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ndgrid

Rectangular grid in N-D space

Syntax

[X1,X2,...,Xn] = ndgrid(x1,x2,...,xn)
[X1,X2,...,Xn] = ndgrid(xg)

Description

example

[X1,X2,...,Xn] = ndgrid(x1,x2,...,xn) replicates the grid vectors x1,x2,...,xn to produce an n-dimensional full grid.

example

[X1,X2,...,Xn] = ndgrid(xg) specifies a single grid vector xg to use for all dimensions. The number of output arguments you specify determines the dimensionality n of the output.

Examples

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Create a 2-D grid from the vectors [1 3 5 7 9 11 13 15 17 19] and [2 4 6 8 10 12].

[X,Y] = ndgrid(1:2:19,2:2:12)
X = 10×6

1     1     1     1     1     1
3     3     3     3     3     3
5     5     5     5     5     5
7     7     7     7     7     7
9     9     9     9     9     9
11    11    11    11    11    11
13    13    13    13    13    13
15    15    15    15    15    15
17    17    17    17    17    17
19    19    19    19    19    19

Y = 10×6

2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12
2     4     6     8    10    12

Evaluate and plot the function

${x}_{1}{e}^{-{x}_{1}^{2}-{x}_{2}^{2}}$

over the gridded domain

$-2<{x}_{1}<2$ and $-2<{x}_{2}<2$.

Create a grid of values for the domain.

[X1,X2] = ndgrid(-2:.2:2);

Evaluate the function over the domain.

Z = X1 .* exp(-X1.^2 - X2.^2);

Generate a mesh plot of the function.

mesh(X1,X2,Z)

In R2016b and later releases, this task does not require the use of ndgrid. Instead, you can construct the grid using implicit expansion with these commands:

x = -2:.2:2;

Z1 = x.' .* exp(-(x.').^2 - x.^2);

Create a 2-D grid and calculate some function values on the grid. Interpolate between the assigned values to refine the grid.

Create a coarse grid for $\left(x,y\right)$ in the range $\left[-5,5\right]$.

[X,Y] = ndgrid(-5:0.5:5);

Calculate some function values on the grid and plot the function.

f = sin(X.^2) * cos(Y.^2);
surf(X,Y,f)

Interpolate between the points using a more refined grid and plot the result.

[X1,Y1] = ndgrid(-5:0.125:5);
F = interpn(X,Y,f,X1,Y1,'spline');
surf(X1,Y1,F)

Input Arguments

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Grid vectors, specified as vectors containing grid coordinates for each dimension. The grid vectors implicitly define the grid. For example, in 2-D:

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

Grid vector for all dimensions, specified as a vector containing grid coordinates. ndgrid uses xg as the grid vector for each dimension.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

Output Arguments

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Full grid representation, returned as separate arrays. For each output array Xi, the ith dimension contains copies of the grid vector xi.

Tips

• The ndgrid function is similar to meshgrid. However, ndgrid supports 1-D to N-D while meshgrid is restricted to 2-D and 3-D.