1059 lines
45 KiB
Python
1059 lines
45 KiB
Python
import math
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import numpy as np
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nx = None
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_s3 = math.sqrt(3)
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from qpms_c import get_mn_y, trans_calculator
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from .qpms_p import cart2sph
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# Functions copied from scattering_xu, additionaly normalized
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from py_gmm.gmm import vec_trans as vc
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#@ujit
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def q_max(m,n,μ,ν):
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return min(n,ν,(n+ν-abs(m+μ))/2)
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q_max_v = np.vectorize(q_max)
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# returns array with indices corresponding to q
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# argument q does nothing for now
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#@ujit
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def a_q(m,n,μ,ν,q = None):
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qm=q_max(m,n,μ,ν)
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res, err= vc.gaunt_xu(m,n,μ,ν,qm)
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if(err):
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print("m,n,μ,ν,qm = ",m,n,μ,ν,qm)
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raise ValueError('Something bad in the fortran subroutine gaunt_xu happened')
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return res
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a_q_v = np.vectorize(a_q)
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# All arguments are single numbers (for now)
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# ZDE VYCHÁZEJÍ DIVNÁ ZNAMÉNKA
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#@ujit
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def Ã(m,n,μ,ν,kdlj,θlj,φlj,r_ge_d,J):
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"""
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The à translation coefficient for spherical vector waves.
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Parameters
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----------
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m, n: int
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The indices (degree and order) of the destination basis.
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μ, ν: int
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The indices of the source basis wave.
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kdlj, θlj, φlj: float
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The spherical coordinates of the relative position of
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the new center vs. the old one (R_new - R_old);
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the distance has to be already multiplied by the wavenumber!
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r_ge_d: TODO
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J: 1, 2, 3 or 4
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Type of the wave in the old center.
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Returns
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-------
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TODO
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Bugs
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----
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gevero's gaunt coefficient implementation fails for large m, n (the unsafe territory
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is somewhere around -72, 80)
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"""
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exponent=(math.lgamma(2*n+1)-math.lgamma(n+2)+math.lgamma(2*ν+3)-math.lgamma(ν+2)
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+math.lgamma(n+ν+m-μ+1)-math.lgamma(n-m+1)-math.lgamma(ν+μ+1)
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+math.lgamma(n+ν+1) - math.lgamma(2*(n+ν)+1))
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presum = math.exp(exponent)
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presum = presum * np.exp(1j*(μ-m)*φlj) * (-1)**m * 1j**(ν+n) / (4*n)
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qmax = math.floor(q_max(-m,n,μ,ν)) #nemá tu být +m?
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q = np.arange(qmax+1, dtype=int)
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# N.B. -m !!!!!!
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a1q = a_q(-m,n,μ,ν) # there is redundant calc. of qmax
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ã1q = a1q / a1q[0]
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p = n+ν-2*q
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if(r_ge_d):
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J = 1
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zp = zJn(n+ν,kdlj,J)[0][p]
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Pp = lpmv(μ-m,p,math.cos(θlj))
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summandq = (n*(n+1) + ν*(ν+1) - p*(p+1)) * (-1)**q * ã1q * zp * Pp
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# Taylor normalisation v2, proven to be equivalent (NS which is better)
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prenormratio = 1j**(ν-n) * math.sqrt(((2*ν+1)/(2*n+1))* math.exp(
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math.lgamma(n+m+1)-math.lgamma(n-m+1)+math.lgamma(ν-μ+1)-math.lgamma(ν+μ+1)))
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presum = presum / prenormratio
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# Taylor normalisation
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#prenormmn = math.sqrt((2*n + 1)*math.factorial(n-m)/(4*π*factorial(n+m)))
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#prenormμν = math.sqrt((2*ν + 1)*math.factorial(ν-μ)/(4*π*factorial(ν+μ)))
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#presum = presum * prenormμν / prenormmn
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return presum * np.sum(summandq)
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# ZDE OPĚT JINAK ZNAMÉNKA než v Xu (J. comp. phys 127, 285)
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#@ujit
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def B̃(m,n,μ,ν,kdlj,θlj,φlj,r_ge_d,J):
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"""
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The B̃ translation coefficient for spherical vector waves.
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Parameters
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----------
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m, n: int
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The indices (degree and order) of the destination basis.
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μ, ν: int
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The indices of the source basis wave.
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kdlj, θlj, φlj: float
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The spherical coordinates of the relative position of
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the new center vs. the old one (R_new - R_old);
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the distance has to be already multiplied by the wavenumber!
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r_ge_d: TODO
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J: 1, 2, 3 or 4
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Type of the wave in the old center.
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Returns:
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--------
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TODO
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"""
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exponent=(math.lgamma(2*n+3)-math.lgamma(n+2)+math.lgamma(2*ν+3)-math.lgamma(ν+2)
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+math.lgamma(n+ν+m-μ+2)-math.lgamma(n-m+1)-math.lgamma(ν+μ+1)
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+math.lgamma(n+ν+2) - math.lgamma(2*(n+ν)+3))
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presum = math.exp(exponent)
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presum = presum * np.exp(1j*(μ-m)*φlj) * (-1)**m * 1j**(ν+n+1) / (
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(4*n)*(n+1)*(n+m+1))
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Qmax = math.floor(q_max(-m,n+1,μ,ν))
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q = np.arange(Qmax+1, dtype=int)
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if (μ == ν): # it would disappear in the sum because of the factor (ν-μ) anyway
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ã2q = 0
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else:
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a2q = a_q(-m-1,n+1,μ+1,ν)
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ã2q = a2q / a2q[0]
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a3q = a_q(-m,n+1,μ,ν)
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ã3q = a3q / a3q[0]
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#print(len(a2q),len(a3q))
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p = n+ν-2*q
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if(r_ge_d):
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J = 1
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zp_ = zJn(n+1+ν,kdlj,J)[0][p+1] # je ta +1 správně?
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Pp_ = lpmv(μ-m,p+1,math.cos(θlj))
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summandq = ((2*(n+1)*(ν-μ)*ã2q
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-(-ν*(ν+1) - n*(n+3) - 2*μ*(n+1)+p*(p+3))* ã3q)
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*(-1)**q * zp_ * Pp_)
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# Taylor normalisation v2, proven to be equivalent
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prenormratio = 1j**(ν-n) * math.sqrt(((2*ν+1)/(2*n+1))* math.exp(
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math.lgamma(n+m+1)-math.lgamma(n-m+1)+math.lgamma(ν-μ+1)-math.lgamma(ν+μ+1)))
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presum = presum / prenormratio
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## Taylor normalisation
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#prenormmn = math.sqrt((2*n + 1)*math.factorial(n-m)/(4*π*factorial(n+m)))
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#prenormμν = math.sqrt((2*ν + 1)*math.factorial(ν-μ)/(4*π*factorial(ν+μ)))
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#presum = presum * prenormμν / prenormmn
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return presum * np.sum(summandq)
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#@ujit
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def G_Mie_scat_precalc_cart(source_cart, dest_cart, RH, RV, a, nmax, k_i, k_e, μ_i=1, μ_e=1, J_ext=1, J_scat=3):
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"""
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r1_cart (destination), r2_cart (source) and the result are in cartesian coordinates
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the result indices are in the source-destination order
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TODO
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"""
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my, ny = get_mn_y(nmax)
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nelem = len(my)
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#source to origin
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so_sph = cart2sph(-source_cart)
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kd_so = k_e * so_sph[0]
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θ_so = so_sph[1]
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φ_so = so_sph[2]
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# Decomposition of the source N_0,1, N_-1,1, and N_1,1 in the nanoparticle center
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p_0 = np.empty((nelem), dtype=np.complex_)
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q_0 = np.empty((nelem), dtype=np.complex_)
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p_minus = np.empty((nelem), dtype=np.complex_)
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q_minus = np.empty((nelem), dtype=np.complex_)
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p_plus = np.empty((nelem), dtype=np.complex_)
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q_plus = np.empty((nelem), dtype=np.complex_)
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for y in range(nelem):
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m = my[y]
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n = ny[y]
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p_0[y] = Ã(m,n, 0,1,kd_so,θ_so,φ_so,False,J=J_scat)
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q_0[y] = B̃(m,n, 0,1,kd_so,θ_so,φ_so,False,J=J_scat)
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p_minus[y] = Ã(m,n,-1,1,kd_so,θ_so,φ_so,False,J=J_scat)
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q_minus[y] = B̃(m,n,-1,1,kd_so,θ_so,φ_so,False,J=J_scat)
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p_plus[y] = Ã(m,n, 1,1,kd_so,θ_so,φ_so,False,J=J_scat)
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q_plus[y] = B̃(m,n, 1,1,kd_so,θ_so,φ_so,False,J=J_scat)
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a_0 = RV[ny] * p_0
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b_0 = RH[ny] * q_0
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a_plus = RV[ny] * p_plus
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b_plus = RH[ny] * q_plus
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a_minus = RV[ny] * p_minus
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b_minus = RH[ny] * q_minus
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orig2dest_sph = cart2sph(dest_cart)
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orig2dest_sph[0] = k_e*orig2dest_sph[0]
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M_dest_y, N_dest_y = vswf_yr1(orig2dest_sph,nmax,J=J_scat)
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# N.B. these are in the local cartesian coordinates (r̂,θ̂,φ̂)
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N_dest_0 = np.sum(a_0[:,ň] * N_dest_y, axis=-2)
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M_dest_0 = np.sum(b_0[:,ň] * M_dest_y, axis=-2)
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N_dest_plus = np.sum(a_plus[:,ň] * N_dest_y, axis=-2)
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M_dest_plus = np.sum(b_plus[:,ň] * M_dest_y, axis=-2)
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N_dest_minus = np.sum(a_minus[:,ň]* N_dest_y, axis=-2)
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M_dest_minus = np.sum(b_minus[:,ň]* M_dest_y, axis=-2)
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prefac = math.sqrt(1/(4*3*π))#/ε_0
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G_sourcez_dest = prefac * (N_dest_0+M_dest_0)
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G_sourcex_dest = prefac * (N_dest_minus+M_dest_minus-N_dest_plus-M_dest_plus)/math.sqrt(2)
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G_sourcey_dest = prefac * (N_dest_minus+M_dest_minus+N_dest_plus+M_dest_plus)/(1j*math.sqrt(2))
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G_source_dest = np.array([G_sourcex_dest, G_sourcey_dest, G_sourcez_dest])
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# To global cartesian coordinates:
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G_source_dest = sph_loccart2cart(G_source_dest, sph=orig2dest_sph, axis=-1)
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return G_source_dest
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#@ujit
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def G_Mie_scat_cart(source_cart, dest_cart, a, nmax, k_i, k_e, μ_i=1, μ_e=1, J_ext=1, J_scat=3):
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"""
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TODO
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"""
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RH, RV, TH, TV = mie_coefficients(a=a, nmax=nmax, k_i=k_i, k_e=k_e, μ_i=μ_i, μ_e=μ_e, J_ext=J_ext, J_scat=J_scat)
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return G_Mie_scat_precalc_cart_new(source_cart, dest_cart, RH, RV, a, nmax, k_i, k_e, μ_i, μ_e, J_ext, J_scat)
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#TODO
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def cross_section_Mie_precalc():
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pass
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def cross_section_Mie(a, nmax, k_i, k_e, μ_i, μ_e,):
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pass
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####################
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# Array simulations
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####################
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def scatter_plane_wave(omega, epsilon_b, positions, Tmatrices, k_dirs, E_0s, #saveto = None
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):
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"""
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Solves the plane wave linear scattering problem for a structure of "non-touching" particles
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for one frequency and arbitrary number K of incoming plane waves.
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Parameters
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----------
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omega : positive number
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The frequency of the field.
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epsilon_b : complex number
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Permittivity of the background medium (which has to be isotropic).
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positions : (N,3)-shaped real array
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Cartesian positions of the particles.
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TMatrices : (N,2,nelem,2,nelem) or compatible
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The T-matrices in the "Taylor convention" describing the scattering on a single nanoparticle.
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If all the particles are identical and equally oriented, only one T-matrix can be given.
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nelems = (lMax + 2) * lMax, where lMax is the highest multipole order to which the scattering
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is calculated.
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k_dirs : (K,3)-shaped real array or compatible
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The direction of the incident field wave vector, normalized to one.
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E_0s : (K,3)-shaped complex array or compatible
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The electric intensity amplitude of the incident field.
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Returns
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-------
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ab : (K, N, 2, nelem)-shaped complex array
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The a (electric wave), b (magnetic wave) coefficients of the outgoing field for each particle
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# Fuck this, it will be wiser to make separate function to calculate those from ab:
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# sigma_xxx : TODO (K, 2, nelem)
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# TODO partial (TODO which?) cross-section for each type of outgoing waves, summed over all
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# nanoparticles (total cross section is given by the sum of this.)
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"""
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nelem = TMatrices.shape[-1]
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if ((nelem != TMatrices.shape[-3]) or (2 != TMatrices.shape[-2]) or (2 != TMatrices.shape[-4])):
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raise ValueError('The T-matrices must be of shape (N, 2, nelem, 2, nelem) but are of shape %s' % (str(TMatrices.shape),))
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lMax = nelem2lMax(nelem)
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if not lMax:
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raise ValueError('The "nelem" dimension of T-matrix has invalid value (%d).' % nelem)
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# TODO perhaps more checks.
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raise Error('Not implemented.')
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pass
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import warnings
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#@ujit
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def scatter_plane_wave_rectarray(omega, epsilon_b, xN, yN, xd, yd, TMatrices, k_dirs, E_0s,
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return_pq_0 = False, return_pq= False, return_xy = False, watch_time = False):
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"""
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Solves the plane wave linear scattering problem for a rectangular array of particles
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for one frequency and arbitrary number K of incoming plane waves.
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Parameters
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----------
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omega : positive number
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The frequency of the field.
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epsilon_b : complex number
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Permittivity of the background medium (which has to be isotropic).
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xN, yN : positive integers
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Particle numbers in the x and y dimensions
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xd, yd : positive numbers
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Periodicities in the x and y direction
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TMatrices : (xN, yN,2,nelem,2,nelem) or compatible or (2,nelem,2,nelem)
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The T-matrices in the "Taylor convention" describing the scattering on a single nanoparticle.
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If all the particles are identical and equally oriented, only one T-matrix can be given.
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nelems = (lMax + 2) * lMax, where lMax is the highest multipole order to which the scattering
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is calculated.
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Electric wave index is 0, magnetic wave index is 1.
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k_dirs : (K,3)-shaped real array or compatible
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The direction of the incident field wave vector, normalized to one.
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E_0s : (K,3)-shaped complex array or compatible
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The electric intensity amplitude of the incident field.
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return_pq_0 : bool
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Return also the multipole decomposition coefficients of the incoming plane wave.
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return_pq : bool NOT IMPLEMENTED
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Return also the multipole decomposition coefficients of the field incoming to each
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particle (inc. the field scattered from other particles.
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return_xy : bool
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Return also the cartesian x, y positions of the particles.
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watch_time : bool
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Inform about the progress on stderr
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Returns
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-------
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ab : (K, xN, yN, 2, nelem)-shaped complex array
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The a (electric wave), b (magnetic wave) coefficients of the outgoing field for each particle.
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If none of return_pq or return_xy is set, the array is not enclosed in a tuple.
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pq_0 : (K, xN, yn, 2, nelem)-shaped complex array
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The p_0 (electric wave), b_0 (magnetic wave) coefficients of the incoming plane wave for each particle.
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pq : (K, xN, yN, 2, nelem)-shaped complex array NOT IMPLEMENTED
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The p (electric wave), q (magnetic wave) coefficients of the total exciting field
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for each particle (including the field scattered from other particles)
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x, y : (xN, yN)-shaped real array
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The x,y positions of the nanoparticles.
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"""
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if (watch_time):
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timec = time.time()
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print('%.4f: running scatter_plane_wave_rectarray' % timec, file = sys.stderr)
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sys.stderr.flush()
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nelem = TMatrices.shape[-1]
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if ((nelem != TMatrices.shape[-3]) or (2 != TMatrices.shape[-2]) or (2 != TMatrices.shape[-4])):
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raise ValueError('The T-matrices must be of shape (N, 2, nelem, 2, nelem) but are of shape %s' % (str(TMatrices.shape),))
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lMax = nelem2lMax(nelem)
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if not lMax:
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raise ValueError('The "nelem" dimension of T-matrix has invalid value (%d).' % nelem)
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if (watch_time):
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print('xN = %d, yN = %d, lMax = %d' % (xN, yN, lMax), file = sys.stderr)
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sys.stderr.flush()
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# TODO perhaps more checks.
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k_out = omega * math.sqrt(epsilon_b) / c # wave number
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my, ny = get_mn_y(lMax)
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N = yN * xN
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J_scat=3
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J_ext=1
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# Do something with this ugly indexing crap
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xind, yind = np.meshgrid(np.arange(xN),np.arange(yN), indexing='ij')
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xind = xind.flatten()
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yind = yind.flatten()
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xyind = np.stack((xind, yind, np.zeros((xind.shape),dtype=int)),axis=-1)
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cart_lattice=xyind * np.array([xd, yd, 0])
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x=cart_lattice[:,0]
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y=cart_lattice[:,1]
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xyind = xyind[:,0:2]
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# Lattice speedup
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if (watch_time):
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timec = time.time()
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print('%.4f: calculating the %d translation matrix elements' % (timec, 8*nelem*nelem*xN*yN), file = sys.stderr)
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sys.stderr.flush()
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Agrid = np.zeros((nelem, 2*xN, 2*yN, nelem),dtype=np.complex_)
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Bgrid = np.zeros((nelem, 2*xN, 2*yN, nelem),dtype=np.complex_)
|
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for yl in range(nelem): # source
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for xij in range(2*xN):
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for yij in range(2*yN):
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for yj in range(nelem): #dest
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if((yij != yN) or (xij != xN)):
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d_l2j = cart2sph(np.array([(xij-xN)*xd, (yij-yN)*yd, 0]))
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Agrid[yj, xij, yij, yl] = Ã(my[yj],ny[yj],my[yl],ny[yl],kdlj=d_l2j[0]*k_out,θlj=d_l2j[1],φlj=d_l2j[2],r_ge_d=False,J=J_scat)
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Bgrid[yj, xij, yij, yl] = B̃(my[yj],ny[yj],my[yl],ny[yl],kdlj=d_l2j[0]*k_out,θlj=d_l2j[1],φlj=d_l2j[2],r_ge_d=False,J=J_scat)
|
||
|
||
# Translation coefficient matrix T
|
||
if (watch_time):
|
||
timecold = timec
|
||
timec = time.time()
|
||
print('%4f: translation matrix elements calculated (elapsed %.2f s), filling the matrix'
|
||
% (timec, timec-timecold), file = sys.stderr)
|
||
sys.stderr.flush()
|
||
transmat = np.zeros((xN* yN, 2, nelem, xN* yN, 2, nelem),dtype=np.complex_)
|
||
for l in range(N):
|
||
xil, yil = xyind[l]
|
||
for j in range(N):
|
||
xij, yij = xyind[j]
|
||
if (l!=j):
|
||
transmat[j,0,:,l,0,:] = Agrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
transmat[j,0,:,l,1,:] = Bgrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
transmat[j,1,:,l,0,:] = Bgrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
transmat[j,1,:,l,1,:] = Agrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
Agrid = None
|
||
Bgrid = None
|
||
if (watch_time):
|
||
timecold = timec
|
||
timec = time.time()
|
||
print('%4f: translation matrix filled (elapsed %.2f s), building the interaction matrix'
|
||
% (timec, timec-timecold), file=sys.stderr)
|
||
sys.stderr.flush()
|
||
|
||
# Now we solve a linear problem (1 - M T) A = M P_0 where M is the T-matrix :-)
|
||
MT = np.empty((N,2,nelem,N,2,nelem),dtype=np.complex_)
|
||
|
||
TMatrices = np.broadcast_to(TMatrices, (xN, yN, 2, nelem, 2, nelem))
|
||
for j in range(N): # I wonder how this can be done without this loop...
|
||
xij, yij = xyind[j]
|
||
MT[j] = np.tensordot(TMatrices[xij, yij],transmat[j],axes=([-2,-1],[0,1]))
|
||
MT.shape = (N*2*nelem, N*2*nelem)
|
||
leftmatrix = np.identity(N*2*nelem) - MT
|
||
MT = None
|
||
if (watch_time):
|
||
timecold = timec
|
||
timec = time.time()
|
||
print('%.4f: interaction matrix complete (elapsed %.2f s)' % (timec, timec-timecold),
|
||
file=sys.stderr)
|
||
sys.stderr.flush()
|
||
|
||
if ((1 == k_dirs.ndim) and (1 == E_0s.ndim)):
|
||
k_cart = k_dirs * k_out # wave vector of the incident plane wave
|
||
pq_0 = np.zeros((N,2,nelem), dtype=np.complex_)
|
||
p_y0, q_y0 = plane_pq_y(lMax, k_cart, E_0s)
|
||
pq_0[:,0,:] = np.exp(1j*np.sum(k_cart[ň,:]*cart_lattice,axis=-1))[:, ň] * p_y0[ň, :]
|
||
pq_0[:,1,:] = np.exp(1j*np.sum(k_cart[ň,:]*cart_lattice,axis=-1))[:, ň] * q_y0[ň, :]
|
||
if (return_pq_0):
|
||
pq_0_arr = pq_0
|
||
MP_0 = np.empty((N,2,nelem),dtype=np.complex_)
|
||
#if (watch_time):
|
||
# print('%4f: building the interaction matrix' % time.time(), file=sys.stderr)
|
||
|
||
for j in range(N): # I wonder how this can be done without this loop...
|
||
MP_0[j] = np.tensordot(TMatrices[xij, yij],pq_0[j],axes=([-2,-1],[-2,-1]))
|
||
MP_0.shape = (N*2*nelem,)
|
||
|
||
if (watch_time):
|
||
timecold = time.time()
|
||
print('%4f: solving the scattering problem for single incoming wave' % timecold,
|
||
file = sys.stderr)
|
||
sys.stderr.flush()
|
||
ab = np.linalg.solve(leftmatrix, MP_0)
|
||
if watch_time:
|
||
timec = time.time()
|
||
print('%4f: solved (elapsed %.2f s)' % (timec, timec-timecold), file=sys.stderr)
|
||
sys.stderr.flush()
|
||
|
||
ab.shape = (xN, yN, 2, nelem)
|
||
else:
|
||
# handle "broadcasting" for k, E
|
||
if 1 == k_dirs.ndim:
|
||
k_dirs = k_dirs[ň,:]
|
||
if 1 == E_0s.ndim:
|
||
E_0s = E_0s[ň,:]
|
||
K = max(E_0s.shape[-2], k_dirs.shape[-2])
|
||
k_dirs = np.broadcast_to(k_dirs,(K,3))
|
||
E_0s = np.broadcast_to(E_0s, (K,3))
|
||
|
||
# А ну, чики-брики и в дамки!
|
||
if watch_time:
|
||
timecold = time.time()
|
||
print('%.4f: factorizing the interaction matrix' % timecold, file=sys.stderr)
|
||
sys.stderr.flush()
|
||
lupiv = scipy.linalg.lu_factor(leftmatrix, overwrite_a=True)
|
||
leftmatrix = None
|
||
if watch_time:
|
||
timec = time.time()
|
||
print('%.4f: factorization complete (elapsed %.2f s)' % (timec, timec-timecold),
|
||
file = sys.stderr)
|
||
print('%.4f: solving the scattering problem for %d incoming waves' % (timec, K),
|
||
file=sys.stderr)
|
||
sys.stderr.flush()
|
||
timecold = timec
|
||
|
||
if (return_pq_0):
|
||
pq_0_arr = np.zeros((K,N,2,nelem), dtype=np.complex_)
|
||
ab = np.empty((K,N*2*nelem), dtype=complex)
|
||
for ki in range(K):
|
||
k_cart = k_dirs[ki] * k_out
|
||
pq_0 = np.zeros((N,2,nelem), dtype=np.complex_)
|
||
p_y0, q_y0 = plane_pq_y(lMax, k_cart, E_0s[ki])
|
||
pq_0[:,0,:] = np.exp(1j*np.sum(k_cart[ň,:]*cart_lattice,axis=-1))[:, ň] * p_y0[ň, :]
|
||
pq_0[:,1,:] = np.exp(1j*np.sum(k_cart[ň,:]*cart_lattice,axis=-1))[:, ň] * q_y0[ň, :]
|
||
if (return_pq_0):
|
||
pq_0_arr[ki] = pq_0
|
||
MP_0 = np.empty((N,2,nelem),dtype=np.complex_)
|
||
for j in range(N): # I wonder how this can be done without this loop...
|
||
MP_0[j] = np.tensordot(TMatrices[xij, yij],pq_0[j],axes=([-2,-1],[-2,-1]))
|
||
MP_0.shape = (N*2*nelem,)
|
||
|
||
ab[ki] = scipy.linalg.lu_solve(lupiv, MP_0)
|
||
ab.shape = (K, xN, yN, 2, nelem)
|
||
if watch_time:
|
||
timec = time.time()
|
||
print('%.4f: done (elapsed %.2f s)' % (timec, timec-timecold),file = sys.stderr)
|
||
sys.stderr.flush()
|
||
if not (return_pq_0 + return_pq + return_xy):
|
||
return ab
|
||
returnlist = [ab]
|
||
if (return_pq_0):
|
||
pq_0_arr.shape = ab.shape
|
||
returnlist.append(pq_0_arr)
|
||
if (return_pq):
|
||
warnings.warn("return_pq not implemented, ignoring")
|
||
# returnlist.append(pq_arr)
|
||
if (return_xy):
|
||
returnlist.append(x)
|
||
returnlist.append(y)
|
||
return tuple(returnlist)
|
||
|
||
|
||
import warnings
|
||
#@ujit
|
||
def scatter_constmultipole_rectarray(omega, epsilon_b, xN, yN, xd, yd, TMatrices, pq_0_c = 1,
|
||
return_pq= False, return_xy = False, watch_time = False):
|
||
"""
|
||
Solves the plane wave linear scattering problem for a rectangular array of particles
|
||
for one frequency and constant exciting spherical waves throughout the array.
|
||
|
||
Parameters
|
||
----------
|
||
omega : positive number
|
||
The frequency of the field.
|
||
epsilon_b : complex number
|
||
Permittivity of the background medium (which has to be isotropic).
|
||
xN, yN : positive integers
|
||
Particle numbers in the x and y dimensions
|
||
xd, yd : positive numbers
|
||
Periodicities in the x and y direction
|
||
TMatrices : (xN, yN,2,nelem,2,nelem) or compatible or (2,nelem,2,nelem)
|
||
The T-matrices in the "Taylor convention" describing the scattering on a single nanoparticle.
|
||
If all the particles are identical and equally oriented, only one T-matrix can be given.
|
||
nelems = (lMax + 2) * lMax, where lMax is the highest multipole order to which the scattering
|
||
is calculated.
|
||
Electric wave index is 0, magnetic wave index is 1.
|
||
pq_0_c : (nelem)-shaped complex array or compatible
|
||
The initial excitation coefficients for the ("complex") multipole waves, in Taylor's convention.
|
||
return_pq : bool NOT IMPLEMENTED
|
||
Return also the multipole decomposition coefficients of the field incoming to each
|
||
particle (inc. the field scattered from other particles.
|
||
return_xy : bool
|
||
Return also the cartesian x, y positions of the particles.
|
||
watch_time : bool
|
||
Inform about the progress on stderr
|
||
|
||
Returns
|
||
-------
|
||
ab : (nelem, xN, yN, 2, nelem)-shaped complex array
|
||
The a (electric wave), b (magnetic wave) coefficients of the outgoing field for each particle.
|
||
If none of return_pq or return_xy is set, the array is not enclosed in a tuple.
|
||
pq : (nelem, xN, yN, 2, nelem)-shaped complex array NOT IMPLEMENTED
|
||
The p (electric wave), q (magnetic wave) coefficients of the total exciting field
|
||
for each particle (including the field scattered from other particles)
|
||
x, y : (xN, yN)-shaped real array
|
||
The x,y positions of the nanoparticles.
|
||
"""
|
||
if (watch_time):
|
||
timec = time.time()
|
||
print('%.4f: running scatter_plane_wave_rectarray' % timec, file = sys.stderr)
|
||
sys.stderr.flush()
|
||
nelem = TMatrices.shape[-1]
|
||
if ((nelem != TMatrices.shape[-3]) or (2 != TMatrices.shape[-2]) or (2 != TMatrices.shape[-4])):
|
||
raise ValueError('The T-matrices must be of shape (N, 2, nelem, 2, nelem) but are of shape %s' % (str(TMatrices.shape),))
|
||
lMax = nelem2lMax(nelem)
|
||
if not lMax:
|
||
raise ValueError('The "nelem" dimension of T-matrix has invalid value (%d).' % nelem)
|
||
if (watch_time):
|
||
print('xN = %d, yN = %d, lMax = %d' % (xN, yN, lMax), file = sys.stderr)
|
||
sys.stderr.flush()
|
||
# TODO perhaps more checks.
|
||
k_out = omega * math.sqrt(epsilon_b) / c # wave number
|
||
my, ny = get_mn_y(lMax)
|
||
N = yN * xN
|
||
|
||
J_scat=3
|
||
J_ext=1
|
||
|
||
# Do something with this ugly indexing crap
|
||
xind, yind = np.meshgrid(np.arange(xN),np.arange(yN), indexing='ij')
|
||
xind = xind.flatten()
|
||
yind = yind.flatten()
|
||
xyind = np.stack((xind, yind, np.zeros((xind.shape),dtype=int)),axis=-1)
|
||
cart_lattice=xyind * np.array([xd, yd, 0])
|
||
x=cart_lattice[:,0]
|
||
y=cart_lattice[:,1]
|
||
xyind = xyind[:,0:2]
|
||
|
||
# Lattice speedup
|
||
if (watch_time):
|
||
timec = time.time()
|
||
print('%.4f: calculating the %d translation matrix elements' % (timec, 8*nelem*nelem*xN*yN), file = sys.stderr)
|
||
sys.stderr.flush()
|
||
Agrid = np.zeros((nelem, 2*xN, 2*yN, nelem),dtype=np.complex_)
|
||
Bgrid = np.zeros((nelem, 2*xN, 2*yN, nelem),dtype=np.complex_)
|
||
for yl in range(nelem): # source
|
||
for xij in range(2*xN):
|
||
for yij in range(2*yN):
|
||
for yj in range(nelem): #dest
|
||
if((yij != yN) or (xij != xN)):
|
||
d_l2j = cart2sph(np.array([(xij-xN)*xd, (yij-yN)*yd, 0]))
|
||
Agrid[yj, xij, yij, yl] = Ã(my[yj],ny[yj],my[yl],ny[yl],kdlj=d_l2j[0]*k_out,θlj=d_l2j[1],φlj=d_l2j[2],r_ge_d=False,J=J_scat)
|
||
Bgrid[yj, xij, yij, yl] = B̃(my[yj],ny[yj],my[yl],ny[yl],kdlj=d_l2j[0]*k_out,θlj=d_l2j[1],φlj=d_l2j[2],r_ge_d=False,J=J_scat)
|
||
|
||
# Translation coefficient matrix T
|
||
if (watch_time):
|
||
timecold = timec
|
||
timec = time.time()
|
||
print('%4f: translation matrix elements calculated (elapsed %.2f s), filling the matrix'
|
||
% (timec, timec-timecold), file = sys.stderr)
|
||
sys.stderr.flush()
|
||
transmat = np.zeros((xN* yN, 2, nelem, xN* yN, 2, nelem),dtype=np.complex_)
|
||
for l in range(N):
|
||
xil, yil = xyind[l]
|
||
for j in range(N):
|
||
xij, yij = xyind[j]
|
||
if (l!=j):
|
||
transmat[j,0,:,l,0,:] = Agrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
transmat[j,0,:,l,1,:] = Bgrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
transmat[j,1,:,l,0,:] = Bgrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
transmat[j,1,:,l,1,:] = Agrid[:, xij - xil + xN, yij - yil + yN, :]
|
||
Agrid = None
|
||
Bgrid = None
|
||
if (watch_time):
|
||
timecold = timec
|
||
timec = time.time()
|
||
print('%4f: translation matrix filled (elapsed %.2f s), building the interaction matrix'
|
||
% (timec, timec-timecold), file=sys.stderr)
|
||
sys.stderr.flush()
|
||
|
||
# Now we solve a linear problem (1 - M T) A = M P_0 where M is the T-matrix :-)
|
||
MT = np.empty((N,2,nelem,N,2,nelem),dtype=np.complex_)
|
||
|
||
TMatrices = np.broadcast_to(TMatrices, (xN, yN, 2, nelem, 2, nelem))
|
||
for j in range(N): # I wonder how this can be done without this loop...
|
||
xij, yij = xyind[j]
|
||
MT[j] = np.tensordot(TMatrices[xij, yij],transmat[j],axes=([-2,-1],[0,1]))
|
||
MT.shape = (N*2*nelem, N*2*nelem)
|
||
leftmatrix = np.identity(N*2*nelem) - MT
|
||
MT = None
|
||
if (watch_time):
|
||
timecold = timec
|
||
timec = time.time()
|
||
print('%.4f: interaction matrix complete (elapsed %.2f s)' % (timec, timec-timecold),
|
||
file=sys.stderr)
|
||
sys.stderr.flush()
|
||
|
||
# А ну, чики-брики и в дамки!
|
||
if watch_time:
|
||
timecold = time.time()
|
||
print('%.4f: factorizing the interaction matrix' % timecold, file=sys.stderr)
|
||
sys.stderr.flush()
|
||
lupiv = scipy.linalg.lu_factor(leftmatrix, overwrite_a=True)
|
||
leftmatrix = None
|
||
if watch_time:
|
||
timec = time.time()
|
||
print('%.4f: factorization complete (elapsed %.2f s)' % (timec, timec-timecold),
|
||
file = sys.stderr)
|
||
print('%.4f: solving the scattering problem for %d incoming multipoles' % (timec, nelem*2),
|
||
file=sys.stderr)
|
||
sys.stderr.flush()
|
||
timecold = timec
|
||
|
||
if(pq_0_c == 1):
|
||
pq_0_c = np.full((2,nelem),1)
|
||
ab = np.empty((2,nelem,N*2*nelem), dtype=complex)
|
||
for N_or_M in range(2):
|
||
for yy in range(nelem):
|
||
pq_0 = np.zeros((2,nelem), dtype=np.complex_)
|
||
pq_0[N_or_M,yy] = pq_0_c[N_or_M,yy]
|
||
pq_0 = np.broadcast_to(pq_0, (N, 2, nelem))
|
||
MP_0 = np.empty((N,2,nelem),dtype=np.complex_)
|
||
for j in range(N): # I wonder how this can be done without this loop...
|
||
xij, yij = xyind[j]
|
||
MP_0[j] = np.tensordot(TMatrices[xij, yij],pq_0[j],axes=([-2,-1],[-2,-1]))
|
||
MP_0.shape = (N*2*nelem,)
|
||
|
||
ab[N_or_M, yy] = scipy.linalg.lu_solve(lupiv, MP_0)
|
||
ab.shape = (2,nelem, xN, yN, 2, nelem)
|
||
if watch_time:
|
||
timec = time.time()
|
||
print('%.4f: done (elapsed %.2f s)' % (timec, timec-timecold),file = sys.stderr)
|
||
sys.stderr.flush()
|
||
if not (return_pq + return_xy):
|
||
return ab
|
||
returnlist = [ab]
|
||
if (return_pq):
|
||
warnings.warn("return_pq not implemented, ignoring")
|
||
# returnlist.append(pq_arr)
|
||
if (return_xy):
|
||
returnlist.append(x)
|
||
returnlist.append(y)
|
||
return tuple(returnlist)
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# -------------- hexagonal lattice translation coefficients ---------------------------
|
||
# Implementation using (C) one-by-one AB-coefficient calculation ufunc
|
||
def hexlattice_precalc_AB_save2(file, lMax, k_hexside, maxlayer, circular=True, savepointinfo = False, J_scat=3):
|
||
params = {
|
||
'lMax' : lMax,
|
||
'k_hexside' : k_hexside,
|
||
'maxlayer' : maxlayer,
|
||
'circular' : circular,
|
||
'savepointinfo' : savepointinfo,
|
||
'J_scat' : J_scat
|
||
}
|
||
tpdict = generate_trianglepoints(maxlayer, v3d=True, circular=circular, sixthindices=True, mirrorindices=True)
|
||
tphcdict = generate_trianglepoints_hexcomplement(maxlayer, v3d=True, circular=circular, thirdindices=True, mirrorindices=True)
|
||
my, ny = get_mn_y(lMax)
|
||
nelem = len(my)
|
||
a_self_nm = np.empty((tpdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
b_self_nm = np.empty((tpdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
a_self_m0 = np.empty((tpdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
b_self_m0 = np.empty((tpdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
a_d2u_nm = np.empty((tphcdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
b_d2u_nm = np.empty((tphcdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
a_d2u_m0 = np.empty((tphcdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
b_d2u_m0 = np.empty((tphcdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
|
||
k_0 = k_hexside*_s3 # not really a wave vector here because of the normalisation!
|
||
tc = trans_calculator(lMax)
|
||
|
||
y = np.arange(nelem)
|
||
|
||
points = tpdict['points'][tpdict['nmi']]
|
||
d_i2j = cart2sph(points)
|
||
a_self_nm, b_self_nm = tc.get_AB(my[nx,:,nx],ny[nx,:,nx],my[nx,nx,:],ny[nx,nx,:],k_0*d_i2j[:,nx,nx,0],d_i2j[:,nx,nx,1],d_i2j[:,nx,nx,2],False,J_scat)
|
||
|
||
points = tpdict['points'][tpdict['mi'][0]]
|
||
d_i2j = cart2sph(points)
|
||
a_self_m0, b_self_m0 = tc.get_AB(my[nx,:,nx],ny[nx,:,nx],my[nx,nx,:],ny[nx,nx,:],k_0*d_i2j[:,nx,nx,0],d_i2j[:,nx,nx,1],d_i2j[:,nx,nx,2],False,J_scat)
|
||
|
||
points = tphcdict['points'][tphcdict['nmi']]
|
||
d_i2j = cart2sph(points)
|
||
a_d2u_nm, b_d2u_nm = tc.get_AB(my[nx,:,nx],ny[nx,:,nx],my[nx,nx,:],ny[nx,nx,:],k_0*d_i2j[:,nx,nx,0],d_i2j[:,nx,nx,1],d_i2j[:,nx,nx,2],False,J_scat)
|
||
|
||
points = tphcdict['points'][tphcdict['mi'][0]]
|
||
d_i2j = cart2sph(points)
|
||
a_d2u_m0, b_d2u_m0 = tc.get_AB(my[nx,:,nx],ny[nx,:,nx],my[nx,nx,:],ny[nx,nx,:],k_0*d_i2j[:,nx,nx,0],d_i2j[:,nx,nx,1],d_i2j[:,nx,nx,2],False,J_scat)
|
||
|
||
tosave = {
|
||
'a_self_nm' : a_self_nm,
|
||
'a_self_m0' : a_self_m0,
|
||
'b_self_nm' : b_self_nm,
|
||
'b_self_m0' : b_self_m0,
|
||
'a_d2u_nm' : a_d2u_nm,
|
||
'a_d2u_m0' : a_d2u_m0,
|
||
'b_d2u_nm' : b_d2u_nm,
|
||
'b_d2u_m0' : b_d2u_m0,
|
||
'precalc_params' : params
|
||
}
|
||
if savepointinfo:
|
||
tosave['tp_points'] = tpdict['points'],
|
||
tosave['tp_si'] = tpdict['si'],
|
||
tosave['tp_mi'] = tpdict['mi'],
|
||
tosave['tp_nmi'] = tpdict['nmi']
|
||
tosave['tphc_points'] = tphcdict['points'],
|
||
tosave['tphc_ti'] = tphcdict['ti'],
|
||
tosave['tphc_mi'] = tphcdict['mi'],
|
||
tosave['tphc_nmi'] = tphcdict['nmi']
|
||
np.savez(file, **tosave)
|
||
|
||
|
||
|
||
# The oldest implementation, using the super-inefficient pure python translation coefficients
|
||
def hexlattice_precalc_AB_save_purepy(file, lMax, k_hexside, maxlayer, circular=True, savepointinfo = False, J_scat=3):
|
||
params = {
|
||
'lMax' : lMax,
|
||
'k_hexside' : k_hexside,
|
||
'maxlayer' : maxlayer,
|
||
'circular' : circular,
|
||
'savepointinfo' : savepointinfo,
|
||
'J_scat' : J_scat
|
||
}
|
||
tpdict = generate_trianglepoints(maxlayer, v3d=True, circular=circular, sixthindices=True, mirrorindices=True)
|
||
tphcdict = generate_trianglepoints_hexcomplement(maxlayer, v3d=True, circular=circular, thirdindices=True, mirrorindices=True)
|
||
my, ny = get_mn_y(lMax)
|
||
nelem = len(my)
|
||
a_self_nm = np.empty((tpdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
b_self_nm = np.empty((tpdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
a_self_m0 = np.empty((tpdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
b_self_m0 = np.empty((tpdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
a_d2u_nm = np.empty((tphcdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
b_d2u_nm = np.empty((tphcdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
a_d2u_m0 = np.empty((tphcdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
b_d2u_m0 = np.empty((tphcdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
|
||
k_0 = k_hexside*_s3 # not really a wave vector here because of the normalisation!
|
||
|
||
points = tpdict['points'][tpdict['nmi']]
|
||
for j in range(points.shape[0]):
|
||
d_i2j = cart2sph(points[j])
|
||
for yi in range(nelem):
|
||
for yj in range(nelem):
|
||
a_self_nm[j, yj, yi] = Ã(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
b_self_nm[j, yj, yi] = B̃(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
points = tpdict['points'][tpdict['mi'][0]]
|
||
for j in range(points.shape[0]):
|
||
d_i2j = cart2sph(points[j])
|
||
for yi in range(nelem):
|
||
for yj in range(nelem):
|
||
a_self_m0[j, yj, yi] = Ã(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
b_self_m0[j, yj, yi] = B̃(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
points = tphcdict['points'][tphcdict['nmi']]
|
||
for j in range(points.shape[0]):
|
||
d_i2j = cart2sph(points[j])
|
||
for yi in range(nelem):
|
||
for yj in range(nelem):
|
||
a_d2u_nm[j, yj, yi] = Ã(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
b_d2u_nm[j, yj, yi] = B̃(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
points = tphcdict['points'][tphcdict['mi'][0]]
|
||
for j in range(points.shape[0]):
|
||
d_i2j = cart2sph(points[j])
|
||
for yi in range(nelem):
|
||
for yj in range(nelem):
|
||
a_d2u_m0[j, yj, yi] = Ã(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
b_d2u_m0[j, yj, yi] = B̃(my[yj],ny[yj],my[yi],ny[yi],kdlj=d_i2j[0]*k_0,θlj=d_i2j[1],φlj=d_i2j[2],r_ge_d=False,J=J_scat)
|
||
tosave = {
|
||
'a_self_nm' : a_self_nm,
|
||
'a_self_m0' : a_self_m0,
|
||
'b_self_nm' : b_self_nm,
|
||
'b_self_m0' : b_self_m0,
|
||
'a_d2u_nm' : a_d2u_nm,
|
||
'a_d2u_m0' : a_d2u_m0,
|
||
'b_d2u_nm' : b_d2u_nm,
|
||
'b_d2u_m0' : b_d2u_m0,
|
||
'precalc_params' : params
|
||
}
|
||
if savepointinfo:
|
||
tosave['tp_points'] = tpdict['points'],
|
||
tosave['tp_si'] = tpdict['si'],
|
||
tosave['tp_mi'] = tpdict['mi'],
|
||
tosave['tp_nmi'] = tpdict['nmi']
|
||
tosave['tphc_points'] = tphcdict['points'],
|
||
tosave['tphc_ti'] = tphcdict['ti'],
|
||
tosave['tphc_mi'] = tphcdict['mi'],
|
||
tosave['tphc_nmi'] = tphcdict['nmi']
|
||
np.savez(file, **tosave)
|
||
|
||
def hexlattice_precalc_AB_loadunwrap(file, tpdict = None, tphcdict = None, return_points = False):
|
||
npz = np.load(file)
|
||
precalc_params = npz['precalc_params'][()]
|
||
my, ny = get_mn_y(precalc_params['lMax'])
|
||
nelem = len(my)
|
||
# this I should have made more universal...
|
||
if precalc_params['savepointinfo']:
|
||
if not tpdict:
|
||
tpdict = {
|
||
'points' : npz['tp_points'],
|
||
'si' : npz['tp_si'],
|
||
'mi' : npz['tp_mi'],
|
||
'nmi' : npz['tp_nmi'],
|
||
}
|
||
if not tphcdict:
|
||
tphcdict = {
|
||
'points' : npz['tphc_points'],
|
||
'ti' : npz['tphc_ti'],
|
||
'mi' : npz['tphc_mi'],
|
||
'nmi' : npz['tphc_nmi']
|
||
}
|
||
else:
|
||
if not tpdict:
|
||
tpdict = generate_trianglepoints(maxlayer = precalc_params['maxlayer'], v3d=True,
|
||
circular=precalc_params['circular'], sixthindices=True, mirrorindices=True)
|
||
if not tphcdict:
|
||
tphcdict = generate_trianglepoints_hexcomplement(maxlayer=precalc_params['maxlayer'], v3d=True,
|
||
circular=precalc_params['circular'], thirdindices=True, mirrorindices=True)
|
||
|
||
# For some obscure reason, I keep getting trailing single-dimension in the beginning for these arrays
|
||
for a in (tpdict['points'], tphcdict['points'], tpdict['si'], tpdict['mi'],
|
||
tphcdict['ti'], tphcdict['mi']):
|
||
if len(a.shape) > 2:
|
||
a.shape = a.shape[1::]
|
||
|
||
self_tr = tpdict['points']
|
||
d2u_tr = tphcdict['points']
|
||
if len(self_tr.shape)>2:
|
||
self_tr = np.reshape(self_tr, self_tr.shape[1::])
|
||
if len(d2u_tr.shape)>2:
|
||
d2u_tr = np.reshape(d2u_tr, d2u_tr.shape[1::])
|
||
u2d_tr = -d2u_tr
|
||
a_self = np.empty((self_tr.shape[0],nelem,nelem), dtype=complex)
|
||
b_self = np.empty((self_tr.shape[0],nelem,nelem), dtype=complex)
|
||
a_d2u = np.empty(( d2u_tr.shape[0],nelem,nelem), dtype=complex)
|
||
b_d2u = np.empty(( d2u_tr.shape[0],nelem,nelem), dtype=complex)
|
||
a_self[tpdict['nmi']]=npz['a_self_nm']
|
||
a_self[tpdict['mi'][0]]=npz['a_self_m0']
|
||
b_self[tpdict['nmi']]=npz['b_self_nm']
|
||
b_self[tpdict['mi'][0]]=npz['b_self_m0']
|
||
mirrorangles = cart2sph(self_tr[tpdict['mi'][1]])[:,2] - cart2sph(self_tr[tpdict['mi'][0]])[:,2]
|
||
a_self[tpdict['mi'][1],:,:] = a_self[tpdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
b_self[tpdict['mi'][1],:,:] = b_self[tpdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
for i in range(1,6):
|
||
a_self[tpdict['si'][i],:,:] = a_self[tpdict['si'][0],:,:] * np.exp(1j*math.pi/3*i*(my[nx,:]-my[:,nx]))
|
||
b_self[tpdict['si'][i],:,:] = b_self[tpdict['si'][0],:,:] * np.exp(1j*math.pi/3*i*(my[nx,:]-my[:,nx]))
|
||
a_d2u[tphcdict['nmi']]=npz['a_d2u_nm']
|
||
a_d2u[tphcdict['mi'][0]]=npz['a_d2u_m0']
|
||
b_d2u[tphcdict['nmi']]=npz['b_d2u_nm']
|
||
b_d2u[tphcdict['mi'][0]]=npz['b_d2u_m0']
|
||
mirrorangles = cart2sph(self_tr[tphcdict['mi'][1]])[:,2] - cart2sph(self_tr[tphcdict['mi'][0]])[:,2]
|
||
a_d2u[tphcdict['mi'][1],:,:] = a_d2u[tphcdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
b_d2u[tphcdict['mi'][1],:,:] = b_d2u[tphcdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
for i in (1,-1):
|
||
a_d2u[tphcdict['ti'][i],:,:] = a_d2u[tphcdict['ti'][0],:,:] * np.exp(i*2j*math.pi/3*(my[nx,:]-my[:,nx]))
|
||
b_d2u[tphcdict['ti'][i],:,:] = b_d2u[tphcdict['ti'][0],:,:] * np.exp(i*2j*math.pi/3*(my[nx,:]-my[:,nx]))
|
||
a_u2d = a_d2u * (-1)**(my[nx,:]-my[:,nx])
|
||
b_u2d = b_d2u * (-1)**(my[nx,:]-my[:,nx])
|
||
d = {
|
||
'a_self' : a_self,
|
||
'b_self' : b_self,
|
||
'a_d2u' : a_d2u,
|
||
'b_d2u' : b_d2u,
|
||
'a_u2d' : a_u2d,
|
||
'b_u2d' : b_u2d,
|
||
}
|
||
for k in precalc_params.keys():
|
||
d[k] = precalc_params[k]
|
||
if return_points:
|
||
d['d2u_tr'] = tphcdict['points']
|
||
d['u2d_tr'] = -tphcdict['points']
|
||
d['self_tr'] = tpdict['points']
|
||
return d
|
||
|
||
def hexlattice_get_AB(lMax, k_hexside, maxlayer, circular=True, return_points = True, J_scat=3):
|
||
params = {
|
||
'lMax' : lMax,
|
||
'k_hexside' : k_hexside,
|
||
'maxlayer' : maxlayer,
|
||
'circular' : circular,
|
||
'savepointinfo' : return_points, # should I delete this key?
|
||
'J_scat' : J_scat
|
||
}
|
||
tpdict = generate_trianglepoints(maxlayer, v3d=True, circular=circular, sixthindices=True, mirrorindices=True)
|
||
tphcdict = generate_trianglepoints_hexcomplement(maxlayer, v3d=True, circular=circular, thirdindices=True, mirrorindices=True)
|
||
my, ny = get_mn_y(lMax)
|
||
nelem = len(my)
|
||
a_self_nm = np.empty((tpdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
b_self_nm = np.empty((tpdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
a_self_m0 = np.empty((tpdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
b_self_m0 = np.empty((tpdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
a_d2u_nm = np.empty((tphcdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
b_d2u_nm = np.empty((tphcdict['nmi'].shape[0],nelem,nelem), dtype=complex)
|
||
a_d2u_m0 = np.empty((tphcdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
b_d2u_m0 = np.empty((tphcdict['mi'].shape[1],nelem,nelem), dtype=complex)
|
||
|
||
k_0 = k_hexside*_s3 # not really a wave vector here because of the normalisation!
|
||
tc = trans_calculator(lMax)
|
||
|
||
y = np.arange(nelem)
|
||
|
||
points = tpdict['points'][tpdict['nmi']]
|
||
d_i2j = cart2sph(points)
|
||
a_self_nm, b_self_nm = tc.get_AB_arrays(k_0*d_i2j[:,0],d_i2j[:,1],d_i2j[:,2],np.array([False]),J_scat)
|
||
|
||
points = tpdict['points'][tpdict['mi'][0]]
|
||
d_i2j = cart2sph(points)
|
||
a_self_m0, b_self_m0 = tc.get_AB_arrays(k_0*d_i2j[:,0],d_i2j[:,1],d_i2j[:,2],np.array([False]),J_scat)
|
||
|
||
points = tphcdict['points'][tphcdict['nmi']]
|
||
d_i2j = cart2sph(points)
|
||
a_d2u_nm, b_d2u_nm = tc.get_AB_arrays(k_0*d_i2j[:,0],d_i2j[:,1],d_i2j[:,2],np.array([False]),J_scat)
|
||
|
||
points = tphcdict['points'][tphcdict['mi'][0]]
|
||
d_i2j = cart2sph(points)
|
||
a_d2u_m0, b_d2u_m0 = tc.get_AB_arrays(k_0*d_i2j[:,0],d_i2j[:,1],d_i2j[:,2],np.array([False]),J_scat)
|
||
'''
|
||
tosave = {
|
||
'a_self_nm' : a_self_nm,
|
||
'a_self_m0' : a_self_m0,
|
||
'b_self_nm' : b_self_nm,
|
||
'b_self_m0' : b_self_m0,
|
||
'a_d2u_nm' : a_d2u_nm,
|
||
'a_d2u_m0' : a_d2u_m0,
|
||
'b_d2u_nm' : b_d2u_nm,
|
||
'b_d2u_m0' : b_d2u_m0,
|
||
'precalc_params' : params
|
||
}
|
||
if savepointinfo:
|
||
tosave['tp_points'] = tpdict['points'],
|
||
tosave['tp_si'] = tpdict['si'],
|
||
tosave['tp_mi'] = tpdict['mi'],
|
||
tosave['tp_nmi'] = tpdict['nmi']
|
||
tosave['tphc_points'] = tphcdict['points'],
|
||
tosave['tphc_ti'] = tphcdict['ti'],
|
||
tosave['tphc_mi'] = tphcdict['mi'],
|
||
tosave['tphc_nmi'] = tphcdict['nmi']
|
||
np.savez(file, **tosave)
|
||
'''
|
||
self_tr = tpdict['points']
|
||
d2u_tr = tphcdict['points']
|
||
if len(self_tr.shape)>2:
|
||
self_tr = np.reshape(self_tr, self_tr.shape[1::])
|
||
if len(d2u_tr.shape)>2:
|
||
d2u_tr = np.reshape(d2u_tr, d2u_tr.shape[1::])
|
||
u2d_tr = -d2u_tr
|
||
a_self = np.empty((self_tr.shape[0],nelem,nelem), dtype=complex)
|
||
b_self = np.empty((self_tr.shape[0],nelem,nelem), dtype=complex)
|
||
a_d2u = np.empty(( d2u_tr.shape[0],nelem,nelem), dtype=complex)
|
||
b_d2u = np.empty(( d2u_tr.shape[0],nelem,nelem), dtype=complex)
|
||
a_self[tpdict['nmi']]=a_self_nm
|
||
a_self[tpdict['mi'][0]]=a_self_m0
|
||
b_self[tpdict['nmi']]=b_self_nm
|
||
b_self[tpdict['mi'][0]]=b_self_m0
|
||
mirrorangles = cart2sph(self_tr[tpdict['mi'][1]])[:,2] - cart2sph(self_tr[tpdict['mi'][0]])[:,2]
|
||
a_self[tpdict['mi'][1],:,:] = a_self[tpdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
b_self[tpdict['mi'][1],:,:] = b_self[tpdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
for i in range(1,6):
|
||
a_self[tpdict['si'][i],:,:] = a_self[tpdict['si'][0],:,:] * np.exp(1j*math.pi/3*i*(my[nx,:]-my[:,nx]))
|
||
b_self[tpdict['si'][i],:,:] = b_self[tpdict['si'][0],:,:] * np.exp(1j*math.pi/3*i*(my[nx,:]-my[:,nx]))
|
||
a_d2u[tphcdict['nmi']]=a_d2u_nm
|
||
a_d2u[tphcdict['mi'][0]]=a_d2u_m0
|
||
b_d2u[tphcdict['nmi']]=b_d2u_nm
|
||
b_d2u[tphcdict['mi'][0]]=b_d2u_m0
|
||
mirrorangles = cart2sph(self_tr[tphcdict['mi'][1]])[:,2] - cart2sph(self_tr[tphcdict['mi'][0]])[:,2]
|
||
a_d2u[tphcdict['mi'][1],:,:] = a_d2u[tphcdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
b_d2u[tphcdict['mi'][1],:,:] = b_d2u[tphcdict['mi'][0],:,:] * np.exp(1j*mirrorangles[:,nx,nx]*(my[nx,nx,:]-my[nx,:,nx]))
|
||
for i in (1,-1):
|
||
a_d2u[tphcdict['ti'][i],:,:] = a_d2u[tphcdict['ti'][0],:,:] * np.exp(i*2j*math.pi/3*(my[nx,:]-my[:,nx]))
|
||
b_d2u[tphcdict['ti'][i],:,:] = b_d2u[tphcdict['ti'][0],:,:] * np.exp(i*2j*math.pi/3*(my[nx,:]-my[:,nx]))
|
||
a_u2d = a_d2u * (-1)**(my[nx,:]-my[:,nx])
|
||
b_u2d = b_d2u * (-1)**(my[nx,:]-my[:,nx])
|
||
d = {
|
||
'a_self' : a_self,
|
||
'b_self' : b_self,
|
||
'a_d2u' : a_d2u,
|
||
'b_d2u' : b_d2u,
|
||
'a_u2d' : a_u2d,
|
||
'b_u2d' : b_u2d,
|
||
}
|
||
for k in params.keys():
|
||
d[k] = params[k]
|
||
if return_points:
|
||
d['d2u_tr'] = tphcdict['points']
|
||
d['u2d_tr'] = -tphcdict['points']
|
||
d['self_tr'] = tpdict['points']
|
||
return d
|
||
|
||
|