dimanche 31 mai 2015

How to generate some identically distributed pseudo-random vectors with a fixed length r in a programming language?

For example, for the dimension d=2, it means that we could generate a random angle 0<=a<2*pi, and then we could just use (x_1,x_2)=(rcos(a),rsin(a)) as the random vector.

However, for the dimension d>=3, we could not just generate an angle and use it to represent the vector. Then how could we generate such a vector (x_1,...,x_d), which is identically distributed on x_1^2+x_2^2+...+x_d^2=r^2?




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