MatrixAlgebra (OpenGamma Strata Math API)

java.lang.Object
- com.opengamma.strata.math.impl.matrix.MatrixAlgebra

Direct Known Subclasses:

CommonsMatrixAlgebra, OGMatrixAlgebra
```
public abstract class MatrixAlgebra
extends Object
```
Parent class for matrix algebra operations. Basic operations (add, subtract, scale) are implemented in this class.

Constructor Summary

Constructors
Constructor and Description

MatrixAlgebra()

Constructors
Constructor and Description
`MatrixAlgebra()`

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method and Description
`Matrix`	`add(Matrix m1, Matrix m2)` Adds two matrices.
`Matrix`	`divide(Matrix m1, Matrix m2)` Returns the quotient of two matrices $C = \frac{A}{B} = AB^{-1}$, where $B^{-1}$ is the pseudo-inverse of $B$ i.e.
`abstract double`	`getCondition(Matrix m)` Returns the condition number of the matrix.
`abstract double`	`getDeterminant(Matrix m)` Returns the determinant of the matrix.
`abstract double`	`getInnerProduct(Matrix m1, Matrix m2)` Returns the inner (or dot) product.
`abstract DoubleMatrix`	`getInverse(Matrix m)` Returns the inverse (or pseudo-inverse) of the matrix.
`abstract double`	`getNorm1(Matrix m)` For a vector, returns the $L_1$ norm (also known as the Taxicab norm or Manhattan norm), i.e.
`abstract double`	`getNorm2(Matrix m)` For a vector, returns $L_2$ norm (also known as the Euclidean norm).
`abstract double`	`getNormInfinity(Matrix m)` For a vector, returns the $L_\infty$ norm.
`abstract DoubleMatrix`	`getOuterProduct(Matrix m1, Matrix m2)` Returns the outer product.
`abstract DoubleMatrix`	`getPower(Matrix m, double p)` Returns a matrix raised to a power, $\mathbf{A}^3 = \mathbf{A}\mathbf{A}\mathbf{A}$.
`abstract DoubleMatrix`	`getPower(Matrix m, int p)` Returns a matrix raised to an integer power, e.g.
`abstract double`	`getTrace(Matrix m)` Returns the trace (i.e.
`abstract DoubleMatrix`	`getTranspose(Matrix m)` Returns the transpose of a matrix.
`Matrix`	`kroneckerProduct(Matrix m1, Matrix m2)` Returns the Kronecker product of two matrices.
`DoubleMatrix`	`matrixTransposeMultiplyMatrix(DoubleMatrix a)` Compute $A^T A$, where A is a matrix.
`abstract Matrix`	`multiply(Matrix m1, Matrix m2)` Multiplies two matrices.
`Matrix`	`scale(Matrix m, double scale)` Scale a vector or matrix by a given amount, i.e.
`Matrix`	`subtract(Matrix m1, Matrix m2)` Subtracts two matrices.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - MatrixAlgebra
```
public MatrixAlgebra()
```
- Method Detail
  - add
```
public Matrix add(Matrix m1,
                  Matrix m2)
```
    Adds two matrices. This operation can only be performed if the matrices are of the same type and dimensions.
    
    Parameters:
    
    m1 - The first matrix, not null
    
    m2 - The second matrix, not null
    
    Returns:
    
    The sum of the two matrices
    
    Throws:
    
    IllegalArgumentException - If the matrices are not of the same type, if the matrices are not the same shape.
  - divide
```
public Matrix divide(Matrix m1,
                     Matrix m2)
```
    Returns the quotient of two matrices $C = \frac{A}{B} = AB^{-1}$, where $B^{-1}$ is the pseudo-inverse of $B$ i.e. $BB^{-1} = \mathbb{1}$.
    
    Parameters:
    
    m1 - The numerator matrix, not null. This matrix must be a DoubleMatrix.
    
    m2 - The denominator, not null. This matrix must be a DoubleMatrix.
    
    Returns:
    
    The result
  - kroneckerProduct
```
public Matrix kroneckerProduct(Matrix m1,
                               Matrix m2)
```
    Returns the Kronecker product of two matrices. If $\mathbf{A}$ is an $m \times n$ matrix and $\mathbf{B}$ is a $p \times q$ matrix, then the Kronecker product $A \otimes B$ is an $mp \times nq$ matrix with elements $$ \begin{align*} A \otimes B &= \begin{pmatrix} a_{11}\mathbf{B} & \cdots & a_{1n}\mathbf{B} \\ \vdots & \ddots & \vdots \\ a_{m1}\mathbf{B} & \cdots & a_{mn}\mathbf{B} \end{pmatrix}\\ &= \begin{pmatrix} a_{11}b_{11} & a_{11}b_{12} & \cdots & a_{11}b_{1q} & \cdots & a_{1n}b_{11} & a_{1n}b_{12} & \cdots & a_{1n}b_{1q}\\ a_{11}b_{21} & a_{11}b_{22} & \cdots & a_{11}b_{2q} & \cdots & a_{1n}b_{21} & a_{1n}b_{22} & \cdots & a_{1n}b_{2q} \\ \vdots & \vdots & \ddots & \vdots & \cdots & \vdots & \vdots & \ddots & \cdots \\ a_{11}b_{p1} & a_{11}b_{p2} & \cdots & a_{11}b_{pq} & \cdots & a_{1n}b_{p1} & a_{1n}b_{p2} & \cdots & a_{1n}b_{pq} \\ \vdots & \vdots & & \vdots & \ddots & \vdots & \vdots & & \cdots \\ a_{m1}b_{11} & a_{m1}b_{12} & \cdots & a_{m1}b_{1q} & \cdots & a_{mn}b_{11} & a_{mn}b_{12} & \cdots & a_{mn}b_{1q} \\ a_{m1}b_{21} & a_{m1}b_{22} & \cdots & a_{m1}b_{2q} & \cdots & a_{mn}b_{21} & a_{mn}b_{22} & \cdots & a_{mn}b_{2q} \\ \vdots & \vdots & \ddots & \vdots & \cdots & \vdots & \vdots & \ddots & \cdots \\ a_{m1}b_{p1} & a_{m1}b_{p2} & \cdots & a_{m1}b_{pq} & \cdots & a_{mn}b_{p1} & a_{mn}b_{p2} & \cdots & a_{mn}b_{pq} \end{pmatrix} \end{align*} $$
    
    Parameters:
    
    m1 - The first matrix, not null. This matrix must be a DoubleMatrix.
    
    m2 - The second matrix, not null. This matrix must be a DoubleMatrix.
    
    Returns:
    
    The Kronecker product
  - multiply
```
public abstract Matrix multiply(Matrix m1,
                                Matrix m2)
```
    Multiplies two matrices.
    
    Parameters:
    
    m1 - The first matrix, not null.
    
    m2 - The second matrix, not null.
    
    Returns:
    
    The product of the two matrices.
  - scale
```
public Matrix scale(Matrix m,
                    double scale)
```
    Scale a vector or matrix by a given amount, i.e. each element is multiplied by the scale.
    
    Parameters:
    
    m - A vector or matrix, not null
    
    scale - The scale
    
    Returns:
    
    the scaled vector or matrix
  - subtract
```
public Matrix subtract(Matrix m1,
                       Matrix m2)
```
    Subtracts two matrices. This operation can only be performed if the matrices are of the same type and dimensions.
    
    Parameters:
    
    m1 - The first matrix, not null
    
    m2 - The second matrix, not null
    
    Returns:
    
    The second matrix subtracted from the first
    
    Throws:
    
    IllegalArgumentException - If the matrices are not of the same type, if the matrices are not the same shape.
  - getCondition
```
public abstract double getCondition(Matrix m)
```
    Returns the condition number of the matrix.
    
    Parameters:
    
    m - A matrix, not null
    
    Returns:
    
    The condition number of the matrix
  - getDeterminant
```
public abstract double getDeterminant(Matrix m)
```
    Returns the determinant of the matrix.
    
    Parameters:
    
    m - A matrix, not null
    
    Returns:
    
    The determinant of the matrix
  - getInverse
```
public abstract DoubleMatrix getInverse(Matrix m)
```
    Returns the inverse (or pseudo-inverse) of the matrix.
    
    Parameters:
    
    m - A matrix, not null
    
    Returns:
    
    The inverse matrix
  - getInnerProduct
```
public abstract double getInnerProduct(Matrix m1,
                                       Matrix m2)
```
    Returns the inner (or dot) product.
    
    Parameters:
    
    m1 - A vector, not null
    
    m2 - A vector, not null
    
    Returns:
    
    The scalar dot product
    
    Throws:
    
    IllegalArgumentException - If the vectors are not the same size
  - getOuterProduct
```
public abstract DoubleMatrix getOuterProduct(Matrix m1,
                                             Matrix m2)
```
    Returns the outer product.
    
    Parameters:
    
    m1 - A vector, not null
    
    m2 - A vector, not null
    
    Returns:
    
    The outer product
    
    Throws:
    
    IllegalArgumentException - If the vectors are not the same size
  - getNorm1
```
public abstract double getNorm1(Matrix m)
```
    For a vector, returns the $L_1$ norm (also known as the Taxicab norm or Manhattan norm), i.e. $\Sigma |x_i|$.
    For a matrix, returns the maximum absolute column sum norm of the matrix.
    
    Parameters:
    
    m - A vector or matrix, not null
    
    Returns:
    
    The $L_1$ norm
  - getNorm2
```
public abstract double getNorm2(Matrix m)
```
    For a vector, returns $L_2$ norm (also known as the Euclidean norm).
    For a matrix, returns the spectral norm
    
    Parameters:
    
    m - A vector or matrix, not null
    
    Returns:
    
    the norm
  - getNormInfinity
```
public abstract double getNormInfinity(Matrix m)
```
    For a vector, returns the $L_\infty$ norm. $L_\infty$ norm is the maximum of the absolute values of the elements.
    For a matrix, returns the maximum absolute row sum norm
    
    Parameters:
    
    m - a vector or a matrix, not null
    
    Returns:
    
    the norm
  - getPower
```
public abstract DoubleMatrix getPower(Matrix m,
                                      int p)
```
    Returns a matrix raised to an integer power, e.g. $\mathbf{A}^3 = \mathbf{A}\mathbf{A}\mathbf{A}$.
    
    Parameters:
    
    m - A square matrix, not null
    
    p - An integer power
    
    Returns:
    
    The result
  - getPower
```
public abstract DoubleMatrix getPower(Matrix m,
                                      double p)
```
    Returns a matrix raised to a power, $\mathbf{A}^3 = \mathbf{A}\mathbf{A}\mathbf{A}$.
    
    Parameters:
    
    m - A square matrix, not null
    
    p - The power
    
    Returns:
    
    The result
  - getTrace
```
public abstract double getTrace(Matrix m)
```
    Returns the trace (i.e. sum of diagonal elements) of a matrix.
    
    Parameters:
    
    m - A matrix, not null. The matrix must be square.
    
    Returns:
    
    The trace
  - getTranspose
```
public abstract DoubleMatrix getTranspose(Matrix m)
```
    Returns the transpose of a matrix.
    
    Parameters:
    
    m - A matrix, not null
    
    Returns:
    
    The transpose matrix
  - matrixTransposeMultiplyMatrix
```
public DoubleMatrix matrixTransposeMultiplyMatrix(DoubleMatrix a)
```
    Compute $A^T A$, where A is a matrix.
    
    Parameters:
    
    a - The matrix
    
    Returns:
    
    The result of $A^T A$

Copyright 2009-Present by OpenGamma Inc. and individual contributors
Apache v2 licensed
Additional documentation can be found at strata.opengamma.io.

Class MatrixAlgebra

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MatrixAlgebra

Method Detail

add

divide

kroneckerProduct

multiply

scale

subtract

getCondition

getDeterminant

getInverse

getInnerProduct

getOuterProduct

getNorm1

getNorm2

getNormInfinity

getPower

getPower

getTrace

getTranspose

matrixTransposeMultiplyMatrix