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

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.Gradient

All Implemented Interfaces:

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

public class Gradient
extends DenseMatrix

The gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and of which the magnitude is the greatest rate of change.

Mathematically, the gradient of a scalar function is a 1xn matrix, where n is the domain dimension of f.

        ∂f         ∂f
 gf = [----, ..., ----]
        ∂x1        ∂x2
 

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

See Also:

FiniteDifference, Wikipedia: Gradient

Constructor Summary

Gradient(RealScalarFunction f, double... x)
Construct a gradient row matrix for a multivariate function f at point x.

Method Summary

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

Gradient

public Gradient(RealScalarFunction f,
                double... x)

Construct a gradient row matrix for a multivariate function f at point x.

Parameters:

f - a multivariate function

x - the point to evaluate the gradient of f at