diff --git a/Work.ipynb b/Work.ipynb index 3628f4d..4063908 100644 --- a/Work.ipynb +++ b/Work.ipynb @@ -2110,7 +2110,266 @@ "execution_count": null, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "(* Localisation de Edminstion *)\n", + "\n", + "(* Définitions de base nécessaire pour la suite *)\n", + "let ee_ints = AOBasis.ee_ints ao_basis;;\n", + "let m_C = MOBasis.mo_coef mo_basis;;\n", + "let n_ao = Mat.dim1 m_C ;;\n", + "let n_mo = Mat.dim2 m_C ;;\n", + "let sum a = \n", + " Array.fold_left (fun accu x -> accu +. x) 0. a\n", + " \n", + "(******************************************************************************************************)\n", + "\n", + "(*Fonction général de calcul des intégrales*) \n", + "let integral_general g i j =\n", + "Array.map (fun a ->\n", + " let v = \n", + " Array.map (fun b ->\n", + " let u = \n", + " Array.map (fun e ->\n", + " let t = Array.map (fun f ->\n", + " (g a b e f i j) *. ERI.get_phys ee_ints a e b f\n", + " ) (Util.array_range 1 n_ao)\n", + " in sum t\n", + " ) (Util.array_range 1 n_ao)\n", + " in sum u\n", + " ) (Util.array_range 1 n_ao)\n", + " in sum v\n", + ") (Util.array_range 1 n_ao)\n", + "|> sum \n", + ";;\n", + "\n", + "\n", + "type alphaij = {\n", + " alpha_max : float;\n", + " indice_ii : int;\n", + " indice_jj : int;};;\n", + " \n", + "let n_rec_alpha = 10;;\n", + "\n", + "(******************************************************************************************************)\n", + "\n", + "let rec final_m_C m_C n =\n", + "\n", + "Printf.printf \"%i\\n%!\" n;\n", + "(*\n", + "Util.debug_matrix \"m_C\" m_C;\n", + "*)\n", + "\n", + "if n == 0 then m_C\n", + " else\n", + "\n", + "let new_m_C m_C =\n", + "\n", + " (* Fonction de calcul de tous les alpha -> Matrice, dépend de m_a12, m_b12 qui dépendent de m_C *)\n", + " let f_alpha m_C =\n", + "\n", + " (* Fonction de calcul de toutes les intégrales B_12 -> Matrice, dépend de m_C *)\n", + " let m_b12 = Mat.init_cols n_ao n_ao (fun i j -> \n", + " integral_general (fun a b e f i j ->\n", + " ( m_C.{a,i} *. m_C.{b,i} -. m_C.{a,j} *. m_C.{b,j} ) *. m_C.{e,i} *. m_C.{f,j}\n", + " ) i j\n", + " )\n", + "\n", + " in\n", + " (* Fonction de calcul de toutes les intégrales A_12 -> Matrice, dépend de m_C *)\n", + " let m_a12 = Mat.init_cols n_ao n_ao (fun i j ->\n", + " integral_general (fun a b e f i j -> m_C.{a,i} *. m_C.{b,j} *. m_C.{e,i} *. m_C.{f,j} \n", + " -. 0.25 *. ( m_C.{e,i} *. m_C.{f,i} -. m_C.{e,j} *. m_C.{f,j} ) \n", + " *. ( m_C.{a,i} *. m_C.{b,i} -. m_C.{a,j} *. m_C.{b,j} )\n", + " ) i j\n", + " )\n", + " in\n", + " Mat.init_cols n_ao n_ao ( fun i j ->\n", + " asin(m_b12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.))))\n", + " in\n", + " \n", + " (* Calcul de D *)\n", + " let s_D m_C = \n", + " let v_D = \n", + " let m_D = Mat.init_cols n_ao n_ao (fun i j ->\n", + " integral_general (fun a b e f i j -> m_C.{a,i} *. m_C.{b,i} *. m_C.{e,i} *. m_C.{f,i} \n", + " ) i j\n", + " )\n", + " in Vec.init n_ao ( fun i -> m_D.{i,1} )\n", + " in Vec.sum v_D \n", + " in\n", + " let critere_D = s_D m_C (* Fonction -> constante *)\n", + " in\n", + " Printf.printf \"%f\\n%!\" critere_D;\n", + " \n", + " let m_alpha = f_alpha m_C (* Fonction -> constante *)\n", + " in\n", + " (*\n", + " Util.debug_matrix \"m_alpha\" m_alpha;\n", + " *)\n", + " \n", + " (* Détermination alpha_max et ses indices i et j.\n", + " Si alpha max > pi/2 on soustrait pi/2 à la matrice des alphas de manière récursive *)\n", + " let rec new_m_alpha m_alpha n_rec_alpha=\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_ao n_ao (fun i j -> \n", + " if (m_alpha.{i,j}) > 3.14 /. 2. \n", + " then (m_alpha.{i,j} -. ( 3.14 /. 2.))\n", + " else if m_alpha.{i,j} < -. 3.14 /. 2.\n", + " then (m_alpha.{i,j} +. ( 3.14 /. 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 du alpha max *)\n", + " let indice_ii = \n", + " let max = max_element3 alpha_m (* Fonction -> constante *)\n", + " in\n", + " (*\n", + " Printf.printf \"%i\\n%!\" max;\n", + " *)\n", + " (max - 1) mod n_ao +1 \n", + " in\n", + " \n", + " (* indice j du alpha max *)\n", + " let indice_jj = \n", + " let max = max_element3 alpha_m (* Fonction -> constante *)\n", + " in\n", + " (max - 1) / n_ao +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", + " (*\n", + " Printf.printf \"%i %i\\n%!\" i j;\n", + " *)\n", + " alpha_m.{i,j}\n", + " \n", + " in\n", + " let alpha_max = alpha alpha_m (* Fonction -> constante *)\n", + " in\n", + " Printf.printf \"%f\\n%!\" alpha_max;\n", + " if alpha_max < 3.14 /. 2.\n", + " then {alpha_max; indice_ii; indice_jj}\n", + " else new_m_alpha alpha_m (n_rec_alpha-1)\n", + " in\n", + " let alphaij = new_m_alpha m_alpha n_rec_alpha (* Fonction -> constante *)\n", + " in\n", + " \n", + " (* Valeur de alpha max après calcul *)\n", + " let alpha = alphaij.alpha_max (* Fonction -> constante *)\n", + " in\n", + " \n", + " (* Matrice de rotation 2 par 2 *)\n", + " let f_R alpha =\n", + " Mat.init_cols 2 2 (fun i j -> if i=j then cos alpha\n", + " else if i>j then sin alpha \n", + " else -. sin alpha)\n", + " in\n", + " (* Indice i et j du alpha max après calcul *)\n", + " let indice_i = alphaij.indice_ii (* Fonction -> constante *)\n", + " in\n", + " let indice_j = alphaij.indice_jj (* Fonction -> constante *)\n", + " in\n", + " (*\n", + " Printf.printf \"%i %i\\n%!\" indice_i indice_j;\n", + " *)\n", + " let m_R = f_R alpha (* Fonction -> constante *)\n", + " in\n", + " \n", + " (* 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 = 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", + " in\n", + " let m_Ksi = f_Ksi indice_i indice_j m_C (* Fonction -> constante *)\n", + " in\n", + " (*\n", + " Util.debug_matrix \"m_Ksi\" m_Ksi;\n", + " *)\n", + " (* 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 = gemm m_Ksi m_R\n", + " in\n", + " let m_Ksi_tilde = f_Ksi_tilde m_R m_Ksi (* Fonction -> constante *)\n", + " in\n", + " (*\n", + " Util.debug_matrix \"m_Ksi_tilde\" m_Ksi_tilde;\n", + " *)\n", + " \n", + " (* Pour la réinjection on créer des matrices intérmédiares, une matrice nulle partout sauf sur \n", + " les colonnes de i et j et de i~ et j~. On fait la différence de la première matrice avec la matrice\n", + " des OMs Phi afin de substituer les colonnes de i et j par des zéro et ensuite sommer cette matrice avec \n", + " celle contenant i~ et j~ *)\n", + " \n", + " (* Matrice intérmédiare pour l'injection de ksi~ (i~ et j~) dans la matrice Phi *)\n", + " let f_Psi_tilde m_Ksi_tilde indice_i indice_j = Mat.init_cols n_ao n_ao (fun i j -> if j=indice_i then m_Ksi_tilde.{i,1}\n", + " else if j=indice_j then m_Ksi_tilde.{i,2}\n", + " else 0.)\n", + "\n", + " in\n", + "\n", + " (* Matrice intermédiaire pour supprimer ksi (i et j) dans la matrice Phi *) \n", + " let f_Psi m_Ksi indice_i indice_j = Mat.init_cols n_ao n_ao (fun i j -> if j=indice_i then m_Ksi.{i,1}\n", + " else if j=indice_j then m_Ksi.{i,2}\n", + " else 0.)\n", + " in\n", + " let m_Psi = f_Psi m_Ksi indice_i indice_j (* Fonction -> constante *)\n", + " in\n", + " (*\n", + " Util.debug_matrix \"m_Psi\" m_Psi;\n", + " *)\n", + " let m_Psi_tilde = f_Psi_tilde m_Ksi_tilde indice_i indice_j (* Fonction -> constante *)\n", + " in\n", + " (*\n", + " Util.debug_matrix \"m_Psi_tilde\" m_Psi_tilde;\n", + " *)\n", + " (* Matrice intérmédiaire où les orbitales i et j ont été supprimées et remplacées par des 0, par soustraction de la matrice Phi\n", + " par la matrice *)\n", + " let f_interm m_C m_Psi = Mat.sub m_C m_Psi\n", + " in\n", + " let m_interm = f_interm m_C m_Psi (* Fonction -> constante *)\n", + "in\n", + "Mat.add m_Psi_tilde m_interm\n", + "in\n", + "let m_new_m_C = new_m_C m_C (* Fonction -> constante *)\n", + "in\n", + "(*\n", + "Util.debug_matrix \"m_new_m_C\" m_new_m_C;\n", + "*)\n", + "final_m_C m_new_m_C (n-1);;\n", + "\n", + "(*****************************)\n", + "\n", + "final_m_C m_C 1000;;\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + " \n" + ] }, { "cell_type": "code",