IntSorting
cern.colt.matrix.tint.algo

## Class IntSorting

• All Implemented Interfaces:
Serializable, Cloneable

```public class IntSorting
extends PersistentObject```
Matrix quicksorts and mergesorts. Use idioms like Sorting.quickSort.sort(...) and Sorting.mergeSort.sort(...) .

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
• ### Field Summary

Fields
Modifier and Type Field and Description
`static IntSorting` `mergeSort`
A prefabricated mergesort.
`static IntSorting` `quickSort`
A prefabricated quicksort.
• ### Method Summary

Methods
Modifier and Type Method and Description
`IntMatrix1D` `sort(IntMatrix1D vector)`
Sorts the vector into ascending order, according to the natural ordering.
`IntMatrix1D` ```sort(IntMatrix1D vector, IntComparator c)```
Sorts the vector into ascending order, according to the order induced by the specified comparator.
`IntMatrix2D` ```sort(IntMatrix2D matrix, int column)```
Sorts the matrix rows into ascending order, according to the natural ordering of the matrix values in the given column.
`IntMatrix2D` ```sort(IntMatrix2D matrix, int[] 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.
`IntMatrix2D` ```sort(IntMatrix2D matrix, IntMatrix1DComparator c)```
Sorts the matrix rows according to the order induced by the specified comparator.
`IntMatrix3D` ```sort(IntMatrix3D 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.
`IntMatrix3D` ```sort(IntMatrix3D matrix, IntMatrix2DComparator c)```
Sorts the matrix slices according to the order induced by the specified comparator.
`int[]` `sortIndex(IntMatrix1D vector)`
Sorts indexes of the `vector` into ascending order.
`int[]` ```sortIndex(IntMatrix1D vector, IntComparator c)```
Sorts indexes of the `vector` according to the comparator `c`.
• ### Methods inherited from class cern.colt.PersistentObject

`clone`
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Field Detail

• #### quickSort

`public static final IntSorting quickSort`
A prefabricated quicksort.
• #### mergeSort

`public static final IntSorting mergeSort`
A prefabricated mergesort.
• ### Method Detail

• #### sort

`public IntMatrix1D sort(IntMatrix1D vector)`
Sorts the vector into ascending order, according to the natural ordering. 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 descending, use flip views ...

Example:

 7, 1, 3, 1 ==> 1, 1, 3, 7 The vector IS NOT SORTED. The new VIEW IS SORTED.
Parameters:
`vector` - the vector to be sorted.
Returns:
a new sorted vector (matrix) view. Note that the original matrix is left unaffected.
• #### sortIndex

`public int[] sortIndex(IntMatrix1D vector)`
Sorts indexes of the `vector` into ascending order.
Parameters:
`vector` -
Returns:
sorted indexes
• #### sort

```public IntMatrix1D sort(IntMatrix1D vector,
IntComparator c)```
Sorts the vector into ascending order, according to the order induced by the specified comparator. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa. The algorithm compares two cells at a time, determinining whether one is smaller, equal or larger than the other. To sort ranges use sub-ranging views. To sort descending, use flip views ...

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);
```
Parameters:
`vector` - the vector to be sorted.
`c` - the comparator to determine the order.
Returns:
a new matrix view sorted as specified. Note that the original vector (matrix) is left unaffected.
• #### sortIndex

```public int[] sortIndex(IntMatrix1D vector,
IntComparator c)```
Sorts indexes of the `vector` according to the comparator `c`.
Parameters:
`vector` -
`c` -
Returns:
sorted indexes
• #### sort

```public IntMatrix2D sort(IntMatrix2D matrix,
int[] 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. Essentially, this algorithm makes expensive comparisons cheap. Normally each element of aggregates is a summary measure of a row. Speedup over comparator based sorting = 2*log(rows), on average. For this operation, quicksort is usually faster.

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: 1, 1 3, 0 4, 4 5, 4 The matrix IS NOT SORTED. The new VIEW IS SORTED.
 ``` // sort 10000 x 1000 matrix by sum of logarithms in a row (i.e. by geometric mean) IntMatrix2D matrix = new DenseIntMatrix2D(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); IntMatrix2D sorted = quickSort(matrix, aggregates); // THE SLOW VERSION (takes some 90 secs) IntMatrix1DComparator comparator = new IntMatrix1DComparator() { public int compare(IntMatrix1D x, IntMatrix1D 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; } }; IntMatrix2D sorted = quickSort(matrix, comparator); ```
Parameters:
`matrix` - the matrix to be sorted.
`aggregates` - the values to sort on. (As a side effect, this array will also get sorted).
Returns:
a new matrix view having rows sorted. Note that the original matrix is left unaffected.
Throws:
`IndexOutOfBoundsException` - if aggregates.length != matrix.rows().
• #### sort

```public IntMatrix2D sort(IntMatrix2D matrix,
int column)```
Sorts the matrix rows into ascending order, according to the natural ordering of the matrix values in the given column. 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:

 4 x 2 matrix: 7, 6 5, 4 3, 2 1, 0 column = 0; view = quickSort(matrix,column); System.out.println(view); ==> 4 x 2 matrix: 1, 0 3, 2 5, 4 7, 6 The matrix IS NOT SORTED. The new VIEW IS SORTED.
Parameters:
`matrix` - the matrix to be sorted.
`column` - the index of the column inducing the order.
Returns:
a new matrix view having rows sorted by the given column. Note that the original matrix is left unaffected.
Throws:
`IndexOutOfBoundsException` - if column < 0 || column >= matrix.columns().
• #### sort

```public IntMatrix2D sort(IntMatrix2D matrix,
IntMatrix1DComparator c)```
Sorts the matrix rows according to the order induced by the specified comparator. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa. The algorithm compares two rows (1-d matrices) at a time, determinining whether one is smaller, equal or larger than the other. To sort ranges use sub-ranging views. To sort columns by rows, use dice views. To sort descending, use flip views ...

Example:

``` // sort by sum of values in a row
IntMatrix1DComparator comp = new IntMatrix1DComparator() {
public int compare(IntMatrix1D a, IntMatrix1D b) {
int as = a.zSum();
int bs = b.zSum();
return as < bs ? -1 : as == bs ? 0 : 1;
}
};
sorted = quickSort(matrix, comp);
```
Parameters:
`matrix` - the matrix to be sorted.
`c` - the comparator to determine the order.
Returns:
a new matrix view having rows sorted as specified. Note that the original matrix is left unaffected.
• #### sort

```public IntMatrix3D sort(IntMatrix3D 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. 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 by other dimensions, use dice views. To sort descending, use flip views ...

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

• A < B iff A.get(row,column) < B.get(row,column)
• A == B iff A.get(row,column) == B.get(row,column)
• A > B iff A.get(row,column) > B.get(row,column)
Parameters:
`matrix` - the matrix to be sorted.
`row` - the index of the row inducing the order.
`column` - the index of the column inducing the order.
Returns:
a new matrix view having slices sorted by the values of the slice view matrix.viewRow(row).viewColumn(column). Note that the original matrix is left unaffected.
Throws:
`IndexOutOfBoundsException` - if row < 0 || row >= matrix.rows() || column < 0 || column >= matrix.columns() .
• #### sort

```public IntMatrix3D sort(IntMatrix3D matrix,
IntMatrix2DComparator c)```
Sorts the matrix slices according to the order induced by the specified comparator. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa. The algorithm compares two slices (2-d matrices) at a time, determinining whether one is smaller, equal or larger than the other. To sort ranges use sub-ranging views. To sort by other dimensions, use dice views. To sort descending, use flip views ...

Example:

``` // sort by sum of values in a slice
IntMatrix2DComparator comp = new IntMatrix2DComparator() {
public int compare(IntMatrix2D a, IntMatrix2D b) {
int as = a.zSum();
int bs = b.zSum();
return as < bs ? -1 : as == bs ? 0 : 1;
}
};
sorted = quickSort(matrix, comp);
```
Parameters:
`matrix` - the matrix to be sorted.
`c` - the comparator to determine the order.
Returns:
a new matrix view having slices sorted as specified. Note that the original matrix is left unaffected.