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# toeplitz

Create Toeplitz matrix

## Syntax

t = toeplitz(a,b)
t = toeplitz(b)

## Description

t = toeplitz(a,b) returns a nonsymmetric Toeplitz matrix having a as its first column and b as its first row. b is cast to the numerictype of a.

t = toeplitz(b) returns the symmetric or Hermitian Toeplitz matrix formed from vector b, where b is the first row of the matrix.

The output fi object t has the same numerictype properties as the leftmost fi object input. If the leftmost fi object input has a local fimath, the output fi object t is assigned the same local fimath. Otherwise, the output fi object t has no local fimath.

## Examples

toeplitz(a,b) casts b into the data type of a. In this example, overflow occurs:

```fipref('NumericTypeDisplay','short');
format short g
a = fi([1 2 3],true,8,5)

a =

1     2     3
s8,5
b = fi([1 4 8],true,16,10)

b =

1     4     8
s16,10
toeplitz(a,b)

ans =

1       3.9688       3.9688
2            1       3.9688
3            2            1
s8,5```

toeplitz(b,a) casts a into the data type of b. In this example, overflow does not occur:

```toeplitz(b,a)

ans =

1     2     3
4     1     2
8     4     1
s16,10```

If one of the arguments of toeplitz is a built-in data type, it is cast to the data type of the fi object.

```x = [1 exp(1) pi]

x =

1       2.7183       3.1416

toeplitz(a,x)

ans =

1       2.7188       3.1563
2            1       2.7188
3            2            1
s8,5
toeplitz(x,a)

ans =

1            2            3
2.7188            1            2
3.1563       2.7188            1
s8,5```