Difference between revisions of "Manuals/calci/CIRCULANT"
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<div style="font-size:30px">'''MATRIX("CIRCULANT",order)'''</div><br/> | <div style="font-size:30px">'''MATRIX("CIRCULANT",order)'''</div><br/> | ||
| − | *<math>order</math> is the order of the | + | *<math>order</math> is the order of the circulant matrix. |
==Description== | ==Description== | ||
| Line 7: | Line 7: | ||
*An n × n circulant matrix is formed from any n vector by cyclically permuting the entries. | *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 | *Starting with [a b c] we can generate the 3 × 3 circulant matrix | ||
| − | C =\begin{vmatrix} | + | <math>C =\begin{vmatrix} |
a & b & c \\ | a & b & c \\ | ||
c & a & b \\ | c & a & b \\ | ||
b & c & a \\ | b & c & a \\ | ||
| − | \end{vmatrix} | + | \end{vmatrix}</math>. |
| − | * | + | *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) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0.15551561512984335 || 0.43306124373339117 || 0.7585938205011189 | ||
| + | |- | ||
| + | | 0.7585938205011189 || 0.15551561512984335 || 0.43306124373339117 | ||
| + | |- | ||
| + | | 0.43306124373339117 || 0.7585938205011189 || 0.15551561512984335 | ||
| + | |} | ||
| + | *MATRIX("circulant",5,20..100..15) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 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== | ||
| + | *[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]] | ||
| + | *[[Manuals/calci/CONFERENCE| CONFERENCE]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Circulant_matrix Circulant matrix] | ||
Latest revision as of 00:43, 26 October 2015
MATRIX("CIRCULANT",order)
- is the order of the circulant matrix.
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
.
.
- 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 |