This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

magic

Syntax

M = magic(n)

Description

example

M = magic(n) returns an n-by-n matrix constructed from the integers 1 through n2 with equal row and column sums. The order n must be a scalar greater than or equal to 3.

Examples

collapse all

Compute the third-order magic square M.

M = magic(3)
M = 3×3

     8     1     6
     3     5     7
     4     9     2

The sum of the elements in each column and the sum of the elements in each row are the same.

sum(M)
ans = 1×3

    15    15    15

sum(M,2)
ans = 3×1

    15
    15
    15

Visually examine the patterns in magic square matrices with orders between 9 and 24 using imagesc. The patterns show that magic uses three different algorithms, depending on whether the value of mod(n,4) is 0, 2, or odd.

for n = 1:16
    subplot(4,4,n)
    ord = n+8;
    m = magic(ord);
    imagesc(m)
    title(num2str(ord))
    axis equal
    axis off
end

Input Arguments

collapse all

Matrix order, specified as a scalar integer greater than or equal to 3. If n is complex, not an integer, or not scalar, then magic converts it into a usable integer with floor(real(double(n(1)))).

If you supply n less than 3, then magic returns either a nonmagic square, or the degenerate magic squares 1 and [].

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char

Extended Capabilities

See Also

|

Introduced before R2006a