def make_grid(ivar):
# takes ivar(orbit from dsnap)
# make grid elements
# uncomment below if the disk is not isothermal
# ff=pc.read_var(trimall=True,ivar=ivar,magic=['TT'])
ff = pc.read_var(trimall=True, ivar=ivar)
rad = ff.x # disk grid points in r
theta = ff.y # disk grid points in theta
ux = ff.ux # disk grid points in vr
uy = ff.uy # disk grid points in vtheta
rho = ff.rho # disk surface density
rad2d, theta2d = np.meshgrid(rad, theta)
x2d = rad2d * np.cos(theta2d)
y2d = rad2d * np.sin(theta2d)
return x2d, y2d, uy, rad, theta, rho
def post_compute(variables=['b2m'], datadir='data'):
"""
Compute diagnostic variables from the VAR files.
call signature::
post_compute(variables = ['urms'], datadir = 'data')
Read the VAR files and compute the diagnostic variables.
Write the result in 'post_evaluation.dat'.
Keyword arguments:
*variables*:
The diagnostic variables to be computed.
*datadir*:
Data directory.
"""
import re
# open the destination file for writing
fd = open(datadir + '/post_evaluation.dat', 'w')
# write the header
fd.write('#--t-------------'.encode('utf-8'))
for variable in variables:
fd.write('--{0:15}'.format(
(variable + '--------------------')[:15]).encode('utf-8'))
fd.write('\n')
# read the list of all VAR files
var_list_file = open('data/proc0/varN.list')
var_list = var_list_file.readlines()
var_list_file.close()
if (len(variables[0]) == 1):
variables = [variables]
# check if bb needs to be computed
bb_flag = False
# array containing the variables which depend on bb
b_dep = [
'ab_int', 'jb_int', 'b1m', 'b2m', 'bm2', 'abm', 'abrms', 'jbm', 'brms',
'gffz'
]
if (len(set(variables + b_dep)) < len(variables + b_dep)):
bb_flag = True
# check if jj needs to be computed
jj_flag = False
# array containing the variables which depend on jj
j_dep = ['jb_int', 'j2m', 'jm2', 'jbm', 'jrms']
if (len(set(variables + j_dep)) < len(variables + j_dep)):
jj_flag = True
for var_file in var_list:
# read the var file
var = pc.read_var(varfile=re.sub(' .*\n$', '', var_file),
datadir=datadir,
quiet=True)
# the output string which will be written in the destination file
out_string = '{0:1.9e} '.format(np.float64(var.t))
aa = var.aa[:, var.n1:var.n2, var.m1:var.m2, var.l1:var.l2]
if bb_flag:
bb = pc.curl(var.aa, var.dx, var.dy, var.dz, var.x, var.y, var.z)
bb = bb[:, var.n1:var.n2, var.m1:var.m2, var.l1:var.l2]
if jj_flag:
jj = pc.curl2(var.aa, var.dx, var.dy, var.dz, var.x, var.y, var.z)
jj = jj[:, var.n1:var.n2, var.m1:var.m2, var.l1:var.l2]
for variable in variables:
if variable == 'b2m':
b2m = (pc.dot2(bb)).mean()
out_string += '{0:1.9e} '.format(np.float64(b2m))
elif variable == 'j2m':
j2m = (pc.dot2(jj)).mean()
out_string += '{0:1.9e} '.format(np.float64(j2m))
break
elif variable == 'abm':
abm = (pc.dot(var.aa, bb)).mean()
out_string += '{0:1.9e} '.format(np.float64(abm))
# generalized flux function (see Yeates, Hornig 2011)
elif variable == 'gffz':
gffz = np.sum(pc.dot(aa, bb)*np.sqrt(pc.dot2(bb)) / \
((bb[2,:,:,:]) * np.mean(np.mean(np.sqrt(pc.dot2(bb)), axis = 2), axis = 1)))
out_string += '{0:1.9e} '.format(np.float64(gffz))
fd.write((out_string + '\n').encode('utf-8'))
fd.close()
def pc2npz(ivar=-1, datadir="data", files="all", quiet=True, trimall=True):
"""Convert pencil outputs to npz files.
Pencil files can be extremely large, making it difficult to transfer files from a remote location to your local machine.
This function helps mitigate that issue by reading these large files and converting them into npz files that are much
easier to transfer.
Inputs:
ivar (int) -- The specific VAR and PVAR file you would like to read. Defaults to -1 (i.e., read var.dat, pvar.dat)
datadir (str) -- Path to the data directory. Defaults to "data".
quiet (bool) -- Suppress much of the print statements when reading the files. Defaults to True
trimall (bool) -- Trim the ghost zones from the f array. Defaults to True.
Returns:
None
"""
datadir2 = datadir + "/"
if ivar < 0:
varfile = "var.dat"
pvarfile = "pvar.dat"
ts_file = "ts.npz"
dim_file = "dim.npz"
grid_file = "grid.npz"
ff_file = "ff.npz"
fp_file = "fp.npz"
else:
varfile = "VAR" + str(ivar)
pvarfile = "PVAR" + str(ivar)
ts_file = "ts{}.npz".format(ivar)
dim_file = "dim{}.npz".format(ivar)
grid_file = "grid{}.npz".format(ivar)
ff_file = "ff{}.npz".format(ivar)
fp_file = "fp{}.npz".format(ivar)
if "ts" in files or "all" in files:
print("Reading time series")
print(" ")
ts = ReadTimeSeries(datadir=datadir)
print(" ")
ts_vars = vars(ts)
print("Saving time series as {}".format(ts_file))
np.savez(ts_file, **ts_vars)
print("...")
print("...")
if "dim" in files or "all" in files:
print("Reading dim files")
print(" ")
dim = read_dim(datadir=datadir2)
print(" ")
dim_vars = vars(dim)
print("Saving dim files as {}".format(dim_file))
np.savez(dim_file, **dim_vars)
print("...")
print("...")
if "grid" in files or "all" in files:
print("Reading grid files")
print(" ")
grid = read_grid(datadir=datadir2, quiet=quiet)
print(" ")
grid_vars = vars(grid)
print("Saving grid files as {}".format(grid_file))
np.savez(grid_file, **grid_vars)
print("...")
print("...")
print("Finished...")
if "ff" in files or "all" in files:
print("Reading {} (this might take a while) ...".format(varfile))
print(" ")
var = read_var(datadir=datadir, trimall=trimall, quiet=quiet, varfile=varfile)
print(" ")
var_vars = vars(var)
print("Saving var files as {}".format(ff_file))
np.savez(ff_file, **var_vars)
print("...")
print("...")
if "fp" in files or "all" in files:
print("Reading {} (this might take a while) ...".format(pvarfile))
print(" ")
pvar = read_pvar(datadir=datadir, varfile=pvarfile)
print(" ")
pvar_vars = vars(pvar)
print("Saving pvar files as {}".format(fp_file))
np.savez(fp_file, **pvar_vars)
print("...")
print("...")
def pc2vtk_vid(ti=0,
tf=1,
datadir='data/',
proc=-1,
variables=['rho', 'uu', 'bb'],
magic=[],
b_ext=False,
destination='animation',
quiet=True):
"""
Convert data from PencilCode format to vtk.
call signature::
pc2vtk(ti = 0, tf = 1, datadir = 'data/', proc = -1,
variables = ['rho','uu','bb'], magic = [],
destination = 'animation')
Read *varfile* and convert its content into vtk format. Write the result
in *destination*.
Keyword arguments:
*ti*:
Initial time.
*tf*:
Final time.
*datadir*:
Directory where the data is stored.
*proc*:
Processor which should be read. Set to -1 for all processors.
*variables* = [ 'rho' , 'lnrho' , 'uu' , 'bb', 'b_mag', 'jj', 'j_mag', 'aa', 'ab', 'TT', 'lnTT', 'cc', 'lncc', 'ss', 'vort' ]
Variables which should be written.
*magic*: [ 'vort' , 'bb' ]
Additional variables which should be written.
*b_ext*:
Add the external magnetic field.
*destination*:
Destination files without '.vtk' extension.
*quiet*:
Keep quiet when reading the var files.
"""
# this should correct for the case the user type only one variable
if (len(variables) > 0):
if (len(variables[0]) == 1):
variables = [variables]
# this should correct for the case the user type only one variable
if (len(magic) > 0):
if (len(magic[0]) == 1):
magic = [magic]
# make sure magic is set when writing 'vort' or 'bb'
try:
index = variables.index('vort')
magic.append('vort')
except:
pass
try:
index = variables.index('bb')
magic.append('bb')
except:
pass
try:
index = variables.index('b_mag')
magic.append('bb')
except:
pass
try:
index = variables.index('jj')
magic.append('jj')
except:
pass
try:
index = variables.index('j_mag')
magic.append('jj')
except:
pass
for i in range(ti, tf + 1):
varfile = 'VAR' + str(i)
# reading pc variables and setting dimensions
var = pc.read_var(varfile=varfile,
datadir=datadir,
proc=proc,
magic=magic,
trimall=True,
quiet=quiet)
grid = pc.read_grid(datadir=datadir, proc=proc, trim=True, quiet=True)
params = pc.read_param(param2=True, quiet=True)
B_ext = np.array(params.b_ext)
# add external magnetic field
if (b_ext == True):
var.bb[0, ...] += B_ext[0]
var.bb[1, ...] += B_ext[1]
var.bb[2, ...] += B_ext[2]
dimx = len(grid.x)
dimy = len(grid.y)
dimz = len(grid.z)
dim = dimx * dimy * dimz
dx = (np.max(grid.x) - np.min(grid.x)) / (dimx - 1)
dy = (np.max(grid.y) - np.min(grid.y)) / (dimy - 1)
dz = (np.max(grid.z) - np.min(grid.z)) / (dimz - 1)
#fd = open(destination + "{0:1.0f}".format(var.t*1e5) + '.vtk', 'wb')
fd = open(destination + str(i) + '.vtk', 'wb')
fd.write('# vtk DataFile Version 2.0\n'.encode('utf-8'))
fd.write('density + magnetic field\n'.encode('utf-8'))
fd.write('BINARY\n'.encode('utf-8'))
fd.write('DATASET STRUCTURED_POINTS\n'.encode('utf-8'))
fd.write('DIMENSIONS {0:9} {1:9} {2:9}\n'.format(dimx, dimy,
dimz).encode('utf-8'))
fd.write('ORIGIN {0:8.12} {1:8.12} {2:8.12}\n'.format(
grid.x[0], grid.y[0], grid.z[0]).encode('utf-8'))
fd.write('SPACING {0:8.12} {1:8.12} {2:8.12}\n'.format(
dx, dy, dz).encode('utf-8'))
fd.write('POINT_DATA {0:9}\n'.format(dim).encode('utf-8'))
try:
index = variables.index('rho')
print('writing rho')
fd.write('SCALARS rho float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.rho[k, j, i]))
except:
pass
try:
index = variables.index('lnrho')
print('writing lnrho')
fd.write('SCALARS lnrho float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.lnrho[k, j, i]))
except:
pass
try:
index = variables.index('uu')
print('writing uu')
fd.write('VECTORS vfield float\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.uu[0, k, j, i]))
fd.write(struct.pack(">f", var.uu[1, k, j, i]))
fd.write(struct.pack(">f", var.uu[2, k, j, i]))
except:
pass
try:
index = variables.index('bb')
print('writing bb')
fd.write('VECTORS bfield float\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.bb[0, k, j, i]))
fd.write(struct.pack(">f", var.bb[1, k, j, i]))
fd.write(struct.pack(">f", var.bb[2, k, j, i]))
except:
pass
try:
index = variables.index('b_mag')
b_mag = np.sqrt(pc.dot2(var.bb))
print('writing b_mag')
fd.write('SCALARS b_mag float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", b_mag[k, j, i]))
except:
pass
try:
index = variables.index('jj')
print('writing jj')
fd.write('VECTORS jfield float\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.jj[0, k, j, i]))
fd.write(struct.pack(">f", var.jj[1, k, j, i]))
fd.write(struct.pack(">f", var.jj[2, k, j, i]))
except:
pass
try:
index = variables.index('j_mag')
j_mag = np.sqrt(pc.dot2(var.jj))
print('writing j_mag')
fd.write('SCALARS j_mag float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", j_mag[k, j, i]))
except:
pass
try:
index = variables.index('aa')
print('writing aa')
fd.write('VECTORS afield float\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.aa[0, k, j, i]))
fd.write(struct.pack(">f", var.aa[1, k, j, i]))
fd.write(struct.pack(">f", var.aa[2, k, j, i]))
except:
pass
try:
index = variables.index('ab')
ab = pc.dot(var.aa, var.bb)
print('writing ab')
fd.write('SCALARS ab float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", ab[k, j, i]))
except:
pass
try:
index = variables.index('TT')
print('writing TT')
fd.write('SCALARS TT float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.TT[k, j, i]))
except:
pass
try:
index = variables.index('lnTT')
print('writing lnTT')
fd.write('SCALARS lnTT float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.lnTT[k, j, i]))
except:
pass
try:
index = variables.index('cc')
print('writing cc')
fd.write('SCALARS cc float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.cc[k, j, i]))
except:
pass
try:
index = variables.index('lncc')
print('writing lncc')
fd.write('SCALARS lncc float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.lncc[k, j, i]))
except:
pass
try:
index = variables.index('ss')
print('writing ss')
fd.write('SCALARS ss float\n'.encode('utf-8'))
fd.write('LOOKUP_TABLE default\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.ss[k, j, i]))
except:
pass
try:
index = variables.index('vort')
print('writing vort')
fd.write('VECTORS vorticity float\n'.encode('utf-8'))
for k in range(dimz):
for j in range(dimy):
for i in range(dimx):
fd.write(struct.pack(">f", var.vort[0, k, j, i]))
fd.write(struct.pack(">f", var.vort[1, k, j, i]))
fd.write(struct.pack(">f", var.vort[2, k, j, i]))
except:
pass
del (var)
fd.close()
# Orbit=MaxOrbits-2
Orbit = 6
#
#
#
KE_Sum = []
UE_Sum = []
UINT_Sum = []
FE_Sum = []
while Int <= Orbit:
ff = pc.read_var(trimall=True, ivar=Int, magic=["TT"])
TT = ff.TT
rad = ff.x
phi = ff.y
uu = ff.uu
ux = ff.ux
uy = ff.uy
rho = ff.rho
drad = np.gradient(rad)
dphi = np.gradient(phi)
radp = []
for index in range(len(Orbit_Len)):
radp = radius[Orbit_Len]
phip = []
for index in range(len(Orbit_Len)):
phip = Omega[Orbit_Len]
def fixed_points(datadir='data/',
fileName='fixed_points_post.dat',
varfile='VAR0',
ti=-1,
tf=-1,
traceField='bb',
hMin=2e-3,
hMax=2e4,
lMax=500,
tol=1e-2,
interpolation='weighted',
trace_sub=1,
integration='simple',
nproc=1):
"""
Find the fixed points.
call signature::
fixed = fixed_points(datadir = 'data/', fileName = 'fixed_points_post.dat', varfile = 'VAR0', ti = -1, tf = -1,
traceField = 'bb', hMin = 2e-3, hMax = 2e4, lMax = 500, tol = 1e-2,
interpolation = 'weighted', trace_sub = 1, integration = 'simple', nproc = 1)
Finds the fixed points. Returns the fixed points positions.
Keyword arguments:
*datadir*:
Data directory.
*fileName*:
Name of the fixed points file.
*varfile*:
Varfile to be read.
*ti*:
Initial VAR file index for tracer time sequences. Overrides 'varfile'.
*tf*:
Final VAR file index for tracer time sequences. Overrides 'varfile'.
*traceField*:
Vector field used for the streamline tracing.
*hMin*:
Minimum step length for and underflow to occur.
*hMax*:
Parameter for the initial step length.
*lMax*:
Maximum length of the streamline. Integration will stop if l >= lMax.
*tol*:
Tolerance for each integration step. Reduces the step length if error >= tol.
*interpolation*:
Interpolation of the vector field.
'mean': takes the mean of the adjacent grid point.
'weighted': weights the adjacent grid points according to their distance.
*trace_sub*:
Number of sub-grid cells for the seeds for the initial mapping.
*intQ*:
Quantities to be integrated along the streamlines.
*integration*:
Integration method.
'simple': low order method.
'RK6': Runge-Kutta 6th order.
*nproc*:
Number of cores for multi core computation.
"""
class data_struct:
def __init__(self):
self.t = []
self.fidx = [] # number of fixed points at this time
self.x = []
self.y = []
self.q = []
# Computes rotation along one edge.
def edge(vv,
p,
sx,
sy,
diff1,
diff2,
phiMin,
rec,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration):
dtot = m.atan2(diff1[0] * diff2[1] - diff2[0] * diff1[1],
diff1[0] * diff2[0] + diff1[1] * diff2[1])
if ((abs(dtot) > phiMin) and (rec < 4)):
xm = 0.5 * (sx[0] + sx[1])
ym = 0.5 * (sy[0] + sy[1])
# trace intermediate field line
s = pc.stream(vv,
p,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration,
xx=np.array([xm, ym, p.Oz]))
tracer = np.concatenate(
(s.tracers[0,
0:2], s.tracers[s.sl - 1, :], np.reshape(s.l, (1))))
# discard any streamline which does not converge or hits the boundary
if ((tracer[5] >= lMax) or (tracer[4] < p.Oz + p.Lz - p.dz)):
dtot = 0.
else:
diffm = np.array(
[tracer[2] - tracer[0], tracer[3] - tracer[1]])
if (sum(diffm**2) != 0):
diffm = diffm / np.sqrt(sum(diffm**2))
dtot = edge(vv, p, [sx[0], xm], [sy[0], ym], diff1, diffm, phiMin, rec+1,
hMin = hMin, hMax = hMax, lMax = lMax, tol = tol, interpolation = interpolation, integration = integration)+ \
edge(vv, p, [xm, sx[1]], [ym, sy[1]], diffm, diff2, phiMin, rec+1,
hMin = hMin, hMax = hMax, lMax = lMax, tol = tol, interpolation = interpolation, integration = integration)
return dtot
# Finds the Poincare index of this grid cell.
def pIndex(vv,
p,
sx,
sy,
diff,
phiMin,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration):
poincare = 0
poincare += edge(vv,
p, [sx[0], sx[1]], [sy[0], sy[0]],
diff[0, :],
diff[1, :],
phiMin,
0,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration)
poincare += edge(vv,
p, [sx[1], sx[1]], [sy[0], sy[1]],
diff[1, :],
diff[2, :],
phiMin,
0,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration)
poincare += edge(vv,
p, [sx[1], sx[0]], [sy[1], sy[1]],
diff[2, :],
diff[3, :],
phiMin,
0,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration)
poincare += edge(vv,
p, [sx[0], sx[0]], [sy[1], sy[0]],
diff[3, :],
diff[0, :],
phiMin,
0,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration)
return poincare
# fixed point finder for a subset of the domain
def subFixed(queue,
ix0,
iy0,
vv,
p,
tracers,
iproc,
hMin=2e-3,
hMax=2e4,
lMax=500,
tol=1e-2,
interpolation='weighted',
integration='simple'):
diff = np.zeros((4, 2))
phiMin = np.pi / 8.
x = []
y = []
q = []
fidx = 0
for ix in ix0:
for iy in iy0:
# compute Poincare index around this cell (!= 0 for potential fixed point)
diff[0, :] = tracers[iy, ix, 0, 2:4] - tracers[iy, ix, 0, 0:2]
diff[1, :] = tracers[iy, ix + 1, 0, 2:4] - tracers[iy, ix + 1,
0, 0:2]
diff[2, :] = tracers[iy + 1, ix + 1, 0,
2:4] - tracers[iy + 1, ix + 1, 0, 0:2]
diff[3, :] = tracers[iy + 1, ix, 0, 2:4] - tracers[iy + 1, ix,
0, 0:2]
if (sum(np.sum(diff**2, axis=1) != 0) == True):
diff = np.swapaxes(
np.swapaxes(diff, 0, 1) /
np.sqrt(np.sum(diff**2, axis=1)), 0, 1)
poincare = pIndex(vv,
p,
tracers[iy, ix:ix + 2, 0, 0],
tracers[iy:iy + 2, ix, 0, 1],
diff,
phiMin,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration)
if (abs(poincare) > 5
): # use 5 instead of 2pi to account for rounding errors
# subsample to get starting point for iteration
nt = 4
xmin = tracers[iy, ix, 0, 0]
ymin = tracers[iy, ix, 0, 1]
xmax = tracers[iy, ix + 1, 0, 0]
ymax = tracers[iy + 1, ix, 0, 1]
xx = np.zeros((nt**2, 3))
tracersSub = np.zeros((nt**2, 5))
i1 = 0
for j1 in range(nt):
for k1 in range(nt):
xx[i1, 0] = xmin + j1 / (nt - 1.) * (xmax - xmin)
xx[i1, 1] = ymin + k1 / (nt - 1.) * (ymax - ymin)
xx[i1, 2] = p.Oz
i1 += 1
for it1 in range(nt**2):
s = pc.stream(vv,
p,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration,
xx=xx[it1, :])
tracersSub[it1, 0:2] = xx[it1, 0:2]
tracersSub[it1, 2:] = s.tracers[s.sl - 1, :]
min2 = 1e6
minx = xmin
miny = ymin
i1 = 0
for j1 in range(nt):
for k1 in range(nt):
diff2 = (tracersSub[i1, 2] - tracersSub[i1, 0]
)**2 + (tracersSub[i1, 3] -
tracersSub[i1, 1])**2
if (diff2 < min2):
min2 = diff2
minx = xmin + j1 / (nt - 1.) * (xmax - xmin)
miny = ymin + k1 / (nt - 1.) * (ymax - ymin)
it1 += 1
# get fixed point from this starting position using Newton's method
#TODO:
dl = np.min(
var.dx, var.dy
) / 100. # step-size for calculating the Jacobian by finite differences
it = 0
# tracers used to find the fixed point
tracersNull = np.zeros((5, 4))
point = np.array([minx, miny])
while True:
# trace field lines at original point and for Jacobian:
# (second order seems to be enough)
xx = np.zeros((5, 3))
xx[0, :] = np.array([point[0], point[1], p.Oz])
xx[1, :] = np.array([point[0] - dl, point[1], p.Oz])
xx[2, :] = np.array([point[0] + dl, point[1], p.Oz])
xx[3, :] = np.array([point[0], point[1] - dl, p.Oz])
xx[4, :] = np.array([point[0], point[1] + dl, p.Oz])
for it1 in range(5):
s = pc.stream(vv,
p,
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
integration=integration,
xx=xx[it1, :])
tracersNull[it1, :2] = xx[it1, :2]
tracersNull[it1, 2:] = s.tracers[s.sl - 1, 0:2]
# check function convergence
ff = np.zeros(2)
ff[0] = tracersNull[0, 2] - tracersNull[0, 0]
ff[1] = tracersNull[0, 3] - tracersNull[0, 1]
#TODO:
if (sum(abs(ff)) <= 1e-4):
fixedPoint = np.array([point[0], point[1]])
break
# compute the Jacobian
fjac = np.zeros((2, 2))
fjac[0, 0] = (
(tracersNull[2, 2] - tracersNull[2, 0]) -
(tracersNull[1, 2] - tracersNull[1, 0])) / 2. / dl
fjac[0, 1] = (
(tracersNull[4, 2] - tracersNull[4, 0]) -
(tracersNull[3, 2] - tracersNull[3, 0])) / 2. / dl
fjac[1, 0] = (
(tracersNull[2, 3] - tracersNull[2, 1]) -
(tracersNull[1, 3] - tracersNull[1, 1])) / 2. / dl
fjac[1, 1] = (
(tracersNull[4, 3] - tracersNull[4, 1]) -
(tracersNull[3, 3] - tracersNull[3, 1])) / 2. / dl
# invert the Jacobian
fjin = np.zeros((2, 2))
det = fjac[0, 0] * fjac[1, 1] - fjac[0, 1] * fjac[1, 0]
#TODO:
if (abs(det) < dl):
fixedPoint = point
break
fjin[0, 0] = fjac[1, 1]
fjin[1, 1] = fjac[0, 0]
fjin[0, 1] = -fjac[0, 1]
fjin[1, 0] = -fjac[1, 0]
fjin = fjin / det
dpoint = np.zeros(2)
dpoint[0] = -fjin[0, 0] * ff[0] - fjin[0, 1] * ff[1]
dpoint[1] = -fjin[1, 0] * ff[0] - fjin[1, 1] * ff[1]
point += dpoint
# check root convergence
#TODO:
if (sum(abs(dpoint)) < 1e-4):
fixedPoint = point
break
if (it > 20):
fixedPoint = point
print("warning: Newton did not converged")
break
it += 1
# check if fixed point lies inside the cell
if ((fixedPoint[0] < tracers[iy, ix, 0, 0])
or (fixedPoint[0] > tracers[iy, ix + 1, 0, 0])
or (fixedPoint[1] < tracers[iy, ix, 0, 1])
or (fixedPoint[1] > tracers[iy + 1, ix, 0, 1])):
print("warning: fixed point lies outside the cell")
else:
x.append(fixedPoint[0])
y.append(fixedPoint[1])
#q.append()
fidx += 1
queue.put((x, y, q, fidx, iproc))
# multi core setup
if (np.isscalar(nproc) == False) or (nproc % 1 != 0):
print("error: invalid processor number")
return -1
queue = mp.Queue()
proc = []
# make sure to read the var files with the correct magic
if (traceField == 'bb'):
magic = 'bb'
if (traceField == 'jj'):
magic = 'jj'
if (traceField == 'vort'):
magic = 'vort'
# read the cpu structure
dim = pc.read_dim(datadir=datadir)
if (dim.nprocz > 1):
print("error: number of cores in z-direction > 1")
var = pc.read_var(varfile=varfile,
datadir=datadir,
magic=magic,
quiet=True,
trimall=True)
grid = pc.read_grid(datadir=datadir, quiet=True, trim=True)
vv = getattr(var, traceField)
# initialize the parameters
p = pc.pClass()
p.dx = var.dx
p.dy = var.dy
p.dz = var.dz
p.Ox = var.x[0]
p.Oy = var.y[0]
p.Oz = var.z[0]
p.Lx = grid.Lx
p.Ly = grid.Ly
p.Lz = grid.Lz
p.nx = dim.nx
p.ny = dim.ny
p.nz = dim.nz
# create the initial mapping
tracers, mapping, t = pc.tracers(traceField='bb',
hMin=hMin,
hMax=hMax,
lMax=lMax,
tol=tol,
interpolation=interpolation,
trace_sub=trace_sub,
varfile=varfile,
integration=integration,
datadir=datadir,
destination='',
nproc=nproc)
# find fixed points
fixed = pc.fixed_struct()
xyq = [] # list of return values from subFixed
ix0 = range(0, p.nx * trace_sub - 1) # set of grid indices for the cores
iy0 = range(0, p.ny * trace_sub - 1) # set of grid indices for the cores
subFixedLambda = lambda queue, ix0, iy0, vv, p, tracers, iproc: \
subFixed(queue, ix0, iy0, vv, p, tracers, iproc, hMin = hMin, hMax = hMax, lMax = lMax, tol = tol,
interpolation = interpolation, integration = integration)
for iproc in range(nproc):
proc.append(
mp.Process(target=subFixedLambda,
args=(queue, ix0[iproc::nproc], iy0, vv, p, tracers,
iproc)))
for iproc in range(nproc):
proc[iproc].start()
for iproc in range(nproc):
xyq.append(queue.get())
for iproc in range(nproc):
proc[iproc].join()
# put together return values from subFixed
fixed.fidx = 0
fixed.t = var.t
for iproc in range(nproc):
fixed.x.append(xyq[xyq[iproc][4]][0])
fixed.y.append(xyq[xyq[iproc][4]][1])
fixed.q.append(xyq[xyq[iproc][4]][2])
fixed.fidx += xyq[xyq[iproc][4]][3]
fixed.t = np.array(fixed.t)
fixed.x = np.array(fixed.x)
fixed.y = np.array(fixed.y)
fixed.q = np.array(fixed.q)
fixed.fidx = np.array(fixed.fidx)
return fixed