SparseMatrix

java.lang.Object
- smile.math.matrix.SparseMatrix

All Implemented Interfaces:

Matrix, MatrixMultiplication<SparseMatrix,SparseMatrix>
```
public class SparseMatrix
extends java.lang.Object
implements Matrix, 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.

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

All Methods Instance Methods Concrete Methods
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.
`EigenValueDecomposition`	`eigen(int k)` Returns the k largest eigen pairs.
`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 java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface smile.math.matrix.Matrix
apply, trace

- 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 interface: Matrix
    
    Returns the number of rows.
    
    Specified by:
    
    nrows in interface Matrix
  - ncols
```
public int ncols()
```
    Description copied from interface: Matrix
    
    Returns the number of columns.
    
    Specified by:
    
    ncols in interface 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 interface: Matrix
    
    Returns the entry value at row i and column j.
    
    Specified by:
    
    get in interface Matrix
  - ax
```
public double[] ax(double[] x,
                   double[] y)
```
    Description copied from interface: Matrix
    
    y = A * x
    
    Specified by:
    
    ax in interface Matrix
    
    Returns:
    
    y
  - axpy
```
public double[] axpy(double[] x,
                     double[] y)
```
    Description copied from interface: Matrix
    
    y = A * x + y
    
    Specified by:
    
    axpy in interface Matrix
    
    Returns:
    
    y
  - axpy
```
public double[] axpy(double[] x,
                     double[] y,
                     double b)
```
    Description copied from interface: Matrix
    
    y = A * x + b * y
    
    Specified by:
    
    axpy in interface Matrix
    
    Returns:
    
    y
  - atx
```
public double[] atx(double[] x,
                    double[] y)
```
    Description copied from interface: Matrix
    
    y = A' * x
    
    Specified by:
    
    atx in interface Matrix
    
    Returns:
    
    y
  - atxpy
```
public double[] atxpy(double[] x,
                      double[] y)
```
    Description copied from interface: Matrix
    
    y = A' * x + y
    
    Specified by:
    
    atxpy in interface Matrix
    
    Returns:
    
    y
  - atxpy
```
public double[] atxpy(double[] x,
                      double[] y,
                      double b)
```
    Description copied from interface: Matrix
    
    y = A' * x + b * y
    
    Specified by:
    
    atxpy in interface Matrix
    
    Returns:
    
    y
  - transpose
```
public SparseMatrix transpose()
```
    Description copied from interface: Matrix
    
    Returns the matrix transpose.
    
    Specified by:
    
    transpose in interface 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 interface: Matrix
    
    Returns A' * A
    
    Specified by:
    
    ata in interface Matrix
  - aat
```
public SparseMatrix aat()
```
    Description copied from interface: Matrix
    
    Returns A * A'
    
    Specified by:
    
    aat in interface Matrix
  - eigen
```
public EigenValueDecomposition eigen(int k)
```
    Returns the k largest eigen pairs. Only works for symmetric matrix.
  - diag
```
public double[] diag()
```
    Description copied from interface: Matrix
    
    Returns the diagonal elements.
    
    Specified by:
    
    diag in interface Matrix
    
    Returns:

Class SparseMatrix

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface smile.math.matrix.Matrix

Constructor Detail

SparseMatrix

SparseMatrix

SparseMatrix

Method Detail

nrows

ncols

size

values

get

ax

axpy

axpy

atx

atxpy

atxpy

transpose

abmm

abtmm

atbmm

ata

aat

eigen

diag