public class LongSorting extends PersistentObject
This is another case demonstrating one primary goal of this library: Delivering easy to use, yet very efficient APIs. The sorts return convenient sort views. This enables the usage of algorithms which scale well with the problem size: For example, sorting a 1000000 x 10000 or a 1000000 x 100 x 100 matrix performs just as fast as sorting a 1000000 x 1 matrix. This is so, because internally the algorithms only move around integer indexes, they do not physically move around entire rows or slices. The original matrix is left unaffected.
The quicksort is a derivative of the JDK 1.2 V1.26 algorithms (which are, in turn, based on Bentley's and McIlroy's fine work). The mergesort is a derivative of the JAL algorithms, with optimisations taken from the JDK algorithms. Mergesort is stable (by definition), while quicksort is not. A stable sort is, for example, helpful, if matrices are sorted successively by multiple columns. It preserves the relative position of equal elements.
GenericSorting,
Sorting,
Arrays,
Serialized Form| Modifier and Type | Field and Description |
|---|---|
static LongSorting |
mergeSort
A prefabricated mergesort.
|
static LongSorting |
quickSort
A prefabricated quicksort.
|
| Modifier and Type | Method and Description |
|---|---|
LongMatrix1D |
sort(LongMatrix1D vector)
Sorts the vector into ascending order, according to the natural
ordering.
|
LongMatrix1D |
sort(LongMatrix1D vector,
LongComparator c)
Sorts the vector into ascending order, according to the order induced by
the specified comparator.
|
LongMatrix2D |
sort(LongMatrix2D matrix,
int column)
Sorts the matrix rows into ascending order, according to the natural
ordering of the matrix values in the given column.
|
LongMatrix2D |
sort(LongMatrix2D matrix,
long[] aggregates)
Sorts the matrix rows into ascending order, according to the natural
ordering of the matrix values in the virtual column
aggregates; Particularly efficient when comparing expensive
aggregates, because aggregates need not be recomputed time and again, as
is the case for comparator based sorts.
|
LongMatrix2D |
sort(LongMatrix2D matrix,
LongMatrix1DComparator c)
Sorts the matrix rows according to the order induced by the specified
comparator.
|
LongMatrix3D |
sort(LongMatrix3D matrix,
int row,
int column)
Sorts the matrix slices into ascending order, according to the natural
ordering of the matrix values in the given [row,column]
position.
|
LongMatrix3D |
sort(LongMatrix3D matrix,
LongMatrix2DComparator c)
Sorts the matrix slices according to the order induced by the specified
comparator.
|
int[] |
sortIndex(LongMatrix1D vector)
Sorts indexes of the
vector into ascending order. |
int[] |
sortIndex(LongMatrix1D vector,
LongComparator c)
Sorts indexes of the
vector according to the comparator
c. |
clonepublic static final LongSorting quickSort
public static final LongSorting mergeSort
public LongMatrix1D sort(LongMatrix1D vector)
Example:
| 7, 1, 3, 1 |
==> 1, 1, 3, 7 |
vector - the vector to be sorted.public int[] sortIndex(LongMatrix1D vector)
vector into ascending order.vector - public LongMatrix1D sort(LongMatrix1D vector, LongComparator c)
Example:
// sort by sinus of cells
IntComparator comp = new IntComparator() {
public int compare(int a, int b) {
int as = Math.sin(a);
int bs = Math.sin(b);
return as < bs ? -1 : as == bs ? 0 : 1;
}
};
sorted = quickSort(vector, comp);
vector - the vector to be sorted.c - the comparator to determine the order.public int[] sortIndex(LongMatrix1D vector, LongComparator c)
vector according to the comparator
c.vector - c - public LongMatrix2D sort(LongMatrix2D matrix, long[] aggregates)
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa. To sort ranges use sub-ranging views. To sort columns by rows, use dice views. To sort descending, use flip views ...
Example: Each aggregate is the sum of a row
| 4 x 2 matrix: 1, 1 5, 4 3, 0 4, 4 |
aggregates= 2 9 3 8 ==> |
4 x 2 matrix: |
// sort 10000 x 1000 matrix by sum of logarithms in a row (i.e. by geometric mean)
LongMatrix2D matrix = new DenseLongMatrix2D(10000, 1000);
matrix.assign(new cern.jet.random.engine.MersenneTwister()); // initialized randomly
cern.jet.math.Functions F = cern.jet.math.Functions.functions; // alias for convenience
// THE QUICK VERSION (takes some 3 secs)
// aggregates[i] = Sum(log(row));
int[] aggregates = new int[matrix.rows()];
for (int i = matrix.rows(); --i >= 0;)
aggregates[i] = matrix.viewRow(i).aggregate(F.plus, F.log);
LongMatrix2D sorted = quickSort(matrix, aggregates);
// THE SLOW VERSION (takes some 90 secs)
LongMatrix1DComparator comparator = new LongMatrix1DComparator() {
public int compare(LongMatrix1D x, LongMatrix1D y) {
int a = x.aggregate(F.plus, F.log);
int b = y.aggregate(F.plus, F.log);
return a < b ? -1 : a == b ? 0 : 1;
}
};
LongMatrix2D sorted = quickSort(matrix, comparator);
|
matrix - the matrix to be sorted.aggregates - the values to sort on. (As a side effect, this array will also
get sorted).IndexOutOfBoundsException - if aggregates.length != matrix.rows().public LongMatrix2D sort(LongMatrix2D matrix, int column)
Example:
| 4 x 2 matrix: 7, 6 5, 4 3, 2 1, 0 |
column = 0; |
4 x 2 matrix: |
matrix - the matrix to be sorted.column - the index of the column inducing the order.IndexOutOfBoundsException - if column < 0 || column >= matrix.columns().public LongMatrix2D sort(LongMatrix2D matrix, LongMatrix1DComparator c)
Example:
// sort by sum of values in a row
LongMatrix1DComparator comp = new LongMatrix1DComparator() {
public int compare(LongMatrix1D a, LongMatrix1D b) {
int as = a.zSum();
int bs = b.zSum();
return as < bs ? -1 : as == bs ? 0 : 1;
}
};
sorted = quickSort(matrix, comp);
matrix - the matrix to be sorted.c - the comparator to determine the order.public LongMatrix3D sort(LongMatrix3D matrix, int row, int column)
The algorithm compares two 2-d slices at a time, determinining whether one is smaller, equal or larger than the other. Comparison is based on the cell [row,column] within a slice. Let A and B be two 2-d slices. Then we have the following rules
matrix - the matrix to be sorted.row - the index of the row inducing the order.column - the index of the column inducing the order.IndexOutOfBoundsException - if
row < 0 || row >= matrix.rows() || column < 0 || column >= matrix.columns()
.public LongMatrix3D sort(LongMatrix3D matrix, LongMatrix2DComparator c)
Example:
// sort by sum of values in a slice
LongMatrix2DComparator comp = new LongMatrix2DComparator() {
public int compare(LongMatrix2D a, LongMatrix2D b) {
int as = a.zSum();
int bs = b.zSum();
return as < bs ? -1 : as == bs ? 0 : 1;
}
};
sorted = quickSort(matrix, comp);
matrix - the matrix to be sorted.c - the comparator to determine the order.Jump to the Parallel Colt Homepage