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15.3 Special Utility Matrices

Built-in Function: eye (x)

Built-in Function: eye (n, m)

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])

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)

Return a matrix 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)

Built-in Function: zeros (x)

Built-in Function: zeros (n, m)

Return a matrix whose elements are all 0. The arguments are handled the same as the arguments for eye.

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.

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 section 4.2 Ranges.

Function File: 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, regardless of the value of prefer_column_vectors.

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: treat_neg_dim_as_zero

If the value of treat_neg_dim_as_zero is nonzero, expressions like

eye (-1)

produce an empty matrix (i.e., row and column dimensions are zero). Otherwise, an error message is printed and control is returned to the top level. The default value is 0.