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

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl<T>
      com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl<DenseMatrix>
          com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix
              com.numericalmethod.suanshu.matrix.doubles.operation.Inverse

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccessor, MatrixRing, Densifiable, MatrixDimension

public class Inverse
extends DenseMatrix

For a square matrix A,

A-1

, if the inverse exists. This equality holds true:

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

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

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

See Also:

Wikipedia: Invertible matrix

Field Summary

int	dim dimension of the square matrix
double	epsilon a precision parameter: when a number |x| ≤ ε, it is considered 0

Constructor Summary

Inverse(LowerTriangularMatrix L, double epsilon)
Invert a lower triangular matrix.

Inverse(Matrix A)
Construct a DenseMatrix that is the inverse of a DenseMatrix A.

Inverse(Matrix A, double epsilon)
Construct a DenseMatrix that is the inverse of a DenseMatrix A.

Inverse(UpperTriangularMatrix U, double epsilon)
Invert an upper triangular matrix.

Method Summary

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

add, deepCopy, getColumn, getColumn, getMatrixData, getRow, getRow, getSample, minus, multiply, multiply, ONE, overwrite, scaled, t, toDense, ZERO

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl

equals, get, hashCode, set, setMatrixData

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl

add, call, minus, multiply, nCols, nRows, opposite, setColumn, setColumn, setRow, setRow, toString

Methods inherited from class java.lang.Object

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

Field Detail

dim

public final int dim

dimension of the square matrix

epsilon

public final double epsilon

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

Constructor Detail

Inverse

public Inverse(Matrix A,
               double epsilon)

Construct a DenseMatrix that is the inverse of a DenseMatrix A.

Parameters:

A - a DenseMatrix

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

Inverse

public Inverse(Matrix A)

Construct a DenseMatrix that is the inverse of a DenseMatrix A.

Parameters:

A - a DenseMatrix

Inverse

public Inverse(UpperTriangularMatrix U,
               double epsilon)

Invert 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:

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

Inverse

public Inverse(LowerTriangularMatrix L,
               double epsilon)

Invert 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:

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