Random Even Logarithmic Distribution Between Two Doubles

Question

Maybe I'm over thinking this, but I'm trying to find a nice way to obtain random numbers between two points that are uniformly logarithmically distributed. Let's say I have two bounds 0.001 and 1000 and I want to find 6 random numbers that are logarithmically evenly distributed. So numbers such as these: 0.002, 0.033, 0.543, 1.634, 34.673, 765.234... now say I'm looking for 7 random numbers instead, they would be ordered approximately evenly in this range as well... I'm using Java

Answer 1

Is this what you want? I took numbers uniformly distributed over the range formed by the logs of the limits, then used Math.exp to convert back to the actual range. I sorted the result array because your examples showed sorted data. Delete the Arrays.sort call if you don't want that.

For simplicity, I skipped the bounds checking. Presumably, 0 < lowerLimit < upperLimit.

The checks for the limits are because rounding error could, at least in theory, lead to results just outside the required range.

import java.util.Arrays;
import java.util.Random;

public class Test {
  public static void main(String[] args) {
    Random rand = new Random(3);
    System.out.println(Arrays.toString(logRandom(rand, 0.001, 1000, 7)));
    System.out.println(Arrays.toString(logRandom(rand, 0.001, 1000, 7)));
    System.out.println(Arrays.toString(logRandom(rand, 0.001, 1000, 7)));
    System.out.println(Arrays.toString(logRandom(rand, 0.001, 1000, 7)));
  }

  public static double[] logRandom(Random rand, double lowerLimit,
      double upperLimit, int count) {
    double[] result = new double[count];
    double logLower = Math.log(lowerLimit);
    double logUpper = Math.log(upperLimit);
    for (int i = 0; i < count; i++) {
      double raw = rand.nextDouble();
      result[i] = Math.exp(raw * (logUpper - logLower) + logLower);
      if (result[i] < lowerLimit) {
        result[i] = lowerLimit;
      } else if (result[i] > upperLimit) {
        result[i] = upperLimit;
      }
    }
    Arrays.sort(result);
    return result;
  }

}