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.

See Also:
  • Constructor Details

    • 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