com.numericalmethod.suanshu.matrix.doubles.operation

Class Inverse

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix

com.numericalmethod.suanshu.matrix.doubles.operation.Inverse

All Implemented Interfaces:

Table, DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccess, MatrixRing, MatrixTable, Densifiable, java.io.Serializable

public class Inverse
extends DenseMatrix

For a square matrix A, the inverse, A^-1, if exists, satisfies

A.multiply(A.inverse()) == A.ONE()

There are multiple ways to compute the inverse of a matrix. They are,

• an analytic solution for small matrices, e.g., 2x2,
• LU Decomposition,
• the Moore-Penrose pseudoinverse.

See Also:

Wikipedia: Invertible matrix, Serialized Form

Constructor Summary

Constructors

Constructor and Description
Inverse(LowerTriangularMatrix L, double epsilon) Construct the inverse of a lower triangular matrix.
Inverse(Matrix A) Construct a the inverse of a matrix.
Inverse(Matrix A, double epsilon) Construct a the inverse of a matrix.
Inverse(UpperTriangularMatrix U, double epsilon) Construct the inverse of an upper triangular matrix.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix

add, deepCopy, equals, get, getColumn, getColumn, getRow, getRow, hashCode, minus, multiply, multiply, nCols, nRows, ONE, opposite, scaled, set, setColumn, setRow, t, toDense, toString, ZERO

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Inverse

public Inverse(Matrix A,
               double epsilon)

Construct a the inverse of a matrix.

Parameters:

A - a matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Inverse

public Inverse(Matrix A)

Construct a the inverse of a matrix.

Parameters:

A - a matrix

Inverse

public Inverse(UpperTriangularMatrix U,
               double epsilon)

Construct the inverse of an upper triangular matrix.

Parameters:

U - an upper triangular matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

See Also:

"G. W. Stewart, "Algorithm 1.10, Basic Decompositions," Matrix Algorithms, Vol 1."

Inverse

public Inverse(LowerTriangularMatrix L,
               double epsilon)

Construct the inverse of a lower triangular matrix.

Parameters:

L - a lower triangular matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

See Also:

"G. W. Stewart, "Algorithm 2.3, Basic Decompositions," Matrix Algorithms, Vol 1."