I am getting this error and this post telling me that I should decrease the sigma but here is the thing this code was working fine a couple of months ago. Nothing change based on the data and the code. I was wondering why this error out of blue.
And the second point, when I lower the sigma such as 13.1, it looks running (but I have been waiting for an hour).
sigma=203.9057
dimyx1=1024
A22den=density(Lnetwork,sigma,distance="path",continuous=TRUE,dimyx=dimyx1) #
About Lnetwork
Point pattern on linear network
69436 points
Linear network with 8417 vertices and 8563 lines
Enclosing window: rectangle = [143516.42, 213981.05] x [3353367, 3399153] units
Error: Required number of iterations = 1087633109 exceeds iterMax = 1e+06 ; either increase iterMax, dx, dt or reduce sigma
This is a question about the spatstat package.
The code for handling data on a linear network is still under active development. It has changed in recent public releases of spatstat, and has changed again in the development version. You need to specify exactly which version you are using.
The error report says that the required number of iterations of the algorithm is too large. This occurs because either the smoothing bandwidth sigma is too large, or the spacing dx between sample points along the network is too small. The number of iterations is proportional to (sigma/dx)^2 in most cases.
First, check that the value of sigma is physically reasonable.
Normally you shouldn't have to worry about the algorithm parameter dx because it is determined automatically by default. However, it's possible that your data are causing the code to choose a very small value of dx.
The internal code which automatically determines the spacing dx of sample points along the network has been changed recently, in order to fix several bugs.
I suggest that you specify the algorithm parameters manually. See the help file for densityHeat for information on how to control the spacings. Setting the parameters manually will also ensure greater consistency of the results between different versions of the software.
The quickest solution is to set finespacing=FALSE. This is not the best solution because it still uses some of the automatic rules which may be giving problems. Please read the help file to understand what that does.
Did you update spatstat since this last worked? Probably the internal code for determining spacing on the network etc. changed a bit. The actual computations are done by the function densityHeat(), and you can see how to manually set spacing etc. in its help file.
Related
I recently learned about the feature of the semi-total derivative approximation. I started to use this feature with bsplines and an explicit component. My current problem is that my design variables are input from two different components similar to the xsdm below. As far as I see it is not possible to set up different finite difference steps for different design variables. So looking at the xsdm again the control points, x and z should have identical FD steps i.e.
model.approx_totals(step=1)
works but
model.approx_totals(step=np.ones(5))
won't work. I guess, one remedy is to use the relative step size but some of my input bounds are varying from 0 to xx so maybe the relative step size is not the best. Is there a way to feed in FD steps as a vector or something similar to ;
for out in outputs:
for dep,fdstep in zip(inputs,inputsteps):
self.declare_partials(of=out,wrt=dep,method='fd',step=fdstep, form='central')
As of OpenMDAO V2.4, you don't have the ability to set per-variable FD step sizes when using approx_totals. The best option is just to use relative step sizes.
I am using the finite difference scheme to find gradients.
Lets say i have 2 outputs (y1,y2) and 1 input (x) in a single component. And in advance I know that the sensitivity of y1 with respect to x is not same as the sensitivity of y2 to x. And thus i could potentially have two different steps for those as in ;
self.declare_partials(of=y1, wrt=x, method='fd',step=0.01, form='central')
self.declare_partials(of=y2, wrt=x, method='fd',step=0.05, form='central')
There is nothing that stops me (algorithmically) but it is not clear what would openmdao gradient calculation exactly do in this case?
does it exchange information from the case where the steps are different by looking at the steps ratios or simply treating them independently and therefore doubling computational time ?
I just tested this, and it does the finite difference twice with the two different step sizes, and only saves the requested outputs for each step. I don't think we could do anything with the ratios as you suggested, as the reason for using different stepsizes to resolve individual outputs is because you don't trust the accuracy of the outputs at the smaller (or large) stepsize.
This is a fair question about the effect of the API. In typical FD applications you would get only 1 function call per design variable for forward and backward difference and 2 function calls for central difference.
However in this case, you have asked for two different step sizes for two different outputs, both with central difference. So here, you'll end up with 4 function calls to compute all the derivatives. dy1_dx will be computed using the step size of .01 and dy2_dx will be computed with a step size of .05.
There is no crosstalk between the two different FD calls, and you do end up with more function calls than you would have if you just specified a single step size via:
self.declare_partials(of='*', wrt=x, method='fd',step=0.05, form='central')
If the cost is something you can bear, and you get improved accuracy, then you could use this method to get different step sizes for different outputs.
Can somebody tell me why this author has used the following code in their normalisation.
The first line appears fine to me they have standardised the training set by the following formula;
(x - mean(x)) / std(x)
However the second line and third line (validation and test) they have used the train mean (trainme) and train standard deviation (trainstd). Should they not have used the validation mean (validationme) and validation standard deviation (validationstd) along with the test mean and test standard deviation?
You can also view the page from the book at the following link (page 173)
What the authors are doing is reasonable and it's what is conventionally done. The idea is that the same normalization is applied to all inputs. This is essentially allocating some new parameters (offset and scale) and estimating them from the training data. In that scheme, if the value 100 is input, then the normalized value is (100 - offset)/scale, no matter where (training, testing, whatever) that 100 came from.
I guess one can also make an argument that the offset and scale should be context dependent in the sense that if you are given a set of data and for some reason the offset and scale are very different from the original training data, maybe what's important is how big each value is relative to the others in the same data set. E.g. maybe you should treat 200 the same as 100, if the scale is twice as big in the data set containing 200.
Whether that data-dependent scaling is reasonable would have to be decided case by case. I don't remember ever having seen it, but it's plausible that it could be the right thing to do in some cases.
By the way, you'll get more interest in general statistical questions at stats.stackexchange.com and/or datascience.stackexchange.com.
I am writing a numerical model in R, for an ecological system, and solving it using "lsoda" from package deSolve.
My model has 14 state variables.
I define the model, set it up fine, and give time duration according to this:
nyears<-60
ndays<-nyears*365+1
times<-seq(0,nyears*365,by=1)
Rates of change of state variables (e.g. the rate of change of variable "A1" is "dA1")are calculated according to existing values for state variables (at time=t) and a set of parameters.
Simplified example:
dA1<-Tf*A1*(ImaxA*p_sub)
Where Tf, ImaxA and p_sub are parameters, and A1 is my state variable at time=t.
When I solve the model, I use the lsoda solver like this:
out<-as.data.frame(lsoda(start,times,model,parms))
Sometimes (depending on my parameter combinations), the model run completes over the entire duration I have specified, however sometimes it stops short of the mark (still giving me output up until the solver "crashes"). When it "crashes", this message is displayed:
DLSODA- At current T (=R1), MXSTEP (=I1) steps
taken on this call before reaching TOUT
In above message, I1 = 5000
In above message, R1 = 11535.5
Warning messages:
1: In lsoda(start, times, model, parms) :
an excessive amount of work (> maxsteps ) was done, but integration was not successful - increase maxsteps
2: In lsoda(start, times, model, parms) :
Returning early. Results are accurate, as far as they go
It commonly appears when one of the state variables is getting exponentially bigger, or is tending very near to zero, however sometimes it crashes when seemingly not much change is happening. I may be wrong, but is it due to the rate of change of state-variables becoming too large? If so, why might it also "crash" when there is not a fast rate of change?
Is there a way that I can make the solver complete its task with the specified parameter values, maybe with a more relaxed tolerance for error?
Thank you all for your contributions. I looked at some of the rates, and at the point of crashing, the model was switching between two metabolic states - and the fast rate of this binary switch caused the solver to stop - rejecting the solution because the rate of change was too large. I have fixed my model by introducing a gradual switch between states (with a logistic curve) instead of this binary switch. I aknowledge that I didn;t give enough info in the original question, so thanks for the help you offered!
(edited)
Is there any library or tool that allows for knowing the maximum accumulated error in arithmetic operations?
For example if I make some iterative calculation ...
myVars = initialValues;
while (notEnded) {
myVars = updateMyVars(myVars)
}
... I want to know at the end not only the calculated values, but also the potential error (the range of posible values if results in each individual operations took the range limits for each operand).
I have already written a Java class called EADouble.java (EA for Error Accounting) which holds and updates the maximum positive and negative errors along with the calculated value, for some basic operations, but I'm afraid I might be reinventing an square wheel.
Any libraries/whatever in Java/whatever? Any suggestions?
Updated on July 11th: Examined existing libraries and added link to sample code.
As commented by fellows, there is the concept of Interval Arithmetic, and there was a previous question ( A good uncertainty (interval) arithmetic library? ) on the topic. There just a couple of small issues about my intent:
I care more about the "main" value than about the upper and lower bounds. However, to add that extra value to an open library should be straight-forward.
Accounting the error as an independent floating point might allow for a finer accuracy (e.g. for addition the upper bound would be incremented just half ULP instead of a whole ULP).
Libraries I had a look at:
ia_math (Java. Just would have to add the main value. My favourite so far)
Boost/numeric/Interval (C++, Very complex/complete)
ErrorProp (Java, accounts value, and error as standard deviation)
The sample code (TestEADouble.java) runs ok a ballistic simulation and a calculation of number e. However those are not very demanding scenarios.
probably way too late, but look at BIAS/Profil: http://www.ti3.tuhh.de/keil/profil/index_e.html
Pretty complete, simple, account for computer error, and if your errors are centered easy access to your nominal (through Mid(...)).