cern.colt.matrix.tint.impl

Class SparseIntMatrix2D

java.lang.Object

cern.colt.PersistentObject

cern.colt.matrix.AbstractMatrix

cern.colt.matrix.AbstractMatrix2D

cern.colt.matrix.tint.IntMatrix2D

cern.colt.matrix.tint.impl.SparseIntMatrix2D

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable

public class SparseIntMatrix2D
extends IntMatrix2D

Sparse hashed 2-d matrix holding int elements. First see the package summary and javadoc tree view to get the broad picture.

Implementation:

Note that this implementation is not synchronized. Uses a OpenIntIntHashMap, which is a compact and performant hashing technique.

Memory requirements:

Cells that

• are never set to non-zero values do not use any memory.
• switch from zero to non-zero state do use memory.
• switch back from non-zero to zero state also do use memory. However, their memory is automatically reclaimed from time to time. It can also manually be reclaimed by calling trimToSize().

worst case: memory [bytes] = (1/minLoadFactor) * nonZeros * 13.
best case: memory [bytes] = (1/maxLoadFactor) * nonZeros * 13.
Where nonZeros = cardinality() is the number of non-zero cells. Thus, a 1000 x 1000 matrix with minLoadFactor=0.25 and maxLoadFactor=0.5 and 1000000 non-zero cells consumes between 25 MB and 50 MB. The same 1000 x 1000 matrix with 1000 non-zero cells consumes between 25 and 50 KB.

Time complexity:

This class offers expected time complexity O(1) (i.e. constant time) for the basic operations get, getQuick, set, setQuick and size assuming the hash function disperses the elements properly among the buckets. Otherwise, pathological cases, although highly improbable, can occur, degrading performance to O(N) in the worst case. As such this sparse class is expected to have no worse time complexity than its dense counterpart DenseIntMatrix2D. However, constant factors are considerably larger.

Cells are internally addressed in row-major. Performance sensitive applications can exploit this fact. Setting values in a loop row-by-row is quicker than column-by-column, because fewer hash collisions occur. Thus

 for (int row = 0; row < rows; row++) {
     for (int column = 0; column < columns; column++) {
         matrix.setQuick(row, column, someValue);
     }
 }
 

is quicker than

 for (int column = 0; column < columns; column++) {
     for (int row = 0; row < rows; row++) {
         matrix.setQuick(row, column, someValue);
     }
 }
 

See Also:

cern.colt.map, OpenIntIntHashMap, Serialized Form

Constructor Summary

Constructors

Constructor and Description
SparseIntMatrix2D(int[][] values) Constructs a matrix with a copy of the given values.
SparseIntMatrix2D(int rows, int columns) Constructs a matrix with a given number of rows and columns and default memory usage.
SparseIntMatrix2D(int rows, int columns, int[] rowIndexes, int[] columnIndexes, int value) Constructs a matrix with a copy of the given indexes and a single value.
SparseIntMatrix2D(int rows, int columns, int[] rowIndexes, int[] columnIndexes, int[] values) Constructs a matrix with a copy of the given indexes and values.
SparseIntMatrix2D(int rows, int columns, int initialCapacity, double minLoadFactor, double maxLoadFactor) Constructs a matrix with a given number of rows and columns using memory as specified.
SparseIntMatrix2D(MatrixVectorReader reader) Constructs a matrix from MatrixVectorReader.

Method Summary

Modifier and Type	Method and Description
IntMatrix2D	assign(int value) Sets all cells to the state specified by value.
SparseIntMatrix2D	assign(int[] rowIndexes, int[] columnIndexes, int[] values, IntIntFunction function) Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]), where y is given in the coordinate form.
SparseIntMatrix2D	assign(int[] rowIndexes, int[] columnIndexes, int value, IntIntFunction function) Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]), where y is given in the coordinate form with single numerical value.
IntMatrix2D	assign(IntFunction function) Assigns the result of a function to each cell; x[row,col] = function(x[row,col]).
IntMatrix2D	assign(IntMatrix2D source) Replaces all cell values of the receiver with the values of another matrix.
IntMatrix2D	assign(IntMatrix2D y, IntIntFunction function) Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]).
int	cardinality() Returns the number of cells having non-zero values; ignores tolerance.
AbstractLongIntMap	elements() Returns the elements of this matrix.
void	ensureCapacity(int minCapacity) Ensures that the receiver can hold at least the specified number of non-zero (non-null) cells without needing to allocate new internal memory.
IntMatrix2D	forEachNonZero(IntIntIntFunction function) Assigns the result of a function to each non-zero cell; x[row,col] = function(x[row,col]).
SparseCCIntMatrix2D	getColumnCompressed(boolean sortRowIndexes) Returns a new matrix that has the same elements as this matrix, but is in a column-compressed form.
SparseCCMIntMatrix2D	getColumnCompressedModified() Returns a new matrix that has the same elements as this matrix, but is in a column-compressed modified form.
int	getQuick(int row, int column) Returns the matrix cell value at coordinate [row,column].
SparseRCIntMatrix2D	getRowCompressed(boolean sortColumnIndexes) Returns a new matrix that has the same elements as this matrix, but is in a row-compressed form.
SparseRCMIntMatrix2D	getRowCompressedModified() Returns a new matrix that has the same elements as this matrix, but is in a row-compressed modified form.
long	index(int row, int column) Returns the position of the given coordinate within the (virtual or non-virtual) internal 1-dimensional array.
IntMatrix2D	like(int rows, int columns) Construct and returns a new empty matrix of the same dynamic type as the receiver, having the specified number of rows and columns.
IntMatrix1D	like1D(int size) Construct and returns a new 1-d matrix of the corresponding dynamic type, entirelly independent of the receiver.
void	setQuick(int row, int column, int value) Sets the matrix cell at coordinate [row,column] to the specified value.
java.lang.String	toString() Returns a string representation using default formatting.
void	trimToSize() Releases any superfluous internal memory.
IntMatrix1D	vectorize() Returns a vector obtained by stacking the columns of the matrix on top of one another.
IntMatrix1D	zMult(IntMatrix1D y, IntMatrix1D z, int alpha, int beta, boolean transposeA) Linear algebraic matrix-vector multiplication; z = alpha * A * y + beta*z.
IntMatrix2D	zMult(IntMatrix2D B, IntMatrix2D C, int alpha, int beta, boolean transposeA, boolean transposeB) Linear algebraic matrix-matrix multiplication; C = alpha * A x B + beta*C.

Methods inherited from class cern.colt.matrix.tint.IntMatrix2D

aggregate, aggregate, aggregate, aggregate, assign, assign, assign, assign, assign, copy, equals, equals, get, getMaxLocation, getMinLocation, getNegativeValues, getNonZeros, getPositiveValues, like, set, toArray, viewColumn, viewColumnFlip, viewDice, viewPart, viewRow, viewRowFlip, viewSelection, viewSelection, viewSelection, viewSorted, viewStrides, zMult, zMult, zSum

Methods inherited from class cern.colt.matrix.AbstractMatrix2D

checkShape, checkShape, columns, columnStride, rows, rowStride, size, toStringShort

Methods inherited from class cern.colt.matrix.AbstractMatrix

isView

Methods inherited from class cern.colt.PersistentObject

clone

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

SparseIntMatrix2D

public SparseIntMatrix2D(int[][] values)

Constructs a matrix with a copy of the given values. values is required to have the form values[row][column] and have exactly the same number of columns in every row.

The values are copied. So subsequent changes in values are not reflected in the matrix, and vice-versa.

Parameters:

values - The values to be filled into the new matrix.

Throws:

java.lang.IllegalArgumentException - if for any 1 <= row < values.length: values[row].length != values[row-1].length .

SparseIntMatrix2D

public SparseIntMatrix2D(int rows,
                         int columns)

Constructs a matrix with a given number of rows and columns and default memory usage. All entries are initially 0.

Parameters:

rows - the number of rows the matrix shall have.

columns - the number of columns the matrix shall have.

Throws:

java.lang.IllegalArgumentException - if rows<0 || columns<0 || (double)columns*rows > Integer.MAX_VALUE .

SparseIntMatrix2D

public SparseIntMatrix2D(int rows,
                         int columns,
                         int initialCapacity,
                         double minLoadFactor,
                         double maxLoadFactor)

Constructs a matrix with a given number of rows and columns using memory as specified. All entries are initially 0. For details related to memory usage see OpenLongIntHashMap.

Parameters:

rows - the number of rows the matrix shall have.

columns - the number of columns the matrix shall have.

initialCapacity - the initial capacity of the hash map. If not known, set initialCapacity=0 or small.

minLoadFactor - the minimum load factor of the hash map.

maxLoadFactor - the maximum load factor of the hash map.

Throws:

java.lang.IllegalArgumentException - if initialCapacity < 0 || (minLoadFactor < 0.0 || minLoadFactor >= 1.0) || (maxLoadFactor <= 0.0 || maxLoadFactor >= 1.0) || (minLoadFactor >= maxLoadFactor) .

java.lang.IllegalArgumentException - if rows<0 || columns<0 || (double)columns*rows > Integer.MAX_VALUE .

SparseIntMatrix2D

public SparseIntMatrix2D(int rows,
                         int columns,
                         int[] rowIndexes,
                         int[] columnIndexes,
                         int value)

Constructs a matrix with a copy of the given indexes and a single value.

Parameters:

rows - the number of rows the matrix shall have.

columns - the number of columns the matrix shall have.

rowIndexes - row indexes

columnIndexes - column indexes

value - numerical value

SparseIntMatrix2D

public SparseIntMatrix2D(int rows,
                         int columns,
                         int[] rowIndexes,
                         int[] columnIndexes,
                         int[] values)

Constructs a matrix with a copy of the given indexes and values.

Parameters:

rows - the number of rows the matrix shall have.

columns - the number of columns the matrix shall have.

rowIndexes - row indexes

columnIndexes - column indexes

values - numerical values

SparseIntMatrix2D

public SparseIntMatrix2D(MatrixVectorReader reader)
                  throws java.io.IOException

Constructs a matrix from MatrixVectorReader.

Parameters:

reader - matrix reader

Throws:

java.io.IOException

Method Detail

assign

public IntMatrix2D assign(IntFunction function)

Description copied from class: IntMatrix2D

Assigns the result of a function to each cell; x[row,col] = function(x[row,col]).

Example:

   matrix = 2 x 2 matrix 
   0.5 1.5      
   2.5 3.5
 
   // change each cell to its sine
   matrix.assign(cern.jet.math.Functions.sin);
   -->
   2 x 2 matrix
   0.479426  0.997495 
   0.598472 -0.350783
 
 

For further examples, see the package doc.

Overrides:

assign in class IntMatrix2D

Parameters:

function - a function object taking as argument the current cell's value.

Returns:

this (for convenience only).

See Also:

IntFunctions

assign

public IntMatrix2D assign(int value)

Description copied from class: IntMatrix2D

Sets all cells to the state specified by value.

Overrides:

assign in class IntMatrix2D

Parameters:

value - the value to be filled into the cells.

Returns:

this (for convenience only).

assign

public IntMatrix2D assign(IntMatrix2D source)

Description copied from class: IntMatrix2D

Replaces all cell values of the receiver with the values of another matrix. Both matrices must have the same number of rows and columns. If both matrices share the same cells (as is the case if they are views derived from the same matrix) and intersect in an ambiguous way, then replaces as if using an intermediate auxiliary deep copy of other.

Overrides:

assign in class IntMatrix2D

Parameters:

source - the source matrix to copy from (may be identical to the receiver).

Returns:

this (for convenience only).

assign

public IntMatrix2D assign(IntMatrix2D y,
                          IntIntFunction function)

Description copied from class: IntMatrix2D

Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]).

Example:

   // assign x[row,col] = x[row,col]<sup>y[row,col]</sup>
   m1 = 2 x 2 matrix 
   0 1 
   2 3
 
   m2 = 2 x 2 matrix 
   0 2 
   4 6
 
   m1.assign(m2, cern.jet.math.Functions.pow);
   -->
   m1 == 2 x 2 matrix
   1   1 
   16 729
 
 

For further examples, see the package doc.

Overrides:

assign in class IntMatrix2D

Parameters:

y - the secondary matrix to operate on.

function - a function object taking as first argument the current cell's value of this, and as second argument the current cell's value of y,

Returns:

this (for convenience only).

See Also:

IntFunctions

assign

public SparseIntMatrix2D assign(int[] rowIndexes,
                                int[] columnIndexes,
                                int value,
                                IntIntFunction function)

Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]), where y is given in the coordinate form with single numerical value.

Parameters:

rowIndexes - row indexes of y

columnIndexes - column indexes of y

value - numerical value of y

function - a function object taking as first argument the current cell's value of this, and as second argument the current cell's value of y,

Returns:

this (for convenience only).

assign

public SparseIntMatrix2D assign(int[] rowIndexes,
                                int[] columnIndexes,
                                int[] values,
                                IntIntFunction function)

Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]), where y is given in the coordinate form.

Parameters:

rowIndexes - row indexes of y

columnIndexes - column indexes of y

values - numerical values of y

function - a function object taking as first argument the current cell's value of this, and as second argument the current cell's value of y,

Returns:

this (for convenience only).

cardinality

public int cardinality()

Description copied from class: IntMatrix2D

Returns the number of cells having non-zero values; ignores tolerance.

Overrides:

cardinality in class IntMatrix2D

Returns:

cardinality

getColumnCompressed

public SparseCCIntMatrix2D getColumnCompressed(boolean sortRowIndexes)

Returns a new matrix that has the same elements as this matrix, but is in a column-compressed form. This method creates a new object (not a view), so changes in the returned matrix are NOT reflected in this matrix.

Parameters:

sortRowIndexes - if true, then row indexes in column compressed matrix are sorted

Returns:

this matrix in a column-compressed form

getColumnCompressedModified

public SparseCCMIntMatrix2D getColumnCompressedModified()

Returns a new matrix that has the same elements as this matrix, but is in a column-compressed modified form. This method creates a new object (not a view), so changes in the returned matrix are NOT reflected in this matrix.

Returns:

this matrix in a column-compressed modified form

getRowCompressed

public SparseRCIntMatrix2D getRowCompressed(boolean sortColumnIndexes)

Returns a new matrix that has the same elements as this matrix, but is in a row-compressed form. This method creates a new object (not a view), so changes in the returned matrix are NOT reflected in this matrix.

Parameters:

sortColumnIndexes - if true, then column indexes in row compressed matrix are sorted

Returns:

this matrix in a row-compressed form

getRowCompressedModified

public SparseRCMIntMatrix2D getRowCompressedModified()

Returns a new matrix that has the same elements as this matrix, but is in a row-compressed modified form. This method creates a new object (not a view), so changes in the returned matrix are NOT reflected in this matrix.

Returns:

this matrix in a row-compressed modified form

elements

public AbstractLongIntMap elements()

Description copied from class: IntMatrix2D

Returns the elements of this matrix.

Specified by:

elements in class IntMatrix2D

Returns:

the elements

ensureCapacity

public void ensureCapacity(int minCapacity)

Description copied from class: AbstractMatrix

Ensures that the receiver can hold at least the specified number of non-zero (non-null) cells without needing to allocate new internal memory. If necessary, allocates new internal memory and increases the capacity of the receiver.

This default implementation does nothing. Override this method if necessary.

Overrides:

ensureCapacity in class AbstractMatrix

Parameters:

minCapacity - the desired minimum number of non-zero (non-null) cells.

forEachNonZero

public IntMatrix2D forEachNonZero(IntIntIntFunction function)

Description copied from class: IntMatrix2D

Assigns the result of a function to each non-zero cell; x[row,col] = function(x[row,col]). Use this method for fast special-purpose iteration. If you want to modify another matrix instead of this (i.e. work in read-only mode), simply return the input value unchanged. Parameters to function are as follows: first==row, second==column, third==nonZeroValue.

Overrides:

forEachNonZero in class IntMatrix2D

Parameters:

function - a function object taking as argument the current non-zero cell's row, column and value.

Returns:

this (for convenience only).

getQuick

public int getQuick(int row,
                    int column)

Description copied from class: IntMatrix2D

Returns the matrix cell value at coordinate [row,column].

Provided with invalid parameters this method may return invalid objects without throwing any exception. You should only use this method when you are absolutely sure that the coordinate is within bounds. Precondition (unchecked): 0 <= column < columns() && 0 <= row < rows().

Specified by:

getQuick in class IntMatrix2D

Parameters:

row - the index of the row-coordinate.

column - the index of the column-coordinate.

Returns:

the value at the specified coordinate.

index

public long index(int row,
                  int column)

Description copied from class: AbstractMatrix2D

Returns the position of the given coordinate within the (virtual or non-virtual) internal 1-dimensional array.

Overrides:

index in class AbstractMatrix2D

Parameters:

row - the index of the row-coordinate.

column - the index of the column-coordinate.

like

public IntMatrix2D like(int rows,
                        int columns)

Description copied from class: IntMatrix2D

Construct and returns a new empty matrix of the same dynamic type as the receiver, having the specified number of rows and columns. For example, if the receiver is an instance of type DenseIntMatrix2D the new matrix must also be of type DenseIntMatrix2D, if the receiver is an instance of type SparseIntMatrix2D the new matrix must also be of type SparseIntMatrix2D, etc. In general, the new matrix should have internal parametrization as similar as possible.

Specified by:

like in class IntMatrix2D

Parameters:

rows - the number of rows the matrix shall have.

columns - the number of columns the matrix shall have.

Returns:

a new empty matrix of the same dynamic type.

like1D

public IntMatrix1D like1D(int size)

Description copied from class: IntMatrix2D

Construct and returns a new 1-d matrix of the corresponding dynamic type, entirelly independent of the receiver. For example, if the receiver is an instance of type DenseIntMatrix2D the new matrix must be of type DenseIntMatrix1D, if the receiver is an instance of type SparseIntMatrix2D the new matrix must be of type SparseIntMatrix1D, etc.

Specified by:

like1D in class IntMatrix2D

Parameters:

size - the number of cells the matrix shall have.

Returns:

a new matrix of the corresponding dynamic type.

setQuick

public void setQuick(int row,
                     int column,
                     int value)

Description copied from class: IntMatrix2D

Sets the matrix cell at coordinate [row,column] to the specified value.

Provided with invalid parameters this method may access illegal indexes without throwing any exception. You should only use this method when you are absolutely sure that the coordinate is within bounds. Precondition (unchecked): 0 <= column < columns() && 0 <= row < rows().

Specified by:

setQuick in class IntMatrix2D

Parameters:

row - the index of the row-coordinate.

column - the index of the column-coordinate.

value - the value to be filled into the specified cell.

toString

public java.lang.String toString()

Description copied from class: IntMatrix2D

Returns a string representation using default formatting.

Overrides:

toString in class IntMatrix2D

See Also:

IntFormatter

trimToSize

public void trimToSize()

Description copied from class: AbstractMatrix

Releases any superfluous internal memory. An application can use this operation to minimize the storage of the receiver.

This default implementation does nothing. Override this method if necessary.

Overrides:

trimToSize in class AbstractMatrix

vectorize

public IntMatrix1D vectorize()

Description copied from class: IntMatrix2D

Returns a vector obtained by stacking the columns of the matrix on top of one another.

Specified by:

vectorize in class IntMatrix2D

Returns:

a vector of columns of this matrix.

zMult

public IntMatrix1D zMult(IntMatrix1D y,
                         IntMatrix1D z,
                         int alpha,
                         int beta,
                         boolean transposeA)

Description copied from class: IntMatrix2D

Linear algebraic matrix-vector multiplication; z = alpha * A * y + beta*z. z[i] = alpha*Sum(A[i,j] * y[j]) + beta*z[i], i=0..A.rows()-1, j=0..y.size()-1 . Where A == this.
Note: Matrix shape conformance is checked after potential transpositions.

Overrides:

zMult in class IntMatrix2D

Parameters:

y - the source vector.

z - the vector where results are to be stored. Set this parameter to null to indicate that a new result vector shall be constructed.

Returns:

z (for convenience only).

zMult

public IntMatrix2D zMult(IntMatrix2D B,
                         IntMatrix2D C,
                         int alpha,
                         int beta,
                         boolean transposeA,
                         boolean transposeB)

Description copied from class: IntMatrix2D

Linear algebraic matrix-matrix multiplication; C = alpha * A x B + beta*C. C[i,j] = alpha*Sum(A[i,k] * B[k,j]) + beta*C[i,j], k=0..n-1.
Matrix shapes: A(m x n), B(n x p), C(m x p).
Note: Matrix shape conformance is checked after potential transpositions.

Overrides:

zMult in class IntMatrix2D

Parameters:

B - the second source matrix.

C - the matrix where results are to be stored. Set this parameter to null to indicate that a new result matrix shall be constructed.

Returns:

C (for convenience only).