cern.colt.matrix.impl
Class RCDoubleMatrix2D

java.lang.Object
  extended by cern.colt.PersistentObject
      extended by cern.colt.matrix.impl.AbstractMatrix
          extended by cern.colt.matrix.impl.AbstractMatrix2D
              extended by cern.colt.matrix.DoubleMatrix2D
                  extended by cern.colt.matrix.impl.RCDoubleMatrix2D
All Implemented Interfaces:
java.io.Serializable, java.lang.Cloneable

public class RCDoubleMatrix2D
extends DoubleMatrix2D

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

Implementation:

Internally uses the standard sparse row-compressed format, with two important differences that broaden the applicability of this storage format:


Note that this implementation is not synchronized.

Memory requirements:

Cells that

memory [bytes] = 4*rows + 12 * nonZeros.
Where nonZeros = cardinality() is the number of non-zero cells. Thus, a 1000 x 1000 matrix with 1000000 non-zero cells consumes 11.5 MB. The same 1000 x 1000 matrix with 1000 non-zero cells consumes 15 KB.

Time complexity:

Getting a cell value takes time O(log nzr) where nzr is the number of non-zeros of the touched row. This is usually quick, because typically there are only few nonzeros per row. So, in practice, get has expected constant time. Setting a cell value takes worst-case time O(nz) where nzr is the total number of non-zeros in the matrix. This can be extremely slow, but if you traverse coordinates properly (i.e. upwards), each write is done much quicker:

// rather quick
matrix.assign(0);
for (int row=0; row < rows; row++) {
   for (int column=0; column < columns; column++) {
      if (someCondition) matrix.setQuick(row,column,someValue);
   }
}

// poor
matrix.assign(0);
for (int row=rows; --row >= 0; ) {
   for (int column=columns; --column >= 0; ) {
      if (someCondition) matrix.setQuick(row,column,someValue);
   }
}
If for whatever reasons you can't iterate properly, consider to create an empty dense matrix, store your non-zeros in it, then call sparse.assign(dense). Under the circumstances, this is still rather quick.

Fast iteration over non-zeros can be done via forEachNonZero(cern.colt.function.IntIntDoubleFunction), which supplies your function with row, column and value of each nonzero. Although the internally implemented version is a bit more sophisticated, here is how a quite efficient user-level matrix-vector multiplication could look like:

// Linear algebraic y = A * x
A.forEachNonZero(
   new cern.colt.function.IntIntDoubleFunction() {
      public double apply(int row, int column, double value) {
         y.setQuick(row,y.getQuick(row) + value * x.getQuick(column));
         return value;
      }
   }
);

Here is how a a quite efficient user-level combined scaling operation could look like:

// Elementwise A = A + alpha*B
B.forEachNonZero(
   new cern.colt.function.IntIntDoubleFunction() {
      public double apply(int row, int column, double value) {
         A.setQuick(row,column,A.getQuick(row,column) + alpha*value);
         return value;
      }
   }
);
Method assign(DoubleMatrix2D,cern.colt.function.DoubleDoubleFunction) does just that if you supply Functions.plusMult(double) as argument.

Author:
wolfgang.hoschek@cern.ch
See Also:
Serialized Form

Field Summary
protected  DoubleMatrix2D content
           
protected  IntArrayList indexes
           
protected  int[] starts
           
protected  DoubleArrayList values
           
 
Fields inherited from class cern.colt.matrix.impl.AbstractMatrix2D
columns, columnStride, columnZero, rows, rowStride, rowZero
 
Fields inherited from class cern.colt.matrix.impl.AbstractMatrix
isNoView
 
Fields inherited from class cern.colt.PersistentObject
serialVersionUID
 
Constructor Summary
RCDoubleMatrix2D(double[][] values)
          Constructs a matrix with a copy of the given values.
RCDoubleMatrix2D(int rows, int columns)
          Constructs a matrix with a given number of rows and columns.
 
Method Summary
 DoubleMatrix2D assign(double value)
          Sets all cells to the state specified by value.
 DoubleMatrix2D assign(DoubleFunction function)
          Assigns the result of a function to each cell; x[row,col] = function(x[row,col]).
 DoubleMatrix2D assign(DoubleMatrix2D source)
          Replaces all cell values of the receiver with the values of another matrix.
 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]).
 DoubleMatrix2D forEachNonZero(IntIntDoubleFunction function)
          Assigns the result of a function to each non-zero cell; x[row,col] = function(x[row,col]).
protected  DoubleMatrix2D getContent()
          Returns the content of this matrix if it is a wrapper; or this otherwise.
 double getQuick(int row, int column)
          Returns the matrix cell value at coordinate [row,column].
protected  void insert(int row, int column, int index, double value)
           
 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.
 DoubleMatrix1D like1D(int size)
          Construct and returns a new 1-d matrix of the corresponding dynamic type, entirelly independent of the receiver.
protected  DoubleMatrix1D like1D(int size, int offset, int stride)
          Construct and returns a new 1-d matrix of the corresponding dynamic type, sharing the same cells.
protected  void remove(int row, int index)
           
 void setQuick(int row, int column, double value)
          Sets the matrix cell at coordinate [row,column] to the specified value.
 void trimToSize()
          Releases any superfluous internal memory.
 DoubleMatrix1D viewColumn(int column)
          Constructs and returns a new slice view representing the rows of the given column.
 DoubleMatrix2D viewColumnFlip()
          Constructs and returns a new flip view along the column axis.
 DoubleMatrix2D viewDice()
          Constructs and returns a new dice (transposition) view; Swaps axes; example: 3 x 4 matrix --> 4 x 3 matrix.
 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].
 DoubleMatrix1D viewRow(int row)
          Constructs and returns a new slice view representing the columns of the given row.
 DoubleMatrix2D viewRowFlip()
          Constructs and returns a new flip view along the row axis.
 DoubleMatrix2D viewSelection(int[] rowIndexes, int[] columnIndexes)
          Constructs and returns a new selection view that is a matrix holding the indicated cells.
protected  DoubleMatrix2D viewSelectionLike(int[] rowOffsets, int[] columnOffsets)
          Construct and returns a new selection view.
 DoubleMatrix2D viewStrides(int _rowStride, int _columnStride)
          Constructs and returns a new stride view which is a sub matrix consisting of every i-th cell.
 DoubleMatrix1D zMult(DoubleMatrix1D y, DoubleMatrix1D z, double alpha, double beta, boolean transposeA)
          Linear algebraic matrix-vector multiplication; z = alpha * A * y + beta*z.
 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.
 
Methods inherited from class cern.colt.matrix.DoubleMatrix2D
aggregate, aggregate, assign, cardinality, copy, equals, equals, get, getNonZeros, haveSharedCells, haveSharedCellsRaw, like, set, toArray, toString, view, viewSelection, viewSorted, zAssign8Neighbors, zMult, zMult, zSum
 
Methods inherited from class cern.colt.matrix.impl.AbstractMatrix2D
_columnOffset, _columnRank, _rowOffset, _rowRank, checkBox, checkColumn, checkColumnIndexes, checkRow, checkRowIndexes, checkShape, checkShape, columns, index, rows, setUp, setUp, size, toStringShort, vColumnFlip, vDice, vPart, vRowFlip, vStrides
 
Methods inherited from class cern.colt.matrix.impl.AbstractMatrix
ensureCapacity, isView
 
Methods inherited from class cern.colt.PersistentObject
clone
 
Methods inherited from class java.lang.Object
finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Field Detail

indexes

protected IntArrayList indexes

values

protected DoubleArrayList values

starts

protected int[] starts

content

protected DoubleMatrix2D content
Constructor Detail

RCDoubleMatrix2D

public RCDoubleMatrix2D(double[][] 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.

RCDoubleMatrix2D

public RCDoubleMatrix2D(int rows,
                        int columns)
Constructs a matrix with a given number of rows and columns. 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.
Method Detail

assign

public DoubleMatrix2D assign(double value)
Sets all cells to the state specified by value.

Overrides:
assign in class DoubleMatrix2D
Parameters:
value - the value to be filled into the cells.
Returns:
this (for convenience only).

assign

public DoubleMatrix2D assign(DoubleFunction function)
Description copied from class: DoubleMatrix2D
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 DoubleMatrix2D
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 source)
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 DoubleMatrix2D
Parameters:
source - the source matrix to copy from (may be identical to the receiver).
Returns:
this (for convenience only).
Throws:
java.lang.IllegalArgumentException - if columns() != source.columns() || rows() != source.rows()

assign

public DoubleMatrix2D assign(DoubleMatrix2D y,
                             DoubleDoubleFunction function)
Description copied from class: DoubleMatrix2D
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.

Overrides:
assign in class DoubleMatrix2D
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:
Functions

forEachNonZero

public DoubleMatrix2D forEachNonZero(IntIntDoubleFunction function)
Description copied from class: DoubleMatrix2D
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 DoubleMatrix2D
Parameters:
function - a function object taking as argument the current non-zero cell's row, column and value.
Returns:
this (for convenience only).

getContent

protected DoubleMatrix2D getContent()
Returns the content of this matrix if it is a wrapper; or this otherwise. Override this method in wrappers.


getQuick

public 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.

insert

protected void insert(int row,
                      int column,
                      int index,
                      double value)

like

public 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 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.

remove

protected void remove(int row,
                      int index)

setQuick

public 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.

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

zMult

public DoubleMatrix1D zMult(DoubleMatrix1D y,
                            DoubleMatrix1D z,
                            double alpha,
                            double beta,
                            boolean transposeA)
Description copied from class: DoubleMatrix2D
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 DoubleMatrix2D
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 DoubleMatrix2D zMult(DoubleMatrix2D B,
                            DoubleMatrix2D C,
                            double alpha,
                            double beta,
                            boolean transposeA,
                            boolean transposeB)
Description copied from class: DoubleMatrix2D
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 DoubleMatrix2D
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).

like1D

protected DoubleMatrix1D like1D(int size,
                                int offset,
                                int stride)
Construct and returns a new 1-d matrix of the corresponding dynamic type, sharing the same cells. 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.

Specified by:
like1D in class DoubleMatrix2D
Parameters:
size - the number of cells the matrix shall have.
offset - the index of the first element.
stride - the number of indexes between any two elements, i.e. index(i+1)-index(i).
Returns:
a new matrix of the corresponding dynamic type.

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

Overrides:
viewColumn in class DoubleMatrix2D
Parameters:
column - the column to fix.
Returns:
a new slice view.
Throws:
java.lang.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

Overrides:
viewColumnFlip in class DoubleMatrix2D
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

Overrides:
viewDice in class DoubleMatrix2D
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.

Overrides:
viewPart in class DoubleMatrix2D
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:
java.lang.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

Overrides:
viewRow in class DoubleMatrix2D
Parameters:
row - the row to fix.
Returns:
a new slice view.
Throws:
java.lang.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

Overrides:
viewRowFlip in class DoubleMatrix2D
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

Overrides:
viewSelection in class DoubleMatrix2D
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:
java.lang.IndexOutOfBoundsException - if !(0 <= rowIndexes[i] < rows()) for any i=0..rowIndexes.length()-1.
java.lang.IndexOutOfBoundsException - if !(0 <= columnIndexes[i] < columns()) for any i=0..columnIndexes.length()-1.

viewSelectionLike

protected DoubleMatrix2D viewSelectionLike(int[] rowOffsets,
                                           int[] columnOffsets)
Construct and returns a new selection view.

Specified by:
viewSelectionLike in class DoubleMatrix2D
Parameters:
rowOffsets - the offsets of the visible elements.
columnOffsets - the offsets of the visible elements.
Returns:
a new view.

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.

Overrides:
viewStrides in class DoubleMatrix2D
Parameters:
rowStride - the row step factor.
columnStride - the column step factor.
Returns:
a new view.
Throws:
java.lang.IndexOutOfBoundsException - if rowStride<=0 || columnStride<=0.