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# ndgrid

build matrices or N-D arrays by replicating some template vectors

### Syntax

[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 of any data types. They may have distinct data types.

- X, Y, Z, ...
matrices in case of 2 input arguments, or hypermatrices otherwise. They all have the same sizes:

`size(x,"*")`

rows,`size(y,"*")`

columns,`size(z,"*")`

layers, etc. They have the datatypes of respective input vectors:`typeof(X)==typeof(x)`

,`typeof(Y)==typeof(y)`

, etc.

### Description

The first application of `ndgrid`

is to build a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3, or more sets `x`

, `y`

, etc.. of "template" coordinates sampled along each direction/dimension of the space that you want to mesh.

Hence, the matrix or hypermatrix `X`

is made by replicating the vector `x`

as all its columns ; the matrix or hypermatrix `Y`

is made by replicating the vector `y`

as all its rows ; `Z`

is made of replicating the vector `z`

along all its local thicknesses (3rd dimension); etc.

--> [X, Y] = ndgrid([1 3 4], [0 2 4 6]) X = 1. 1. 1. 1. 3. 3. 3. 3. 4. 4. 4. 4. Y = 0. 2. 4. 6. 0. 2. 4. 6. 0. 2. 4. 6.

Then, the coordinates of the node(i,j) in the 2D space will be simply `[x(i), y(j)]`

now given by `[X(i,j), Y(i,j)]`

. As well, the coordinates of a `node(i,j,k)`

of a 3D grid will be `[x(i), y(j), z(k)]`

now given by `[X(i,j,k), Y(i,j,k), Z(i,j,k)]`

.

This replication scheme can be generalized to any number of dimensions, as well to any type of uniform data. Let's for instance consider 2 attributes:

- The first is a number, to be chosen from the vector say
`n= [ 3 7 ]`

- The second is a letter, to be chosen from the vector say
`c= ["a" "e" "i" "o" "u" "y"]`

--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"]) C = !a e i o u y ! !a e i o u y ! N = 3. 3. 3. 3. 3. 3. 7. 7. 7. 7. 7. 7.

Then, the object(i,j) will have the properties `{n(i) c(j)}`

that now can be addressed with `{N(i,j) C(i,j)}`

. This kind of grid may be useful to initialize an array of structures.

Following examples show how to use `X, Y, Z`

in most frequent applications.

### Examples

**Example #1:**

// Create a simple 2d grid x = linspace(-10,2,40); y = linspace(-5,5,40); [X,Y] = ndgrid(x,y); // Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y) Z = X - 3*X.*sin(X).*cos(Y-4) ; clf() plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()

**Example #2:**

// 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], 66, 61,leg="X@Y@Z") xtitle("A 3d grid !"); show_window()

**Example #3: Creates a table of digrams:**

[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"]) c1+c2

--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"]) c2 = !a b c d e f g h ! !a b c d e f g h ! !a b c d e f g h ! c1 = !a a a a a a a a ! !b b b b b b b b ! !c c c c c c c c ! --> c1+c2 ans = !aa ab ac ad ae af ag ah ! !ba bb bc bd be bf bg bh ! !ca cb cc cd ce cf cg ch !

### See also

### History

Version | Description |

6.0 | Extension to all homogeneous datatypes ([], booleans, encoded integers, polynomials, rationals, strings). Revision of the help page. |

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