I'm setting up a custom class that accepts some Number parameters, but i need to limit those parameters and would like to know the best way of doing so.
currently, i'm simply calling if statements, and throwing an error if the number is above or below what's accepted. for example, there is a parameter that accepts and angle, but only between 0 and 90. in the case i've typed it as a uint so now i only have to check to see if it's above 90. there's also a parameter Number typed parameter that only accepts values between the range of 0.0 and 1.0.
Is my method of using if statements and throwing erros the usual way of filtering parameters?
Yes. The only way to get around this is to use the type system, e.g. create an AcuteAngle class that can only contain a number between 0 and 90. However, for what you're doing, it's better to just have if statements.
Your only other option is to silently clip inputs to the desirable range (for example, angle = angle % 90;). The official AS libraries tend to use this approach more often than not, but they're not terribly consistent.
Related
Following code is part of contnrs unit of FreePascal
constructor TFPCustomHashTable.Create;
begin
CreateWith(196613,#RSHash);
end;
I am curious about 196613. I know it is hash table size. Is there any particular reason why this value is used?
In my test, constructor took about 3-4 ms to execute, which in my particular situation is not accepted. I suspect this is related to this constant value.
Update:
My question are:
Why 196613 is chosen? Why not other prime number?
Does it affect constructor call execution time?
196613 is one of the numbers being recommended for hash tables sizes (prime and far away from powers of two), for more info see e.g. https://planetmath.org/goodhashtableprimes.
It affects the constructor call execution time, yes. You can always construct TFPCustomHashTable using CreateWith and pass a size of your choice (any number is fine, as resizing algorithm checks for suitable sizes anyways) as well as your own hash function (or the pre-defined RSHash):
MyHashTable:=TFPCustomHashTable.CreateWith(193,#RSHash);
Keep in mind though, that resizing a hash table is an expensive operation as it requires to recalculate the hash function for all elements, so starting with a too small value is neither a good idea.
I have a huge lib of math functions, like pdf or cdf of statistical distributions. But often e.g. the inverse cdf can be only calculated numerically, e.g. using Newton-Raphson or bisection, in the latter we would need to check if cdf(x) is > or < then the target y0.
However, many functions have further parameters like a Gaussian distribution having certain mean and sigma, so cdf is cdf(x,mean,sigma). Whereas other functions, such as standard normal cdf, have no further parameters, or some have even 3 or 4 further parameters.
A similar problem would happen if you want to apply bisection for either linear functions (2 parameters) or parabolas (3 parameters). Or if you want not the inverse function, but e.g. the integral of f.
The easiest implementation would be to define cdf as global function f(x); and to check for >y0 or global variables.
However, this is a very old-fashioned way, and Freepascal also supports procedural parameters, for calls like x=icdf(0.9987,#cdfStdNorm)
Even overloading is supported to allow calls like x2=icdf(0.9987,0,2,#cdfNorm) to pass also mean and sigma.
But this ends up still in two separate code blocks (even whole functions), because in one case we need to call cdf only with x, and in 2nd example also with mean and sigma.
Is there an elegant solution for this problem in Freepascal? Maybe using variant records? Or an object-oriented approach? I have no glue about OO, but I know the variant object style would require to change at least the headers of many functions because I want to apply the technique not only for inverse cdf calculation, but also to numerical integration, root finding, optimization, etc.
Or is it "best" just to define a real function type with e.g. x + 5 parameters (maybe as array), and to ignore the unused parameters? But for me it looks that then I would need many "wrapper" functions or to re-code all the existing functions (to use the arrays, even if they are sometimes not needed!).
Maybe macros can help as well? Any Freepascal hints are very welcome!
If you make it a (function .. of object), mean and sigma could be part of the class, and the function could internally just access it. Only the really changing parameters during the iteration would be parameters. (read: x)
Anonymous methods as talked about by David and Rudy is a further step to avoid having to declare a class for each such invocation, but that is convenience thing and IMHO not the core of the question. At the expense of declaring the class, your core code is free of global variable use and anonymous methods might also come with a performance cost, depending on usage.
Free Pascal also supports nested functions (function... is nested), which is the original Pascal closure-like way which was never adopted by Pascal compilers from Borland. A nested procedure passed as callback can access local variables in the procedure where it was declared. The Free Pascal numlib numeric math package uses this in some cases for similar cases like yours. For math it is even more natural.
Delphi never implements old constructs because borrowing syntax from other languages looks better on bulletlists and keeps the subscriptions flowing.
I'm trying to get started with neural network and implement boolean functions like AND/OR.
Instead of using 0, and 1 as binary inputs, they use -1 and +1. Is there a reason why we cannot use (0, 1)?
As an example: http://www.youtube.com/watch?v=Ih5Mr93E-2c
If you really mean inputs, there is no restriction on using {-1,1}. You can just as easily use {0,1} or any other pair of real numbers (e.g., {6,42}) to define your True/False input values.
What may be confusing you in the charts is that {-1,1} are used as the outputs of the neurons. The reason for that, as #Memming stated, is because of the activation function used for the neuron. If tanh is used for the activation function, the neuron's output will be in the range (-1,1), whereas if you use a logistic function, its output will be in the range (0,1). Either will work for a multi-layer perceptron - you just have to define your target value (expected output) accordingly.
In most cases there's no difference. Just use logistic function activation instead of tanh. In some special forms, e.g., Ising model, it could nontrivially change the parameter space though.
I need to write my own function which has the form f(x,y)=Integrate(g(x,y,z),z from 0 to inf). so the code I used was:
function y=f(x,y)
g=#(z)exp(-z.^2)./(z.^x).*(z.^2+y.^2).^(x/2);% as a function of x,y and z
y=quadgk(g,0,inf)
and if I call it for a single value like f(x0,y0), it works but if I try to calculate something like f([1:10],y0), then the error message says that there is something wrong with the times and dimension. In principle I can use for loops but then my code slows down and takes forever. Is there any help I can get from you guys? or references?
I'm trying to avoid the for loop since in matlab it's much faster to use matrix computation than to use for loop. I wonder if there is any trick that I can take advantage of this feature.
Thanks for any help in advance,
Lynn
Perhaps you can try to transpose the interval, creating row based values instead of column based f([1:10]',y0). Otherwise something in your function might be wrong, for example to get x^y to work with lists as input, you have to prefix with a dot x.^y. The same for mulitply and division I think..
If loop is no problem for you, you should do something like:
function y2=f(x,y)
y2=zeros(size(x));
for n=1:numel(x)
g=#(z)exp(-z.^2)./(z.^x(n)).*(z.^2+y.^2).^(x(n)/2);% as a function of x,y and z
y2(n)=quadgk(g,0,inf)
end
The problem here is that quadk itself uses vectors as argument for g. Then you have in g somethink like z.^x, which is the power of two vectors that is only defined if z and x have the same dimension. But this is not what you want.
I assume that you want to evaluate the function for all arguments in x and that the output vector has the same dimension as x. But this does not seem to be possible since even this simple example
g=#(x)[x;x.^2]
quad(g,0,1)
does not work:
Error using quad (line 79)
The integrand function must return an output vector of the same length as the
input vector.
A similar error shows when using quadgk. The documentation also says that this routine works only for scalar functions and this is not surprising since an adaptive quadrature rule would in general use different points for each function to evaluate the integral.
You have to use quadvinstead, which can integrate vector valued functions. But this gives wrong results since your function is integrated in the interval [0,\infty).
in xxxx.mxml (from flex) i have called the remote remote method (of java) the method return type is float
in the xxxx.mxml's remote objects result handler i need get the float values as Numeric.....or String..i tried with string...i did Alert.show to see the value some times i get exact value for eg, 0.5 is the value returning from java methid but here it will show 0.50000454...so on..how get the exact value?
It is because of the way floating point numbers are stored; basically they can't be stored precisely. A quick search in SO would reveal a lot of threads about this. Also read "What Every Computer Scientist Should Know About Floating-Point Arithmetic"
Thus the problem of getting the exact value boils down to what you define exact to be. Try rounding it to a given number of floating points at java end, convert the rounded number to a string (I'm not sure if this conversion would preserve the precision) and send that string.