I need to know how to represent the following as a mathematical formula using proper math notation:
I have a $1\times n$-matrix of $3$-tuples $[a, r, x]$. I need to represent the following logic mathematically:
for each element in the matrix set $x = a r-a+1$ then $$X = x_0 \cdot x_1\cdot\ldots\cdot x_n$$ $$A = \operatorname{average}(a_0,\ldots,a_n)$$ $$Z = X \cdot A$$
In C#:
struct Element
{
public double a;
public double r;
public double x;
}
private void button15_Click(object sender, EventArgs e)
{
// define the matrix
Element[] matrix = new Element[3];
Element elem;
// populate the matrix with something
matrix[0] = new Element { a = 1, r = 0.9 };
matrix[1] = new Element { a = 0.75, r = 0.2 };
matrix[2] = new Element { a = 1, r = 1 };
// for each element, calculate x
for (int i = 0; i < matrix.Length; i++)
{
elem = matrix[i];
elem.x = elem.a * elem.r - elem.a + 1;
}
// determine X and A
elem = matrix[0];
double X = elem.x;
double A = elem.a;
// calculate for each element, starting at 1
for (int i = 1; i < matrix.Length; i++)
{
elem = matrix[i];
X *= elem.x;
A += elem.a;
}
A /= matrix.Length;
// X is equal to matrix[0].x * matrix[1].x * matrix[2].x
// A is equal to Average(matrix[0].a, matrix[1].r, matrix[2].r)
double Z = X * A;
}