Finite differences

<diff> - Difference and approximate derivative.

DIFF Difference and approximate derivative.

DIFF(X), for a vector X, is [X(2)-X(1) X(3)-X(2) ... X(n)-X(n-1)].

DIFF(X), for a matrix X, is the matrix of row differences,

[X(2:n,:) - X(1:n-1,:)].

DIFF(X), for an N-D array X, is the difference along the first

non-singleton dimension of X.

DIFF(X,N) is the N-th order difference along the first non-singleton

dimension (denote it by DIM). If N >= size(X,DIM), DIFF takes

successive differences along the next non-singleton dimension.

DIFF(X,N,DIM) is the Nth difference function along dimension DIM.

If N >= size(X,DIM), DIFF returns an empty array.

Examples:

h = .001; x = 0:h:pi;

diff(sin(x.^2))/h is an approximation to 2*cos(x.^2).*x

diff((1:10).^2) is 3:2:19

If X = [3 7 5

0 9 2]

then diff(X,1,1) is [-3 2 -3], diff(X,1,2) is [4 -2

9 -7],

diff(X,2,2) is the 2nd order difference along the dimension 2, and

diff(X,3,2) is the empty matrix.

See also gradient, sum, prod.

Overloaded methods:

char/diff

fints/diff

iddata/diff

localtruncps/diff

localpspline/diff

localpoly/diff

umat/diff

ndlft/diff

sym/diff

Reference page in Help browser

doc diff

<gradient> - Approximate gradient.

GRADIENT Approximate gradient.

[FX,FY] = GRADIENT(F) returns the numerical gradient of the

matrix F. FX corresponds to dF/dx, the differences in x (horizontal)

direction. FY corresponds to dF/dy, the differences in y (vertical)

direction. The spacing between points in each direction is assumed to

be one. When F is a vector, DF = GRADIENT(F)is the 1-D gradient.

[FX,FY] = GRADIENT(F,H), where H is a scalar, uses H as the

spacing between points in each direction.

[FX,FY] = GRADIENT(F,HX,HY), when F is 2-D, uses the spacing

specified by HX and HY. HX and HY can either be scalars to specify

the spacing between coordinates or vectors to specify the

coordinates of the points. If HX and HY are vectors, their length

must match the corresponding dimension of F.

[FX,FY,FZ] = GRADIENT(F), when F is a 3-D array, returns the

numerical gradient of F. FZ corresponds to dF/dz, the differences

In the z direction. Gradient(f,h), where h is a scalar,

uses H as the spacing between points in each direction.

[FX,FY,FZ] = GRADIENT(F,HX,HY,HZ) uses the spacing given by

HX, HY, HZ.

[FX,FY,FZ,...] = GRADIENT(F,...) extends similarly when F is N-D

and must be invoked with N outputs and either 2 or N+1 inputs.

Note: The first output FX is always the gradient along the 2nd

dimension of F, going across columns. The second output FY is always

the gradient along the 1st dimension of F, going across rows. For the

third output FZ and the outputs that follow, the Nth output is the

gradient along the Nth dimension of F.

Examples:

[x,y] = meshgrid(-2:.2:2, -2:.2:2);

z = x .* exp(-x.^2 - y.^2);

[px,py] = gradient(z,.2,.2);

contour(z), hold on, quiver(px,py), hold off

Class support for input F:

float: double, single

See also diff, del2.

Overloaded methods:

cgnormfunction/gradient

cglookuptwo/gradient

Reference page in Help browser

doc gradient

<del2> - Discrete Laplacian.

DEL2 Discrete Laplacian.

L = DEL2(U), when U is a matrix, is a discrete approximation of

0.25*del^2 u = (d^2u/dx^2 + d^2u/dy^2)/4. The matrix L is the same

size as U, with each element equal to the difference between an

element of U and the average of its four neighbors.

L = DEL2(U), when U is an N-D array, returns an approximation of

(del^2 u)/2/n, where n is ndims(u).

L = DEL2(U,H), where H is a scalar, uses H as the spacing between

points in each direction (H=1 by default).

L = DEL2(U,HX,HY), when U is 2-D, uses the spacing specified by HX

and HY. If HX is a scalar, it gives the spacing between points in

the x-direction. If HX is a vector, it must be of length SIZE(U,2)

and specifies the x-coordinates of the points. Similarly, if HY