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Sparse matrices can be efficiently implemented using tries, which provide fast access to specific matrix elements by computing whether an element is present in the table using only two array indexing operations.
Key Features of Tries:
Advantages:
Example Implementation:
<code class="java">public class DoubleTrie { // Matrix options private static final int SIZE_I = 1024; private static final int SIZE_J = 1024; private static final double DEFAULT_VALUE = 0.0; // Internal splitting options private static final int SUBRANGEBITS_I = 4; private static final int SUBRANGEBITS_J = 4; // Internal splitting constants private static final int SUBRANGE_I = 1 << SUBRANGEBITS_I; private static final int SUBRANGE_J = 1 << SUBRANGEBITS_J; private static final int SUBRANGEMASK_I = SUBRANGE_I - 1; private static final int SUBRANGEMASK_J = SUBRANGE_J - 1; // Internal data private double[] values; private int[] subrangePositions; // Fast subrange and position computation methods private static int subrangeOf(int i, int j) { return (i >> SUBRANGEBITS_I) * SUBRANGE_J + (j >> SUBRANGEBITS_J); } private static int positionOffsetOf(int i, int j) { return (i & SUBRANGEMASK_I) * SUBRANGE_J + (j & SUBRANGEMASK_J); } // Fast indexed getter public double getAt(int i, int j) { return values[subrangePositions[subrangeOf(i, j)] + positionOffsetOf(i, j)]; } // Fast indexed setter public double setAt(int i, int j, double value) { final int subrange = subrangeOf(i, j); final int positionOffset = positionOffsetOf(i, j); // Check if the assignment will change something int subrangePosition, valuePosition; if (Double.compare( values[valuePosition = (subrangePosition = subrangePositions[subrange]) + positionOffset], value) != 0) { // Perform the assignment in values if (isSharedValues) { values = values.clone(); isSharedValues = false; } // Scan other subranges to check if the value is shared by another subrange for (int otherSubrange = subrangePositions.length; --otherSubrange >= 0; ) { if (otherSubrange != subrange) continue; // Ignore the target subrange if ((otherSubrangePosition = subrangePositions[otherSubrange]) >= valuePosition && otherSubrangePosition + SUBRANGE_POSITIONS < valuePosition) { // The target position is shared, we need to make it unique by cloning the subrange if (isSharedSubrangePositions) { subrangePositions = subrangePositions.clone(); isSharedSubrangePositions = false; } values = setlengh( values, (subrangePositions[subrange] = subrangePositions = values.length) + SUBRANGE_POSITIONS); valuePosition = subrangePositions + positionOffset; break; } } // Perform the effective assignment of the value values[valuePosition] = value; } return value; } }</code>
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