Can someone advise what unit of time t_duration is in, below:
local timer = os.clock()
*insert script here*
t_duration = string.format("%.9f", os.clock() - timer)
I am getting conflicting answers elsewhere.
Have been unable to test properly myself.
The first time called os.clock() in timer will be substracted from the actual os.clock() in t_duration with a constant format of 9 digits after the floatingpoint.
In short: It will be measure the runtime of *insert script here* in seconds as a floatingpoint converted to a string with string.format()
PS: "seconds" is not a integer it will be a floatingpoint number
Example:
> print(os.clock())
1.892664
> print(string.format("%.9f", os.clock()))
1.911050000
With Lua i learned a new Datatype: HEX FLOAT
> print(string.format("%a", os.clock()))
0x1.f96638433d6c7p+0
> print(0x1.f96638433d6c7p+0)
1.974216
In my experience Matlab performs publish subscribe operations with ROS slow for some reason. I work with components as defined in an object class as shown below, where I made a test-class. Normally objects of comparable structure are used to control mobile robots.
To quantify performance tested required time for an operation and got the following results:
1x publishing a message + 1x simple subscriber callback : 3.7ms
Simply counting in a callback (per count): 2.1318e-03 ms
Creating a new message with msg1 = rosmessage(obj.publisher) adds 3.6-4.3ms per iteration
Pinging myself indicated communication latency of 0.05 ms
The times required for a simple publish + start of a subscribe callback seems oddly slow.
I want to have multiple system components as objects in my workspace such that they respond to ROS topic updates or on timer events. The pc used for testing is not a monster but should not be garbage either.
Do you also think the shown time requirements are unneccesary large? this allows barely to publish a single topic at 200hz without doing anything else. Normally I have multiple lower frequency topics (e.g.20hz) but the total consumed time becomes significant.
Do you know any practices to make the system operate quicker?
What do you think of the OOP style of making control system components in general?
classdef subpubspeedMonitor < handle
% Use: call in matlab console, after initializing ros:
%
% SPM1 = subpubspeedMonitor()
%
% This will create an object which starts a set repetitive task upon creation
% and finally destructs itself after posting results in console.
properties
node
subscriber
publisher
timestart
messagetotal
end
methods
function obj = subpubspeedMonitor()
obj.node = ros.Node('subspeedmonitor1');
obj.subscriber = ros.Subscriber(obj.node,'topic1','sensor_msgs/NavSatFix',{#obj.rosSubCallback});
obj.publisher = ros.Publisher(obj.node,'topic1','sensor_msgs/NavSatFix');
obj.timestart = tic;
obj.messagetotal = 0;
msg1 = rosmessage(obj.publisher);
% Choose to evaluate subscriber + publisher loop or just counting
if 1
send(obj.publisher,msg1);
else
countAndDisplay(obj)
end
end
%% Test method one: repetitive publishing and subscribing
function rosSubCallback(obj,~,msg_) % ~3.7 ms per loop for a simple publish+subscribe action
% Latency to self is 0.05ms on average, according to "pinging" in terminal
obj.messagetotal = obj.messagetotal+1;
if obj.messagetotal <10000
%msg1 = rosmessage(obj.publisher); % this line adds 4.3000ms per loop
msg_.Longitude = 51; % this line adds 0.25000 ms per loop
send(obj.publisher,msg_)
else
% Display some results
timepassed = toc(obj.timestart);
time_per_pubsub = timepassed/obj.messagetotal
delete(obj);
end
end
%% Test method two: simply counting
function countAndDisplay(obj) % this costs 2.1318e-03 ms(!) per loop
obj.messagetotal = obj.messagetotal+1;
if obj.messagetotal <10000
%msg1 = rosmessage(obj.publisher); %adds 3.6ms per loop
%i = 1% adds 5.7532e-03 ms per loop
%msg1 = rosmessage("std_msgs/Bool"); %adds 1.5ms per loop
countAndDisplay(obj);
else
% Display some results
timepassed = toc(obj.timestart);
time_per_count_FCN = timepassed/obj.messagetotal
delete(obj);
end
end
%% Deconstructor
function delete(obj)
delete(obj.subscriber)
delete(obj.publisher)
delete(obj.node)
end
end
end
I'm trying to learn more about pyhf and my understanding of what the goals are might be limited. I would love to fit my HEP data outside of ROOT, but I could be imposing expectations on pyhf which are not what the authors intended for it's use.
I'd like to write myself a hello-world example, but I might just not know what I'm doing. My misunderstanding could also be gaps in my statistical knowledge.
With that preface, let me explain what I'm trying to explore.
I have some observed set of events for which I calculate some observable and make a binned histogram of that data. I hypothesize that there are two contributing physics processes, which I call signal and background. I generate some Monte Carlo samples for these processes and the theorized total number of events is close to, but not exactly what I observe.
I would like to:
Fit the data to this two process hypothesis
Get from the fit the optimal values for the number of events for each process
Get the uncertainties on these fitted values
If appropriate, calculate an upper limit on the number of signal events.
My starter code is below, where all I'm doing is an ML fit but I'm not sure where to go. I know it's not set up to do what I want, but I'm getting lost in the examples I find on RTD. I'm sure it's me, this is not a criticism of the documentation.
import pyhf
import numpy as np
import matplotlib.pyplot as plt
nbins = 15
# Generate a background and signal MC sample`
MC_signal_events = np.random.normal(5,1.0,200)
MC_background_events = 10*np.random.random(1000)
signal_data = np.histogram(MC_signal_events,bins=nbins)[0]
bkg_data = np.histogram(MC_background_events,bins=nbins)[0]
# Generate an observed dataset with a slightly different
# number of events
signal_events = np.random.normal(5,1.0,180)
background_events = 10*np.random.random(1050)
observed_events = np.array(signal_events.tolist() + background_events.tolist())
observed_sample = np.histogram(observed_events,bins=nbins)[0]
# Plot these samples, if you like
plt.figure(figsize=(12,4))
plt.subplot(1,3,1)
plt.hist(observed_events,bins=nbins,label='Observations')
plt.legend()
plt.subplot(1,3,2)
plt.hist(MC_signal_events,bins=nbins,label='MC signal')
plt.legend()
plt.subplot(1,3,3)
plt.hist(MC_background_events,bins=nbins,label='MC background')
plt.legend()
# Use a very naive estimate of the background
# uncertainties
bkg_uncerts = np.sqrt(bkg_data)
print("Defining the PDF.......")
pdf = pyhf.simplemodels.hepdata_like(signal_data=signal_data.tolist(), \
bkg_data=bkg_data.tolist(), \
bkg_uncerts=bkg_uncerts.tolist())
print("Fit.......")
data = pyhf.tensorlib.astensor(observed_sample.tolist() + pdf.config.auxdata)
bestfit_pars, twice_nll = pyhf.infer.mle.fit(data, pdf, return_fitted_val=True)
print(bestfit_pars)
print(twice_nll)
plt.show()
Note: this answer is based on pyhf v0.5.2.
Alright, so it looks like you've managed to figure most of the big pieces for sure. However, there's two different ways to do this depending on how you prefer to set things up. In both cases, I assume you want an unconstrained fit and you want to...
fit your signal+background model to observed data
fit your background model to observed data
First, let's discuss uncertainties briefly. At the moment, we default to numpy for the tensor background and scipy for the optimizer. See documentation:
numpy backend
scipy optimizer
However, one unfortunate drawback right now with the scipy optimizer is that it cannot return the uncertainties. What you need to do anywhere in your code before the fit (although we generally recommend as early as possible) is to use the minuit optimizer instead:
pyhf.set_backend('numpy', 'minuit')
This will get you the nice features of being able to get the correlation matrix, the uncertainties on the fitted parameters, and the hessian -- amongst other things. We're working to make this consistent for scipy as well, but this is not ready right now.
All optimizations go through our optimizer API which you can currently view through the mixin here in our documentation. Specifically, the signature is
minimize(
objective,
data,
pdf,
init_pars,
par_bounds,
fixed_vals=None,
return_fitted_val=False,
return_result_obj=False,
do_grad=None,
do_stitch=False,
**kwargs)
There are a lot of options here. Let's just focus on the fact that one of the keyword arguments we can pass through is return_uncertainties which will change the bestfit parameters by adding a column for the fitted parameter uncertainty which you want.
1. Signal+Background
In this case, we want to just use the default model
result, twice_nll = pyhf.infer.mle.fit(
data,
pdf,
return_uncertainties=True,
return_fitted_val=True
)
bestfit_pars, errors = result.T
2. Background-Only
In this case, we need to turn off the signal. The way we do this is by setting the parameter of interest (POI) fixed to 0.0. Then we can get the fitted parameters for the background-only model in a similar way, but using fixed_poi_fit instead of an unconstrained fit:
result, twice_nll = pyhf.infer.mle.fixed_poi_fit(
0.0,
data,
pdf,
return_uncertainties=True,
return_fitted_val=True
)
bestfit_pars, errors = result.T
Note that this is quite simply a quick way of doing the following unconstrained fit
bkg_params = pdf.config.suggested_init()
fixed_params = pdf.config.suggested_fixed()
bkg_params[pdf.config.poi_index] = 0.0
fixed_params[pdf.config.poi_index] = True
result, twice_nll = pyhf.infer.mle.fit(
data,
pdf,
init_pars=bkg_params,
fixed_params=fixed_params,
return_uncertainties=True,
return_fitted_val=True
)
bestfit_pars, errors = result.T
Hopefully that clarifies things up more!
Giordon's solution should answer all of your question, but I thought I'd also write out the code to basically address everything we can.
I also take the liberty of changing some of your values a bit so that the signal isn't so strong that the observed CLs value isn't far off to the right of the Brazil band (the results aren't wrong obviously, but it probably makes more sense to be talking about using the discovery test statistic at that point then setting limits. :))
Environment
For this example I'm going to setup a clean Python 3 virtual environment and then install the dependencies (here we're going to be using pyhf v0.5.2)
$ python3 -m venv "${HOME}/.venvs/question"
$ . "${HOME}/.venvs/question/bin/activate"
(question) $ cat requirements.txt
pyhf[minuit,contrib]~=0.5.2
black
(question) $ python -m pip install -r requirements.txt
Code
While we can't easily get the best fit value for both the number of signal events as well as the background events we definitely can do inference to get the best fit value for the signal strength.
The following chunk of code (which is long only because of the visualization) should address all of the points of your question.
# answer.py
import numpy as np
import pyhf
import matplotlib.pyplot as plt
import pyhf.contrib.viz.brazil
# Goals:
# - Fit the model to the observed data
# - Infer the best fit signal strength given the model
# - Get the uncertainties on the best fit signal strength
# - Calculate an 95% CL upper limit on the signal strength
def plot_hist(ax, bins, data, bottom=0, color=None, label=None):
bin_width = bins[1] - bins[0]
bin_leftedges = bins[:-1]
bin_centers = [edge + bin_width / 2.0 for edge in bin_leftedges]
ax.bar(
bin_centers, data, bin_width, bottom=bottom, alpha=0.5, color=color, label=label
)
def plot_data(ax, bins, data, label="Data"):
bin_width = bins[1] - bins[0]
bin_leftedges = bins[:-1]
bin_centers = [edge + bin_width / 2.0 for edge in bin_leftedges]
ax.scatter(bin_centers, data, color="black", label=label)
def invert_interval(test_mus, hypo_tests, test_size=0.05):
# This will be taken care of in v0.5.3
cls_obs = np.array([test[0] for test in hypo_tests]).flatten()
cls_exp = [
np.array([test[1][idx] for test in hypo_tests]).flatten() for idx in range(5)
]
crossing_test_stats = {"exp": [], "obs": None}
for cls_exp_sigma in cls_exp:
crossing_test_stats["exp"].append(
np.interp(
test_size, list(reversed(cls_exp_sigma)), list(reversed(test_mus))
)
)
crossing_test_stats["obs"] = np.interp(
test_size, list(reversed(cls_obs)), list(reversed(test_mus))
)
return crossing_test_stats
def main():
np.random.seed(0)
pyhf.set_backend("numpy", "minuit")
observable_range = [0.0, 10.0]
bin_width = 0.5
_bins = np.arange(observable_range[0], observable_range[1] + bin_width, bin_width)
n_bkg = 2000
n_signal = int(np.sqrt(n_bkg))
# Generate simulation
bkg_simulation = 10 * np.random.random(n_bkg)
signal_simulation = np.random.normal(5, 1.0, n_signal)
bkg_sample, _ = np.histogram(bkg_simulation, bins=_bins)
signal_sample, _ = np.histogram(signal_simulation, bins=_bins)
# Generate observations
signal_events = np.random.normal(5, 1.0, int(n_signal * 0.8))
bkg_events = 10 * np.random.random(int(n_bkg + np.sqrt(n_bkg)))
observed_events = np.array(signal_events.tolist() + bkg_events.tolist())
observed_sample, _ = np.histogram(observed_events, bins=_bins)
# Visualize the simulation and observations
fig, ax = plt.subplots()
fig.set_size_inches(7, 5)
plot_hist(ax, _bins, bkg_sample, label="Background")
plot_hist(ax, _bins, signal_sample, bottom=bkg_sample, label="Signal")
plot_data(ax, _bins, observed_sample)
ax.legend(loc="best")
ax.set_ylim(top=np.max(observed_sample) * 1.4)
ax.set_xlabel("Observable")
ax.set_ylabel("Count")
fig.savefig("components.png")
# Build the model
bkg_uncerts = np.sqrt(bkg_sample)
model = pyhf.simplemodels.hepdata_like(
signal_data=signal_sample.tolist(),
bkg_data=bkg_sample.tolist(),
bkg_uncerts=bkg_uncerts.tolist(),
)
data = pyhf.tensorlib.astensor(observed_sample.tolist() + model.config.auxdata)
# Perform inference
fit_result = pyhf.infer.mle.fit(data, model, return_uncertainties=True)
bestfit_pars, par_uncerts = fit_result.T
print(
f"best fit parameters:\
\n * signal strength: {bestfit_pars[0]} +/- {par_uncerts[0]}\
\n * nuisance parameters: {bestfit_pars[1:]}\
\n * nuisance parameter uncertainties: {par_uncerts[1:]}"
)
# Perform hypothesis test scan
_start = 0.0
_stop = 5
_step = 0.1
poi_tests = np.arange(_start, _stop + _step, _step)
print("\nPerforming hypothesis tests\n")
hypo_tests = [
pyhf.infer.hypotest(
mu_test,
data,
model,
return_expected_set=True,
return_test_statistics=True,
qtilde=True,
)
for mu_test in poi_tests
]
# Upper limits on signal strength
results = invert_interval(poi_tests, hypo_tests)
print(f"Observed Limit on µ: {results['obs']:.2f}")
print("-----")
for idx, n_sigma in enumerate(np.arange(-2, 3)):
print(
"Expected {}Limit on µ: {:.3f}".format(
" " if n_sigma == 0 else "({} σ) ".format(n_sigma),
results["exp"][idx],
)
)
# Visualize the "Brazil band"
fig, ax = plt.subplots()
fig.set_size_inches(7, 5)
ax.set_title("Hypothesis Tests")
ax.set_ylabel(r"$\mathrm{CL}_{s}$")
ax.set_xlabel(r"$\mu$")
pyhf.contrib.viz.brazil.plot_results(ax, poi_tests, hypo_tests)
fig.savefig("brazil_band.png")
if __name__ == "__main__":
main()
which when run gives
(question) $ python answer.py
best fit parameters:
* signal strength: 1.5884737977889158 +/- 0.7803435235862329
* nuisance parameters: [0.99020988 1.06040191 0.90488207 1.03531383 1.09093327 1.00942088
1.07789316 1.01125627 1.06202964 0.95780043 0.94990993 1.04893286
1.0560711 0.9758487 0.93692481 1.04683181 1.05785515 0.92381263
0.93812855 0.96751869]
* nuisance parameter uncertainties: [0.06966439 0.07632218 0.0611428 0.07230328 0.07872258 0.06899675
0.07472849 0.07403246 0.07613661 0.08606657 0.08002775 0.08655314
0.07564512 0.07308117 0.06743479 0.07383134 0.07460864 0.06632003
0.06683251 0.06270965]
Performing hypothesis tests
/home/stackoverflow/.venvs/question/lib/python3.7/site-packages/pyhf/infer/calculators.py:229: RuntimeWarning: invalid value encountered in double_scalars
teststat = (qmu - qmu_A) / (2 * self.sqrtqmuA_v)
Observed Limit on µ: 2.89
-----
Expected (-2 σ) Limit on µ: 0.829
Expected (-1 σ) Limit on µ: 1.110
Expected Limit on µ: 1.542
Expected (1 σ) Limit on µ: 2.147
Expected (2 σ) Limit on µ: 2.882
Let us know if you have any further questions!
I have a big dataset divided in files.
I would like to read and process my data one file at the time and for this I have this keras generator:
def myGenerator():
while 1:
rnd = random.randint(1,200)
strRnd = str(rnd)
lenRnd = len(strRnd)
rndPadded = strRnd.rjust(5, '0')
nSearchesInBatch = 100
f = "path/part-" + rndPadded + "*" #read one block of data
data = sqlContext.read.load(f).toPandas()
imax = int(data.shape[0]/nSearchesInBatch) #number of batches that will be created sequentially from the generator
for i in range(imax):
data_batch = data[i*nSearchesInBatch:(i+1)*nSearchesInBatch]
features = data_batch['features']
output = data_batch['output']
yield features, output
The problem is that the reading takes the biggest part (each file is around 200mb), and in the meanwhile the GPU sits waiting, it is possible to pre-read the next batch while the GPU is traning on the previous one?
At the moment one file is read and split in steps (the inner loop), the CPUs are hidden and the GPU training, as soon as the epoch finishes, the GPU goes idle and the cpu start reading (which takes 20/30 seconds).
Any solution to parallelize this?
I am currently runnuing training in matlab on a matrix of logspecrum samples I am constantly dealing with underflow problems.I understood that I need to work with log's in order to deal with underflowing.
I am still strugling with uderflow though , when i calculate the mean (mue) bucause it is negetive i cant work with logs so i need the real values that underflow.
These are equasions i am working with:
In MATLAB code i calulate log_tau in oreder avoid underflow but when calulating mue i need exp(log(tau)) which goes to zero.
I am attaching relevent MATLAB code
**in the code i called the variable alpha is tau ...
for i = 1 : 50
log_c = Logsum(log_alpha,1) - log(N);
c = exp(log_c);
mue = DataMat*alpha./(repmat(exp(Logsum(log_alpha,1)),FrameSize,1));
log_abs_mue = log(abs(mue));
log_SigmaSqr = log((DataMat.^2)*alpha) - repmat(Logsum(log_alpha,1),FrameSize,1) - 2*log_abs_mue;
SigmaSqr = exp(log_SigmaSqr);
for j=1:N
rep_DataMat(:,:,j) = repmat(DataMat(:,j),1,M);
log_gamma(j,:) = log_c - 0.5*(FrameSize*log(2*pi)+sum(log_SigmaSqr)) + sum((rep_DataMat(:,:,j) - mue).^2./(2*SigmaSqr));
end
log_alpha = log_gamma - repmat(Logsum(log_gamma,2),1,M);
alpha = exp(log_alpha);
end
c = exp(log_c);
SigmaSqr = exp(log_SigmaSqr);
does any one see how i can avoid this? or what needs to be fixed in code?
What i did was add this line to the MATLAB code:
mue(isnan(mue))=0; %fix 0/0 problem
and this one:
SigmaSqr(SigmaSqr==0)=1;%fix if mue_k = x_k
not sure if this is the best solution but is seems to work...
any have a better idea?