# Class Jacobian

java.lang.Object
dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.DenseMatrix
dev.nm.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->Rm function, we have a $$m \times n$$ matrix. $J=\begin{bmatrix} \dfrac{\partial y_1}{\partial x_1} invalid input: '&' \cdots invalid input: '&' \dfrac{\partial y_1}{\partial x_n} \\ \vdots invalid input: '&' \ddots invalid input: '&' \vdots \\ \dfrac{\partial y_m}{\partial x_1} invalid input: '&' \cdots invalid input: '&' \dfrac{\partial y_m}{\partial x_n} \end{bmatrix}$

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

• ## Constructor Summary

Constructors
Constructor
Description
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.
Jacobian(List<RealScalarFunction> f, Vector x)
Construct the Jacobian matrix for a multivariate function f at point x.
• ## Method Summary

### 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 Details

• ### Jacobian

public Jacobian
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