def dipole_map_value(fld, pts, r=1.0, fillna=None, cotr=None,
crd_system=None, interp_kind='linear'):
"""Map values assuming they're constant along ideal dipole lines
Args:
fld (Field): values to interpolate onto the mapped pts
pts (ndarray): 3xN for N (x, y, z) points that will be mapped
r (float): radius of resulting map
cotr (None): if given, use cotr to perform mapping in sm
crd_system (str): crd system of pts
interp_kind (str): how to interpolate fld onto source points
Returns:
ndarray: ndarray of mapped values, one for each of the N points
"""
if crd_system is None:
crd_system = viscid.as_crd_system(fld, 'gse')
if fld.is_spherical:
# TODO: verify that crd_system works as expected for ionosphere
# fields (ie, meaning of +x and phi = 0)
fld = viscid.as_spherefield(fld, order=('theta', 'phi'))['r=newaxis, ...']
else:
pass
# pts should be shaped 3xNX*NY*NZ or similar such that the points
# are in the same order as the flattened c-contiguous array
mapped_pts = dipole_map(pts, r=r, cotr=cotr, crd_system=crd_system,
as_spherical=fld.is_spherical)
ret = viscid.interp(fld, mapped_pts, kind=interp_kind, wrap=False)
if fillna is not None:
ret[np.isnan(ret)] = fillna
return ret
def run_test(fld, seeds, kind, show=False):
plt.clf()
vlt.plot(viscid.interp(fld, seeds, kind=kind))
plt.title(kind)
plt.savefig(next_plot_fname(__file__))
if show:
vlt.show()
def run_test(fld, seeds, kind, show=False):
plt.clf()
vlt.plot(viscid.interp(fld, seeds, kind=kind))
plt.title(kind)
plt.savefig(next_plot_fname(__file__))
if show:
vlt.show()
def integrate_along_lines(lines,
fld,
reduction="dot",
mask_func=None,
interp_kind='trilin'):
"""Integrate the value of fld along a list of lines
Args:
lines (list): list of 3xN ndarrays, N needs not be the same for
all lines
fld (Field): Field to interpolate / integrate
reduction (str): If fld is a vector field, what quantity to
integrate. Can be "dot" to dot the vectors with ds along
the line, or "mag" to integrate the magnitude.
interp_kind (str): which interpolation to use, const or trilin
Returns:
ndarray with shape (len(lines), )
"""
arr = np.zeros((len(lines), ), dtype=fld.dtype)
cum_n = np.cumsum([0] + [line.shape[1] for line in lines])
all_verts = np.concatenate(lines, axis=1)
fld_on_verts = viscid.interp(fld, all_verts, kind=interp_kind).data
for i, start, stop in izip(count(), cum_n[:-1], cum_n[1:]):
ds = np.linalg.norm(lines[i][:, 1:] - lines[i][:, :-1], axis=0)
if len(fld_on_verts.shape) > 1:
reduction = reduction.strip().lower()
if reduction == "dot":
dsvec = lines[i][:, 1:] - lines[i][:, :-1]
dsvec = dsvec / np.linalg.norm(dsvec, axis=0)
values = 0.5 * (fld_on_verts[start:stop - 1, :] +
fld_on_verts[start + 1:stop, :])
values = values * dsvec.T
if mask_func is not None:
values = np.ma.masked_where(mask_func(values), values)
values = np.sum(values, axis=1)
elif reduction in ["mag", "magnitude", "norm"]:
mag = np.linalg.norm(fld_on_verts[start:stop], axis=1)
values = 0.5 * (mag[start:stop - 1] + mag[start + 1:stop])
else:
raise ValueError("Unknown reduction: {0}".format(reduction))
else:
values = 0.5 * (fld_on_verts[start:stop - 1] +
fld_on_verts[start + 1:stop])
arr[i] = np.sum(values * ds)
return arr
def integrate_along_lines(lines, fld, reduction="dot", mask_func=None,
interp_kind='trilin'):
"""Integrate the value of fld along a list of lines
Args:
lines (list): list of 3xN ndarrays, N needs not be the same for
all lines
fld (Field): Field to interpolate / integrate
reduction (str): If fld is a vector field, what quantity to
integrate. Can be "dot" to dot the vectors with ds along
the line, or "mag" to integrate the magnitude.
interp_kind (str): which interpolation to use, const or trilin
Returns:
ndarray with shape (len(lines), )
"""
arr = np.zeros((len(lines),), dtype=fld.dtype)
cum_n = np.cumsum([0] + [line.shape[1] for line in lines])
all_verts = np.concatenate(lines, axis=1)
fld_on_verts = viscid.interp(fld, all_verts, kind=interp_kind).data
for i, start, stop in izip(count(), cum_n[:-1], cum_n[1:]):
ds = np.linalg.norm(lines[i][:, 1:] - lines[i][:, :-1], axis=0)
if len(fld_on_verts.shape) > 1:
reduction = reduction.strip().lower()
if reduction == "dot":
dsvec = lines[i][:, 1:] - lines[i][:, :-1]
dsvec = dsvec / np.linalg.norm(dsvec, axis=0)
values = 0.5 * (fld_on_verts[start:stop - 1, :] +
fld_on_verts[start + 1:stop, :])
values = values * dsvec.T
if mask_func is not None:
values = np.ma.masked_where(mask_func(values), values)
values = np.sum(values, axis=1)
elif reduction in ["mag", "magnitude", "norm"]:
mag = np.linalg.norm(fld_on_verts[start:stop], axis=1)
values = 0.5 * (mag[start:stop - 1] + mag[start + 1:stop])
else:
raise ValueError("Unknown reduction: {0}".format(reduction))
else:
values = 0.5 * (fld_on_verts[start:stop - 1] +
fld_on_verts[start + 1:stop])
arr[i] = np.sum(values * ds)
return arr
def project_along_line(line, fld, interp_kind='trilin'):
"""Project a Vector Field Parallel to a streamline
Args:
line (ndarray): 3xN of points along the
fld (VectorField): Field to interpolate and project onto the
line
interp_kind (str): which interpolation to use, const or trilin
"""
fld_on_verts = viscid.interp(fld, line, kind=interp_kind)
# FIXME: here in lies a bug, which axis am I actually summing over?
# maybe that's not the bug, but there must be something wrong
# here as indicated by kris_scripts/work/iono_xi_mismatch/analytic_pot.py
dsvec = line[:, 2:] - line[:, :-2]
dsvec = np.concatenate([dsvec[:, 0:1], dsvec, dsvec[:, -2:-1]], axis=1)
dsvec = dsvec / np.linalg.norm(dsvec, axis=0)
return np.sum(fld_on_verts * dsvec.T, axis=1)
def project_along_line(line, fld, interp_kind='trilin'):
"""Project a Vector Field Parallel to a streamline
Args:
line (ndarray): 3xN of points along the
fld (VectorField): Field to interpolate and project onto the
line
interp_kind (str): which interpolation to use, const or trilin
"""
fld_on_verts = viscid.interp(fld, line, kind=interp_kind)
# FIXME: here in lies a bug, which axis am I actually summing over?
# maybe that's not the bug, but there must be something wrong
# here as indicated by kris_scripts/work/iono_xi_mismatch/analytic_pot.py
dsvec = line[:, 2:] - line[:, :-2]
dsvec = np.concatenate([dsvec[:, 0:1], dsvec, dsvec[:, -2:-1]], axis=1)
dsvec = dsvec / np.linalg.norm(dsvec, axis=0)
return np.sum(fld_on_verts * dsvec.T, axis=1)