def interp_phi(df, x, y, z, df_alt=None, plot=True):
"""First thing's first. Plot the xyz point, and the immediate cube around it."""
df_trimmed = df.query('{0}<=X<={1} and {2}<=Y<={3} and {4}<=Z<={5}'.format(
x - 25, x + 25, y - 25, y + 25, z - 25, z + 25))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_true = df_trimmed.query('X=={0} and Y=={1} and Z=={2}'.format(x, y, z))
if len(df_true) == 1:
bx_interp = df_true.Bx
by_interp = df_true.By
bz_interp = df_true.Bz
else:
if len(df_trimmed.X.unique()) == len(df_trimmed.Y.unique()) == len(
df_trimmed.Z.unique()):
df_trimmed = df_trimmed.query(
'X!={0} and Y!={1} and Z!={2}'.format(x, y, z))
else:
xs = np.sort(df_trimmed.X.unique())
ys = np.sort(df_trimmed.Y.unique())
zs = np.sort(df_trimmed.Z.unique())
df_trimmed = df_trimmed.query(
'(X=={0} or X=={1}) and (Y=={2} or Y=={3}) and (Z=={4} or Z=={5})'
.format(xs[0], xs[1], ys[0], ys[1], zs[0], zs[1]))
df_trimmed = df_trimmed.sort_values(['X', 'Y',
'Z']).reset_index(drop=True)
# indices: 0 1 2 3 4 5 6 7
df_trimmed['Vertex'] = [
'p000', 'p001', 'p010', 'p011', 'p100', 'p101', 'p110', 'p111'
]
x_rel = (x - df_trimmed.ix[0].X) / (df_trimmed.ix[4].X -
df_trimmed.ix[0].X)
y_rel = (y - df_trimmed.ix[0].Y) / (df_trimmed.ix[2].Y -
df_trimmed.ix[0].Y)
z_rel = (z - df_trimmed.ix[0].Z) / (df_trimmed.ix[1].Z -
df_trimmed.ix[0].Z)
# print x_rel
bx_interp = ((y_rel) * (z_rel) * (x_rel * df_trimmed.ix[7].Bx +
(1 - x_rel) * df_trimmed.ix[3].Bx) +
(1 - y_rel) * (z_rel) *
(x_rel * df_trimmed.ix[5].Bx +
(1 - x_rel) * df_trimmed.ix[1].Bx) + (y_rel) *
(1 - z_rel) * (x_rel * df_trimmed.ix[6].Bx +
(1 - x_rel) * df_trimmed.ix[2].Bx) +
(1 - y_rel) * (1 - z_rel) *
(x_rel * df_trimmed.ix[4].Bx +
(1 - x_rel) * df_trimmed.ix[0].Bx))
by_interp = ((x_rel) * (z_rel) * (y_rel * df_trimmed.ix[7].By +
(1 - y_rel) * df_trimmed.ix[5].By) +
(1 - x_rel) * (z_rel) *
(y_rel * df_trimmed.ix[3].By +
(1 - y_rel) * df_trimmed.ix[1].By) + (x_rel) *
(1 - z_rel) * (y_rel * df_trimmed.ix[6].By +
(1 - y_rel) * df_trimmed.ix[4].By) +
(1 - x_rel) * (1 - z_rel) *
(y_rel * df_trimmed.ix[2].By +
(1 - y_rel) * df_trimmed.ix[0].By))
bz_interp = ((x_rel) * (y_rel) * (z_rel * df_trimmed.ix[7].Bz +
(1 - z_rel) * df_trimmed.ix[6].Bz) +
(1 - x_rel) * (y_rel) *
(z_rel * df_trimmed.ix[3].Bz +
(1 - z_rel) * df_trimmed.ix[2].Bz) + (x_rel) *
(1 - y_rel) * (z_rel * df_trimmed.ix[5].Bz +
(1 - z_rel) * df_trimmed.ix[4].Bz) +
(1 - x_rel) * (1 - y_rel) *
(z_rel * df_trimmed.ix[1].Bz +
(1 - z_rel) * df_trimmed.ix[0].Bz))
if plot:
init_notebook_mode()
trace1 = go.Scatter3d(
x=df_trimmed.X,
y=df_trimmed.Y,
z=df_trimmed.Z,
mode='markers',
marker=dict(
size=12,
line=dict(color='rgba(217, 217, 217, 0.14)', width=0.5),
opacity=0.8,
),
text=df_trimmed.Vertex,
)
trace2 = go.Scatter3d(x=[x],
y=[y],
z=[z],
mode='markers',
marker=dict(color='rgb(127, 127, 127)',
size=12,
symbol='circle',
line=dict(color='rgb(204, 204, 204)',
width=1),
opacity=0.9))
data = [trace1, trace2]
layout = go.Layout(margin=dict(l=0, r=0, b=0, t=0), )
fig = go.Figure(data=data, layout=layout)
iplot(fig)
return df_trimmed, [bx_interp, by_interp, bz_interp]
def interp_phi_quad(df, x, y, z, plot=False):
df_trimmed = df.query('{0}<=X<={1} and {2}<=Y<={3} and {4}<=Z<={5}'.format(
x - 37.5, x + 37.5, y - 37.5, y + 37.5, z - 37.5, z + 37.5))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y', 'Z']).reset_index(drop=True)
#df_true = df_trimmed.query('X=={0} and Y=={1} and Z=={2}'.format(x, y, z))
#if len(df_true) == 1:
#pass
# bx_interp = df_true.Bx
# by_interp = df_true.By
# bz_interp = df_true.Bz
if False:
pass
else:
df_trimmed['Vertex'] = [
# 0 1 2 3 4 5 6 7 8
'-1-1-1',
'-1-10',
'-1-11',
'-10-1',
'-100',
'-101',
'-11-1',
'-110',
'-111',
# 9 10 11 12 13 14 15 16 17
'0-1-1',
'0-10',
'0-11',
'00-1',
'000',
'001',
'01-1',
'010',
'011',
# 18 19 20 21 22 23 24 25 26
'1-1-1',
'1-10',
'1-11',
'10-1',
'100',
'101',
'11-1',
'110',
'111',
]
x_rel = (x - df_trimmed.ix[13].X) / (25.0)
y_rel = (y - df_trimmed.ix[13].Y) / (25.0)
z_rel = (z - df_trimmed.ix[13].Z) / (25.0)
# print x_rel, y_rel, z_rel
bxs = df_trimmed.Bx
bys = df_trimmed.By
bzs = df_trimmed.Bz
tuning = 0.02
bx_interp = -(tuning *
(x_rel *
((x_rel + 1) * bxs[13] - x_rel * bxs[4]) - x_rel *
((1 - x_rel) * bxs[13] + x_rel * bxs[22])) + -(
((bxs[4] + bxs[22]) / 2.0 - bxs[13]) * x_rel**2 +
((bxs[22] - bxs[4]) / 2.0) * x_rel + bxs[13]))
#bx_interp = -(
# x_rel*0.5*(bxs[4]+bxs[13]) - x_rel*0.5*(bxs[13]+bxs[22]) -
# (1.0/6.0)*(bxs[4]+4*bxs[13]+bxs[22])
#)
#bx_interp = (
# ((
# #(min(0, x_rel)*(abs(x_rel)*bxs[9]-(1-abs(x_rel))*bxs[18])) -
# (((bxs[0]+bxs[18])/2.0-bxs[9])*x_rel**2+((bxs[18]-bxs[0])/2.0)*x_rel+bxs[9])) *
# 0.5*(y_rel**2-y_rel) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[12]-(1-abs(x_rel))*bxs[21])) -
# (((bxs[3]+bxs[21])/2.0-bxs[12])*x_rel**2+((bxs[21]-bxs[3])/2.0)*x_rel+bxs[12])) *
# (-y_rel**2+1) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[15]-(1-abs(x_rel))*bxs[24])) -
# (((bxs[6]+bxs[24])/2.0-bxs[15])*x_rel**2+((bxs[24]-bxs[6])/2.0)*x_rel+bxs[15])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2-z_rel) +
#((
# #(min(0, x_rel)*(abs(x_rel)*bxs[10]-(1-abs(x_rel))*bxs[19])) -
# (((bxs[1]+bxs[19])/2.0-bxs[10])*x_rel**2+((bxs[19]-bxs[1])/2.0)*x_rel+bxs[10])) *
# 0.5*(y_rel**2-y_rel) +
# (
#(min(0, x_rel)*(abs(x_rel)*bxs[13]-(1-abs(x_rel))*bxs[22])) -
# (((bxs[4]+bxs[22])/2.0-bxs[13])*x_rel**2+((bxs[22]-bxs[4])/2.0)*x_rel+bxs[13])) *
# (-y_rel**2+1) #+
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[16]-(1-abs(x_rel))*bxs[25])) -
# (((bxs[7]+bxs[25])/2.0-bxs[16])*x_rel**2+((bxs[25]-bxs[7])/2.0)*x_rel+bxs[16])) *
# 0.5*(y_rel**2+y_rel))*(-z_rel**2+1) +
#((
# #(min(0, x_rel)*(abs(x_rel)*bxs[11]-(1-abs(x_rel))*bxs[20])) -
# (((bxs[2]+bxs[20])/2.0-bxs[11])*x_rel**2+((bxs[20]-bxs[2])/2.0)*x_rel+bxs[11])) *
# 0.5*(y_rel**2-y_rel) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[14]-(1-abs(x_rel))*bxs[23])) -
# (((bxs[5]+bxs[23])/2.0-bxs[14])*x_rel**2+((bxs[23]-bxs[5])/2.0)*x_rel+bxs[14])) *
# (-y_rel**2+1) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[17]-(1-abs(x_rel))*bxs[26])) -
# (((bxs[8]+bxs[26])/2.0-bxs[17])*x_rel**2+((bxs[26]-bxs[8])/2.0)*x_rel+bxs[17])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2+z_rel)
#)
# bx_interp = -(
# ((-(((bxs[0]+bxs[18])/2.0-bxs[9])*x_rel**2+((bxs[18]-bxs[0])/2.0)*x_rel+bxs[9])) *
# 0.5*(y_rel**2-y_rel) +
# (-(((bxs[3]+bxs[21])/2.0-bxs[12])*x_rel**2+((bxs[21]-bxs[3])/2.0)*x_rel+bxs[12])) *
# (-y_rel**2+1) +
# (-(((bxs[6]+bxs[24])/2.0-bxs[15])*x_rel**2+((bxs[24]-bxs[6])/2.0)*x_rel+bxs[15])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2-z_rel) +
# ((-(((bxs[1]+bxs[19])/2.0-bxs[10])*x_rel**2+((bxs[19]-bxs[1])/2.0)*x_rel+bxs[10])) *
# 0.5*(y_rel**2-y_rel) +
# (-(((bxs[4]+bxs[22])/2.0-bxs[13])*x_rel**2+((bxs[22]-bxs[4])/2.0)*x_rel+bxs[13])) *
# (-y_rel**2+1) +
# (-(((bxs[7]+bxs[25])/2.0-bxs[16])*x_rel**2+((bxs[25]-bxs[7])/2.0)*x_rel+bxs[16])) *
# 0.5*(y_rel**2+y_rel))*(-z_rel**2+1) +
# ((-(((bxs[2]+bxs[20])/2.0-bxs[11])*x_rel**2+((bxs[20]-bxs[2])/2.0)*x_rel+bxs[11])) *
# 0.5*(y_rel**2-y_rel) +
# (-(((bxs[5]+bxs[23])/2.0-bxs[14])*x_rel**2+((bxs[23]-bxs[5])/2.0)*x_rel+bxs[14])) *
# (-y_rel**2+1) +
# (-(((bxs[8]+bxs[26])/2.0-bxs[17])*x_rel**2+((bxs[26]-bxs[8])/2.0)*x_rel+bxs[17])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2+z_rel)
# )
by_interp = -(
((-(((bys[0] + bys[6]) / 2.0 - bys[3]) * y_rel**2 +
((bys[6] - bys[0]) / 2.0) * y_rel + bys[3])) * 0.5 *
(x_rel**2 - x_rel) +
(-(((bys[9] + bys[15]) / 2.0 - bys[12]) * y_rel**2 +
((bys[15] - bys[9]) / 2.0) * y_rel + bys[12])) *
(-x_rel**2 + 1) +
(-(((bys[18] + bys[24]) / 2.0 - bys[21]) * y_rel**2 +
((bys[24] - bys[18]) / 2.0) * y_rel + bys[21])) * 0.5 *
(x_rel**2 + x_rel)) * 0.5 * (z_rel**2 - z_rel) +
((-(((bys[1] + bys[7]) / 2.0 - bys[4]) * y_rel**2 +
((bys[7] - bys[1]) / 2.0) * y_rel + bys[4])) * 0.5 *
(x_rel**2 - x_rel) +
(-(((bys[10] + bys[16]) / 2.0 - bys[13]) * y_rel**2 +
((bys[16] - bys[10]) / 2.0) * y_rel + bys[13])) *
(-x_rel**2 + 1) +
(-(((bys[19] + bys[25]) / 2.0 - bys[22]) * y_rel**2 +
((bys[25] - bys[19]) / 2.0) * y_rel + bys[22])) * 0.5 *
(x_rel**2 + x_rel)) * (-z_rel**2 + 1) +
((-(((bys[2] + bys[8]) / 2.0 - bys[5]) * y_rel**2 +
((bys[8] - bys[2]) / 2.0) * y_rel + bys[5])) * 0.5 *
(x_rel**2 - x_rel) +
(-(((bys[11] + bys[17]) / 2.0 - bys[14]) * y_rel**2 +
((bys[17] - bys[11]) / 2.0) * y_rel + bys[14])) *
(-x_rel**2 + 1) +
(-(((bys[20] + bys[26]) / 2.0 - bys[23]) * y_rel**2 +
((bys[26] - bys[20]) / 2.0) * y_rel + bys[23])) * 0.5 *
(x_rel**2 + x_rel)) * 0.5 * (z_rel**2 + z_rel))
bz_interp = -(
((-(((bzs[0] + bzs[2]) / 2.0 - bzs[1]) * z_rel**2 +
((bzs[2] - bzs[0]) / 2.0) * z_rel + bzs[1])) * 0.5 *
(x_rel**2 - x_rel) +
(-(((bzs[9] + bzs[11]) / 2.0 - bzs[10]) * z_rel**2 +
((bzs[11] - bzs[9]) / 2.0) * z_rel + bzs[10])) *
(-x_rel**2 + 1) +
(-(((bzs[18] + bzs[20]) / 2.0 - bzs[19]) * z_rel**2 +
((bzs[20] - bzs[18]) / 2.0) * z_rel + bzs[19])) * 0.5 *
(x_rel**2 + x_rel)) * 0.5 * (y_rel**2 - y_rel) +
((-(((bzs[3] + bzs[5]) / 2.0 - bzs[4]) * z_rel**2 +
((bzs[5] - bzs[3]) / 2.0) * z_rel + bzs[4])) * 0.5 *
(x_rel**2 - x_rel) +
(-(((bzs[12] + bzs[14]) / 2.0 - bzs[13]) * z_rel**2 +
((bzs[14] - bzs[12]) / 2.0) * z_rel + bzs[13])) *
(-x_rel**2 + 1) +
(-(((bzs[21] + bzs[23]) / 2.0 - bzs[22]) * z_rel**2 +
((bzs[23] - bzs[21]) / 2.0) * z_rel + bzs[22])) * 0.5 *
(x_rel**2 + x_rel)) * (-y_rel**2 + 1) +
((-(((bzs[6] + bzs[8]) / 2.0 - bzs[7]) * z_rel**2 +
((bzs[8] - bzs[6]) / 2.0) * z_rel + bzs[7])) * 0.5 *
(x_rel**2 - x_rel) +
(-(((bzs[15] + bzs[17]) / 2.0 - bzs[16]) * z_rel**2 +
((bzs[17] - bzs[15]) / 2.0) * z_rel + bzs[16])) *
(-x_rel**2 + 1) +
(-(((bzs[24] + bzs[26]) / 2.0 - bzs[25]) * z_rel**2 +
((bzs[26] - bzs[24]) / 2.0) * z_rel + bzs[25])) * 0.5 *
(x_rel**2 + x_rel)) * 0.5 * (y_rel**2 + y_rel))
if plot:
init_notebook_mode()
trace1 = go.Scatter3d(
x=df_trimmed.X,
y=df_trimmed.Y,
z=df_trimmed.Z,
mode='markers',
marker=dict(
size=12,
line=dict(color='rgba(217, 217, 217, 0.14)', width=0.5),
opacity=0.8,
),
text=df_trimmed.Vertex,
)
trace2 = go.Scatter3d(x=[x],
y=[y],
z=[z],
mode='markers',
marker=dict(color='rgb(127, 127, 127)',
size=12,
symbol='circle',
line=dict(color='rgb(204, 204, 204)',
width=1),
opacity=0.9))
data = [trace1, trace2]
layout = go.Layout(margin=dict(l=0, r=0, b=0, t=0), )
fig = go.Figure(data=data, layout=layout)
iplot(fig)
return df_trimmed, [bx_interp, by_interp, bz_interp]
def interp_phi_cubic(df, x, y, z, plot=False, mode='lacey', shift=0):
if shift == 0:
df_trimmed = df.query(
'{0}<=X<{1} and {2}<=Y<{3} and {4}<=Z<{5}'.format(
x - 50, x + 50, y - 50, y + 50, z - 50, z + 50))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y',
'Z']).reset_index(drop=True)
elif shift == -1:
df_trimmed = df.query(
'{0}<=X<{1} and {2}<=Y<{3} and {4}<=Z<{5}'.format(
x - 25, x + 75, y - 50, y + 50, z - 50, z + 50))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y',
'Z']).reset_index(drop=True)
elif shift == 1:
df_trimmed = df.query(
'{0}<=X<{1} and {2}<=Y<{3} and {4}<=Z<{5}'.format(
x - 75, x + 25, y - 50, y + 50, z - 50, z + 50))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y',
'Z']).reset_index(drop=True)
else:
raise KeyError('wrong shift')
#df_true = df_trimmed.query('X=={0} and Y=={1} and Z=={2}'.format(x, y, z))
#if len(df_true) == 1:
#pass
# bx_interp = df_true.Bx
# by_interp = df_true.By
# bz_interp = df_true.Bz
if False:
pass
else:
df_trimmed['Vertex'] = [
# 0 1 2 3 4 5 6 7
'-1-1-1',
'-1-10',
'-1-11',
'-1-12',
'-10-1',
'-100',
'-101',
'-102',
# 8 9 10 11 12 13 14 15
'-11-1',
'-110',
'-111',
'-112',
'-12-1',
'-120',
'-121',
'-122',
# 16 17 18 19 20 21 22 23
'0-1-1',
'0-10',
'0-11',
'0-12',
'00-1',
'000',
'001',
'002',
# 24 25 26 27 28 29 30 31
'01-1',
'010',
'011',
'012',
'02-1',
'020',
'021',
'022',
# 32 33 34 35 36 37 38 39
'1-1-1',
'1-10',
'1-11',
'1-12',
'10-1',
'100',
'101',
'102',
# 40 41 42 43 44 45 46 47
'11-1',
'110',
'111',
'112',
'12-1',
'120',
'121',
'122',
# 48 49 50 51 52 53 54 55
'2-1-1',
'2-10',
'2-11',
'2-12',
'20-1',
'200',
'201',
'202',
# 56 57 58 59 60 61 62 63
'21-1',
'210',
'211',
'212',
'22-1',
'220',
'221',
'222',
]
index_list = list(range(0, 64))
vertex_dict = dict(list(zip(df_trimmed.Vertex, index_list)))
# Define some lagrange polynomials
def lg_mone(n):
return -(n**3 - 3 * n**2 + 2 * n) / 6.0
def lg_zero(n):
return (n**3 - 2 * n**2 - n + 2) / 2.0
def lg_one(n):
return -(n**3 - n**2 - 2 * n) / 2.0
def lg_two(n):
return (n**3 - n) / 6.0
# Numerical integration
def _int_methods(b, rel, *verts):
if len(verts) == 2:
return (b.ix[vertex_dict[verts[0]]] +
b.ix[vertex_dict[verts[1]]]) / 2.0
elif len(verts) == 3:
return (b.ix[vertex_dict[verts[0]]] +
4 * b.ix[vertex_dict[verts[1]]] +
b.ix[vertex_dict[verts[2]]]) / 3.0
else:
if mode == 'lacey':
return (b.ix[vertex_dict[verts[0]]] +
3 * b.ix[vertex_dict[verts[1]]] +
3 * b.ix[vertex_dict[verts[2]]] +
b.ix[vertex_dict[verts[3]]]) * (3.0 / 8.0)
else:
A = (-3 * b.ix[vertex_dict[verts[2]]] -
b.ix[vertex_dict[verts[0]]] +
3 * b.ix[vertex_dict[verts[1]]] +
b.ix[vertex_dict[verts[3]]]) / 6.0
B = (b.ix[vertex_dict[verts[0]]] +
b.ix[vertex_dict[verts[2]]] -
2 * b.ix[vertex_dict[verts[1]]]) / 2.0
C = (6 * b.ix[vertex_dict[verts[2]]] -
2 * b.ix[vertex_dict[verts[0]]] -
3 * b.ix[vertex_dict[verts[1]]] -
b.ix[vertex_dict[verts[3]]]) / 6.0
D = b.ix[vertex_dict[verts[1]]]
return (A * rel**3 + B * rel**2 + C * rel + D)
def num_int(b, rel, x, y, z):
if isinstance(x, collections.Sequence):
verts = [
str(i) + str(y) + str(z) for i in range(x[0], x[-1] + 1)
]
elif isinstance(y, collections.Sequence):
verts = [
str(x) + str(i) + str(z) for i in range(y[0], y[-1] + 1)
]
elif isinstance(z, collections.Sequence):
verts = [
str(x) + str(y) + str(i) for i in range(z[0], z[-1] + 1)
]
else:
raise AttributeError(
'exactly one arg in num_int must be a collection')
return _int_methods(b, rel, *verts)
def int_collection(b, rel, x, y, z):
if x == 'var':
int1 = num_int(b, rel, (-1, 2), y, z)
int2 = num_int(b, rel, (0, 1), y, z)
int3 = num_int(b, rel, (-1, 0), y, z)
int4 = int2
int5 = num_int(b, rel, (-1, 1), y, z)
int6 = int2
int7 = num_int(b, rel, (1, 2), y, z)
elif y == 'var':
int1 = num_int(b, rel, x, (-1, 2), z)
int2 = num_int(b, rel, x, (0, 1), z)
int3 = num_int(b, rel, x, (-1, 0), z)
int4 = int2
int5 = num_int(b, rel, x, (-1, 1), z)
int6 = int2
int7 = num_int(b, rel, x, (1, 2), z)
else:
int1 = num_int(b, rel, x, y, (-1, 2))
int2 = num_int(b, rel, x, y, (0, 1))
int3 = num_int(b, rel, x, y, (-1, 0))
int4 = int2
int5 = num_int(b, rel, x, y, (-1, 1))
int6 = int2
int7 = num_int(b, rel, x, y, (1, 2))
if mode == 'lacey':
return ((-rel**2 / 2.0) * int1 + (3 * rel**2 / 2.0) * int2 +
rel * int3 - rel * int4 - (1 / 3.0) * int5 -
0.5 * int6 + (1 / 6.0) * int7)
else:
return -int1
x_rel = (x - df_trimmed.ix[21].X) / (25.0)
y_rel = (y - df_trimmed.ix[21].Y) / (25.0)
z_rel = (z - df_trimmed.ix[21].Z) / (25.0)
# print x_rel, y_rel, z_rel
bxs = df_trimmed.Bx
bys = df_trimmed.By
bzs = df_trimmed.Bz
bx_interp = -(
lg_mone(z_rel) *
(lg_mone(y_rel) *
(int_collection(bxs, x_rel, 'var', -1, -1)) + lg_zero(y_rel) *
(int_collection(bxs, x_rel, 'var', 0, -1)) + lg_one(y_rel) *
(int_collection(bxs, x_rel, 'var', 1, -1)) + lg_two(y_rel) *
(int_collection(bxs, x_rel, 'var', 2, -1))) + lg_zero(z_rel) *
(lg_mone(y_rel) *
(int_collection(bxs, x_rel, 'var', -1, 0)) + lg_zero(y_rel) *
(int_collection(bxs, x_rel, 'var', 0, 0)) + lg_one(y_rel) *
(int_collection(bxs, x_rel, 'var', 1, 0)) + lg_two(y_rel) *
(int_collection(bxs, x_rel, 'var', 2, 0))) + lg_one(z_rel) *
(lg_mone(y_rel) *
(int_collection(bxs, x_rel, 'var', -1, 1)) + lg_zero(y_rel) *
(int_collection(bxs, x_rel, 'var', 0, 1)) + lg_one(y_rel) *
(int_collection(bxs, x_rel, 'var', 1, 1)) + lg_two(y_rel) *
(int_collection(bxs, x_rel, 'var', 2, 1))) + lg_two(z_rel) *
(lg_mone(y_rel) *
(int_collection(bxs, x_rel, 'var', -1, 2)) + lg_zero(y_rel) *
(int_collection(bxs, x_rel, 'var', 0, 2)) + lg_one(y_rel) *
(int_collection(bxs, x_rel, 'var', 1, 2)) + lg_two(y_rel) *
(int_collection(bxs, x_rel, 'var', 2, 2))))
by_interp = -(
lg_mone(z_rel) *
(lg_mone(x_rel) *
(int_collection(bys, y_rel, -1, 'var', -1)) + lg_zero(x_rel) *
(int_collection(bys, y_rel, 0, 'var', -1)) + lg_one(x_rel) *
(int_collection(bys, y_rel, 1, 'var', -1)) + lg_two(x_rel) *
(int_collection(bys, y_rel, 2, 'var', -1))) + lg_zero(z_rel) *
(lg_mone(x_rel) *
(int_collection(bys, y_rel, -1, 'var', 0)) + lg_zero(x_rel) *
(int_collection(bys, y_rel, 0, 'var', 0)) + lg_one(x_rel) *
(int_collection(bys, y_rel, 1, 'var', 0)) + lg_two(x_rel) *
(int_collection(bys, y_rel, 2, 'var', 0))) + lg_one(z_rel) *
(lg_mone(x_rel) *
(int_collection(bys, y_rel, -1, 'var', 1)) + lg_zero(x_rel) *
(int_collection(bys, y_rel, 0, 'var', 1)) + lg_one(x_rel) *
(int_collection(bys, y_rel, 1, 'var', 1)) + lg_two(x_rel) *
(int_collection(bys, y_rel, 2, 'var', 1))) + lg_two(z_rel) *
(lg_mone(x_rel) *
(int_collection(bys, y_rel, -1, 'var', 2)) + lg_zero(x_rel) *
(int_collection(bys, y_rel, 0, 'var', 2)) + lg_one(x_rel) *
(int_collection(bys, y_rel, 1, 'var', 2)) + lg_two(x_rel) *
(int_collection(bys, y_rel, 2, 'var', 2))))
bz_interp = -(
lg_mone(y_rel) *
(lg_mone(x_rel) *
(int_collection(bzs, z_rel, -1, -1, 'var')) + lg_zero(x_rel) *
(int_collection(bzs, z_rel, 0, -1, 'var')) + lg_one(x_rel) *
(int_collection(bzs, z_rel, 1, -1, 'var')) + lg_two(x_rel) *
(int_collection(bzs, z_rel, 2, -1, 'var'))) + lg_zero(y_rel) *
(lg_mone(x_rel) *
(int_collection(bzs, z_rel, -1, 0, 'var')) + lg_zero(x_rel) *
(int_collection(bzs, z_rel, 0, 0, 'var')) + lg_one(x_rel) *
(int_collection(bzs, z_rel, 1, 0, 'var')) + lg_two(x_rel) *
(int_collection(bzs, z_rel, 2, 0, 'var'))) + lg_one(y_rel) *
(lg_mone(x_rel) *
(int_collection(bzs, z_rel, -1, 1, 'var')) + lg_zero(x_rel) *
(int_collection(bzs, z_rel, 0, 1, 'var')) + lg_one(x_rel) *
(int_collection(bzs, z_rel, 1, 1, 'var')) + lg_two(x_rel) *
(int_collection(bzs, z_rel, 2, 1, 'var'))) + lg_two(y_rel) *
(lg_mone(x_rel) *
(int_collection(bzs, z_rel, -1, 2, 'var')) + lg_zero(x_rel) *
(int_collection(bzs, z_rel, 0, 2, 'var')) + lg_one(x_rel) *
(int_collection(bzs, z_rel, 1, 2, 'var')) + lg_two(x_rel) *
(int_collection(bzs, z_rel, 2, 2, 'var'))))
if plot:
init_notebook_mode()
trace1 = go.Scatter3d(
x=df_trimmed.X,
y=df_trimmed.Y,
z=df_trimmed.Z,
mode='markers',
marker=dict(
size=12,
line=dict(color='rgba(217, 217, 217, 0.14)', width=0.5),
opacity=0.8,
),
text=df_trimmed.Vertex,
)
trace2 = go.Scatter3d(x=[x],
y=[y],
z=[z],
mode='markers',
marker=dict(color='rgb(127, 127, 127)',
size=12,
symbol='circle',
line=dict(color='rgb(204, 204, 204)',
width=1),
opacity=0.9))
data = [trace1, trace2]
layout = go.Layout(margin=dict(l=0, r=0, b=0, t=0), )
fig = go.Figure(data=data, layout=layout)
iplot(fig)
print(x_rel)
return df_trimmed, [bx_interp, by_interp, bz_interp]
def interp_phi(df, x, y, z, df_alt=None, plot=True):
"""First thing's first. Plot the xyz point, and the immediate cube around it."""
df_trimmed = df.query('{0}<=X<={1} and {2}<=Y<={3} and {4}<=Z<={5}'.format(
x-25, x+25, y-25, y+25, z-25, z+25))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_true = df_trimmed.query('X=={0} and Y=={1} and Z=={2}'.format(x, y, z))
if len(df_true) == 1:
bx_interp = df_true.Bx
by_interp = df_true.By
bz_interp = df_true.Bz
else:
if len(df_trimmed.X.unique()) == len(df_trimmed.Y.unique()) == len(df_trimmed.Z.unique()):
df_trimmed = df_trimmed.query('X!={0} and Y!={1} and Z!={2}'.format(
x, y, z))
else:
xs = np.sort(df_trimmed.X.unique())
ys = np.sort(df_trimmed.Y.unique())
zs = np.sort(df_trimmed.Z.unique())
df_trimmed = df_trimmed.query(
'(X=={0} or X=={1}) and (Y=={2} or Y=={3}) and (Z=={4} or Z=={5})'.format(
xs[0], xs[1], ys[0], ys[1], zs[0], zs[1]))
df_trimmed = df_trimmed.sort_values(['X', 'Y', 'Z']).reset_index(drop=True)
# indices: 0 1 2 3 4 5 6 7
df_trimmed['Vertex'] = ['p000', 'p001', 'p010', 'p011', 'p100', 'p101', 'p110', 'p111']
x_rel = (x - df_trimmed.ix[0].X) / (df_trimmed.ix[4].X-df_trimmed.ix[0].X)
y_rel = (y - df_trimmed.ix[0].Y) / (df_trimmed.ix[2].Y-df_trimmed.ix[0].Y)
z_rel = (z - df_trimmed.ix[0].Z) / (df_trimmed.ix[1].Z-df_trimmed.ix[0].Z)
# print x_rel
bx_interp = ((y_rel)*(z_rel)*(x_rel*df_trimmed.ix[7].Bx + (1-x_rel)*df_trimmed.ix[3].Bx) +
(1-y_rel) * (z_rel) * (x_rel*df_trimmed.ix[5].Bx + (1-x_rel)*df_trimmed.ix[1].Bx) +
(y_rel) * (1-z_rel) * (x_rel*df_trimmed.ix[6].Bx + (1-x_rel)*df_trimmed.ix[2].Bx) +
(1-y_rel) * (1-z_rel)*(x_rel*df_trimmed.ix[4].Bx + (1-x_rel)*df_trimmed.ix[0].Bx))
by_interp = ((x_rel)*(z_rel)*(y_rel*df_trimmed.ix[7].By + (1-y_rel)*df_trimmed.ix[5].By) +
(1-x_rel) * (z_rel) * (y_rel*df_trimmed.ix[3].By + (1-y_rel)*df_trimmed.ix[1].By) +
(x_rel) * (1-z_rel) * (y_rel*df_trimmed.ix[6].By + (1-y_rel)*df_trimmed.ix[4].By) +
(1-x_rel) * (1-z_rel)*(y_rel*df_trimmed.ix[2].By + (1-y_rel)*df_trimmed.ix[0].By))
bz_interp = ((x_rel)*(y_rel)*(z_rel*df_trimmed.ix[7].Bz + (1-z_rel)*df_trimmed.ix[6].Bz) +
(1-x_rel) * (y_rel) * (z_rel*df_trimmed.ix[3].Bz + (1-z_rel)*df_trimmed.ix[2].Bz) +
(x_rel) * (1-y_rel) * (z_rel*df_trimmed.ix[5].Bz + (1-z_rel)*df_trimmed.ix[4].Bz) +
(1-x_rel) * (1-y_rel)*(z_rel*df_trimmed.ix[1].Bz + (1-z_rel)*df_trimmed.ix[0].Bz))
if plot:
init_notebook_mode()
trace1 = go.Scatter3d(
x=df_trimmed.X,
y=df_trimmed.Y,
z=df_trimmed.Z,
mode='markers',
marker=dict(
size=12,
line=dict(
color='rgba(217, 217, 217, 0.14)',
width=0.5
),
opacity=0.8,
),
text=df_trimmed.Vertex,
)
trace2 = go.Scatter3d(
x=[x],
y=[y],
z=[z],
mode='markers',
marker=dict(
color='rgb(127, 127, 127)',
size=12,
symbol='circle',
line=dict(
color='rgb(204, 204, 204)',
width=1
),
opacity=0.9
)
)
data = [trace1, trace2]
layout = go.Layout(
margin=dict(
l=0,
r=0,
b=0,
t=0
),
)
fig = go.Figure(data=data, layout=layout)
iplot(fig)
return df_trimmed, [bx_interp, by_interp, bz_interp]
def interp_phi_quad(df, x, y, z, plot=False):
df_trimmed = df.query('{0}<=X<={1} and {2}<=Y<={3} and {4}<=Z<={5}'.format(
x-37.5, x+37.5, y-37.5, y+37.5, z-37.5, z+37.5))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y', 'Z']).reset_index(drop=True)
#df_true = df_trimmed.query('X=={0} and Y=={1} and Z=={2}'.format(x, y, z))
#if len(df_true) == 1:
#pass
# bx_interp = df_true.Bx
# by_interp = df_true.By
# bz_interp = df_true.Bz
if False:
pass
else:
df_trimmed['Vertex'] = [
# 0 1 2 3 4 5 6 7 8
'-1-1-1' , '-1-10' , '-1-11' , '-10-1' , '-100' , '-101' , '-11-1' , '-110' , '-111' ,
# 9 10 11 12 13 14 15 16 17
'0-1-1' , '0-10' , '0-11' , '00-1' , '000' , '001' , '01-1' , '010' , '011' ,
# 18 19 20 21 22 23 24 25 26
'1-1-1' , '1-10' , '1-11' , '10-1' , '100' , '101' , '11-1' , '110' , '111' ,
]
x_rel = (x - df_trimmed.ix[13].X) / (25.0)
y_rel = (y - df_trimmed.ix[13].Y) / (25.0)
z_rel = (z - df_trimmed.ix[13].Z) / (25.0)
# print x_rel, y_rel, z_rel
bxs = df_trimmed.Bx
bys = df_trimmed.By
bzs = df_trimmed.Bz
tuning = 0.02
bx_interp = -(
tuning*(x_rel*((x_rel+1)*bxs[13]-x_rel*bxs[4]) -
x_rel*((1-x_rel)*bxs[13]+x_rel*bxs[22]))+
-(((bxs[4]+bxs[22])/2.0-bxs[13])*x_rel**2+((bxs[22]-bxs[4])/2.0)*x_rel+bxs[13])
)
#bx_interp = -(
# x_rel*0.5*(bxs[4]+bxs[13]) - x_rel*0.5*(bxs[13]+bxs[22]) -
# (1.0/6.0)*(bxs[4]+4*bxs[13]+bxs[22])
#)
#bx_interp = (
# ((
# #(min(0, x_rel)*(abs(x_rel)*bxs[9]-(1-abs(x_rel))*bxs[18])) -
# (((bxs[0]+bxs[18])/2.0-bxs[9])*x_rel**2+((bxs[18]-bxs[0])/2.0)*x_rel+bxs[9])) *
# 0.5*(y_rel**2-y_rel) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[12]-(1-abs(x_rel))*bxs[21])) -
# (((bxs[3]+bxs[21])/2.0-bxs[12])*x_rel**2+((bxs[21]-bxs[3])/2.0)*x_rel+bxs[12])) *
# (-y_rel**2+1) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[15]-(1-abs(x_rel))*bxs[24])) -
# (((bxs[6]+bxs[24])/2.0-bxs[15])*x_rel**2+((bxs[24]-bxs[6])/2.0)*x_rel+bxs[15])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2-z_rel) +
#((
# #(min(0, x_rel)*(abs(x_rel)*bxs[10]-(1-abs(x_rel))*bxs[19])) -
# (((bxs[1]+bxs[19])/2.0-bxs[10])*x_rel**2+((bxs[19]-bxs[1])/2.0)*x_rel+bxs[10])) *
# 0.5*(y_rel**2-y_rel) +
# (
#(min(0, x_rel)*(abs(x_rel)*bxs[13]-(1-abs(x_rel))*bxs[22])) -
# (((bxs[4]+bxs[22])/2.0-bxs[13])*x_rel**2+((bxs[22]-bxs[4])/2.0)*x_rel+bxs[13])) *
# (-y_rel**2+1) #+
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[16]-(1-abs(x_rel))*bxs[25])) -
# (((bxs[7]+bxs[25])/2.0-bxs[16])*x_rel**2+((bxs[25]-bxs[7])/2.0)*x_rel+bxs[16])) *
# 0.5*(y_rel**2+y_rel))*(-z_rel**2+1) +
#((
# #(min(0, x_rel)*(abs(x_rel)*bxs[11]-(1-abs(x_rel))*bxs[20])) -
# (((bxs[2]+bxs[20])/2.0-bxs[11])*x_rel**2+((bxs[20]-bxs[2])/2.0)*x_rel+bxs[11])) *
# 0.5*(y_rel**2-y_rel) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[14]-(1-abs(x_rel))*bxs[23])) -
# (((bxs[5]+bxs[23])/2.0-bxs[14])*x_rel**2+((bxs[23]-bxs[5])/2.0)*x_rel+bxs[14])) *
# (-y_rel**2+1) +
# (
# #(min(0, x_rel)*(abs(x_rel)*bxs[17]-(1-abs(x_rel))*bxs[26])) -
# (((bxs[8]+bxs[26])/2.0-bxs[17])*x_rel**2+((bxs[26]-bxs[8])/2.0)*x_rel+bxs[17])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2+z_rel)
#)
# bx_interp = -(
# ((-(((bxs[0]+bxs[18])/2.0-bxs[9])*x_rel**2+((bxs[18]-bxs[0])/2.0)*x_rel+bxs[9])) *
# 0.5*(y_rel**2-y_rel) +
# (-(((bxs[3]+bxs[21])/2.0-bxs[12])*x_rel**2+((bxs[21]-bxs[3])/2.0)*x_rel+bxs[12])) *
# (-y_rel**2+1) +
# (-(((bxs[6]+bxs[24])/2.0-bxs[15])*x_rel**2+((bxs[24]-bxs[6])/2.0)*x_rel+bxs[15])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2-z_rel) +
# ((-(((bxs[1]+bxs[19])/2.0-bxs[10])*x_rel**2+((bxs[19]-bxs[1])/2.0)*x_rel+bxs[10])) *
# 0.5*(y_rel**2-y_rel) +
# (-(((bxs[4]+bxs[22])/2.0-bxs[13])*x_rel**2+((bxs[22]-bxs[4])/2.0)*x_rel+bxs[13])) *
# (-y_rel**2+1) +
# (-(((bxs[7]+bxs[25])/2.0-bxs[16])*x_rel**2+((bxs[25]-bxs[7])/2.0)*x_rel+bxs[16])) *
# 0.5*(y_rel**2+y_rel))*(-z_rel**2+1) +
# ((-(((bxs[2]+bxs[20])/2.0-bxs[11])*x_rel**2+((bxs[20]-bxs[2])/2.0)*x_rel+bxs[11])) *
# 0.5*(y_rel**2-y_rel) +
# (-(((bxs[5]+bxs[23])/2.0-bxs[14])*x_rel**2+((bxs[23]-bxs[5])/2.0)*x_rel+bxs[14])) *
# (-y_rel**2+1) +
# (-(((bxs[8]+bxs[26])/2.0-bxs[17])*x_rel**2+((bxs[26]-bxs[8])/2.0)*x_rel+bxs[17])) *
# 0.5*(y_rel**2+y_rel))*0.5*(z_rel**2+z_rel)
# )
by_interp = -(
((-(((bys[0]+bys[6])/2.0-bys[3])*y_rel**2+((bys[6]-bys[0])/2.0)*y_rel+bys[3])) *
0.5*(x_rel**2-x_rel) +
(-(((bys[9]+bys[15])/2.0-bys[12])*y_rel**2+((bys[15]-bys[9])/2.0)*y_rel+bys[12])) *
(-x_rel**2+1) +
(-(((bys[18]+bys[24])/2.0-bys[21])*y_rel**2+((bys[24]-bys[18])/2.0)*y_rel+bys[21])) *
0.5*(x_rel**2+x_rel))*0.5*(z_rel**2-z_rel) +
((-(((bys[1]+bys[7])/2.0-bys[4])*y_rel**2+((bys[7]-bys[1])/2.0)*y_rel+bys[4])) *
0.5*(x_rel**2-x_rel) +
(-(((bys[10]+bys[16])/2.0-bys[13])*y_rel**2+((bys[16]-bys[10])/2.0)*y_rel+bys[13])) *
(-x_rel**2+1) +
(-(((bys[19]+bys[25])/2.0-bys[22])*y_rel**2+((bys[25]-bys[19])/2.0)*y_rel+bys[22])) *
0.5*(x_rel**2+x_rel))*(-z_rel**2+1) +
((-(((bys[2]+bys[8])/2.0-bys[5])*y_rel**2+((bys[8]-bys[2])/2.0)*y_rel+bys[5])) *
0.5*(x_rel**2-x_rel) +
(-(((bys[11]+bys[17])/2.0-bys[14])*y_rel**2+((bys[17]-bys[11])/2.0)*y_rel+bys[14])) *
(-x_rel**2+1) +
(-(((bys[20]+bys[26])/2.0-bys[23])*y_rel**2+((bys[26]-bys[20])/2.0)*y_rel+bys[23])) *
0.5*(x_rel**2+x_rel))*0.5*(z_rel**2+z_rel)
)
bz_interp = -(
((-(((bzs[0]+bzs[2])/2.0-bzs[1])*z_rel**2+((bzs[2]-bzs[0])/2.0)*z_rel+bzs[1])) *
0.5*(x_rel**2-x_rel) +
(-(((bzs[9]+bzs[11])/2.0-bzs[10])*z_rel**2+((bzs[11]-bzs[9])/2.0)*z_rel+bzs[10])) *
(-x_rel**2+1) +
(-(((bzs[18]+bzs[20])/2.0-bzs[19])*z_rel**2+((bzs[20]-bzs[18])/2.0)*z_rel+bzs[19])) *
0.5*(x_rel**2+x_rel))*0.5*(y_rel**2-y_rel) +
((-(((bzs[3]+bzs[5])/2.0-bzs[4])*z_rel**2+((bzs[5]-bzs[3])/2.0)*z_rel+bzs[4])) *
0.5*(x_rel**2-x_rel) +
(-(((bzs[12]+bzs[14])/2.0-bzs[13])*z_rel**2+((bzs[14]-bzs[12])/2.0)*z_rel+bzs[13])) *
(-x_rel**2+1) +
(-(((bzs[21]+bzs[23])/2.0-bzs[22])*z_rel**2+((bzs[23]-bzs[21])/2.0)*z_rel+bzs[22])) *
0.5*(x_rel**2+x_rel))*(-y_rel**2+1) +
((-(((bzs[6]+bzs[8])/2.0-bzs[7])*z_rel**2+((bzs[8]-bzs[6])/2.0)*z_rel+bzs[7])) *
0.5*(x_rel**2-x_rel) +
(-(((bzs[15]+bzs[17])/2.0-bzs[16])*z_rel**2+((bzs[17]-bzs[15])/2.0)*z_rel+bzs[16])) *
(-x_rel**2+1) +
(-(((bzs[24]+bzs[26])/2.0-bzs[25])*z_rel**2+((bzs[26]-bzs[24])/2.0)*z_rel+bzs[25])) *
0.5*(x_rel**2+x_rel))*0.5*(y_rel**2+y_rel)
)
if plot:
init_notebook_mode()
trace1 = go.Scatter3d(
x=df_trimmed.X,
y=df_trimmed.Y,
z=df_trimmed.Z,
mode='markers',
marker=dict(
size=12,
line=dict(
color='rgba(217, 217, 217, 0.14)',
width=0.5
),
opacity=0.8,
),
text=df_trimmed.Vertex,
)
trace2 = go.Scatter3d(
x=[x],
y=[y],
z=[z],
mode='markers',
marker=dict(
color='rgb(127, 127, 127)',
size=12,
symbol='circle',
line=dict(
color='rgb(204, 204, 204)',
width=1
),
opacity=0.9
)
)
data = [trace1, trace2]
layout = go.Layout(
margin=dict(
l=0,
r=0,
b=0,
t=0
),
)
fig = go.Figure(data=data, layout=layout)
iplot(fig)
return df_trimmed, [bx_interp, by_interp, bz_interp]
def interp_phi_cubic(df, x, y, z, plot=False, mode='lacey', shift=0):
if shift == 0:
df_trimmed = df.query('{0}<=X<{1} and {2}<=Y<{3} and {4}<=Z<{5}'.format(
x-50, x+50, y-50, y+50, z-50, z+50))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y', 'Z']).reset_index(drop=True)
elif shift == -1:
df_trimmed = df.query('{0}<=X<{1} and {2}<=Y<{3} and {4}<=Z<{5}'.format(
x-25, x+75, y-50, y+50, z-50, z+50))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y', 'Z']).reset_index(drop=True)
elif shift == 1:
df_trimmed = df.query('{0}<=X<{1} and {2}<=Y<{3} and {4}<=Z<{5}'.format(
x-75, x+25, y-50, y+50, z-50, z+50))
df_trimmed = df_trimmed[['X', 'Y', 'Z', 'Bx', 'By', 'Bz']]
df_trimmed = df_trimmed.sort_values(['X', 'Y', 'Z']).reset_index(drop=True)
else:
raise KeyError('wrong shift')
#df_true = df_trimmed.query('X=={0} and Y=={1} and Z=={2}'.format(x, y, z))
#if len(df_true) == 1:
#pass
# bx_interp = df_true.Bx
# by_interp = df_true.By
# bz_interp = df_true.Bz
if False:
pass
else:
df_trimmed['Vertex'] = [
# 0 1 2 3 4 5 6 7
'-1-1-1' , '-1-10' , '-1-11' , '-1-12' , '-10-1' , '-100' , '-101' , '-102' ,
# 8 9 10 11 12 13 14 15
'-11-1' , '-110' , '-111' , '-112' , '-12-1' , '-120' , '-121' , '-122' ,
# 16 17 18 19 20 21 22 23
'0-1-1' , '0-10' , '0-11' , '0-12' , '00-1' , '000' , '001' , '002' ,
# 24 25 26 27 28 29 30 31
'01-1' , '010' , '011' , '012' , '02-1' , '020' , '021' , '022' ,
# 32 33 34 35 36 37 38 39
'1-1-1' , '1-10' , '1-11' , '1-12' , '10-1' , '100' , '101' , '102' ,
# 40 41 42 43 44 45 46 47
'11-1' , '110' , '111' , '112' , '12-1' , '120' , '121' , '122' ,
# 48 49 50 51 52 53 54 55
'2-1-1' , '2-10' , '2-11' , '2-12' , '20-1' , '200' , '201' , '202' ,
# 56 57 58 59 60 61 62 63
'21-1' , '210' , '211' , '212' , '22-1' , '220' , '221' , '222' ,
]
index_list = list(range(0,64))
vertex_dict = dict(list(zip(df_trimmed.Vertex, index_list)))
# Define some lagrange polynomials
def lg_mone(n):
return -(n**3-3*n**2+2*n)/6.0
def lg_zero(n):
return (n**3-2*n**2-n+2)/2.0
def lg_one(n):
return -(n**3-n**2-2*n)/2.0
def lg_two(n):
return (n**3-n)/6.0
# Numerical integration
def _int_methods(b, rel, *verts):
if len(verts) == 2:
return (b.ix[vertex_dict[verts[0]]] + b.ix[vertex_dict[verts[1]]])/2.0
elif len(verts) == 3:
return (b.ix[vertex_dict[verts[0]]] + 4*b.ix[vertex_dict[verts[1]]] +
b.ix[vertex_dict[verts[2]]])/3.0
else:
if mode == 'lacey':
return (b.ix[vertex_dict[verts[0]]] + 3*b.ix[vertex_dict[verts[1]]] +
3*b.ix[vertex_dict[verts[2]]] + b.ix[vertex_dict[verts[3]]])*(3.0/8.0)
else:
A = (-3*b.ix[vertex_dict[verts[2]]] - b.ix[vertex_dict[verts[0]]] +
3*b.ix[vertex_dict[verts[1]]] + b.ix[vertex_dict[verts[3]]])/6.0
B = (b.ix[vertex_dict[verts[0]]] + b.ix[vertex_dict[verts[2]]] -
2*b.ix[vertex_dict[verts[1]]])/2.0
C = (6*b.ix[vertex_dict[verts[2]]] - 2*b.ix[vertex_dict[verts[0]]] -
3*b.ix[vertex_dict[verts[1]]] - b.ix[vertex_dict[verts[3]]])/6.0
D = b.ix[vertex_dict[verts[1]]]
return (A*rel**3 + B*rel**2 + C*rel + D)
def num_int(b, rel, x, y, z):
if isinstance(x, collections.Sequence):
verts = [str(i)+str(y)+str(z) for i in range(x[0], x[-1]+1)]
elif isinstance(y, collections.Sequence):
verts = [str(x)+str(i)+str(z) for i in range(y[0], y[-1]+1)]
elif isinstance(z, collections.Sequence):
verts = [str(x)+str(y)+str(i) for i in range(z[0], z[-1]+1)]
else:
raise AttributeError('exactly one arg in num_int must be a collection')
return _int_methods(b, rel, *verts)
def int_collection(b, rel, x, y, z):
if x == 'var':
int1 = num_int(b, rel, (-1, 2), y, z)
int2 = num_int(b, rel, (0, 1), y, z)
int3 = num_int(b, rel, (-1, 0), y, z)
int4 = int2
int5 = num_int(b, rel, (-1, 1), y, z)
int6 = int2
int7 = num_int(b, rel, (1, 2), y, z)
elif y == 'var':
int1 = num_int(b, rel, x, (-1, 2), z)
int2 = num_int(b, rel, x, (0, 1), z)
int3 = num_int(b, rel, x, (-1, 0), z)
int4 = int2
int5 = num_int(b, rel, x, (-1, 1), z)
int6 = int2
int7 = num_int(b, rel, x, (1, 2), z)
else:
int1 = num_int(b, rel, x, y, (-1, 2))
int2 = num_int(b, rel, x, y, (0, 1))
int3 = num_int(b, rel, x, y, (-1, 0))
int4 = int2
int5 = num_int(b, rel, x, y, (-1, 1))
int6 = int2
int7 = num_int(b, rel, x, y, (1, 2))
if mode == 'lacey':
return ((-rel**2/2.0)*int1 + (3*rel**2/2.0)*int2 + rel*int3 - rel*int4 -
(1/3.0)*int5 - 0.5*int6 + (1/6.0)*int7)
else:
return -int1
x_rel = (x - df_trimmed.ix[21].X) / (25.0)
y_rel = (y - df_trimmed.ix[21].Y) / (25.0)
z_rel = (z - df_trimmed.ix[21].Z) / (25.0)
# print x_rel, y_rel, z_rel
bxs = df_trimmed.Bx
bys = df_trimmed.By
bzs = df_trimmed.Bz
bx_interp = -(lg_mone(z_rel)*(lg_mone(y_rel)*(int_collection(bxs, x_rel, 'var', -1, -1)) +
lg_zero(y_rel)*(int_collection(bxs, x_rel, 'var', 0, -1)) +
lg_one(y_rel)*(int_collection(bxs, x_rel, 'var', 1, -1)) +
lg_two(y_rel)*(int_collection(bxs, x_rel, 'var', 2, -1))) +
lg_zero(z_rel)*(lg_mone(y_rel)*(int_collection(bxs, x_rel, 'var', -1, 0)) +
lg_zero(y_rel)*(int_collection(bxs, x_rel, 'var', 0, 0)) +
lg_one(y_rel)*(int_collection(bxs, x_rel, 'var', 1, 0)) +
lg_two(y_rel)*(int_collection(bxs, x_rel, 'var', 2, 0))) +
lg_one(z_rel)*(lg_mone(y_rel)*(int_collection(bxs, x_rel, 'var', -1, 1)) +
lg_zero(y_rel)*(int_collection(bxs, x_rel, 'var', 0, 1)) +
lg_one(y_rel)*(int_collection(bxs, x_rel, 'var', 1, 1)) +
lg_two(y_rel)*(int_collection(bxs, x_rel, 'var', 2, 1))) +
lg_two(z_rel)*(lg_mone(y_rel)*(int_collection(bxs, x_rel, 'var', -1, 2)) +
lg_zero(y_rel)*(int_collection(bxs, x_rel, 'var', 0, 2)) +
lg_one(y_rel)*(int_collection(bxs, x_rel, 'var', 1, 2)) +
lg_two(y_rel)*(int_collection(bxs, x_rel, 'var', 2, 2)))
)
by_interp = -(lg_mone(z_rel)*(lg_mone(x_rel)*(int_collection(bys, y_rel, -1, 'var', -1)) +
lg_zero(x_rel)*(int_collection(bys, y_rel, 0, 'var', -1)) +
lg_one(x_rel)*(int_collection(bys, y_rel, 1, 'var', -1)) +
lg_two(x_rel)*(int_collection(bys, y_rel, 2, 'var', -1))) +
lg_zero(z_rel)*(lg_mone(x_rel)*(int_collection(bys, y_rel, -1, 'var', 0)) +
lg_zero(x_rel)*(int_collection(bys, y_rel, 0, 'var', 0)) +
lg_one(x_rel)*(int_collection(bys, y_rel, 1, 'var', 0)) +
lg_two(x_rel)*(int_collection(bys, y_rel, 2, 'var', 0))) +
lg_one(z_rel)*(lg_mone(x_rel)*(int_collection(bys, y_rel, -1, 'var', 1)) +
lg_zero(x_rel)*(int_collection(bys, y_rel, 0, 'var', 1)) +
lg_one(x_rel)*(int_collection(bys, y_rel, 1, 'var', 1)) +
lg_two(x_rel)*(int_collection(bys, y_rel, 2, 'var', 1))) +
lg_two(z_rel)*(lg_mone(x_rel)*(int_collection(bys, y_rel, -1, 'var', 2)) +
lg_zero(x_rel)*(int_collection(bys, y_rel, 0, 'var', 2)) +
lg_one(x_rel)*(int_collection(bys, y_rel, 1, 'var', 2)) +
lg_two(x_rel)*(int_collection(bys, y_rel, 2, 'var', 2)))
)
bz_interp = -(lg_mone(y_rel)*(lg_mone(x_rel)*(int_collection(bzs, z_rel, -1, -1, 'var')) +
lg_zero(x_rel)*(int_collection(bzs, z_rel, 0, -1, 'var')) +
lg_one(x_rel)*(int_collection(bzs, z_rel, 1, -1, 'var')) +
lg_two(x_rel)*(int_collection(bzs, z_rel, 2, -1, 'var'))) +
lg_zero(y_rel)*(lg_mone(x_rel)*(int_collection(bzs, z_rel, -1, 0, 'var')) +
lg_zero(x_rel)*(int_collection(bzs, z_rel, 0, 0, 'var')) +
lg_one(x_rel)*(int_collection(bzs, z_rel, 1, 0, 'var')) +
lg_two(x_rel)*(int_collection(bzs, z_rel, 2, 0, 'var'))) +
lg_one(y_rel)*(lg_mone(x_rel)*(int_collection(bzs, z_rel, -1, 1, 'var')) +
lg_zero(x_rel)*(int_collection(bzs, z_rel, 0, 1, 'var')) +
lg_one(x_rel)*(int_collection(bzs, z_rel, 1, 1, 'var')) +
lg_two(x_rel)*(int_collection(bzs, z_rel, 2, 1, 'var'))) +
lg_two(y_rel)*(lg_mone(x_rel)*(int_collection(bzs, z_rel, -1, 2, 'var')) +
lg_zero(x_rel)*(int_collection(bzs, z_rel, 0, 2, 'var')) +
lg_one(x_rel)*(int_collection(bzs, z_rel, 1, 2, 'var')) +
lg_two(x_rel)*(int_collection(bzs, z_rel, 2, 2, 'var')))
)
if plot:
init_notebook_mode()
trace1 = go.Scatter3d(
x=df_trimmed.X,
y=df_trimmed.Y,
z=df_trimmed.Z,
mode='markers',
marker=dict(
size=12,
line=dict(
color='rgba(217, 217, 217, 0.14)',
width=0.5
),
opacity=0.8,
),
text=df_trimmed.Vertex,
)
trace2 = go.Scatter3d(
x=[x],
y=[y],
z=[z],
mode='markers',
marker=dict(
color='rgb(127, 127, 127)',
size=12,
symbol='circle',
line=dict(
color='rgb(204, 204, 204)',
width=1
),
opacity=0.9
)
)
data = [trace1, trace2]
layout = go.Layout(
margin=dict(
l=0,
r=0,
b=0,
t=0
),
)
fig = go.Figure(data=data, layout=layout)
iplot(fig)
print(x_rel)
return df_trimmed, [bx_interp, by_interp, bz_interp]