:32 +01:00
"source": [
"let m_0122_Haa = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa\n",
" ) )\n",
" \n",
"let m_0122_Hab = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta\n",
" ) )\n",
"\n",
"\n",
"let integral_value ki kj = \n",
" (* mos unoccupied in both I and J *)\n",
" let mos_virt_a, mos_virt_b = \n",
" Array.init mo_num (fun i -> Some (i+1)) , \n",
" Array.init mo_num (fun i -> Some (i+1)) \n",
" in\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
" \n",
" let mos_virt_a, mos_virt_b = \n",
" Array.to_list mos_virt_a |> Util.list_some,\n",
" Array.to_list mos_virt_b |> Util.list_some\n",
" in\n",
" \n",
" let result = \n",
" sum (mos_a ki) (fun i -> \n",
" sum (mos_b ki) (fun j -> \n",
" sum mos_virt_b (fun k -> m_0122_Hab.{i,j,k} )))\n",
" +.\n",
" sum (mos_b ki) (fun i -> \n",
" sum (mos_a ki) (fun j -> \n",
" sum mos_virt_a (fun k -> m_0122_Hab.{i,j,k} )))\n",
" +.\n",
" (* Alpha-Alpha / Beta-Beta *)\n",
" List.fold_left (fun accu (mos_virt,mos) -> \n",
" accu +.\n",
" sum mos (fun j -> \n",
" sum mos (fun i -> if i <= j then 0. else\n",
" sum mos_virt (fun k -> m_0122_Haa.{i,j,k} )))\n",
" ) 0. [ (mos_virt_a,mos_a ki) ; (mos_virt_b,mos_b ki)]\n",
" in \n",
" result\n",
" \n",
"let _ =\n",
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" check 100 integral_value 0 1 2 2\n",
2019-12-18 19:04:32 +01:00
" "
]
},
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. 0 2 22"
2019-12-04 18:13:54 +01:00
]
2019-12-03 14:40:08 +01:00
},
{
"cell_type": "code",
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"execution_count": 47,
2019-12-04 18:13:54 +01:00
"metadata": {
"scrolled": true
},
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"outputs": [
{
"data": {
"image/png": "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
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"- : Jupyter_notebook.display_id = <abstr>\n"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
2019-12-03 18:52:03 +01:00
"source": [
2019-12-19 19:23:02 +01:00
"let _ = png_image \"0_2_22.png\""
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
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"\n",
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"$\\sum_i \\sum_a \\sum_j \\sum_b \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{ij}$\n",
"\n",
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"\\begin{align}\n",
"\\sum_{a} \\sum_{b>a} \\sum_{i} \\sum_{j<i}\n",
" \\langle i j || a b \\rangle \n",
" \\left[ a b || i j \\right] + \n",
"\\sum_{a} \\sum_{\\bar{b}} \\sum_{i} \\sum_{\\bar{j}}\n",
" \\langle i \\bar{j} | a \\bar{b} \\rangle \n",
" \\left[ a \\bar{b} | i \\bar{j} \\right] + \\\\\n",
"\\sum_{\\bar{a}} \\sum_{b} \\sum_{\\bar{i}} \\sum_{j}\n",
" \\langle \\bar{i} j | \\bar{a} b \\rangle \n",
" \\left[ \\bar{a} b | \\bar{i} j \\right] + \n",
"\\sum_{\\bar{a}} \\sum_{\\bar{b}>\\bar{a}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
" \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{b} \\rangle \n",
" \\left[ \\bar{a} \\bar{b} || \\bar{i} \\bar{j} \\right] \n",
"\\end{align}"
2019-12-03 18:52:03 +01:00
]
},
{
"cell_type": "code",
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"execution_count": 48,
2019-12-03 18:52:03 +01:00
"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val integral_value : Determinant.t -> 'a -> float = <fun>\n"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking ... \n",
" - 10 %\n",
" - 20 %\n",
" - 30 %\n",
" - 40 %\n",
" - 50 %\n",
" - 60 %\n",
" - 70 %\n",
" - 80 %\n",
" - 90 %\n",
" - 100 %\n",
"OK: (95, 95) | -1.697991e-02 -1.697991e-02 | 2.775558e-17 | cpu : 3.329183 0.257722\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let integral_value ki kj = \n",
" (* Alpha-Beta *)\n",
" let s, s' = Spin.(Alfa, Beta) in\n",
2019-12-12 18:41:14 +01:00
" sum mos_cabs (fun a -> \n",
" sum mos_cabs (fun b -> \n",
" sum (mos_a ki) (fun i -> \n",
" sum (mos_b ki) (fun j -> \n",
" h_two i j a b s s' *. f_two a b i j s s'\n",
" ))))\n",
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" +.\n",
" (* Alpha-Alpha / Beta-Beta *)\n",
" List.fold_left (fun accu (mos,s) -> \n",
" let s' = s in accu +.\n",
2019-12-12 18:41:14 +01:00
" sum mos_cabs (fun b -> \n",
" sum mos_cabs (fun a -> if b > a then 0. else\n",
" sum mos (fun j -> \n",
" sum mos (fun i -> if i < j then 0. else\n",
" h_two i j a b s s' *. f_two a b i j s s'\n",
" ))))\n",
" ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
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" \n",
"let _ =\n",
2019-12-20 16:09:02 +01:00
" check 100 integral_value 0 2 2 2\n",
2019-12-04 18:13:54 +01:00
" "
]
},
2019-12-18 19:04:32 +01:00
{
"cell_type": "code",
2020-02-05 12:15:47 +01:00
"execution_count": 49,
2019-12-18 19:04:32 +01:00
"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
"text/plain": [
"val m_0222_Haa : Lacaml.D.mat =\n",
" \n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0 -1.0063E-05 -0.000334496 -0.000347188 -0.000267608\n",
" 2 -1.0063E-05 0 -0.00016695 -0.000173345 -0.000134367\n",
" 3 -0.000334496 -0.00016695 0 -0.00370788 -0.00334839\n",
" ... ... ... ... ...\n",
" 7 -0.000232416 -0.000151236 -0.000542986 -0.000572891 -2.9266E-05\n",
" 8 -4.11752E-05 -3.98219E-05 -0.000454591 -0.00047264 -0.000369248\n",
" 9 -0.000152836 -0.000112257 -0.000183496 -2.9266E-05 -0.000103812\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 -0.000165528 -0.000232416 -4.11752E-05 -0.000152836\n",
" 2 -0.000118652 -0.000151236 -3.98219E-05 -0.000112257\n",
" 3 -2.9266E-05 -0.000542986 -0.000454591 -0.000183496\n",
" ... ... ... ...\n",
" 7 -0.00083789 0 -0.000621663 -0.000807984\n",
" 8 -0.00053632 -0.000621663 0 -0.000518271\n",
" 9 -0.000728301 -0.000807984 -0.000518271 0\n",
" \n"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_0222_Hab : Lacaml.D.mat =\n",
" \n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 -0.0026356 -8.37274E-05 -0.000318312 -0.000329372 -0.000258412\n",
" 2 -8.37274E-05 -0.00329888 -0.00055028 -0.00055898 -0.000498185\n",
" 3 -0.000318312 -0.00055028 -0.00651939 -0.00351919 -0.00318906\n",
" ... ... ... ... ...\n",
" 7 -0.000177876 -0.000280993 -0.000526737 -0.000561143 -0.000637823\n",
" 8 -7.32564E-05 -0.000232089 -0.00062993 -0.000653508 -0.000521154\n",
" 9 -0.000106915 -0.000220198 -0.000196607 -0.000319215 -0.000105067\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 -0.000117975 -0.000177876 -7.32564E-05 -0.000106915\n",
" 2 -0.000228899 -0.000280993 -0.000232089 -0.000220198\n",
" 3 -0.000355709 -0.000526737 -0.00062993 -0.000196607\n",
" ... ... ... ...\n",
" 7 -0.00104342 -0.00180231 -0.000934604 -0.00100902\n",
" 8 -0.000825828 -0.000934604 -0.000964699 -0.00080225\n",
" 9 -0.000917478 -0.00100902 -0.00080225 -0.00135053\n",
" \n"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val integral_value : Determinant.t -> 'a -> float = <fun>\n"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking ... \n",
" - 10 %\n",
" - 20 %\n",
" - 30 %\n",
" - 40 %\n",
" - 50 %\n",
" - 60 %\n",
" - 70 %\n",
" - 80 %\n",
" - 90 %\n",
" - 100 %\n",
"OK: (58, 58) | -2.336186e-02 -2.336186e-02 | 3.122502e-17 | cpu : 3.329266 0.000941\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
2019-12-18 19:04:32 +01:00
"source": [
"let m_0222_Haa = \n",
" Mat.init_cols mo_num mo_num (fun i j ->\n",
" sum mos_cabs (fun a ->\n",
" sum mos_cabs (fun b -> if b >= a then 0. else\n",
" h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa\n",
" ) )\n",
" )\n",
" \n",
"let m_0222_Hab = \n",
" Mat.init_cols mo_num mo_num (fun i j ->\n",
" sum mos_cabs (fun a ->\n",
" sum mos_cabs (fun b ->\n",
" h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta\n",
" ) )\n",
" )\n",
" \n",
"let integral_value ki kj = \n",
" (* Alpha-Beta *)\n",
" sum (mos_a ki) (fun i -> \n",
" sum (mos_b ki) (fun j -> \n",
" m_0222_Hab.{i,j} \n",
" ))\n",
" +.\n",
" (* Alpha-Alpha / Beta-Beta *)\n",
" List.fold_left (fun accu (mos) -> \n",
" accu +.\n",
" sum mos (fun j -> \n",
" sum mos (fun i -> if i < j then 0. else\n",
" m_0222_Haa.{i,j} \n",
" ))\n",
" ) 0. [ (mos_a ki) ; (mos_b ki)]\n",
" \n",
"let _ =\n",
2019-12-20 16:09:02 +01:00
" check 100 integral_value 0 2 2 2\n",
2019-12-18 19:04:32 +01:00
" "
]
},
2019-12-04 18:13:54 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-05 22:45:30 +01:00
"# 4. 1 1 11"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "code",
2020-02-05 12:15:47 +01:00
"execution_count": 50,
2019-12-05 16:16:00 +01:00
"metadata": {},
2020-02-05 12:15:47 +01:00
"outputs": [
{
"data": {
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},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"- : Jupyter_notebook.display_id = <abstr>\n"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
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"let _ = png_image \"1_1_11.png\""
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
"\n",
"$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
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"$\\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{k}$\n",
"\n",
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"\\begin{align}\n",
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" \\sum_{a} \n",
" \\left( h_{ia} +\\sum_{j} \\langle i j || a j \\rangle +\n",
" \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right)\n",
" \\left( f_{ak} +\\sum_{j} \\left[ a j || k j \\right] + \n",
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" \\sum_{\\bar{j}} \\left[ a \\bar{j} | k \\bar{j} \\right]\\right) \\\\\n",
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"\\end{align}"
]
},
{
"cell_type": "code",
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"execution_count": 51,
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"metadata": {},
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"outputs": [
{
"data": {
"text/plain": [
"val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Checking ... \n",
" - 10 %\n",
" - 20 %\n",
" - 30 %\n",
" - 40 %\n",
" - 50 %\n",
" - 60 %\n",
" - 70 %\n",
" - 80 %\n",
" - 90 %\n",
" - 100 %\n",
"OK: (0, 0) | 0.000000e+00 0.000000e+00 | 0.000000e+00 | cpu : 4.151429 1.045428\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
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"source": [
"let integral_value ki kj = \n",
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
"\n",
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" let mos_i, mos_i' =\n",
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" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
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" let mos_j, mos_j' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a kj, mos_b kj\n",
" | Spin.Beta -> mos_b kj, mos_a kj\n",
" in\n",
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"\n",
" let result = \n",
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" let s' = Spin.other s in\n",
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" \n",
" sum mos_cabs (fun a -> \n",
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" (h_one i a s +. \n",
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" sum mos_i (fun j -> h_two i j a j s s ) +.\n",
" sum mos_i' (fun j -> h_two i j a j s s') ) *.\n",
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" (f_one a k s +. \n",
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" sum mos_j (fun j -> f_two a j k j s s ) +.\n",
" sum mos_j' (fun j -> f_two a j k j s s') ) \n",
" )\n",
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" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
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"let _ = check 0 integral_value 1 1 1 1"
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]
},
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{
"cell_type": "code",
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"execution_count": null,
2020-01-06 19:43:55 +01:00
"metadata": {},
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"outputs": [],
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"source": [
"let ki = det_I.(77)\n",
"let kj = det_I.(83)\n",
"\n",
"let _ = integral_value ki kj"
]
},
{
"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": false
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},
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"outputs": [],
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"source": [
"let m_1111_1H_1F = \n",
" Mat.init_cols mo_num mo_num (fun i k -> \n",
" sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))\n",
"\n",
"\n",
"let m_1111_1H_2Fa = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa ))\n",
"\n",
" \n",
"let m_1111_1H_2Fb = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta ))\n",
"\n",
"\n",
"let m_1111_2Ha_1F = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa ))\n",
"\n",
" \n",
"let m_1111_2Hb_1F = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa ))\n",
"\n",
"\n",
"let m_1111_2Ha_2Fa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Alfa *.\n",
" f_two a l k l Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_1111_2Hb_2Fa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Beta *.\n",
" f_two a l k l Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_1111_2Ha_2Fb =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Alfa *.\n",
" f_two a l k l Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_1111_2Hb_2Fb =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a j Spin.Alfa Spin.Beta *.\n",
" f_two a l k l Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
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"let integral_value_11 ki kj = \n",
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" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" let mos_a, mos_b =\n",
" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in \n",
" \n",
" let result = \n",
" m_1111_1H_1F.{i,k} +. \n",
" sum mos_a (fun j -> if j = i then 0. else\n",
" m_1111_1H_2Fa.{i,j,k} +. m_1111_2Ha_1F.{i,j,k} +.\n",
" sum mos_a (fun l -> if l = i then 0. else m_1111_2Ha_2Fa.{i,j,k,l}) +.\n",
" sum mos_b (fun l -> m_1111_2Ha_2Fb.{i,j,k,l})) +.\n",
" sum mos_b (fun j ->\n",
" m_1111_1H_2Fb.{i,j,k} +. m_1111_2Hb_1F.{i,j,k} +.\n",
" sum mos_a (fun l -> if l = i then 0. else m_1111_2Hb_2Fa.{i,j,k,l}) +.\n",
" sum mos_b (fun l -> m_1111_2Hb_2Fb.{i,j,k,l}))\n",
" in\n",
" \n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
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" \n",
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"let _ =\n",
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" check 0 integral_value_11 1 1 1 1\n",
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" "
]
},
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 5. 1 1 12"
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]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
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"let _ = png_image \"1_1_12.png\""
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
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"\n",
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"$\\sum_{j} \\sum_a \\hat{T}_{j}^{a} \\hat{T}_{ai}^{jk}$\n",
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"\n",
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"$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
"\\begin{align}\n",
" \\sum_{a} \\sum_{j} \n",
" \\left( h_{ja} +\\sum_{m} \\langle j m || a m \\rangle +\n",
" \\sum_{\\bar{m}} \\langle j \\bar{m} | a \\bar{m} \\rangle \\right)\n",
" \\left[ a i || j k \\right] + \\\\\n",
" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n",
" \\left( h_{\\bar{j}\\bar{a}} +\\sum_{m} \\langle \\bar{j} m | \\bar{a} m \\rangle +\n",
" \\sum_{\\bar{m}} \\langle \\bar{j} \\bar{m} || \\bar{a} \\bar{m} \\rangle \\right)\n",
" \\left[ \\bar{a} i | \\bar{j} k \\right] \n",
"\\end{align}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"let integral_value ki kj = \n",
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
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" in\n",
"\n",
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" let mos_j, mos_j' =\n",
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
" in\n",
" \n",
" let mos_i, mos_i' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
"\n",
" let result = \n",
" let s' = Spin.other s in\n",
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" sum mos_cabs (fun a -> \n",
" sum mos_j (fun j -> \n",
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" (h_one j a s +. \n",
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" sum mos_i (fun m -> h_two j m a m s s ) +.\n",
" sum mos_i' (fun m -> h_two j m a m s s') ) *.\n",
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" (f_two a i j k s s )\n",
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" ) \n",
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" +.\n",
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" sum mos_j' (fun j -> \n",
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" (h_one j a s +. \n",
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" sum mos_i (fun m -> h_two j m a m s' s ) +.\n",
" sum mos_i' (fun m -> h_two j m a m s' s') ) *.\n",
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" (f_two a i j k s' s )\n",
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" ) \n",
" ) \n",
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" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
2019-12-20 16:09:02 +01:00
"let _ = check 100 integral_value 1 1 1 2"
2019-12-05 16:16:00 +01:00
]
},
2019-12-19 19:23:02 +01:00
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2019-12-19 19:23:02 +01:00
"metadata": {},
2020-01-07 16:45:14 +01:00
"outputs": [],
2019-12-19 19:23:02 +01:00
"source": [
"let m_1112_1H_2Fa = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa ))\n",
"\n",
" \n",
"let m_1112_1H_2Fb = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta ))\n",
"\n",
"\n",
"let m_1112_2Ha_2Fa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two j m a m Spin.Alfa Spin.Alfa *.\n",
" f_two a i j k Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_1112_2Hb_2Fa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two j m a m Spin.Alfa Spin.Beta *.\n",
" f_two a i j k Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"let m_1112_2Ha_2Fb =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two j m a m Spin.Alfa Spin.Alfa *.\n",
" f_two a i j k Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_1112_2Hb_2Fb =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two j m a m Spin.Alfa Spin.Beta *.\n",
" f_two a i j k Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
2020-01-06 19:43:55 +01:00
"let integral_value_12 ki kj = \n",
2019-12-19 19:23:02 +01:00
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" let mos_j, mos_j' =\n",
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
" in\n",
" \n",
" let mos_i, mos_i' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
" \n",
" let result = \n",
" sum mos_j (fun j -> \n",
" m_1112_1H_2Fa.{i,j,k} +. \n",
" sum mos_i (fun m -> m_1112_2Ha_2Fa.{i,j,k,m}) +.\n",
" sum mos_i' (fun m -> m_1112_2Hb_2Fa.{i,j,k,m})) +.\n",
" sum mos_j' (fun j ->\n",
" m_1112_1H_2Fb.{i,j,k} +. \n",
" sum mos_i (fun m -> m_1112_2Hb_2Fb.{i,j,k,m}) +.\n",
" sum mos_i' (fun m -> m_1112_2Ha_2Fb.{i,j,k,m}))\n",
" in\n",
" \n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
" \n",
"\n",
2020-01-07 16:45:14 +01:00
"let _ = check 100 integral_value_12 1 1 1 2"
2019-12-19 19:23:02 +01:00
]
},
2019-12-05 16:16:00 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-12 16:28:30 +01:00
"# 6. 1 1 21"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
2019-12-09 19:37:58 +01:00
"metadata": {
"scrolled": false
},
2019-12-05 16:16:00 +01:00
"outputs": [],
"source": [
2019-12-19 19:23:02 +01:00
"let _ = png_image \"1_1_21.png\""
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-09 19:37:58 +01:00
"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
"\n",
"$\\sum_{j} \\sum_a \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{j}$\n",
"\n",
"$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
"\\begin{align}\n",
" \\sum_{a} \\sum_{j} \n",
" \\langle i j || k a \\rangle \n",
" \\left( f_{aj} +\\sum_{m} \\left[ m a || m j \\right] +\n",
" \\sum_{\\bar{m}} \\left[ \\bar{m} a | \\bar{m} j \\right] \\right) + \\\\\n",
" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n",
" \\langle i \\bar{j} | k \\bar{a} \\rangle\n",
" \\left( f_{\\bar{a}\\bar{j}} +\\sum_{m} \\left[ m \\bar{a} | m \\bar{j} \\right] +\n",
" \\sum_{\\bar{m}} \\left[ \\bar{m} \\bar{a} || \\bar{m} \\bar{j} \\right] \\right)\n",
"\\end{align}"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
2019-12-09 19:37:58 +01:00
"let integral_value ki kj = \n",
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
"\n",
" let mos_j, mos_j' =\n",
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
" in\n",
" \n",
" let mos_i, mos_i' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a kj, mos_b kj\n",
" | Spin.Beta -> mos_b kj, mos_a kj\n",
" in\n",
"\n",
" let result = \n",
" let s' = Spin.other s in\n",
2019-12-12 18:41:14 +01:00
" sum mos_cabs (fun a -> \n",
" sum mos_j (fun j -> \n",
2019-12-09 19:37:58 +01:00
" (h_two i j k a s s ) *.\n",
" (f_one a j s +. \n",
2019-12-12 18:41:14 +01:00
" sum mos_i (fun m -> f_two m a m j s s) +.\n",
" sum mos_i' (fun m -> f_two m a m j s' s) ) \n",
" ) \n",
" +.\n",
" sum mos_j' (fun j -> \n",
2019-12-09 19:37:58 +01:00
" (h_two i j k a s s') *.\n",
" (f_one a j s' +. \n",
2019-12-12 18:41:14 +01:00
" sum mos_i (fun m -> f_two m a m j s s') +.\n",
" sum mos_i' (fun m -> f_two m a m j s' s') ) \n",
" )) \n",
2019-12-09 19:37:58 +01:00
" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
2019-12-20 16:09:02 +01:00
"let _ = check 100 integral_value 1 1 2 1"
2019-12-12 16:28:30 +01:00
]
},
2019-12-19 19:23:02 +01:00
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2019-12-19 19:23:02 +01:00
"metadata": {},
2020-01-07 16:45:14 +01:00
"outputs": [],
2019-12-19 19:23:02 +01:00
"source": [
"let m_1121_2Ha_1F = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa))\n",
"\n",
" \n",
"let m_1121_2Hb_1F = \n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta))\n",
"\n",
"\n",
"let m_1121_2Ha_2Fa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j k a Spin.Alfa Spin.Alfa *.\n",
" f_two m a m j Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_1121_2Hb_2Fa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j k a Spin.Alfa Spin.Beta *.\n",
" f_two m a m j Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"let m_1121_2Ha_2Fb =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j k a Spin.Alfa Spin.Alfa *.\n",
" f_two m a m j Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
"let m_1121_2Hb_2Fb =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j k a Spin.Alfa Spin.Beta *.\n",
" f_two m a m j Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
"\n",
2020-01-06 19:43:55 +01:00
"let integral_value_21 ki kj = \n",
2019-12-19 19:23:02 +01:00
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" let mos_j, mos_j' =\n",
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
" in\n",
" \n",
" let mos_i, mos_i' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a kj, mos_b kj\n",
" | Spin.Beta -> mos_b kj, mos_a kj\n",
" in\n",
" \n",
" let result = \n",
" sum mos_j (fun j -> \n",
" m_1121_2Ha_1F.{i,j,k} +. \n",
" sum mos_i (fun m -> m_1121_2Ha_2Fa.{i,j,k,m}) +.\n",
" sum mos_i' (fun m -> m_1121_2Ha_2Fb.{i,j,k,m})) +.\n",
" sum mos_j' (fun j ->\n",
" m_1121_2Hb_1F.{i,j,k} +. \n",
" sum mos_i (fun m -> m_1121_2Hb_2Fb.{i,j,k,m}) +.\n",
" sum mos_i' (fun m -> m_1121_2Hb_2Fa.{i,j,k,m}))\n",
" in\n",
" \n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
" \n",
"\n",
2020-01-07 16:45:14 +01:00
"let _ = check 100 integral_value_21 1 1 2 1"
2019-12-19 19:23:02 +01:00
]
},
2019-12-12 16:28:30 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-17 19:03:55 +01:00
"# 7. 1 1 22"
2019-12-09 19:37:58 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
2019-12-19 19:23:02 +01:00
"let _ = png_image \"1_1_22.png\""
2019-12-12 16:28:30 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
2019-12-09 19:37:58 +01:00
"\n",
2019-12-12 18:41:14 +01:00
"$\\sum_{j} \\sum_{a} \\sum_{m}\n",
2019-12-17 19:03:55 +01:00
" \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kj} - \n",
2019-12-12 18:41:14 +01:00
" \\hat{T}_{lj}^{ka} \\hat{T}_{ia}^{lj} + \\\\\n",
"\\sum_{\\bar{j}} \\sum_{\\bar{a}} \\sum_{m}\n",
2019-12-19 19:23:02 +01:00
" \\hat{T}_{i\\bar{j}}^{m\\bar{a}} \\hat{T}_{m\\bar{a}}^{k\\bar{j}} - \n",
" \\hat{T}_{l\\bar{j}}^{k\\bar{a}} \\hat{T}_{i\\bar{a}}^{l\\bar{j}} +\n",
"\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{m}}\n",
" \\hat{T}_{i\\bar{j}}^{a\\bar{m}} \\hat{T}_{a\\bar{m}}^{k\\bar{j}} \n",
2019-12-12 18:41:14 +01:00
"$\n",
2019-12-09 19:37:58 +01:00
"\n",
2019-12-12 16:28:30 +01:00
"$j,l$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
"$m$ : orbital indices of virtual MOs, unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n",
2019-12-09 19:37:58 +01:00
"\n",
2019-12-12 18:41:14 +01:00
"$a$ : orbital indices of CABS MOs\n",
"\n",
2019-12-12 16:28:30 +01:00
"\\begin{align}\n",
2019-12-19 19:23:02 +01:00
" \\sum_{a} \\sum_{j} \\sum_{m}\n",
" \\langle i j || m a \\rangle \\left[ m a || k j \\right] - \\\\\n",
" \\sum_{a} \\sum_{j} \\sum_{l}\n",
" \\langle l j || k a \\rangle \\left[ i a || l j \\right] + \\\\\n",
" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{m}\n",
" \\langle i \\bar{j} | m \\bar{a} \\rangle \\left[ m \\bar{a} | k \\bar{j} \\right] + \\\\\n",
" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{l}\n",
" \\langle l \\bar{j} | k \\bar{a} \\rangle \\left[ i \\bar{a} | l \\bar{j} \\right] - \\\\\n",
" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{\\bar{m}}\n",
" \\langle i \\bar{j} | a \\bar{m} \\rangle \\left[ a \\bar{m} | k \\bar{j} \\right] \n",
2019-12-12 16:28:30 +01:00
"\\end{align}"
2019-12-05 16:16:00 +01:00
]
},
2019-12-20 16:09:02 +01:00
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"(*\n",
"let ki = det_I.(6)\n",
"let kj = det_I.(58)\n",
"\n",
"let _ = \n",
" Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
"generate_alphas ki kj 1 1 2 2\n",
"|> Array.of_list\n",
"|> Array.mapi (fun kk alpha -> \n",
"\n",
"(*\n",
"let _ = Determinant.to_lists ki\n",
"let _ = Determinant.to_lists alpha\n",
"let _ = Determinant.to_lists kj\n",
"\n",
" \n",
"let _ = \n",
" Format.printf \"|I> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det ki kj);\n",
" Format.printf \"|I> -> |a> : %a\\n@.\" Excitation.pp (Excitation.of_det ki alpha);\n",
" Format.printf \"|a> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det alpha kj)\n",
"*)\n",
"\n",
" let integral_value ki kj = \n",
" \n",
" let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n",
" let exc1 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n",
" let exc2 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n",
" \n",
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin } )) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
" let spin = function\n",
" | Spin.Alfa -> 0\n",
" | _ -> 1\n",
" in\n",
" exc0.(i).(spin s ) <- \"i\" \n",
" ; exc0.(k).(spin s ) <- \"k\" \n",
" ;\n",
" let s0 = s in\n",
" \n",
" let i, j, k, l, s, s', p1 =\n",
" match Excitation.of_det ki alpha with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"n\";\n",
" if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"n\";\n",
" if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n",
" if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n",
" \n",
" let string_h = \n",
" Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n",
" exc0.(i).(spin s )\n",
" exc0.(j).(spin s')\n",
" exc0.(k).(spin s )\n",
" exc0.(l).(spin s')\n",
" (if s = s0 then \"s \" else \"s'\")\n",
" (if s' = s0 then \"s \" else \"s'\")\n",
" (*\n",
" (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s \" else \n",
" if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \"s''\")\n",
" (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s \" else \n",
" if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \"s''\")\n",
" *)\n",
" in \n",
" \n",
" let i, j, k, l, s, s', p2 =\n",
" match Excitation.of_det alpha kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" let string_f = \n",
" Printf.sprintf \"f_two %s %s %s %s %s %s\" \n",
" exc0.(i).(spin s )\n",
" exc0.(j).(spin s')\n",
" exc0.(k).(spin s )\n",
" exc0.(l).(spin s')\n",
" (*\n",
" (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s \" else \n",
" if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \n",
" if exc0.(i).(spin s ) = \"n\" || exc0.(k).(spin s ) = \"n\" then \"s''\" else\n",
" if s = s0 then \"s\" else \"s'\")\n",
" (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s \" else \n",
" if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \n",
" if exc0.(j).(spin s') = \"n\" || exc0.(l).(spin s') = \"n\" then \"s''\" else\n",
" if s' = s0 then \"s\" else \"s'\")\n",
" *)\n",
" (if s = s0 then \"s \" else \"s'\")\n",
" (if s' = s0 then \"s \" else \"s'\")\n",
" in\n",
" \n",
" Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n",
" Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n",
" \n",
" let sign = \n",
" if Phase.add p1 p2 = phase then \"+. \" else \"-. \"\n",
" in\n",
"sign ^ string_h ^ string_f\n",
"(*\n",
" \n",
" let mos, mos' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
"\n",
" let result = \n",
" let k=4 and l=5 in\n",
" let i=1 and j=2 in\n",
" let n=2 and a=7 in\n",
" let s = Spin.Alfa\n",
" and s' = Spin.Alfa\n",
" and s'' = Spin.Beta\n",
" in\n",
" (* \n",
" h_two j n l a s' s'' *. f_two a i n k s s''\n",
" *)\n",
" h_two i n k a s s'' *. f_two j a l n s s''\n",
" in\n",
"\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" *)\n",
"\n",
"in\n",
"integral_value ki kj\n",
"(*\n",
"let a = (compute_HaaF ki [alpha] kj)\n",
"and b = (integral_value ki kj)\n",
"in\n",
"if kk = 31 then\n",
" Format.printf \"%6d %e %e@.@.\" (kk) a b\n",
" *)\n",
")\n",
"|> Array.to_list\n",
"|> List.sort_uniq compare\n",
"\n",
"let _ = compute_HaaF ki (generate_alphas ki kj 1 1 2 2) kj\n",
"\n",
"let _ = integral_value ki kj\n",
"\n",
"*)"
]
},
2019-12-05 16:16:00 +01:00
{
2019-12-12 16:28:30 +01:00
"cell_type": "code",
"execution_count": null,
"metadata": {
2019-12-20 16:09:02 +01:00
"scrolled": false
2019-12-12 16:28:30 +01:00
},
"outputs": [],
2019-12-05 16:16:00 +01:00
"source": [
2019-12-20 16:09:02 +01:00
"let integral_value ki kj = \n",
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" (* MOs unoccupied in both I and J *)\n",
" let mos_virt_a, mos_virt_b = \n",
" Array.init mo_num (fun i -> Some (i+1)) , \n",
" Array.init mo_num (fun i -> Some (i+1)) \n",
" in\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
" \n",
" let mos_virt_a, mos_virt_b = \n",
" Array.to_list mos_virt_a |> Util.list_some,\n",
" Array.to_list mos_virt_b |> Util.list_some\n",
" in\n",
2019-12-19 19:23:02 +01:00
"\n",
2019-12-20 16:09:02 +01:00
" let mos_virt, mos_virt' =\n",
" match s with\n",
" | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
" | Spin.Beta -> mos_virt_b, mos_virt_a\n",
" in\n",
" \n",
" let mos_j, mos_j' =\n",
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
" in\n",
" let result = \n",
" let s' = Spin.other s in\n",
" sum mos_cabs (fun a -> \n",
" sum mos_j (fun n -> \n",
" sum mos_virt (fun m -> \n",
" h_two n i a m s s *. f_two m a k n s s \n",
" ))) +.\n",
" sum mos_cabs (fun a' -> \n",
" sum mos_j' (fun n' -> \n",
" sum mos_virt (fun m -> \n",
" h_two i n' m a' s s' *. f_two m a' k n' s s'\n",
" ))) +.\n",
" sum mos_cabs (fun a -> \n",
" sum mos_j' (fun n' -> \n",
" sum mos_virt' (fun m' -> \n",
" h_two i n' a m' s s' *. f_two a m' k n' s s'\n",
" ))) -. \n",
" sum mos_cabs (fun a -> \n",
" sum mos_j (fun n -> \n",
" sum mos_j (fun l -> if l <=n then 0. else\n",
" h_two n l a k s s *. f_two i a l n s s \n",
" ))) -. \n",
" sum mos_cabs (fun a' -> \n",
" sum mos_j' (fun n' -> \n",
" sum mos_j (fun l -> \n",
" h_two l n' k a' s s' *. f_two i a' l n' s s'\n",
" ))) \n",
" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
2020-01-07 16:45:14 +01:00
"let _ = check 100 integral_value 1 1 2 2\n",
2019-12-20 16:09:02 +01:00
"\n"
]
},
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2019-12-20 16:09:02 +01:00
"metadata": {
"scrolled": false
},
2020-01-07 16:45:14 +01:00
"outputs": [],
2019-12-20 16:09:02 +01:00
"source": [
2019-12-19 19:23:02 +01:00
"let m_1122_va =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
2019-12-20 16:09:02 +01:00
" h_two j i a m Spin.Alfa Spin.Alfa *.\n",
2019-12-19 19:23:02 +01:00
" f_two m a k j Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
2019-12-20 16:09:02 +01:00
"let m_1122_v2 =\n",
2019-12-19 19:23:02 +01:00
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j m a Spin.Alfa Spin.Beta *.\n",
" f_two m a k j Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
2019-12-20 16:09:02 +01:00
"let m_1122_v3 =\n",
2019-12-19 19:23:02 +01:00
" array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a m Spin.Alfa Spin.Beta *.\n",
" f_two a m k j Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
2019-12-20 16:09:02 +01:00
"let m_1122_oa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two j l a k Spin.Alfa Spin.Alfa *.\n",
" f_two i a l j Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
"\n",
"let m_1122_o =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two l j k a Spin.Alfa Spin.Beta *.\n",
" f_two i a l j Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
"\n",
2019-12-19 19:23:02 +01:00
"\n",
2020-01-06 19:43:55 +01:00
"let integral_value_22 ki kj = \n",
2019-12-12 16:28:30 +01:00
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
2019-12-12 18:41:14 +01:00
" (* MOs unoccupied in both I and J *)\n",
2019-12-12 16:28:30 +01:00
" let mos_virt_a, mos_virt_b = \n",
" Array.init mo_num (fun i -> Some (i+1)) , \n",
" Array.init mo_num (fun i -> Some (i+1)) \n",
" in\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
" \n",
" let mos_virt_a, mos_virt_b = \n",
" Array.to_list mos_virt_a |> Util.list_some,\n",
" Array.to_list mos_virt_b |> Util.list_some\n",
" in\n",
"\n",
2019-12-20 16:09:02 +01:00
" let mos_virt, mos_virt' =\n",
2019-12-12 16:28:30 +01:00
" match s with\n",
2019-12-12 18:41:14 +01:00
" | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
" | Spin.Beta -> mos_virt_b, mos_virt_a\n",
2019-12-20 16:09:02 +01:00
" in\n",
2019-12-12 16:28:30 +01:00
" \n",
2019-12-20 16:09:02 +01:00
" let mos_j, mos_j' =\n",
2019-12-12 16:28:30 +01:00
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
2019-12-20 16:09:02 +01:00
" in\n",
" \n",
2019-12-12 16:28:30 +01:00
" let result = \n",
2019-12-12 18:41:14 +01:00
" sum mos_j (fun j -> \n",
" sum mos_virt (fun m -> \n",
2019-12-19 19:23:02 +01:00
" m_1122_va.{i,j,k,m}\n",
" )) +.\n",
2019-12-12 18:41:14 +01:00
" sum mos_j' (fun j -> \n",
" sum mos_virt (fun m -> \n",
2019-12-20 16:09:02 +01:00
" m_1122_v2.{i,j,k,m}\n",
2019-12-19 19:23:02 +01:00
" )) +.\n",
2020-01-06 19:43:55 +01:00
" \n",
2019-12-12 18:41:14 +01:00
" sum mos_j' (fun j -> \n",
" sum mos_virt' (fun m -> \n",
2019-12-20 16:09:02 +01:00
" m_1122_v3.{i,j,k,m}\n",
2019-12-19 19:23:02 +01:00
" )) -.\n",
2019-12-12 18:41:14 +01:00
" sum mos_j (fun j -> \n",
2019-12-20 16:09:02 +01:00
" sum mos_j (fun l -> if l <= j then 0. else\n",
2019-12-19 19:23:02 +01:00
" m_1122_oa.{i,j,k,l}\n",
" )) -. \n",
2019-12-12 18:41:14 +01:00
" sum mos_j' (fun j -> \n",
2019-12-20 16:09:02 +01:00
" sum mos_j (fun l -> \n",
2019-12-19 19:23:02 +01:00
" m_1122_o.{i,j,k,l}\n",
" )) \n",
2019-12-12 16:28:30 +01:00
" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
2020-01-06 19:43:55 +01:00
"let _ = check 100 integral_value_22 1 1 2 2\n",
2019-12-12 16:28:30 +01:00
"\n",
"\n"
2019-12-05 16:16:00 +01:00
]
},
2020-01-06 19:43:55 +01:00
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2020-01-06 19:43:55 +01:00
"metadata": {},
2020-01-07 16:45:14 +01:00
"outputs": [],
2020-01-06 19:43:55 +01:00
"source": [
"let ki = det_I.(77) and kj = det_I.(83)\n",
"\n",
"let _ =\n",
"integral_value_11 ki kj\n",
"+. integral_value_12 ki kj\n",
"+. integral_value_21 ki kj\n",
"+. integral_value_22 ki kj "
]
},
2019-12-05 16:16:00 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-18 12:56:35 +01:00
"# 8. 1 2 22"
2019-12-04 18:13:54 +01:00
]
2019-12-03 18:52:03 +01:00
},
{
"cell_type": "code",
"execution_count": null,
2019-12-04 18:13:54 +01:00
"metadata": {},
2019-12-03 18:52:03 +01:00
"outputs": [],
"source": [
2019-12-19 19:23:02 +01:00
"let _ = png_image \"1_2_22.png\""
2019-12-03 18:52:03 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-04 18:13:54 +01:00
"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
"\n",
"$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
2019-12-17 19:03:55 +01:00
"$\\sum_{j} \\sum_{a} \\sum_{b}\n",
" \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{kj} +\n",
"\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{b}}\n",
" \\hat{T}_{i\\bar{j}}^{a\\bar{b}} \\hat{T}_{a\\bar{b}}^{k\\bar{j}} \n",
"$\n",
"\n",
2019-12-04 18:13:54 +01:00
"\n",
"$$\n",
"\\sum_{j} \\sum_{b}\\sum_{a<b}\n",
2019-12-17 19:03:55 +01:00
" \\langle i j || a b \\rangle \\left[ ab || kj \\right] + \n",
"\\sum_{\\bar{j}} \\sum_{\\bar{b}}\\sum_{a}\n",
" \\langle i \\bar{j} | a \\bar{b} \\rangle \\left[ a \\bar{b} | k \\bar{j} \\right] \n",
2019-12-04 18:13:54 +01:00
"$$"
2019-12-03 18:52:03 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
2019-12-03 12:25:31 +01:00
"source": [
2019-12-04 18:13:54 +01:00
"let integral_value ki kj = \n",
2019-12-05 16:16:00 +01:00
" let h, p, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
2019-12-04 18:13:54 +01:00
" in\n",
"\n",
2019-12-05 16:16:00 +01:00
" let mos, mos' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
2019-12-12 16:28:30 +01:00
" \n",
" \n",
2019-12-05 16:16:00 +01:00
"\n",
" let result = \n",
" (* Alpha-Beta *)\n",
2019-12-12 18:41:14 +01:00
" let s' = Spin.other s in\n",
" sum mos_cabs (fun b -> \n",
" sum mos_cabs (fun a -> \n",
" sum mos' (fun j -> h_two h j a b s s' *. f_two a b p j s s')\n",
" ))\n",
2019-12-05 16:16:00 +01:00
" +.\n",
" (* Alpha-Alpha / Beta-Beta *)\n",
2019-12-12 18:41:14 +01:00
" sum mos_cabs (fun b -> \n",
" sum mos_cabs (fun a -> if b >= a then 0. else\n",
" sum mos (fun j -> h_two h j a b s s *. f_two a b p j s s)\n",
" )) \n",
2019-12-05 16:16:00 +01:00
" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
2019-12-20 16:09:02 +01:00
"let _ = check 100 integral_value 1 2 2 2"
2019-12-05 16:16:00 +01:00
]
},
2019-12-19 19:23:02 +01:00
{
"cell_type": "code",
"execution_count": null,
"metadata": {
2019-12-20 16:09:02 +01:00
"scrolled": false
2019-12-19 19:23:02 +01:00
},
"outputs": [],
"source": [
"let m_1222a =\n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" sum mos_cabs (fun b -> if b > a then 0. else\n",
" h_two i j a b Spin.Alfa Spin.Alfa *.\n",
" f_two a b k j Spin.Alfa Spin.Alfa \n",
" )\n",
" )\n",
" )\n",
"\n",
"let m_1222 =\n",
" array_3_init mo_num mo_num mo_num (fun i j k ->\n",
" sum mos_cabs (fun a ->\n",
" sum mos_cabs (fun b ->\n",
" h_two i j a b Spin.Alfa Spin.Beta *.\n",
" f_two a b k j Spin.Alfa Spin.Beta \n",
" )\n",
" )\n",
" )\n",
" \n",
"\n",
"let integral_value ki kj = \n",
" let i, k, s, phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
" hole, particle, spin, phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" (* MOs unoccupied in both I and J *)\n",
" let mos_j, mos_j' =\n",
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
" in\n",
"\n",
" let result = \n",
" sum mos_j (fun j -> m_1222a.{i,j,k} ) +.\n",
" sum mos_j' (fun j -> m_1222.{i,j,k} )\n",
" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
2019-12-20 16:09:02 +01:00
"let _ = check 100 integral_value 1 2 2 2\n",
2019-12-19 19:23:02 +01:00
"\n",
"\n"
]
},
2019-12-05 16:16:00 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-19 19:23:02 +01:00
"# 9. 2 1 12"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
2019-12-19 19:23:02 +01:00
"let _ = png_image \"2_1_12.png\""
2019-12-05 16:16:00 +01:00
]
},
2019-12-17 19:03:55 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
"\n",
"$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
"$n$ : orbital indices of MOs occupied in $|I\\rangle$\n",
"\n",
"$\\sum_{a} \n",
" \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n",
2019-12-19 19:23:02 +01:00
" \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n",
2019-12-17 19:03:55 +01:00
"$\n",
"\n",
"\n",
"$$\n",
"\\sum_{a}\n",
" \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n",
"\\sum_{a}\n",
2019-12-19 19:23:02 +01:00
" \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n",
2019-12-17 19:03:55 +01:00
"$$"
]
},
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2019-12-19 19:23:02 +01:00
"metadata": {
"scrolled": true
},
2020-01-07 16:45:14 +01:00
"outputs": [],
2019-12-17 19:03:55 +01:00
"source": [
"let integral_value ki kj = \n",
" let i, j, k, l, s, s', phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
"\n",
" let mos, mos' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
2019-12-19 19:23:02 +01:00
" \n",
" let mos2, mos2' =\n",
" match s' with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
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"\n",
" let result = \n",
" sum mos_cabs (fun a -> \n",
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" let s'' = Spin.other s in\n",
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" ( h_one i a s +.\n",
2019-12-19 19:23:02 +01:00
" sum mos (fun n -> h_two i n a n s s ) +.\n",
" sum mos' (fun n -> h_two i n a n s s'') \n",
" ) *. f_two a j k l s s'\n",
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" ) +.\n",
" sum mos_cabs (fun a -> \n",
2019-12-19 19:23:02 +01:00
" let s'' = Spin.other s' in\n",
" ( h_one j a s' +.\n",
" sum mos2 (fun n -> h_two j n a n s' s' ) +.\n",
" sum mos2' (fun n -> h_two j n a n s' s'') \n",
" ) *. f_two i a k l s s'\n",
2019-12-17 19:03:55 +01:00
" ) \n",
" in\n",
"\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
"\n",
"\n",
2020-01-06 19:43:55 +01:00
"let _ = check 100 integral_value 2 1 1 2\n"
2019-12-17 19:03:55 +01:00
]
},
2019-12-19 19:23:02 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
"\n",
"$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
"$n$ : orbital indices of MOs occupied in $|I\\rangle$\n",
"\n",
"$\\sum_{a} \n",
" \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n",
" \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n",
"$\n",
"\n",
"\n",
"$$\n",
"\\sum_{a}\n",
" \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n",
"\\sum_{a}\n",
" \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n",
"$$"
]
},
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2019-12-19 19:23:02 +01:00
"metadata": {
2019-12-20 16:09:02 +01:00
"scrolled": false
2019-12-19 19:23:02 +01:00
},
2020-01-07 16:45:14 +01:00
"outputs": [],
2019-12-19 19:23:02 +01:00
"source": [
"let m_2112_1H_2Fa =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.\n",
" h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa )\n",
" )\n",
"\n",
"let m_2112_1H_2Fb =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n",
" h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta)\n",
" )\n",
"\n",
"let m_2112_2Ha_2Fa =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i n a n Spin.Alfa Spin.Alfa *.\n",
" f_two a j k l Spin.Alfa Spin.Alfa )\n",
" )\n",
" \n",
"let m_2112_2Hb_2Fa =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i n a n Spin.Alfa Spin.Beta *.\n",
" f_two a j k l Spin.Alfa Spin.Alfa )\n",
" )\n",
" \n",
"let m_2112_2Ha_2Fb =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i n a n Spin.Alfa Spin.Alfa *.\n",
" f_two a j k l Spin.Alfa Spin.Beta )\n",
" )\n",
" \n",
"let m_2112_2Hb_2Fb =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i n a n Spin.Alfa Spin.Beta *.\n",
" f_two a j k l Spin.Alfa Spin.Beta )\n",
" )\n",
" \n",
"let integral_value ki kj = \n",
" let i, j, k, l, s, s', phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" let mos, mos' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a ki, mos_b ki\n",
" | Spin.Beta -> mos_b ki, mos_a ki\n",
" in\n",
" \n",
" let result = \n",
" if s = s' then\n",
" m_2112_1H_2Fa.{i,j,k,l} +. \n",
" sum mos (fun n ->\n",
" m_2112_2Ha_2Fa.{i,j,k,l,n} +. m_2112_2Ha_2Fa.{j,i,l,k,n}\n",
" ) +.\n",
" sum mos' (fun n ->\n",
" m_2112_2Hb_2Fa.{i,j,k,l,n} +. m_2112_2Hb_2Fa.{j,i,l,k,n}\n",
" ) \n",
" else\n",
" m_2112_1H_2Fb.{i,j,k,l} +.\n",
" sum mos (fun n ->\n",
" m_2112_2Ha_2Fb.{i,j,k,l,n} +. m_2112_2Hb_2Fb.{j,i,l,k,n}\n",
" ) +.\n",
" sum mos' (fun n ->\n",
" m_2112_2Hb_2Fb.{i,j,k,l,n} +. m_2112_2Ha_2Fb.{j,i,l,k,n}\n",
" ) \n",
" in\n",
"\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
2019-12-20 16:09:02 +01:00
"let _ = check 100 integral_value 2 1 1 2\n",
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"\n",
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"let ki = det_I.(2)\n",
"let kj = det_I.(33)\n",
"\n",
"let _ = integral_value ki kj\n",
"let _ = \n",
" let alphas = generate_alphas ki kj 2 1 1 2\n",
" in compute_HaaF ki alphas kj\n",
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"\n"
]
},
2019-12-18 12:56:35 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 10. 2 1 21"
]
},
2019-12-17 19:03:55 +01:00
{
"cell_type": "code",
"execution_count": null,
2019-12-18 12:56:35 +01:00
"metadata": {},
2019-12-17 19:03:55 +01:00
"outputs": [],
"source": [
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"let _ = png_image \"2_1_21.png\""
2019-12-18 12:56:35 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
2019-12-17 19:03:55 +01:00
"\n",
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"$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n",
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"\n",
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"$n$ : orbital indices of MOs occupied in $|J\\rangle$\n",
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"\n",
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"$\\sum_{a} \n",
" \\hat{T}_{ij}^{al} \\hat{T}_{a}^{k} +\n",
" \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{l} +\n",
" \\hat{T}_{i\\bar{j}}^{a\\bar{l}} \\hat{T}_{a}^{k} +\n",
" \\hat{T}_{i\\bar{j}}^{k\\bar{a}} \\hat{T}_{\\bar{a}}^{\\bar{l}}\n",
"$\n",
"\n",
"\n",
"$$\n",
"\\sum_{a}\n",
" \\langle i j || a l \\rangle \\left( f_{ak} + \\sum_{n} \\left[ a n || k n \\right] + \\sum_{\\bar{n}} \\left[ a \\bar{n} | k \\bar{n} \\right] \\right) + \\\\\n",
"\\sum_{a}\n",
" \\langle i j || k a \\rangle \\left( f_{al} + \\sum_{n} \\left[ n a || n l \\right] + \\sum_{\\bar{n}} \\left[ \\bar{n} a | \\bar{n} l \\right] \\right) \n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"let integral_value ki kj = \n",
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" let i, j, k, l, s, s', phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
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" hole, hole', particle, particle', spin, spin', phase\n",
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" | _ -> assert false\n",
" in\n",
"\n",
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" let result = \n",
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" \n",
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" let mos, mos', s'' =\n",
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" match s with\n",
2019-12-18 12:56:35 +01:00
" | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n",
" | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n",
2019-12-17 19:03:55 +01:00
" in\n",
2019-12-18 12:56:35 +01:00
" sum mos_cabs (fun a -> \n",
" h_two i j a l s s' *.\n",
" ( f_one a k s +.\n",
" sum mos (fun n -> f_two a n k n s s) +.\n",
" sum mos' (fun n -> f_two a n k n s s'') \n",
" ) ) +.\n",
"\n",
" let mos, mos', s'' =\n",
" match s' with\n",
" | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n",
" | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n",
" in\n",
" sum mos_cabs (fun a -> \n",
2019-12-19 19:23:02 +01:00
" h_two j i a k s' s *.\n",
2019-12-18 12:56:35 +01:00
" ( f_one a l s' +.\n",
2019-12-19 19:23:02 +01:00
" sum mos (fun n -> f_two a n l n s' s') +.\n",
" sum mos' (fun n -> f_two a n l n s' s'') \n",
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" ) \n",
" ) \n",
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" in\n",
"\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
"\n",
2019-12-18 12:56:35 +01:00
"\n",
2019-12-20 16:09:02 +01:00
"let _ = check 100 integral_value 2 1 2 1"
2019-12-17 19:03:55 +01:00
]
},
2019-12-19 19:23:02 +01:00
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2019-12-19 19:23:02 +01:00
"metadata": {
2019-12-20 16:09:02 +01:00
"scrolled": false
2019-12-19 19:23:02 +01:00
},
2020-01-07 16:45:14 +01:00
"outputs": [],
2019-12-19 19:23:02 +01:00
"source": [
"let m_2121_2Ha_1F =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n",
" h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa)\n",
" )\n",
"\n",
"let m_2121_2Hb_1F =\n",
" array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n",
" h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa)\n",
" )\n",
"\n",
"let m_2121_2Ha_2Fa =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a l Spin.Alfa Spin.Alfa *.\n",
" f_two a n k n Spin.Alfa Spin.Alfa )\n",
" )\n",
" \n",
"let m_2121_2Hb_2Fa =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a l Spin.Alfa Spin.Beta *.\n",
" f_two a n k n Spin.Alfa Spin.Alfa )\n",
" )\n",
" \n",
"let m_2121_2Ha_2Fb =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a l Spin.Alfa Spin.Alfa *.\n",
" f_two a n k n Spin.Alfa Spin.Beta )\n",
" )\n",
" \n",
"let m_2121_2Hb_2Fb =\n",
" array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
" sum mos_cabs (fun a ->\n",
" h_two i j a l Spin.Alfa Spin.Beta *.\n",
" f_two a n k n Spin.Alfa Spin.Beta )\n",
" )\n",
" \n",
"let integral_value ki kj = \n",
" let i, j, k, l, s, s', phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" let mos, mos' =\n",
" match s with\n",
" | Spin.Alfa -> mos_a kj, mos_b kj\n",
" | Spin.Beta -> mos_b kj, mos_a kj\n",
" in\n",
" \n",
" let result = \n",
" if s = s' then\n",
" m_2121_2Ha_1F.{i,j,k,l} +. \n",
" sum mos (fun n ->\n",
" m_2121_2Ha_2Fa.{i,j,k,l,n} +. m_2121_2Ha_2Fa.{j,i,l,k,n}\n",
" ) +.\n",
" sum mos' (fun n ->\n",
" m_2121_2Ha_2Fb.{i,j,k,l,n} +. m_2121_2Ha_2Fb.{j,i,l,k,n}\n",
" ) \n",
" else\n",
" m_2121_2Hb_1F.{i,j,k,l} +.\n",
" sum mos (fun n ->\n",
" m_2121_2Hb_2Fa.{i,j,k,l,n} +. m_2121_2Hb_2Fb.{j,i,l,k,n}\n",
" ) +.\n",
" sum mos' (fun n ->\n",
" m_2121_2Hb_2Fb.{i,j,k,l,n} +. m_2121_2Hb_2Fa.{j,i,l,k,n}\n",
" ) \n",
" in\n",
"\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
2019-12-20 16:09:02 +01:00
"let _ = check 100 integral_value 2 1 2 1\n",
2019-12-19 19:23:02 +01:00
"\n",
2020-01-06 19:43:55 +01:00
"(*\n",
"let ki = det_I.(2)\n",
"let kj = det_I.(33)\n",
"\n",
"let _ = integral_value ki kj\n",
"let _ = \n",
" let alphas = generate_alphas ki kj 2 1 2 1\n",
" in compute_HaaF ki alphas kj\n",
"*)\n",
"\n",
2019-12-19 19:23:02 +01:00
"\n"
]
},
2019-12-05 16:16:00 +01:00
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-20 16:09:02 +01:00
"# 11. 2 1 22"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
2019-12-19 19:23:02 +01:00
"let _ = png_image \"2_1_22.png\""
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
2019-12-18 12:56:35 +01:00
"$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
"\n",
"$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n",
"\n",
2019-12-19 19:23:02 +01:00
"$n$ : orbital indices of MOs occupied in both $|I\\rangle$ and $|J\\rangle$ .\n",
2019-12-18 12:56:35 +01:00
"\n",
"$\\sum_{a} \n",
" \\hat{T}_{ij}^{am} \\hat{T}_{am}^{kl} +\n",
" \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kl} -\n",
" \\hat{T}_{in}^{al} \\hat{T}_{aj}^{kn} -\n",
2019-12-19 19:23:02 +01:00
" \\hat{T}_{nj}^{ka} \\hat{T}_{ia}^{nl} +\n",
" \\sum_{n}\n",
" \\hat{T}_{i\\bar{n}}^{k\\bar{a}} \\hat{T}_{\\bar{a}j}^{\\bar{n}l}\n",
2019-12-18 12:56:35 +01:00
"$\n",
"\n",
"\n",
"$$\n",
"\\sum_{a}\n",
"\\sum_{m} \\langle i j || a m \\rangle \\left[ a m || k l \\right] + \\langle i j || m a \\rangle \\left[ m a || k l \\right] - \\\\\n",
"\\sum_{n} \\langle i n || a l \\rangle \\left[ a j || k n \\right] + \\langle n j || k a \\rangle \\left[ i a || n l \\right] \n",
"$$"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
2019-12-18 12:56:35 +01:00
"let integral_value ki kj = \n",
" let i, j, k, l, s, s', phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
"\n",
" let mos_virt_a, mos_virt_b = \n",
" Array.init mo_num (fun i -> Some (i+1)) , \n",
" Array.init mo_num (fun i -> Some (i+1)) \n",
" in\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
"\n",
" let mos_virt_a, mos_virt_b = \n",
" Array.to_list mos_virt_a |> Util.list_some,\n",
" Array.to_list mos_virt_b |> Util.list_some\n",
" in\n",
" \n",
" let result = \n",
" \n",
2019-12-20 16:09:02 +01:00
" let mos_virt, mos_virt' =\n",
2019-12-18 12:56:35 +01:00
" match s with\n",
2019-12-20 16:09:02 +01:00
" | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
" | Spin.Beta -> mos_virt_b, mos_virt_a\n",
2019-12-18 12:56:35 +01:00
" in\n",
" \n",
2019-12-20 16:09:02 +01:00
" let mos, mos' =\n",
" let alfa = \n",
" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" let beta = \n",
" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
" Bitstring.to_list (Bitstring.logand i j)\n",
" in\n",
" match s with\n",
" | Spin.Alfa -> alfa, beta\n",
" | Spin.Beta -> beta, alfa\n",
2019-12-18 12:56:35 +01:00
" in\n",
2019-12-20 16:09:02 +01:00
"\n",
" if s = s' then \n",
" let s'' = Spin.other s' in\n",
" sum mos_cabs (fun a -> \n",
2019-12-19 19:23:02 +01:00
" sum mos (fun n ->\n",
2019-12-20 16:09:02 +01:00
" h_two i n a k s s *. f_two j a n l s s \n",
" +. h_two i n a l s s *. f_two j a k n s s \n",
" -. h_two j n a k s s *. f_two i a n l s s \n",
" -. h_two j n a l s s *. f_two i a k n s s\n",
" )\n",
" +. sum mos_virt (fun m ->\n",
" -. h_two i j a m s s *. f_two m a k l s s )\n",
" +. sum mos' (fun n ->\n",
" h_two i n k a s s'' *. f_two j a l n s s''\n",
" +. h_two j n l a s s'' *. f_two i a k n s s''\n",
" -. h_two i n l a s s'' *. f_two j a k n s s''\n",
" -. h_two j n k a s s'' *. f_two i a l n s s''\n",
" )\n",
" )\n",
" else\n",
" sum mos_cabs (fun a ->\n",
" sum mos_virt' (fun m ->\n",
" h_two i j a m s s' *. f_two a m k l s s' ) +.\n",
" sum mos_virt (fun m ->\n",
" h_two i j m a s s' *. f_two m a k l s s' ) +.\n",
" sum mos (fun n ->\n",
" h_two n i a k s s *. f_two a j n l s s'\n",
" +. h_two n j a l s s' *. f_two i a k n s s \n",
" -. h_two n j k a s s' *. f_two i a n l s s'\n",
" ) +.\n",
" sum mos' (fun n -> if n >= j then 0. else \n",
" h_two i n k a s s' *. f_two j a l n s' s'\n",
" +. h_two n j a l s' s' *. f_two i a k n s s' ) +. \n",
" sum mos' (fun n -> if n <= j then 0. else \n",
" -. h_two i n k a s s' *. f_two j a n l s' s' \n",
" -. h_two j n a l s' s' *. f_two i a k n s s' ) +.\n",
2019-12-19 19:23:02 +01:00
" sum mos' (fun n -> \n",
2019-12-20 16:09:02 +01:00
" -. h_two i n a l s s' *. f_two a j k n s s'\n",
" )\n",
" )\n",
2019-12-18 12:56:35 +01:00
" in\n",
"\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
"\n",
"\n",
2019-12-20 16:09:02 +01:00
"let _ = check 300 integral_value 2 1 2 2"
2019-12-19 19:23:02 +01:00
]
},
{
2020-01-06 19:43:55 +01:00
"cell_type": "raw",
2019-12-20 16:09:02 +01:00
"metadata": {
2020-01-06 19:43:55 +01:00
"raw_mimetype": "text/markdown",
2019-12-20 16:09:02 +01:00
"scrolled": false
},
2019-12-19 19:23:02 +01:00
"source": [
2019-12-20 16:09:02 +01:00
"let ki = det_I.(99)\n",
"let kj = det_I.(193)\n",
2019-12-19 19:23:02 +01:00
"\n",
2019-12-20 16:09:02 +01:00
"let alpha_to_string alpha = \n",
2019-12-19 19:23:02 +01:00
" \n",
2019-12-20 16:09:02 +01:00
" let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n",
" \n",
" let i, j, k, l, s, s', phase =\n",
2019-12-19 19:23:02 +01:00
" match Excitation.of_det ki kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
2019-12-20 16:09:02 +01:00
" hole, hole', particle, particle', spin, spin', phase\n",
2019-12-19 19:23:02 +01:00
" | _ -> assert false\n",
2019-12-20 16:09:02 +01:00
" in\n",
" let spin = function\n",
" | Spin.Alfa -> 0\n",
" | _ -> 1\n",
" in\n",
" exc0.(i).(spin s ) <- \"i\" \n",
" ; exc0.(j).(spin s') <- \"j\" \n",
" ; exc0.(k).(spin s ) <- \"k\" \n",
" ; exc0.(l).(spin s') <- \"l\" \n",
" ;\n",
" let s0, s0' = s, s' in\n",
" \n",
" let i, j, k, l, s, s', p1 =\n",
" match Excitation.of_det ki alpha with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"n\";\n",
" if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"n\";\n",
" if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n",
" if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n",
" \n",
" let string_h = \n",
" Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n",
" exc0.(i).(spin s )\n",
" exc0.(j).(spin s')\n",
" exc0.(k).(spin s )\n",
" exc0.(l).(spin s')\n",
" (if s = s0 then \"s \" else \"s'\")\n",
" (if s' = s0 then \"s \" else \"s'\")\n",
" in \n",
" \n",
" let i, j, k, l, s, s', p2 =\n",
" match Excitation.of_det alpha kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" let string_f = \n",
" Printf.sprintf \"f_two %s %s %s %s %s %s\" \n",
" exc0.(i).(spin s )\n",
" exc0.(j).(spin s')\n",
" exc0.(k).(spin s )\n",
" exc0.(l).(spin s')\n",
" (if s = s0 then \"s \" else \"s'\")\n",
" (if s' = s0 then \"s \" else \"s'\")\n",
" in\n",
"(*\n",
" Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n",
" Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n",
" *)\n",
2019-12-19 19:23:02 +01:00
"\n",
2019-12-20 16:09:02 +01:00
" \n",
" let sign = \n",
" if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n",
2019-12-19 19:23:02 +01:00
" in\n",
2019-12-20 16:09:02 +01:00
" sign ^ string_h ^ string_f\n",
" \n",
2019-12-19 19:23:02 +01:00
"\n",
2019-12-20 16:09:02 +01:00
"let alpha_debug alpha = \n",
" \n",
" let i, j, k, l, s, s', p1 =\n",
" match Excitation.of_det ki alpha with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" Printf.printf \"%d %d %d %d \" i j k l;\n",
" \n",
" let i, j, k, l, s, s', p2 =\n",
" match Excitation.of_det alpha kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" (*\n",
" Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n",
" Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n",
2019-12-19 19:23:02 +01:00
" *)\n",
2019-12-20 16:09:02 +01:00
" Printf.printf \"%d %d %d %d \\n%!\" i j k l\n",
2019-12-19 19:23:02 +01:00
"\n",
2019-12-20 16:09:02 +01:00
" \n",
"let strings = \n",
" Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
" generate_alphas ki kj 2 1 2 2\n",
" |> Array.of_list\n",
" |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n",
" |> Array.to_list\n",
" |> List.sort_uniq compare\n",
" |> Array.of_list\n",
2019-12-19 19:23:02 +01:00
"\n",
2019-12-20 16:09:02 +01:00
"let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n",
2019-12-19 19:23:02 +01:00
"\n",
2019-12-20 16:09:02 +01:00
"let _ =\n",
" let v =\n",
" let alphas =\n",
" generate_alphas ki kj 2 1 2 2\n",
" (*\n",
" |> List.filter (fun alpha ->\n",
" let x = alpha_to_string alpha in\n",
" x = strings.(6)\n",
" )\n",
" *)\n",
" in\n",
" (*\n",
" List.iter alpha_debug alphas ;\n",
" Printf.printf \"\\n%!\";\n",
" *)\n",
" compute_HaaF ki alphas kj \n",
" in\n",
" let x = (integral_value ki kj) in\n",
" Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 12. 2 2 22"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
2020-01-06 19:43:55 +01:00
"let _ = png_image \"2_2_22.png\""
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
"\n",
"$$\n",
"\\sum_{b}\\sum_{a<b}\n",
" \\langle i j || a b \\rangle \n",
" \\left[ ab || kj \\right]\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"let integral_value ki kj = \n",
" let h, h', p, p', s, s', phase =\n",
" match Excitation.of_det ki kj with\n",
" | Excitation.(Double (phase,\n",
" { hole=h ; particle=p ; spin=s },\n",
" { hole=h'; particle=p'; spin=s'}) ) -> h, h', p, p', s, s', phase\n",
" | _ -> assert false\n",
" in\n",
"\n",
" let result = \n",
" if s <> s' then (* Alpha-Beta *)\n",
2019-12-12 18:41:14 +01:00
" sum mos_cabs (fun b -> \n",
" sum mos_cabs (fun a -> \n",
" h_two h h' a b s s' *. f_two a b p p' s s'\n",
" )) \n",
2019-12-05 16:16:00 +01:00
" else (* Alpha-Alpha / Beta-Beta *)\n",
2019-12-12 18:41:14 +01:00
" sum mos_cabs (fun b -> \n",
" sum mos_cabs (fun a -> if b >= a then 0. else\n",
" h_two h h' a b s s' *. f_two a b p p' s s'\n",
" )) \n",
2019-12-05 16:16:00 +01:00
" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
" \n",
"\n",
"let _ = check 100 integral_value 2 2 2 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
2020-01-07 16:45:14 +01:00
"# 13. 3 1 2 2"
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
2020-01-06 19:43:55 +01:00
"let _ = png_image \"3_1_22.png\""
2019-12-05 16:16:00 +01:00
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$|J\\rangle = \\hat{T}_{ijm}^{kln}|I\\rangle$\n",
"\n",
2019-12-18 12:56:35 +01:00
"$\\sum_{a}\n",
" \\hat{T}_{ij}^{al} \\hat{T}_{am}^{kn} \n",
" + \\hat{T}_{ij}^{ka} \\hat{T}_{am}^{ln} \n",
" + \\hat{T}_{im}^{ka} \\hat{T}_{ja}^{ln} \n",
" + \\hat{T}_{im}^{an} \\hat{T}_{aj}^{kl} \n",
" + \\hat{T}_{jm}^{an} \\hat{T}_{ia}^{kl} \n",
" + \\hat{T}_{jm}^{la} \\hat{T}_{ia}^{kn} \n",
"$\n",
"\n",
2019-12-05 16:16:00 +01:00
"$$\n",
2019-12-18 12:56:35 +01:00
"\\sum_{a} \\langle i j || a l \\rangle \\left[ a m || k n \\right] +\n",
" \\langle i j || k a \\rangle \\left[ a m || l n \\right] +\n",
" \\langle i m || k a \\rangle \\left[ j a || l n \\right] +\n",
" \\langle i m || a n \\rangle \\left[ a j || k l \\right] +\n",
" \\langle j m || a n \\rangle \\left[ i a || k l \\right] +\n",
" \\langle j m || l a \\rangle \\left[ i a || k n \\right] \n",
2019-12-05 16:16:00 +01:00
"$$"
]
},
{
"cell_type": "code",
2020-01-07 16:45:14 +01:00
"execution_count": null,
2019-12-05 16:16:00 +01:00
"metadata": {},
2020-01-07 16:45:14 +01:00
"outputs": [],
2019-12-05 16:16:00 +01:00
"source": [
"let integral_value ki kj = \n",
2019-12-18 12:56:35 +01:00
" let i, j, m, k, l, n, s1, s2, s3, phase =\n",
2019-12-05 16:16:00 +01:00
" match Excitation.of_det ki kj with\n",
" | Excitation.(Triple (phase,\n",
" { hole=h1 ; particle=p1 ; spin=s1 },\n",
" { hole=h2 ; particle=p2 ; spin=s2 },\n",
" { hole=h3 ; particle=p3 ; spin=s3 }) ) -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase\n",
" | _ -> assert false\n",
" in\n",
"\n",
" let result = \n",
2020-01-06 19:43:55 +01:00
" let open Spin in \n",
" match s1, s2, s3 with\n",
" | Alfa, Alfa, Alfa\n",
" | Beta, Beta, Beta -> \n",
" sum mos_cabs (fun a -> \n",
" h_two i j a k s1 s2 *. f_two m a l n s3 s3 \n",
" +. h_two i j a n s1 s2 *. f_two m a k l s3 s2 \n",
" +. h_two i m a l s1 s3 *. f_two j a k n s2 s3 \n",
" +. h_two j m a k s2 s3 *. f_two i a l n s1 s3 \n",
" +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n",
" -. h_two i j a l s1 s2 *. f_two m a k n s3 s3 \n",
" -. h_two i m a k s1 s3 *. f_two j a l n s2 s3 \n",
" -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n",
" -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 )\n",
" | Alfa, Alfa, Beta\n",
" | Beta, Beta, Alfa -> \n",
" sum mos_cabs (fun a -> \n",
" h_two i j a l s1 s2 *. f_two a m k n s1 s3\n",
" +. h_two i m k a s1 s3 *. f_two j a l n s2 s3\n",
" +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n",
" +. h_two j m l a s2 s3 *. f_two i a k n s1 s3\n",
" -. h_two i j a k s1 s2 *. f_two a m l n s1 s3\n",
" -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n",
" -. h_two i m l a s1 s3 *. f_two j a k n s2 s3\n",
" -. h_two j m k a s2 s3 *. f_two i a l n s1 s3\n",
2019-12-18 12:56:35 +01:00
" ) \n",
2020-01-06 19:43:55 +01:00
" | Alfa, Beta, Beta\n",
" | Beta, Alfa, Alfa -> \n",
" sum mos_cabs (fun a -> \n",
" h_two i j a l s1 s2 *. f_two a m k n s1 s3 \n",
" +. h_two i m a n s1 s3 *. f_two a j k l s1 s2 \n",
" +. h_two i m k a s1 s3 *. f_two j a l n s2 s3 \n",
" +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n",
" -. h_two i j a n s1 s2 *. f_two a m k l s1 s2 \n",
" -. h_two i j k a s1 s2 *. f_two m a l n s2 s3 \n",
" -. h_two i m a l s1 s3 *. f_two a j k n s1 s3 \n",
" -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 \n",
" ) \n",
" | Beta, Alfa, Beta\n",
" | Alfa, Beta, Alfa -> assert false (*TODO *)\n",
2019-12-05 16:16:00 +01:00
" in\n",
" match phase with\n",
" | Phase.Pos -> result\n",
" | Phase.Neg -> -. result\n",
2019-12-04 18:13:54 +01:00
" \n",
"\n",
2020-01-06 19:43:55 +01:00
"let _ = check 200 integral_value 3 1 2 2"
2019-12-18 12:56:35 +01:00
]
},
{
2020-01-06 19:43:55 +01:00
"cell_type": "code",
"execution_count": null,
2019-12-18 12:56:35 +01:00
"metadata": {
2020-01-06 19:43:55 +01:00
"scrolled": false
2019-12-18 12:56:35 +01:00
},
2020-01-06 19:43:55 +01:00
"outputs": [],
2019-12-18 12:56:35 +01:00
"source": [
2020-01-06 19:43:55 +01:00
"let ki = det_I.(129)\n",
"let kj = det_I.(349)\n",
2019-12-18 12:56:35 +01:00
"\n",
2020-01-06 19:43:55 +01:00
"let alpha_to_string alpha = \n",
2019-12-18 12:56:35 +01:00
" \n",
2020-01-06 19:43:55 +01:00
" let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n",
" \n",
" let i, j, m, k, l, n, s, s', s'', phase =\n",
2019-12-18 12:56:35 +01:00
" match Excitation.of_det ki kj with\n",
2020-01-06 19:43:55 +01:00
" | Excitation.(Triple (phase,\n",
" { hole ; particle ; spin },\n",
" {hole=hole' ; particle=particle' ; spin=spin' }, \n",
" {hole=hole''; particle=particle''; spin=spin''} )) ->\n",
" hole, hole', hole'', particle, particle', particle'', spin, spin', spin'', phase\n",
" | _ -> assert false\n",
" in\n",
" let spin = function\n",
" | Spin.Alfa -> 0\n",
" | _ -> 1\n",
" in\n",
" exc0.(i).(spin s ) <- \"i\" \n",
" ; exc0.(j).(spin s' ) <- \"j\" \n",
" ; exc0.(k).(spin s ) <- \"k\" \n",
" ; exc0.(l).(spin s' ) <- \"l\" \n",
" ; exc0.(m).(spin s'') <- \"m\" \n",
" ; exc0.(n).(spin s'') <- \"n\" \n",
" ;\n",
" let s0, s0', s0'' = s, s', s'' in\n",
" \n",
" let i, j, k, l, s, s', p1 =\n",
" match Excitation.of_det ki alpha with\n",
2019-12-18 12:56:35 +01:00
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
2020-01-06 19:43:55 +01:00
" hole, hole', particle, particle', spin, spin', phase\n",
2019-12-18 12:56:35 +01:00
" | _ -> assert false\n",
2020-01-06 19:43:55 +01:00
" in\n",
" \n",
" if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"p\";\n",
" if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"p\";\n",
" if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"q\";\n",
" if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"q\";\n",
" \n",
" let string_h = \n",
" Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n",
" exc0.(i).(spin s )\n",
" exc0.(j).(spin s')\n",
" exc0.(k).(spin s )\n",
" exc0.(l).(spin s')\n",
" (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n",
" (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n",
" in \n",
" \n",
" let i, j, k, l, s, s', p2 =\n",
" match Excitation.of_det alpha kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" \n",
" let string_f = \n",
" Printf.sprintf \"f_two %s %s %s %s %s %s\" \n",
" exc0.(i).(spin s )\n",
" exc0.(j).(spin s')\n",
" exc0.(k).(spin s )\n",
" exc0.(l).(spin s')\n",
" (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n",
" (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n",
" in\n",
" (*\n",
" Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n",
" Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n",
2019-12-18 12:56:35 +01:00
" *)\n",
"\n",
" \n",
2020-01-06 19:43:55 +01:00
" let sign = \n",
" if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n",
2019-12-18 12:56:35 +01:00
" in\n",
2020-01-06 19:43:55 +01:00
" sign ^ string_h ^ string_f\n",
" \n",
2019-12-18 12:56:35 +01:00
"\n",
2020-01-06 19:43:55 +01:00
"let alpha_debug alpha = \n",
" \n",
" let i, j, k, l, s, s', p1 =\n",
" match Excitation.of_det ki alpha with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" Printf.printf \"%d %d %d %d \" i j k l;\n",
" \n",
" let i, j, k, l, s, s', p2 =\n",
" match Excitation.of_det alpha kj with\n",
" | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
" hole, hole', particle, particle', spin, spin', phase\n",
" | _ -> assert false\n",
" in\n",
" (*\n",
" Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n",
" Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n",
" *)\n",
" Printf.printf \"%d %d %d %d \\n%!\" i j k l\n",
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"\n",
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" \n",
"let strings = \n",
" Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
" generate_alphas ki kj 3 1 2 2\n",
" |> Array.of_list\n",
" |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n",
" |> Array.to_list\n",
" |> List.sort_uniq compare\n",
" |> Array.of_list\n",
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"\n",
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"let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n",
"\n",
"let _ =\n",
" let v =\n",
" let alphas =\n",
" generate_alphas ki kj 3 1 2 2\n",
" (*\n",
" |> List.filter (fun alpha ->\n",
" let x = alpha_to_string alpha in\n",
" x = strings.(6)\n",
" )\n",
" *)\n",
" in\n",
" (*\n",
" List.iter alpha_debug alphas ;\n",
" Printf.printf \"\\n%!\";\n",
" *)\n",
" compute_HaaF ki alphas kj \n",
" in\n",
" let x = (integral_value ki kj) in\n",
" Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n"
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]
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