def read_class_nqvar_red(datadir='./data',
pfile='qvar.dat',
proc=0,
verbose=False):
dims = pc.read_dim(datadir, proc)
qdims = pc.read_qdim(datadir)
nqpar = read_qpar(datadir=datadir, pfile=pfile, proc=proc)
if (verbose):
#print npar_loc,' particles on processor: ',proc # Python 2
print(nqpar + 'massive particles on processor: ' + proc)
mvars = pdims.mqaux + pdims.mqvar
ltot = nqpar * mvars
if (dims.precision == 'S'):
REAL = '<f4'
else:
REAL = '<f8'
array_shape = np.dtype([('header', '<i4'), ('nqpar', '<i4'),
('footer', '<i4'), ('header2', '<i4'),
('ipar', '<i4', nqpar), ('footer2', '<i4'),
('header3', '<i4'), ('fq', REAL, ltot),
('footer3', '<i4'), ('header4', '<i4'),
('t', REAL), ('x', REAL, dims.mx),
('y', REAL, dims.my), ('z', REAL, dims.mz),
('dx', REAL), ('dy', REAL), ('dz', REAL),
('footer4', '<i4')])
p_data = np.fromfile(datadir + '/proc' + str(proc) + '/' + pfile,
dtype=array_shape)
partpars = np.array(p_data['fq'].reshape(mvars, npar_loc))
ipar = np.squeeze(p_data['ipar'].reshape(p_data['ipar'].size))
return ipar, partpars
def loadData(field, extension):
global data
# check if data has already been loaded
if (field + extension in data.loaded) == False:
data.slices[field + extension], data.t = pc.read_slices(
datadir='data', field=field, extension=extension, proc=-1)
data.dim[field + extension] = pc.read_dim() # system dimensions
data.param[field + extension] = pc.read_param(
quiet=True) # system parameters
data.loaded.add(field + extension)
def read_class_nqvar(datadir='data', pfile='', proc=0, verbose=False):
dims = pc.read_dim(datadir, proc)
if (dims.precision == 'S'):
REAL = '<f4'
else:
REAL = '<f8'
qdims = pc.read_qdim(datadir)
nqpars = qdims.nqpar
mqvars = qdims.mqvar
ltot = nqpars * mqvars
if (verbose):
print(nqpars + 'massqvarve particles on processor: ' + proc)
# MR modified array_shape
array_shape = np.dtype([('header', '<i4'), ('ipar', '<i4'),
('footer', '<i4'), ('header2', '<i4'),
('fq', REAL, ltot), ('footer2', '<i4'),
('header3', '<i4'), ('t', REAL),
('footer3', '<i4')])
p_data = np.fromfile(datadir + '/proc0/' + pfile, dtype=array_shape)
ipar = np.squeeze(p_data[0]['ipar'].reshape(p_data[0]['ipar'].size))
partpars = np.array(p_data[0]['fq'].reshape(mqvars, nqpars))
t = p_data[0]['t']
return ipar, partpars, t
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 read_class_npvar_red(datadir='./data',
pfile='pvar.dat',
proc=0,
verbose=False,
reduce_to=-1,
set_reduce=-1):
dims = pc.read_dim(datadir,proc)
pdims = pc.read_pdim(datadir)
npar_loc = read_npar_loc(datadir=datadir,pfile=pfile,proc=proc)
#
# the Next bit calculates how many particles are written for all but
# the last processor. The last processor is assigned a number of particles
# to write so that the required number of particles is obtained
#
if (reduce_to > 0):
if (set_reduce <= 0):
reductionfactor = float(reduce_to)/float(pdims.npar)
npar_red = int(round(npar_loc*reductionfactor))
else:
npar_red = set_reduce
if (verbose):
#print 'reducing '+str(npar_loc)+' to '+str(npar_red)+ ' on proc'+str(proc)
print('reducing {} to {} on proc {}'.format(
npar_loc, npar_red, proc))
written_parts=npar_red
else:
written_parts=set_reduce
if (verbose):
#print npar_loc,' particles on processor: ',proc # Python 2
print(str(npar_loc)+' particles on processor: '+str(proc))
mvars = pdims.mpaux+pdims.mpvar
ltot = npar_loc*mvars
if (dims.precision == 'S'):
REAL = '<f4'
else:
REAL = '<f8'
array_shape= np.dtype([('header','<i4'),
('npar_loc','<i4'),
('footer','<i4'),
('header2','<i4'),
('ipar','<i4',npar_loc),
('footer2','<i4'),
('header3','<i4'),
('fp',REAL,ltot),
('footer3','<i4'),
('header4','<i4'),
('t',REAL),
('x',REAL,dims.mx),
('y',REAL,dims.my),
('z',REAL,dims.mz),
('dx',REAL),
('dy',REAL),
('dz',REAL),
('footer4','<i4')])
p_data = np.fromfile(datadir+'/proc'+str(proc)+'/'+pfile,dtype=array_shape)
partpars = np.array(p_data['fp'].reshape(mvars,npar_loc))
if (reduce_to>0):
particle_list = map(lambda x: int(x),np.linspace(0.0,npar_loc,num=npar_red,endpoint=False))
red_parts = partpars[:,particle_list]
red_shape = np.dtype([('header','<i4'),
('npar_loc','<i4'),
('footer','<i4'),
('header2','<i4'),
('ipar','<i4',(npar_red),),
('footer2','<i4'),
('header3','<i4'),
('fp',REAL,npar_red*mvars),
('footer3','<i4'),
('header4','<i4'),
('t',REAL),
('x',REAL,(dims.mx,)),
('y',REAL,(dims.my,)),
('z',REAL,(dims.mz,)),
('dx',REAL),
('dy',REAL),
('dz',REAL),
('footer4','<i4')])
p_red =np.array([(4,
npar_red,
4,
(npar_red*4),
(np.squeeze(p_data['ipar'][0,:npar_red])),
(npar_red*4),
(npar_red*mvars*8),
(np.squeeze(np.ravel(red_parts))),
(npar_red*mvars*8),
(p_data['header4'][0]),
(p_data['t']),
(p_data['x']),
(p_data['y']),
(p_data['z']),
(p_data['dx']),
(p_data['dy']),
(p_data['dz']),
p_data['footer4'][0])
],dtype=red_shape)
p_red.tofile(datadir+'/proc'+str(proc)+'/'+str(reduce_to)+'_'+pfile)
ipar = np.squeeze(p_data['ipar'].reshape(p_data['ipar'].size))
return ipar, partpars, written_parts
def calc_tensors(datatopdir,
lskip_zeros=False,
datadir='data/',
rank=0,
size=1,
comm=None,
proc=[0],
l_mpi=True,
iuxmxy=0,
irhomxy=7,
iTTmxy=6,
first_alpha=9,
l_correction=False,
t_correction=0.,
fskip=2,
mskip=1,
trange=(0, None),
tindex=(0, None, 1),
yindex=[]):
nt = None
alltmp = 100000
dim = pc.read_dim()
gc.garbage
if len(yindex) == 0:
iy = np.arange(dim.ny)
else:
iy = yindex
os.chdir(datatopdir) # return to working directory
av = []
if l_mpi:
from mpi4py import MPI
if proc.size < dim.nprocz:
print('rank {}: proc.size {} < dim.nprocz {}'.format(
rank, proc.size, dim.nprocz))
yproc = proc[0] / dim.nprocz
aav, time = pc.read_zaver(datadir,
trange=trange,
tindex=tindex,
proc=yproc)
tmp = time.size
else:
print('rank {}: proc.size {} >= dim.nprocz {}'.format(
rank, proc.size, dim.nprocz))
for iproc in range(0, proc.size, dim.nprocz):
if iproc == 0:
aav, time = pc.read_zaver(datadir,
trange=trange,
tindex=tindex,
proc=proc[iproc] / dim.nprocz)
tmp = time.size
else:
aav, time = pc.read_zaver(datadir,
proc=proc[iproc] / dim.nprocz)
tmp = min(time.size, tmp)
else:
av, time = pc.read_zaver(datadir, trange=trange, tindex=tindex)
gc.garbage
if l_mpi:
print('rank {}: tmp {}'.format(rank, tmp))
if rank != 0:
comm.send(tmp, dest=0, tag=rank)
else:
for irank in range(1, size):
tmp = comm.recv(source=irank, tag=irank)
alltmp = min(alltmp, tmp)
nt = comm.bcast(alltmp, root=0)
print('rank {}: nt {}'.format(rank, nt))
if proc.size < dim.nprocz:
yndx = iy - yproc * (dim.nygrid / dim.nprocy)
print('rank {}: yndx[0] {}'.format(rank, yndx[0]))
av = aav[:nt, :, yndx, :]
else:
av = aav[:nt]
for iproc in range(dim.nprocz, proc.size, dim.nprocz):
aav, time = pc.read_zaver(datadir,
tindex=(0, nt, 1),
proc=proc[iproc] / dim.nprocz)
av = np.concatenate((av, aav), axis=2)
aav = []
print('rank {}: loaded av'.format(rank))
#where testfield calculated under old incorrect spec apply correction
gc.garbage
if l_correction:
itcorr = np.where(time < t_correction)[0]
av[itcorr, first_alpha + 2] *= -dim.nprocz / (dim.nprocz - 2.)
for j in range(0, 3):
av[itcorr, first_alpha + 5 + j] *= -dim.nprocz / (dim.nprocz - 2.)
av[itcorr, first_alpha + 11] *= -dim.nprocz / (dim.nprocz - 2.)
for j in range(0, 3):
av[itcorr, first_alpha + 14 + j] *= -dim.nprocz / (dim.nprocz - 2.)
av[itcorr, first_alpha + 20] *= -dim.nprocz / (dim.nprocz - 2.)
for j in range(0, 3):
av[itcorr, first_alpha + 23 + j] *= -dim.nprocz / (dim.nprocz - 2.)
#factor by which to rescale code time to years
trescale = 0.62 / 2.7e-6 / (365. * 86400.) #0.007281508
time *= trescale
grid = pc.read_grid(datadir, trim=True, quiet=True)
r, theta = np.meshgrid(grid.x, grid.y[iy])
gc.garbage
#exclude zeros and next point if resetting of test fields is used
#trim reset data and neighbours as required fskip after zeros and mskip before zeros.
if lskip_zeros:
if l_mpi:
if rank == 0:
izer0 = np.where(av[:, 9, av.shape[2] / 2,
av.shape[3] / 2] == 0)[0]
for ii in range(1, fskip):
izer1 = np.where(av[:, 9, av.shape[2] / 2,
av.shape[3] / 2] == 0)[0] + ii
izer0 = np.append(izer0, izer1)
for ii in range(1, mskip):
izer1 = np.where(av[:, 9, av.shape[2] / 2,
av.shape[3] / 2] == 0)[0] - ii
izer0 = np.append(izer0, izer1)
if izer0.size > 0:
imask = np.delete(np.where(time), [izer0])
else:
imask = np.where(time)[0]
else:
imask = None
imask = comm.bcast(imask, root=0)
else:
izer0 = np.where(av[:, 9, av.shape[2] / 2,
av.shape[3] / 2] == 0)[0]
for ii in range(1, fskip):
izer1 = np.where(av[:, 9, av.shape[2] / 2,
av.shape[3] / 2] == 0)[0] + ii
izer0 = np.append(izer0, izer1)
for ii in range(1, mskip):
izer1 = np.where(av[:, 9, av.shape[2] / 2,
av.shape[3] / 2] == 0)[0] - ii
izer0 = np.append(izer0, izer1)
if izer0.size > 0:
imask = np.delete(np.where(time), [izer0])
else:
imask = np.where(time)[0]
else:
imask = np.arange(time.size)
#if lskip_zeros:
# izer0=np.where(av[:,first_alpha,av.shape[2]/2,av.shape[3]/2]==0)[0]
# izer1=np.where(av[:,first_alpha,av.shape[2]/2,av.shape[3]/2]==0)[0]+1
# if izer0.size>0:
# imask=np.delete(np.where(time[:nt]),[izer0,izer1])
# else:
# imask=np.where(time[:nt])[0]
#else:
# imask=np.arange(time[:nt].size)
if rank == 0:
print('rank {}: calculating alp'.format(rank))
alp = np.zeros([3, 3, imask.size, av.shape[2], av.shape[3]])
eta = np.zeros([3, 3, 3, imask.size, av.shape[2], av.shape[3]])
urmst = np.zeros([3, 3, av.shape[2], av.shape[3]])
etat0 = np.zeros([3, 3, 3, av.shape[2], av.shape[3]])
#eta0 = np.zeros([3,3,3,imask.size,av.shape[2],av.shape[3]])
Hp = np.zeros([av.shape[2], av.shape[3]])
#compute rms velocity normalisation
if rank == 0:
print('rank {}: calculating urms'.format(rank))
urms = np.sqrt(
np.mean(av[imask, iuxmxy + 3, :, :] - av[imask, iuxmxy + 0, :, :]**2 +
av[imask, iuxmxy + 4, :, :] - av[imask, iuxmxy + 1, :, :]**2 +
av[imask, iuxmxy + 5, :, :] - av[imask, iuxmxy + 2, :, :]**2,
axis=0))
#compute turbulent diffusion normalisation
cv, gm, alp_MLT = 0.6, 5. / 3, 5. / 3
pp = np.mean(av[imask, iTTmxy, :, :] * av[imask, irhomxy, :, :] * cv *
(gm - 1),
axis=0)
if rank == 0:
print('rank {}: completed pressure'.format(rank))
for i in range(0, av.shape[2]):
Hp[i, :] = -1. / np.gradient(np.log(pp[i, :]), grid.dx)
grid, pp = [], []
for i in range(0, 3):
for j in range(0, 3):
alp[i, j, :, :, :] = av[imask, first_alpha + 3 * j + i, :, :]
urmst[i, j, :, :] = urms / 3.
for k in range(0, 3):
etat0[i, j, k, :, :] = urms * alp_MLT * Hp / 3.
#for i in range(0,imask.size):
# eta0[i,:,:,:,:,:] = etat0
if rank == 0:
print('rank {}: calculating eta'.format(rank))
for j in range(0, 3):
for k in range(0, 3):
# Sign difference with Schrinner + r correction
eta[j, k, 1, :, :, :] = -av[imask,
first_alpha + 18 + 3 * k + j, :, :] * r
eta[j, k,
0, :, :, :] = -av[imask, first_alpha + 9 + 3 * k + j, :, :]
nnt, ny, nx = imask.size, av.shape[2], av.shape[3]
av = []
irr, ith, iph = 0, 1, 2
# Create output tensors
if rank == 0:
print('rank {}: setting alp'.format(rank))
alpha = np.zeros([3, 3, nnt, ny, nx])
beta = np.zeros([3, 3, nnt, ny, nx])
gamma = np.zeros([3, nnt, ny, nx])
delta = np.zeros([3, nnt, ny, nx])
kappa = np.zeros([3, 3, 3, nnt, ny, nx])
# Alpha tensor
if rank == 0:
print('rank {}: calculating alpha'.format(rank))
alpha[irr, irr, :, :, :] = (alp[irr, irr, :, :, :] -
eta[irr, ith, ith, :, :, :] / r)
alpha[irr, ith, :, :, :] = 0.5 * (
alp[irr, ith, :, :, :] + eta[irr, irr, ith, :, :, :] / r +
alp[ith, irr, :, :, :] - eta[ith, ith, ith, :, :, :] / r)
alpha[irr, iph, :, :, :] = 0.5 * (alp[iph, irr, :, :, :] +
alp[irr, iph, :, :, :] -
eta[iph, ith, ith, :, :, :] / r)
alpha[ith, irr, :, :, :] = alpha[irr, ith, :, :, :]
alpha[ith, ith, :, :, :] = (alp[ith, ith, :, :, :] +
eta[ith, irr, ith, :, :, :] / r)
alpha[ith, iph, :, :, :] = 0.5 * (alp[iph, ith, :, :, :] +
alp[ith, iph, :, :, :] +
eta[iph, irr, ith, :, :, :] / r)
alpha[iph, irr, :, :, :] = alpha[irr, iph, :, :, :]
alpha[iph, ith, :, :, :] = alpha[ith, iph, :, :, :]
alpha[iph, iph, :, :, :] = alp[iph, iph, :, :, :]
# Gamma vector
gamma[irr, :, :, :] = -0.5 * (alp[ith, iph, :, :, :] -
alp[iph, ith, :, :, :] -
eta[iph, irr, ith, :, :, :] / r)
gamma[ith, :, :, :] = -0.5 * (alp[iph, irr, :, :, :] -
alp[irr, iph, :, :, :] -
eta[iph, ith, ith, :, :, :] / r)
gamma[iph, :, :, :] = -0.5 * (
alp[irr, ith, :, :, :] - alp[ith, irr, :, :, :] +
eta[irr, irr, ith, :, :, :] / r + eta[ith, ith, ith, :, :, :] / r)
if rank == 0:
print('rank {}: calculating beta'.format(rank))
alp = []
# Beta tensor
beta[irr, irr, :, :, :] = -0.5 * eta[irr, iph, ith, :, :, :]
beta[irr, ith, :, :, :] = 0.25 * (eta[irr, iph, irr, :, :, :] -
eta[ith, iph, ith, :, :, :])
beta[irr, iph, :, :, :] = 0.25 * (eta[irr, irr, ith, :, :, :] -
eta[iph, iph, ith, :, :, :] -
eta[irr, ith, irr, :, :, :])
beta[ith, ith, :, :, :] = 0.5 * eta[ith, iph, irr, :, :, :]
beta[ith, iph, :, :, :] = 0.25 * (eta[ith, irr, ith, :, :, :] +
eta[iph, iph, irr, :, :, :] -
eta[ith, ith, irr, :, :, :])
beta[iph, iph, :, :, :] = 0.5 * (eta[iph, irr, ith, :, :, :] -
eta[iph, ith, irr, :, :, :])
beta[ith, irr, :, :, :] = beta[irr, ith, :, :, :]
beta[iph, irr, :, :, :] = beta[irr, iph, :, :, :]
beta[iph, ith, :, :, :] = beta[ith, iph, :, :, :]
# Delta vector
delta[irr, :, :, :] = 0.25 * (eta[ith, ith, irr, :, :, :] -
eta[ith, irr, ith, :, :, :] +
eta[iph, iph, irr, :, :, :])
delta[ith, :, :, :] = 0.25 * (eta[irr, irr, ith, :, :, :] -
eta[irr, ith, irr, :, :, :] +
eta[iph, iph, ith, :, :, :])
delta[iph, :, :, :] = -0.25 * (eta[irr, iph, irr, :, :, :] +
eta[ith, iph, ith, :, :, :])
# Kappa tensor
if rank == 0:
print('rank {}: calculating kappa'.format(rank))
for i in range(0, 3):
kappa[i, irr, irr, :, :, :] = -eta[i, irr, irr, :, :, :]
kappa[i, irr, ith, :, :, :] = -0.5 * (eta[i, ith, irr, :, :, :] +
eta[i, irr, ith, :, :, :])
kappa[i, irr, iph, :, :, :] = -0.5 * eta[i, iph, irr, :, :, :]
kappa[i, ith, irr, :, :, :] = kappa[i, irr, ith, :, :, :]
kappa[i, ith, ith, :, :, :] = -eta[i, ith, ith, :, :, :]
kappa[i, ith, iph, :, :, :] = -0.5 * eta[i, iph, ith, :, :, :]
kappa[i, iph, irr, :, :, :] = kappa[i, irr, iph, :, :, :]
kappa[i, iph, ith, :, :, :] = kappa[i, ith, iph, :, :, :]
#for it in range(0,nnt):
# kappa[i,iph,iph,it,:,:]= 1e-9*etat0[i,0,0,:,:]
eta = []
return alpha, beta, gamma, delta, kappa,\
time[imask], urmst, etat0
def read_fixed_points(datadir='data/', fileName='fixed_points.dat', hm=1):
"""
Reads the fixed points files.
call signature::
fixed = read_fixed_points(datadir = 'data/', fileName = 'fixed_points.dat', hm = 1)
Reads from the fixed points files. Returns the fixed points positions.
Keyword arguments:
*datadir*:
Data directory.
*fileName*:
Name of the fixed points file.
*hm*:
Header multiplication factor in case Fortran's binary data writes extra large
header. For most cases hm = 1 is sufficient. For the cluster in St Andrews use hm = 2.
"""
# read the cpu structure
dim = pc.read_dim(datadir=datadir)
if (dim.nprocz > 1):
print("error: number of cores in z-direction > 1")
data = []
# read the data
fixed_file = open(datadir + fileName, 'rb')
tmp = fixed_file.read(4 * hm)
data = pc.fixed_struct()
eof = 0
# length of longest array of fixed points
fixedMax = 0
if tmp == '':
eof = 1
while (eof == 0):
data.t.append(
struct.unpack("<" + str(hm + 1) + "f",
fixed_file.read(4 * (hm + 1)))[0])
n_fixed = int(
struct.unpack("<" + str(2 * hm + 1) + "f",
fixed_file.read(4 * (2 * hm + 1)))[1 + int(hm / 2)])
x = list(np.zeros(n_fixed))
y = list(np.zeros(n_fixed))
q = list(np.zeros(n_fixed))
for j in range(n_fixed):
x[j] = struct.unpack("<" + str(hm + 1) + "f",
fixed_file.read(4 * (hm + 1)))[-1]
y[j] = struct.unpack("<f", fixed_file.read(4))[0]
q[j] = struct.unpack("<" + str(hm + 1) + "f",
fixed_file.read(4 * (hm + 1)))[0]
data.x.append(x)
data.y.append(y)
data.q.append(q)
data.fidx.append(n_fixed)
tmp = fixed_file.read(4 * hm)
if tmp == '':
eof = 1
if fixedMax < len(x):
fixedMax = len(x)
fixed_file.close()
# add NaN to fill up the times with smaller number of fixed points
fixed = pc.fixed_struct()
for i in range(len(data.t)):
annex = list(np.zeros(fixedMax - len(data.x[i])) + np.nan)
fixed.t.append(data.t[i])
fixed.x.append(data.x[i] + annex)
fixed.y.append(data.y[i] + annex)
fixed.q.append(data.q[i] + annex)
fixed.fidx.append(data.fidx[i])
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
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
