def get_trilinear_field():
xl, xh, nx = -1.0, 1.0, 41
yl, yh, ny = -1.5, 1.5, 41
zl, zh, nz = -2.0, 2.0, 41
x = np.linspace(xl, xh, nx)
y = np.linspace(yl, yh, ny)
z = np.linspace(zl, zh, nz)
crds = coordinate.wrap_crds("nonuniform_cartesian",
[('x', x), ('y', y), ('z', z)])
b = field.empty(crds, name="f", nr_comps=3, center="Cell",
layout="interlaced")
X, Y, Z = b.get_crds(shaped=True)
x01, y01, z01 = 0.5, 0.5, 0.5
x02, y02, z02 = 0.5, 0.5, 0.5
x03, y03, z03 = 0.5, 0.5, 0.5
b['x'][:] = 0.0 + 1.0 * (X - x01) + 1.0 * (Y - y01) + 1.0 * (Z - z01) + \
1.0 * (X - x01) * (Y - y01) + 1.0 * (Y - y01) * (Z - z01) + \
1.0 * (X - x01) * (Y - y01) * (Z - z01)
b['y'][:] = 0.0 + 1.0 * (X - x02) - 1.0 * (Y - y02) + 1.0 * (Z - z02) + \
1.0 * (X - x02) * (Y - y02) + 1.0 * (Y - y02) * (Z - z02) - \
1.0 * (X - x02) * (Y - y02) * (Z - z02)
b['z'][:] = 0.0 + 1.0 * (X - x03) + 1.0 * (Y - y03) - 1.0 * (Z - z03) + \
1.0 * (X - x03) * (Y - y03) + 1.0 * (Y - y03) * (Z - z03) + \
1.0 * (X - x03) * (Y - y03) * (Z - z03)
return b
def make_dipole(m=(0, 0, -DEFAULT_STRENGTH), strength=None, l=None, h=None,
n=None, center='cell', dtype='f8', twod=False,
nonuniform=False, crd_system='gse', name='b'):
"""Generate a dipole field with magnetic moment m [x, y, z]"""
if l is None:
l = [-5] * 3
if h is None:
h = [5] * 3
if n is None:
n = [256] * 3
if center.strip().lower() == 'cell':
n = [ni + 1 for ni in n]
x = np.array(np.linspace(l[0], h[0], n[0]), dtype=dtype)
y = np.array(np.linspace(l[1], h[1], n[1]), dtype=dtype)
z = np.array(np.linspace(l[2], h[2], n[2]), dtype=dtype)
if twod:
y = np.array(np.linspace(-0.1, 0.1, 2), dtype=dtype)
if nonuniform:
z += 0.01 * ((h[2] - l[2]) / n[2]) * np.sin(np.linspace(0, np.pi, n[2]))
B = field.empty([x, y, z], nr_comps=3, name=name, center=center,
layout='interlaced', dtype=dtype)
B.set_info('crd_system', viscid.as_crd_system(crd_system))
B.set_info('cotr', viscid.dipole_moment2cotr(m, crd_system=crd_system))
return fill_dipole(B, m=m, strength=strength)
def get_dipole(m=None, l=None, h=None, n=None, twod=False):
dtype = 'float64'
if l is None:
l = [-5] * 3
if h is None:
h = [5] * 3
if n is None:
n = [256] * 3
x = np.array(np.linspace(l[0], h[0], n[0]), dtype=dtype)
y = np.array(np.linspace(l[1], h[1], n[1]), dtype=dtype)
z = np.array(np.linspace(l[2], h[2], n[2]), dtype=dtype)
if twod:
y = np.array(np.linspace(-0.1, 0.1, 2), dtype=dtype)
B = field.empty([x, y, z], nr_comps=3, name="B", center='cell',
layout='interlaced', dtype=dtype)
Xcc, Ycc, Zcc = B.get_crds_cc(shaped=True) #pylint: disable=W0612
one = np.array([1.0], dtype=dtype) #pylint: disable=W0612
three = np.array([3.0], dtype=dtype) #pylint: disable=W0612
if m is None:
m = [0.0, 0.0, -1.0]
m = np.array(m, dtype=dtype)
mx, my, mz = m #pylint: disable=W0612
if _HAS_NUMEXPR:
rsq = ne.evaluate("Xcc**2 + Ycc**2 + Zcc**2") #pylint: disable=W0612
mdotr = ne.evaluate("mx * Xcc + my * Ycc + mz * Zcc") #pylint: disable=W0612
B['x'] = ne.evaluate("((three * Xcc * mdotr / rsq) - mx) / rsq**1.5")
B['y'] = ne.evaluate("((three * Ycc * mdotr / rsq) - my) / rsq**1.5")
B['z'] = ne.evaluate("((three * Zcc * mdotr / rsq) - mz) / rsq**1.5")
else:
rsq = Xcc**2 + Ycc**2 + Zcc**2
mdotr = mx * Xcc + my * Ycc + mz * Zcc
B['x'] = ((three * Xcc * mdotr / rsq) - mx) / rsq**1.5
B['y'] = ((three * Ycc * mdotr / rsq) - my) / rsq**1.5
B['z'] = ((three * Zcc * mdotr / rsq) - mz) / rsq**1.5
return B
def main():
xl, xh, nx = -1.0, 1.0, 41
yl, yh, ny = -1.5, 1.5, 41
zl, zh, nz = -2.0, 2.0, 41
x = np.linspace(xl, xh, nx)
y = np.linspace(yl, yh, ny)
z = np.linspace(zl, zh, nz)
crds = coordinate.wrap_crds("nonuniform_cartesian",
[('z', z), ('y', y), ('x', x)])
bx = field.empty(crds, name="$B_x$", center="Node")
by = field.empty(crds, name="$B_y$", center="Node")
bz = field.empty(crds, name="$B_z$", center="Node")
fld = field.empty(crds, name="B", nr_comps=3, center="Node",
layout="interlaced")
X, Y, Z = crds.get_crds(shaped=True)
x01, y01, z01 = 0.5, 0.5, 0.5
x02, y02, z02 = 0.5, 0.5, 0.5
x03, y03, z03 = 0.5, 0.5, 0.5
bx[:] = 0.0 + 1.0 * (X - x01) + 1.0 * (Y - y01) + 1.0 * (Z - z01) + \
1.0 * (X - x01) * (Y - y01) + 1.0 * (Y - y01) * (Z - z01) + \
1.0 * (X - x01) * (Y - y01) * (Z - z01)
by[:] = 0.0 + 1.0 * (X - x02) - 1.0 * (Y - y02) + 1.0 * (Z - z02) + \
1.0 * (X - x02) * (Y - y02) + 1.0 * (Y - y02) * (Z - z02) - \
1.0 * (X - x02) * (Y - y02) * (Z - z02)
bz[:] = 0.0 + 1.0 * (X - x03) + 1.0 * (Y - y03) - 1.0 * (Z - z03) + \
1.0 * (X - x03) * (Y - y03) + 1.0 * (Y - y03) * (Z - z03) + \
1.0 * (X - x03) * (Y - y03) * (Z - z03)
fld[..., 0] = bx
fld[..., 1] = by
fld[..., 2] = bz
fig = mlab.figure(size=(1150, 850),
bgcolor=(1.0, 1.0, 1.0),
fgcolor=(0.0, 0.0, 0.0))
f1_src = vlab.add_field(bx)
f2_src = vlab.add_field(by)
f3_src = vlab.add_field(bz)
mlab.pipeline.iso_surface(f1_src, contours=[0.0],
opacity=1.0, color=(1.0, 0.0, 0.0))
mlab.pipeline.iso_surface(f2_src, contours=[0.0],
opacity=1.0, color=(0.0, 1.0, 0.0))
mlab.pipeline.iso_surface(f3_src, contours=[0.0],
opacity=1.0, color=(0.0, 0.0, 1.0))
mlab.axes()
mlab.show()
nullpt = cycalc.interp_trilin(fld, [(0.5, 0.5, 0.5)])
print("f(0.5, 0.5, 0.5):", nullpt)
_, axes = plt.subplots(4, 3, sharex=True, sharey=True)
all_roots = []
positive_roots = []
ix = iy = iz = 0
for di, d in enumerate([0, -1]):
#### XY face
a1 = bx[iz + d, iy, ix]
b1 = bx[iz + d, iy, ix - 1] - a1
c1 = bx[iz + d, iy - 1, ix] - a1
d1 = bx[iz + d, iy - 1, ix - 1] - c1 - b1 - a1
a2 = by[iz + d, iy, ix]
b2 = by[iz + d, iy, ix - 1] - a2
c2 = by[iz + d, iy - 1, ix] - a2
d2 = by[iz + d, iy - 1, ix - 1] - c2 - b2 - a2
a3 = bz[iz + d, iy, ix]
b3 = bz[iz + d, iy, ix - 1] - a3
c3 = bz[iz + d, iy - 1, ix] - a3
d3 = bz[iz + d, iy - 1, ix - 1] - c3 - b3 - a3
roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2)
# for rt1, rt2 in zip(roots1, roots2):
# print("=")
# print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2)
# print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2)
# print("=")
# find f3 at the root points
f3 = np.empty_like(roots1)
markers = [None] * len(f3)
for i, rt1, rt2 in zip(count(), roots1, roots2):
f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2
all_roots.append((rt1, rt2, d)) # switch order here
if f3[i] >= 0.0:
markers[i] = 'k^'
positive_roots.append((rt1, rt2, d)) # switch order here
else:
markers[i] = 'w^'
# rescale the roots to the original domain
roots1 = (xh - xl) * roots1 + xl
roots2 = (yh - yl) * roots2 + yl
xp = np.linspace(0.0, 1.0, nx)
vlt.plot(fld['x'], "z={0}i".format(d), ax=axes[0 + 2 * di, 0],
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, yl, yh))
y1 = - (a1 + b1 * xp) / (c1 + d1 * xp)
plt.plot(x, (yh - yl) * y1 + yl, 'k')
for i, xrt, yrt in zip(count(), roots1, roots2):
plt.plot(xrt, yrt, markers[i])
vlt.plot(fld['y'], "z={0}i".format(d), ax=axes[1 + 2 * di, 0],
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, yl, yh))
y2 = - (a2 + b2 * xp) / (c2 + d2 * xp)
plt.plot(x, (yh - yl) * y2 + yl, 'k')
for xrt, yrt in zip(roots1, roots2):
plt.plot(xrt, yrt, markers[i])
#### YZ face
a1 = bx[iz, iy, ix + d]
b1 = bx[iz, iy - 1, ix + d] - a1
c1 = bx[iz - 1, iy, ix + d] - a1
d1 = bx[iz - 1, iy - 1, ix + d] - c1 - b1 - a1
a2 = by[iz, iy, ix + d]
b2 = by[iz, iy - 1, ix + d] - a2
c2 = by[iz - 1, iy, ix + d] - a2
d2 = by[iz - 1, iy - 1, ix + d] - c2 - b2 - a2
a3 = bz[iz, iy, ix + d]
b3 = bz[iz, iy - 1, ix + d] - a3
c3 = bz[iz - 1, iy, ix + d] - a3
d3 = bz[iz - 1, iy - 1, ix + d] - c3 - b3 - a3
roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2)
# for rt1, rt2 in zip(roots1, roots2):
# print("=")
# print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2)
# print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2)
# print("=")
# find f3 at the root points
f3 = np.empty_like(roots1)
markers = [None] * len(f3)
for i, rt1, rt2 in zip(count(), roots1, roots2):
f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2
all_roots.append((d, rt1, rt2)) # switch order here
if f3[i] >= 0.0:
markers[i] = 'k^'
positive_roots.append((d, rt1, rt2)) # switch order here
else:
markers[i] = 'w^'
# rescale the roots to the original domain
roots1 = (yh - yl) * roots1 + yl
roots2 = (zh - zl) * roots2 + zl
yp = np.linspace(0.0, 1.0, ny)
# plt.subplot(121)
vlt.plot(fld['x'], "x={0}i".format(d), ax=axes[0 + 2 * di, 1],
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(yl, yh, zl, zh))
z1 = - (a1 + b1 * yp) / (c1 + d1 * yp)
plt.plot(y, (zh - zl) * z1 + zl, 'k')
for i, yrt, zrt in zip(count(), roots1, roots2):
plt.plot(yrt, zrt, markers[i])
# plt.subplot(122)
vlt.plot(fld['y'], "x={0}i".format(d), ax=axes[1 + 2 * di, 1],
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(yl, yh, zl, zh))
z1 = - (a2 + b2 * yp) / (c2 + d2 * yp)
plt.plot(y, (zh - zl) * z1 + zl, 'k')
for i, yrt, zrt in zip(count(), roots1, roots2):
plt.plot(yrt, zrt, markers[i])
#### ZX face
a1 = bx[iz, iy + d, ix]
b1 = bx[iz - 1, iy + d, ix] - a1
c1 = bx[iz, iy + d, ix - 1] - a1
d1 = bx[iz - 1, iy + d, ix - 1] - c1 - b1 - a1
a2 = by[iz, iy + d, ix]
b2 = by[iz - 1, iy + d, ix] - a2
c2 = by[iz, iy + d, ix - 1] - a2
d2 = by[iz - 1, iy + d, ix - 1] - c2 - b2 - a2
a3 = bz[iz, iy + d, ix]
b3 = bz[iz - 1, iy + d, ix] - a3
c3 = bz[iz, iy + d, ix - 1] - a3
d3 = bz[iz - 1, iy + d, ix - 1] - c3 - b3 - a3
roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2)
# for rt1, rt2 in zip(roots1, roots2):
# print("=")
# print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2)
# print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2)
# print("=")
# find f3 at the root points
f3 = np.empty_like(roots1)
markers = [None] * len(f3)
for i, rt1, rt2 in zip(count(), roots1, roots2):
f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2
all_roots.append((rt2, d, rt1)) # switch order here
if f3[i] >= 0.0:
markers[i] = 'k^'
positive_roots.append((rt2, d, rt1)) # switch order here
else:
markers[i] = 'w^'
# rescale the roots to the original domain
roots1 = (zh - zl) * roots1 + zl
roots2 = (xh - xl) * roots2 + xl
zp = np.linspace(0.0, 1.0, nz)
# plt.subplot(121)
vlt.plot(fld['x'], "y={0}i".format(d), ax=axes[0 + 2 * di, 2],
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, zl, zh))
x1 = - (a1 + b1 * zp) / (c1 + d1 * zp)
plt.plot(z, (xh - xl) * x1 + xl, 'k')
for i, zrt, xrt in zip(count(), roots1, roots2):
plt.plot(xrt, zrt, markers[i])
# plt.subplot(121)
vlt.plot(fld['y'], "y={0}i".format(d), ax=axes[1 + 2 * di, 2],
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(xl, xh, zl, zh))
x1 = - (a2 + b2 * zp) / (c2 + d2 * zp)
plt.plot(z, (xh - xl) * x1 + xl, 'k')
for i, zrt, xrt in zip(count(), roots1, roots2):
plt.plot(xrt, zrt, markers[i])
print("all:", len(all_roots), "positive:", len(positive_roots))
if len(all_roots) % 2 == 1:
print("something is fishy, there are an odd number of root points "
"on the surface of your cube, there is probably a degenerate "
"line or surface of nulls")
print("Null Point?", (len(positive_roots) % 2 == 1))
plt.show()
def main():
xl, xh, nx = -1.0, 1.0, 41
yl, yh, ny = -1.5, 1.5, 41
zl, zh, nz = -2.0, 2.0, 41
x = np.linspace(xl, xh, nx)
y = np.linspace(yl, yh, ny)
z = np.linspace(zl, zh, nz)
crds = coordinate.wrap_crds("nonuniform_cartesian", [('z', z), ('y', y),
('x', x)])
bx = field.empty(crds, name="$B_x$", center="Node")
by = field.empty(crds, name="$B_y$", center="Node")
bz = field.empty(crds, name="$B_z$", center="Node")
fld = field.empty(crds,
name="B",
nr_comps=3,
center="Node",
layout="interlaced")
X, Y, Z = crds.get_crds(shaped=True)
x01, y01, z01 = 0.5, 0.5, 0.5
x02, y02, z02 = 0.5, 0.5, 0.5
x03, y03, z03 = 0.5, 0.5, 0.5
bx[:] = 0.0 + 1.0 * (X - x01) + 1.0 * (Y - y01) + 1.0 * (Z - z01) + \
1.0 * (X - x01) * (Y - y01) + 1.0 * (Y - y01) * (Z - z01) + \
1.0 * (X - x01) * (Y - y01) * (Z - z01)
by[:] = 0.0 + 1.0 * (X - x02) - 1.0 * (Y - y02) + 1.0 * (Z - z02) + \
1.0 * (X - x02) * (Y - y02) + 1.0 * (Y - y02) * (Z - z02) - \
1.0 * (X - x02) * (Y - y02) * (Z - z02)
bz[:] = 0.0 + 1.0 * (X - x03) + 1.0 * (Y - y03) - 1.0 * (Z - z03) + \
1.0 * (X - x03) * (Y - y03) + 1.0 * (Y - y03) * (Z - z03) + \
1.0 * (X - x03) * (Y - y03) * (Z - z03)
fld[..., 0] = bx
fld[..., 1] = by
fld[..., 2] = bz
fig = mlab.figure(size=(1150, 850),
bgcolor=(1.0, 1.0, 1.0),
fgcolor=(0.0, 0.0, 0.0))
f1_src = vlab.add_field(bx)
f2_src = vlab.add_field(by)
f3_src = vlab.add_field(bz)
mlab.pipeline.iso_surface(f1_src,
contours=[0.0],
opacity=1.0,
color=(1.0, 0.0, 0.0))
mlab.pipeline.iso_surface(f2_src,
contours=[0.0],
opacity=1.0,
color=(0.0, 1.0, 0.0))
mlab.pipeline.iso_surface(f3_src,
contours=[0.0],
opacity=1.0,
color=(0.0, 0.0, 1.0))
mlab.axes()
mlab.show()
nullpt = cycalc.interp_trilin(fld, [(0.5, 0.5, 0.5)])
print("f(0.5, 0.5, 0.5):", nullpt)
ax1 = plt.subplot2grid((4, 3), (0, 0))
all_roots = []
positive_roots = []
ix = iy = iz = 0
for di, d in enumerate([0, -1]):
#### XY face
a1 = bx[iz + d, iy, ix]
b1 = bx[iz + d, iy, ix - 1] - a1
c1 = bx[iz + d, iy - 1, ix] - a1
d1 = bx[iz + d, iy - 1, ix - 1] - c1 - b1 - a1
a2 = by[iz + d, iy, ix]
b2 = by[iz + d, iy, ix - 1] - a2
c2 = by[iz + d, iy - 1, ix] - a2
d2 = by[iz + d, iy - 1, ix - 1] - c2 - b2 - a2
a3 = bz[iz + d, iy, ix]
b3 = bz[iz + d, iy, ix - 1] - a3
c3 = bz[iz + d, iy - 1, ix] - a3
d3 = bz[iz + d, iy - 1, ix - 1] - c3 - b3 - a3
roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2)
# for rt1, rt2 in zip(roots1, roots2):
# print("=")
# print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2)
# print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2)
# print("=")
# find f3 at the root points
f3 = np.empty_like(roots1)
markers = [None] * len(f3)
for i, rt1, rt2 in zip(count(), roots1, roots2):
f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2
all_roots.append((rt1, rt2, d)) # switch order here
if f3[i] >= 0.0:
markers[i] = 'k^'
positive_roots.append((rt1, rt2, d)) # switch order here
else:
markers[i] = 'w^'
# rescale the roots to the original domain
roots1 = (xh - xl) * roots1 + xl
roots2 = (yh - yl) * roots2 + yl
xp = np.linspace(0.0, 1.0, nx)
# plt.subplot(121)
plt.subplot2grid((4, 3), (0 + 2 * di, 0), sharex=ax1, sharey=ax1)
vlt.plot(fld['x'],
"z={0}i".format(d),
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(
xl, xh, yl, yh))
y1 = -(a1 + b1 * xp) / (c1 + d1 * xp)
plt.plot(x, (yh - yl) * y1 + yl, 'k')
for i, xrt, yrt in zip(count(), roots1, roots2):
plt.plot(xrt, yrt, markers[i])
# plt.subplot(122)
plt.subplot2grid((4, 3), (1 + 2 * di, 0), sharex=ax1, sharey=ax1)
vlt.plot(fld['y'],
"z={0}i".format(d),
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(
xl, xh, yl, yh))
y2 = -(a2 + b2 * xp) / (c2 + d2 * xp)
plt.plot(x, (yh - yl) * y2 + yl, 'k')
for xrt, yrt in zip(roots1, roots2):
plt.plot(xrt, yrt, markers[i])
#### YZ face
a1 = bx[iz, iy, ix + d]
b1 = bx[iz, iy - 1, ix + d] - a1
c1 = bx[iz - 1, iy, ix + d] - a1
d1 = bx[iz - 1, iy - 1, ix + d] - c1 - b1 - a1
a2 = by[iz, iy, ix + d]
b2 = by[iz, iy - 1, ix + d] - a2
c2 = by[iz - 1, iy, ix + d] - a2
d2 = by[iz - 1, iy - 1, ix + d] - c2 - b2 - a2
a3 = bz[iz, iy, ix + d]
b3 = bz[iz, iy - 1, ix + d] - a3
c3 = bz[iz - 1, iy, ix + d] - a3
d3 = bz[iz - 1, iy - 1, ix + d] - c3 - b3 - a3
roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2)
# for rt1, rt2 in zip(roots1, roots2):
# print("=")
# print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2)
# print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2)
# print("=")
# find f3 at the root points
f3 = np.empty_like(roots1)
markers = [None] * len(f3)
for i, rt1, rt2 in zip(count(), roots1, roots2):
f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2
all_roots.append((d, rt1, rt2)) # switch order here
if f3[i] >= 0.0:
markers[i] = 'k^'
positive_roots.append((d, rt1, rt2)) # switch order here
else:
markers[i] = 'w^'
# rescale the roots to the original domain
roots1 = (yh - yl) * roots1 + yl
roots2 = (zh - zl) * roots2 + zl
yp = np.linspace(0.0, 1.0, ny)
# plt.subplot(121)
plt.subplot2grid((4, 3), (0 + 2 * di, 1), sharex=ax1, sharey=ax1)
vlt.plot(fld['x'],
"x={0}i".format(d),
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(
yl, yh, zl, zh))
z1 = -(a1 + b1 * yp) / (c1 + d1 * yp)
plt.plot(y, (zh - zl) * z1 + zl, 'k')
for i, yrt, zrt in zip(count(), roots1, roots2):
plt.plot(yrt, zrt, markers[i])
# plt.subplot(122)
plt.subplot2grid((4, 3), (1 + 2 * di, 1), sharex=ax1, sharey=ax1)
vlt.plot(fld['y'],
"x={0}i".format(d),
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(
yl, yh, zl, zh))
z1 = -(a2 + b2 * yp) / (c2 + d2 * yp)
plt.plot(y, (zh - zl) * z1 + zl, 'k')
for i, yrt, zrt in zip(count(), roots1, roots2):
plt.plot(yrt, zrt, markers[i])
#### ZX face
a1 = bx[iz, iy + d, ix]
b1 = bx[iz - 1, iy + d, ix] - a1
c1 = bx[iz, iy + d, ix - 1] - a1
d1 = bx[iz - 1, iy + d, ix - 1] - c1 - b1 - a1
a2 = by[iz, iy + d, ix]
b2 = by[iz - 1, iy + d, ix] - a2
c2 = by[iz, iy + d, ix - 1] - a2
d2 = by[iz - 1, iy + d, ix - 1] - c2 - b2 - a2
a3 = bz[iz, iy + d, ix]
b3 = bz[iz - 1, iy + d, ix] - a3
c3 = bz[iz, iy + d, ix - 1] - a3
d3 = bz[iz - 1, iy + d, ix - 1] - c3 - b3 - a3
roots1, roots2 = find_roots_face(a1, b1, c1, d1, a2, b2, c2, d2)
# for rt1, rt2 in zip(roots1, roots2):
# print("=")
# print("fx", a1 + b1 * rt1 + c1 * rt2 + d1 * rt1 * rt2)
# print("fy", a2 + b2 * rt1 + c2 * rt2 + d2 * rt1 * rt2)
# print("=")
# find f3 at the root points
f3 = np.empty_like(roots1)
markers = [None] * len(f3)
for i, rt1, rt2 in zip(count(), roots1, roots2):
f3[i] = a3 + b3 * rt1 + c3 * rt2 + d3 * rt1 * rt2
all_roots.append((rt2, d, rt1)) # switch order here
if f3[i] >= 0.0:
markers[i] = 'k^'
positive_roots.append((rt2, d, rt1)) # switch order here
else:
markers[i] = 'w^'
# rescale the roots to the original domain
roots1 = (zh - zl) * roots1 + zl
roots2 = (xh - xl) * roots2 + xl
zp = np.linspace(0.0, 1.0, nz)
# plt.subplot(121)
plt.subplot2grid((4, 3), (0 + 2 * di, 2), sharex=ax1, sharey=ax1)
vlt.plot(fld['x'],
"y={0}i".format(d),
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(
xl, xh, zl, zh))
x1 = -(a1 + b1 * zp) / (c1 + d1 * zp)
plt.plot(z, (xh - xl) * x1 + xl, 'k')
for i, zrt, xrt in zip(count(), roots1, roots2):
plt.plot(xrt, zrt, markers[i])
# plt.subplot(121)
plt.subplot2grid((4, 3), (1 + 2 * di, 2), sharex=ax1, sharey=ax1)
vlt.plot(fld['y'],
"y={0}i".format(d),
plot_opts="x={0}_{1},y={2}_{3},lin_-10_10".format(
xl, xh, zl, zh))
x1 = -(a2 + b2 * zp) / (c2 + d2 * zp)
plt.plot(z, (xh - xl) * x1 + xl, 'k')
for i, zrt, xrt in zip(count(), roots1, roots2):
plt.plot(xrt, zrt, markers[i])
print("all:", len(all_roots), "positive:", len(positive_roots))
if len(all_roots) % 2 == 1:
print("something is fishy, there are an odd number of root points "
"on the surface of your cube, there is probably a degenerate "
"line or surface of nulls")
print("Null Point?", (len(positive_roots) % 2 == 1))
plt.show()