cern.colt.matrix
Class DoubleMatrix2D

java.lang.Object
  cern.colt.PersistentObject
      cern.colt.matrix.impl.AbstractMatrix
          cern.colt.matrix.impl.AbstractMatrix2D
              cern.colt.matrix.DoubleMatrix2D

All Implemented Interfaces:

Cloneable, Serializable

Direct Known Subclasses:

DenseDoubleMatrix2D, SparseDoubleMatrix2D, cern.colt.matrix.impl.WrapperDoubleMatrix2D

public abstract class DoubleMatrix2D

extends AbstractMatrix2D

Abstract base class for 2-d matrices holding double elements. First see the package summary and javadoc tree view to get the broad picture.

A matrix has a number of rows and columns, which are assigned upon instance construction - The matrix's size is then rows()*columns(). Elements are accessed via [row,column] coordinates. Legal coordinates range from [0,0] to [rows()-1,columns()-1]. Any attempt to access an element at a coordinate column<0 || column>=columns() || row<0 || row>=rows() will throw an IndexOutOfBoundsException.

Note that this implementation is not synchronized.

Version:

1.0, 09/24/99

See Also:

Serialized Form

aggregate

public double aggregate(DoubleDoubleFunction aggr,
                        DoubleFunction f)

Applies a function to each cell and aggregates the results. Returns a value v such that v==a(size()) where a(i) == aggr( a(i-1), f(get(row,column)) ) and terminators are a(1) == f(get(0,0)), a(0)==Double.NaN.

Example:

cern.jet.math.Functions F = cern.jet.math.Functions.functions;
2 x 2 matrix
0 1
2 3

// Sum( x[row,col]*x[row,col] ) 
matrix.aggregate(F.plus,F.square);
--> 14

For further examples, see the package doc.

Parameters:

aggr - an aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.

f - a function transforming the current cell value.

Returns:

the aggregated measure.

See Also:

Functions

aggregate

public double aggregate(DoubleMatrix2D other,
                        DoubleDoubleFunction aggr,
                        DoubleDoubleFunction f)

Applies a function to each corresponding cell of two matrices and aggregates the results. Returns a value v such that v==a(size()) where a(i) == aggr( a(i-1), f(get(row,column),other.get(row,column)) ) and terminators are a(1) == f(get(0,0),other.get(0,0)), a(0)==Double.NaN.

Example:

cern.jet.math.Functions F = cern.jet.math.Functions.functions;
x == 2 x 2 matrix
0 1
2 3

y == 2 x 2 matrix
0 1
2 3

// Sum( x[row,col] * y[row,col] ) 
x.aggregate(y, F.plus, F.mult);
--> 14

// Sum( (x[row,col] + y[row,col])^2 )
x.aggregate(y, F.plus, F.chain(F.square,F.plus));
--> 56

For further examples, see the package doc.

Parameters:

aggr - an aggregation function taking as first argument the current aggregation and as second argument the transformed current cell values.

f - a function transforming the current cell values.

Returns:

the aggregated measure.

Throws:

IllegalArgumentException - if columns() != other.columns() || rows() != other.rows()

See Also:

Functions

assign

public DoubleMatrix2D assign(double[][] values)

Sets all cells to the state specified by values. values is required to have the form values[row][column] and have exactly the same number of rows and columns as the receiver.

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 cells.

Returns:

this (for convenience only).

Throws:

IllegalArgumentException - if values.length != rows() || for any 0 <= row < rows(): values[row].length != columns().

assign

public DoubleMatrix2D assign(double value)

Sets all cells to the state specified by value.

Parameters:

value - the value to be filled into the cells.

Returns:

this (for convenience only).

assign

public DoubleMatrix2D assign(DoubleFunction function)

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.

Parameters:

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

Returns:

this (for convenience only).

See Also:

Functions

assign

public DoubleMatrix2D assign(DoubleMatrix2D other)

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.

Parameters:

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

Returns:

this (for convenience only).

Throws:

IllegalArgumentException - if columns() != other.columns() || rows() != other.rows()

assign

public DoubleMatrix2D assign(DoubleMatrix2D y,
                             DoubleDoubleFunction function)

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]y[row,col]
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.

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).

Throws:

IllegalArgumentException - if columns() != other.columns() || rows() != other.rows()

See Also:

Functions

cardinality

public int cardinality()

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

copy

public DoubleMatrix2D copy()

Constructs and returns a deep copy of the receiver.

Note that the returned matrix is an independent deep copy. The returned matrix is not backed by this matrix, so changes in the returned matrix are not reflected in this matrix, and vice-versa.

Returns:

a deep copy of the receiver.

equals

public boolean equals(double value)

Returns whether all cells are equal to the given value.

Parameters:

value - the value to test against.

Returns:

true if all cells are equal to the given value, false otherwise.

equals

public boolean equals(Object obj)

Compares this object against the specified object. The result is true if and only if the argument is not null and is at least a DoubleMatrix2D object that has the same number of columns and rows as the receiver and has exactly the same values at the same coordinates.

Parameters:

obj - the object to compare with.

Returns:

true if the objects are the same; false otherwise.

forEachNonZero

public DoubleMatrix2D forEachNonZero(IntIntDoubleFunction function)

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.

Parameters:

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

Returns:

this (for convenience only).

get

public double get(int row,
                  int column)

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

Parameters:

row - the index of the row-coordinate.

column - the index of the column-coordinate.

Returns:

the value of the specified cell.

Throws:

IndexOutOfBoundsException - if column<0 || column>=columns() || row<0 || row>=rows()

getNonZeros

public void getNonZeros(IntArrayList rowList,
                        IntArrayList columnList,
                        DoubleArrayList valueList)

Fills the coordinates and values of cells having non-zero values into the specified lists. Fills into the lists, starting at index 0. After this call returns the specified lists all have a new size, the number of non-zero values.

In general, fill order is unspecified. This implementation fills like for (row = 0..rows-1) for (column = 0..columns-1) do ... . However, subclasses are free to us any other order, even an order that may change over time as cell values are changed. (Of course, result lists indexes are guaranteed to correspond to the same cell).

Example:

2 x 3 matrix:
0, 0, 8
0, 7, 0
-->
rowList    = (0,1)
columnList = (2,1)
valueList  = (8,7)

In other words, get(0,2)==8, get(1,1)==7.

Parameters:

rowList - the list to be filled with row indexes, can have any size.

columnList - the list to be filled with column indexes, can have any size.

valueList - the list to be filled with values, can have any size.

getQuick

public abstract double getQuick(int row,
                                int column)

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().

Parameters:

row - the index of the row-coordinate.

column - the index of the column-coordinate.

Returns:

the value at the specified coordinate.

like

public DoubleMatrix2D like()

Construct and returns a new empty matrix of the same dynamic type as the receiver, having the same number of rows and columns. For example, if the receiver is an instance of type DenseDoubleMatrix2D the new matrix must also be of type DenseDoubleMatrix2D, if the receiver is an instance of type SparseDoubleMatrix2D the new matrix must also be of type SparseDoubleMatrix2D, etc. In general, the new matrix should have internal parametrization as similar as possible.

Returns:

a new empty matrix of the same dynamic type.

like

public abstract DoubleMatrix2D 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. For example, if the receiver is an instance of type DenseDoubleMatrix2D the new matrix must also be of type DenseDoubleMatrix2D, if the receiver is an instance of type SparseDoubleMatrix2D the new matrix must also be of type SparseDoubleMatrix2D, etc. In general, the new matrix should have internal parametrization as similar as possible.

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 abstract DoubleMatrix1D like1D(int size)

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 DenseDoubleMatrix2D the new matrix must be of type DenseDoubleMatrix1D, if the receiver is an instance of type SparseDoubleMatrix2D the new matrix must be of type SparseDoubleMatrix1D, etc.

Parameters:

size - the number of cells the matrix shall have.

Returns:

a new matrix of the corresponding dynamic type.

set

public void set(int row,
                int column,
                double value)

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

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.

Throws:

IndexOutOfBoundsException - if column<0 || column>=columns() || row<0 || row>=rows()

setQuick

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

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().

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.

toArray

public double[][] toArray()

Constructs and returns a 2-dimensional array containing the cell values. The returned array values has the form values[row][column] and has the same number of rows and columns as the receiver.

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

Returns:

an array filled with the values of the cells.

toString

public String toString()

Returns a string representation using default formatting.

See Also:

Formatter

viewColumn

public DoubleMatrix1D viewColumn(int column)

Constructs and returns a new slice view representing the rows of 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 obtain a slice view on subranges, construct a sub-ranging view (viewPart(...)), then apply this method to the sub-range view.

Example:

2 x 3 matrix: 1, 2, 3 4, 5, 6

viewColumn(0) ==>

Matrix1D of size 2: 1, 4

Parameters:

column - the column to fix.

Returns:

a new slice view.

Throws:

IndexOutOfBoundsException - if column < 0 || column >= columns().

See Also:

viewRow(int)

viewColumnFlip

public DoubleMatrix2D viewColumnFlip()

Constructs and returns a new flip view along the column axis. What used to be column 0 is now column columns()-1, ..., what used to be column columns()-1 is now column 0. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

Example:

2 x 3 matrix: 1, 2, 3 4, 5, 6

columnFlip ==>

2 x 3 matrix: 3, 2, 1 6, 5, 4

columnFlip ==>

2 x 3 matrix: 1, 2, 3 4, 5, 6

Returns:

a new flip view.

See Also:

viewRowFlip()

viewDice

public DoubleMatrix2D viewDice()

Constructs and returns a new dice (transposition) view; Swaps axes; example: 3 x 4 matrix --> 4 x 3 matrix. The view has both dimensions exchanged; what used to be columns become rows, what used to be rows become columns. In other words: view.get(row,column)==this.get(column,row). This is a zero-copy transposition, taking O(1), i.e. constant time. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa. Use idioms like result = viewDice(A).copy() to generate an independent transposed matrix.

Example:

2 x 3 matrix: 1, 2, 3 4, 5, 6

transpose ==>

3 x 2 matrix: 1, 4 2, 5 3, 6

transpose ==>

2 x 3 matrix: 1, 2, 3 4, 5, 6

Returns:

a new dice view.

viewPart

public DoubleMatrix2D viewPart(int row,
                               int column,
                               int height,
                               int width)

Constructs and returns a new sub-range view that is a height x width sub matrix starting at [row,column]. Operations on the returned view can only be applied to the restricted range. Any attempt to access coordinates not contained in the view will throw an IndexOutOfBoundsException.

Note that the view is really just a range restriction: The returned matrix is backed by this matrix, so changes in the returned matrix are reflected in this matrix, and vice-versa.

The view contains the cells from [row,column] to [row+height-1,column+width-1], all inclusive. and has view.rows() == height; view.columns() == width;. A view's legal coordinates are again zero based, as usual. In other words, legal coordinates of the view range from [0,0] to [view.rows()-1==height-1,view.columns()-1==width-1]. As usual, any attempt to access a cell at a coordinate column<0 || column>=view.columns() || row<0 || row>=view.rows() will throw an IndexOutOfBoundsException.

Parameters:

row - The index of the row-coordinate.

column - The index of the column-coordinate.

height - The height of the box.

width - The width of the box.

Returns:

the new view.

Throws:

IndexOutOfBoundsException - if column<0 || width<0 || column+width>columns() || row<0 || height<0 || row+height>rows()

viewRow

public DoubleMatrix1D viewRow(int row)

Constructs and returns a new slice view representing the columns of the given row. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa. To obtain a slice view on subranges, construct a sub-ranging view (viewPart(...)), then apply this method to the sub-range view.

Example:

2 x 3 matrix: 1, 2, 3 4, 5, 6

viewRow(0) ==>

Matrix1D of size 3: 1, 2, 3

Parameters:

row - the row to fix.

Returns:

a new slice view.

Throws:

IndexOutOfBoundsException - if row < 0 || row >= rows().

See Also:

viewColumn(int)

viewRowFlip

public DoubleMatrix2D viewRowFlip()

Constructs and returns a new flip view along the row axis. What used to be row 0 is now row rows()-1, ..., what used to be row rows()-1 is now row 0. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

Example:

2 x 3 matrix: 1, 2, 3 4, 5, 6

rowFlip ==>

2 x 3 matrix: 4, 5, 6 1, 2, 3

rowFlip ==>

2 x 3 matrix: 1, 2, 3 4, 5, 6

Returns:

a new flip view.

See Also:

viewColumnFlip()

viewSelection

public DoubleMatrix2D viewSelection(int[] rowIndexes,
                                    int[] columnIndexes)

Constructs and returns a new selection view that is a matrix holding the indicated cells. There holds view.rows() == rowIndexes.length, view.columns() == columnIndexes.length and view.get(i,j) == this.get(rowIndexes[i],columnIndexes[j]). Indexes can occur multiple times and can be in arbitrary order.

Example:

this = 2 x 3 matrix:
1, 2, 3
4, 5, 6
rowIndexes     = (0,1)
columnIndexes  = (1,0,1,0)
-->
view = 2 x 4 matrix:
2, 1, 2, 1
5, 4, 5, 4

Note that modifying the index arguments after this call has returned has no effect on the view. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

To indicate "all" rows or "all columns", simply set the respective parameter

Parameters:

rowIndexes - The rows of the cells that shall be visible in the new view. To indicate that all rows shall be visible, simply set this parameter to null.

columnIndexes - The columns of the cells that shall be visible in the new view. To indicate that all columns shall be visible, simply set this parameter to null.

Returns:

the new view.

Throws:

IndexOutOfBoundsException - if !(0 <= rowIndexes[i] < rows()) for any i=0..rowIndexes.length()-1.

IndexOutOfBoundsException - if !(0 <= columnIndexes[i] < columns()) for any i=0..columnIndexes.length()-1.

viewSelection

public DoubleMatrix2D viewSelection(DoubleMatrix1DProcedure condition)

Constructs and returns a new selection view that is a matrix holding all rows matching the given condition. Applies the condition to each row and takes only those row where condition.apply(viewRow(i)) yields true. To match columns, use a dice view.

Example:

// extract and view all rows which have a value < threshold in the first column (representing "age")
final double threshold = 16;
matrix.viewSelection( 
   new DoubleMatrix1DProcedure() {
      public final boolean apply(DoubleMatrix1D m) { return m.get(0) < threshold; }
   }
);

// extract and view all rows with RMS < threshold
// The RMS (Root-Mean-Square) is a measure of the average "size" of the elements of a data sequence.
matrix = 0 1 2 3
final double threshold = 0.5;
matrix.viewSelection( 
   new DoubleMatrix1DProcedure() {
      public final boolean apply(DoubleMatrix1D m) { return Math.sqrt(m.aggregate(F.plus,F.square) / m.size()) < threshold; }
   }
);

For further examples, see the package doc. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

Parameters:

condition - The condition to be matched.

Returns:

the new view.

viewSorted

public DoubleMatrix2D viewSorted(int column)

Sorts the matrix rows into ascending order, according to the natural ordering of the matrix values in the given column. This sort is guaranteed to be stable. For further information, see Sorting.sort(DoubleMatrix2D,int). For more advanced sorting functionality, see Sorting.

Returns:

a new sorted vector (matrix) view.

Throws:

IndexOutOfBoundsException - if column < 0 || column >= columns().

viewStrides

public DoubleMatrix2D viewStrides(int rowStride,
                                  int columnStride)

Constructs and returns a new stride view which is a sub matrix consisting of every i-th cell. More specifically, the view has this.rows()/rowStride rows and this.columns()/columnStride columns holding cells this.get(i*rowStride,j*columnStride) for all i = 0..rows()/rowStride - 1, j = 0..columns()/columnStride - 1. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

Parameters:

rowStride - the row step factor.

columnStride - the column step factor.

Returns:

a new view.

Throws:

IndexOutOfBoundsException - if rowStride<=0 || columnStride<=0.

zAssign8Neighbors

public void zAssign8Neighbors(DoubleMatrix2D B,
                              Double9Function function)

8 neighbor stencil transformation. For efficient finite difference operations. Applies a function to a moving 3 x 3 window. Does nothing if rows() < 3 || columns() < 3.

B[i,j] = function.apply(
   A[i-1,j-1], A[i-1,j], A[i-1,j+1],
   A[i,  j-1], A[i,  j], A[i,  j+1],
   A[i+1,j-1], A[i+1,j], A[i+1,j+1]
   )

x x x -     - x x x     - - - - 
x o x -     - x o x     - - - - 
x x x -     - x x x ... - x x x 
- - - -     - - - -     - x o x 
- - - -     - - - -     - x x x 

Make sure that cells of this and B do not overlap. In case of overlapping views, behaviour is unspecified.

Example:

final double alpha = 0.25;
final double beta = 0.75;

// 8 neighbors
cern.colt.function.Double9Function f = new cern.colt.function.Double9Function() {
   public final double apply(
      double a00, double a01, double a02,
      double a10, double a11, double a12,
      double a20, double a21, double a22) {
         return beta*a11 + alpha*(a00+a01+a02 + a10+a12 + a20+a21+a22);
      }
};
A.zAssign8Neighbors(B,f);

// 4 neighbors
cern.colt.function.Double9Function g = new cern.colt.function.Double9Function() {
   public final double apply(
      double a00, double a01, double a02,
      double a10, double a11, double a12,
      double a20, double a21, double a22) {
      return beta*a11 + alpha*(a01+a10+a12+a21);
   }
C.zAssign8Neighbors(B,g); // fast, even though it doesn't look like it
};

Parameters:

B - the matrix to hold the results.

function - the function to be applied to the 9 cells.

Throws:

NullPointerException - if function==null.

IllegalArgumentException - if rows() != B.rows() || columns() != B.columns().

zMult

public DoubleMatrix1D zMult(DoubleMatrix1D y,
                            DoubleMatrix1D z)

Linear algebraic matrix-vector multiplication; z = A * y; Equivalent to return A.zMult(y,z,1,0);

zMult

public DoubleMatrix1D zMult(DoubleMatrix1D y,
                            DoubleMatrix1D z,
                            double alpha,
                            double beta,
                            boolean transposeA)

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.

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).

Throws:

IllegalArgumentException - if A.columns() != y.size() || A.rows() > z.size()).

zMult

public DoubleMatrix2D zMult(DoubleMatrix2D B,
                            DoubleMatrix2D C)

Linear algebraic matrix-matrix multiplication; C = A x B; Equivalent to A.zMult(B,C,1,0,false,false).

zMult

public DoubleMatrix2D zMult(DoubleMatrix2D B,
                            DoubleMatrix2D C,
                            double alpha,
                            double beta,
                            boolean transposeA,
                            boolean transposeB)

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.

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).

Throws:

IllegalArgumentException - if B.rows() != A.columns().

IllegalArgumentException - if C.rows() != A.rows() || C.columns() != B.columns().

IllegalArgumentException - if A == C || B == C.

zSum

public double zSum()

Returns the sum of all cells; Sum( x[i,j] ).

Returns:

the sum.