def test_math_module():
"Operations with the math module"
x = uncertainties.ufloat((-1.5, 0.1))
# The exponent must not be differentiated, when calculating the
# following (the partial derivative with respect to the exponent
# is not defined):
assert (x**2).nominal_value == 2.25
# Regular operations are chosen to be unchanged:
assert isinstance(umath.sin(3), float)
# Python >=2.6 functions:
if sys.version_info[:2] >= (2, 6):
# factorial() must not be "damaged" by the umath module, so as
# to help make it a drop-in replacement for math (even though
# factorial() does not work on numbers with uncertainties
# because it is restricted to integers, as for
# math.factorial()):
assert umath.factorial(4) == 24
# Boolean functions:
assert not umath.isinf(x)
# Comparison, possibly between an AffineScalarFunc object and a
# boolean, which makes things more difficult for this code:
assert umath.isinf(x) == False
# fsum is special because it does not take a fixed number of
# variables:
assert umath.fsum([x, x]).nominal_value == -3
def test_math_module():
"Operations with the math module"
x = uncertainties.ufloat((-1.5, 0.1))
# The exponent must not be differentiated, when calculating the
# following (the partial derivative with respect to the exponent
# is not defined):
assert (x**2).nominal_value == 2.25
# Regular operations are chosen to be unchanged:
assert isinstance(umath.sin(3), float)
# Python >=2.6 functions:
if sys.version_info[:2] >= (2, 6):
# factorial() must not be "damaged" by the umath module, so as
# to help make it a drop-in replacement for math (even though
# factorial() does not work on numbers with uncertainties
# because it is restricted to integers, as for
# math.factorial()):
assert umath.factorial(4) == 24
# Boolean functions:
assert not umath.isinf(x)
# Comparison, possibly between an AffineScalarFunc object and a
# boolean, which makes things more difficult for this code:
assert umath.isinf(x) == False
# fsum is special because it does not take a fixed number of
# variables:
assert umath.fsum([x, x]).nominal_value == -3
def test_math_module():
"Operations with the math module"
x = ufloat(-1.5, 0.1)
# The exponent must not be differentiated, when calculating the
# following (the partial derivative with respect to the exponent
# is not defined):
assert (x**2).nominal_value == 2.25
# Regular operations are chosen to be unchanged:
assert isinstance(umath.sin(3), float)
# Python >=2.6 functions:
if sys.version_info >= (2, 6):
# factorial() must not be "damaged" by the umath module, so as
# to help make it a drop-in replacement for math (even though
# factorial() does not work on numbers with uncertainties
# because it is restricted to integers, as for
# math.factorial()):
assert umath.factorial(4) == 24
# Boolean functions:
assert not umath.isinf(x)
# Comparison, possibly between an AffineScalarFunc object and a
# boolean, which makes things more difficult for this code:
assert umath.isinf(x) == False
# fsum is special because it does not take a fixed number of
# variables:
assert umath.fsum([x, x]).nominal_value == -3
# The same exceptions should be generated when numbers with uncertainties
# are used:
## !! The Nose testing framework seems to catch an exception when
## it is aliased: "exc = OverflowError; ... except exc:..."
## surprisingly catches OverflowError. So, tests are written in a
## version-specific manner (until the Nose issue is resolved).
if sys.version_info < (2, 6):
try:
math.log(0)
except OverflowError, err_math: # "as", for Python 2.6+
pass
else:
raise Exception('OverflowError exception expected')
try:
umath.log(0)
except OverflowError, err_ufloat: # "as", for Python 2.6+
assert err_math.args == err_ufloat.args
def getCocktailSum(e0, e1, eCocktail, uCocktail):
"""get the cocktail sum for a given data bin range"""
# get mask and according indices
mask = (eCocktail >= e0) & (eCocktail <= e1)
# data bin range wider than single cocktail bin
if np.any(mask):
idx = getMaskIndices(mask)
# determine coinciding flags
eCl, eCu = eCocktail[idx[0]], eCocktail[idx[1]]
not_coinc_low, not_coinc_upp = (eCl != e0), (eCu != e1)
# get cocktail sum in data bin (always w/o last bin)
uCocktailSum = fsum(uCocktail[mask[:-1]][:-1])
logging.debug(' sum: {}'.format(uCocktailSum))
# get correction for non-coinciding edges
if not_coinc_low:
eCl_bw = eCl - eCocktail[idx[0]-1]
corr_low = (eCl - e0) / eCl_bw
abs_corr_low = float(corr_low) * uCocktail[idx[0]-1]
uCocktailSum += abs_corr_low
logging.debug((' low: %g == %g -> %g (%g) -> %g -> {} -> {}' % (
e0, eCl, eCl - e0, eCl_bw, corr_low
)).format(abs_corr_low, uCocktailSum))
if not_coinc_upp:
if idx[1]+1 < len(eCocktail):
eCu_bw = eCocktail[idx[1]+1] - eCu
corr_upp = (e1 - eCu) / eCu_bw
abs_corr_upp = float(corr_upp) * uCocktail[idx[1]]
else:# catch last index (quick fix!)
abs_corr_upp = eCu_bw = corr_upp = 0
uCocktailSum += abs_corr_upp
logging.debug((' upp: %g == %g -> %g (%g) -> %g -> {} -> {}' % (
e1, eCu, e1 - eCu, eCu_bw, corr_upp
)).format(abs_corr_upp, uCocktailSum))
else:
mask = (eCocktail >= e0)
idx = getMaskIndices(mask) # only use first index
# catch if already at last index
if idx[0] == idx[1] and idx[0] == len(eCocktail)-1:
corr = (e1 - e0) / (eCocktail[idx[0]] - eCocktail[idx[0]-1])
uCocktailSum = float(corr) * uCocktail[idx[0]-1]
else: # default case
corr = (e1 - e0) / (eCocktail[idx[0]+1] - eCocktail[idx[0]])
uCocktailSum = float(corr) * uCocktail[idx[0]]
logging.debug(' sum: {}'.format(uCocktailSum))
return uCocktailSum
def test_math_module():
"Operations with the math module"
x = ufloat(-1.5, 0.1)
# The exponent must not be differentiated, when calculating the
# following (the partial derivative with respect to the exponent
# is not defined):
assert (x**2).nominal_value == 2.25
# Regular operations are chosen to be unchanged:
assert isinstance(umath.sin(3), float)
# Python >=2.6 functions:
if sys.version_info >= (2, 6):
# factorial() must not be "damaged" by the umath module, so as
# to help make it a drop-in replacement for math (even though
# factorial() does not work on numbers with uncertainties
# because it is restricted to integers, as for
# math.factorial()):
assert umath.factorial(4) == 24
# fsum is special because it does not take a fixed number of
# variables:
assert umath.fsum([x, x]).nominal_value == -3
# Functions that give locally constant results are tested: they
# should give the same result as their float equivalent:
for name in umath.locally_cst_funcs:
try:
func = getattr(umath, name)
except AttributeError:
continue # Not in the math module, so not in umath either
assert func(x) == func(x.nominal_value)
# The type should be left untouched. For example, isnan()
# should always give a boolean:
assert type(func(x)) == type(func(x.nominal_value))
# The same exceptions should be generated when numbers with uncertainties
# are used:
## !! The Nose testing framework seems to catch an exception when
## it is aliased: "exc = OverflowError; ... except exc:..."
## surprisingly catches OverflowError. So, tests are written in a
## version-specific manner (until the Nose issue is resolved).
if sys.version_info < (2, 6):
try:
math.log(0)
except OverflowError, err_math: # "as", for Python 2.6+
pass
else:
raise Exception('OverflowError exception expected')
try:
umath.log(0)
except OverflowError, err_ufloat: # "as", for Python 2.6+
assert err_math.args == err_ufloat.args
def test_math_module():
"Operations with the math module"
x = ufloat(-1.5, 0.1)
# The exponent must not be differentiated, when calculating the
# following (the partial derivative with respect to the exponent
# is not defined):
assert (x**2).nominal_value == 2.25
# Regular operations are chosen to be unchanged:
assert isinstance(umath.sin(3), float)
# factorial() must not be "damaged" by the umath module, so as
# to help make it a drop-in replacement for math (even though
# factorial() does not work on numbers with uncertainties
# because it is restricted to integers, as for
# math.factorial()):
assert umath.factorial(4) == 24
# fsum is special because it does not take a fixed number of
# variables:
assert umath.fsum([x, x]).nominal_value == -3
# Functions that give locally constant results are tested: they
# should give the same result as their float equivalent:
for name in umath.locally_cst_funcs:
try:
func = getattr(umath, name)
except AttributeError:
continue # Not in the math module, so not in umath either
assert func(x) == func(x.nominal_value)
# The type should be left untouched. For example, isnan()
# should always give a boolean:
assert type(func(x)) == type(func(x.nominal_value))
# The same exceptions should be generated when numbers with uncertainties
# are used:
## !! The Nose testing framework seems to catch an exception when
## it is aliased: "exc = OverflowError; ... except exc:..."
## surprisingly catches OverflowError. So, tests are written in a
## version-specific manner (until the Nose issue is resolved).
try:
math.log(0)
except ValueError as err_math:
# Python 3 does not make exceptions local variables: they are
# restricted to their except block:
err_math_args = err_math.args
else:
raise Exception('ValueError exception expected')
try:
umath.log(0)
except ValueError as err_ufloat:
assert err_math_args == err_ufloat.args
else:
raise Exception('ValueError exception expected')
try:
umath.log(ufloat(0, 0))
except ValueError as err_ufloat:
assert err_math_args == err_ufloat.args
else:
raise Exception('ValueError exception expected')
try:
umath.log(ufloat(0, 1))
except ValueError as err_ufloat:
assert err_math_args == err_ufloat.args
else:
raise Exception('ValueError exception expected')
def gp_ptspec():
"""example for a 2D-panel plot etc."""
fenergies = ['19', '27', '39', '62', ]# '200']
nen = len(fenergies)
mee_keys = ['pi0', 'LMR', 'omega', 'phi', 'IMR', 'jpsi']
#mee_keys = ['LMR', ]
mee_dict = OrderedDict((k,'') for k in mee_keys)
yscale = { '200': '300', '62': '5000', '39': '50', '27': '0.3', '19': '0.001' }
inDir, outDir = getWorkDirs()
data, data_avpt, dpt_dict = {}, {}, {}
yvals, yvalsPt = [], []
scale = {
'19': 1.3410566491548412, '200': 1.0, '39': 1.2719203877292842,
'27': 1.350873678084769, '62': 1.2664666321635087
}
lmr_label = None
for filename in os.listdir(inDir):
# import data
file_url = os.path.join(inDir, filename)
filebase = os.path.splitext(filename)[0] # unique
energy, mee_name, mee_range, data_type = splitFileName(filebase)
if mee_name == 'LMR':
mee_range_split = map(float, mee_range.split('-'))
lmr_label = 'LMR: %g < M_{ee} < %g GeV/c^{2}' % (
mee_range_split[0], mee_range_split[1]
)
if energy == '200': continue
if mee_name not in mee_keys: continue
mee_dict[mee_name] = mee_range
data[filebase] = np.loadtxt(open(file_url, 'rb'))
if data_type == 'data':
#print data[filebase]
data[filebase] = data[filebase][:-1] # skip mT<0.4 point
if energy == '200': data[filebase][:,(1,3,4)] /= 0.5
# calculate average pT first
mask = (data[filebase][:,0] > 0.4) & (data[filebase][:,0] < 2.2)
avpt_data = data[filebase][mask]
pTs = avpt_data[:,0]
wghts = avpt_data[:,1]
probs = unp.uarray(avpt_data[:,1], avpt_data[:,3]) # dN/pT
probs /= umath.fsum(probs) # probabilities
avpt = umath.fsum(pTs*probs)
logging.info(('%s: {} %g' % (
filebase, np.average(pTs, weights = wghts)
)).format(avpt)) # TODO: syst. uncertainties
# save datapoint for average pT and append to yvalsPt for yaxis range
dp = [ float(getEnergy4Key(energy)), avpt.nominal_value, 0., avpt.std_dev, 0. ]
avpt_key = mee_name
if data_type == 'cocktail': avpt_key += '_c'
if data_type == 'medium': avpt_key += '_m'
if data_type == 'mediumMedOnly': avpt_key += '_mMed'
if data_type == 'mediumQgpOnly': avpt_key += '_mQgp'
if avpt_key in data_avpt: data_avpt[avpt_key].append(dp)
else: data_avpt[avpt_key] = [ dp ]
yvalsPt.append(avpt.nominal_value)
# now adjust data for panel plot and append to yvals
if data_type != 'data':
data[filebase][:,(1,3,4)] /= scale[energy]
data[filebase][:,(1,3,4)] *= float(yscale[energy])
if data_type == 'cocktail' or fnmatch(data_type, '*medium*'):
data[filebase][:,2:] = 0.
yvals += [v for v in data[filebase][:,1] if v > 0]
# prepare dict for panel plot
dpt_dict_key = getSubplotTitle(mee_name, mee_range)
if dpt_dict_key not in dpt_dict:
ndsets = nen*2
# TODO: currently only 19/39/62 medium avail. w/ med/qgp/tot for each
# July14: all energies available; TODO: fix dsidx
if mee_name == 'LMR': ndsets += 4*3
dpt_dict[dpt_dict_key] = [ [None]*ndsets, [None]*ndsets, [None]*ndsets ]
enidx = fenergies.index(energy)
dsidx = enidx
if fnmatch(data_type, '*medium*'):
# 19: 0-2, 27: 3-5, 39: 6-8, 62: 9-11
dsidx = (energy=='19')*0 + (energy=='27')*3 + (energy=='39')*6 + (energy=='62')*9
dsidx += (data_type=='mediumQgpOnly')*0 + (data_type=='mediumMedOnly')*1
dsidx += (data_type=='medium')*2
else:
dsidx += int(mee_name == 'LMR') * 4 * 3 # number of medium calc avail.
dsidx += int(data_type == 'data') * len(fenergies)
dpt_dict[dpt_dict_key][0][dsidx] = data[filebase] # data
if data_type == 'data': # properties
dpt_dict[dpt_dict_key][1][dsidx] = 'lt 1 lw 4 ps 1.5 lc %s pt 18' % default_colors[enidx]
elif data_type == 'medium':
dpt_dict[dpt_dict_key][1][dsidx] = 'with lines lt 1 lw 5 lc %s' % default_colors[enidx]
else:
dpt_dict[dpt_dict_key][1][dsidx] = 'with lines lt %d lw 5 lc %s' % (
2+(data_type=='mediumMedOnly')+(data_type=='mediumQgpOnly')*2, default_colors[enidx]
)
dpt_dict[dpt_dict_key][2][dsidx] = ' '.join([ # legend titles
getEnergy4Key(energy), 'GeV', '{/Symbol \264} %g' % (
Decimal(yscale[energy])#.as_tuple().exponent
)
]) if data_type == 'data' else ''
# use mass range in dict key to sort dpt_dict with increasing mass
plot_key_order = dpt_dict.keys()
plot_key_order.sort(key=lambda x: float(x.split(':')[1].split('-')[0]))
# sort data_avpt by energy and apply x-shift for better visibility
for k in data_avpt: data_avpt[k].sort(key=lambda x: x[0])
energies = [ dp[0] for dp in data_avpt[mee_keys[0]] ]
energies.append(215.) # TODO: think of better upper limit
linsp = {}
for start,stop in zip(energies[:-1],energies[1:]):
linsp[start] = np.linspace(start, stop, num = 4*len(mee_keys))
for k in data_avpt:
key = k.split('_')[0]
for i in xrange(len(data_avpt[k])):
data_avpt[k][i][0] = linsp[energies[i]][mee_keys.index(key)]
# make panel plot
yMin, yMax = 0.5*min(yvals), 3*max(yvals)
make_panel(
dpt_dict = OrderedDict((k,dpt_dict[k]) for k in plot_key_order),
name = os.path.join(outDir, 'ptspec'),
ylabel = '1/N@_{mb}^{evt} d^{2}N@_{ee}^{acc.}/dp_{T}dM_{ee} (c^3/GeV^2)',
xlabel = 'dielectron transverse momentum, p_{T} (GeV/c)',
ylog = True, xr = [0, 2.2], yr = [1e-9, 1e4],
#lmargin = 0.12, bmargin = 0.10, tmargin = 1., rmargin = 1.,
key = ['bottom left', 'samplen 0.5', 'width -2', 'opaque'],
arrow_bar = 0.002, layout = '3x2', size = '8in,8in'
)
#make plot for LMR spectra only
#lmr_key = getSubplotTitle('LMR', '0.4-0.76')
#if energy == '200':
# lmr_key = getSubplotTitle('LMR', '0.3-0.76')
#pseudo_point = np.array([[-1,0,0,0,0]])
#model_titles = ['Cocktail + Model', 'Cocktail', 'in-Medium', 'QGP']
#model_props = [
# 'with lines lc %s lw 5 lt %d' % (default_colors[-2], i+1)
# for i in xrange(len(model_titles))
#]
#make_plot(
# data = dpt_dict[lmr_key][0] + [ pseudo_point ] * len(model_titles),
# properties = dpt_dict[lmr_key][1] + model_props,
# titles = dpt_dict[lmr_key][2] + model_titles,
# name = os.path.join(outDir, 'ptspecLMR'),
# ylabel = '1/N@_{mb}^{evt} d^{2}N@_{ee}^{acc.}/dp_{T}dM_{ee} (c^3/GeV^2)',
# xlabel = 'dielectron transverse momentum, p_{T} (GeV/c)',
# ylog = True, xr = [0, 2.0], yr = [1e-8, 100],
# lmargin = 0.15, bmargin = 0.08, rmargin = 0.98, tmargin = 0.84,
# key = ['maxrows 4', 'samplen 0.7', 'width -2', 'at graph 1.,1.2'],
# arrow_bar = 0.005, size = '10in,13in',
# labels = {
# 'stat. errors only': [0.7,0.95,False], lmr_label: [0.05,0.03,False],
# 'STAR Preliminary': [0.05,0.07,False],
# }
#)
# make mean pt plot
#yMinPt, yMaxPt = 0.95*min(yvalsPt), 1.05*max(yvalsPt)
#make_plot(
# data = [ # cocktail
# np.array(data_avpt[k+'_c']) for k in mee_keys
# ] + [ # medium
# np.array(data_avpt['LMR_m'])
# ] + [ # data
# np.array(data_avpt[k]) for k in mee_keys
# ],
# properties = [
# 'with lines lt 1 lw 4 lc %s' % default_colors[i if i < 5 else i+1]
# for i in xrange(len(mee_keys))
# ] + [
# 'with lines lt 2 lw 4 lc %s' % default_colors[mee_keys.index('LMR')]
# ] + [
# 'lt 1 lw 4 ps 1.5 lc %s pt 18' % default_colors[i if i < 5 else i+1]
# for i in xrange(len(mee_keys))
# ],
# titles = [ getMeeLabel(k) for k in mee_keys ] + ['']*(len(mee_keys)+1),
# name = os.path.join(outDir, 'meanPt'),
# xlabel = '{/Symbol \326}s_{NN} (GeV)',
# ylabel = '{/Symbol \341}p_{T}{/Symbol \361} in STAR Acceptance (GeV/c)',
# xlog = True, xr = [17,220], yr = [yMinPt, yMaxPt], size = '11in,9in',
# key = [ 'maxrows 1', 'at graph 1, 1.1' ],
# lmargin = 0.11, bmargin = 0.11, tmargin = 1., rmargin = 1.,
# gpcalls = [
# 'format x "%g"',
# 'xtics (20,"" 30, 40,"" 50, 60,"" 70,"" 80,"" 90, 100, 200)',
# ]
#)
## make mean pt plot for LMR only
#make_plot(
# data = [
# np.array(data_avpt['LMR_c']),
# np.array(data_avpt['LMR_m']),
# np.array(data_avpt['LMR'])
# ],
# properties = [
# 'with lines lt 2 lw 4 lc %s' % default_colors[0],
# 'with lines lt 1 lw 4 lc %s' % default_colors[0],
# 'lt 1 lw 4 ps 1.5 lc %s pt 18' % default_colors[0]
# ],
# titles = [
# 'cocktail', 'HMBT', getMeeLabel('data')
# ],
# name = os.path.join(outDir, 'meanPtLMR'),
# xlabel = '{/Symbol \326}s_{NN} (GeV)',
# ylabel = 'LMR {/Symbol \341}p_{T}{/Symbol \361} in STAR Acceptance (GeV/c)',
# lmargin = 0.17, bmargin = 0.15, tmargin = 0.95, xlog = True, xr = [17,80],
# yr = [0.65,1.05], #yr = [yMinPt, yMaxPt],
# key = [ 'bottom right' ],
# gpcalls = [
# 'format x "%g"',
# 'xtics (20, 30, 40,"" 50, 60,"" 70,"" 80,"" 90, 100, 200)',
# ],
# labels = {
# 'stat. errors only': [0.7,0.95,False], lmr_label: [0.05,0.07,False],
# '0.4 < p_{T} < 2.2 GeV/c': [0.05,0.14,False]
# }
#)
return 'done'
def test_math_module():
"Operations with the math module"
x = uncertainties.ufloat((-1.5, 0.1))
# The exponent must not be differentiated, when calculating the
# following (the partial derivative with respect to the exponent
# is not defined):
assert (x**2).nominal_value == 2.25
# Regular operations are chosen to be unchanged:
assert isinstance(umath.sin(3), float)
# Python >=2.6 functions:
if sys.version_info >= (2, 6):
# factorial() must not be "damaged" by the umath module, so as
# to help make it a drop-in replacement for math (even though
# factorial() does not work on numbers with uncertainties
# because it is restricted to integers, as for
# math.factorial()):
assert umath.factorial(4) == 24
# Boolean functions:
assert not umath.isinf(x)
# Comparison, possibly between an AffineScalarFunc object and a
# boolean, which makes things more difficult for this code:
assert umath.isinf(x) == False
# fsum is special because it does not take a fixed number of
# variables:
assert umath.fsum([x, x]).nominal_value == -3
# The same exceptions should be generated when numbers with uncertainties
# are used:
## !! The Nose testing framework seems to catch an exception when
## it is aliased: "exc = OverflowError; ... except exc:..."
## surprisingly catches OverflowError. So, tests are written in a
## version-specific manner (until the Nose issue is resolved).
if sys.version_info < (2, 6):
try:
math.log(0)
except OverflowError(err_math): # "as", for Python 2.6+
pass
else:
raise Exception('OverflowError exception expected')
try:
umath.log(0)
except OverflowError(err_ufloat): # "as", for Python 2.6+
assert err_math.args == err_ufloat.args
else:
raise Exception('OverflowError exception expected')
try:
umath.log(uncertainties.ufloat((0, 0)))
except OverflowError( err_ufloat): # "as", for Python 2.6+
assert err_math.args == err_ufloat.args
else:
raise Exception('OverflowError exception expected')
try:
umath.log(uncertainties.ufloat((0, 1)))
except OverflowError( err_ufloat): # "as", for Python 2.6+
assert err_math.args == err_ufloat.args
else:
raise Exception('OverflowError exception expected')
elif sys.version_info < (3,):
try:
math.log(0)
except ValueError( err_math):
pass
else:
raise Exception('ValueError exception expected')
try:
umath.log(0)
except ValueError( err_ufloat):
assert err_math.args == err_ufloat.args
else:
raise Exception('ValueError exception expected')
try:
umath.log(uncertainties.ufloat((0, 0)))
except ValueError( err_ufloat):
assert err_math.args == err_ufloat.args
else:
raise Exception('ValueError exception expected')
try:
umath.log(uncertainties.ufloat((0, 1)))
except ValueError( err_ufloat):
assert err_math.args == err_ufloat.args
else:
raise Exception('ValueError exception expected')
else: # Python 3+
# !!! The tests should be made to work with Python 3 too!
pass