{"id":4721,"date":"2021-07-26T16:47:47","date_gmt":"2021-07-26T20:47:47","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/?p=4721"},"modified":"2021-07-26T16:47:47","modified_gmt":"2021-07-26T20:47:47","slug":"use-less-meshgrid-and-repmat","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2021\/07\/26\/use-less-meshgrid-and-repmat\/","title":{"rendered":"Use less meshgrid and repmat"},"content":{"rendered":"
The functions <\/span>meshgrid<\/span> and <\/span>repmat<\/span> have a long and rich history in MATLAB. Today, I'll try to convince you to use them less.<\/span><\/div>

meshgrid<\/span><\/h2>
The function <\/span>meshgrid<\/span> is typically used to take a vector of x-coordinates and a vector of y-coordinates and turn them into two matrices, <\/span>X<\/span> and <\/span>Y<\/span>, that can be used to compute a function of two variables. Here is a small example.<\/span><\/div>
x = [0 1 2];<\/span><\/span><\/div><\/div>
y = [0 10 20 30];<\/span><\/span><\/div><\/div>
[X,Y] = meshgrid(x,y)<\/span><\/span><\/div>
X = <\/span>4\u00d73<\/span><\/div><\/div>
0 1 2\r\n 0 1 2\r\n 0 1 2\r\n 0 1 2\r\n<\/div>
<\/div>
<\/div><\/div><\/div><\/div>
Y = <\/span>4\u00d73<\/span><\/div><\/div>
0 0 0\r\n 10 10 10\r\n 20 20 20\r\n 30 30 30\r\n<\/div>
<\/div>
<\/div><\/div><\/div><\/div><\/div><\/div><\/div>
Here is another example that illustrates how <\/span>meshgrid<\/span> is typically used. The example, taken from the 2nd edition (2009) of <\/span>Digital Image Processing Using MATLAB, <\/span>constructs a surface plot of the function <\/span>$ f(x,y) = xe^{-(x^2 + y^2)} $<\/span>.<\/span><\/div>
x = -2:0.1:2;<\/span><\/span><\/div><\/div>
y = -2:0.1:2;<\/span><\/span><\/div><\/div>
[X,Y] = meshgrid(x,y);<\/span><\/span><\/div><\/div>
Z = X.*exp(-(X.^2 + Y.^2));<\/span><\/span><\/div><\/div>
surf(Z)<\/span><\/span><\/div>
<\/div><\/div><\/div><\/div><\/div>
The variables <\/span>x<\/span> and <\/span>y<\/span> are vectors, and the variables <\/span>X<\/span> and <\/span>Y<\/span> are matrices:<\/span><\/div>
whos <\/span>x y X Y<\/span><\/span><\/div>
Name Size Bytes Class Attributes\r\n\r\n X 41x41 13448 double \r\n Y 41x41 13448 double \r\n x 1x41 328 double \r\n y 1x41 328 double <\/div><\/div><\/div><\/div><\/div>
The function <\/span>meshgrid<\/span> has been used to construct same-sized matrices so that they can be combined together in various element-wise arithmetic operations on matrices that represent two spatial coordinates.<\/span><\/div>

repmat<\/span><\/h2>
The function name <\/span>repmat<\/span> is an abbrevation of \"replicate matrix.\" One common use for <\/span>repmat<\/span> is to replicate a vector to be the size of a matrix, or to replicate a matrix to be the size of a 3-D array. A classic example is to subtract the column means from a matrix:<\/span><\/div>
A = rand(4)<\/span><\/span><\/div>
A = <\/span>4\u00d74<\/span><\/div><\/div>
0.8147 0.6324 0.9575 0.9572\r\n 0.9058 0.0975 0.9649 0.4854\r\n 0.1270 0.2785 0.1576 0.8003\r\n 0.9134 0.5469 0.9706 0.1419\r\n<\/div>
<\/div>
<\/div><\/div><\/div><\/div><\/div><\/div>
col_means = mean(A,1)<\/span><\/span><\/div>
col_means = <\/span>1\u00d74<\/span><\/div><\/div>
0.6902 0.3888 0.7627 0.5962\r\n<\/div>
<\/div>
<\/div><\/div><\/div><\/div><\/div><\/div>
B = repmat(col_means,size(A,1),1)<\/span><\/span><\/div>
B = <\/span>4\u00d74<\/span><\/div><\/div>
0.6902 0.3888 0.7627 0.5962\r\n 0.6902 0.3888 0.7627 0.5962\r\n 0.6902 0.3888 0.7627 0.5962\r\n 0.6902 0.3888 0.7627 0.5962\r\n<\/div>
<\/div>
<\/div><\/div><\/div><\/div><\/div><\/div>
C = A - B<\/span><\/span><\/div>
C = <\/span>4\u00d74<\/span><\/div><\/div>
0.1245 0.2435 0.1949 0.3610\r\n 0.2156 -0.2913 0.2022 -0.1108\r\n -0.5632 -0.1103 -0.6050 0.2041\r\n 0.2232 0.1581 0.2079 -0.4543\r\n<\/div>
<\/div>
<\/div><\/div><\/div><\/div><\/div><\/div><\/div>

Five-Year Anniversary of MATLAB Arithmetic Operator Change<\/span><\/h2>
Five years ago, with the R2016b release of MATLAB, some MATLAB operators and functions were generalized in a way that made many uses of <\/span>meshgrid<\/span> and <\/span>repmat<\/span> no longer necessary. With that release, operators such as <\/span>+<\/span> and <\/span>-<\/span> that take two operands could automatically handle operands with different sizes, as long as the size differences took a specific form. In the example above, <\/span>A<\/span> has size 4x4, and <\/span>col_means<\/span> has size 1x4. Prior to the R2016b release, the expression <\/span>A - col_means <\/span>would produce an error because of the mismatched sizes. Starting in R2016b, though, arithmetic operators (and some other operators and functions) can automatically match up different sizes when one or the other operand has a dimension of 1 in the mismatched dimension.<\/span><\/div>
This means that you no longer need to call <\/span>repmat<\/span> to subtract the column means from a matrix. You can do it just with the <\/span>-<\/span> operator:<\/span><\/div>
C = A - mean(A,1)<\/span><\/span><\/div>
C = <\/span>4\u00d74<\/span><\/div><\/div>
0.1245 0.2435 0.1949 0.3610\r\n 0.2156 -0.2913 0.2022 -0.1108\r\n -0.5632 -0.1103 -0.6050 0.2041\r\n 0.2232 0.1581 0.2079 -0.4543\r\n<\/div>
<\/div>
<\/div><\/div><\/div><\/div><\/div><\/div><\/div>
Also, you usually no longer need to use <\/span>meshgrid<\/span> as shown above to compute a function of two variables. The code in the previous example can now be written as:<\/span><\/div>
x = -2:0.1:2;<\/span><\/span><\/div><\/div>
y = (-2:0.1:2)';<\/span><\/span><\/div><\/div>
Z = x.*exp(-(x.^2 + y.^2));<\/span><\/span><\/div><\/div>
surf(Z)<\/span><\/span><\/div>
<\/div><\/div><\/div><\/div><\/div>
The 3rd edition (2020) of <\/span>Digital Image Processing Using MATLAB<\/span> was revised accordingly.<\/span><\/div>

For More Information<\/span><\/h2>
For more information about the details and history of this change, I recommend these sources. The first three of these appear on Loren Shure's Art of MATLAB blog; the first two were guest-written by me. The last source is a MATLAB documentation page.<\/span><\/div>