Work: modif boucle test alpha<pi/2, match

This commit is contained in:
Yann Damour 2020-05-04 14:42:00 +02:00
parent 2151c8927c
commit 26507ec7a0

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@ -1034,7 +1034,7 @@
"let n_ao = Mat.dim1 m_C ;;\n", "let n_ao = Mat.dim1 m_C ;;\n",
"let n_mo = n_ao - 1;;\n", "let n_mo = n_ao - 1;;\n",
"\n", "\n",
"let m_alpha_boys multipoles = \n", "let m_alpha_boys = \n",
"\n", "\n",
" let multipoles = \n", " let multipoles = \n",
" AOBasis.multipole ao_basis\n", " AOBasis.multipole ao_basis\n",
@ -1054,55 +1054,22 @@
" in \n", " in \n",
"\n", "\n",
" let m_b12= \n", " let m_b12= \n",
" let b12 g = Mat.init_cols n_mo n_mo ( fun i j ->\n", " let b12 g = Mat.init_cols n_ao n_ao ( fun i j ->\n",
" (g.{i,i} -. g.{j,j}) *. g.{i,j})\n", " (g.{i,i} -. g.{j,j}) *. g.{i,j})\n",
"\n", "\n",
" in \n", " in \n",
" Mat.add (b12 phi_x_phi) ( Mat.add (b12 phi_y_phi) (b12 phi_z_phi))\n", " Mat.add (b12 phi_x_phi) ( Mat.add (b12 phi_y_phi) (b12 phi_z_phi))\n",
" in \n", " in \n",
" let m_a12 =\n", " let m_a12 =\n",
" let a12 g = Mat.init_cols n_mo n_mo ( fun i j -> \n", " let a12 g = Mat.init_cols n_ao n_ao ( fun i j -> \n",
" g.{i,j} *. g.{i,j} \n", " g.{i,j} *. g.{i,j} \n",
" -. (1. /. 4.) *. (g.{i,i} -. g.{j,j} *. g.{i,i} -. g.{j,j}))\n", " -. (1. /. 4.) *. (g.{i,i} -. g.{j,j} *. g.{i,i} -. g.{j,j}))\n",
" in\n", " in\n",
" Mat.add (a12 phi_x_phi) ( Mat.add (a12 phi_y_phi) (a12 phi_z_phi))\n", " Mat.add (a12 phi_x_phi) ( Mat.add (a12 phi_y_phi) (a12 phi_z_phi))\n",
" in\n", " in\n",
" Mat.init_cols n_mo n_mo ( fun i j ->\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", " asin(m_b12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.) )));;\n",
"\n", " \n"
"\n",
"(* let m_a12 =\n",
" \n",
" let m_a12_x = Mat.init_cols n_mo n_mo ( fun i j -> \n",
" phi_x_phi.{i,j} *. phi_x_phi.{i,j} \n",
" -. (1. /. 4.)(phi_x_phi.{i,i} -. phi_x_phi.{j,j} *. phi_x_phi.{i,i} -. phi_x_phi.{j,j}))\n",
" in\n",
" let m_a12_y = Mat.init_cols n_mo n_mo ( fun i j -> \n",
" phi_y_phi.{i,j} *. phi_y_phi.{i,j} \n",
" -. (1. /. 4.)(phi_y_phi.{i,i} -. phi_y_phi.{j,j} *. phi_y_phi.{i,i} -. phi_y_phi.{j,j}))\n",
" in\n",
" let m_a12_z = Mat.init_cols n_mo n_mo ( fun i j -> \n",
" phi_z_phi.{i,j} *. phi_z_phi.{i,j} \n",
" -. (1. /. 4.)(phi_z_phi.{i,i} -. phi_z_phi.{j,j} *. phi_z_phi.{i,i} -. phi_z_phi.{j,j}))\n",
" in \n",
" Mat.add m_a12_x Mat.add (m_a12_y m_a12_z)\n",
"\n",
" let m_b12 = \n",
"\n",
" let m_b12_x = Mat.init_cols n_mo n_mo ( fun i j ->\n",
" (phi_x_phi.{i,i} -. phi_x_phi.{j,j}) *. phi_x_phi.{i,j})\n",
" in \n",
" let m_b12_y = Mat.init_cols n_mo n_mo ( fun i j ->\n",
" (phi_y_phi.{i,i} -. phi_y_phi.{j,j}) *. phi_y_phi.{i,j})\n",
" in \n",
" let m_b12_z = Mat.init_cols n_mo n_mo ( fun i j ->\n",
" (phi_z_phi.{i,i} -. phi_z_phi.{j,j}) *. phi_z_phi.{i,j})\n",
" in \n",
" Mat.add m_b12_x Mat.add (m_b12_y m_b12_z)\n",
"\n",
"in\n",
"Mat.init_cols n_mo n_mo ( fun i j ->\n",
" asin(m_b12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.) )));;*)\n"
] ]
}, },
{ {
@ -1358,14 +1325,14 @@
"outputs": [], "outputs": [],
"source": [ "source": [
"(* Calcul de toutes les intégrales B_12 -> Matrice *)\n", "(* Calcul de toutes les intégrales B_12 -> Matrice *)\n",
"let m_b12 = Mat.init_cols n_mo n_mo (fun i j -> \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", "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", " ( 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", " ) i j\n",
" )\n", " )\n",
"\n", "\n",
"(* Calcul de toutes les intégrales A_12 -> Matrice *)\n", "(* Calcul de toutes les intégrales A_12 -> Matrice *)\n",
"let m_a12 = Mat.init_cols n_mo n_mo (fun i j ->\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,i} *. m_C.{e,i} *. m_C.{f,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,j} \n",
" -. 0.25 *. ( m_C.{e,i} *. m_C.{f,i} -. m_C.{e,j} *. 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", " *. ( m_C.{a,i} *. m_C.{b,i} -. m_C.{a,j} *. m_C.{b,j} )\n",
@ -1373,7 +1340,7 @@
" )\n", " )\n",
"\n", "\n",
"(* Calcul de tous les alpha -> Matrice *)\n", "(* Calcul de tous les alpha -> Matrice *)\n",
"let m_alpha = Mat.init_cols n_mo n_mo ( fun i j ->\n", "let m_alpha = 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", " asin(m_b12.{i,j} /. sqrt((m_a12.{i,j}**2.) +. (m_b12.{i,j}**2.) )\n",
" )\n", " )\n",
" )" " )"
@ -1390,13 +1357,104 @@
"|> iamax;;\n", "|> iamax;;\n",
"\n", "\n",
"(* Indices du plus grand angle alpha *)\n", "(* Indices du plus grand angle alpha *)\n",
"let indice_i = ij_max_alpha mod n_mo;;\n", "let indice_i = ij_max_alpha mod n_ao;;\n",
"let indice_j = ij_max_alpha / n_mo + 1;;\n", "let indice_j = ij_max_alpha / n_ao + 1;;\n",
"\n", "\n",
"(* Valeur du plus grand angle alpha*)\n", "(* Valeur du plus grand angle alpha*)\n",
"let alpha = m_alpha.{indice_i,indice_j};;" "let alpha = m_alpha.{indice_i,indice_j};;"
] ]
}, },
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"(* Test algo alpha < pi/. 2. *)\n",
"let prev_alpha = m_alpha\n",
"\n",
"let rec m_new_alpha m_alpha n = \n",
" \n",
" Printf.printf \"%d\\n%!\" n;\n",
" if n == 0 then\n",
" prev_alpha\n",
" else\n",
" \n",
" \n",
" let m_alpha =\n",
"\n",
" Mat.init_cols n_ao n_ao (fun i j -> if m_alpha.{i,j} > (3.14159265359 /. 2.) \n",
" then (m_alpha.{i,j} -. (3.14159265359 /. 2.))\n",
" else m_alpha.{i,j})\n",
"\n",
" in\n",
" (* Extraction du plus grand angle alpha*)\n",
" let ij_max_alpha = Mat.as_vec m_alpha\n",
" |> iamax\n",
" in\n",
" (* Indices du plus grand angle alpha *)\n",
" let indice_i = ij_max_alpha mod n_ao\n",
" in\n",
" let indice_j = ij_max_alpha / n_ao + 1\n",
" in\n",
" (* Valeur du plus grand angle alpha*)\n",
" let alpha = m_alpha.{indice_i,indice_j}\n",
" in\n",
"\n",
" if alpha < (3.14159265359 /. 2.)\n",
" then\n",
" m_alpha\n",
" else\n",
" let m_alpha = prev_alpha\n",
" in\n",
" m_new_alpha m_alpha (n-1);;"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"m_new_alpha m_alpha 2;;\n",
"alpha;;"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"(* Test méthode de calcul de alpha *)\n",
"let calcul_alpha_2 methode = \n",
"\n",
"let alpha_boys = 1.\n",
"in\n",
"let alpha_er = 2.\n",
"in\n",
"let alpha methode =\n",
" match methode with \n",
" | \"Boys\"\n",
" | \"boys\" -> alpha_boys\n",
" | \"ER\"\n",
" | \"er\" -> alpha_er\n",
" | _ -> invalid_arg \"Unknown method, please enter Boys or ER\"\n",
"\n",
"in \n",
"(alpha methode)**2.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"calcul_alpha_2 \"ER\";;\n"
]
},
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
@ -1485,6 +1543,163 @@
"## Réécriture pour itérerer ER" "## Réécriture pour itérerer ER"
] ]
}, },
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"(* Fonction pour itérer , cc critère de convergence*) \n",
"(* Localisation de Edminstion *)\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 = n_ao - 1;;\n",
"let sum a = \n",
" Array.fold_left (fun accu x -> accu +. x) 0. a\n",
";;\n",
"\n",
"(*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",
"let m_Phi = m_C;;\n",
"\n",
"type iteration = \n",
"{ coef : Mat.t ;\n",
" loc : float ;\n",
"}\n",
"\n",
"let prev_iter = {coef = m_Phi ;loc = 0. }\n",
"\n",
"(* Calcul de la nouvelle matrice Phi après rotations *)\n",
"let rec new_Phi prev_iter n = \n",
" Printf.printf \"%d\\n%!\" n;\n",
" if n == 0 then\n",
" prev_iter\n",
" else\n",
"(*\n",
" (* Calcul de tous les alpha -> Matrice *)\n",
" let m_alpha m_Phi =\n",
"\n",
" (* Calcul de toutes les intégrales B_12 -> Matrice *)\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_Phi.{a,i} *. m_Phi.{b,i} -. m_Phi.{a,j} *. m_Phi.{b,j} ) *. m_Phi.{e,i} *. m_Phi.{f,j}\n",
" ) i j\n",
" )\n",
" in\n",
" (* Calcul de toutes les intégrales A_12 -> Matrice *)\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_Phi.{a,i} *. m_Phi.{b,i} *. m_Phi.{e,i} *. m_Phi.{f,j} \n",
" -. 0.25 *. ( m_Phi.{e,i} *. m_Phi.{f,i} -. m_Phi.{e,j} *. m_Phi.{f,j} ) \n",
" *. ( m_Phi.{a,i} *. m_Phi.{b,i} -. m_Phi.{a,j} *. m_Phi.{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",
" )\n",
" )\n",
"\n",
" in\n",
" (* Matrice de rotation 2 par 2 *)\n",
" let m_R m_alpha = \n",
"\n",
" (* Valeur du plus grand angle alpha*)\n",
" let alpha = \n",
"\n",
" (* Extraction du plus grand angle alpha*)\n",
" let ij_max_alpha = Mat.as_vec m_alpha\n",
" |> iamax\n",
" in\n",
"\n",
" (* Indices du plus grand angle alpha *)\n",
" let indice_i = ij_max_alpha mod n_ao\n",
" in\n",
" let indice_j = ij_max_alpha / n_ao + 1\n",
"\n",
" in\n",
" m_alpha.{indice_i,indice_j}\n",
" in\n",
" Printf.printf \"%f\\n%!\" alpha;\n",
"\n",
" \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",
"\n",
" in\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 m_Ksi_tilde m_R = \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",
" (n par 2) pour appliquer R afin d'effectuer la rotation des orbitales *) (* {1,2} -> 1ere ligne, 2e colonne *)\n",
" let p = indice_i\n",
" in\n",
" let q = indice_j\n",
" in\n",
" 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",
" in\n",
" gemm m_Ksi m_R\n",
"\n",
" in\n",
" (* Construction de la nouvelle matrice d'OMs phi~ *)\n",
" let m_Phi_tilde m_Ksi m_Ksi_tilde = \n",
"\n",
" (* Matrice intérmédiaire où les orbitales i et j ont été supprimées et remplacées par des 0, par soustraction de la \n",
" matrice Phi par la matrice *)\n",
" let m_interm = \n",
"\n",
" (* Matrice intérmédiare pour l'injection de ksi~ (i~ et j~) dans la matrice Phi *)\n",
" let m_Psi_tilde = Mat.init_cols n_ao n_ao (fun i j -> if j=q then m_Ksi_tilde.{i,2}\n",
" else if j=p then m_Ksi_tilde.{i,1}\n",
" else 0.)\n",
" in\n",
" (* Matrice intermédiaire pour supprimer ksi (i et j) dans la matrice Phi *) \n",
" let m_Psi = Mat.init_cols n_ao n_ao (fun i j -> if j=q then m_Ksi.{i,2}\n",
" else if j=p then m_Ksi.{i,1}\n",
" else 0.)\n",
"\n",
" in\n",
" Mat.sub m_Phi m_Psi\n",
" in\n",
" *)\n",
" let coef = Mat.add m_Psi_tilde m_interm in\n",
" let loc = alpha \n",
" in\n",
" let result = \n",
" { coef ; loc }\n",
" in\n",
" if loc -. prev_iter.loc < 1.e-5 \n",
" then\n",
" result\n",
" else\n",
" let result = prev_iter\n",
" in\n",
" new_Phi result (n-1)\n",
"\n",
"\n",
"\n",
"\n"
]
},
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
@ -1581,7 +1796,7 @@
" in\n", " in\n",
" Printf.printf \"%f\\n%!\" alpha;\n", " Printf.printf \"%f\\n%!\" alpha;\n",
"\n", "\n",
" \n", "\n",
" Mat.init_cols 2 2 (fun i j -> if i=j then cos 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 if i>j then sin alpha \n",
" else -. sin alpha )\n", " else -. sin alpha )\n",
@ -1620,9 +1835,9 @@
" else 0.)\n", " else 0.)\n",
"\n", "\n",
" in\n", " in\n",
" Mat.sub m_C m_Psi\n", " Mat.sub m_Phi m_Psi\n",
" in\n", " in\n",
" \n", "\n",
" let coef = Mat.add m_Psi_tilde m_interm in\n", " let coef = Mat.add m_Psi_tilde m_interm in\n",
" let loc = alpha \n", " let loc = alpha \n",
" in\n", " in\n",
@ -1634,11 +1849,7 @@
" else\n", " else\n",
" let result = prev_iter\n", " let result = prev_iter\n",
" in\n", " in\n",
" new_Phi result (n-1)\n", " new_Phi result (n-1)"
"\n",
"\n",
"\n",
"\n"
] ]
}, },
{ {