doing operations on 1xN struct

i have a structure that holds some data,

the structure is an array of structures (size of 1xN, N is an integer)

one of the data each struct holds is a 3 by 3 matrics with xyz positions of 3 points in space.

so a 1x2 structure will hold 2 matrics 3x3.

i need the square root of each row, but i dont know how to do it without a loop.

is there a way to get the square root of each row, within all the structures in the array without a loop?

Answer 1

[Voss]

Constructing a structure array:

N = 2;
S = struct('matrix_field',permute(num2cell(rand(3,3,N),[1 2]),[1 3 2]),'other_field',{'something','else'})

S = 1x2 struct array with fields:
    matrix_field
    other_field

S(1)

ans = struct with fields:
    matrix_field: [3x3 double]
     other_field: 'something'

S(2)

ans = struct with fields:
    matrix_field: [3x3 double]
     other_field: 'else'

If it's convenient for subsequent operations you need to do, you can concatenate all N 3x3 matrices into a 3x3xN array and take the square root of that, resulting in another 3x3xN array:

M = sqrt(cat(3,S.matrix_field));
disp(M)

(:,:,1) =

    0.7156    0.3034    0.9401
    0.8949    0.9009    0.7890
    0.2553    0.7022    0.2558


(:,:,2) =

    0.5955    0.3100    0.4549
    0.9599    0.8806    0.8985
    0.4852    0.8184    0.8393

Otherwise, you can use arrayfun, which is a loop, and which results in a cell array of 3x3 matrices:

C = arrayfun(@(s)sqrt(s.matrix_field),S,'UniformOutput',false)

C = 1x2 cell array
    {3x3 double}    {3x3 double}

celldisp(C)

 
C{1} =
 
    0.7156    0.3034    0.9401
    0.8949    0.9009    0.7890
    0.2553    0.7022    0.2558

 
 
C{2} =
 
    0.5955    0.3100    0.4549
    0.9599    0.8806    0.8985
    0.4852    0.8184    0.8393

 

Since that gives you a cell array, it's convenient to put the result in a new field in the original structure array, if that's ultimately what you want:

[S.sqrt_matrix_field] = C{:}

S = 1x2 struct array with fields:
    matrix_field
    other_field
    sqrt_matrix_field

S(1).sqrt_matrix_field

ans = 3×3

0.7156 0.3034 0.9401 0.8949 0.9009 0.7890 0.2553 0.7022 0.2558

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S(2).sqrt_matrix_field

ans = 3×3

0.5955 0.3100 0.4549 0.9599 0.8806 0.8985 0.4852 0.8184 0.8393

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Both of those approaches take the square root of each element of each matrix. Since you mentioned taking the square root of each row of each matrix, I'll make a guess at what that means (squaring each element, summing across each row, and taking the square root of that), and show it using both approches.

First the concatenation approach:

M = sqrt(sum(cat(3,S.matrix_field).^2,2));
disp(M)

(:,:,1) =

    1.0256
    1.2990
    0.5017


(:,:,2) =

    0.4217
    1.4498
    1.0001

It may be convenient to permute that 3x1xN array into a 3xN matrix:

M = permute(M,[1 3 2])

M = 3×2

1.0256 0.4217 1.2990 1.4498 0.5017 1.0001

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And the arrayfun approach:

C = arrayfun(@(s)sqrt(sum(s.matrix_field.^2,2)),S,'UniformOutput',false)

C = 1x2 cell array
    {3x1 double}    {3x1 double}

celldisp(C)

 
C{1} =
 
    1.0256
    1.2990
    0.5017

 
 
C{2} =
 
    0.4217
    1.4498
    1.0001

 

And putting those results into the original structure array:

[S.sqrt_matrix_field] = C{:}

S = 1x2 struct array with fields:
    matrix_field
    other_field
    sqrt_matrix_field

S(1).sqrt_matrix_field

ans = 3×1

1.0256 1.2990 0.5017

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S(2).sqrt_matrix_field

ans = 3×1

0.4217 1.4498 1.0001

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You could also concatenate the contents of each cell of C together to form a 3xN matrix:

M = [C{:}]

M = 3×2

1.0256 0.4217 1.2990 1.4498 0.5017 1.0001

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but if that's the form of the result you need, it's better to skip the cell array entirely and use the concatenation approach.