Shrink an array of double elements (uniformly)

Question

Is there a way to avoid the first loop in the method shrink? (if and while...)

The utility method shrink should reduce the elements of a double array by picking up elements from the original array "with a regular step respectively offset size"... but the first element should always be included, and the last element too, if possible.

    public static double[] shrink(final double[] data, final int len) {
        if (data.length == 0 || len < 1) {
            throw new IllegalArgumentException("data.length == 0 || len < 1");
        }
        double[] d = new double[len];
        double step = (double) data.length / len;
        if (len > 1) {
            int i = 1;
            while (Math.round(step * (len - 1)) < data.length - 1) {
                step = (double) (data.length + i) / len;
                i++;
            }
        }
        for (int i = 0; i < len; i++) {
            int j = (int) Math.round(i * step);
            d[i] = data[j];
        }
        return d;
    }

    public static void testShrink() {
        double[] data1 = {1, 2, 3, 4, 5, 6};
        for (int i = 1; i <= data1.length; i++) {
            double[] data = new double[i];
            System.arraycopy(data1, 0, data, 0, i);
            for (int j = 1; j <= i; j++) {
                double[] result = shrink(data, j);
                System.out.println(i + " " + j + " " + Arrays.toString(result));
            }
        }
    }

The output of the method testShrink should look like the following:

1 1 [1.0]
2 1 [1.0]
2 2 [1.0, 2.0]
3 1 [1.0]
3 2 [1.0, 3.0]
3 3 [1.0, 2.0, 3.0]
4 1 [1.0]
4 2 [1.0, 4.0]
4 3 [1.0, 2.0, 4.0]
4 4 [1.0, 2.0, 3.0, 4.0]
5 1 [1.0]
5 2 [1.0, 5.0]
5 3 [1.0, 3.0, 5.0]
5 4 [1.0, 2.0, 4.0, 5.0]
5 5 [1.0, 2.0, 3.0, 4.0, 5.0]
6 1 [1.0]
6 2 [1.0, 6.0]
6 3 [1.0, 3.0, 6.0]
6 4 [1.0, 3.0, 4.0, 6.0]
6 5 [1.0, 2.0, 3.0, 5.0, 6.0]
6 6 [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]

I think, it's also a mathematical-like question.

Your interface does not lend itself to a regular step, since you only ask for an output length. A good implementation would vary between two different steps in a dithered manner, or would interpolate. — Reinderien
– Reinderien, Commented Oct 5, 2023 at 12:47
What is the purpose and application of this function? Should it interpolate; i.e. should it take the average of two values when it "lands in the middle" between them? — Reinderien
– Reinderien, Commented Oct 5, 2023 at 12:50
(your current implementation with round() is basically the dithered one, with a non-uniform step; but could be improved) — Reinderien
– Reinderien, Commented Oct 5, 2023 at 13:11
Thanks for your comment @Reinderien. The purpose of the method is to compress a stock market chart horizontally. Therefore, it is unimportant (for me) whether an average would be formed or whether the corresponding elements simply no longer occur. — Tobias Grothe
– Tobias Grothe, Commented Oct 5, 2023 at 13:17

Reinderien · Accepted Answer · 2023-10-05 23:51:07Z

I don't understand the first loop. It seems like a successive approximation calculation for the step size, but that shouldn't be necessary. Instead, we know that you have two defined endpoints of a linear function:

$$f(0) = 0$$ $$f(n-1) = m-1$$ $$i = f(j) = \frac {j(m-1)} {n-1}$$

That gives you your step size. It's easy enough to prevent divide-by-zero by having 1 as the minimum denominator; this also allows for len=0 to act as expected (returning an empty array).

public static double[] shrink(double[] data, int len) {
    if (data.length < 1 || len < 0)
        throw new IllegalArgumentException("data.length < 1 || len < 0");

    double[] d = new double[len];
    double step = (data.length - 1.0d)/Integer.max(len - 1, 1);
    
    for (int j = 0; j < len; ++j) {
        int i = (int)Math.round(j * step);
        d[j] = data[i];
    }
    return d;
}

Note that since this doesn't use interpolation, it introduces alias error.

Thanks, I simply didn't have seen this: double step = (double) (data.length - 1) / (len - 1);. — Tobias Grothe
– Tobias Grothe, Commented Oct 6, 2023 at 7:38

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