How to pass on arguments in the form of two grids and return a matrix the elements of which involve conditional statements?

Question

idermann 2023-3-27

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1935969-how-to-pass-on-arguments-in-the-form-of-two-grids-and-return-a-matrix-the-elements-of-which-involve

评论： VBBV 2023-3-27

在 MATLAB Online 中打开

Consider the following function of the two variables r and t which returns 5 if

and 8 if

:

function a = f(r, t)
a = 5 * (t < r) + 8 * (r < t);
end

I would like to evaluate this function on a grid. The following implementation does the job:

N = 4;
DT = 1/N;
t = linspace(DT/2, 1-DT/2, N)';
r = t + 0.3 * DT;
[rr, tt] = ndgrid(r, t);
a = f(rr, tt)

Now suppose that 5 and 8 are actually very expensive operations that should only be evaluated at the corresponding condition.

I tried the following naive code but I only obtained a scalar and not the desired matrix.

function a = f(r, t)
if (t < r)
a = 5;
else
a = 8;
end
end

I was wondering what could be missing in my implementation. Any help is highly appreciated. Thank you!

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

idermann 2023-3-27

编辑：idermann 2023-3-27

It would of course be possible in the Matlab script to call the function

times using 2 for loops but this is obviously very slow.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

VBBV 2023-3-27

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1935969-how-to-pass-on-arguments-in-the-form-of-two-grids-and-return-a-matrix-the-elements-of-which-involve#answer_1201979

在 MATLAB Online 中打开

N = 4;
DT = 1/N;
t = linspace(DT/2, 1-DT/2, N)';
r = t + 0.3 * DT;
[rr, tt] = ndgrid(r, t);
a = f(rr, tt)
a = 1×16
     5     5     5     5     5     5     5     5     5     5     8     8     8     8     8     8
 
function a = f(r, t)
    
    idx1 = (t < r);  % 
    
    a1 = 5*ones(numel(idx1(idx1==1)),1);
    
    idx2 = r < t;    
    a2 = 8*ones(numel(idx2(idx2==1)),1);    
    
    a = [a1.' a2.'];
end

2 个评论
显示无隐藏无

idermann 2023-3-27

在 MATLAB Online 中打开

Thanks for the answer. What one should get is rather

   8     8     8
   5     8     8
   5     5     8
   5     5     5

Reshaping what we get from the function you wrote gives something different. But I should be able to figure out the rest myself.

VBBV 2023-3-27

在 MATLAB Online 中打开

This is easier method than before, and something that you actually want

N = 4;
DT = 1/N;
t = linspace(DT/2, 1-DT/2, N)';
r = t + 0.3 * DT;
[rr, tt] = ndgrid(r, t);
a = f(rr, tt)
a = 4×4
     5     8     8     8
     5     5     8     8
     5     5     5     8
     5     5     5     5
 
 
function a = f(r, t)
    
    idx1 = (t < r);  % 
    A = idx1*5;    % this is easier than before
    
    idx2 = r < t;   
    B = idx2*8;    
    
    a = A+B;
end

请先登录，再进行评论。

Answer 2

Dyuman Joshi 2023-3-27

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1935969-how-to-pass-on-arguments-in-the-form-of-two-grids-and-return-a-matrix-the-elements-of-which-involve#answer_1202004

编辑：Dyuman Joshi 2023-3-27

在 MATLAB Online 中打开

"I tried the following naive code but I only obtained a scalar and not the desired matrix"

You obtained a scalar because you assigned a scalar.

And you are using non-scalar value as a condition to if-else statements, which evaluates all the values to a condition and proceeds accordingly.

if [0 1; 1 2]
    disp('if')
elseif 3*ones(5)
    disp('elseif')
else
    disp('else')
end
elseif

It depends on the operation but this should work for a good amount of cases. If this doesn't work, please specify the 'expensive operation' you are trying to implement.

function a = f(r, t)
id1 = r>t;
%do expensive operation on these indices
id2 = r<t; %or id2 = ~id1
%do expensive operation on these indices
end

4 个评论
显示 2更早的评论隐藏 2更早的评论

idermann 2023-3-27

g1 and g2 involve infinite sums of terms involving hypergeom functions. They are really very complicated and there is no real interest in providing their expressions explicitly here I guess. If we could have a solution for general g1 and g2, that would be a dream. Thanks Dyuman.

idermann 2023-3-27

I realized that using parfor for parallel computation leads to a quick evaluation of the kernel functions without the need for vectorizing the implementation. Sometimes simple approaches save both time and energy. Thanks for your valuable help anyway.

请先登录，再进行评论。

How to pass on arguments in the form of two grids and return a matrix the elements of which involve conditional statements?

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

回答（2 个）

2 个评论
显示无隐藏无

4 个评论
显示 2更早的评论隐藏 2更早的评论

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

How to pass on arguments in the form of two grids and return a matrix the elements of which involve conditional statements?

1 个评论 显示 -1更早的评论隐藏 -1更早的评论

回答（2 个）

2 个评论 显示 无隐藏 无

4 个评论 显示 2更早的评论隐藏 2更早的评论

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

2 个评论
显示无隐藏无

4 个评论
显示 2更早的评论隐藏 2更早的评论