If your current implementation has complexity O(log N) for interpolating a value, the implementation I just made up may be for you:
package so2675929;
import java.util.Arrays;
public abstract class AbstractInterpolator {
private double[] keys;
private double[] values;
private int size;
public AbstractInterpolator(int initialCapacity) {
keys = new double[initialCapacity];
values = new double[initialCapacity];
}
public final void put(double key, double value) {
int index = indexOf(key);
if (index >= 0) {
values[index] = value;
} else {
if (size == keys.length) {
keys = Arrays.copyOf(keys, size + 32);
values = Arrays.copyOf(values, size + 32);
}
int insertionPoint = insertionPointFromIndex(index);
System.arraycopy(keys, insertionPoint, keys, insertionPoint + 1, size - insertionPoint);
System.arraycopy(values, insertionPoint, values, insertionPoint + 1, size - insertionPoint);
keys[insertionPoint] = key;
values[insertionPoint] = value;
size++;
}
}
public final boolean containsKey(double key) {
int index = indexOf(key);
return index >= 0;
}
protected final int indexOf(double key) {
return Arrays.binarySearch(keys, 0, size, key);
}
public final int size() {
return size;
}
protected void ensureValidIndex(int index) {
if (!(0 <= index && index < size))
throw new IndexOutOfBoundsException("index=" + index + ", size=" + size);
}
protected final double getKeyAt(int index) {
ensureValidIndex(index);
return keys[index];
}
protected final double getValueAt(int index) {
ensureValidIndex(index);
return values[index];
}
public abstract double get(double key);
protected static int insertionPointFromIndex(int index) {
return -(1 + index);
}
}
The concrete interpolators will only have to implement the get(double) function.
For example:
package so2675929;
public class LinearInterpolator extends AbstractInterpolator {
public LinearInterpolator(int initialCapacity) {
super(initialCapacity);
}
@Override
public double get(double key) {
final double minKey = getKeyAt(0);
final double maxKey = getKeyAt(size() - 1);
if (!(minKey <= key && key <= maxKey))
throw new IndexOutOfBoundsException("key=" + key + ", min=" + minKey + ", max=" + maxKey);
int index = indexOf(key);
if (index >= 0)
return getValueAt(index);
index = insertionPointFromIndex(index);
double lowerKey = getKeyAt(index - 1);
double lowerValue = getValueAt(index - 1);
double higherKey = getKeyAt(index);
double higherValue = getValueAt(index);
double rate = (higherValue - lowerValue) / (higherKey - lowerKey);
return lowerValue + (key - lowerKey) * rate;
}
}
And, finally, a unit test:
package so2675929;
import static org.junit.Assert.*;
import org.junit.Test;
public class LinearInterpolatorTest {
@Test
public void simple() {
LinearInterpolator interp = new LinearInterpolator(2);
interp.put(0.0, 0.0);
interp.put(1.0, 1.0);
assertEquals(0.0, interp.getValueAt(0), 0.0);
assertEquals(1.0, interp.getValueAt(1), 0.0);
assertEquals(0.0, interp.get(0.0), 0.0);
assertEquals(0.1, interp.get(0.1), 0.0);
assertEquals(0.5, interp.get(0.5), 0.0);
assertEquals(0.9, interp.get(0.9), 0.0);
assertEquals(1.0, interp.get(1.0), 0.0);
interp.put(0.5, 0.0);
assertEquals(0.0, interp.getValueAt(0), 0.0);
assertEquals(0.0, interp.getValueAt(1), 0.0);
assertEquals(1.0, interp.getValueAt(2), 0.0);
assertEquals(0.0, interp.get(0.0), 0.0);
assertEquals(0.0, interp.get(0.1), 0.0);
assertEquals(0.0, interp.get(0.5), 0.0);
assertEquals(0.75, interp.get(0.875), 0.0);
assertEquals(1.0, interp.get(1.0), 0.0);
}
@Test
public void largeKeys() {
LinearInterpolator interp = new LinearInterpolator(10);
interp.put(100.0, 30.0);
interp.put(200.0, 40.0);
assertEquals(30.0, interp.get(100.0), 0.0);
assertEquals(35.0, interp.get(150.0), 0.0);
assertEquals(40.0, interp.get(200.0), 0.0);
try {
interp.get(99.0);
fail();
} catch (IndexOutOfBoundsException e) {
assertEquals("key=99.0, min=100.0, max=200.0", e.getMessage());
}
try {
interp.get(201.0);
fail();
} catch (IndexOutOfBoundsException e) {
assertEquals("key=201.0, min=100.0, max=200.0", e.getMessage());
}
}
private static final int N = 10 * 1000 * 1000;
private double measure(int size) {
LinearInterpolator interp = new LinearInterpolator(size);
for (int i = 0; i < size; i++)
interp.put(i, i);
double max = interp.size() - 1;
double sum = 0.0;
for (int i = 0; i < N; i++)
sum += interp.get(max * i / N);
return sum;
}
@Test
public void speed10() {
assertTrue(measure(10) > 0.0);
}
@Test
public void speed10000() {
assertTrue(measure(10000) > 0.0);
}
@Test
public void speed1000000() {
assertTrue(measure(1000000) > 0.0);
}
}
So the functionality seems to work. I only measured speed in some simple cases, and these suggest that scaling will be better than linear.
Update (2010-10-17T23:45+0200): I made some stupid mistakes in checking the key argument in the LinearInterpolator, and my unit tests didn't catch them. Now I extended the tests and fixed the code accordingly.