def main():
# make environment
t1 = time.time()
pot_region = (2 / np.sqrt(3), 2 / np.sqrt(3), 2 / np.sqrt(3))
radius = np.sqrt(pot_region[0]**2 + pot_region[1]**2 + pot_region[2]**2)
region = (radius, radius, radius)
nr = 201
gridpx = 200
gridpy = 200
gridpz = 200
x, y, z = grid(gridpx, gridpy, gridpz, region)
xx, yy, zz = np.meshgrid(x, y, z)
#make mesh
#linear mesh
#r =np.linspace(0.0001,region,nr)
#log mesh
#a = np.log(2) / (nr - 1)
a = 0.03
b = radius / (np.e**(a * (nr - 1)) - 1)
rofi = np.array([b * (np.e**(a * i) - 1) for i in range(nr)])
# make potential
V = makepotential(xx,
yy,
zz,
pot_region,
pottype="cubic",
potbottom=-1,
potshow_f=False)
# surface integral
V_radial = surfaceintegral(x,
y,
z,
rofi,
V,
method="lebedev_py",
potshow_f=False)
vofi = np.array(V_radial) # select method of surface integral
"""
#test 20191029
V_test = np.zeros(nr,dtype=np.float64)
for i in range(nr):
ri = rofi[i]
if ri < pot_region[0]:
V_test[i] = -1
elif ri >= pot_region[0] and ri < pot_region[0] * np.sqrt(2) :
V_test[i] = -1 * ( 1 - 12 * np.pi * ri * ( ri - 0.5 * radius )/(4 * np.pi * ri**2))
elif ri >= pot_region[0] * np.sqrt(2) and ri <=radius:
V_test[i] = -1 * ( ri - 0.5 * np.sqrt(3) * radius ) * ( 2 - 3 * np.sqrt(2) * ( np.sqrt(2) - 1 ) ) / ( ri**2 * (np.sqrt(2) - np.sqrt(3))**2)
#plt.plot(rofi,V_test,marker=".")
#plt.show()
V_radial = V_test
vofi = V_test
"""
# make basis
node_open = 1
node_close = 2
node = node_open + node_close
LMAX = 3
nstates = node * LMAX**2
all_basis = []
for lvalsh in range(LMAX):
l_basis = []
# for open channel
val = 1.
slo = 0.
for no in range(node_open):
basis = Basis(nr)
emin = -10.
emax = 100.
basis.make_basis(a, b, emin, emax, lvalsh, no, nr, rofi, slo, vofi,
val)
l_basis.append(basis)
# for close channel
val = 0.
slo = -1.
for nc in range(node_close):
basis = Basis(nr)
emin = -10.
emax = 100.
basis.make_basis(a, b, emin, emax, lvalsh, nc, nr, rofi, slo, vofi,
val)
l_basis.append(basis)
all_basis.append(l_basis)
with open("wavefunc_2.dat", mode="w") as fw_w:
fw_w.write("#r, l, node, open or close = ")
for l_basis in all_basis:
for nyu_basis in l_basis:
fw_w.write(str(nyu_basis.l))
fw_w.write(str(nyu_basis.node))
if nyu_basis.open:
fw_w.write("open")
else:
fw_w.write("close")
fw_w.write(" ")
fw_w.write("\n")
for i in range(nr):
fw_w.write("{:>13.8f}".format(rofi[i]))
for l_basis in all_basis:
for nyu_basis in l_basis:
fw_w.write("{:>13.8f}".format(nyu_basis.g[i]))
fw_w.write("\n")
Smat = np.zeros((LMAX, LMAX, node, node), dtype=np.float64)
hsmat = np.zeros((LMAX, LMAX, node, node), dtype=np.float64)
lmat = np.zeros((LMAX, LMAX, node, node), dtype=np.float64)
qmat = np.zeros((LMAX, LMAX, node, node), dtype=np.float64)
"""
for l1 in range (LMAX):
for n1 in range (node_open + node_close):
print("l1 = ",l1,"n1 = ",n1,all_basis[l1][n1].val,all_basis[l1][n1].g[nr-1])
sys.exit()
"""
for l1 in range(LMAX):
for l2 in range(LMAX):
if l1 != l2:
continue
for n1 in range(node):
for n2 in range(node):
if all_basis[l1][n1].l != l1 or all_basis[l2][n2].l != l2:
print("error: L is differnt")
sys.exit()
Smat[l1][l2][n1][n2] = integrate(
all_basis[l1][n1].g[:nr] * all_basis[l2][n2].g[:nr],
rofi, nr)
hsmat[l1][l2][n1][
n2] = Smat[l1][l2][n1][n2] * all_basis[l2][n2].e
lmat[l1][l2][n1][
n2] = all_basis[l1][n1].val * all_basis[l2][n2].slo
qmat[l1][l2][n1][
n2] = all_basis[l1][n1].val * all_basis[l2][n2].val
print("\nSmat")
print(Smat)
print("\nhsmat")
print(hsmat)
print("\nlmat")
print(lmat)
print("\nqmat")
print(qmat)
hs_L = np.zeros((LMAX, LMAX, node, node))
"""
for l1 in range(LMAX):
for n1 in range(node):
for l2 in range(LMAX):
for n2 in range(node):
print("{:>8.4f}".format(lmat[l1][l2][n1][n2]),end="")
print("")
print("")
"""
print("hs_L")
for l1 in range(LMAX):
for n1 in range(node):
for l2 in range(LMAX):
for n2 in range(node):
hs_L[l1][l2][n1][
n2] = hsmat[l1][l2][n1][n2] + lmat[l1][l2][n1][n2]
print("{:>8.4f}".format(hs_L[l1][l2][n1][n2]), end="")
print("")
#make not spherical potential
my_radial_interfunc = interpolate.interp1d(rofi, V_radial)
V_ang = np.where(
np.sqrt(xx * xx + yy * yy + zz * zz) < rofi[-1],
V - my_radial_interfunc(np.sqrt(xx**2 + yy**2 + zz**2)), 0.)
"""
for i in range(gridpx):
for j in range(gridpy):
for k in range(gridpz):
print(V_ang[i][j][k],end=" ")
print("")
print("\n")
sys.exit()
"""
#WARING!!!!!!!!!!!!!!!!!!!!!!
"""
Fujikata rewrote ~/.local/lib/python3.6/site-packages/scipy/interpolate/interpolate.py line 690~702
To avoid exit with error "A value in x_new is below the interpolation range."
"""
#!!!!!!!!!!!!!!!!!!!!!!!!!!!
"""
with open ("V_ang.dat",mode = "w") as fw_a:
for i in range(len(V_ang)):
fw_a.write("{:>13.8f}".format(xx[50][i][50]))
fw_a.write("{:>13.8f}\n".format(V_ang[i][50][50]))
"""
#mayavi.mlab.plot3d(xx,yy,V_ang)
# mlab.contour3d(V_ang,color = (1,1,1),opacity = 0.1)
# obj = mlab.volume_slice(V_ang)
# mlab.show()
umat_av = np.zeros((node, node, LMAX, LMAX, 2 * LMAX + 1, 2 * LMAX + 1),
dtype=np.complex64)
gridstart = 50
gridend = 60
gridrange = gridend - gridstart + 1
for ngrid in range(gridstart, gridend + 1):
t1 = time.time()
fw_u = open("umat_grid" + str(ngrid) + ".dat", mode="w")
umat = np.zeros((node, node, LMAX, LMAX, 2 * LMAX + 1, 2 * LMAX + 1),
dtype=np.complex64)
my_V_ang_inter_func = RegularGridInterpolator((x, y, z), V_ang)
igridpx = ngrid
igridpy = ngrid
igridpz = ngrid
ix, iy, iz = grid(igridpx, igridpy, igridpz, region)
ixx, iyy, izz = np.meshgrid(ix, iy, iz)
V_ang_i = my_V_ang_inter_func((ixx, iyy, izz))
#mlab.contour3d(V_ang_i,color = (1,1,1),opacity = 0.1)
#obj = mlab.volume_slice(V_ang_i)
#mlab.show()
dis = np.sqrt(ixx**2 + iyy**2 + izz**2)
dis2 = ixx**2 + iyy**2 + izz**2
theta = np.where(dis != 0., np.arccos(izz / dis), 0.)
phi = np.where(
iyy**2 + ixx**2 != 0,
np.where(iyy >= 0, np.arccos(ixx / np.sqrt(ixx**2 + iyy**2)),
np.pi + np.arccos(ixx / np.sqrt(ixx**2 + iyy**2))), 0.)
#phi = np.where( iyy != 0. , phi, 0.)
#phi = np.where(iyy > 0, phi,-phi)
# region_t = np.where(dis < rofi[-1],1,0)
sph_harm_mat = np.zeros(
(LMAX, 2 * LMAX + 1, igridpx, igridpy, igridpz),
dtype=np.complex64)
for l1 in range(LMAX):
for m1 in range(-l1, l1 + 1):
sph_harm_mat[l1][m1] = np.where(dis != 0.,
sph_harm(m1, l1, phi, theta),
0.)
g_ln_mat = np.zeros((node, LMAX, igridpx, igridpy, igridpz),
dtype=np.float64)
for n1 in range(node):
for l1 in range(LMAX):
my_radial_g_inter_func = interpolate.interp1d(
rofi, all_basis[l1][n1].g[:nr])
g_ln_mat[n1][l1] = my_radial_g_inter_func(
np.sqrt(ixx**2 + iyy**2 + izz**2))
for n1 in range(node):
for n2 in range(node):
for l1 in range(LMAX):
for l2 in range(LMAX):
if all_basis[l1][n1].l != l1 or all_basis[l2][
n2].l != l2:
print("error: L is differnt")
sys.exit()
# to avoid nan in region where it can not interpolate ie: dis > rofi
g_V_g = np.where(
dis < rofi[-1],
g_ln_mat[n1][l1] * V_ang_i * g_ln_mat[n2][l2], 0.)
for m1 in range(-l1, l1 + 1):
for m2 in range(-l2, l2 + 1):
#print("n1 = {} n2 = {} l1 = {} l2 = {} m1 = {} m2 = {}".format(n1,n2,l1,l2,m1,m2))
umat[n1][n2][l1][l2][m1][m2] = np.sum(
np.where(
dis2 != 0.,
sph_harm_mat[l1][m1].conjugate() *
g_V_g * sph_harm_mat[l2][m2] / dis2,
0.)) * (2 * region[0] * 2 * region[1] *
2 * region[2]) / (igridpx *
igridpy *
igridpz)
#print(umat[n1][n2][l1][l2][m1][m2])
count = 0
for l1 in range(LMAX):
for l2 in range(LMAX):
for m1 in range(-l1, l1 + 1):
for m2 in range(-l2, l2 + 1):
for n1 in range(node):
for n2 in range(node):
fw_u.write(str(count))
fw_u.write("{:>15.8f}{:>15.8f}\n".format(
umat[n1][n2][l1][l2][m1][m2].real,
umat[n1][n2][l1][l2][m1][m2].imag))
count += 1
umat_av += umat
fw_u.close()
t2 = time.time()
print("grid = ", ngrid, "time = ", t2 - t1)
umat_av /= gridrange
count = 0
fw_u_av = open("umat_grid_av" + str(gridstart) + "_" + str(gridend) +
".dat",
mode="w")
for l1 in range(LMAX):
for l2 in range(LMAX):
for m1 in range(-l1, l1 + 1):
for m2 in range(-l2, l2 + 1):
for n1 in range(node):
for n2 in range(node):
fw_u_av.write(str(count))
fw_u_av.write("{:>15.8f}{:>15.8f}\n".format(
umat_av[n1][n2][l1][l2][m1][m2].real,
umat_av[n1][n2][l1][l2][m1][m2].imag))
count += 1
fw_u_av.close()
ham_mat = np.zeros((nstates * nstates), dtype=np.float64)
qmetric_mat = np.zeros((nstates * nstates), dtype=np.float64)
for l1 in range(LMAX):
for m1 in range(-l1, l1 + 1):
for n1 in range(node):
for l2 in range(LMAX):
for m2 in range(-l2, l2 + 1):
for n2 in range(node):
if l1 == l2 and m1 == m2:
ham_mat[l1**2 * node * LMAX**2 * node +
(l1 + m1) * node * LMAX**2 * node +
n1 * LMAX**2 * node + l2**2 * node +
(l2 + m2) * node +
n2] += hs_L[l1][l2][n1][n2]
qmetric_mat[l1**2 * node * LMAX**2 * node +
(l1 + m1) * node * LMAX**2 * node +
n1 * LMAX**2 * node +
l2**2 * node + (l2 + m2) * node +
n2] = qmat[l1][l2][n1][n2]
ham_mat[l1**2 * node * LMAX**2 * node +
(l1 + m1) * node * LMAX**2 * node +
n1 * LMAX**2 * node + l2**2 * node +
(l2 + m2) * node +
n2] += umat_av[n1][n2][l1][l2][m1][m2].real
lambda_mat = np.zeros(nstates * nstates, dtype=np.float64)
alphalong = np.zeros(nstates)
betalong = np.zeros(nstates)
revec = np.zeros(nstates * nstates)
for e_num in range(1, 2):
E = e_num * 10
lambda_mat = np.zeros(nstates * nstates, dtype=np.float64)
lambda_mat -= ham_mat
"""
for i in range(nstates):
lambda_mat[i + i * nstates] += E
"""
count = 0
fw_lam = open("lambda.dat", mode="w")
for l1 in range(LMAX):
for m1 in range(-l1, l1 + 1):
for n1 in range(node):
for l2 in range(LMAX):
for m2 in range(-l2, l2 + 1):
for n2 in range(node):
if l1 == l2 and m1 == m2:
lambda_mat[l1**2 * node * LMAX**2 * node +
(l1 + m1) * node * LMAX**2 *
node + n1 * LMAX**2 * node +
l2**2 * node +
(l2 + m2) * node +
n2] += Smat[l1][l2][n1][n2] * E
fw_lam.write(str(count))
fw_lam.write("{:>15.8f}\n".format(
lambda_mat[l1**2 * node * LMAX**2 * node +
(l1 + m1) * node * LMAX**2 *
node + n1 * LMAX**2 * node +
l2**2 * node +
(l2 + m2) * node + n2]))
count += 1
info = solve_genev(nstates, lambda_mat, qmetric_mat, alphalong,
betalong, revec)
print("info = ", info)
print("alphalong")
print(alphalong)
print("betalong")
print(betalong)
#print(revec)
k = 0
jk = np.zeros(nstates, dtype=np.int32)
for i in range(nstates):
if betalong[i] != 0.:
jk[k] = i
k += 1
fw_revec = open("revec.dat", mode="w")
print("revec")
for j in range(nstates):
fw_revec.write("{:>4}".format(j))
for i in range(LMAX**2):
fw_revec.write("{:>13.8f}".format(revec[j + jk[i] * nstates]))
print("{:>11.6f}".format(revec[j + jk[i] * nstates]), end="")
print("")
fw_revec.write("\n")
print("")
def main():
# make environment
fw_t = open("time_log",mode="w")
t1 = time.time()
pot_region,bound_rad,radius,region,nr,gridpx,gridpy,gridpz,x,y,z,xx,yy,zz,a,b,rofi,pot_type,pot_bottom,pot_show_f,si_method,radial_pot_show_f,new_radial_pot_show_f,node_open,node_close,LMAX = make_environment()
# make potential
V = makepotential(xx,yy,zz,pot_region,pot_type=pot_type,pot_bottom=pot_bottom,pot_show_f=pot_show_f)
# surface integral
V_radial = surfaceintegral(x,y,z,rofi,V,si_method=si_method,radial_pot_show_f=radial_pot_show_f)
V_radial_new = make_V_radial_new(V_radial,rofi,pot_region,bound_rad,new_radial_pot_show_f=new_radial_pot_show_f)
vofi = np.array (V_radial_new) # select method of surface integral
# make basis
node = node_open + node_close
nstates = node * LMAX**2
all_basis = make_basis(LMAX,node_open,node_close,nr,a,b,rofi,vofi)
#make spherical matrix element
Smat = np.zeros((LMAX,LMAX,node,node),dtype = np.float64)
hsmat = np.zeros((LMAX,LMAX,node,node),dtype = np.float64)
lmat = np.zeros((LMAX,LMAX,node,node), dtype = np.float64)
qmat = np.zeros((LMAX,LMAX,node,node), dtype = np.float64)
for l1 in range (LMAX):
for l2 in range (LMAX):
if l1 != l2 :
continue
for n1 in range (node):
for n2 in range (node):
if all_basis[l1][n1].l != l1 or all_basis[l2][n2].l != l2:
print("error: L is differnt")
sys.exit()
Smat[l1][l2][n1][n2] = integrate(all_basis[l1][n1].g[:nr] * all_basis[l2][n2].g[:nr],rofi,nr)
hsmat[l1][l2][n1][n2] = Smat[l1][l2][n1][n2] * all_basis[l2][n2].e
lmat[l1][l2][n1][n2] = all_basis[l1][n1].val * all_basis[l2][n2].slo
qmat[l1][l2][n1][n2] = all_basis[l1][n1].val * all_basis[l2][n2].val
print("\nSmat")
print(Smat)
print ("\nhsmat")
print (hsmat)
print ("\nlmat")
print (lmat)
print ("\nqmat")
print (qmat)
hs_L = np.zeros((LMAX,LMAX,node,node))
"""
for l1 in range(LMAX):
for n1 in range(node):
for l2 in range(LMAX):
for n2 in range(node):
print("{:>8.4f}".format(lmat[l1][l2][n1][n2]),end="")
print("")
print("")
"""
print("hs_L")
for l1 in range(LMAX):
for n1 in range(node):
for l2 in range(LMAX):
for n2 in range(node):
hs_L[l1][l2][n1][n2] = hsmat[l1][l2][n1][n2] + lmat[l1][l2][n1][n2]
print("{:>8.4f}".format(hs_L[l1][l2][n1][n2]),end="")
print("")
t2 = time.time()
fw_t.write("make environment, make basis and calculate spherical matrix element\n")
fw_t.write("time = {:>11.8}s\n".format(t2-t1))
t1 = time.time()
#make not spherical potential
my_radial_interfunc = interpolate.interp1d(rofi, V_radial_new)
V_ang = np.where(np.sqrt(xx * xx + yy * yy + zz * zz) < rofi[-1] , V - my_radial_interfunc(np.sqrt(xx **2 + yy **2 + zz **2)),0. )
"""
for i in range(gridpx):
for j in range(gridpy):
for k in range(gridpz):
print(V_ang[i][j][k],end=" ")
print("")
print("\n")
sys.exit()
"""
#WARING!!!!!!!!!!!!!!!!!!!!!!
"""
Fujikata rewrote ~/.local/lib/python3.6/site-packages/scipy/interpolate/interpolate.py line 690~702
To avoid exit with error "A value in x_new is below the interpolation range."
"""
#!!!!!!!!!!!!!!!!!!!!!!!!!!!
"""
with open ("V_ang.dat",mode = "w") as fw_a:
for i in range(len(V_ang)):
fw_a.write("{:>13.8f}".format(xx[50][i][50]))
fw_a.write("{:>13.8f}\n".format(V_ang[i][50][50]))
"""
#mayavi.mlab.plot3d(xx,yy,V_ang)
# mlab.contour3d(V_ang,color = (1,1,1),opacity = 0.1)
# obj = mlab.volume_slice(V_ang)
# mlab.show()
ngrid = 10
fw_u = open("umat_gauss.dat",mode="w")
umat = np.zeros((node,node,LMAX,LMAX,2 * LMAX + 1,2 * LMAX + 1), dtype = np.complex64)
igridpx = ngrid
igridpy = ngrid
igridpz = ngrid
gauss_px,gauss_wx = np.polynomial.legendre.leggauss(igridpx)
gauss_py,gauss_wy = np.polynomial.legendre.leggauss(igridpy)
gauss_pz,gauss_wz = np.polynomial.legendre.leggauss(igridpz)
ix,iy,iz = gauss_px * pot_region[0],gauss_py * pot_region[1],gauss_pz * pot_region[2]
ixx,iyy,izz = np.meshgrid(ix,iy,iz)
gauss_weight = np.zeros((igridpx,igridpy,igridpz))
for i in range(igridpx):
for j in range(igridpy):
for k in range(igridpz):
gauss_weight[i][j][k] = gauss_wx[i] * gauss_wy[j] * gauss_wz[k]
#my_V_ang_inter_func = RegularGridInterpolator((x, y, z), V_ang)
#V_ang_i = my_V_ang_inter_func((ixx,iyy,izz))
V_ang_i = np.zeros((igridpx,igridpy,igridpz))
V_ang_i = -1. - my_radial_interfunc(np.sqrt(ixx * ixx + iyy * iyy + izz * izz))
#mlab.contour3d(V_ang_i,color = (1,1,1),opacity = 0.1)
#obj = mlab.volume_slice(V_ang_i)
#mlab.show()
dis = np.sqrt(ixx **2 + iyy **2 + izz **2)
dis2 = ixx **2 + iyy **2 + izz **2
theta = np.where( dis != 0., np.arccos(izz / dis), 0.)
phi = np.where( iyy**2 + ixx **2 != 0 , np.where(iyy >= 0, np.arccos(ixx / np.sqrt(ixx **2 + iyy **2)), np.pi + np.arccos(ixx / np.sqrt(ixx **2 + iyy **2))), 0.)
#phi = np.where( iyy != 0. , phi, 0.)
#phi = np.where(iyy > 0, phi,-phi)
# region_t = np.where(dis < rofi[-1],1,0)
sph_harm_mat = np.zeros((LMAX,2 * LMAX + 1, igridpx,igridpy,igridpz),dtype = np.complex64)
for l1 in range (LMAX):
for m1 in range (-l1,l1 + 1):
sph_harm_mat[l1][m1] = np.where(dis != 0., sph_harm(m1,l1,phi,theta),0.)
g_ln_mat = np.zeros((node,LMAX,igridpx,igridpy,igridpz),dtype = np.float64)
for n1 in range (node):
for l1 in range (LMAX):
my_radial_g_inter_func = interpolate.interp1d(rofi,all_basis[l1][n1].g[:nr])
g_ln_mat[n1][l1] = my_radial_g_inter_func(np.sqrt(ixx **2 + iyy **2 + izz **2))
for n1 in range (node):
for n2 in range (node):
for l1 in range (LMAX):
for l2 in range (LMAX):
if all_basis[l1][n1].l != l1 or all_basis[l2][n2].l != l2:
print("error: L is differnt")
sys.exit()
# to avoid nan in region where it can not interpolate ie: dis > rofi
g_V_g = np.where(dis < rofi[-1], g_ln_mat[n1][l1] * V_ang_i * g_ln_mat[n2][l2], 0.)
for m1 in range (-l1,l1+1):
for m2 in range (-l2,l2+1):
#print("n1 = {} n2 = {} l1 = {} l2 = {} m1 = {} m2 = {}".format(n1,n2,l1,l2,m1,m2))
umat[n1][n2][l1][l2][m1][m2] = np.sum(np.where( dis2 != 0., sph_harm_mat[l1][m1].conjugate() * g_V_g * sph_harm_mat[l2][m2] / dis2 * gauss_weight, 0.)) * pot_region[0] * pot_region[1] * pot_region[2]
#print(umat[n1][n2][l1][l2][m1][m2])
count = 0
for l1 in range (LMAX):
for l2 in range (LMAX):
for m1 in range (-l1,l1+1):
for m2 in range (-l2,l2+1):
for n1 in range (node):
for n2 in range (node):
fw_u.write(str(count))
fw_u.write("{:>15.8f}{:>15.8f}\n".format(umat[n1][n2][l1][l2][m1][m2].real,umat[n1][n2][l1][l2][m1][m2].imag))
count += 1
fw_u.close()
t2 = time.time()
fw_t.write("calculate U-matrix\n")
fw_t.write("grid = {:<5} time ={:>11.8}s\n".format(ngrid,t2 - t1))
t1 = time.time()
ham_mat = np.zeros((nstates * nstates),dtype = np.float64)
qmetric_mat = np.zeros((nstates * nstates),dtype = np.float64)
for l1 in range(LMAX):
for m1 in range (-l1,l1+1):
for n1 in range(node):
for l2 in range(LMAX):
for m2 in range(-l2,l2+1):
for n2 in range(node):
if l1 == l2 and m1 == m2 :
ham_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] += hs_L[l1][l2][n1][n2]
qmetric_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] = qmat[l1][l2][n1][n2]
ham_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] += umat[n1][n2][l1][l2][m1][m2].real
lambda_mat = np.zeros(nstates * nstates,dtype = np.float64)
alphalong = np.zeros(nstates)
betalong = np.zeros(nstates)
alpha = np.zeros(LMAX**2)
beta = np.zeros(LMAX**2)
reveclong = np.zeros(nstates * nstates)
revec = np.zeros((LMAX**2,nstates))
for e_num in range(1,2):
E = e_num * 1
lambda_mat = np.zeros(nstates * nstates,dtype = np.float64)
lambda_mat -= ham_mat
"""
for i in range(nstates):
lambda_mat[i + i * nstates] += E
"""
count = 0
fw_lam = open("lambda.dat",mode="w")
for l1 in range(LMAX):
for m1 in range (-l1,l1+1):
for n1 in range(node):
for l2 in range(LMAX):
for m2 in range(-l2,l2+1):
for n2 in range(node):
if l1 == l2 and m1 == m2 :
lambda_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] += Smat[l1][l2][n1][n2] * E
fw_lam.write(str(count))
fw_lam.write("{:>15.8f}\n".format(lambda_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2]))
count += 1
fw_lam.close()
info = solve_genev(nstates,lambda_mat,qmetric_mat,alphalong,betalong,reveclong)
print("info = ",info)
print("alphalong")
print(alphalong)
print("betalong")
print(betalong)
#print(revec)
k = 0
jk = np.zeros(nstates,dtype=np.int32)
for i in range(nstates):
if abs(betalong[i]) > BETAZERO :
jk[k] = i
k += 1
if k != LMAX**2:
print(" main PANIC: solution of genev has rank k != nchannels ")
sys.exit()
for k in range(LMAX**2):
j = jk[k]
alpha[k] = alphalong[j]
beta[k] = betalong[j]
revec[k] = reveclong[j * nstates : (j + 1) * nstates]
fw_revec = open("revec.dat",mode="w")
print("revec")
for j in range(nstates):
fw_revec.write("{:>4}".format(j))
for i in range(LMAX**2):
fw_revec.write("{:>13.8f}".format(revec[i][j]))
print("{:>11.6f}".format(revec[i][j]),end="")
print("")
fw_revec.write("\n")
print("")
fw_revec.close()
t2 = time.time()
fw_t.write("solve eigenvalue progrem\n")
fw_t.write("time = {:>11.8}s\n".format(t2-t1))
fw_t.close()
def main():
# make environment
fw_t = open("time_log",mode="w")
t1 = time.time()
pot_region,bound_rad,radius,region,nr,gridpx,gridpy,gridpz,x,y,z,xx,yy,zz,a,b,rofi,pot_type,pot_bottom,pot_show_f,si_method,radial_pot_show_f,new_radial_pot_show_f,node_open,node_close,LMAX = make_environment()
# make potential
V = makepotential(xx,yy,zz,pot_region,pot_type=pot_type,pot_bottom=pot_bottom,pot_show_f=pot_show_f)
# surface integral
V_radial = surfaceintegral(x,y,z,rofi,V,si_method=si_method,radial_pot_show_f=radial_pot_show_f)
V_radial_new = make_V_radial_new(V_radial,rofi,pot_region,bound_rad,new_radial_pot_show_f=new_radial_pot_show_f)
vofi = np.array (V_radial_new) # select method of surface integral
# make basis
node = node_open + node_close
nstates = node * LMAX**2
all_basis = make_basis(LMAX,node_open,node_close,nr,a,b,rofi,vofi)
#make spherical matrix element
Smat = np.zeros((LMAX,LMAX,node,node),dtype = np.float64)
hsmat = np.zeros((LMAX,LMAX,node,node),dtype = np.float64)
lmat = np.zeros((LMAX,LMAX,node,node), dtype = np.float64)
qmat = np.zeros((LMAX,LMAX,node,node), dtype = np.float64)
for l1 in range (LMAX):
for l2 in range (LMAX):
if l1 != l2 :
continue
for n1 in range (node):
for n2 in range (node):
if all_basis[l1][n1].l != l1 or all_basis[l2][n2].l != l2:
print("error: L is differnt")
sys.exit()
Smat[l1][l2][n1][n2] = integrate(all_basis[l1][n1].g[:nr] * all_basis[l2][n2].g[:nr],rofi,nr)
hsmat[l1][l2][n1][n2] = Smat[l1][l2][n1][n2] * all_basis[l2][n2].e
lmat[l1][l2][n1][n2] = all_basis[l1][n1].val * all_basis[l2][n2].slo
qmat[l1][l2][n1][n2] = all_basis[l1][n1].val * all_basis[l2][n2].val
print("\nSmat")
print(Smat)
print ("\nhsmat")
print (hsmat)
print ("\nlmat")
print (lmat)
print ("\nqmat")
print (qmat)
hs_L = np.zeros((LMAX,LMAX,node,node))
"""
for l1 in range(LMAX):
for n1 in range(node):
for l2 in range(LMAX):
for n2 in range(node):
print("{:>8.4f}".format(lmat[l1][l2][n1][n2]),end="")
print("")
print("")
"""
print("hs_L")
for l1 in range(LMAX):
for n1 in range(node):
for l2 in range(LMAX):
for n2 in range(node):
hs_L[l1][l2][n1][n2] = hsmat[l1][l2][n1][n2] + lmat[l1][l2][n1][n2]
print("{:>8.4f}".format(hs_L[l1][l2][n1][n2]),end="")
print("")
t2 = time.time()
fw_t.write("make environment, make basis and calculate spherical matrix element\n")
fw_t.write("time = {:>11.8}s\n".format(t2-t1))
t1 = time.time()
#make not spherical potential
my_radial_interfunc = interpolate.interp1d(rofi, V_radial_new)
V_ang = np.where(np.sqrt(xx * xx + yy * yy + zz * zz) < rofi[-1] , V - my_radial_interfunc(np.sqrt(xx **2 + yy **2 + zz **2)),0. )
"""
for i in range(gridpx):
for j in range(gridpy):
for k in range(gridpz):
print(V_ang[i][j][k],end=" ")
print("")
print("\n")
sys.exit()
"""
#WARING!!!!!!!!!!!!!!!!!!!!!!
"""
Fujikata rewrote ~/.local/lib/python3.6/site-packages/scipy/interpolate/interpolate.py line 690~702
To avoid exit with error "A value in x_new is below the interpolation range."
"""
#!!!!!!!!!!!!!!!!!!!!!!!!!!!
"""
with open ("V_ang.dat",mode = "w") as fw_a:
for i in range(len(V_ang)):
fw_a.write("{:>13.8f}".format(xx[50][i][50]))
fw_a.write("{:>13.8f}\n".format(V_ang[i][50][50]))
"""
#mayavi.mlab.plot3d(xx,yy,V_ang)
# mlab.contour3d(V_ang,color = (1,1,1),opacity = 0.1)
# obj = mlab.volume_slice(V_ang)
# mlab.show()
ngrid = 10
fw_u = open("umat_gauss.dat",mode="w")
umat = np.zeros((LMAX,2 * LMAX + 1,node,LMAX,2 * LMAX + 1,node), dtype = np.complex64)
igridpx = ngrid
igridpy = ngrid
igridpz = ngrid
gauss_px,gauss_wx = np.polynomial.legendre.leggauss(igridpx)
gauss_py,gauss_wy = np.polynomial.legendre.leggauss(igridpy)
gauss_pz,gauss_wz = np.polynomial.legendre.leggauss(igridpz)
ix,iy,iz = gauss_px * pot_region[0],gauss_py * pot_region[1],gauss_pz * pot_region[2]
ixx,iyy,izz = np.meshgrid(ix,iy,iz)
gauss_weight = np.zeros((igridpx,igridpy,igridpz))
for i in range(igridpx):
for j in range(igridpy):
for k in range(igridpz):
gauss_weight[i][j][k] = gauss_wx[i] * gauss_wy[j] * gauss_wz[k]
#my_V_ang_inter_func = RegularGridInterpolator((x, y, z), V_ang)
#V_ang_i = my_V_ang_inter_func((ixx,iyy,izz))
V_ang_i = np.zeros((igridpx,igridpy,igridpz))
V_ang_i = -1. - my_radial_interfunc(np.sqrt(ixx * ixx + iyy * iyy + izz * izz))
#mlab.contour3d(V_ang_i,color = (1,1,1),opacity = 0.1)
#obj = mlab.volume_slice(V_ang_i)
#mlab.show()
dis = np.sqrt(ixx **2 + iyy **2 + izz **2)
dis2 = ixx **2 + iyy **2 + izz **2
theta = np.where( dis != 0., np.arccos(izz / dis), 0.)
phi = np.where( iyy**2 + ixx **2 != 0 , np.where(iyy >= 0, np.arccos(ixx / np.sqrt(ixx **2 + iyy **2)), np.pi + np.arccos(ixx / np.sqrt(ixx **2 + iyy **2))), 0.)
#phi = np.where( iyy != 0. , phi, 0.)
#phi = np.where(iyy > 0, phi,-phi)
# region_t = np.where(dis < rofi[-1],1,0)
sph_harm_mat = np.zeros((LMAX,2 * LMAX + 1, igridpx,igridpy,igridpz),dtype = np.complex64)
g_V_g = np.zeros((LMAX,node,LMAX,node,igridpx,igridpy,igridpz))
for l1 in range (LMAX):
for m1 in range (-l1,l1 + 1):
sph_harm_mat[l1][m1] = np.where(dis != 0., sph_harm(m1,l1,phi,theta),0.)
g_ln_mat = np.zeros((LMAX,node,igridpx,igridpy,igridpz),dtype = np.float64)
for l1 in range (LMAX):
for n1 in range (node):
my_radial_g_inter_func = interpolate.interp1d(rofi,all_basis[l1][n1].g[:nr])
g_ln_mat[l1][n1] = my_radial_g_inter_func(np.sqrt(ixx **2 + iyy **2 + izz **2))
for l1 in range (LMAX):
for n1 in range (node):
for l2 in range (LMAX):
for n2 in range (node):
# to avoid nan in region where it can not interpolate ie: dis > rofi
g_V_g[l1][n1][l2][n2] = np.where(dis < rofi[-1], g_ln_mat[l1][n1] * V_ang_i * g_ln_mat[l2][n2], 0.)
for l1 in range (LMAX):
for m1 in range (-l1,l1+1):
for l2 in range (l1+1):
for m2 in range (-l2,l2+1):
if all_basis[l1][n1].l != l1 or all_basis[l2][n2].l != l2:
print("error: L is differnt")
sys.exit()
for n1 in range (node):
for n2 in range (node):
#print("n1 = {} n2 = {} l1 = {} l2 = {} m1 = {} m2 = {}".format(n1,n2,l1,l2,m1,m2))
umat[l1][m1][n1][l2][m2][n2] = np.sum(np.where( dis2 != 0., sph_harm_mat[l1][m1].conjugate() * g_V_g[l1][n1][l2][n2] * sph_harm_mat[l2][m2] / dis2 * gauss_weight, 0.)) * pot_region[0] * pot_region[1] * pot_region[2]
#print(umat[n1][n2][l1][l2][m1][m2])
for l1 in range (LMAX):
for m1 in range (-l1,l1+1):
for l2 in range (l1+1,LMAX):
for m2 in range (-l2,l2+1):
if all_basis[l1][n1].l != l1 or all_basis[l2][n2].l != l2:
print("error: L is differnt")
sys.exit()
for n1 in range (node):
for n2 in range (node):
#print("n1 = {} n2 = {} l1 = {} l2 = {} m1 = {} m2 = {}".format(n1,n2,l1,l2,m1,m2))
umat[l1][m1][n1][l2][m2][n2] = umat[l2][m2][n2][l1][m1][n1].conjugate()
#print(umat[n1][n2][l1][l2][m1][m2])
count = 0
for l1 in range (LMAX):
for l2 in range (LMAX):
for m1 in range (-l1,l1+1):
for m2 in range (-l2,l2+1):
for n1 in range (node):
for n2 in range (node):
fw_u.write(str(count))
fw_u.write("{:>15.8f}{:>15.8f}\n".format(umat[l1][m1][n1][l2][m2][n2].real,umat[l1][m1][n1][l2][m2][n2].imag))
count += 1
fw_u.close()
t2 = time.time()
fw_t.write("calculate U-matrix\n")
fw_t.write("grid = {:<5} time ={:>11.8}s\n".format(ngrid,t2 - t1))
fw_q = open("qmat.dat",mode="w")
ham_mat = np.zeros((nstates * nstates),dtype = np.float64)
qmetric_mat = np.zeros((nstates * nstates),dtype = np.float64)
count = 0
for l1 in range(LMAX):
for m1 in range (-l1,l1+1):
for n1 in range(node):
for l2 in range(LMAX):
for m2 in range(-l2,l2+1):
for n2 in range(node):
if l1 == l2 and m1 == m2 :
ham_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] += hs_L[l1][l2][n1][n2]
qmetric_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] = qmat[l1][l2][n1][n2]
ham_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] += umat[l1][m1][n1][l2][m2][n2].real
fw_q.write(str(count))
fw_q.write("{:>15.8f}\n".format(qmetric_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2]))
count += 1
fw_q.close()
fw_e=open("tmatrix_s.dat",mode="w")
for e_num in range(1,2):
lambda_mat = np.zeros(nstates * nstates,dtype = np.float64)
alphalong = np.zeros(nstates)
betalong = np.zeros(nstates)
alpha = np.zeros(LMAX**2)
beta = np.zeros(LMAX**2)
reveclong = np.zeros(nstates * nstates)
revec = np.zeros((LMAX**2,nstates))
normfac = np.zeros(LMAX**2)
Wlk = np.zeros((LMAX**2,LMAX**2))
R_matrix = np.zeros((LMAX**2,LMAX**2))
t1 = time.time()
E = e_num *0.1
lambda_mat = np.zeros(nstates * nstates,dtype = np.float64)
lambda_mat -= ham_mat
"""
for i in range(nstates):
lambda_mat[i + i * nstates] += E
"""
count = 0
fw_lam = open("lambda.dat",mode="w")
for l1 in range(LMAX):
for m1 in range (-l1,l1+1):
for n1 in range(node):
for l2 in range(LMAX):
for m2 in range(-l2,l2+1):
for n2 in range(node):
if l1 == l2 and m1 == m2 :
lambda_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2] += Smat[l1][l2][n1][n2] * E
fw_lam.write(str(count))
fw_lam.write("{:>15.8f}\n".format(lambda_mat[l1 **2 * node * LMAX**2 * node + (l1 + m1) * node * LMAX**2 * node + n1 * LMAX**2 * node + l2 **2 * node + (l2 + m2) * node + n2]))
count += 1
fw_lam.close()
info = solve_genev(nstates,lambda_mat,qmetric_mat,alphalong,betalong,reveclong)
fw_rev = open("reveclong.dat",mode="w")
for i in range(nstates,2 * nstates):
fw_rev.write(str(i))
fw_rev.write("{:>15.8f}\n".format(reveclong[i]))
fw_rev.close()
print("info = ",info)
print("alphalong")
print(alphalong)
print("betalong")
print(betalong)
#print(revec)
k = 0
jk = np.zeros(nstates,dtype=np.int32)
for i in range(nstates):
if abs(betalong[i]) > BETAZERO :
jk[k] = i
k += 1
if k != LMAX**2:
print(" main PANIC: solution of genev has rank k != nchannels ")
sys.exit()
for k in range(LMAX**2):
j = jk[k]
alpha[k] = alphalong[j]
beta[k] = betalong[j]
revec[k] = reveclong[j * nstates : (j + 1) * nstates]
Wdagger = np.zeros(nstates*nstates)
for k in range(LMAX**2):
dum = 0
for l in range(LMAX):
for m in range(-l,l+1):
for n in range(node):
Wlk[l**2 + (l+m)][k] += revec[k][l**2*node + (l+m)*node + n] * all_basis[l][n].val#.g[nr-1]
dum += Wlk[l**2 + (l+m)][k] **2
normfac[k] = 1 / np.sqrt(dum)
Wlk[:,k] *= normfac[k]
lm1=0
for l in range(LMAX):
for m in range(-l,l+1):
Wdagger[lm1 * LMAX**2+k] = Wlk[l**2 + (l+m)][k]
lm1 += 1
"""
for l in range(LMAX):
for m in range(-l,l+1):
Wlk[l**2 + (l+m)][k] *= normfac[k]
"""
print("Wlk")
for l in range(LMAX):
for m in range(-l,l+1):
for k in range(LMAX**2):
print("{:>8.4f}".format(Wlk[l**2 + (l + m)][k]),end=" ")
print("")
print("Wdagger")
for k in range(LMAX**2):
for l in range(LMAX):
for m in range(-l,l+1):
print("{:>8.4f}".format(Wdagger[(l**2 + (l + m)) * LMAX**2+ k]),end=" ")
print("")
print("R-matrix")
for l1 in range(LMAX):
for m1 in range(-l1,l1+1):
for l2 in range(LMAX):
for m2 in range(-l2,l2+1):
for k in range(LMAX**2):
R_matrix[l1**2+(l1+m1)][l2**2+(l2+m2)] -= Wlk[l1**2 + (l1+m1)][k] * beta[k] / alpha[k] * Wlk[l2**2 + (l2+m2)][k]
print ("{:>8.4f}".format(R_matrix[l1**2+(l1+m1)][l2**2+(l2+m2)]),end="")
print("")
fw_revec = open("revec.dat",mode="w")
print("revec")
for j in range(nstates):
fw_revec.write("{:>4}".format(j))
for i in range(LMAX**2):
fw_revec.write("{:>13.8f}".format(revec[i][j]))
print("{:>11.6f}".format(revec[i][j]),end="")
print("")
fw_revec.write("\n")
print("")
fw_revec.close()
t2 = time.time()
fw_t.write("solve eigenvalue progrem\n")
fw_t.write("time = {:>11.8}s\n".format(t2-t1))
rkbes = np.zeros(LMAX**2)
drkbes = np.zeros(LMAX**2)
rkneu = np.zeros(LMAX**2)
drkneu = np.zeros(LMAX**2)
mat1 = np.zeros((LMAX**2*LMAX**2))
mat2 = np.zeros((LMAX**2,LMAX**2))
X_matrix = np.zeros((LMAX**2,LMAX**2))
t_matrix = np.zeros((LMAX**2,LMAX**2),dtype=np.complex64)
if E < 0 :
modified = 1
realk = np.sqrt(-E)
else:
modified = 0
realk = np.sqrt(E)
kr = realk * radius
for l in range(LMAX):
for m in range(-l,l+1):
jl,nl,jlp,nlp = besneu(modified,kr,l)
rkbes[l**2 + (l+m)] = kr * jl
drkbes[l**2 + (l+m)] = realk * jl + realk * kr * jlp
rkneu[l**2 + (l+m)] = kr * nl
drkneu[l**2 + (l+m)] = realk * nl * realk * kr * nlp
mat1 = np.zeros((LMAX**2 * LMAX**2))
for i in range(LMAX**2):
for j in range(LMAX**2):
wij = Wdagger[i + LMAX**2 * j]
mat1[i + LMAX**2 * j] = alpha[i] * wij * rkbes[j] + beta[i] *wij * drkbes[j]
print("mat1")
for i in range(LMAX**2):
for j in range(LMAX**2):
print("{:>8.4f}".format(mat1[j*LMAX**2 + i]),end="")
print("")
inv_remat(LMAX**2,mat1)
mat1line = np.zeros(LMAX**2)
for i in range(LMAX**2):
for j in range(LMAX**2):
mat1line[j] = mat1[i + LMAX**2 * j]
for j in range(LMAX**2):
sum_ = 0
for k in range(LMAX**2):
wkj = Wdagger[k+LMAX**2*j]
mat2kj = alpha[k] * wkj * rkneu[ j ] + beta[k] * wkj * drkneu[ j ]
sum_ += mat1line[k] * mat2kj
mat1[ i + LMAX**2 * j ] = sum_
tau = np.zeros(LMAX**2*LMAX**2*2)
for i in range(LMAX**2):
for j in range(LMAX**2):
xij = mat1[i+LMAX**2*j]
if i ==j:
deltaij = 1
else:
deltaij = 0
ijre = 2 *(i+LMAX**2*j)
tau[ijre ] = - realk * xij
if modified:
tau[ijre ] += - realk * deltaij
tau[ijre+1] = 0
else:
tau[ijre+1] = - realk * deltaij
print("t_matrix_real_inv")
for i in range(LMAX**2):
for j in range(LMAX**2):
ijre = 2 *(i+LMAX**2*j)
print("{:>8.4f}".format(tau[ijre]),end="")
print("")
sys.exit()
t_matrix = np.linalg.inv(t_matrix)
print("t_matrix_real")
for i in range(LMAX**2):
for j in range(LMAX**2):
print("{:>8.4f}".format(t_matrix[i][j].real),end="")
print("")
fw_e.write("{:>13.8f}{:>13.8f}\n".format(E,t_matrix[0][0].real))
fw_e.close()
fw_t.close()