MATLAB POLYSPACE RELEASE NOTES Manuel d'utilisateur télécharger pdf (Page 40)

2 Matrices and Arra ys

9.0 6.0 7.0 12.0

4.0 15.0 14.0 1.0 ];

The statement

magik

reads the file and creates a variable, A, containing the example matrix.

Concatenation

Concatenation is the proce ss of joining small matrices to make bigger ones. In

fact, you made your first matrix by concatenating its individual elements. The

pair of square brackets,

[], is the concatenation operator. For an example,

start with the 4-by-4 magic square,

A,andform

B = [A A+32; A+48 A+16]

The result is an 8-by-8 m atrix, obtained by joining the four submatrice s:

16 3 2 1 3 48 35 34 45

5 10 11 8 37 42 43 40

9 6 7 1 2 41 38 39 44

4 15 14 1 36 47 46 33

64 51 50 61 32 19 18 29

53 58 59 56 21 26 27 24

57 54 55 60 25 22 23 28

52 63 62 49 20 31 30 17

This matrix is halfway to being another magic square. Its elements are a

rearrangement of the integers

1:64. Its column sums are the correct value

for an 8-by-8 magic square:

sum(B)

ans =

260 260 260 260 260 260 260 260

But its row sums, sum(B')', are not all the same. Further m anipulation is

necessary to make this a valid 8-by-8 magic square.

2-18

1 2 ... 35 36 37 38 39 40 41 42 43 44 45 ... 239 240

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MATLAB POLYSPACE RELEASE NOTES Manuel d'utilisateur Page 40