dev.nm.algebra.linear.matrix.doubles.operation

Class Pow

java.lang.Object

dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.DenseMatrix

dev.nm.algebra.linear.matrix.doubles.operation.Pow

All Implemented Interfaces:

Matrix, MatrixAccess, MatrixRing, MatrixTable, Densifiable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Table, DeepCopyable

public class Pow
extends DenseMatrix

This is a square matrix A to the power of an integer n, \(A^{n}\). To avoid overflow of double precision, we represent the result as a product of \[ A^{n} = \mathrm{base}^{\mathrm{scale}} \cdot B; \] E.g., \[ A^{n} = (10^{100})^{\mathrm{scale}} \cdot B = 10^{100 \cdot \mathrm{scale}} \cdot B \] All entries in B can be represented in double precision.

Constructor Summary

Constructors

Constructor and Description
Pow(Matrix A, int n) Construct the power matrix \(A^{n}\) so that \[ A^{n} = (10^{100})^{\mathrm{scale}} \cdot B \]
Pow(Matrix A, int n, double base) Construct the power matrix \(A^{n}\) so that \[ A^{n} = \mathrm{base}^{\mathrm{scale}} \cdot B \]

Method Summary

Modifier and Type	Method and Description
ImmutableMatrix	B() Get the double precision matrix.
double	base() Get the radix or base of the coefficient.
int	scale() Get the exponential of the coefficient.

Methods inherited from class dev.nm.algebra.linear.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

Methods inherited from interface dev.nm.algebra.linear.matrix.doubles.Matrix

toCSV

Constructor Detail

Pow

public Pow(Matrix A,
           int n,
           double base)

Construct the power matrix \(A^{n}\) so that \[ A^{n} = \mathrm{base}^{\mathrm{scale}} \cdot B \]

Parameters:

A - a matrix

n - a positive integer exponent

base - the base to scale down the product to avoid overflow

Pow

public Pow(Matrix A,
           int n)

Construct the power matrix \(A^{n}\) so that \[ A^{n} = (10^{100})^{\mathrm{scale}} \cdot B \]

Parameters:

A - a matrix

n - a positive integer exponent

Method Detail

base

public double base()

Get the radix or base of the coefficient.

Returns:

the base

See Also:

Wikipedia: Radix

scale

public int scale()

Get the exponential of the coefficient.

Returns:

the exponential of the coefficient

B

public ImmutableMatrix B()

Get the double precision matrix.

Returns:

the double precision matrix