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gradient

Numerical gradient

Syntax

Definition

The gradient of a function of two variables, , is defined as

and can be thought of as a collection of vectors pointing in the direction of increasing values of . In MATLAB, numerical gradients (differences) can be computed for functions with any number of variables. For a function of variables, ,

Description

FX = gradient(F) where F is a vector returns the one-dimensional numerical gradient of F. FX corresponds to , the differences in the direction.

[FX,FY] = gradient(F) where F is a matrix returns the and components of the two-dimensional numerical gradient. FX corresponds to , the differences in the (column) direction. FY corresponds to , the differences in the (row) direction. The spacing between points in each direction is assumed to be one.

[FX,FY,FZ,...] = gradient(F) where F has N dimensions returns the N components of the gradient of F. There are two ways to control the spacing between values in F:

[...] = gradient(F,h) where h is a scalar uses h as the spacing between points in each direction.

[...] = gradient(F,h1,h2,...) with N spacing parameters specifies the spacing for each dimension of F.

Examples

The statements

produce

Given,

takes dx = dy = dz = 1.

takes dx = 0.2, dy = 0.1, and dz = 0.2.

See Also

del2, diff


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