# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.analysis.differentiation.multivariate

## Class 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->Rm 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.

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.

• ### 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