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

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl<T>
      com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl<DenseMatrix>
          com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix
              com.numericalmethod.suanshu.analysis.differentiation.multivariate.Jacobian

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccessor, MatrixRing, Densifiable, MatrixDimension

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

      |∂y1         ∂y1  |
      |----, ..., ----  |
      |∂x1         ∂xn  |
      |  .              |
 J =  |  .              |
      |  .              |
      |∂ym         ∂ym  |
      |----, ..., ----  |
      |∂x1         ∂xn  |
 

The Jacobian matrix is computed numerically using the finite difference method.

See Also:

FiniteDifference, Wikipedia: Jacobian matrix and determinant

Constructor Summary

Jacobian(RealVectorFunction f, double... x)
Construct an m x n Jacobian matrix for a multivariate function f at point x, where m is the dimension of the function range, and n the dimension of the function domain.

Method Summary

double

determinant() Compute the Jacobian determinant or simply the "Jacobian".

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix

add, deepCopy, getColumn, getColumn, getMatrixData, getRow, getRow, getSample, minus, multiply, multiply, ONE, overwrite, scaled, t, toDense, ZERO

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl

equals, get, hashCode, set, setMatrixData

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl

add, call, minus, multiply, nCols, nRows, opposite, setColumn, setColumn, setRow, setRow, toString

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Jacobian

public Jacobian(RealVectorFunction f,
                double... x)

Construct an m x n Jacobian matrix for a multivariate function f at point x, where m is the dimension of the function range, and n the dimension of the function domain.

Parameters:

f - a multivariate function

x - the point to compute the Jacobian matrix at

Method Detail

determinant

public double determinant()

Compute the Jacobian determinant or simply the "Jacobian".

Returns:

the Jacobian determinant