def __init__(self,
formula_str,
df,
factors=None,
resid_formula_str=None,
**lmer_opts):
"""
"""
# get the pred_var
pred_var = formula_str.split('~')[0].strip()
# convert df to a recarray if it's a dataframe
if isinstance(df, pd.DataFrame):
df = df.to_records()
# add column if necessary
if pred_var not in df.dtype.names:
# must add it
df = append_fields(df, pred_var, [0.0] * len(df), usemask=False)
# make factor list if necessary
if factors is None:
factors = {}
# add in missingarg for any potential factor not provided
for k in df.dtype.names:
if isinstance(df[k][0], str) and k not in factors:
factors[k] = MissingArg
for f in factors:
if factors[f] is None:
factors[f] = MissingArg
# checking for both types of R Vectors for rpy2 variations
elif (not isinstance(factors[f], Vector)
and not factors[f] == MissingArg):
factors[f] = Vector(factors[f])
# convert the recarray to a DataFrame (releveling if desired)
self._rdf = DataFrame({
k: (FactorVector(df[k], levels=factors[k]) if
(k in factors) or isinstance(df[k][0], str) else df[k])
for k in df.dtype.names
})
# get the column index
self._col_ind = list(self._rdf.colnames).index(pred_var)
# make a formula obj
self._rformula = Formula(formula_str)
# make one for resid if necessary
if resid_formula_str:
self._rformula_resid = Formula(resid_formula_str)
else:
self._rformula_resid = None
# save the args
self._lmer_opts = lmer_opts
# model is null to start
self._ms = None
def qcrop2(xlist, ylist, labels=None, nq=4.):
if labels is None:
labels = map(str, range(len(xlist)))
x = []
y = []
xcrop = []
ycrop = []
facet = []
for i, (onex, oney) in enumerate(zip(xlist, ylist)):
xmin, xmax = qlim1(onex, nq)
ymin, ymax = qlim1(oney, nq)
cropx, cropy = zip(*[(
nan,
nan) if vy > ymax or vy < ymin or vx < xmin or vx > xmax else (vx,
vy)
for vx, vy in zip(onex, oney)])
xcrop += cropx
ycrop += cropy
x += onex
y += oney
facet += [labels[i]] * len(onex)
df = DataFrame({
'x':
FloatVector(x),
'y':
FloatVector(y),
'xcrop':
FloatVector(xcrop),
'ycrop':
FloatVector(ycrop),
'facet':
FactorVector(StrVector(facet), levels=StrVector(labels))
})
return df
def __init__(self,
count_matrix,
design_matrix,
conditions,
gene_column='id'):
self.dds = None
self.deseq_result = None
self.resLFC = None
self.comparison = None
self.normalized_count_matrix = None
self.gene_column = gene_column
self.gene_id = count_matrix[self.gene_column]
self.count_matrix = pandas2ri.py2rpy(
count_matrix.drop(gene_column, axis=1))
design_formula = "~ "
for col in conditions:
levels = design_matrix[col].unique()
levels = robjects._convert_rpy2py_strvector(levels)
as_factor = r["as.factor"]
design_matrix[col] = FactorVector(design_matrix[col],
levels=levels)
design_matrix[col] = as_factor(design_matrix[col])
design_formula = design_formula + col + " +"
design_formula = design_formula[:-2]
self.design_matrix = pandas2ri.py2rpy(design_matrix)
self.design_formula = Formula(design_formula)
def tupls2RDataframe(data, titles):
cols = [[] for _ in titles]
for datum in data:
for i, e in enumerate(datum):
cols[i].append(e)
col_d = {}
for i, t in enumerate(titles):
col_d[t] = StrVector(tuple(cols[i]))
col_d[t] = FactorVector(col_d[t])
dataf = DataFrame(col_d)
return dataf
def FitChiralCont_1Slope_Cross(self, a_r0_sqr, Categorical_Var):
import rpy2.robjects as robjects
from rpy2.robjects import FloatVector
from rpy2.robjects import FactorVector
from rpy2.robjects.packages import importr
self.NumSlope = 1
stats = importr('stats')
base = importr('base')
Temp_Jack_Mean_List = self.EnsembleJAvgList
self.CoeffList = []
robjects.globalenv["a_r0_sqr"] = FloatVector(a_r0_sqr)
robjects.globalenv["Spacing"] = FactorVector(Categorical_Var)
robjects.globalenv["M_pi_sqr"] = FloatVector(self.Indep_Var_List)
r_weight = [pow(x, 2) for x in self.EnsembleWeight]
robjects.globalenv["PointValueList"] = FloatVector(self.PointValueList)
for j in range(0, len(self.EnsembleNameList), 1):
for x in (self.EnsembleJackList[j]):
Temp_Jack_Mean_List[j] = x
robjects.globalenv["TempJackMean"] = FloatVector(
Temp_Jack_Mean_List)
#Coeff=(stats.lm("TempJackMean ~ Spacing:M_pi_sqr+a_r0_sqr","weights=EnsembleWeight"))[0]
Coeff = np.asarray(
(stats.lm("TempJackMean ~ M_pi_sqr*a_r0_sqr",
weights=FloatVector(r_weight)))[0])
#Coeff=np.polyfit(self.Indep_Var_List,Temp_Jack_Mean_List,1)
# vector=numpy.asarray(vector_R)
self.CoeffList.append(Coeff)
Temp_Jack_Mean_List = self.EnsembleJAvgList
self.StdErr = self.ComputeStdError(self.CoeffList)
JackAvg = sum(self.CoeffList) / len(self.CoeffList)
self.FitAvg = np.asarray(
(stats.lm("PointValueList ~ M_pi_sqr*a_r0_sqr",
weights=FloatVector(r_weight)))[0])
#print(self.StdErr)
#CoeffList
self.InterceptError = self.StdErr[1]
self.SlopeError = self.StdErr[0]
self.FitCoeff = self.FitAvg ####Fix
#self.FitCoeff=self.FitAvg - (len(self.CoeffList)-1)*(JackAvg-self.FitAvg) ##Fix this to be unbiased
self.Intercept = self.FitCoeff[1]
self.Slope = self.FitCoeff[0]
self.PrintResults()
def __init__(
self,
fe_formula,
re_formula,
re_group,
dep_data,
ind_data,
factors=None,
row_mask=None,
use_ranks=False,
use_norm=True,
memmap=False,
memmap_dir=None,
resid_formula=None,
null_formula=None,
num_null_boot=0,
svd_terms=None,
use_ssvd=False,
#nperms=500, nboot=100,
n_jobs=1,
verbose=10,
lmer_opts=None):
"""
"""
if verbose > 0:
sys.stdout.write('Initializing...')
sys.stdout.flush()
start_time = time.time()
# save the formula
self._formula_str = fe_formula + ' + ' + re_formula
# see if there's a resid formula
if resid_formula:
# the random effects are the same
self._resid_formula_str = resid_formula + ' + ' + re_formula
else:
self._resid_formula_str = None
# see if there's a null formula
if null_formula:
# the random effects are the same
self._null_formula_str = null_formula + ' + ' + re_formula
else:
self._null_formula_str = None
self._num_null_boot = num_null_boot
# save whether using ranks
self._use_ranks = use_ranks
# see whether to use sparse svd
self._use_ssvd = use_ssvd
# see if memmapping
self._memmap = memmap
# save job info
self._n_jobs = n_jobs
self._verbose = verbose
# eventually fill the feature shape
self._feat_shape = None
# fill A,M,O,D
self._A = {}
self._M = {}
self._O = {}
self._D = {}
O = []
# loop over unique grouping var
self._re_group = re_group
if isinstance(ind_data, dict):
# groups are the keys
self._groups = np.array(list(ind_data.keys()))
else:
# groups need to be extracted from the recarray
self._groups = np.unique(ind_data[re_group])
for g in self._groups:
# get that subj inds
if isinstance(ind_data, dict):
# the index is just the group into that dict
ind_ind = g
else:
# select the rows based on the group
ind_ind = ind_data[re_group] == g
# process the row mask
if row_mask is None:
# no mask, so all good
row_ind = np.ones(len(ind_data[ind_ind]), dtype=np.bool)
elif isinstance(row_mask, dict):
# pull the row_mask from the dict
row_ind = row_mask[g]
else:
# index into it with ind_ind
row_ind = row_mask[ind_ind]
# extract that group's A,M,O
# first save the observations (rows of A)
self._O[g] = ind_data[ind_ind][row_ind]
if use_ranks:
# loop over non-factors and rank them
for n in self._O[g].dtype.names:
if (n in factors) or isinstance(self._O[g][n][0], str):
continue
self._O[g][n] = rankdata(self._O[g][n])
O.append(self._O[g])
# eventually allow for dict of data files for dep_data
if isinstance(dep_data, dict):
# the index is just the group into that dict
dep_ind = g
else:
# select the rows based on the group
dep_ind = ind_ind
# save feature shape if necessary
if self._feat_shape is None:
self._feat_shape = dep_data[dep_ind].shape[1:]
# Save D index into data
self._D[g] = dep_data[dep_ind][row_ind]
# reshape it
self._D[g] = self._D[g].reshape((self._D[g].shape[0], -1))
if use_ranks:
if verbose > 0:
sys.stdout.write('Ranking %s...' % (str(g)))
sys.stdout.flush()
for i in range(self._D[g].shape[1]):
self._D[g][:, i] = rankdata(self._D[g][:, i])
# reshape M, so we don't have to do it repeatedly
self._M[g] = self._D[g].copy(
) #dep_data[ind].reshape((dep_data[ind].shape[0],-1))
# normalize M
if use_norm:
self._M[g] -= self._M[g].mean(0)
self._M[g] /= np.sqrt((self._M[g]**2).sum(0))
# determine A from the model.matrix
rdf = DataFrame({
k: (FactorVector(self._O[g][k])
if k in factors else self._O[g][k])
for k in self._O[g].dtype.names
})
# model spec as data frame
ms = r['data.frame'](r_model_matrix(Formula(fe_formula), data=rdf))
cols = list(r['names'](ms))
if svd_terms is None:
self._svd_terms = [c for c in cols if not 'Intercept' in c]
else:
self._svd_terms = svd_terms
self._A[g] = np.concatenate(
[np.array(ms.rx(c)) for c in self._svd_terms]).T
#for c in cols if not 'Intercept' in c]).T
if use_ranks:
for i in range(self._A[g].shape[1]):
self._A[g][:, i] = rankdata(self._A[g][:, i])
# normalize A
if True: #use_norm:
self._A[g] -= self._A[g].mean(0)
self._A[g] /= np.sqrt((self._A[g]**2).sum(0))
# memmap if desired
if self._memmap:
self._M[g] = _memmap_array(self._M[g], memmap_dir)
self._D[g] = _memmap_array(self._D[g], memmap_dir)
# concat the Os together and make an LMER instance
#O = np.concatenate(O)
#self._O = np.vstack(O)
#self._O = np.array(O)
self._O = O
if lmer_opts is None:
lmer_opts = {}
self._lmer_opts = lmer_opts
self._factors = factors
#self._lmer = LMER(self._formula_str, O, factors=factors, **lmer_opts)
# prepare for the perms and boots
self._perms = []
self._boots = []
self._tp = []
self._tb = []
if verbose > 0:
sys.stdout.write('Done (%.2g sec)\n' % (time.time() - start_time))
sys.stdout.write('Processing actual data...')
sys.stdout.flush()
start_time = time.time()
global _global_meld
_global_meld[id(self)] = self
# run for actual data (returns both perm and boot vals)
self._R = None
self._ss = None
self._mer = None
self._mer_null = None
tp, tb, R, feat_mask, ss, mer, mer_null = _eval_model(
id(self), None, None)
self._R = R
self._tp.append(tp)
self._tb.append(tb)
self._feat_mask = feat_mask
self._ss = ss
self._mer = mer
self._mer_null = mer_null
if verbose > 0:
sys.stdout.write('Done (%.2g sec)\n' % (time.time() - start_time))
sys.stdout.flush()
def lmer_feature(formula_str,
dat,
perms=None,
val=None,
factors=None,
**kwargs):
"""
Run LMER on a number of permutations of the predicted data.
"""
# get the perm_var
perm_var = formula_str.split('~')[0].strip()
# set the val if necessary
if not val is None:
dat[perm_var] = val
# make factor list if necessary
if factors is None:
factors = []
# convert the recarray to a DataFrame
rdf = DataFrame({
k: (FactorVector(dat[k]) if
(k in factors) or isinstance(dat[k][0], str) else dat[k])
for k in dat.dtype.names
})
#rdf = com.convert_to_r_dataframe(pd.DataFrame(dat),strings_as_factors=True)
# get the column index
col_ind = list(rdf.colnames).index(perm_var)
# make a formula obj
rformula = Formula(formula_str)
# just apply to actual data if no perms
if perms is None:
#perms = [np.arange(len(dat))]
perms = [None]
# run on each permutation
tvals = None
for i, perm in enumerate(perms):
if not perm is None:
# set the perm
rdf[col_ind] = rdf[col_ind].rx(perm + 1)
# inside try block to catch convergence errors
try:
ms = lme4.lmer(rformula, data=rdf, **kwargs)
except:
continue
#tvals.append(np.array([np.nan]))
# extract the result
df = r['data.frame'](r_coef(r['summary'](ms)))
if tvals is None:
# init the data
# get the row names
rows = list(r['row.names'](df))
tvals = np.rec.fromarrays(
[np.ones(len(perms)) * np.nan for ro in range(len(rows))],
names=','.join(rows))
tvals[i] = tuple(df.rx2('t.value'))
return tvals
def __init__(self,
fe_formula,
re_formula,
re_group,
dep_data,
ind_data,
factors=None,
row_mask=None,
dep_mask=None,
use_ranks=False,
use_norm=True,
memmap=False,
memmap_dir=None,
resid_formula=None,
svd_terms=None,
feat_thresh=0.05,
feat_nboot=1000,
do_tfce=False,
connectivity=None,
shape=None,
dt=.01,
E=2 / 3.,
H=2.0,
n_jobs=1,
verbose=10,
lmer_opts=None):
"""
dep_data can be an array or a dict of arrays (possibly
memmapped), one for each group.
ind_data can be a rec_array for each group or one large rec_array
with a grouping variable.
"""
if verbose > 0:
sys.stdout.write('Initializing...')
sys.stdout.flush()
start_time = time.time()
# save the formula
self._formula_str = fe_formula + ' + ' + re_formula
# see if there's a resid formula
if resid_formula:
# the random effects are the same
self._resid_formula_str = resid_formula + ' + ' + re_formula
else:
self._resid_formula_str = None
# save whether using ranks
self._use_ranks = use_ranks
# see the thresh for keeping a feature
self._feat_thresh = feat_thresh
self._feat_nboot = feat_nboot
self._do_tfce = do_tfce
self._connectivity = connectivity
self._dt = dt
self._E = E
self._H = H
# see if memmapping
self._memmap = memmap
# save job info
self._n_jobs = n_jobs
self._verbose = verbose
# eventually fill the feature shape
self._feat_shape = None
# handle the dep_mask
self._dep_mask = dep_mask
# fill A,M,O,D
self._A = {}
self._M = {}
self._O = {}
self._D = {}
O = []
# loop over unique grouping var
self._re_group = re_group
if isinstance(ind_data, dict):
# groups are the keys
self._groups = np.array(ind_data.keys())
else:
# groups need to be extracted from the recarray
self._groups = np.unique(ind_data[re_group])
for g in self._groups:
# get that subj inds
if isinstance(ind_data, dict):
# the index is just the group into that dict
ind_ind = g
else:
# select the rows based on the group
ind_ind = ind_data[re_group] == g
# process the row mask
if row_mask is None:
# no mask, so all good
row_ind = np.ones(len(ind_data[ind_ind]), dtype=np.bool)
elif isinstance(row_mask, dict):
# pull the row_mask from the dict
row_ind = row_mask[g]
else:
# index into it with ind_ind
row_ind = row_mask[ind_ind]
# extract that group's A,M,O
# first save the observations (rows of A)
self._O[g] = ind_data[ind_ind][row_ind]
if use_ranks:
# loop over non-factors and rank them
for n in self._O[g].dtype.names:
if (n in factors) or isinstance(self._O[g][n][0], str):
continue
self._O[g][n] = rankdata(self._O[g][n])
O.append(self._O[g])
# eventually allow for dict of data files for dep_data
if isinstance(dep_data, dict):
# the index is just the group into that dict
dep_ind = g
else:
# select the rows based on the group
dep_ind = ind_ind
# save feature shape if necessary
if self._feat_shape is None:
self._feat_shape = dep_data[dep_ind].shape[1:]
# handle the mask
if self._dep_mask is None:
self._dep_mask = np.ones(self._feat_shape, dtype=np.bool)
# create the connectivity (will mask later)
if self._do_tfce and self._connectivity is None and \
(len(self._dep_mask.flatten()) > self._dep_mask.sum()):
# create the connectivity
self._connectivity = cluster.sparse_dim_connectivity(
[cluster.simple_neighbors_1d(n) for n in self._feat_shape])
# Save D index into data (apply row and feature masks
# This will also reshape it
self._D[g] = dep_data[dep_ind][row_ind][:, self._dep_mask].copy()
# reshape it
#self._D[g] = self._D[g].reshape((self._D[g].shape[0], -1))
if use_ranks:
if verbose > 0:
sys.stdout.write('Ranking %s...' % (str(g)))
sys.stdout.flush()
for i in xrange(self._D[g].shape[1]):
# rank it
self._D[g][:, i] = rankdata(self._D[g][:, i])
# normalize it
self._D[g][:, i] = ((self._D[g][:, i] - 1) /
(len(self._D[g][:, i]) - 1))
# save M from D so we can have a normalized version
self._M[g] = self._D[g].copy()
# remove any NaN's in dep_data
self._D[g][np.isnan(self._D[g])] = 0.0
# normalize M
if use_norm:
self._M[g] -= self._M[g].mean(0)
self._M[g] /= np.sqrt((self._M[g]**2).sum(0))
# determine A from the model.matrix
rdf = DataFrame({
k: (FactorVector(self._O[g][k])
if k in factors else self._O[g][k])
for k in self._O[g].dtype.names
})
# model spec as data frame
ms = r['data.frame'](r_model_matrix(Formula(fe_formula), data=rdf))
cols = list(r['names'](ms))
if svd_terms is None:
self._svd_terms = [c for c in cols if 'Intercept' not in c]
else:
self._svd_terms = svd_terms
# self._A[g] = np.vstack([ms[c] #np.array(ms.rx(c))
self._A[g] = np.concatenate(
[np.array(ms.rx(c)) for c in self._svd_terms]).T
if use_ranks:
for i in xrange(self._A[g].shape[1]):
# rank it
self._A[g][:, i] = rankdata(self._A[g][:, i])
# normalize it
self._A[g][:, i] = ((self._A[g][:, i] - 1) /
(len(self._A[g][:, i]) - 1))
# normalize A
if True: # use_norm:
self._A[g] -= self._A[g].mean(0)
self._A[g] /= np.sqrt((self._A[g]**2).sum(0))
# memmap if desired
if self._memmap:
self._M[g] = _memmap_array(self._M[g],
memmap_dir,
unique_id=str(g))
self._D[g] = _memmap_array(self._D[g],
memmap_dir,
unique_id=str(g))
# save the new O
self._O = O
if lmer_opts is None:
lmer_opts = {}
self._lmer_opts = lmer_opts
self._factors = factors
# mask the connectivity
if self._do_tfce and (len(self._dep_mask.flatten()) >
self._dep_mask.sum()):
self._connectivity = self._connectivity.tolil()[
self._dep_mask.flatten()][:, self._dep_mask.flatten()].tocoo()
# prepare for the perms and boots and jackknife
self._perms = []
self._tp = []
self._tb = []
self._tj = []
self._pfmask = []
if verbose > 0:
sys.stdout.write('Done (%.2g sec)\n' % (time.time() - start_time))
sys.stdout.write('Processing actual data...')
sys.stdout.flush()
start_time = time.time()
global _global_meld
_global_meld[id(self)] = self
# run for actual data (returns both perm and boot vals)
self._R = None
self._ss = None
self._mer = None
tp, tb, R, feat_mask, ss, mer = _eval_model(id(self), None)
self._R = R
self._tp.append(tp)
self._tb.append(tb)
self._feat_mask = feat_mask
self._fmask = ~feat_mask[0]
self._pfmask.append(~feat_mask[0])
self._ss = ss
self._mer = mer
if verbose > 0:
sys.stdout.write('Done (%.2g sec)\n' % (time.time() - start_time))
sys.stdout.flush()
def FitChiralCont_1Slope_Cross_wSubtraction_NoIntercept(
self, a_r0_sqr, Categorical_Var, filepath):
import rpy2.robjects as robjects
from rpy2.robjects import FloatVector
from rpy2.robjects import FactorVector
from rpy2.robjects.packages import importr
self.NumSlope = 1
stats = importr('stats')
base = importr('base')
Temp_Jack_Mean_List = self.EnsembleJAvgList
SubtractionJackList = []
self.CoeffList = []
robjects.globalenv["a_r0_sqr"] = FloatVector(a_r0_sqr)
robjects.globalenv["Spacing"] = FactorVector(Categorical_Var)
robjects.globalenv["M_pi_sqr"] = FloatVector(self.Indep_Var_List)
r_weight = [pow(x, 2) for x in self.EnsembleWeight]
robjects.globalenv["PointValueList"] = FloatVector(self.PointValueList)
for j in range(0, len(self.EnsembleNameList), 1):
for x in (self.EnsembleJackList[j]):
Temp_Jack_Mean_List[j] = x
robjects.globalenv["TempJackMean"] = FloatVector(
Temp_Jack_Mean_List)
#Coeff=(stats.lm("TempJackMean ~ Spacing:M_pi_sqr+a_r0_sqr","weights=EnsembleWeight"))[0]
Coeff = np.asarray(
(stats.lm("TempJackMean ~0.0+ M_pi_sqr*a_r0_sqr",
weights=FloatVector(r_weight)))[0])
#Coeff=np.polyfit(self.Indep_Var_List,Temp_Jack_Mean_List,1)
# vector=numpy.asarray(vector_R)
self.CoeffList.append(Coeff)
SubtractionList = []
for k in range(0, len(a_r0_sqr), 1): ###### FIX
SubtractionList.append(Temp_Jack_Mean_List[k] -
a_r0_sqr[k] * Coeff[1] -
a_r0_sqr[k] *
self.Indep_Var_List[k] * Coeff[2])
# SubtractionList.append(Temp_Jack_Mean_List[k])
SubtractionJackList.append(SubtractionList)
Temp_Jack_Mean_List = self.EnsembleJAvgList
self.StdErr = self.ComputeStdError(self.CoeffList)
JackAvg = sum(self.CoeffList) / len(self.CoeffList)
self.FitAvg = np.asarray(
(stats.lm("PointValueList ~ 0+ M_pi_sqr*a_r0_sqr",
weights=FloatVector(r_weight)))[0])
Rev_SubtractionJackList = []
# print(len(SubtractionJackList[]))
SubtractJackAvg = []
SubtractJackErr = []
for i in range(0, len(a_r0_sqr), 1):
Temp = []
for j in range(0, len(SubtractionJackList), 1):
Temp.append(SubtractionJackList[j][i])
Rev_SubtractionJackList.append(Temp)
#SubtractJackAvg.append(sum(Rev_SubtractionJackList[i])/len(Rev_SubtractionJackList))
#SubtractJackErr.append(self.ComputeStdError(Rev_SubtractionJackList[i]))
print(len(Rev_SubtractionJackList[1]))
#print(self.StdErr)
#CoeffList
for x in Rev_SubtractionJackList:
#SubtractJackAvg.append(sum(x)/len(x))
# print(len(x))
# SubtractJackAvg.append()
SubtractJackErr.append(self.ComputeStdError(x))
#SubtractJackAvg=self.PointValueList
for k in range(0, len(a_r0_sqr), 1): ###FIX
SubtractJackAvg.append(self.PointValueList[k] -
a_r0_sqr[k] * self.FitAvg[1] - a_r0_sqr[k] *
self.Indep_Var_List[k] * self.FitAvg[2])
# print(self.FitAvg)
self.InterceptError = self.StdErr[1]
self.SlopeError = self.StdErr[0]
self.FitCoeff = self.FitAvg ####Fix
#self.FitCoeff=self.FitAvg - (len(self.CoeffList)-1)*(JackAvg-self.FitAvg) ##Fix this to be unbiased
self.Intercept = self.FitCoeff[1]
self.Slope = self.FitCoeff[0]
self.PrintResults()
f = open(filepath, "w")
output = 'PointName,TopSus,TopSus_Error,r0_Mpi_sqr,PlotName,PointId\n'
f.write(output)
for i in range(0, len(self.EnsembleNameList), 1):
output = self.EnsembleNameList[i] + ',' + str(
SubtractJackAvg[i]) + ',' + str(
SubtractJackErr[i]) + ',' + str(
self.Indep_Var_List[i]) + ',' + str(
self.Name) + ',' + str(self.PointIdList[i]) + '\n'
f.write(output)
f.close()
