public class RCDoubleMatrix2D extends DoubleMatrix2D
Implementation:
Internally uses the standard sparse row-compressed format, with two important differences that broaden the applicability of this storage format:
IntArrayList and DoubleArrayList to hold the column indexes and nonzero values, respectively.
This improves set(...) performance, because the standard way of using non-resizable primitive arrays causes excessive memory allocation, garbage collection and array copying.
The small downside of this is that set(...,0) does not free memory (The capacity of an arraylist does not shrink upon element removal).
Memory requirements:
Cells that
trimToSize().
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);
}
}
|
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;
}
}
);
|
assign(DoubleMatrix2D,cern.colt.function.DoubleDoubleFunction) does just that if you supply Functions.plusMult(double) as argument.| Modifier and Type | Field and Description |
|---|---|
protected DoubleMatrix2D |
content |
protected IntArrayList |
indexes |
protected int[] |
starts |
protected DoubleArrayList |
values |
columns, columnStride, columnZero, rows, rowStride, rowZeroisNoViewserialVersionUID| Constructor and Description |
|---|
RCDoubleMatrix2D(double[][] values)
Constructs a matrix with a copy of the given values.
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RCDoubleMatrix2D(int rows,
int columns)
Constructs a matrix with a given number of rows and columns.
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| Modifier and Type | Method and Description |
|---|---|
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.
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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.
|
aggregate, aggregate, assign, cardinality, copy, equals, equals, get, getNonZeros, haveSharedCells, haveSharedCellsRaw, like, set, toArray, toString, view, viewSelection, viewSorted, zAssign8Neighbors, zMult, zMult, zSum_columnOffset, _columnRank, _rowOffset, _rowRank, checkBox, checkColumn, checkColumnIndexes, checkRow, checkRowIndexes, checkShape, checkShape, columns, index, rows, setUp, setUp, size, toStringShort, vColumnFlip, vDice, vPart, vRowFlip, vStridesensureCapacity, isViewcloneprotected IntArrayList indexes
protected DoubleArrayList values
protected int[] starts
protected DoubleMatrix2D content
public RCDoubleMatrix2D(double[][] values)
The values are copied. So subsequent changes in values are not reflected in the matrix, and vice-versa.
values - The values to be filled into the new matrix.IllegalArgumentException - if for any 1 <= row < values.length: values[row].length != values[row-1].length.public RCDoubleMatrix2D(int rows,
int columns)
rows - the number of rows the matrix shall have.columns - the number of columns the matrix shall have.IllegalArgumentException - if rows<0 || columns<0 || (double)columns*rows > Integer.MAX_VALUE.public DoubleMatrix2D assign(double value)
assign in class DoubleMatrix2Dvalue - the value to be filled into the cells.public DoubleMatrix2D assign(DoubleFunction function)
DoubleMatrix2DExample:
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 -0.350783For further examples, see the package doc.
assign in class DoubleMatrix2Dfunction - a function object taking as argument the current cell's value.Functionspublic DoubleMatrix2D assign(DoubleMatrix2D source)
assign in class DoubleMatrix2Dsource - the source matrix to copy from (may be identical to the receiver).IllegalArgumentException - if columns() != source.columns() || rows() != source.rows()public DoubleMatrix2D assign(DoubleMatrix2D y, DoubleDoubleFunction function)
DoubleMatrix2DExample:
// 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 729For further examples, see the package doc.
assign in class DoubleMatrix2Dy - 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,Functionspublic DoubleMatrix2D forEachNonZero(IntIntDoubleFunction function)
DoubleMatrix2DforEachNonZero in class DoubleMatrix2Dfunction - a function object taking as argument the current non-zero cell's row, column and value.protected DoubleMatrix2D getContent()
public double getQuick(int row,
int 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().
row - the index of the row-coordinate.column - the index of the column-coordinate.protected void insert(int row,
int column,
int index,
double value)
public DoubleMatrix2D like(int rows, int columns)
rows - the number of rows the matrix shall have.columns - the number of columns the matrix shall have.public DoubleMatrix1D like1D(int size)
size - the number of cells the matrix shall have.protected void remove(int row,
int index)
public void setQuick(int row,
int column,
double 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().
row - the index of the row-coordinate.column - the index of the column-coordinate.value - the value to be filled into the specified cell.public void trimToSize()
AbstractMatrixThis default implementation does nothing. Override this method if necessary.
trimToSize in class AbstractMatrixpublic DoubleMatrix1D zMult(DoubleMatrix1D y, DoubleMatrix1D z, double alpha, double beta, boolean transposeA)
DoubleMatrix2DzMult in class DoubleMatrix2Dy - 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.public DoubleMatrix2D zMult(DoubleMatrix2D B, DoubleMatrix2D C, double alpha, double beta, boolean transposeA, boolean transposeB)
DoubleMatrix2DzMult in class DoubleMatrix2DB - 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.protected DoubleMatrix1D like1D(int size, int offset, int stride)
like1D in class DoubleMatrix2Dsize - 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).public DoubleMatrix1D viewColumn(int column)
Example:
| 2 x 3 matrix: 1, 2, 3 4, 5, 6 |
viewColumn(0) ==> | Matrix1D of size 2: 1, 4 |
viewColumn in class DoubleMatrix2Dcolumn - the column to fix.IndexOutOfBoundsException - if column < 0 || column >= columns().viewRow(int)public DoubleMatrix2D viewColumnFlip()
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 |
viewColumnFlip in class DoubleMatrix2DviewRowFlip()public DoubleMatrix2D viewDice()
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 |
viewDice in class DoubleMatrix2Dpublic DoubleMatrix2D viewPart(int row, int column, int height, int width)
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.
viewPart in class DoubleMatrix2Drow - 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.IndexOutOfBoundsException - if column<0 || width<0 || column+width>columns() || row<0 || height<0 || row+height>rows()public DoubleMatrix1D viewRow(int row)
Example:
| 2 x 3 matrix: 1, 2, 3 4, 5, 6 |
viewRow(0) ==> | Matrix1D of size 3: 1, 2, 3 |
viewRow in class DoubleMatrix2Drow - the row to fix.IndexOutOfBoundsException - if row < 0 || row >= rows().viewColumn(int)public DoubleMatrix2D viewRowFlip()
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 |
viewRowFlip in class DoubleMatrix2DviewColumnFlip()public DoubleMatrix2D viewSelection(int[] rowIndexes, int[] columnIndexes)
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, 4Note 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
viewSelection in class DoubleMatrix2DrowIndexes - 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.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.protected DoubleMatrix2D viewSelectionLike(int[] rowOffsets, int[] columnOffsets)
viewSelectionLike in class DoubleMatrix2DrowOffsets - the offsets of the visible elements.columnOffsets - the offsets of the visible elements.public DoubleMatrix2D viewStrides(int _rowStride, int _columnStride)
viewStrides in class DoubleMatrix2DrowStride - the row step factor.columnStride - the column step factor.IndexOutOfBoundsException - if rowStride<=0 || columnStride<=0.Copyright © 2006–2019 SYSTAP, LLC DBA Blazegraph. All rights reserved.