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```

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