ndgrid and meshgrid functions-Matlab

tags: Matlab

ndgridFunction andmeshgridThe function is similar, but the former supports from 1 to n dimensions, while the latter is only limited to 2 and 3 dimensions. In 2D and 3D, the coordinate output of the two functions is the same. The difference lies in the shape of the output array. For grid vectors x1gv, x2gv, x3gv, the lengths are M, N, and P respectively.ndgrid（x1gv, x2gv）The function outputs an array of MXN, andmeshgrid（x1gv, x2gv）Output an N*M array, similarly,ndgrid（x1gv, x2gv, x3gv）The function outputs an array of M*N*P, andmeshgrid（x1gv, x2gv, x3gv）Output an array of N*M*P .

The following example illustrates

[cpp] view plain copy
  1. x1gv =  [1 2];  
  2. x2gv =  [4 5 6];  
  3. x3gv =  [4 5 6 7];  
  4. a = ndgrid(x1gv,x2gv,x3gv)  
  5. b = meshgrid(x1gv,x2gv,x3gv)  

Result output

[cpp] view plain copy
  1. a(:,:,1) =  
  2.      1     1     1  
  3.      2     2     2  
  4.   
  5. a(:,:,2) =  
  6.      1     1     1  
  7.      2     2     2  
  8.   
  9. a(:,:,3) =  
  10.      1     1     1  
  11.      2     2     2  
  12.   
  13. a(:,:,4) =  
  14.      1     1     1  
  15.      2     2     2  
[cpp] view plain copy
  1. b(:,:,1) =  
  2.      1     2  
  3.      1     2  
  4.      1     2  
  5.   
  6. b(:,:,2) =  
  7.      1     2  
  8.      1     2  
  9.      1     2  
  10.   
  11. b(:,:,3) =  
  12.      1     2  
  13.      1     2  
  14.      1     2  
  15.   
  16. b(:,:,4) =  
  17.      1     2  
  18.      1     2  
  19.      1     2  


For example, the dimensions of x1gv, x2gv, and x3gv are 2, 3, and 4 respectively. After executing the two functions, a = ndgrid(x1gv,x2gv,x3gv), the dimensions of the output a is 2x3x4, and b = meshgrid(x1gv,x2gv,x3gv), the output dimension is 3x2x4.


The following explains the ndgrid() function in detail

 [X1,X2,X3,...] = ndgrid(x1gv,x2gv,x3gv,...), copy the values ​​of x1gv,x2gv,x3gv,... to generate a rectangular grid coordinate (X1,X2,X3,...). The element of the i-th dimension of the output array Xi is copied from the grid vector xigv. For example, the grid vector x1gv forms the rows of X1, the grid vector x2gv forms the columns of X2, and so on...

The above may be more convoluted, for a simple example,

[cpp] view plain copy
  1. x1gv =1:.1:2;  
  2. x2gv =4:.2:5;  
  3. [a b]= ndgrid(x1gv,x2gv)  
among them,

x1gv = [1 1.1 1.2 1.3 1.4 1.4 1.5 1.6 1.7 1.8 1.8 1.9 2], dimension is 1*11, length is 11, x2gv = [4 4.2 4.4 4.6 4.8 5], dimension The number is 1*6 and the length is 6, then, the rows of the output a are copied from the elements of x1gv, and the columns of the output b are also copied from the elements of x2gv.

The output result is as follows: As mentioned above, the dimension of the output array should be 11*6. Compare the contents of a and b with x1gv and x2gv, and you can understand the above Mouth place.

[cpp] view plain copy
  1. a =  
  2.     1.0000    1.0000    1.0000    1.0000    1.0000    1.0000  
  3.     1.1000    1.1000    1.1000    1.1000    1.1000    1.1000  
  4.     1.2000    1.2000    1.2000    1.2000    1.2000    1.2000  
  5.     1.3000    1.3000    1.3000    1.3000    1.3000    1.3000  
  6.     1.4000    1.4000    1.4000    1.4000    1.4000    1.4000  
  7.     1.5000    1.5000    1.5000    1.5000    1.5000    1.5000  
  8.     1.6000    1.6000    1.6000    1.6000    1.6000    1.6000  
  9.     1.7000    1.7000    1.7000    1.7000    1.7000    1.7000  
  10.     1.8000    1.8000    1.8000    1.8000    1.8000    1.8000  
  11.     1.9000    1.9000    1.9000    1.9000    1.9000    1.9000  
  12.     2.0000    2.0000    2.0000    2.0000    2.0000    2.0000  
  13.   
  14. b =  
  15.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  16.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  17.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  18.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  19.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  20.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  21.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  22.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  23.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  24.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  
  25.     4.0000    4.2000    4.4000    4.6000    4.8000    5.0000  

Finally, the dimension of the output array is determined by the number of output variables, which is determined byndgrid（……）Determined by the number of output lists on the right side of the function. This sentence means that if the number of outputs is 1, then the dimension is N*1, and N is the length of the grid vector, if the number of outputs is 2, then the dimension of each is N*N.

[cpp] view plain copy
  1. x1gv =1:.1:2;  
  2. [a]= ndgrid(x1gv)  

[cpp] view plain copy
  1. a =  
  2.     1.0000  
  3.     1.1000  
  4.     1.2000  
  5.     1.3000  
  6.     1.4000  
  7.     1.5000  
  8.     1.6000  
  9.     1.7000  
  10.     1.8000  
  11.     1.9000  
  12.     2.0000  

[cpp] view plain copy
  1. x1gv =1:.1:2;  
  2. [a b]= ndgrid(x1gv)  

 
   
 
   
 
    
 
     
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  1.  a =  
    2. 
     
  2.    Columns 1 through 9  
    3. 
     
  3.      1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000  
    4. 
     
  4.      1.1000    1.1000    1.1000    1.1000    1.1000    1.1000    1.1000    1.1000    1.1000  
    5. 
     
  5.      1.2000    1.2000    1.2000    1.2000    1.2000    1.2000    1.2000    1.2000    1.2000  
    6. 
     
  6.      1.3000    1.3000    1.3000    1.3000    1.3000    1.3000    1.3000    1.3000    1.3000  
    7. 
     
  7.      1.4000    1.4000    1.4000    1.4000    1.4000    1.4000    1.4000    1.4000    1.4000  
    8. 
     
  8.      1.5000    1.5000    1.5000    1.5000    1.5000    1.5000    1.5000    1.5000    1.5000  
    9. 
     
  9.      1.6000    1.6000    1.6000    1.6000    1.6000    1.6000    1.6000    1.6000    1.6000  
    10. 
     
  10.      1.7000    1.7000    1.7000    1.7000    1.7000    1.7000    1.7000    1.7000    1.7000  
    11. 
     
  11.      1.8000    1.8000    1.8000    1.8000    1.8000    1.8000    1.8000    1.8000    1.8000  
    12. 
     
  12.      1.9000    1.9000    1.9000    1.9000    1.9000    1.9000    1.9000    1.9000    1.9000  
    13. 
     
  13.      2.0000    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000  
    14. 
     
  14.    
    15. 
     
  15.    Columns 10 through 11  
    16. 
     
  16.      1.0000    1.0000  
    17. 
     
  17.      1.1000    1.1000  
    18. 
     
  18.      1.2000    1.2000  
    19. 
     
  19.      1.3000    1.3000  
    20. 
     
  20.      1.4000    1.4000  
    21. 
     
  21.      1.5000    1.5000  
    22. 
     
  22.      1.6000    1.6000  
    23. 
     
  23.      1.7000    1.7000  
    24. 
     
  24.      1.8000    1.8000  
    25. 
     
  25.      1.9000    1.9000  
    26. 
     
  26.      2.0000    2.0000  
    27. 
     
  27.    
    28. 
     
  28.  b =  
    29. 
     
  29.    Columns 1 through 9  
    30. 
     
  30.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    31. 
     
  31.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    32. 
     
  32.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    33. 
     
  33.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    34. 
     
  34.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    35. 
     
  35.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    36. 
     
  36.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    37. 
     
  37.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    38. 
     
  38.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    39. 
     
  39.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    40. 
     
  40.      1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000  
    41. 
     
  41.    
    42. 
     
  42.    Columns 10 through 11  
    43. 
     
  43.      1.9000    2.0000  
    44. 
     
  44.      1.9000    2.0000  
    45. 
     
  45.      1.9000    2.0000  
    46. 
     
  46.      1.9000    2.0000  
    47. 
     
  47.      1.9000    2.0000  
    48. 
     
  48.      1.9000    2.0000  
    49. 
     
  49.      1.9000    2.0000  
    50. 
     
  50.      1.9000    2.0000  
    51. 
     
  51.      1.9000    2.0000  
    52. 
     
  52.      1.9000    2.0000  
    53. 
     
  53.      1.9000    2.0000  
    54. 
    

   
 
   

   
 
 
   
 
 
   
 gives a dazzling drawing method
 
   
 
 
   
 
    
 
     
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  1.  [x1,x2,x3] = ndgrid(-2:.2:2, -2:.25:2, -2:.16:2);  
    2. 
     
  2.  z = x2 .* exp(-x1.^2 - x2.^2 - x3.^2);  
    3. 
     
  3.  slice(x2,x1,x3,z,[-1.2 .8 2],2,[-2 -.2]);  
    4. 
    

   
 
   

   

   
 
 
   
 
    
   
 
   

   
 
 
   
 
 
   
 The above explanation may not be very clear, you can refer to the help file of matlab for details
 
   
 Attach the link:http://cn.mathworks.com/help/matlab/ref/ndgrid.html
 
  








				

				






				
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