I try to employ vegas routine (by G.P. Lepage) on Fortran90 to calculate multidimensional integral from function of 7 arguments and 1 parameter.
I took a code of this subroutine vegas in famous book Numerical Recipes in Fortran90. Here is declaration of the subroutine:
SUBROUTINE vegas(region,func,init,ncall,itmx,nprn,tgral,sd,chi2a)
The second argument is described as
user-supplied d-dimensional function func over a rectangular volume specified by region, a vector of length 2d consisting of d “lower left” coordinates of the region followed by d “upper right” coordinates.
So, here is my question: how can I pass to this function func one extra argument that is a parameter in my function. Accordingly to description of the function it has exactly as many arguments as there are integration variables (d = 7 in my case) while I need to pass one more argument to this function.
Solved.
I am trying to integrate two Fortran-90 subroutines in one main function. The algorithm used in both the subroutines is logically similar but differs in array sizes (e.g. using 4 parameters to calculate a value instead of 3 etc).
I can either declare the array, allocate memory in main function and pass it as argument to subroutine or have the subroutine do it when called. In former case I will end up passing on a lot of arguments and in the latter case I will end up allocating and de-allocating variables a lot of times but passing only few arguments during subroutine call.
As the code might end up calling the subroutines several thousand times, I want to make sure that I choose the mot efficient way to achieve my goal. Can somebody shed any light on this?
If the arguments are conceptually linked you could create an object (derived data type) containing the parameters you want to use as arguments and pass the object to the subroutine.
I was under the impression that the main differences between subroutines and functions in Fortran was that functions returned values, while subroutines change some or all of the values passed as arguments. But then I learned that you could modify variables passed in to functions as arguments too. I'm confused, and can't find a good reference for the differences between them.
So, what are the differences between the two constructs, and when and why should one be preferred over the other?
Whether to use one or another is more or less a matter of programming style. You are allowed to write the arguments of both functions and subroutines as intent(in), intent(inout) or intent(out).
My personal style is however to only use the intent(in) arguments for functions, which is also a requirement for pure functions. An exception to this rule can be made when en error code intent(out) argument is necessary.
There is a subtle trap hidden in functions which return different results for the same input argument value. Consider a hypothetical function returning a random number
real function rnd()
end function
calling it once
x = rnd()
is completely OK. Calling it multiple times in a single expression
x = (rnd() + rnd()) / 2
can result in the function being called only once. Fortran language rules allow such behaviour. Therefore, the standard Fortran procedure for getting random numbers random_number() is a subroutine (and because all intrinsic functions are pure).
Where ever you cannot use a function, use a subroutine.
Any function can by converted to a subroutine by moving the result variable to a dummy argument with intent(out). The opposite process may be more problematic.
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).
What is the difference between a function and a subroutine? I was told that the difference between a function and a subroutine is as follows:
A function takes parameters, works locally and does not alter any value or work with any value outside its scope (high cohesion). It also returns some value. A subroutine works directly with the values of the caller or code segment which invoked it and does not return values (low cohesion), i.e. branching some code to some other code in order to do some processing and come back.
Is this true? Or is there no difference, just two terms to denote one?
I disagree. If you pass a parameter by reference to a function, you would be able to modify that value outside the scope of the function. Furthermore, functions do not have to return a value. Consider void some_func() in C. So the premises in the OP are invalid.
In my mind, the difference between function and subroutine is semantic. That is to say some languages use different terminology.
A function returns a value whereas a subroutine does not. A function should not change the values of actual arguments whereas a subroutine could change them.
Thats my definition of them ;-)
If we talk in C, C++, Java and other related high level language:
a. A subroutine is a logical construct used in writing Algorithms (or flowcharts) to designate processing functionality in one place. The subroutine provides some output based on input where the processing may remain unchanged.
b. A function is a realization of the Subroutine concept in the programming language
Both function and subroutine return a value but while the function can not change the value of the arguments coming IN on its way OUT, a subroutine can. Also, you need to define a variable name for outgoing value, where as for function you only need to define the ingoing variables. For e.g., a function:
double multi(double x, double y)
{
double result;
result = x*y;
return(result)
}
will have only input arguments and won't need the output variable for the returning value. On the other hand same operation done through a subroutine will look like this:
double mult(double x, double y, double result)
{
result = x*y;
x=20;
y = 2;
return()
}
This will do the same as the function did, that is return the product of x and y but in this case you (1) you need to define result as a variable and (2) you can change the values of x and y on its way back.
One of the differences could be from the origin where the terminology comes from.
Subroutine is more of a computer architecture/organization terminology which means a reusable group of instructions which performs one task. It is is stored in memory once, but used as often as necessary.
Function got its origin from mathematical function where the basic idea is mapping a set of inputs to a set of permissible outputs with the property that each input is related to exactly one output.
In terms of Visual Basic a subroutine is a set of instructions that carries out a well defined task. The instructions are placed within Sub and End Sub statements.
Functions are similar to subroutines, except that the functions return a value. Subroutines perform a task but do not report anything to the calling program. A function commonly carries out some calculations and reports the result to the caller.
Based on Wikipedia subroutine definition:
In computer programming, a subroutine is a sequence of program
instructions that perform a specific task, packaged as a unit. This
unit can then be used in programs wherever that particular task should
be performed.
Subroutines may be defined within programs, or separately in libraries
that can be used by many programs. In different programming languages,
a subroutine may be called a procedure, a function, a routine, a
method, or a subprogram. The generic term callable unit is sometimes
used.
In Python, there is no distinction between subroutines and functions.
In VB/VB.NET function can return some result/data, and subroutine/sub can't.
In C# both subroutine and function referred to a method.
Sometimes in OOP the function that belongs to the class is called a method.
There is no more need to distinguish between function, subroutine and procedure because of hight level languages abstract that difference, so in the end, there is very little semantic difference between those two.
Yes, they are different, similar to what you mentioned.
A function has deterministic output and no side effects.
A subroutine does not have these restrictions.
A classic example of a function is int multiply(int a, int b)
It is deterministic as multiply(2, 3) will always give you 6.
It has no side effects because it does not modify any values outside its scope, including the values of a and b.
An example of a subroutine is void consume(Food sandwich)
It has no output so it is not a function.
It has side effects as calling this code will consume the sandwich and you can't call any operations on the same sandwich anymore.
You can think of a function as f(x) = y, or for the case of multiply, f(a, b) = c. Yes, this is programming and not math. But math models and begs to be used. So we use math in cs. If you are interested to know why the distinction between function and subroutine, you should check out functional programming. It works like magic.
From the view of the user, there is no difference between a programming function and a subroutine but in theory, there definitely is!
The concept itself is different between a subroutine and a function. Formally, the OP's definition is correct. Subroutines don't take arguments or give return values by formal semantics. That's just an interpretion with conventions. And variables in subroutines are accessible in other subroutines of the same file although this can be achieved as well in C with some difficulties.
Summary:
Subroutines work only based on side-effects, in the view of the programming language you are programming with. The concept itself has no explicit arguments or return values. You have to use side effects to simulate them.
Functions are mappings of input to output value(s) in the original sense, some kind of general substitution operation. In the adopted sense of the programming world, functions are an abstraction of subroutines with information about return value and arguments, inspired by mathematical functions. The additional formal abstraction differentiates a function from a subroutine in programming context.
Details:
The subroutine originally is simply a repeatable snippet of code which you can call in between other code. It originates in Assembly or Machine language programming and designates the instruction sequence itself. In the light of this meaning, Perl also uses the term subroutine for its callable code snippets.
Subroutines are concrete objects.
This is what I understood: the concept of a (pure) function is a mathematical concept which is a special case of mathematical relations with an own formal notation. You have an input or argument and it is defined what value is represented by the function with the given argument. The original function concept is entirely unrelated to instructions or calculations. Mathematical operations (or instructions in the programming world) only are a popular formal representation (description) of the actual mapping. The original function term itself is not defined as code. Calculations do not constitute the function, so that functions actually don't have any computational overhead because they are direct mappings. Function complexity considerations only arrived as there is an overhead to find the mapping.
Functions are abstract objects.
Now, since the whole PC-stuff is running on small machine instructions, the easiest way to model (or instantiate) mathematics is with a sequence of instructions itself. Computer Science has been founded by mathematicians (noteworthy: Alan Turing) and the first programming concepts are based on it so there is a need to bring mathematics into the machine. That's how I imagine the reason why "function" is the name of something which is implemented as subroutine and why the term "pure" function was coined to differentiate the original function concept from the overly broad term-use in programming languages.
Note: in Assembly Language Programming, it is typically said, that a subroutine has been passed arguments and gives a return value. This is an interpretation on top of the concrete formal semantics. Calling conventions specify the location where values, to be considered as arguments and return values, should be written to before calling a subroutine or returning. The call itself takes only a subroutine address, and has no formal arguments or return values.
PS: functions in programming languages don't necessarily need to be a subroutine (even though programming language terminology developed this way). Functions in functional programming languages can be constant variables, arrays or hash tables. Isn't every datastructure in ECMAScript a function?
The difference is isolation. A subroutine is just a piece of the program that begins with a label and ends with a go to. A function is outside the namespace of the rest of the program. It is like a separate program that can have the same variable names as used in the calling program, and whatever it does to them does not affect the state of those variables with the same name in the calling program.
From a coding perspective, the isolation means that you don’t have to use the variable names that are local to the function.
Sub double:
a = a + a
Return
fnDouble(whatever):
whatever = whatever + whatever
Return whatever
The subroutine works only on a. If you want to double b you have to set a = b before calling the subroutine. Then you may need to set a to null or zero after. Then when you want to double c you have to again set a to equal c.
Also the sub might have in it some other variable, z, that is changed when the sub is jumped to, which is a bit dangerous.
The essential is isolation of names to the function (unless declared global in the function.)
I am writing this answer from a VBA for excel perspective. If you are writing a function then you can use it as an expression i. e. you can call it from any cell in excel.
eg: normal vlookup function in excel cannot look up values > 256 characters. So I used this function:
Function MyVlookup(Lval As Range, c As Range, oset As Long) As Variant
Dim cl As Range
For Each cl In c.Columns(1).Cells
If UCase(Lval) = UCase(cl) Then
MyVlookup = cl.Offset(, oset - 1)
Exit Function
End If
Next
End Function
This is not my code. Got it from another internet post. It works fine.
But the real advantage is I can now call it from any cell in excel. If wrote a subroutine I couldn't do that.
Every subroutine performs some specific task. For some subroutines, that task is to compute or retrieve some data value. Subroutines of this type are called functions. We say that a function returns a value. Generally, the returned value is meant to be used somehow in the program that calls the function.