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Special Utility Matrices

eye (x) Built-in Function
eye (n m) Built-in Function
eye (... class) Built-in Function
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 (nm, "uint8")

For compatibility with MATLAB calling eye with no arguments is equivalent to calling it with an argument of 1.

ones (x) Built-in Function
ones (n m) Built-in Function
ones (n m, k, ...) Built-in Function
ones (... class) Built-in Function
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 (nm, "uint8")

zeros (x) Built-in Function
zeros (n m) Built-in Function
zeros (n m, k, ...) Built-in Function
zeros (... class) Built-in Function
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 (nm, "uint8")

repmat (A m, n) Function File
repmat (A [m n]) Function File
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.

rand (x) Loadable Function
rand (n m) Loadable Function
rand ("seed" x) Loadable Function
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.

randn (x) Loadable Function
randn (n m) Loadable Function
randn ("seed" x) Loadable Function
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.

randperm (n) Function File
Return a row vector containing a random permutation of the integers from 1 to n.

diag (v k) Built-in Function
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.

linspace (base limit, n) Built-in Function
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.

logspace (base limit, n) Function File
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.

warn_neg_dim_as_zero Built-in Variable
If the value of warn_neg_dim_as_zero is nonzero print a warning for expressions like 
          eye (-1)

The default value is 0.

warn_imag_to_real Built-in Variable
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.