Package org.flag4j.linalg

Class MatrixNorms

java.lang.Object

org.flag4j.linalg.MatrixNorms

public class MatrixNorms
extends Object

Utility class for computing norms of matrices.

Constructor Summary

Constructors

Modifier	Constructor	Description
private	MatrixNorms()

Method Summary

Modifier and Type	Method	Description
static double	infNorm(CMatrix src)	Computes the maximum/infinite norm of this tensor.
static double	infNorm(Matrix src)	Computes the infinite norm of this matrix.
private static double	matrixInfNorm(double[] src, Shape shape)	Computes the infinity/maximum norm of a matrix.
private static double	matrixInfNorm(CNumber[] src, Shape shape)	Computes the infinity/maximum norm of a matrix.
private static double	matrixMaxNorm(double[] src)	Computes the infinity/maximum norm of a matrix.
private static double	matrixMaxNorm(CNumber[] src)	Computes the infinity/maximum norm of a matrix.
private static double	matrixNormL2(CNumber[] src, Shape shape)	Compute the L2 norm of a matrix.
private static double	matrixNormLp(CNumber[] src, Shape shape, double p)	Compute the Lp norm of a matrix.
static double	matrixNormLpq(double[] src, Shape shape, double p, double q)	Compute the Lp, q norm of a matrix.
static double	matrixNormLpq(CsrMatrix src, double p, double q)	Compute the Lp,q norm of a sparse CSR matrix.
private static double	matrixNormLpq(CNumber[] src, Shape shape, double p, double q)	Compute the Lp, q norm of a matrix.
static double	maxNorm(CMatrix src)	Computes the max norm of a matrix.
static double	maxNorm(Matrix src)	Computes the maximum norm of this matrix.
static double	maxNorm(CooCMatrix src)	Computes the max norm of a matrix.
static double	maxNorm(CooMatrix src)	Computes the max norm of a matrix.
static double	maxNorm(CsrMatrix src)	Computes the max norm of a matrix.
static double	norm(CMatrix src)	Computes the 2-norm of this tensor.
static double	norm(CMatrix src, double p)	Computes the p-norm of this tensor.
static double	norm(CMatrix src, double p, double q)	Computes the Lp, q norm of this matrix.
static double	norm(Matrix src)	Computes the 2-norm of this tensor.
static double	norm(Matrix src, double p)	Computes the p-norm of this tensor.
static double	norm(Matrix src, double p, double q)	Computes the Lp, q norm of this matrix.
static double	norm(CooCMatrix src)	Computes the 2-norm of this tensor.
static double	norm(CooCMatrix src, double p)	Computes the p-norm of this tensor.
static double	norm(CooCMatrix src, double p, double q)	Computes the Lp, q norm of this matrix.
static double	norm(CooMatrix src)	Computes the 2-norm of this tensor.
static double	norm(CooMatrix src, double p)	Computes the p-norm of this tensor.
static double	norm(CooMatrix src, double p, double q)	Computes the Lp, q norm of this matrix.
double	norm(CsrMatrix src)	Computes the 2-norm of this tensor.
double	norm(CsrMatrix src, double p)	Computes the p-norm of this tensor.
static double	norm(CsrMatrix src, double p, double q)	Computes the Lp, q norm of this matrix.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

MatrixNorms

private MatrixNorms()

Method Details

norm

public static double norm(Matrix src)

Computes the 2-norm of this tensor. This is equivalent to norm(2). This will be equal to the largest singular value of the matrix.

Parameters:

src - Matrix to compute norm of.

Returns:

the 2-norm of this tensor.

norm

public static double norm(Matrix src,
 double p)

Computes the p-norm of this tensor. Equivalent to calling norm(p, p)

Parameters:

src - Matrix to compute norm of.

p - The p value in the p-norm.
- If p is inf, then this method computes the maximum/infinite norm.

Returns:

The p-norm of this tensor.

Throws:

IllegalArgumentException - If p is less than 1.

maxNorm

public static double maxNorm(Matrix src)

Computes the maximum norm of this matrix. That is, the maximum value in the matrix.

Parameters:

src - Matrix to compute norm of.

Returns:

The maximum norm of this matrix.

See Also:

• infNorm(Matrix)

infNorm

public static double infNorm(Matrix src)

Computes the infinite norm of this matrix. that is the maximum row sum in the matrix.

Parameters:

src - Matrix to compute norm of.

Returns:

The infinite norm of this matrix.

See Also:

• maxNorm(Matrix)

norm

public static double norm(Matrix src,
 double p,
 double q)

Computes the L_{p, q} norm of this matrix.

Parameters:

p - P value in the L_{p, q} norm.

q - Q value in the L_{p, q} norm.

Returns:

The L_{p, q} norm of this matrix.

norm

public static double norm(CMatrix src,
 double p,
 double q)

Computes the L_{p, q} norm of this matrix.

Parameters:

src - Matrix to compute norm of.

p - P value in the L_{p, q} norm.

q - Q value in the L_{p, q} norm.

Returns:

The L_{p, q} norm of this matrix.

maxNorm

public static double maxNorm(CMatrix src)

Computes the max norm of a matrix.

Parameters:

src - Matrix to compute norm of.

Returns:

The max norm of this matrix.

norm

public static double norm(CMatrix src)

Computes the 2-norm of this tensor. This is equivalent to norm(2).

Parameters:

src - Matrix to compute norm of.

Returns:

the 2-norm of this tensor.

norm

public static double norm(CMatrix src,
 double p)

Computes the p-norm of this tensor.

Parameters:

src - Matrix to compute norm of.

p - The p value in the p-norm.
- If p is inf, then this method computes the maximum/infinite norm.

Returns:

The p-norm of this tensor.

Throws:

IllegalArgumentException - If p is less than 1.

infNorm

public static double infNorm(CMatrix src)

Computes the maximum/infinite norm of this tensor.

Parameters:

src - Matrix to compute norm of.

Returns:

The maximum/infinite norm of this tensor.

norm

public static double norm(CooMatrix src,
 double p,
 double q)

Computes the L_{p, q} norm of this matrix.

Parameters:

src - Matrix to compute norm of.

p - P value in the L_{p, q} norm.

q - Q value in the L_{p, q} norm.

Returns:

The L_{p, q} norm of this matrix.

maxNorm

public static double maxNorm(CooMatrix src)

Computes the max norm of a matrix.

Parameters:

src - Matrix to compute norm of.

Returns:

The max norm of this matrix.

norm

public static double norm(CooMatrix src)

Computes the 2-norm of this tensor. This is equivalent to norm(2).

Parameters:

src - Matrix to compute norm of.

Returns:

the 2-norm of this tensor.

norm

public static double norm(CooMatrix src,
 double p)

Computes the p-norm of this tensor.

Parameters:

src - Matrix to compute norm of.

p - The p value in the p-norm.
- If p is inf, then this method computes the maximum/infinite norm.

Returns:

The p-norm of this tensor.

Throws:

IllegalArgumentException - If p is less than 1.

norm

public static double norm(CooCMatrix src,
 double p,
 double q)

Computes the L_{p, q} norm of this matrix.

Parameters:

src - Matrix to compute norm of.

p - P value in the L_{p, q} norm.

q - Q value in the L_{p, q} norm.

Returns:

The L_{p, q} norm of this matrix.

maxNorm

public static double maxNorm(CooCMatrix src)

Computes the max norm of a matrix.

Parameters:

src - Matrix to compute norm of.

Returns:

The max norm of this matrix.

norm

public static double norm(CooCMatrix src)

Computes the 2-norm of this tensor. This is equivalent to norm(2).

Parameters:

src - Matrix to compute the norm.

Returns:

the 2-norm of this tensor.

norm

public static double norm(CooCMatrix src,
 double p)

Computes the p-norm of this tensor.

Parameters:

src - Matrix to compute the norm.

p - The p value in the p-norm.
- If p is inf, then this method computes the maximum/infinite norm.

Returns:

The p-norm of this tensor.

Throws:

IllegalArgumentException - If p is less than 1.

norm

public static double norm(CsrMatrix src,
 double p,
 double q)

Computes the L_{p, q} norm of this matrix.

Parameters:

src - Matrix to compute norm of.

p - P value in the L_{p, q} norm.

q - Q value in the L_{p, q} norm.

Returns:

The L_{p, q} norm of this matrix.

maxNorm

public static double maxNorm(CsrMatrix src)

Computes the max norm of a matrix.

Parameters:

src - Matrix to compute norm of.

Returns:

The max norm of this matrix.

norm

public double norm(CsrMatrix src)

Computes the 2-norm of this tensor. This is equivalent to norm(2).

Parameters:

src - Matrix to compute the norm of.

Returns:

the 2-norm of this tensor.

norm

public double norm(CsrMatrix src,
 double p)

Computes the p-norm of this tensor.

Parameters:

src - Matrix to compute norm of.

p - The p value in the p-norm.
- If p is inf, then this method computes the maximum/infinite norm.

Returns:

The p-norm of this tensor.

Throws:

IllegalArgumentException - If p is less than 1.

matrixMaxNorm

private static double matrixMaxNorm(double[] src)

Computes the infinity/maximum norm of a matrix. That is, the maximum value in this matrix.

Parameters:

src - Entries of the matrix.

Returns:

The infinity norm of the matrix.

matrixInfNorm

private static double matrixInfNorm(double[] src,
 Shape shape)

Computes the infinity/maximum norm of a matrix. That is, the maximum value in this matrix.

Parameters:

src - Entries of the matrix.

shape - Shape of the matrix.

Returns:

The infinity norm of the matrix.

matrixNormLpq

private static double matrixNormLpq(CNumber[] src,
 Shape shape,
 double p,
 double q)

Compute the L_{p, q} norm of a matrix.

Parameters:

src - Entries of the matrix.

shape - Shape of the matrix.

p - First parameter in L_{p, q} norm.

q - Second parameter in L_{p, q} norm.

Returns:

The L_{p, q} norm of the matrix.

Throws:

IllegalArgumentException - If p or q is less than 1.

matrixNormLp

private static double matrixNormLp(CNumber[] src,
 Shape shape,
 double p)

Compute the L_p norm of a matrix. This is equivalent to passing q=1 to matrixNormLpq(CNumber[], Shape, double, double)

Parameters:

src - Entries of the matrix.

shape - Shape of the matrix.

p - Parameter in L_p norm.

Returns:

The L_p norm of the matrix.

Throws:

IllegalArgumentException - If p is less than 1.

matrixNormL2

private static double matrixNormL2(CNumber[] src,
 Shape shape)

Compute the L₂ norm of a matrix. This is equivalent to passing q=1 to matrixNormLpq(CNumber[], Shape, double, double)

Parameters:

src - Entries of the matrix.

shape - Shape of the matrix.

Returns:

The L₂ norm of the matrix.

matrixMaxNorm

private static double matrixMaxNorm(CNumber[] src)

Computes the infinity/maximum norm of a matrix. That is, the maximum value in this matrix.

Parameters:

src - Entries of the matrix.

Returns:

The infinity norm of the matrix.

matrixInfNorm

private static double matrixInfNorm(CNumber[] src,
 Shape shape)

Computes the infinity/maximum norm of a matrix. That is, the maximum absolute value in this matrix.

Parameters:

src - Entries of the matrix.

Returns:

The infinity norm of the matrix.

matrixNormLpq

public static double matrixNormLpq(CsrMatrix src,
 double p,
 double q)

Compute the L_p,q norm of a sparse CSR matrix.

Parameters:

src - Sparse CSR matrix to compute norm of.

Returns:

The L_p,q norm of the matrix.

matrixNormLpq

public static double matrixNormLpq(double[] src,
 Shape shape,
 double p,
 double q)

Compute the L_{p, q} norm of a matrix.

Parameters:

src - Entries of the matrix.

shape - Shape of the matrix.

p - First parameter in L_{p, q} norm.

q - Second parameter in L_{p, q} norm.

Returns:

The L_{p, q} norm of the matrix.

Throws:

IllegalArgumentException - If p or q is less than 1.