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ndgrid
arrays for multidimensional function evaluation on grid
Calling Sequence
[X, Y] = ndgrid(x,y) [X, Y, Z] = ndgrid(x,y,z) [X, Y, Z, T] = ndgrid(x,y,z,t) [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
Arguments
- x, y, z, ...
vectors
- X, Y, Z, ...
matrices in case of 2 input arguments, or else hypermatrices
Description
This is an utility routine useful to create arrays for function
evaluation on 2, 3, ..., n dimensional grids. For instance in 2d, a grid
is defined by two vectors, x
and y
of length nx and ny, and you want to evaluate a function (says
f) on all the grid points, that is on all the points
of coordinates (x(i),y(j)) with
i=1,..,nx and j=1,..,ny. In this
case, this function can compute the two matrices X,Y
of
size nx x ny such that :
X(i,j) = x(i) for all i in [1,nx] Y(i,j) = y(j) and j in [1,ny]
and the evaluation may be done with Z=f(X,Y)
(at
the condition that you have coded f
for evaluation on
vector arguments, which is done (in general) by using the element-wise
operators .*
, ./
and
.^
in place of *
,
/
and ^
).
In the 3d case, considering 3 vectors x,y,z
of
length nx, ny and nz, X,Y,Z
are 3 hypermatrices of size
nx x ny x nz such that :
X(i,j,k) = x(i) Y(i,j,k) = y(j) for all (i,j,k) in [1,nx]x[1,ny]x[1,nz] Z(i,j,k) = z(k)
In the general case of m input arguments x1, x2, ..,
xm
,then the m output arguments X1, X2, ..,
Xm
are hypermatrices of size nx1 x nx2 x ... x
nxm
and :
Xj(i1,i2,...,ij,...,im) = xj(ij) for all (i1,i2,...,im) in [1,nx1]x[1,nx2]x...x[1,nxm]
Examples
// create a simple 2d grid nx = 40; ny = 40; x = linspace(-1,1,nx); y = linspace(-1,1,ny); [X,Y] = ndgrid(x,y); // compute a function on the grid and plot it //deff("z=f(x,y)","z=128*x.^2 .*(1-x).^2 .*y.^2 .*(1-y).^2"); deff("z=f(x,y)","z=x.^2 + y.^3") Z = f(X,Y); clf() plot3d(x,y,Z, flag=[2 6 4]); show_window()
// create a simple 3d grid nx = 10; ny = 6; nz = 4; x = linspace(0,2,nx); y = linspace(0,1,ny); z = linspace(0,0.5,nz); [X,Y,Z] = ndgrid(x,y,z); // try to display this 3d grid ... XF=[]; YF=[]; ZF=[]; for k=1:nz [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k)); XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; end for j=1:ny [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),... matrix(Y(:,j,:),[nx,nz]),... matrix(Z(:,j,:),[nx,nz])); XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; end clf() plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z") xtitle("A 3d grid !"); show_window()
See Also
- kron — Kronecker product (.*.)
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