— 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, 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])

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 ("state", x)
— 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.

You can query the state of the random number generator using the form

          v = rand ("state")
     

This returns a column vector v of length 625. Later, you can restore the random number generator to the state v using the form

          rand ("state", v)
     

You may also initialize the state vector from an arbitrary vector of length <= 625 for v. This new state will be a hash based on the value of v, not v itself.

By default, the generator is initialized from /dev/urandom if it is available, otherwise from cpu time, wall clock time and the current fraction of a second.

rand uses the Mersenne Twister with a period of 2^19937-1 (See M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator”, ACM Trans. on Modeling and Computer Simulation Vol. 8, No. 1, Januray pp.3-30 1998, http://www.math.keio.ac.jp/~matumoto/emt.html). Do NOT use for CRYPTOGRAPHY without securely hashing several returned values together, otherwise the generator state can be learned after reading 624 consecutive values.

rand includes a second random number generator, that was the previous generator used in Octave. The new generator is used by default as it is significantly faster than the old generator, and produces random numbers with a significantly longer cycle time. However, in some circumstances it might be desirable to obtain the same random sequences as used by the old generators. To do this the keyword "seed" is used to specify that the old generators should be use, as in

          rand ("seed", val)
     

which sets the seed of the generator to val. The seed of the generator can be queried with

          s = rand ("seed")
     

However, it should be noted that querying the seed will not cause rand to use the old generators, only setting the seed will. To cause rand to once again use the new generators, the keyword "state" should be used to reset the state of the rand.

See also: randn, rande, randg, randp.

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

Return a matrix with normally distributed random elements. The arguments are handled the same as the arguments for rand.

By default, randn uses a Marsaglia and Tsang Ziggurat technique to transform from a uniform to a normal distribution. (G. Marsaglia and W.W. Tsang, 'Ziggurat method for generating random variables', J. Statistical Software, vol 5, 2000, http://www.jstatsoft.org/v05/i08/)

See also: rand,rande,randg,randp.

— Loadable Function: rande (x)
— Loadable Function: rande (n, m)
— Loadable Function: rande ("state", x)
— Loadable Function: rande ("seed", x)

Return a matrix with exponentially distributed random elements. The arguments are handled the same as the arguments for rand.

By default, randn uses a Marsaglia and Tsang Ziggurat technique to transform from a uniform to a exponential distribution. (G. Marsaglia and W.W. Tsang, 'Ziggurat method for generating random variables', J. Statistical Software, vol 5, 2000, http://www.jstatsoft.org/v05/i08/)

See also: rand,randn,randg,randp.

— Loadable Function: randp (l, x)
— Loadable Function: randp (l, n, m)
— Loadable Function: randp ("state", x)
— Loadable Function: randp ("seed", x)

Return a matrix with Poisson distributed random elements. The arguments are handled the same as the arguments for rand, except for the argument l.

Five different algorithms are used depending on the range of l and whether or not l is a scalar or a matrix.

For scalar l <= 12, use direct method.

Press, et al., 'Numerical Recipes in C', Cambridge University Press, 1992.

For scalar l > 12, use rejection method.[1]

Press, et al., 'Numerical Recipes in C', Cambridge University Press, 1992.

For matrix l <= 10, use inversion method.[2]

Stadlober E., et al., WinRand source code, available via FTP.

For matrix l > 10, use patchwork rejection method.

Stadlober E., et al., WinRand source code, available via FTP, or H. Zechner, 'Efficient sampling from continuous and discrete unimodal distributions', Doctoral Dissertaion, 156pp., Technical University Graz, Austria, 1994.

For l > 1e8, use normal approximation.

L. Montanet, et al., 'Review of Particle Properties', Physical Review D 50 p1284, 1994

See also: rand,randn,rande,randg.

— Loadable Function: randg (a, x)
— Loadable Function: randg (a, n, m)
— Loadable Function: randg ("state", x)
— Loadable Function: randg ("seed", x)

Return a matrix with gamma(a,1) distributed random elements. The arguments are handled the same as the arguments for rand, except for the argument a.

This can be used to generate many distributions:

gamma (a,b) for a > -1, b > 0

               r = b*randg(a)
          

beta(a,b) for a > -1, b > -1

               r1 = randg(a,1)
               r = r1 / (r1 + randg(b,1))
          

Erlang(a, n)

               r = a*randg(n)
          

chisq(df) for df > 0

               r = 2*randg(df/2)
          

t(df) for 0 < df < inf (use randn if df is infinite)

               r = randn() / sqrt(2*randg(df/2)/df)
          

F(n1,n2) for 0 < n1, 0 < n2

               r1 = 2*randg(n1/2)/n1 or 1 if n1 is infinite
               r2 = 2*randg(n2/2)/n2 or 1 if n2 is infinite
               r = r1 / r2
               
          

negative binomial (n, p) for n > 0, 0 < p <= 1

               r = randp((1-p)/p * randg(n))
          

non-central chisq(df,L), for df >= 0 and L > 0

(use chisq if L = 0)

               r = randp(L/2)
               r(r > 0) = 2*randg(r(r > 0))
               r(df > 0) += 2*randg(df(df > 0)/2)
          

Dirichlet(a1,...,ak)

               r = (randg(a1),...,randg(ak))
               r = r / sum(r)
          

See also: rand,randn,rande,randp.

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

     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

— 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
     

— 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.

See also: linspace.