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Reshaping and Rearranging Arrays

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Many functions in MATLAB® can take the elements of an existing array and put them in a different shape or sequence. This can be helpful for preprocessing your data for subsequent computations or analyzing the data.

Reshaping

The reshape function changes the size and shape of an array. For example, reshape a 3-by-4 matrix to a 2-by-6 matrix.

A = [1 4 7 10; 2 5 8 11; 3 6 9 12]
A = 3×4

     1     4     7    10
     2     5     8    11
     3     6     9    12


B = reshape(A,2,6)
B = 2×6

     1     3     5     7     9    11
     2     4     6     8    10    12

As long as the number of elements in each shape are the same, you can reshape them into an array with any number of dimensions. Using the elements from A, create a 2-by-2-by-3 multidimensional array.

C = reshape(A,2,2,3)
C = 
C(:,:,1) =

     1     3
     2     4


C(:,:,2) =

     5     7
     6     8


C(:,:,3) =

     9    11
    10    12

Transposing and Flipping

A common task in linear algebra is to work with the transpose of a matrix, which turns the rows into columns and the columns into rows. To do this, use the transpose function or the .' operator.

Create a 3-by-3 matrix and compute its transpose.

A = magic(3)
A = 3×3

     8     1     6
     3     5     7
     4     9     2


B = A.'
B = 3×3

     8     3     4
     1     5     9
     6     7     2

A similar operator ' computes the conjugate transpose for complex matrices. This operation computes the complex conjugate of each element and transposes it. Create a 2-by-2 complex matrix and compute its conjugate transpose.

A = [1+i 1-i; -i i]
A = 2×2 complex

   1.0000 + 1.0000i   1.0000 - 1.0000i
   0.0000 - 1.0000i   0.0000 + 1.0000i


B = A'
B = 2×2 complex

   1.0000 - 1.0000i   0.0000 + 1.0000i
   1.0000 + 1.0000i   0.0000 - 1.0000i

flipud flips the rows of a matrix in an up-to-down direction, and fliplr flips the columns in a left-to-right direction.

A = [1 2; 3 4]
A = 2×2

     1     2
     3     4


B = flipud(A)
B = 2×2

     3     4
     1     2


C = fliplr(A)
C = 2×2

     2     1
     4     3

Shifting and Rotating

You can shift elements of an array by a certain number of positions using the circshift function. For example, create a 3-by-4 matrix and shift its columns to the right by 2. The second argument [0 2] tells circshift to shift the rows 0 places and shift the columns 2 places to the right.

A = [1 2 3 4; 5 6 7 8; 9 10 11 12]
A = 3×4

     1     2     3     4
     5     6     7     8
     9    10    11    12


B = circshift(A,[0 2])
B = 3×4

     3     4     1     2
     7     8     5     6
    11    12     9    10

To shift the rows of A up by 1 and keep the columns in place, specify the second argument as [-1 0].

C = circshift(A,[-1 0])
C = 3×4

     5     6     7     8
     9    10    11    12
     1     2     3     4

The rot90 function can rotate a matrix counterclockwise by 90 degrees.

A = [1 2; 3 4]
A = 2×2

     1     2
     3     4


B = rot90(A)
B = 2×2

     2     4
     1     3

If you rotate 3 more times by using the second argument to specify the number of rotations, you end up with the original matrix A.

C = rot90(B,3)
C = 2×2

     1     2
     3     4

Sorting

Sorting the data in an array is also a valuable tool, and MATLAB offers a number of approaches. For example, the sort function sorts the elements of each row or column of a matrix separately in ascending or descending order. Create a matrix A and sort each column of A in ascending order.

A = magic(4)
A = 4×4

    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1


B = sort(A)
B = 4×4

     4     2     3     1
     5     7     6     8
     9    11    10    12
    16    14    15    13

Sort each row in descending order. The second argument value 2 specifies that you want to sort row-wise.

C = sort(A,2,'descend')
C = 4×4

    16    13     3     2
    11    10     8     5
    12     9     7     6
    15    14     4     1

To sort entire rows or columns relative to each other, use the sortrows function. For example, sort the rows of A in ascending order according to the elements in the first column. The positions of the rows change, but the order of the elements in each row are preserved. 

D = sortrows(A) 
D = 4×4

     4    14    15     1
     5    11    10     8
     9     7     6    12
    16     2     3    13

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