Work : modifs intérations
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Work.ipynb
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Work.ipynb
@ -1593,9 +1593,10 @@
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" if n == 0 then\n",
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" prev_iter\n",
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" else\n",
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"(*\n",
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" let m_Phi = prev_iter.coef\n",
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" in\n",
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" (* Calcul de tous les alpha -> Matrice *)\n",
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" let m_alpha m_Phi =\n",
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" let f_alpha m_Phi =\n",
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"\n",
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" (* Calcul de toutes les intégrales B_12 -> Matrice *)\n",
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" let m_b12 = Mat.init_cols n_ao n_ao (fun i j -> \n",
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@ -1612,15 +1613,17 @@
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" ) i j\n",
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" )\n",
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" in\n",
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" Mat.init_cols n_ao n_ao ( fun i j ->\n",
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" asin(m_b12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.) )\n",
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" )\n",
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" Mat.init_cols n_ao n_ao ( fun i j ->\n",
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" asin(m_b12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.) )\n",
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" )\n",
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" )\n",
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"\n",
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" in\n",
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" (* Matrice de rotation 2 par 2 *)\n",
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" let m_R m_alpha = \n",
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" let m_R = \n",
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"\n",
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" let m_alpha = f_alpha m_Phi\n",
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" in\n",
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" (* Valeur du plus grand angle alpha*)\n",
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" let alpha = \n",
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"\n",
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@ -1634,20 +1637,19 @@
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" in\n",
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" let indice_j = ij_max_alpha / n_ao + 1\n",
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"\n",
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" in\n",
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" m_alpha.{indice_i,indice_j}\n",
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" in\n",
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" m_alpha.{indice_i,indice_j}\n",
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" in\n",
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" Printf.printf \"%f\\n%!\" alpha;\n",
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"\n",
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" \n",
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" Mat.init_cols 2 2 (fun i j -> if i=j then cos alpha\n",
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" Mat.init_cols 2 2 (fun i j -> if i=j then cos alpha\n",
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" else if i>j then sin alpha \n",
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" else -. sin alpha )\n",
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"\n",
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" in\n",
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" (* Fonction de calcul de ksi~ (matrice n par 2), nouvelle matrice par application de la matrice de rotation dans laquelle \n",
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" on obtient les deux orbitales que l'on va réinjecter dans la matrice Phi*)\n",
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" let m_Ksi_tilde m_R = \n",
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" let m_Ksi_tilde = \n",
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"\n",
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" (* Fonction d'extraction des 2 vecteurs propres i et j de la matrice des OMs pour les mettres dans la matrice Ksi \n",
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" (n par 2) pour appliquer R afin d'effectuer la rotation des orbitales *) (* {1,2} -> 1ere ligne, 2e colonne *)\n",
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@ -1656,42 +1658,43 @@
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" let q = indice_j\n",
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" in\n",
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" let m_Ksi = Mat.init_cols n_ao 2 (fun i j -> if j=1 then m_Phi.{i,p} else m_Phi.{i,q} )\n",
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" in\n",
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" gemm m_Ksi m_R\n",
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" in\n",
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" gemm m_Ksi m_R\n",
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"\n",
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" in\n",
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" (* Construction de la nouvelle matrice d'OMs phi~ *)\n",
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" let m_Phi_tilde m_Ksi m_Ksi_tilde = \n",
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"\n",
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" \n",
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" (* Matrice intérmédiare pour l'injection de ksi~ (i~ et j~) dans la matrice Phi *)\n",
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" let m_Psi_tilde = Mat.init_cols n_ao n_ao (fun i j -> if j=q then m_Ksi_tilde.{i,2}\n",
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" else if j=p then m_Ksi_tilde.{i,1}\n",
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" else 0.)\n",
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" in\n",
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" (* Matrice intérmédiaire où les orbitales i et j ont été supprimées et remplacées par des 0, par soustraction de la \n",
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" matrice Phi par la matrice *)\n",
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" let m_interm = \n",
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"\n",
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" (* Matrice intérmédiare pour l'injection de ksi~ (i~ et j~) dans la matrice Phi *)\n",
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" let m_Psi_tilde = Mat.init_cols n_ao n_ao (fun i j -> if j=q then m_Ksi_tilde.{i,2}\n",
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" else if j=p then m_Ksi_tilde.{i,1}\n",
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" else 0.)\n",
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" in\n",
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" (* Matrice intermédiaire pour supprimer ksi (i et j) dans la matrice Phi *) \n",
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" let m_Psi = Mat.init_cols n_ao n_ao (fun i j -> if j=q then m_Ksi.{i,2}\n",
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" else if j=p then m_Ksi.{i,1}\n",
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" else 0.)\n",
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"\n",
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" in\n",
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" Mat.sub m_Phi m_Psi\n",
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" in\n",
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" Mat.sub m_Phi m_Psi\n",
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" Mat.add m_Psi_tilde m_interm\n",
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" in \n",
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" let coef = m_Phi_tilde m_Ksi m_Ksi_tilde\n",
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" in\n",
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" *)\n",
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" let coef = Mat.add m_Psi_tilde m_interm in\n",
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" let loc = alpha \n",
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" in\n",
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" let result = \n",
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" { coef ; loc }\n",
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" in\n",
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" if loc -. prev_iter.loc < 1.e-5 \n",
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" if abs_float (loc -. prev_iter.loc) < 1.e-5 \n",
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" then\n",
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" result\n",
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" { coef ; loc }\n",
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" else\n",
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" let result = prev_iter\n",
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" prev_iter\n",
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" in\n",
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" new_Phi result (n-1)\n",
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"\n",
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@ -1706,159 +1709,7 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"(* Fonction pour itérer , cc critère de convergence*) \n",
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"(* Localisation de Edminstion *)\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 = n_ao - 1;;\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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"\n",
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"(*Calcul des intégrales*) \n",
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"let integral_general g i j =\n",
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"Array.map (fun a ->\n",
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" let v = \n",
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" Array.map (fun b ->\n",
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" let u = \n",
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" Array.map (fun e ->\n",
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" let t = Array.map (fun f ->\n",
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" (g a b e f i j) *. ERI.get_phys ee_ints a e b f\n",
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" ) (Util.array_range 1 n_ao)\n",
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" in sum t\n",
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" ) (Util.array_range 1 n_ao)\n",
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" in sum u\n",
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" ) (Util.array_range 1 n_ao)\n",
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" in sum v\n",
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") (Util.array_range 1 n_ao)\n",
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"|> sum \n",
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"\n",
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"\n",
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"let m_Phi = m_C;;\n",
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"\n",
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"type iteration = \n",
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"{ coef : Mat.t ;\n",
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" loc : float ;\n",
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"}\n",
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"\n",
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"let prev_iter = {coef = m_Phi ;loc = 0. }\n",
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"\n",
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"(* Calcul de la nouvelle matrice Phi après rotations *)\n",
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"let rec new_Phi prev_iter n = \n",
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" Printf.printf \"%d\\n%!\" n;\n",
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" if n == 0 then\n",
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" prev_iter\n",
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" else\n",
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"\n",
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" (* Calcul de tous les alpha -> Matrice *)\n",
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" let m_alpha m_Phi =\n",
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"\n",
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" (* Calcul de toutes les intégrales B_12 -> Matrice *)\n",
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" let m_b12 = Mat.init_cols n_mo n_mo (fun i j -> \n",
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" integral_general (fun a b e f i j ->\n",
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" ( m_Phi.{a,i} *. m_Phi.{b,i} -. m_Phi.{a,j} *. m_Phi.{b,j} ) *. m_Phi.{e,i} *. m_Phi.{f,j}\n",
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" ) i j\n",
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" )\n",
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" in\n",
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" (* Calcul de toutes les intégrales A_12 -> Matrice *)\n",
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" let m_a12 = Mat.init_cols n_mo n_mo (fun i j ->\n",
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" integral_general (fun a b e f i j -> m_Phi.{a,i} *. m_Phi.{b,i} *. m_Phi.{e,i} *. m_Phi.{f,j} \n",
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" -. 0.25 *. ( m_Phi.{e,i} *. m_Phi.{f,i} -. m_Phi.{e,j} *. m_Phi.{f,j} ) \n",
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" *. ( m_Phi.{a,i} *. m_Phi.{b,i} -. m_Phi.{a,j} *. m_Phi.{b,j} )\n",
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" ) i j\n",
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" )\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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" asin(m_b12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.) )\n",
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" )\n",
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" )\n",
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"\n",
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" in\n",
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" (* Matrice de rotation 2 par 2 *)\n",
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" let m_R m_alpha = \n",
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"\n",
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" (* Valeur du plus grand angle alpha*)\n",
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" let alpha = \n",
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"\n",
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" (* Extraction du plus grand angle alpha*)\n",
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" let ij_max_alpha = Mat.as_vec m_alpha\n",
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" |> iamax\n",
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" in\n",
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"\n",
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" (* Indices du plus grand angle alpha *)\n",
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" let indice_i = ij_max_alpha mod n_mo\n",
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" in\n",
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" let indice_j = ij_max_alpha / n_mo + 1\n",
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"\n",
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" in\n",
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" m_alpha.{indice_i,indice_j}\n",
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" in\n",
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" Printf.printf \"%f\\n%!\" alpha;\n",
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"\n",
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"\n",
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" Mat.init_cols 2 2 (fun i j -> if i=j then cos alpha\n",
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" else if i>j then sin alpha \n",
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" else -. sin alpha )\n",
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"\n",
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" in\n",
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" (* Fonction de calcul de ksi~ (matrice n par 2), nouvelle matrice par application de la matrice de rotation dans laquelle \n",
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" on obtient les deux orbitales que l'on va réinjecter dans la matrice Phi*)\n",
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" let m_Ksi_tilde m_R = \n",
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"\n",
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" (* Fonction d'extraction des 2 vecteurs propres i et j de la matrice des OMs pour les mettres dans la matrice Ksi \n",
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" (n par 2) pour appliquer R afin d'effectuer la rotation des orbitales *) (* {1,2} -> 1ere ligne, 2e colonne *)\n",
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" let p = indice_i\n",
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" in\n",
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" let q = indice_j\n",
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" in\n",
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" let m_Ksi = Mat.init_cols n_ao 2 (fun i j -> if j=1 then m_Phi.{i,p} else m_Phi.{i,q} )\n",
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" in\n",
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" gemm m_Ksi m_R\n",
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"\n",
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" in\n",
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" (* Construction de la nouvelle matrice d'OMs phi~ *)\n",
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" let m_Phi_tilde m_Ksi m_Ksi_tilde = \n",
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"\n",
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" (* Matrice intérmédiaire où les orbitales i et j ont été supprimées et remplacées par des 0, par soustraction de la \n",
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" matrice Phi par la matrice *)\n",
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" let m_interm = \n",
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"\n",
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" (* Matrice intérmédiare pour l'injection de ksi~ (i~ et j~) dans la matrice Phi *)\n",
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" let m_Psi_tilde = Mat.init_cols n_ao n_ao (fun i j -> if j=q then m_Ksi_tilde.{i,2}\n",
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" else if j=p then m_Ksi_tilde.{i,1}\n",
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" else 0.)\n",
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" in\n",
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" (* Matrice intermédiaire pour supprimer ksi (i et j) dans la matrice Phi *) \n",
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" let m_Psi = Mat.init_cols n_ao n_ao (fun i j -> if j=q then m_Ksi.{i,2}\n",
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" else if j=p then m_Ksi.{i,1}\n",
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" else 0.)\n",
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"\n",
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" in\n",
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" Mat.sub m_Phi m_Psi\n",
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" in\n",
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"\n",
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" let coef = Mat.add m_Psi_tilde m_interm in\n",
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" let loc = alpha \n",
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" in\n",
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" let result = \n",
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" { coef ; loc }\n",
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" in\n",
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" if loc -. prev_iter.loc < 1.e-5 then\n",
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" result\n",
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" else\n",
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" let result = prev_iter\n",
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" in\n",
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" new_Phi result (n-1)"
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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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" new_Phi prev_iter 10;;"
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" new_Phi prev_iter 3;;"
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]
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},
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{
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