Reshaping and Rearranging Arrays

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