Work_test : nouvelle boucle avec variation du pas
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"hidden": true
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},
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"outputs": [],
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"source": [
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"(* Algorithme de localisation des orbitales : Méthode de Boys ou Edminston-Ruedenberg *)\n",
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"\n",
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"(*I : Position et base atomique*)\n",
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" (* 1. Fonction création chaîne linéaire de n H *)\n",
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" (* 2. Base atomique *)\n",
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"\n",
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"(* II : Hartree-Fock *)\n",
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" (* 1. Def pour HF *)\n",
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" (* 2. Calcul de Hartree-Fock*)\n",
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" \n",
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"(* III : Définition des fonctions pour la localisation *)\n",
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" (* 1. Définitions de base nécessaire pour la suite *) \n",
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" (* 2. Fonction de calcul de tous les alpha ER *)\n",
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" (* 3. Fonction de calcul de tous les alpha Boys *)\n",
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" (* 4. Pattern matching : calcul de alpha et de D *)\n",
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" (* 5. Norme de alpha *)\n",
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" (* 6. Détermination alpha_max et ses indices i et j *) \n",
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" (* 7. Matrice de rotation 2 par 2 *)\n",
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" (* 8. Fonction : i,j -> matrice Ksi (n par 2) *)\n",
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" (* 9. Fonction : i~,j~ -> matrice Ksi~ (n par 2) *)\n",
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" (* 10. Matrice intermédiaire pour supprimer i j et ajouter i~ et j~ *)\n",
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" (* 11. Matrice intérmédiaire où les orbitales i et j ont été supprimées et remplacées par des 0*)\n",
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" \n",
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"(* IV : Boucle de localisation des OMs *) \n",
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"\n",
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"(* V : Fonctions pour la séparation et le rassemblement des matrices *)\n",
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" (* 1. Fonction de création d'une list d'entier à partir d'un vecteur de float*)\n",
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" (* 2. Fonction créant une liste à partir des éléments manquant d'une autre liste, dans l'intervalle [1 ; n_mo] *)\n",
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" (* 3. Fonction de séparation d'une matrice en 2 sous matrice *)\n",
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" (* 4. Liste des OMs occupées *)\n",
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" (* 5. Fonction de rassemblement de 2 matrices *) \n",
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" (* 6. Séparation des OMs -> m_occ : OMs occupées; m_vir : OMs vacantes *)\n",
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" \n",
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"(* VI : Calcul et assemblage des OMs occupées/virtuels *) \n",
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" \n",
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"(* VII : Calcul Coef CI *)\n",
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" (* 1. Def de la mo_basis pour le HF pre CI *)\n",
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" (* 2. HF pour CI *)\n",
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" (* 3. Calcul de coef CI *)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"open Lacaml.D\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(*I : Position et base atomique*)\n",
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"\n",
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"(* 1. Fonction création chaîne linéaire de n H *)\n",
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"\n",
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"let xyz d n = \n",
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" let accu = \"\"\n",
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" in\n",
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" let rec toto accu d n =\n",
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" let accu = \n",
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" if n=0 \n",
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" then accu ^ \"\"\n",
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" else\n",
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" match n with \n",
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" | 1 -> \"H 0. 0. 0.\\n\" ^ accu\n",
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" | x -> toto (\"H\" ^ \" \" ^ string_of_float( d *. float_of_int(n-1)) ^ \" 0. 0.\\n\" ^ accu ) d (n-1)\n",
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" in\n",
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" accu\n",
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" in string_of_int(n) ^ \"\\nH\" ^ string_of_int(n) ^ \"\\n\" ^ toto accu d n;;\n",
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" \n",
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"let xyz_string = xyz 1.8 20;;\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"hidden": true
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},
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"outputs": [],
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"source": [
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"(* 2. Base atomique *)\n",
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"\n",
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"let basis_string = \n",
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"\"\n",
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"HYDROGEN\n",
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"S 6\n",
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"1 0.3552322122E+02 0.9163596281E-02\n",
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"2 0.6513143725E+01 0.4936149294E-01\n",
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"3 0.1822142904E+01 0.1685383049E+00\n",
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"4 0.6259552659E+00 0.3705627997E+00\n",
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"5 0.2430767471E+00 0.4164915298E+00\n",
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"6 0.1001124280E+00 0.1303340841E+00\n",
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"\"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"hidden": true
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},
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"outputs": [],
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"source": [
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"(* II : Hartree-Fock *)\n",
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"\n",
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"(* 1. Def pour HF *)\n",
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"\n",
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"let nuclei =\n",
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" Nuclei.of_xyz_string xyz_string\n",
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" \n",
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"let basis = \n",
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" Basis.of_nuclei_and_basis_string nuclei basis_string\n",
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" \n",
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"let simulation = \n",
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" Simulation.make ~charge:0 ~multiplicity:1 ~nuclei basis\n",
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" \n",
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"let ao_basis = \n",
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" Simulation.ao_basis simulation\n",
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" \n",
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"let nocc =\n",
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" let elec = Simulation.electrons simulation in\n",
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" Electrons.n_alfa elec\n",
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" "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"hidden": true
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},
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"outputs": [],
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"source": [
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"(* 2. Calcul de Hartree-Fock*)\n",
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"\n",
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"let hf = HartreeFock.make simulation\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"hidden": true
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},
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"outputs": [],
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"source": [
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"let mo_basis = MOBasis.of_hartree_fock hf\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"hidden": true
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},
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"outputs": [],
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"source": [
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"let mo_coef = MOBasis.mo_coef mo_basis\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(* III : Définition des fonctions pour la localisation *)\n",
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"\n",
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"(* 1. Définitions de base nécessaire pour la suite *)\n",
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"let ee_ints = AOBasis.ee_ints ao_basis;;\n",
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"let m_C = MOBasis.mo_coef mo_basis;;\n",
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"let n_ao = Mat.dim1 m_C ;;\n",
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"let n_mo = Mat.dim2 m_C ;;\n",
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"let multipoles = \n",
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" AOBasis.multipole ao_basis;;\n",
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" \n",
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"let sum a = \n",
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" Array.fold_left (fun accu x -> accu +. x) 0. a\n",
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" \n",
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"let pi = 3.14159265358979323846264338;;\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(* 2. Fonction de calcul de tous les alpha ER *)\n",
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"let f_alpha m_C =\n",
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"\n",
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" let n_mo = Mat.dim2 m_C in\n",
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" (*let t0 = Sys.time () in*)\n",
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" \n",
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" let m_b12 = Mat.init_cols n_mo n_mo (fun i j -> 0.) in\n",
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" let m_a12 = Mat.init_cols n_mo n_mo (fun i j -> 0.) in\n",
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" let v_d = Vec.init n_mo (fun i -> 0.) in\n",
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" \n",
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" (* Tableaux temporaires *)\n",
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" let m_pqr =\n",
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" Bigarray.(Array3.create Float64 fortran_layout n_ao n_ao n_ao)\n",
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" in\n",
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" let m_qr_i = Mat.create (n_ao*n_ao) n_mo in\n",
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" let m_ri_j = Mat.create (n_ao*n_mo) n_mo in\n",
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" let m_ij_k = Mat.create (n_mo*n_mo) n_mo in\n",
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" \n",
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" Array.iter (fun s ->\n",
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" (* Grosse boucle externe sur s *)\n",
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" Array.iter (fun r ->\n",
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" Array.iter (fun q ->\n",
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" Array.iter (fun p ->\n",
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" m_pqr.{p,q,r} <- ERI.get_phys ee_ints p q r s\n",
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" ) (Util.array_range 1 n_ao)\n",
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" ) (Util.array_range 1 n_ao)\n",
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" ) (Util.array_range 1 n_ao);\n",
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" \n",
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" (* Conversion d'un tableau a 3 indices en une matrice nao x nao^2 *)\n",
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" let m_p_qr =\n",
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" Bigarray.reshape (Bigarray.genarray_of_array3 m_pqr) [| n_ao ; n_ao*n_ao |]\n",
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" |> Bigarray.array2_of_genarray\n",
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" in\n",
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" \n",
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" let m_qr_i =\n",
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" (* (qr,i) = <i r|q s> = \\sum_p <p r | q s> C_{pi} *)\n",
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" gemm ~transa:`T ~c:m_qr_i m_p_qr m_C\n",
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" in\n",
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" \n",
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" let m_q_ri =\n",
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" (* Transformation de la matrice (qr,i) en (q,ri) *)\n",
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" Bigarray.reshape_2 (Bigarray.genarray_of_array2 m_qr_i) n_ao (n_ao*n_mo)\n",
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" in\n",
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" \n",
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" let m_ri_j =\n",
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" (* (ri,j) = <i r | j s> = \\sum_q <i r | q s> C_{bj} *)\n",
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" gemm ~transa:`T ~c:m_ri_j m_q_ri m_C\n",
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" in\n",
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" \n",
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" let m_r_ij =\n",
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" (* Transformation de la matrice (ri,j) en (r,ij) *)\n",
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" Bigarray.reshape_2 (Bigarray.genarray_of_array2 m_ri_j) n_ao (n_mo*n_mo)\n",
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" in\n",
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" \n",
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" let m_ij_k =\n",
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" (* (ij,k) = <i k | j s> = \\sum_r <i r | j s> C_{rk} *)\n",
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" gemm ~transa:`T ~c:m_ij_k m_r_ij m_C\n",
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" in\n",
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" \n",
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" let m_ijk =\n",
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" (* Transformation de la matrice (ei,j) en (e,ij) *)\n",
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" Bigarray.reshape (Bigarray.genarray_of_array2 m_ij_k) [| n_mo ; n_mo ; n_mo |]\n",
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" |> Bigarray.array3_of_genarray\n",
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" in\n",
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" \n",
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" Array.iter (fun j ->\n",
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" Array.iter (fun i ->\n",
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" m_b12.{i,j} <- m_b12.{i,j} +. m_C.{s,j} *. (m_ijk.{i,i,i} -. m_ijk.{j,i,j});\n",
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" m_a12.{i,j} <- m_a12.{i,j} +. m_ijk.{i,i,j} *. m_C.{s,j} -.\n",
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" 0.25 *. ( (m_ijk.{i,i,i} -. m_ijk.{j,i,j}) *. m_C.{s,i} +.\n",
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" (m_ijk.{j,j,j} -. m_ijk.{i,j,i}) *. m_C.{s,j})\n",
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" ) (Util.array_range 1 n_mo);\n",
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" v_d.{j} <- v_d.{j} +. m_ijk.{j,j,j} *. m_C.{s,j}\n",
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" ) (Util.array_range 1 n_mo)\n",
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" ) (Util.array_range 1 n_ao);\n",
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" \n",
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" (*let t1 = Sys.time () in\n",
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" Printf.printf \"t = %f s\\n%!\" (t1 -. t0);*)\n",
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" \n",
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" (Mat.init_cols n_mo n_mo ( fun i j ->\n",
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" if i= j then 0.\n",
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" else 0.25 *. (acos(-. m_a12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2. ))))\n",
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" ),Vec.sum v_d);;\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(* 3. Fonction de calcul de tous les alpha Boys *)\n",
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"let f_alpha_boys m_C = \n",
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" let n_mo = Mat.dim2 m_C\n",
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" in\n",
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" let phi_x_phi =\n",
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" Multipole.matrix_x multipoles \n",
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" |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C\n",
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" in \n",
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" let phi_y_phi =\n",
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" Multipole.matrix_y multipoles \n",
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" |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C\n",
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" in\n",
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" let phi_z_phi =\n",
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" Multipole.matrix_z multipoles \n",
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" |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C\n",
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" in \n",
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"\n",
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" let m_b12= \n",
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" let b12 g = Mat.init_cols n_mo n_mo ( fun i j ->\n",
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" (g.{i,i} -. g.{j,j}) *. g.{i,j})\n",
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"\n",
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" in \n",
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" Mat.add (b12 phi_x_phi) ( Mat.add (b12 phi_y_phi) (b12 phi_z_phi))\n",
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" in \n",
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" let m_a12 =\n",
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" let a12 g = Mat.init_cols n_mo n_mo ( fun i j -> \n",
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" g.{i,j} *. g.{i,j} -. 0.25 *. ((g.{i,i} -. g.{j,j}) *. (g.{i,i} -. g.{j,j})))\n",
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" in\n",
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" Mat.add (a12 phi_x_phi) ( Mat.add (a12 phi_y_phi) (a12 phi_z_phi))\n",
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" in\n",
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" (Mat.init_cols n_mo n_mo ( fun i j -> \n",
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" if i=j \n",
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" then 0.\n",
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" else 0.25 *. acos(-. m_a12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.) ))),\n",
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" Vec.sum(Vec.init n_mo ( fun i -> (phi_x_phi.{i,i})**2. +. (phi_y_phi.{i,i})**2. +. (phi_z_phi.{i,i})**2.)));;\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(* 4. Pattern matching : calcul de alpha et de D *)\n",
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"type alphad = {\n",
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"m_alpha : Mat.t;\n",
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"d : float;\n",
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"}\n",
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"\n",
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"let m_alpha_d methode m_C = \n",
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" let alpha methode =\n",
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" \n",
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" match methode with \n",
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" | \"Boys\"\n",
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" | \"boys\" -> let alpha_boys , d_boys = f_alpha_boys m_C in {m_alpha = alpha_boys; d = d_boys}\n",
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" | \"ER\"\n",
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" | \"er\" -> let alpha_er , d_er = f_alpha m_C in {m_alpha = alpha_er; d = d_er}\n",
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" | _ -> invalid_arg \"Unknown method, please enter Boys or ER\"\n",
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"\n",
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"in \n",
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"alpha methode;;\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(* 5. Norme de alpha *)\n",
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"\n",
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"let norme m = \n",
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" let vec_m = Mat.as_vec m\n",
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" in\n",
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" let vec2 = Vec.sqr vec_m\n",
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"in sqrt(Vec.sum vec2);;\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(* 6. Détermination alpha_max et ses indices i et j.\n",
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"Si alpha max > pi/2 on soustrait pi/2 à la matrice des alphas de manière récursive *)\n",
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"type alphaij = {\n",
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" alpha_max : float;\n",
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" indice_ii : int;\n",
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" indice_jj : int;};;\n",
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"\n",
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"let rec new_m_alpha m_alpha m_C n_rec_alpha=\n",
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"\n",
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" let n_mo = Mat.dim2 m_C\n",
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||||
" in\n",
|
||||
" let alpha_m =\n",
|
||||
" \n",
|
||||
" (*Printf.printf \"%i\\n%!\" n_rec_alpha;*)\n",
|
||||
" \n",
|
||||
" if n_rec_alpha == 0 \n",
|
||||
" then m_alpha \n",
|
||||
" else Mat.init_cols n_mo n_mo (fun i j -> \n",
|
||||
" if (m_alpha.{i,j}) > (pi /. 2.) \n",
|
||||
" then (m_alpha.{i,j} -. ( pi /. 2.))\n",
|
||||
" else if m_alpha.{i,j} < -. pi /. 2.\n",
|
||||
" then (m_alpha.{i,j} +. ( pi /. 2.))\n",
|
||||
" else if m_alpha.{i,j} < 0. \n",
|
||||
" then -. m_alpha.{i,j}\n",
|
||||
" else m_alpha.{i,j} )\n",
|
||||
" in \n",
|
||||
" \n",
|
||||
" (*Util.debug_matrix \"alpha_m\" alpha_m;*)\n",
|
||||
" \n",
|
||||
" (* Détermination de l'emplacement du alpha max *)\n",
|
||||
" let max_element3 alpha_m = \n",
|
||||
" Mat.as_vec alpha_m\n",
|
||||
" |> iamax\n",
|
||||
" in\n",
|
||||
" \n",
|
||||
" (* indice i et j du alpha max *)\n",
|
||||
" let indice_ii, indice_jj = \n",
|
||||
" let max = max_element3 alpha_m \n",
|
||||
" in\n",
|
||||
" (max - 1) mod n_mo +1, (max - 1) / n_mo +1\n",
|
||||
" in\n",
|
||||
" \n",
|
||||
" (* Valeur du alpha max*)\n",
|
||||
" let alpha alpha_m = \n",
|
||||
" let i = indice_ii \n",
|
||||
" in\n",
|
||||
" let j = indice_jj \n",
|
||||
" in\n",
|
||||
" alpha_m.{i,j}\n",
|
||||
" \n",
|
||||
" (*Printf.printf \"%i %i\\n%!\" i j;*)\n",
|
||||
" \n",
|
||||
" in\n",
|
||||
" let alpha_max = alpha alpha_m \n",
|
||||
" in\n",
|
||||
" \n",
|
||||
" (*Printf.printf \"%f\\n%!\" alpha_max;*)\n",
|
||||
" \n",
|
||||
" if alpha_max < pi /. 2.\n",
|
||||
" then {alpha_max; indice_ii; indice_jj}\n",
|
||||
" else new_m_alpha alpha_m m_C (n_rec_alpha-1);;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* 7. Matrice de rotation 2 par 2 *)\n",
|
||||
"let f_R alpha =\n",
|
||||
" Mat.init_cols 2 2 (fun i j -> \n",
|
||||
" if i=j \n",
|
||||
" then cos alpha\n",
|
||||
" else if i>j \n",
|
||||
" then sin alpha \n",
|
||||
" else -. sin alpha )\n",
|
||||
";;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* 8. Fonction d'extraction des 2 vecteurs propres i et j de la matrice des OMs pour les mettres dans la matrice Ksi (n par 2)\n",
|
||||
"pour appliquer R afin d'effectuer la rotation des orbitales *) (* {1,2} -> 1ere ligne, 2e colonne *)\n",
|
||||
"let f_Ksi indice_i indice_j m_C =\n",
|
||||
" let n_ao = Mat.dim1 m_C\n",
|
||||
"in\n",
|
||||
"Mat.init_cols n_ao 2 (fun i j -> if j=1 then m_C.{i,indice_i} else m_C.{i,indice_j} );;\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* 9. Fonction de calcul de ksi~ (matrice n par 2), nouvelle matrice par application de la matrice de rotation dans laquelle\n",
|
||||
"on obtient les deux orbitales que l'on va réinjecter dans la matrice Phi*)\n",
|
||||
"let f_Ksi_tilde m_R m_Ksi m_C = gemm m_Ksi m_R;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* 10. Fonction pour la création de matrice intermédiaire pour supprimer i j et ajouter i~ et j~ *)\n",
|
||||
"let f_k mat indice_i indice_j m_C = \n",
|
||||
"let n_mo = Mat.dim2 m_C\n",
|
||||
" in\n",
|
||||
" let n_ao = Mat.dim1 m_C\n",
|
||||
"in\n",
|
||||
"Mat.init_cols n_ao n_mo (fun i j -> \n",
|
||||
" if j=indice_i \n",
|
||||
" then mat.{i,1}\n",
|
||||
" else if j=indice_j \n",
|
||||
" then mat.{i,2}\n",
|
||||
" else 0.)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* 11. Matrice intérmédiaire où les orbitales i et j ont été supprimées et remplacées par des 0, par soustraction de la matrice\n",
|
||||
"des coefs par la matrice *)\n",
|
||||
"let f_interm m_C m_Psi = Mat.sub m_C m_Psi;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* Fonction de calcul de la nouvelle matrice de coef après rotation d'un angle alpha *)\n",
|
||||
"let new_m_C m_C methode m_alpha epsilon =\n",
|
||||
" \n",
|
||||
" (* alphaij contient le alpha max ainsi que ses indices i et j *)\n",
|
||||
" let n_rec_alpha = 10 (* Nombre ditération max pour réduire les valeurs de alpha *)\n",
|
||||
" in\n",
|
||||
" let alphaij = new_m_alpha m_alpha m_C n_rec_alpha \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (* Valeur de alpha max après calcul *) (* Epsilon = Pas <1. , 1. -> normal, sinon Pas plus petit *)\n",
|
||||
" let alpha = (alphaij.alpha_max) *. epsilon \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (*Printf.printf \"%f\\n%!\" alpha;*)\n",
|
||||
" \n",
|
||||
" (* Indice i et j du alpha max après calcul *)\n",
|
||||
" let indice_i = alphaij.indice_ii \n",
|
||||
" in\n",
|
||||
" let indice_j = alphaij.indice_jj \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (*Printf.printf \"%i %i\\n%!\" indice_i indice_j;*)\n",
|
||||
" \n",
|
||||
" (* Matrice de rotation *)\n",
|
||||
" let m_R = f_R alpha \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (*Util.debug_matrix \"m_R\" m_R;*)\n",
|
||||
"\n",
|
||||
" (* Matrice qui va subir la rotation *)\n",
|
||||
" let m_Ksi = f_Ksi indice_i indice_j m_C \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (*Util.debug_matrix \"m_Ksi\" m_Ksi;*)\n",
|
||||
"\n",
|
||||
" (* Matrice ayant subit la rotation *)\n",
|
||||
" let m_Ksi_tilde = f_Ksi_tilde m_R m_Ksi m_C \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (*Util.debug_matrix \"m_Ksi_tilde\" m_Ksi_tilde;*)\n",
|
||||
"\n",
|
||||
" (* Matrice pour supprimerles coef des orbitales i et j dans la matrice des coef *)\n",
|
||||
" let m_Psi = f_k m_Ksi indice_i indice_j m_C\n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (*Util.debug_matrix \"m_Psi\" m_Psi;*)\n",
|
||||
"\n",
|
||||
" (* Matrice pour ajouter les coef des orbitales i~ et j~ dans la matrice des coef *)\n",
|
||||
" let m_Psi_tilde = f_k m_Ksi_tilde indice_i indice_j m_C \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" (*Util.debug_matrix \"m_Psi_tilde\" m_Psi_tilde;*)\n",
|
||||
"\n",
|
||||
" (* Matrice avec les coef des orbitales i et j remplacés par 0 *)\n",
|
||||
" let m_interm = f_interm m_C m_Psi \n",
|
||||
" in\n",
|
||||
" \n",
|
||||
" (*Util.debug_matrix \"m_interm\" m_interm;*)\n",
|
||||
" \n",
|
||||
"(* Matrice après rotation *)\n",
|
||||
"Mat.add m_Psi_tilde m_interm"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"\n",
|
||||
"(* Localisation de Edminstion ou de Boys *)\n",
|
||||
"\n",
|
||||
"(* Calcul de la nouvelle matrice des coefficient après n rotation d'orbitales *)\n",
|
||||
"let rec localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc max_D=\n",
|
||||
"\n",
|
||||
" (*Printf.printf \"%i\\n%!\" n;\n",
|
||||
" Printf.printf \"%f\\n%!\" epsilon;*)\n",
|
||||
"\n",
|
||||
" (*Util.debug_matrix \"m_C\" m_C;*)\n",
|
||||
"\n",
|
||||
" (*Util.debug_matrix \"new_alpha_m\" prev_m_alpha;*)\n",
|
||||
"\n",
|
||||
"if n == 0 \n",
|
||||
" then m_C\n",
|
||||
" else\n",
|
||||
"\n",
|
||||
" let m_new_m_C = new_m_C m_C methode prev_m_alpha epsilon\n",
|
||||
" in\n",
|
||||
" (* Fonction de pattern matching en fonction de la méthode *)\n",
|
||||
" let alphad = m_alpha_d methode m_new_m_C\n",
|
||||
" in\n",
|
||||
" \n",
|
||||
" (* D critère à maximiser *)\n",
|
||||
" let critere_D = alphad.d \n",
|
||||
" in\n",
|
||||
" let diff = max_D -. critere_D \n",
|
||||
" in\n",
|
||||
" let max_D =\n",
|
||||
" if diff > 0.\n",
|
||||
" then max_D\n",
|
||||
" else critere_D\n",
|
||||
" in\n",
|
||||
" (*Printf.printf \"%f\\n%!\" max_D;*)\n",
|
||||
" Printf.printf \"%e\\n%!\" critere_D;\n",
|
||||
" (*Printf.printf \"%f\\n%!\" diff;*)\n",
|
||||
" \n",
|
||||
" (* Matrice des alphas *)\n",
|
||||
" let m_alpha = alphad.m_alpha\n",
|
||||
" in\n",
|
||||
" (*let norme_alpha = norme m_alpha\n",
|
||||
" in \n",
|
||||
" Printf.printf \"%f\\n%!\" norme_alpha;*)\n",
|
||||
"if diff > 0. && epsilon >= 0.1\n",
|
||||
" then localisation m_C methode (epsilon /. 2.) (n-1) critere_D prev_m_alpha cc max_D\n",
|
||||
" else\n",
|
||||
" let epsilon = 1.\n",
|
||||
" in\n",
|
||||
" \n",
|
||||
"(*Util.debug_matrix \"new_alpha_m\" m_alpha;*)\n",
|
||||
"(*Util.debug_matrix \"m_new_m_C\" m_new_m_C;*)\n",
|
||||
"\n",
|
||||
"if diff**2. < cc**2.\n",
|
||||
" then m_new_m_C\n",
|
||||
" else\n",
|
||||
"localisation m_new_m_C methode epsilon (n-1) critere_D m_alpha cc max_D;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"let localise localisation m_C methode epsilon n cc=\n",
|
||||
" let alphad = m_alpha_d methode m_C \n",
|
||||
" in\n",
|
||||
" let prev_m_alpha = alphad.m_alpha\n",
|
||||
" in \n",
|
||||
" let prev_critere_D = 0.\n",
|
||||
" in\n",
|
||||
" let max_D = 0.\n",
|
||||
"in\n",
|
||||
"localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc max_D;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* V : Fonctions pour la séparation et le rassemblement des matrices *)\n",
|
||||
"\n",
|
||||
"(* 1. Fonction de création d'une list d'entier à partir d'un vecteur de float*)\n",
|
||||
"let int_list vec = \n",
|
||||
" let float_list = Vec.to_list vec\n",
|
||||
" in\n",
|
||||
" let g a = int_of_float(a)\n",
|
||||
"in List.map g float_list;;\n",
|
||||
"\n",
|
||||
"(* 2. Fonction créant une liste à partir des éléments manquant d'une autre liste, dans l'intervalle [1 ; n_mo] *)\n",
|
||||
"let miss_elem mat list = \n",
|
||||
" let n_mo = Mat.dim2 mat\n",
|
||||
" in\n",
|
||||
" let vec = Vec.init (n_mo) (fun i ->\n",
|
||||
" if List.mem i list\n",
|
||||
" then 0.\n",
|
||||
" else float_of_int(i))\n",
|
||||
" in\n",
|
||||
" let list_int = int_list vec \n",
|
||||
"in\n",
|
||||
"List.filter (fun x -> x > 0) list_int;;\n",
|
||||
"\n",
|
||||
"(* 3. Fonction de séparation d'une matrice en 2 sous matrice, la première matrice correspondant aux colonnes de la matrice dont le numéro est présent\n",
|
||||
"dans la liste et la seconde à celles dont le numéro de colonne n'est pas présent dans la liste *)\n",
|
||||
"let split_mat mat list =\n",
|
||||
" let vec_of_mat = Mat.to_col_vecs mat\n",
|
||||
" in\n",
|
||||
" let f a = vec_of_mat.(a-1)\n",
|
||||
" in\n",
|
||||
" let vec_list_1 = List.map f list\n",
|
||||
" in\n",
|
||||
" let list_2 = miss_elem mat list\n",
|
||||
" in\n",
|
||||
" let vec_list_2 = List.map f list_2\n",
|
||||
"in (Mat.of_col_vecs_list vec_list_1,Mat.of_col_vecs_list vec_list_2);;\n",
|
||||
"\n",
|
||||
"(* 4. Liste des OMs occupées *)\n",
|
||||
"let list_occ = \n",
|
||||
" let vec_occ = Vec.init (nocc) (fun i -> float_of_int(i))\n",
|
||||
"in int_list vec_occ;;\n",
|
||||
"\n",
|
||||
"(* 5. Fonction de rassemblement de 2 matrices *)\n",
|
||||
"let assemble m_occ m_vir = Mat.init_cols n_ao n_mo ( fun i j ->\n",
|
||||
" if j > nocc \n",
|
||||
" then m_vir.{i,j-(n_mo - nocc)}\n",
|
||||
" else m_occ.{i,j});;\n",
|
||||
" \n",
|
||||
"(* 6. Séparation des OMs -> m_occ : OMs occupées; m_vir : OMs vacantes *)\n",
|
||||
"let m_occ , m_vir = split_mat m_C list_occ;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"localise localisation m_occ \"Boys\" 1. 1000 10e-5;;"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "OCaml 4.10.0",
|
||||
"language": "OCaml",
|
||||
"name": "ocaml-jupyter"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": "text/x-ocaml",
|
||||
"file_extension": ".ml",
|
||||
"mimetype": "text/x-ocaml",
|
||||
"name": "OCaml",
|
||||
"nbconverter_exporter": null,
|
||||
"pygments_lexer": "OCaml",
|
||||
"version": "4.10.0"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 4
|
||||
}
|
||||
|
|
@ -161,14 +161,40 @@
|
|||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"let xyz_string = \n",
|
||||
"(*let xyz_string = \n",
|
||||
"\"3\n",
|
||||
"Water\n",
|
||||
"O 0. 0. 0.\n",
|
||||
"H -0.756950272703377558 0. -0.585882234512562827\n",
|
||||
"H 0.756950272703377558 0. -0.585882234512562827\n",
|
||||
"\"\n",
|
||||
" "
|
||||
" *)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(* Fonction création chaîne linéaire de n H *)\n",
|
||||
"\n",
|
||||
"let xyz d n = \n",
|
||||
" let accu = \"\"\n",
|
||||
" in\n",
|
||||
" let rec toto accu d n =\n",
|
||||
" let accu = \n",
|
||||
" if n=0 \n",
|
||||
" then accu ^ \"\"\n",
|
||||
" else\n",
|
||||
" match n with \n",
|
||||
" | 1 -> \"H 0. 0. 0.\\n\" ^ accu\n",
|
||||
" | x -> toto (\"H\" ^ \" \" ^ string_of_float( d *. float_of_int(n-1)) ^ \" 0. 0.\\n\" ^ accu ) d (n-1)\n",
|
||||
" in\n",
|
||||
" accu\n",
|
||||
" in string_of_int(n) ^ \"\\nH\" ^ string_of_int(n) ^ \"\\n\" ^ toto accu d n;;\n",
|
||||
" \n",
|
||||
"let xyz_string = xyz 1.8 10;;"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -199,7 +225,24 @@
|
|||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"let basis_string = \"\n",
|
||||
"\n",
|
||||
"let basis_string = \n",
|
||||
"\"\n",
|
||||
"HYDROGEN\n",
|
||||
"S 6\n",
|
||||
"1 0.3552322122E+02 0.9163596281E-02\n",
|
||||
"2 0.6513143725E+01 0.4936149294E-01\n",
|
||||
"3 0.1822142904E+01 0.1685383049E+00\n",
|
||||
"4 0.6259552659E+00 0.3705627997E+00\n",
|
||||
"5 0.2430767471E+00 0.4164915298E+00\n",
|
||||
"6 0.1001124280E+00 0.1303340841E+00\n",
|
||||
"\"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"(*let basis_string = \"\n",
|
||||
"HYDROGEN\n",
|
||||
"S 4\n",
|
||||
"1 1.301000E+01 1.968500E-02\n",
|
||||
|
|
@ -244,7 +287,8 @@
|
|||
"D 1\n",
|
||||
"1 1.185000E+00 1.0000000\n",
|
||||
"\n",
|
||||
"\""
|
||||
"\"\n",
|
||||
"*)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
|
|||
31
Work.ipynb
31
Work.ipynb
|
|
@ -320,6 +320,29 @@
|
|||
"hidden": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(*let nuclei =\n",
|
||||
" Nuclei.of_xyz_string xyz_string\n",
|
||||
" \n",
|
||||
"let basis = \n",
|
||||
" Basis.of_nuclei_and_basis_string nuclei basis_string\n",
|
||||
" \n",
|
||||
"let simulation = \n",
|
||||
" Simulation.make ~charge:0 ~multiplicity:1 ~nuclei basis\n",
|
||||
" \n",
|
||||
"let ao_basis = \n",
|
||||
" Simulation.ao_basis simulation\n",
|
||||
" \n",
|
||||
"let nocc =\n",
|
||||
" let elec = Simulation.electrons simulation in\n",
|
||||
" Electrons.n_alfa elec*)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"let nuclei =\n",
|
||||
" Nuclei.of_xyz_string xyz_string\n",
|
||||
|
|
@ -1818,7 +1841,7 @@
|
|||
" in\n",
|
||||
" (*let norme_alpha = norme m_alpha\n",
|
||||
" in*)\n",
|
||||
" Util.debug_matrix \"new_alpha_m\" m_alpha;\n",
|
||||
" (*Util.debug_matrix \"new_alpha_m\" m_alpha;*)\n",
|
||||
" (*Printf.printf \"%f\\n%!\" norme_alpha;*)\n",
|
||||
" \n",
|
||||
" (*Util.debug_matrix \"m_alpha\" m_alpha;*)\n",
|
||||
|
|
@ -1833,7 +1856,7 @@
|
|||
" let alpha = (alphaij.alpha_max) *. epsilon \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" Printf.printf \"%f\\n%!\" alpha;\n",
|
||||
" (*Printf.printf \"%f\\n%!\" alpha;*)\n",
|
||||
" \n",
|
||||
" (* Indice i et j du alpha max après calcul *)\n",
|
||||
" let indice_i = alphaij.indice_ii \n",
|
||||
|
|
@ -1890,7 +1913,7 @@
|
|||
"in\n",
|
||||
"\n",
|
||||
"(*Util.debug_matrix \"new_alpha_m\" (f_alpha m_C);*)\n",
|
||||
"Util.debug_matrix \"m_new_m_C\" m_new_m_C;\n",
|
||||
"(*Util.debug_matrix \"m_new_m_C\" m_new_m_C;*)\n",
|
||||
"\n",
|
||||
"if diff**2. < cc**2.\n",
|
||||
" then m_new_m_C\n",
|
||||
|
|
@ -1908,7 +1931,7 @@
|
|||
"(* Fonction / Matrice des coef / Méthode(\"Boys\" ou \"ER\") / Pas(<=1.) \n",
|
||||
"/ Nombre d'itérations max / 0. (valeur de D pour initier la boucle) / critère de convergence sur D*)\n",
|
||||
"\n",
|
||||
"let new_m_boys = localisation m_C \"boys\" 1. 5 0. 10e-7;;\n",
|
||||
"let new_m_boys = localisation m_C \"boys\" 1. 20 0. 10e-7;;\n",
|
||||
"(*let new_m_er = localisation m_C \"ER\" 1. 100 0. 10e-7;;\n",
|
||||
"*)\n"
|
||||
]
|
||||
|
|
|
|||
|
|
@ -204,7 +204,7 @@
|
|||
" accu\n",
|
||||
" in string_of_int(n) ^ \"\\nH\" ^ string_of_int(n) ^ \"\\n\" ^ toto accu d n;;\n",
|
||||
" \n",
|
||||
"let xyz_string = xyz 1.8 10;;\n"
|
||||
"let xyz_string = xyz 1.8 20;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -305,15 +305,6 @@
|
|||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"hidden": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"let nuclei =\n",
|
||||
" Nuclei.of_xyz_string xyz_string\n",
|
||||
|
|
@ -1467,7 +1458,7 @@
|
|||
" let alpha = (alphaij.alpha_max) *. epsilon \n",
|
||||
" in\n",
|
||||
"\n",
|
||||
" Printf.printf \"%f\\n%!\" alpha;\n",
|
||||
" (*Printf.printf \"%f\\n%!\" alpha;*)\n",
|
||||
" \n",
|
||||
" (* Indice i et j du alpha max après calcul *)\n",
|
||||
" let indice_i = alphaij.indice_ii \n",
|
||||
|
|
@ -1528,13 +1519,14 @@
|
|||
"(* Localisation de Edminstion ou de Boys *)\n",
|
||||
"\n",
|
||||
"(* Calcul de la nouvelle matrice des coefficient après n rotation d'orbitales *)\n",
|
||||
"let rec localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc=\n",
|
||||
"let rec localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc max_D=\n",
|
||||
"\n",
|
||||
" Printf.printf \"%i\\n%!\" n;\n",
|
||||
" (*Printf.printf \"%i\\n%!\" n;\n",
|
||||
" Printf.printf \"%f\\n%!\" epsilon;*)\n",
|
||||
"\n",
|
||||
" Util.debug_matrix \"m_C\" m_C;\n",
|
||||
" (*Util.debug_matrix \"m_C\" m_C;*)\n",
|
||||
"\n",
|
||||
" Util.debug_matrix \"new_alpha_m\" prev_m_alpha;\n",
|
||||
" (*Util.debug_matrix \"new_alpha_m\" prev_m_alpha;*)\n",
|
||||
"\n",
|
||||
"if n == 0 \n",
|
||||
" then m_C\n",
|
||||
|
|
@ -1549,8 +1541,16 @@
|
|||
" (* D critère à maximiser *)\n",
|
||||
" let critere_D = alphad.d \n",
|
||||
" in\n",
|
||||
" \n",
|
||||
" Printf.printf \"%f\\n%!\" critere_D;\n",
|
||||
" let diff = max_D -. critere_D \n",
|
||||
" in\n",
|
||||
" let max_D =\n",
|
||||
" if diff > 0.\n",
|
||||
" then max_D\n",
|
||||
" else critere_D\n",
|
||||
" in\n",
|
||||
" (*Printf.printf \"%f\\n%!\" max_D;*)\n",
|
||||
" Printf.printf \"%e\\n%!\" critere_D;\n",
|
||||
" (*Printf.printf \"%f\\n%!\" diff;*)\n",
|
||||
" \n",
|
||||
" (* Matrice des alphas *)\n",
|
||||
" let m_alpha = alphad.m_alpha\n",
|
||||
|
|
@ -1558,18 +1558,19 @@
|
|||
" (*let norme_alpha = norme m_alpha\n",
|
||||
" in \n",
|
||||
" Printf.printf \"%f\\n%!\" norme_alpha;*)\n",
|
||||
"if diff > 0. && epsilon > 0.09\n",
|
||||
" then localisation m_C methode (epsilon /. 2.) (n-1) critere_D prev_m_alpha cc max_D\n",
|
||||
" else\n",
|
||||
" let epsilon = 1.\n",
|
||||
" in\n",
|
||||
" \n",
|
||||
" let diff = prev_critere_D -. critere_D\n",
|
||||
"\n",
|
||||
"in\n",
|
||||
"\n",
|
||||
"(*Util.debug_matrix \"new_alpha_m\" m_alpha;*)\n",
|
||||
"(*Util.debug_matrix \"m_new_m_C\" m_new_m_C;*)\n",
|
||||
"\n",
|
||||
"if diff**2. < cc**2.\n",
|
||||
" then m_new_m_C\n",
|
||||
" else\n",
|
||||
"localisation m_new_m_C methode epsilon (n-1) critere_D m_alpha cc;;\n"
|
||||
"localisation m_new_m_C methode epsilon (n-1) critere_D m_alpha cc max_D;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1578,26 +1579,19 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"(*\n",
|
||||
"\n",
|
||||
"let localise localisation m_C methode epsilon n cc=\n",
|
||||
" let alphad = m_alpha_d methode m_C \n",
|
||||
" in\n",
|
||||
" let prev_m_alpha = alphad.m_alpha\n",
|
||||
" in \n",
|
||||
" let prev_critere_D = 0.\n",
|
||||
" in\n",
|
||||
" let max_D = 0.\n",
|
||||
"in\n",
|
||||
"localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc;;\n",
|
||||
"localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc max_D;;\n",
|
||||
"\n",
|
||||
"localise localisation m_C \"Boys\" 1. 100 10e-7;;\n",
|
||||
"*)\n",
|
||||
"m_C;;\n",
|
||||
"\n",
|
||||
"let alphad = m_alpha_d \"boys\" m_C \n",
|
||||
"\n",
|
||||
"let prev_m_alpha = alphad.m_alpha\n",
|
||||
"let prev_critere_D = 0.;;\n",
|
||||
"\n",
|
||||
"localisation m_C \"Boys\" 1. 5 prev_critere_D prev_m_alpha 10e-7;;"
|
||||
"localise localisation m_C \"Boys\" 1. 1000 10e-5;;\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
Loading…
Reference in New Issue