Generates a Toeplitz matrix.
TOEPLITZ(c, r)
c |
- |
A series, the first column of the output array. |
r |
- |
Optional, a series, the first row of the output array. Defaults to c. |
An array, a symmetric or unsymmetric Toeplitz matrix.
c = {1, 2, 3};
t = toeplitz(c);
t == {{1, 2, 3},
{2, 1, 2},
{3, 3, 1}}
The first row and column of t is identical to c.
c = {1, 2, 3};
r = {1, 8, 9};
t = toeplitz(c, r);
t == {{1, 8, 9},
{2, 1, 8},
{3, 2, 1}}
The first row is identical to r and the first column is identical to c.
For column c and row r, a square Toeplitz matrix takes the form:
c[1] r[2] r[3] ... r[n]
c[2] c[1] r[2] ... r[n-1]
c[3] c[2] c[1] ... r[n-2]
. . . . .
. . . . .
. . . . .
c[n] c[n-1] c[n-2] ... c[1]
If r is not specified, a symmetric Toeplitz matrix is returned where c represents the first row and column.
If r is specified, an unsymmetric Toeplitz matrix is returned where the first column is c and the first row is r. In this case, if c[1] ≠ r[1], c[1] is used as the first element.