How to use series in the GR-tensor package? - maple

How can I use the series command for a specific quantity to find it up to a certain order of magnitude?
Is it possible to have an expanded series of a tensor in GR-tensor package?

Yes. You can apply series expansion to an object using the grmap() command.
The help for this function gives an example:
e.g. to do a taylor series expansion about r=a to second order
grmap(R(dn,dn,dn,dn), taylor, 'x',r=a,2);
See the help for grmap: ?grmap

Related

confusion regarding matlab command "fir1"

What is the meaning & signficance of using higlighted arguments like"DC-0" or "DC-1" as 3rd argument in fir1 command? Will my design remain valid if i skip these type of arguments?
'DC-0' specifies that the first band of a multiband filter is a stopband. 'DC-0' is the default when Wn has more than two elements.
'DC-1' specifies that the first band of a multiband filter is a passband.
for details see the matlab online help, click here

MATLAB - EEGLAB: surpress GUI for pop_eegfiltnew()

I am working on some scripts for which I use several functions from the EEGLAB package for matlab. Most of these functions make it possible to surpress the GUI from showing, for example using f( ... 'gui','off'), or by using a different version of the same function. However, I can not figure out how to do this for the function pop_eegfiltnew(). Two similar functions are eegfilt(), which seems to be an outdated version of the function, and firfilt() however, pop_eegfiltnew() has more arguments than these other two, so they are certainly not the same in functional terms.
Anyone knows how to get around this?
If you supply enough arguments to pop_eegfiltnew it does not pop up a GUI.
For example if you wanted to filter your signal 1 Hz highpass you would:
EEG = pop_eegfiltnew(EEG, 1, 0);
This is because the first argument of pop_eegfilt is EEG structure, the second is locutoff (lower edge of the passband) and the third is hicutoff (higher edge of the passband).

is it possible to use multiple groups with cvpartition in matlab?

thank you in advance for the input. I am using cvpartition to produce sets that I will use for training and validation on some data. In particular I'm using
c = cvpartition(a,'kfold',5)
where a is a single group. I would like to be able to generate training and testing sets using two groups, say a and b, rather than just a. In other words I'm looking for something like this
c = cvpartition([a b],'kfold',5)
%I haven't tried this; I would like to know ahead of time if this will work
Is this possible to do using cvpartition? If not is there another way that I could easily do this without hard coding a solution?
I was able to find a solution on my own. Albeit not really my desired solution. In my case a and b are integers so I divided a by 10 then added it to b to get a.b. I then used this as my grouping variable. In other words, I created a combined variable that encodes information from a and b, is one to one given a and b, and allows me to use cvpartition to the desired affect.

When using a multiple-output matlab function, do i need to callback all variables?

When using a multiple-output matlab function, do i need to callback all variables? or can I just take the first two variables? (if so..is it not recommended?)
lets say in function.m
[a, b, c] = function( )
in main.m
[var1, var2] = function;
When calling (almost) any function in matlab you can request fewer outputs than it specifies. So, yes the example you give should work perfectly fine.
There are some clever things you can do with this, such as using nargout within a function to see how many output arguments have been requested and only calculating the values that have been requested as an optimisation trick.
It depends on the definition of the function, and exactly which of the outputs you want to get.
Not all the function allow to do it, you can find all the options for each function in the beginning of the help documentation on the specific function.
If you want only the 2nd, or 3rd outputs, and you want also to save the computation-time of the results that does not interesting, you can use ~ option, like this (for versions 2009b and later):
[~, var1, var2]=function
Many functions allow for options to passed that change how the function behaves. I used/wrote various numerical solving functions a bit and one that nice amount of option, for instance is the LSMR function(s).
Otherwise, if you can manipulate the original either introduce an input(s) to do so before or at the end with an inline subroutine to generate the outputs you want.
Or if you can't it will return as either a cell array or a vector and you can pass an anonymous function to generate the desired outputs that way.
Really, can be done many ways. Very contextual.

Gaps In Plot Of Piecewise Function in Matlab

I want to plot a piecewise function, but I don't want any gaps to appear
at the junctures, for example:
t=[1:8784];
b=(26.045792 + 13.075558*sin(0.0008531214*t - 2.7773943)).*((heaviside(t-2184))-(heaviside(t-7440)));
plot(b,'r','LineWidth', 1.5);grid on
there should not be any gaps appearing in
the plot between the three intervals , but they do.
I want the graph to be continueous without gaps.
Any suggestions on how to achieve that.
Thanks in advance.
EDIT
Actually, my aim is to find the carrier function colored by yellow in the figure below. I divide the whole interval into 3 intervals: 1-constant 2-sinusoidal 3- constant, then I want to find the overall function from the these three functions
Of course there are "gaps". The composite function is identically zero for all t<2184, and for all t>7440. The relationships can only be non-zero inside of that interval. And you have not chosen a function that is zero at the endpoints, so how can you expect there not to be "gaps"?
What values does your function take on at the endpoints of the interval?
>> t = [2184 7440];
>> (26.045792 + 13.075558*sin(0.0008531214*t - 2.7773943))
ans =
15.689 20.616
So look at the hat function part of this. I'll be lazy and use ezplot.
>> ezplot(#(t) ((heaviside(t-2184))-(heaviside(t-7440))),[0,8784])
Now, combine this, multiplying it by a trig piece, and of course the result is identically zero outside of that domain.
>> ezplot(#(t) (26.045792 + 13.075558*sin(0.0008531214*t - 2.7773943)).*((heaviside(t-2184))-(heaviside(t-7440))),[0,8784])
But if your goal is some sort of continuous function across the two chosen points in the hat function, you need to chose the trig part such that it is zero at those same two points. Mathematics is not spelled mathemagics. Wishing that you get a continuous function will not make it so.
So is your real question how to chose that internal piece (segment) as one such that the final result is continuous? If so, then we need to know why you have chosen the arbitrary constants in there. Surely these numbers, {26.045792, 13.075558, 0.0008531214, 2.7773943} all must have some significance to you. And if they are important, then how can we possibly make the result a continuous function?
Perhaps, and I'm just guessing here, you want some other result out of this, such that the function is not identically zero outside of those bounds. Perhaps you wish to extrapolate as a constant function outside of those points. But to help you, you must help us.