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Optimization and cleaning
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5456852b0e
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@ -225,38 +225,48 @@ let localize mo_basis =
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let multipoles = AOBasis.multipole ao_basis in
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let n_mo = Mat.dim2 m_C in
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let phi_x_phi =
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let x =
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Multipole.matrix_x multipoles
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|> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C
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in
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let phi_y_phi =
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let y =
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Multipole.matrix_y multipoles
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|> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C
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in
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let phi_z_phi =
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let z =
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Multipole.matrix_z multipoles
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|> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C
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in
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let m_b12=
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let b12 g = Mat.init_cols n_mo n_mo ( fun i j ->
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(g.{i,i} -. g.{j,j}) *. g.{i,j})
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in
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Mat.add (b12 phi_x_phi) ( Mat.add (b12 phi_y_phi) (b12 phi_z_phi))
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Mat.init_cols n_mo n_mo ( fun i j ->
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(x.{i,i} -. x.{j,j}) *. x.{i,j} +.
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(y.{i,i} -. y.{j,j}) *. y.{i,j} +.
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(z.{i,i} -. z.{j,j}) *. z.{i,j})
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in
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let m_a12 =
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let a12 g = Mat.init_cols n_mo n_mo ( fun i j ->
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g.{i,j} *. g.{i,j} -. 0.25 *. ((g.{i,i} -. g.{j,j}) *. (g.{i,i} -. g.{j,j})))
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in
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Mat.add (a12 phi_x_phi) ( Mat.add (a12 phi_y_phi) (a12 phi_z_phi))
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Mat.init_cols n_mo n_mo ( fun i j ->
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let x' = x.{i,i} -. x.{j,j}
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and y' = y.{i,i} -. y.{j,j}
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and z' = z.{i,i} -. z.{j,j} in
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x.{i,j} *. x.{i,j} +.
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y.{i,j} *. y.{i,j} +.
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z.{i,j} *. z.{i,j} -.
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0.25 *. (x'*.x' +. y'*.y' +. z'*.z')
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)
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in
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(Mat.init_cols n_mo n_mo ( fun i j ->
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if i=j
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then 0.
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else if +. 0.25 *. atan2 m_b12.{i,j} m_a12.{i,j} >= 0.
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then pi /. 4. -. 0.25 *. atan2 m_b12.{i,j} m_a12.{i,j}
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else -. pi /. 4. -. 0.25 *. atan2 m_b12.{i,j} m_a12.{i,j})
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,0.5 *. 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.)))
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else
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let w = atan2 m_b12.{i,j} m_a12.{i,j} in
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if w >= 0.
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then 0.25 *. (pi -. w)
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else -. 0.25 *. (pi +. w)
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) , 0.5 *. (Vec.sum @@ Vec.init n_mo ( fun i ->
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x.{i,i} *. x.{i,i} +.
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y.{i,i} *. y.{i,i} +.
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z.{i,i} *. z.{i,i} ) )
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)
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in
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(* 4. Function for the original Boys localization *)
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(* Coefficient matrix n_ao x n_mo -> (n_mo x n_mo matrix with angle between orbitals, localization criterion *)
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@ -400,27 +410,24 @@ let localize mo_basis =
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let multipoles = AOBasis.multipole ao_basis in
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let n_mo = Mat.dim2 m_C
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in
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let phi_x_phi =
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let x =
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Multipole.matrix_x multipoles
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|> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C
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in
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let phi_y_phi =
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let y =
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Multipole.matrix_y multipoles
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|> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C
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in
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let phi_z_phi =
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let z =
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Multipole.matrix_z multipoles
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|> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C
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in
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let phi_r2_phi =
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let r2 =
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Multipole.matrix_r2 multipoles
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|> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C
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in
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let m_beta =
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let x = phi_x_phi
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and y = phi_y_phi
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and z = phi_z_phi in
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Mat.init_cols n_mo 2 (fun i j ->
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if j = 1 then
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@ -448,7 +455,7 @@ let localize mo_basis =
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if j = 1
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then 4. *. g.{i,j1} *. (g.{i,i} -. g.{j1,j1})
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else 4. *. g.{i,j2} *. (g.{i,i} -. g.{j2,j2}))
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in Mat.add (gamma phi_x_phi) (Mat.add (gamma phi_y_phi) (gamma phi_z_phi))
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in Mat.add (gamma x) (Mat.add (gamma y) (gamma z))
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in
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let m_theta = Mat.init_cols n_mo 2 (fun i j ->
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@ -459,7 +466,7 @@ let localize mo_basis =
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else +. 0.25 *. atan2 m_gamma.{i,j} m_beta.{i,j})
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in
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let m_critere_B = Vec.init n_mo (fun i ->
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phi_r2_phi.{i,i} -. phi_x_phi.{i,i}**2. -. phi_y_phi.{i,i}**2. -. phi_z_phi.{i,i}**2.)
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r2.{i,i} -. x.{i,i}**2. -. y.{i,i}**2. -. z.{i,i}**2.)
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in m_theta, Vec.sum( m_critere_B)
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in
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@ -517,17 +524,19 @@ let localize mo_basis =
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(* matrix, matrix, integer -> float, integer, integer *)
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let rec new_m_alpha m_alpha m_C n_rec_alpha=
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let pi_2 = 0.5 *. pi in
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let n_mo = Mat.dim2 m_C in
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let alpha_m =
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if n_rec_alpha == 0
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then m_alpha
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if n_rec_alpha == 0 then
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m_alpha
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else
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Mat.init_cols n_mo n_mo (fun i j ->
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if (m_alpha.{i,j}) >= (pi /. 2.)
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then (m_alpha.{i,j} -. ( pi /. 2.))
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else if m_alpha.{i,j} <= -. pi /. 2.
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then (m_alpha.{i,j} +. ( pi /. 2.))
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else m_alpha.{i,j} )
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if m_alpha.{i,j} >= pi_2 then
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m_alpha.{i,j} -. pi_2
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else if m_alpha.{i,j} <= -. pi_2 then
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m_alpha.{i,j} +. pi_2
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else m_alpha.{i,j}
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)
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in
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(* Location of the max angle in the matrix *)
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@ -558,9 +567,10 @@ let localize mo_basis =
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let alpha_max = alpha alpha_m
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in
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if alpha_max < pi /. 2.
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then {alpha_max; indice_ii; indice_jj}
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else new_m_alpha alpha_m m_C (n_rec_alpha-1)
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if alpha_max < pi_2 then
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{alpha_max; indice_ii; indice_jj}
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else
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new_m_alpha alpha_m m_C (n_rec_alpha-1)
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in
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(* 8. Rotation matrix 2x2 *)
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@ -620,7 +630,7 @@ let localize mo_basis =
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(* Calculation of cos tau from the vector tau *)
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(* -> cos(tau) *)
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(* -> integer *)
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(* -> float *)
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let cos_tau = Vec.cos tau in
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(* Matrix cos tau *)
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@ -648,11 +658,6 @@ let localize mo_basis =
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else 0.)
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in
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(* Calculation of the transposed matrix of W (X²) *)
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(* -> transposed matrix of W *)
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(* -> matrix *)
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let transpose_mm = Mat.transpose_copy mm in
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(* Calculation of the vector tau^-1 *)
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(* -> vector tau^-1 *)
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(* -> vector *)
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@ -674,17 +679,17 @@ let localize mo_basis =
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else 0.)
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in
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(* gemm mm (gemm m_cos_tau transpose_mm) -> W cos(tau) Wt *)
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(* W cos(tau) Wt *)
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(* -> matrix *)
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let a = gemm mm (gemm m_cos_tau transpose_mm) in
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let a = gemm mm @@ gemm ~transb:`T m_cos_tau mm in
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(* gemm mm (gemm m_tau_1 ( gemm m_sin_tau (gemm transpose_mm m))) -> W tau^-1 sin(tau) Wt X *)
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(* W tau^-1 sin(tau) Wt X *)
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(* -> matrix *)
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let b = gemm mm (gemm m_tau_1 ( gemm m_sin_tau (gemm transpose_mm m))) in
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let b = gemm mm @@ gemm m_tau_1 @@ gemm m_sin_tau @@ gemm ~transa:`T mm m in
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(* Sum of a + b -> Rotation matrix *)
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(* -> Rotation matrix *)
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(* -> matrix *)
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(* -> matrix *)
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let m_r = Mat.add a b
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in
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gemm m_C m_r
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@ -705,7 +710,7 @@ let localize mo_basis =
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(* Function to apply a rotation with a 2x2 rotation matrix on a n_mo x 2 matrix that contains i and j *)
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(* 2x2 rotation matrix, n_mo x 2 eigenvetors(i and j) matrix -> n_mo x 2 new eigenvetors(i~ and j~) after rotation *)
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(* matrix, matrix -> matrix *)
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(* matrix, matrix -> matrix *)
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let f_Ksi_tilde m_R m_Ksi = gemm m_Ksi m_R
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in
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@ -867,41 +872,30 @@ let localize mo_basis =
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(* IV : Functions to split and assemble matrix *)
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(* Function to create a integer list from a vector of float *)
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(* float vector -> integer list *)
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let int_list vec =
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let float_list = Vec.to_list vec in
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let g a = int_of_float(a)
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in
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List.map g float_list
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in
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(* Function to create a list from the missing elements of an other list*)
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(* Coefficient matrix n_ao x n_mo, list -> list of missing element of the previous list *)
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(* matrix, integer list -> integer list *)
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let miss_elem mat list =
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let miss_elem mat lst =
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let n_mo = Mat.dim2 mat in
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let vec = Vec.init (n_mo) (fun i ->
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if List.mem i list
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then 0.
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else float_of_int(i))
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in
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let list_int = int_list vec
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in
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List.filter (fun x -> x > 0) list_int
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Util.list_range 1 n_mo
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|> List.map (fun i ->
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if List.mem i lst
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then 0
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else i)
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|> List.filter (fun x -> x > 0)
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in
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(* Function to split a matrix in 2 matrix, the first matrix corresponds to the column number whose number is in the list, the second matrix corresponds to the column which are not in the list *)
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(* Coefficient matrix n_ao x n_mo, list -> matrix, matrix *)
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(* matrix, integer list -> matrix, matrix*)
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let split_mat mat list =
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let split_mat mat lst =
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let vec_of_mat = Mat.to_col_vecs mat in
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let f a = vec_of_mat.(a-1) in
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let vec_list_1 = List.map f list in
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let list_2 = miss_elem mat list in
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let vec_list_1 = List.map f lst in
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let list_2 = miss_elem mat lst in
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let vec_list_2 = List.map f list_2
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in
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(Mat.of_col_vecs_list vec_list_1,Mat.of_col_vecs_list vec_list_2)
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@ -911,27 +905,23 @@ let localize mo_basis =
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(* Function to create a matrix from a list*)
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(* Coefficient matrix n_ao x n_mo, list of orbitals -> matrix with these orbitals *)
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(* matrix, integer list -> matrix*)
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let create_mat mat list =
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let create_mat mat lst =
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let vec_of_mat = Mat.to_col_vecs mat in
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let f a = vec_of_mat.(a-1) in
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let vec_list = List.map f list
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let vec_list = List.map f lst
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in
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Mat.of_col_vecs_list vec_list
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in
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(* List of the occupied MOs *)
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let list_occ =
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let vec_occ = Vec.init (nocc) (fun i -> float_of_int(i))
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in
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int_list vec_occ
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Util.list_range 1 nocc
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in
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(* List of the core MOs *)
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let list_core =
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let vec_core = Vec.init (n_core) (fun i -> float_of_int(i))
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in int_list vec_core
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Util.list_range 1 n_core
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in
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(* Function to create a list of pi MOs *)
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@ -940,24 +930,22 @@ let localize mo_basis =
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let list_pi mat =
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let n_mo = Mat.dim2 mat in
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let m_pi = Mat.init_cols n_ao (n_mo+1) ( fun i j ->
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if j=1 && m_C.{i,j}**2. < 10e-8**2.
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if j=1 && abs_float m_C.{i,j} < 1.e-8
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then 0.
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else if j=1
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then m_C.{i,j}
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else if mat.{i,j-1}**2. < 10e-8**2.
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else if abs_float mat.{i,j-1} < 1.e-8
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then 0.
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else mat.{i,j-1})
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in
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let vec = Mat.to_col_vecs m_pi in
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let vec_dot = Vec.init ((Mat.dim2 mat)) (fun i -> dot vec.(0) vec.(i)) in
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let vec_pi = Vec.init ((Mat.dim2 mat)) (fun i ->
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if vec_dot.{i} = 0.
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then float_of_int(i)
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else 0.)
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(* TODO gemv *)
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let vec_dot = Vec.init (Mat.dim2 mat) (fun i -> dot vec.(0) vec.(i)) in
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let list_pi =
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Util.list_range 1 (Mat.dim2 mat)
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|> List.map (fun i -> if vec_dot.{i} = 0. then i else 0)
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in
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let list_pi = int_list vec_pi in
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let rec remove x list =
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match list with
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let rec remove x = function
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| [] -> []
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| var :: tail -> if var = x
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then remove x tail
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@ -971,9 +959,7 @@ let localize mo_basis =
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(* matrix -> integer list *)
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let list_x_end mat =
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let n = Mat.dim2 mat in
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let vec_x_end = Vec.init (n-x_end) (fun i -> float_of_int(i))
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in
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int_list vec_x_end
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Util.list_range 1 (n-x_end)
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in
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(* Function to create a list of the (n/2) first MOs of a matrix *)
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@ -981,9 +967,7 @@ let localize mo_basis =
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(* matrix -> integer list *)
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let list_s_12 mat =
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let n = Mat.dim2 mat in
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let vec_12 = Vec.init (n/2) (fun i -> float_of_int(i))
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in
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int_list vec_12
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Util.list_range 1 (n/2)
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in
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(* Function to assemble to matrix with the same number of line *)
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