smile.math.matrix

Class SparseMatrix

java.lang.Object

smile.math.matrix.Matrix

smile.math.matrix.SparseMatrix

All Implemented Interfaces:

java.io.Serializable, MatrixMultiplication<SparseMatrix,SparseMatrix>

public class SparseMatrix
extends Matrix
implements MatrixMultiplication<SparseMatrix,SparseMatrix>

A sparse matrix is a matrix populated primarily with zeros. Conceptually, sparsity corresponds to systems which are loosely coupled. Huge sparse matrices often appear when solving partial differential equations.

Operations using standard dense matrix structures and algorithms are slow and consume large amounts of memory when applied to large sparse matrices. Indeed, some very large sparse matrices are infeasible to manipulate with the standard dense algorithms. Sparse data is by nature easily compressed, and this compression almost always results in significantly less computer data storage usage.

This class employs Harwell-Boeing column-compressed sparse matrix format. Nonzero values are stored in an array (top-to-bottom, then left-to-right-bottom). The row indices corresponding to the values are also stored. Besides, a list of pointers are indexes where each column starts. This format is efficient for arithmetic operations, column slicing, and matrix-vector products. One typically uses SparseDataset for construction of SparseMatrix.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
SparseMatrix(double[][] D) Constructor.
SparseMatrix(double[][] D, double tol) Constructor.
SparseMatrix(int nrows, int ncols, double[] x, int[] rowIndex, int[] colIndex) Constructor.

Method Summary

Modifier and Type	Method and Description
SparseMatrix	aat() Returns A * A'
SparseMatrix	abmm(SparseMatrix B) Returns the matrix multiplication C = A * B.
SparseMatrix	abtmm(SparseMatrix B) Returns the result of matrix multiplication A * B'.
SparseMatrix	ata() Returns A' * A
SparseMatrix	atbmm(SparseMatrix B) Returns the result of matrix multiplication A' * B.
double[]	atx(double[] x, double[] y) y = A' * x
double[]	atxpy(double[] x, double[] y) y = A' * x + y
double[]	atxpy(double[] x, double[] y, double b) y = A' * x + b * y
double[]	ax(double[] x, double[] y) y = A * x
double[]	axpy(double[] x, double[] y) y = A * x + y
double[]	axpy(double[] x, double[] y, double b) y = A * x + b * y
double[]	diag() Returns the diagonal elements.
double	get(int i, int j) Returns the entry value at row i and column j.
int	ncols() Returns the number of columns.
int	nrows() Returns the number of rows.
int	size() Returns the number of nonzero values.
SparseMatrix	transpose() Returns the matrix transpose.
double[]	values() Returns all nonzero values.

Methods inherited from class smile.math.matrix.Matrix

apply, diag, eigen, eigen, eye, eye, isSymmetric, newInstance, newInstance, newInstance, ones, randn, randn, setSymmetric, svd, svd, toString, toString, trace, zeros

Methods inherited from class java.lang.Object

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

Constructor Detail

SparseMatrix

public SparseMatrix(int nrows,
                    int ncols,
                    double[] x,
                    int[] rowIndex,
                    int[] colIndex)

Constructor.

Parameters:

nrows - the number of rows in the matrix.

ncols - the number of columns in the matrix.

rowIndex - the row indices of nonzero values.

colIndex - the index of the start of columns.

x - the array of nonzero values stored column by column.

SparseMatrix

public SparseMatrix(double[][] D)

Constructor.

Parameters:

D - a dense matrix to converted into sparse matrix format.

SparseMatrix

public SparseMatrix(double[][] D,
                    double tol)

Constructor.

Parameters:

D - a dense matrix to converted into sparse matrix format.

tol - the tolerance to regard a value as zero if |x| < tol.

Method Detail

nrows

public int nrows()

Description copied from class: Matrix

Returns the number of rows.

Specified by:

nrows in class Matrix

ncols

public int ncols()

Description copied from class: Matrix

Returns the number of columns.

Specified by:

ncols in class Matrix

size

public int size()

Returns the number of nonzero values.

values

public double[] values()

Returns all nonzero values.

Returns:

all nonzero values

get

public double get(int i,
                  int j)

Description copied from class: Matrix

Returns the entry value at row i and column j.

Specified by:

get in class Matrix

ax

public double[] ax(double[] x,
                   double[] y)

Description copied from class: Matrix

y = A * x

Specified by:

ax in class Matrix

Returns:

y

axpy

public double[] axpy(double[] x,
                     double[] y)

Description copied from class: Matrix

y = A * x + y

Specified by:

axpy in class Matrix

Returns:

y

axpy

public double[] axpy(double[] x,
                     double[] y,
                     double b)

Description copied from class: Matrix

y = A * x + b * y

Specified by:

axpy in class Matrix

Returns:

y

atx

public double[] atx(double[] x,
                    double[] y)

Description copied from class: Matrix

y = A' * x

Specified by:

atx in class Matrix

Returns:

y

atxpy

public double[] atxpy(double[] x,
                      double[] y)

Description copied from class: Matrix

y = A' * x + y

Specified by:

atxpy in class Matrix

Returns:

y

atxpy

public double[] atxpy(double[] x,
                      double[] y,
                      double b)

Description copied from class: Matrix

y = A' * x + b * y

Specified by:

atxpy in class Matrix

Returns:

y

transpose

public SparseMatrix transpose()

Description copied from class: Matrix

Returns the matrix transpose.

Specified by:

transpose in class Matrix

abmm

public SparseMatrix abmm(SparseMatrix B)

Returns the matrix multiplication C = A * B.

Specified by:

abmm in interface MatrixMultiplication<SparseMatrix,SparseMatrix>

abtmm

public SparseMatrix abtmm(SparseMatrix B)

Description copied from interface: MatrixMultiplication

Returns the result of matrix multiplication A * B'.

Specified by:

abtmm in interface MatrixMultiplication<SparseMatrix,SparseMatrix>

atbmm

public SparseMatrix atbmm(SparseMatrix B)

Description copied from interface: MatrixMultiplication

Returns the result of matrix multiplication A' * B.

Specified by:

atbmm in interface MatrixMultiplication<SparseMatrix,SparseMatrix>

ata

public SparseMatrix ata()

Description copied from class: Matrix

Returns A' * A

Specified by:

ata in class Matrix

aat

public SparseMatrix aat()

Description copied from class: Matrix

Returns A * A'

Specified by:

aat in class Matrix

diag

public double[] diag()

Description copied from class: Matrix

Returns the diagonal elements.

Overrides:

diag in class Matrix