### 18.3 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")

> For compatibility with Matlab, calling `eye` with no arguments is equivalent to calling it with an argument of 1.

— 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, like

>               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, like

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

— Function File: repmat (A, m, n)
— Function File: repmat (A, [m n])

> 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.

— Loadable Function: rand (x)
— Loadable Function: rand (n, m)
— Loadable Function: rand (`"seed"`, x)

> Return a matrix with random elements uniformly distributed on the interval (0, 1). The arguments are handled the same as the arguments for `eye`. In addition, you can set the seed for the random number generator using the form

>               rand ("seed", x)

> where x is a scalar value. If called as

>               rand ("seed")

> `rand` returns the current value of the seed.

— Loadable Function: randn (x)
— Loadable Function: randn (n, m)
— Loadable Function: randn (`"seed"`, x)

> Return a matrix with normally distributed random elements. The arguments are handled the same as the arguments for `eye`. In addition, you can set the seed for the random number generator using the form

>               randn ("seed", x)

> where x is a scalar value. If called as

>               randn ("seed")

> `randn` returns the current value of the seed.

The `rand` and `randn` functions use separate generators. This ensures that

         rand ("seed", 13);
         randn ("seed", 13);
         u = rand (100, 1);
         n = randn (100, 1);

and

         rand ("seed", 13);
         randn ("seed", 13);
         u = zeros (100, 1);
         n = zeros (100, 1);
         for i = 1:100
           u(i) = rand ();
           n(i) = randn ();
         end

produce equivalent results.

Normally, `rand` and `randn` obtain their initial seeds from the system clock, so that the sequence of random numbers is not the same each time you run Octave. If you really do need for to reproduce a sequence of numbers exactly, you can set the seed to a specific value.

If it is invoked without arguments, `rand` and `randn` return a single element of a random sequence.

The `rand` and `randn` functions use Fortran code from Ranlib, a library of fortran routines for random number generation, compiled by Barry W. Brown and James Lovato of the Department of Biomathematics at The University of Texas, M.D. Anderson Cancer Center, Houston, TX 77030.

— Function File: randperm (n)

> Return a row vector containing a random permutation of the integers from 1 to n.

— 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

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

— Built-in Function: linspace (base, limit, n)

> Return a row vector with n linearly spaced elements between base and limit. The number of elements, n, must be greater than 1. 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.

— 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.

— Built-in Variable: warn_neg_dim_as_zero

> If the value of `warn_neg_dim_as_zero` is nonzero, print a warning for expressions like

>               eye (-1)

> The default value is 0.

— Built-in Variable: warn_imag_to_real

> If the value of `warn_imag_to_real` is nonzero, a warning is printed for implicit conversions of complex numbers to real numbers. The default value is 0.