Manuals/calci/CIRCULANT

MATRIX("CIRCULANT",order)

• $order$ is the order of the circulant matrix.

Description

• This function gives the Circulant matrices of given order.
• A circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector.
• An n × n circulant matrix is formed from any n vector by cyclically permuting the entries.
• Starting with [a b c] we can generate the 3 × 3 circulant matrix

$C={\begin{vmatrix}a&b&c\\c&a&b\\b&c&a\\\end{vmatrix}}$.

• In Calci, MATRIX("circulant") is giving the circulant matrix for random numbers in decimal.
• Circulant matrices are very useful in digital image processing, and the n×n circulant matrix is implemented as CirculantMatrix.

Examples

• MATRIX("circulant")= 0.793114245403558
• MATRIX("circulant",3)

0.15551561512984335	0.43306124373339117	0.7585938205011189
0.7585938205011189	0.15551561512984335	0.43306124373339117
0.43306124373339117	0.7585938205011189	0.15551561512984335

• MATRIX("circulant",5,20..100..15)

20	80	65	50	35
35	20	80	65	50
50	35	20	80	65
65	50	35	20	80
80	65	50	35	20

See Also

• ANTIDIAGONAL
• CONFERENCE

References

• Circulant matrix