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Using nonlinear square fit in C#

I'm trying to find a fit function that has the form:
f(x) = P / (1 + e^((x + m) / s)
Where P is a known constant. I'm fitting this function to a list of measured doubles (between 20-100 elements) and all these values has a corresponding x-value. I'm relatively new to C# and not very in to the maths either so I find it kind of hard to read the documentation available.
I have tried using AlgLib, but don't know where to start or what function to use.
Edit: So to precise what I#m looking for: I'd like to find a C# method where i can pass the functions form, aswell as some coordinates (x- and y-values) and have the method returning the two unknown variables (s and m above).

I use AlgLib daily for exactly this purpose. If you go to the link http://www.alglib.net/docs.php and scroll all the way down, you'll find the documentation with code examples in a number of languages (including C#) that I think will help you immensely: http://www.alglib.net/translator/man/manual.csharp.html
For your problem, you should consider all the constraints you need, but a simple example of obtaining a nonlinear least-squares fit given your input function and data would look something like this:
public SomeReturnObject Optimize(SortedDictionary<double, double> dataToFitTo, double p, double initialGuessM, double initialGuessS)
{
var x = new double[dataToFitTo.Count,1];
for(int i=0; i < dataToFitTo.Count; i++)
{
x[i, 0] = dataToFitTo.Keys.ElementAt(i);
}
var y = dataToFitTo.Values.ToArray();
var c = new[] {initialGuessM, initialGuessS};
int info;
alglib.lsfitstate state;
alglib.lsfitreport rep;
alglib.lsfitcreatef(x, y, c, 0.0001, out state);
alglib.lsfitsetcond(state, epsf, 0, 0);
alglib.lsfitfit(state, MyFunc, null, p);
alglib.lsfitresults(state, out info, out c, out rep);
/* When you get here, the c[] array should have the optimized values
for m and s, so you'll want to handle accordingly depending on your
needs. I'm not sure if you want out parameters for m and s or an
object that has m and s as properties. */
}
private void MyFunc(double[] c, double[] x, ref double func, object obj)
{
var xPt = x[0];
var m = c[0];
var s = c[1];
var P = (double)obj;
func = P / (1 + Math.Exp((xPt + m) / s));
}
Mind you, this is just a quick and dirty example. There is a lot of built-in functionality in Alglib so you'll need to adjust the problem code here to suit your needs with boundary constraints, weighting, step size, variable scaling....etc. It should be clear how to do all that from the examples and documentation in the second link.
Also note that Alglib is very particular about the method signature of MyFunc, so I would avoid moving around those inputs or adding any more.
Alternatively, you can write your own Levenberg-Marquardt algorithm if Alglib doesn't satisfy all your needs.

Datatype to store math expressions and do operations with

I would like to store math expressions and do operations with, something like:
a=x^2+2x+1
b=2x+3
c=a+b
writeln(c(4)) - would calculate and write the answer of 36
Is there a math library that allows this kind of coding in C# ?

If you want to calculate the same expressions every time, delegates are a good idea as #Paul Griffin suggested. But if you have very different expressions, you will likely have to build your own parsing algorithm or find an existing one. In this case it would be a duplicate of Parse Math Expression.

I don't know about a math library per se, but you could certainly do what you are showing us here with delegates. Off the top of my head (EDIT: a little better example):
delegate int myDelegate(int x);
var a = new myDelegate(x => (Math.Pow(x, 2)) + (2*x) + 1));
var b = new myDelegate(x => (2*x) + 3);
var c = new myDelegate(x => a(x) + b(x));
Console.WriteLine(c(4));
//Output: 36

Converting string to function

I want to build in my application the possibility of drawing mathematical functions. In the plotting library that I'm using (OxyPlot) there is a great support for that. See this example:
y = ax³ + bx² + cx + d = 0
is being plotted this way:
new FunctionSeries( x => a*x*x*x + b*x*x + c*x + d, /* other stuff, spacing, number of points, etc */ )
Trigonometrical functions are done the same way:
y = sin(3x) + 5cos(x)
is
new FunctionSeries(x => Math.Sin(3*x) + 5*Math.Cos(x) , ....);
I would be very happy if someone could guide me in the conversion between a string (written in a textbox for example) and a call of a method that has inside the syntax shown.
EDIT: the first parameter in the FunctionSeries(a, ....) a is Func<double, double>
EDIT2: Is there a way to say to the compiler, hey, believe me "x => 5*x*x" is a Func, take it literally
something like :
Func<double, double> f = (Func<double, double>)myString;

Here I have a partial solution:
var expresionData = new List<DataPoint>();
Regex pattern = new Regex("[x]");
for (int i = 0; i < 100; i++)
{
string a = pattern.Replace(ExpresionString, i.ToString());
NCalc.Expression exp = new NCalc.Expression(a);
expresionData.Add(new DataPoint(i,Double.Parse(exp.Evaluate().ToString())));
}
I'm doing a little trick here: I transform each 'x' in the typed string to i, then I evaluate the expression and add the point. It's pretty slow. I'm still very interested in the original question:
How to transform a string to Func<double, double> (or just make the compiler take it literally).

How to parse the following string

I am trying to generate a formula which could be anything like this, this is just a sample,
A + B + C > D - A
Now, A, B, C, D, etc are Column Names of a sheet (like excel sheet) i will be accessing in memory.
I need to generate a Rule, like the above A + B + C > D - A which will decide what kind of values user can add in a Cell.
Currently this is how i have begun:
string toValidate = "A + B + C > D + E - A";
string lhs = "", rhs = "";
string[] comparisonOperators = new string[] { "=", ">", "<", "<>", "!=" };
char[] arithmeticOperators = { '+', '-', '/', '*' };
toValidate = toValidate.Replace(#" ", "");
for (int i = 0; i < comparisonOperators.Length; i++)
{
if (toValidate.Contains(comparisonOperators[i]))
{
operatorIndex = toValidate.IndexOf(comparisonOperators[i]);
break;
}
}
lhs = toValidate.Substring(0, operatorIndex);
rhs = toValidate.Substring(operatorIndex + 1);
string[] columnLhsList = lhs.Split(arithmeticOperators);
string[] columnRhsList = rhs.Split(arithmeticOperators);
However even though i have the strings as lhs and rhs and even my operator which > in the above code, i am not able to understand how can i apply the formula on the sheet itself. I just need to know which Column has which operator associated.
Since i have the individual column names, but not the operator before them, for e.g,
+ before A - before A in another case.
How do i parse the above please help.

It is, however, a very fun question if you want to make simple formula parsers like this yourself.
I advice you to check out this article, since it is very clearly written and understandable because of it.
Shunting-yard Algorithm

Personally, I would never try/dare to create my own formula expression parser. Instead, I would (and did) use one of the may available ones, e.g. NCalc over at CodePlex.com.
Using these tools, it is as easy as writing
Expression e = new Expression("2 + 3 * 5");
Debug.Assert(17 == e.Evaluate());
to get your formula evaluated.
Usually such libraries are very solid, well tested and have a rich function set. It would take ages (if ever) to do such a high quality library on my own.
To further cite the NCalc website, you can even use variables like e.g.:
Expression e = new Expression("Round(Pow([Pi], 2) + Pow([Pi2], 2) + [X], 2)");
e.Parameters["Pi2"] = new Expression("Pi * [Pi]");
e.Parameters["X"] = 10;
e.EvaluateParameter +=
delegate(string name, ParameterArgs args)
{
if (name == "Pi")
args.Result = 3.14;
};
Debug.Assert(117.07 == e.Evaluate());

Perform calculation on values in a string "3+4"

What is the best way to do calculations on values in a string, for example:
"(3.25 * 4) / 1.25 + 10"

You need to write math formula parser.
If you don't want to write your own, check out this one
http://www.codeproject.com/KB/cs/MathParserLibrary.aspx

Have you seen http://ncalc.codeplex.com ?
It's extensible, fast (e.g. has its own cache) enables you to provide custom functions and varaibles at run time by handling EvaluateFunction/EvaluateParameter events. Example expressions it can parse:
Expression e = new Expression("Round(Pow(Pi, 2) + Pow([Pi2], 2) + X, 2)");
e.Parameters["Pi2"] = new Expression("Pi * Pi");
e.Parameters["X"] = 10;
e.EvaluateParameter += delegate(string name, ParameterArgs args)
{
if (name == "Pi")
args.Result = 3.14;
};
Debug.Assert(117.07 == e.Evaluate());
It also handles unicode & many data type natively. It comes with an antler file if you want to change the grammer. There is also a fork which supports MEF to load new functions.
It also supports logical operators, date/time's strings and if statements.

Converting from infix to postfix notation is one way of solving this problem, as you can use a stack to parse and compute the expression.
There are a dozen solutions available online. Here's one of them.