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How can I execute a function using a variable name?

Here is my code:
$(function(){
function myfunc(){
alert("executed");
}
var function_name = "myfunc";
window[function_name]();
})
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
As you can see, that function is not defined. Why? And how can I make it working?

The function is not defined in the global scope so it’s not a member of the window object.
You can attach the function to the window object like this.
$(function(){
window.myfunc = function(){
alert("executed");
};
var function_name = "myfunc";
window[function_name]();
})

It works only for global functions, because the scope is identically with the window object.
You could assing a function to a wanted property of the window object, just as to any other object.
function myfunc(){
alert("executed");
}
$(function(){
var function_name = "myfunc";
window[function_name]();
window.foo = _ => console.log('foo');
window.foo();
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

While the direct answer to your question is that your function wasn't defined as a Global and so, attempting to call it as a property of window fails, putting your function into Global scope is not really a good answer.
Instead, make the function a method of a user-defined object (that can be put into any scope you like) and call the function as a property of that object:
// Immediately-Invoked Function Expression (IIFE)
// that keeps all of its contents out of the Global scope
(function(){
let functionHolder = {
someFunction : function(){ console.log("You did it!"); }
};
// Set up a variable that has the same name as the function
let funcName = "someFunction";
// Call the function via the object
functionHolder[funcName]();
})()

javascript: access all variables of a parent function

I decided to create a funcB function that I call from funcA. I want all variables from funcA to be available in the funcB so func B can change that variables.
How to modify the code below so it meets my requirements? I doubt passing all variables it the only possible and the best way.
function funcB(){
alert(var1);//how to make it alert 5
alert(var20);//how to make it alert 50
}
function funcA(){
var var1=5;
...
var var20=50;
funcB();
}

var obj = {
one : "A",
two : "B",
fnA : function() {
this.fnB(); // without fnB method result will be displayed as A B, with fnB as C D
console.log(this.one + " " + this.two);
},
fnB : function() {
this.one = "C";
this.two = "D";
}
};
obj.fnA();
this keyword refers to obj object
You can define object with properties and methods inside it. With methods all the variables can be manipulated as you wish, from this example with fnB I'm changing values of properties which are displayed from fnA method
JSFiddle

One way is to drop the var keyword:
function funcB(){
alert(var1);//how to make it alert 5
alert(var20);//how to make it alert 50
}
function funcA(){
var1 = 5;
var20 = 50;
funcB();
}
This will expose them to the global scope so funcB can access them. Notice you can also create the varaibles in the global scope itself, with the var keyword, but both methods will ultimately have the same effect.
Note:
This may not work if there is already a var1 or var20 in the global scope. In such case, it will modify the global value and may result in unwanted errors.
This method is not preferred for official code, and is bad practice Reason

This is not possible as when you declare a variable with the var keyword, they are scoped to the function in which they are declared.
If you avoid the var keyword, they are instead defined as a global variable. This is deemed very bad practice.
I would recommend you read up on javascript coding patterns, particularly the module pattern.
For example:
var myNamespace = (function () {
var foo, bar;
return {
func1: function() {
foo = "baz";
console.log(foo);
},
func2: function (input) {
foo = input;
console.log(foo);
}
};
})();
Usage:
myNamespace.func1();
// "baz"
myNamespace.func2("hello");
// "hello"

What is difference between these two functions?

I have tried folllowing two ways of referring a function:
First
let a = function() {
somefunction();
}
Second
let a = somefunction;
Where somefunction is the following in both cases:
function somefunction() {
alert("hello");
}
Is there any difference between these two ways?

Yes, there is a difference between your two examples.
In the first case, you are defining a new anonymous (unnamed) function which calls somefunction. You are then assigning your new function definition to the variable a. a holds a reference to your new function.
In the second case, you are simply assigning your original function of somefunction to the variable a. The variable a then holds a reference to somefunction. You are not creating a new function as you are in the first case.

I think this example may make the difference clear. arguments is an array like object that contains each of the arguments passed to a function.
Try running each of these lines on your favorite browser console.
var somefunction = function() { console.log(arguments); };
Your first example demonstrates defining a named function a that closes around the named function somefunction.
var a = function() { somefunction(); };
Your second example makes a reference, b, directly to somefunction. This makes invoking b the same as invoking somefunction.
var b = somefunction;
Now if you call each of these a and b with some arguments you will see the difference.
=> a('a', 1);
[]
=> b('a', 1);
['a', 1]
In the first case the arguments object is empty. That's because the arguments that were passed to a were not forwarded onto somefunction.
In the second case the arguments are available to somefunction, because some function is being called directly.
Here is how you could redefine a so that it were functionally equivalent using apply
var a = function() { somefunction.apply(this, arguments); }
Running this at your console prints the argument array.
=> a('a', 1);
['a', 1]

var a = function(){
somefunction();
}
Is an Anonymous Function attributed to a variable.
somefunction :function() {
alert("hello");
}
Is an declaration of a function throungh the Object Literal notation.
The diference are shown when you are creating an object. The anonymous function are not acessible as a "public" method, instead in the Object Literal notation, that are acessible from outside.
As Douglas Crockford said, in JS the Good Parts, the first declaration are just a function and the second one could be a method.

In the first case, you are creating a function which calls someFunction(), then you assign that function to a, so now calling a() calls an anonymous function which in turn calls someFunction().
In the second case, a and someFunction become the exact same thing, calling a() is the same as calling someFunction().

The way you're setting var a by accessing the function is clearly out of scope.
So I suspect you have a typo : instead of = :
var somefunction = function() {
alert("hello");
};
somefunction(); // hello
...Now that your first and second makes sense with the code above:
Anonymous Function stored in variable:
var a = function(){
alert('Hey');
somefunction();
};
a(); // Hey // hello
Variable as Function Reference
var a = somefunction;
a(); // hello
In the other case than:
var objLiteral = {
somefunction : function() {
alert("hello");
}
};
var a = objLiteral.somefunction;
a(); // hello

How to execute a YUI function from Javascript?

How can i call a YUI function that is wrapped inside a YUI().use from javascript?
example
Below is a YUI function "runShowAnim" which executes animShow.run(); for an animation effect...
var runShowAnim = function(e) {
animShow.run();
};
I want this effect to happen when i validate something in a javascript function. I tried to call it as below. But it doesn't seem to work.
function notifyUser(message) {
document.getElementById("msgArea").innerHTML = message;
runShowAnim();
}

I achieved this by sandwiching the YUI function completely inside a function and calling that function..
var runShowAnim = function() {
YUI().use('anim', 'node', function(Y) {
var animShow = new Y.Anim({
node: '#msgArea',
to: { height: 50,opacity:1 }
});
animShow.run();
});
};
now i can call runShowAnim without any problem like in the below sample function..
function notifyUser(message) {
document.getElementById("msgArea").innerHTML = message;
runShowAnim();
}

If you want to call a function, you have to suffix the function name with () and include 0 or more comma separated arguments between them.
runShowAnim();
If the function doesn't have global scope (as yours will have if it is declared inside a function passed to use()) and not passed outside in some way then you can only do this from the same scope.

I think you're missing the parentheses.
function notifyUser(message) {
document.getElementById("msgArea").innerHTML = message;
runShowAnim(); // right here
}

YUI.thefunction()?
I think you need to call it with namespace too
something similar to
var X = function(){};
X.Y = function(){};
X.Y.Z = function(){};
X.Y.Z.foo = function(e){alert(e);}
//foo("me");<-error
X.Y.Z.foo("me");

If you want to call a function that has been defined inside the closure (the function passed as the last parameter to YUI.use) from outside it, you need to expose the function globally.
Either define a global variable outside the closure and assign your function to it, or assign your function to the window object
i.e.
var runShowAnim;
YUI().use(function(e){
runShowAnim = function(){alert('called');}
});
runShowAnim();

JavaScript function declaration

Are the JavaScript code snippets given below some sort of function declaration? If not can someone please give an overview of what they are?
some_func = function(value) {
// some code here
}
and
show:function(value){
// some code here
}

There are six ways/contexts in which to create functions:
1) Standard declarative notation (most familiar to people with C background)
function foo() {}
All the rest are function expressions:
2) As a method of an object literal
var obj = {
foo: function() {}
};
3) As a method of an instantiated object (created each time new is exectued)
var Obj = function() {
this.foo = function() {};
};
4) As a method of a prototype (created only once, regardless of how many times new is executed)
var Obj = function() {};
Obj.prototype.foo = function() {};
5) As an anonymous function with a reference (same effect as #1) *
var foo = function() {};
6) As an immediately executed anonymous function (completely anonymous)
(function() {})();
* When I look at this statement, I consider the result. As such, I don't really consider these as anonymous, because a reference is immediately created to the function and is therefore no longer anonymous. But it's all the same to most people.

The first one is simply creating an anonymous function and assigning it to a variable some_func. So using some_func() will call the function.
The second one should be part of an object notation
var obj = {
show:function(value){
// some code here
}
};
So, obj.show() will call the function
In both cases, you are creating an anonymous function. But in the first case, you are simply assigning it to a variable. Whereas in the second case you are assigning it as a member of an object (possibly among many others).

First is local (or global) variable with assigned anonymous function.
var some_name = function(val) {};
some_name(42);
Second is property of some object (or function with label in front of it) with assigned anonymous function.
var obj = {
show: function(val) {},
// ...
};
obj.show(42);
Functions are first-class citizens in JavaScript, so you could assign them to variables and call those functions from variable.
You can even declare function with other name than variable which that function will be assigned to. It is handy when you want to define recursive methods, for example instead of this:
var obj = {
show: function(val) {
if (val > 0) { this.show(val-1); }
print(val);
}
};
you could write:
var obj = {
show: function f(val) {
if (val > 0) { f(val-1); }
print(val);
}
};

One way of doing it:
var some_func = function(value) {
// some code here
}
Another way:
function some_funct() {
}
Yet another way:
var some_object={};
some_object["some_func"] = function() {};
or:
var some_object={};
some_object.some_func = function() {};
In other words, they are many ways to declare a function in JS.
Your second example is not correct.

The first one is a function declaration assigned to a variable (at least it should be, despite the fact that it's missing the variable type declaration first), the second one is probably related to a object declaration.

They are called anonymous functions; you can read more about them here:
http://www.ejball.com/EdAtWork/2005/03/28/JavaScriptAnonymousFunctions.aspx

The first example creates a global variable (if a local variable of that name doesn't already exist) called some_func, and assigns a function to it, so that some_func() may be invoked.
The second example is a function declaration inside an object. it assigns a function as the value of the show property of an object:
var myObj = {
propString: "abc",
propFunction: function() { alert('test'); }
};
myObj.propFunction();

The first one...
some_func = function(value) {
// some code here
}
is declaring a variable and assigned an anonymous function to it, which is equivalent to...
function some_func (value) {
// some code here
}
The second one should look like this...
obj = {
show:function(value){
// some code here
}
}
// obj.show(value)
and equivalent to...
//pseudo code
class MyClass {
function show (value) {
// some code here
}
}
obj = new MyClass(); // obj.show(value)
Cheers