gradient

Purpose

Approximate gradient.

Synopsis

[PX,PY] = gradient(Z)
[PX,PY] = gradient(Z,x,y)
[PX,PY] = gradient(Z,dx,dy)
p = gradient(Z,...)
          
d = gradient(y)
d = gradient(y,x)
d = gradient(y,dx)

Description

[PX,PY] = gradient(Z), with a single matrix argument, computes a numerical approximation to the gradient field of the function tabulated in Z. The result is ordinarily two matrices, the same size as Z, containing horizontal and vertical first differences. One-sided differences are used at the edges of the matrix and centered differences are used in the interior.

[PX,PY] = gradient(Z,x,y), with one matrix and two vector arguments, uses divided differences involving the vector x in the horizontal direction and the vector y in the vertical direction.

[PX,PY] = gradient(Z,dx,dy), with one matrix and two scalar arguments, divides the horizontal difference by the scalar dx and the vertical difference by the scalar dy.

P = gradient(Z,...), with one output argument, returns a complex result, P = PX + i*PY.

d = gradient(y), with a single vector argument, computes a numerical approximation to the first derivative of the function tabulated in y. The result is a vector, the same size as y, containing first differences. One-sided differences are used at the ends of the vector and centered differences are used in the interior.

d = gradient(y,x), with two vector arguments, uses divided differences to approximate the derivative.

d = gradient(y,dx), with one vector and one scalar argument, divides the first difference by the scalar dx.

Examples

The statements

x = -pi:pi/20:pi;
y = -1:.05:1;
[X,Y] = meshgrid(x,y);
Z = sin(X) + Y.^3;
[PX,PY] = gradient(Z,x,y);
produce a matrix PX approximating the partial derivative with respect to x, which is cos(X), and a matrix PY approximating the partial derivative with respect to y, which is 3*Y.^2.

The statements

x = -pi:pi/500:pi;
y = tan(sin(x)) - sin(tan(x));
d = gradient(y,x);
produce a vector which approximates the derivative dy/dx.

See Also

contour, del2, diff, quiver

(c) Copyright 1994 by The MathWorks, Inc.