com.numericalmethod.suanshu.analysis.differentiation.multivariate

Class Jacobian

java.lang.Object

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

com.numericalmethod.suanshu.analysis.differentiation.multivariate.Jacobian

All Implemented Interfaces:

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

public class Jacobian
extends DenseMatrix

The Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. For a Rⁿ->R^m function, we have a \(m \times n\) matrix. \[ J=\begin{bmatrix} \dfrac{\partial y_1}{\partial x_1} & \cdots & \dfrac{\partial y_1}{\partial x_n} \\ \vdots & \ddots & \vdots \\ \dfrac{\partial y_m}{\partial x_1} & \cdots & \dfrac{\partial y_m}{\partial x_n} \end{bmatrix} \]

This implementation computes the Jacobian matrix numerically using the finite difference method.

See Also:

Wikipedia: Jacobian matrix and determinant

Constructor Summary

Constructors

Constructor and Description
Jacobian(List<RealScalarFunction> f, Vector x) Construct the Jacobian matrix for a multivariate function f at point x.
Jacobian(RealScalarFunction[] f, Vector x) Construct the Jacobian matrix for a multivariate function f at point x.
Jacobian(RealVectorFunction f, Vector x) Construct the Jacobian matrix for a multivariate function f at point x.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.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

Constructor Detail

Jacobian

public Jacobian(RealVectorFunction f,
                Vector x)

Construct the Jacobian matrix for a multivariate function f at point x.

Parameters:

f - a multivariate function

x - the point to evaluate the Jacobian matrix at

Jacobian

public Jacobian(RealScalarFunction[] f,
                Vector x)

Construct the Jacobian matrix for a multivariate function f at point x.

Parameters:

f - a multivariate function in the form of an array of univariate functions

x - the point to evaluate the Jacobian matrix at

Jacobian

public Jacobian(List<RealScalarFunction> f,
                Vector x)

Construct the Jacobian matrix for a multivariate function f at point x.

Parameters:

f - a multivariate function in the form of a list of univariate functions

x - the point to evaluate the Jacobian matrix at