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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
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