Matlab Array

Array

• MATLAB is designed around arrays: every data type is stored and operated on in array form
• “Array” is meant in a generalized sense — it can have a single element, be a row or a column of elements, be two-dimensional, multi-dimensional, and so on
• Elements may be of any data type, e.g. numeric, logical, character, cell
  • However, in non-heterogeneous arrays (i.e. anything other than cell and structure arrays) all elements must share the same type
• MATLAB arrays support an analogue of Python Sequence Unpacking
  • Unlike Python, where parentheses can typically be omitted, MATLAB always requires the square brackets []
• Within an array, elements at the same dimension are separated by commas , or whitespace
• Operations that return a value always return a new array

Array Categories

• By number of elements and arrangement:
  • Empty array — 0 elements
    • An empty array has class double
  • Scalar — 1 element (one row, one column)
  • Vector — one row or one column of elements (1-D array)
  • 2-D array
  • N-D array
  • In most contexts, MATLAB still treats empty arrays, scalars, and vectors as 2-D.
• By storage:
  • Full (regular) array
  • Sparse array (most elements are zero)
• By element type:
  • Numeric array
  • Character array
  • Logical array, etc.

Array Properties

• Structural test functions (returning logical values)
  • isempty
  • ismatrix
  • isvector
  • isrow
  • iscolumn
  • isscalar
  • issparse
  • $\text{scalar}\subset \text{vector}=\text{row}\cup \text{column}\subset \text{matrix}$
• Array size
  • Function Matlab Functions - size
  • Function Matlab Functions - length
  • Function numel — total number of elements, equivalent to prod(size(A))
  • Function ndims — number of dimensions, equivalent to length(size(A))
• Type test functions
  • isnumeric
  • isreal
  • isfloat
  • isinteger
  • islogical
  • ischar
  • isstruct
  • iscell
  • iscellstr
• Order test functions
  • issorted: issorted(A,__) = isequal(A,sort(A,__))
  • issortedrows: issortedrows(A,__) = isequal(A,sortrows(A,__))

Matlab Array - Indexing

Array indexing can be used to:

• Access or extract a portion of the array
• Expand the array
• Delete elements: A(index) = []

Matlab Array - Creating

Matlab Array - Concatenating

Expanding

You can grow an array by writing to a position index beyond its current size, as below:

>> A = ones(3)
A =
     1     1     1
     1     1     1
     1     1     1
 
>> A(5,5) = 2
A =
     1     1     1     0     0
     1     1     1     0     0
     1     1     1     0     0
     0     0     0     0     0
     0     0     0     0     2

• The position index must lie outside A’s current size, otherwise the operation just modifies an existing element
• Newly created positions are filled with 0

Reshaping

• All operations below return a new array.

• Flipping

  • Function flip
  • Function flipud(A) flips top–bottom (i.e. along dimension 1)
  • Function fliplr(A) flips left–right (i.e. along dimension 2)
  • Function rot90(A,<k>)
    • Rotates A counter-clockwise by $k\times 90°$
    • For N-D arrays, the rotation acts on the plane spanned by dimensions 1 and 2

N-D arrays

Dimensions of an N-D array beyond the second are called “pages” — intuitively, each page stores a matrix.

A useful rule of thumb: most operations defined for matrices extend naturally to N-D arrays, acting on the plane spanned by dimensions 1 and 2, i.e. on each page.

• Permuting dimensionsA
  • Function permute
  • Function ipermute
• Transpose '
• Function reshape
• Function squeeze(A) removes singleton dimensions while keeping at least two dimensions; the elements are unchanged

Rearranging

• Cyclic shifting
  • Function circshift
  • Function B = shiftdim(A,n) shifts the dimensions of an array A by n positions
• Sorting
  • Function sort
  • Function sortrows

Finding

See Matlab Functions - find.