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java.lang.Object cern.colt.PersistentObject cern.colt.matrix.doublealgo.Sorting
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
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Sorting
,
Arrays
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Serialized FormField Summary  
static Sorting 
mergeSort
A prefabricated mergesort. 
static Sorting 
quickSort
A prefabricated quicksort. 
Fields inherited from class cern.colt.PersistentObject 
serialVersionUID 
Method Summary  
DoubleMatrix1D 
sort(DoubleMatrix1D vector)
Sorts the vector into ascending order, according to the natural ordering. 
DoubleMatrix1D 
sort(DoubleMatrix1D vector,
DoubleComparator c)
Sorts the vector into ascending order, according to the order induced by the specified comparator. 
DoubleMatrix2D 
sort(DoubleMatrix2D matrix,
BinFunction1D aggregate)
Sorts the matrix rows into ascending order, according to the natural ordering of the values computed by applying the given aggregation function to each row; Particularly efficient when comparing expensive aggregates, because aggregates need not be recomputed time and again, as is the case for comparator based sorts. 
DoubleMatrix2D 
sort(DoubleMatrix2D matrix,
double[] 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. 
DoubleMatrix2D 
sort(DoubleMatrix2D matrix,
DoubleMatrix1DComparator c)
Sorts the matrix rows according to the order induced by the specified comparator. 
DoubleMatrix2D 
sort(DoubleMatrix2D matrix,
int column)
Sorts the matrix rows into ascending order, according to the natural ordering of the matrix values in the given column. 
DoubleMatrix3D 
sort(DoubleMatrix3D matrix,
DoubleMatrix2DComparator c)
Sorts the matrix slices according to the order induced by the specified comparator. 
DoubleMatrix3D 
sort(DoubleMatrix3D 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. 
static void 
zdemo1()
Demonstrates advanced sorting. 
static void 
zdemo2()
Demonstrates advanced sorting. 
static void 
zdemo3()
Demonstrates advanced sorting. 
static void 
zdemo5(int rows,
int columns,
boolean print)
Demonstrates sorting with precomputation of aggregates (median and sum of logarithms). 
static void 
zdemo6()
Demonstrates advanced sorting. 
static void 
zdemo7(int rows,
int columns,
boolean print)
Demonstrates sorting with precomputation of aggregates, comparing mergesort with quicksort. 
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 
public static final Sorting quickSort
public static final Sorting mergeSort
Method Detail 
public DoubleMatrix1D sort(DoubleMatrix1D vector)
Example:
7, 1, 3, 1 
==> 1, 1, 3, 7 
vector
 the vector to be sorted.
public DoubleMatrix1D sort(DoubleMatrix1D vector, DoubleComparator c)
Example:
// sort by sinus of cells DoubleComparator comp = new DoubleComparator() { public int compare(double a, double b) { double as = Math.sin(a); double 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 DoubleMatrix2D sort(DoubleMatrix2D matrix, double[] aggregates)
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and viceversa. To sort ranges use subranging 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) DoubleMatrix2D matrix = new DenseDoubleMatrix2D(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)); double[] aggregates = new double[matrix.rows()]; for (int i = matrix.rows(); i >= 0; ) aggregates[i] = matrix.viewRow(i).aggregate(F.plus, F.log); DoubleMatrix2D sorted = quickSort(matrix,aggregates); // THE SLOW VERSION (takes some 90 secs) DoubleMatrix1DComparator comparator = new DoubleMatrix1DComparator() { public int compare(DoubleMatrix1D x, DoubleMatrix1D y) { double a = x.aggregate(F.plus,F.log); double b = y.aggregate(F.plus,F.log); return a < b ? 1 : a==b ? 0 : 1; } }; DoubleMatrix2D 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 DoubleMatrix2D sort(DoubleMatrix2D 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 DoubleMatrix2D sort(DoubleMatrix2D matrix, DoubleMatrix1DComparator c)
Example:
// sort by sum of values in a row DoubleMatrix1DComparator comp = new DoubleMatrix1DComparator() { public int compare(DoubleMatrix1D a, DoubleMatrix1D b) { double as = a.zSum(); double 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 DoubleMatrix2D sort(DoubleMatrix2D matrix, BinFunction1D aggregate)
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and viceversa. To sort ranges use subranging 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= hep.aida.bin.BinFunctions1D.sum ==> 
4 x 2 matrix: 
// sort 10000 x 1000 matrix by median or by sum of logarithms in a row (i.e. by geometric mean) DoubleMatrix2D matrix = new DenseDoubleMatrix2D(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 10 secs) DoubleMatrix2D sorted = quickSort(matrix,hep.aida.bin.BinFunctions1D.median); //DoubleMatrix2D sorted = quickSort(matrix,hep.aida.bin.BinFunctions1D.sumOfLogarithms); // THE SLOW VERSION (takes some 300 secs) DoubleMatrix1DComparator comparator = new DoubleMatrix1DComparator() { public int compare(DoubleMatrix1D x, DoubleMatrix1D y) { double a = cern.colt.matrix.doublealgo.Statistic.bin(x).median(); double b = cern.colt.matrix.doublealgo.Statistic.bin(y).median(); // double a = x.aggregate(F.plus,F.log); // double b = y.aggregate(F.plus,F.log); return a < b ? 1 : a==b ? 0 : 1; } }; DoubleMatrix2D sorted = quickSort(matrix,comparator); 
matrix
 the matrix to be sorted.aggregate
 the function to sort on; aggregates values in a row.
public DoubleMatrix3D sort(DoubleMatrix3D matrix, int row, int column)
The algorithm compares two 2d 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 2d 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 DoubleMatrix3D sort(DoubleMatrix3D matrix, DoubleMatrix2DComparator c)
Example:
// sort by sum of values in a slice DoubleMatrix2DComparator comp = new DoubleMatrix2DComparator() { public int compare(DoubleMatrix2D a, DoubleMatrix2D b) { double as = a.zSum(); double 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 static void zdemo1()
public static void zdemo2()
public static void zdemo3()
public static void zdemo5(int rows, int columns, boolean print)
public static void zdemo6()
public static void zdemo7(int rows, int columns, boolean print)

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