import LinearAlgebra from 'konpeito/src/math/core/tools/LinearAlgebra.js'

public class | source

LinearAlgebra

Class for linear algebra for Matrix class.

These methods can be used in the Matrix method chain.
This class cannot be called directly.

Static Method Summary

Static Public Methods
public static	cond(mat: KMatrixInputData, p: KMatrixInputData): number Condition number of the matrix
public static	det(mat: KMatrixInputData): Matrix Determinant.
public static	eig(mat: KMatrixInputData): {V: Matrix, D: Matrix} Eigendecomposition of symmetric matrix.
public static	inner(A: KMatrixInputData, B: KMatrixInputData, dimension: KMatrixInputData): Matrix Inner product/Dot product.
public static	inv(mat: KMatrixInputData): Matrix Inverse matrix of this matrix.
public static	linsolve(mat: KMatrixInputData, number: KMatrixInputData): Matrix Solving a system of linear equations to be Ax = B
public static	lu(mat: KMatrixInputData): {L: Matrix, U: Matrix} LU decomposition.
public static	lup(mat: KMatrixInputData): {P: Matrix, L: Matrix, U: Matrix} LUP decomposition.
public static	norm(mat: KMatrixInputData, p: KMatrixInputData): number p-norm.
public static	pinv(mat: KMatrixInputData): Matrix Pseudo-inverse matrix.
public static	qr(mat: KMatrixInputData): {Q: Matrix, R: Matrix} QR decomposition.
public static	rank(mat: KMatrixInputData, tolerance: KMatrixInputData): number Rank.
public static	rcond(mat: KMatrixInputData): number Inverse condition number.
public static	svd(mat: KMatrixInputData): {U: Matrix, S: Matrix, V: Matrix} Singular Value Decomposition (SVD).
public static	trace(mat: KMatrixInputData): Complex Trace of a matrix.
public static	tridiagonalize(mat: KMatrixInputData): {P: Matrix, H: Matrix} Tridiagonalization of symmetric matrix.

Static Public Methods

public static cond(mat: KMatrixInputData, p: KMatrixInputData): number source

Condition number of the matrix

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData
p	KMatrixInputData	optional default: 2

Return:

number

public static det(mat: KMatrixInputData): Matrix source

Determinant.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData

Return:

Matrix

|A|

public static eig(mat: KMatrixInputData): {V: Matrix, D: Matrix} source

Eigendecomposition of symmetric matrix.

Don't support complex numbers.
VDV'=A.
V is orthonormal matrix. and columns of V are the right eigenvectors.
D is a matrix containing the eigenvalues on the diagonal component.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

{V: Matrix, D: Matrix}

{D, V}

TODO:

対称行列しか対応できていないので、対称行列ではないものはQR分解を用いた手法に切り替える予定。

public static inner(A: KMatrixInputData, B: KMatrixInputData, dimension: KMatrixInputData): Matrix source

Inner product/Dot product.

Params:

Name	Type	Attribute	Description
A	KMatrixInputData
B	KMatrixInputData
dimension	KMatrixInputData	optional default: 1	Dimension of matrix used for calculation. (1 or 2)

Return:

Matrix

A・B

public static inv(mat: KMatrixInputData): Matrix source

Inverse matrix of this matrix.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

Matrix

A^-1

public static linsolve(mat: KMatrixInputData, number: KMatrixInputData): Matrix source

Solving a system of linear equations to be Ax = B

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A
number	KMatrixInputData		B

Return:

Matrix

TODO:

安定化のためQR分解を用いた手法に切り替える。あるいはlup分解を使用した関数に作り替える。

public static lu(mat: KMatrixInputData): {L: Matrix, U: Matrix} source

LU decomposition.

L*U=A
L is lower triangular matrix.
U is upper triangular matrix.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

{L: Matrix, U: Matrix}

{L, U}

public static lup(mat: KMatrixInputData): {P: Matrix, L: Matrix, U: Matrix} source

LUP decomposition.

P'LU=A
P is permutation matrix.
L is lower triangular matrix.
U is upper triangular matrix.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

{P: Matrix, L: Matrix, U: Matrix}

{L, U, P}

public static norm(mat: KMatrixInputData, p: KMatrixInputData): number source

p-norm.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData
p	KMatrixInputData	optional default: 2

Return:

number

public static pinv(mat: KMatrixInputData): Matrix source

Pseudo-inverse matrix.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

Matrix

A^+

public static qr(mat: KMatrixInputData): {Q: Matrix, R: Matrix} source

QR decomposition.

Q*R=A
Q is orthonormal matrix.
R is upper triangular matrix.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

{Q: Matrix, R: Matrix}

{Q, R}

public static rank(mat: KMatrixInputData, tolerance: KMatrixInputData): number source

Rank.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData
tolerance	KMatrixInputData	optional	Calculation tolerance of calculation.

Return:

number

rank(A)

public static rcond(mat: KMatrixInputData): number source

Inverse condition number.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData

Return:

number

public static svd(mat: KMatrixInputData): {U: Matrix, S: Matrix, V: Matrix} source

Singular Value Decomposition (SVD).

USV'=A
U and V are orthonormal matrices.
S is a matrix with singular values in the diagonal.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

{U: Matrix, S: Matrix, V: Matrix}

USV'=A

public static trace(mat: KMatrixInputData): Complex source

Trace of a matrix. Sum of diagonal elements.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData

Return:

Complex

public static tridiagonalize(mat: KMatrixInputData): {P: Matrix, H: Matrix} source

Tridiagonalization of symmetric matrix.

Don't support complex numbers.
PHP'=A
P is orthonormal matrix.
H is tridiagonal matrix.
The eigenvalues of H match the eigenvalues of A.

Params:

Name	Type	Attribute	Description
mat	KMatrixInputData		A

Return:

{P: Matrix, H: Matrix}

{P, H}