Quick Beginner Question

[gh24]

Hi Guys,

This is a very quick question. I am using newmat so matrices can be used as if they are simple variables from my understanding. I am writing a recursive code and need to do something like the following:

Matrix * [recursive function]

Is this possible?

Can you multiply a number and a function?

[Mathhead200]

double f(double x) {
    return x*x - 4;
}

int main() {
    int y = 2 * f(5); //y = 2 * (5*5 - 4)
    //Your not multiplying by a function, but by whatever value it returns.
}

[gh24]

That's a much better way to look at it. Thanks.

[gh24]

So I thought I had figured this one out but I can only get singular solutions that don't apply to all inputs.... shoooooot. Here is my actual code for the matrix * recursive function part that I am trying to figure out:

	if(k > 1 && k % 2!= 0){
		cout << 2 << endl;
		C=(B*B);
	B * repeated_squaring(B*B, n, (k-1)/2);

A bit of an explanation. I am trying to write a recursive code for the Repeated Squaring Algorithm, but with a matrix instead of an integer. B is my matrix, n is an input specifying the matrix size and does not change, this is only for a square matrix so multiplication is always possible, and k is the power that the matrix is being multiplied to. This is the part of the function that should be initiated when k is odd.

ALSO: C is in there because I was trying to manipulate the recursive solution to not have to be multiplied by B by changing the multiplication inside the matrix. Unfortunately this can't be done so that it works for any n or k.

[gh24]

here is the full code for the repeated squaring function:

void repeated_squaring(Matrix B, int n, int k)
{
	Matrix C;
	Matrix D(n,n);D=2;
	{
	if (k == 1){
		cout << 1 << endl;
		cout << B << endl;
		exit(0);
	}

	if(k > 1 && k % 2!= 0){
		cout << 2 << endl;
		C=(B*B);
	B * repeated_squaring(B*B, n, (k-1)/2);
	
	}
	else{
		cout << 3 << endl; 
			cout<< B << endl;
		repeated_squaring(B*B,n,k/2);
	}
	}
}

[gh24]

Please help if you happen to still be awake! I do appreciate anything and everything and any suggestion is worth a shot, i'm frankly out of ideas at this point.

[Mathhead200]

I used this for a reference as I've never used this algorithm before: http://en.wikipedia.org/wiki/Exponentiation_by_squaring#Underlying_idea

//Assume to following matrix class is used:

class Matrix
{
 private:
	//internal stuff
	...

 public:
	const int rows;
	const int cols;

	/**
	 * @return The identity matrix of size n by n
	 * @throws InvalidArgumentException if n == 0
	 */
	static Matrix identity(unsigned int n);
	
	/**
	 * @return The inverse matrix
	 * @throws NonSquareMatrixException
	 * @throws SingularMatrixException
	 */
	Matrix inverse();
	
	/**
	 * @param a
	 * @param b
	 * @return a times b, using standard matrix multiplication
	 * @throws InvalidArgumentException if a.cols != b.rows
	 */
	friend Matrix operaotr*(const Matrix &a, const Matrix &b);
	
	/**
	 * (exponentiation)
	 * @param n, the exponent
	 * @return the given matrix to the power of n if n is positive,
	 *         the identity matrix if n is negative,
	 *         or the inverse of the given matrix to the -n power if n is negative
	 * @throws NonSquareMatrixException
	 * @throws SingularMatrixException if n is less then 0 and the given matrix is singular
	 */
	Matrix pow(int n);
};


//definitions for Matrix class's members and friends
...

Matrix Matrix::pow(int n) {
	if( rows != cols )
		throw NonSquareMatrixException();

	if( n == 1 )
		return Matrix::identity(rows);

	if( n < 0 )
		return pow(-n).inverse();
	
	//to avoid infinite recursion
	if( n == 2 )
		return (*this) * (*this);
	
	//n is odd
	if( n % 2 != 0 )
		return *this * pow((n - 1) / 2).pow(2);
	
	//n is even
	return pow(n / 2).pow(2);
}