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 GNU Octave Manual Version 3 by John W. Eaton, David Bateman, Søren HaubergPaperback (6"x9"), 568 pagesISBN 095461206XRRP £24.95 (\$39.95)

## 16.4 Special Utility Matrices

Built-in Function: eye (x)
Built-in Function: eye (n, m)
Built-in Function: eye (..., class)
Return an identity matrix. If invoked with a single scalar argument, `eye` returns a square matrix with the dimension specified. If you supply two scalar arguments, `eye` takes them to be the number of rows and columns. If given a vector with two elements, `eye` uses the values of the elements as the number of rows and columns, respectively. For example,

```eye (3)
=>  1  0  0
0  1  0
0  0  1
```

The following expressions all produce the same result:

```eye (2)
==
eye (2, 2)
==
eye (size ([1, 2; 3, 4])
```

The optional argument class, allows `eye` to return an array of the specified type, like

```val = zeros (n,m, "uint8")
```

Calling `eye` with no arguments is equivalent to calling it with an argument of 1. This odd definition is for compatibility with Matlab.

Built-in Function: ones (x)
Built-in Function: ones (n, m)
Built-in Function: ones (n, m, k, ...)
Built-in Function: ones (..., class)
Return a matrix or N-dimensional array whose elements are all 1. The arguments are handled the same as the arguments for `eye`.

If you need to create a matrix whose values are all the same, you should use an expression like

```val_matrix = val * ones (n, m)
```

The optional argument class, allows `ones` to return an array of the specified type, for example

```val = ones (n,m, "uint8")
```

Built-in Function: zeros (x)
Built-in Function: zeros (n, m)
Built-in Function: zeros (n, m, k, ...)
Built-in Function: zeros (..., class)
Return a matrix or N-dimensional array whose elements are all 0. The arguments are handled the same as the arguments for `eye`.

The optional argument class, allows `zeros` to return an array of the specified type, for example

```val = zeros (n,m, "uint8")
```

Function File: repmat (A, m, n)
Function File: repmat (A, [m n])
Function File: repmat (A, [m n p ...])
Form a block matrix of size m by n, with a copy of matrix A as each element. If n is not specified, form an m by m block matrix.

Built-in Function: diag (v, k)
Return a diagonal matrix with vector v on diagonal k. The second argument is optional. If it is positive, the vector is placed on the k-th super-diagonal. If it is negative, it is placed on the -k-th sub-diagonal. The default value of k is 0, and the vector is placed on the main diagonal. For example,

```diag ([1, 2, 3], 1)
=>  0  1  0  0
0  0  2  0
0  0  0  3
0  0  0  0
```

Given a matrix argument, instead of a vector, `diag` extracts the k-th diagonal of the matrix.

The functions `linspace` and `logspace` make it very easy to create vectors with evenly or logarithmically spaced elements. See section 4.2 Ranges.

Built-in Function: linspace (base, limit, n)
Return a row vector with n linearly spaced elements between base and limit. If the number of elements is greater than one, then the base and limit are always included in the range. If base is greater than limit, the elements are stored in decreasing order. If the number of points is not specified, a value of 100 is used.

The `linspace` function always returns a row vector.

For compatibility with Matlab, return the second argument if fewer than two values are requested.

Function File: logspace (base, limit, n)
Similar to `linspace` except that the values are logarithmically spaced from 10^base to 10^limit.

If limit is equal to pi,

the points are between 10^base and pi,

not 10^base and 10^pi,

in order to be compatible with the corresponding Matlab function.

Also for compatibility, return the second argument if fewer than two values are requested.