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+@cindex quasi-random sequences
+@cindex low discrepancy sequences
+@cindex Sobol sequence
+@cindex Niederreiter sequence
+This chapter describes functions for generating quasi-random sequences
+in arbitrary dimensions.  A quasi-random sequence progressively covers a
+@math{d}-dimensional space with a set of points that are uniformly
+distributed.  Quasi-random sequences are also known as low-discrepancy
+sequences.  The quasi-random sequence generators use an interface that
+is similar to the interface for random number generators, except that
+seeding is not required---each generator produces a single sequence.
+
+The functions described in this section are declared in the header file
+@file{gsl_qrng.h}.
+
+@menu
+* Quasi-random number generator initialization::  
+* Sampling from a quasi-random number generator::  
+* Auxiliary quasi-random number generator functions::  
+* Saving and resorting quasi-random number generator state::  
+* Quasi-random number generator algorithms::  
+* Quasi-random number generator examples::  
+* Quasi-random number references::  
+@end menu
+
+@node Quasi-random number generator initialization
+@section Quasi-random number generator initialization
+
+@deftypefun {gsl_qrng *} gsl_qrng_alloc (const gsl_qrng_type * @var{T}, unsigned int @var{d})
+This function returns a pointer to a newly-created instance of a
+quasi-random sequence generator of type @var{T} and dimension @var{d}.
+If there is insufficient memory to create the generator then the
+function returns a null pointer and the error handler is invoked with an
+error code of @code{GSL_ENOMEM}.
+@end deftypefun
+
+@deftypefun void gsl_qrng_free (gsl_qrng * @var{q})
+This function frees all the memory associated with the generator
+@var{q}.
+@end deftypefun
+
+@deftypefun void gsl_qrng_init (gsl_qrng * @var{q})
+This function reinitializes the generator @var{q} to its starting point.
+Note that quasi-random sequences do not use a seed and always produce
+the same set of values.
+@end deftypefun
+
+@node Sampling from a quasi-random number generator
+@section Sampling from a quasi-random number generator
+
+@deftypefun int gsl_qrng_get (const gsl_qrng * @var{q}, double @var{x}[])
+This function stores the next point from the sequence generator @var{q}
+in the array @var{x}.  The space available for @var{x} must match the
+dimension of the generator.  The point @var{x} will lie in the range
+@math{0 < x_i < 1} for each @math{x_i}.
+@end deftypefun
+
+@node Auxiliary quasi-random number generator functions
+@section Auxiliary quasi-random number generator functions
+
+@deftypefun {const char *} gsl_qrng_name (const gsl_qrng * @var{q})
+This function returns a pointer to the name of the generator.
+@end deftypefun 
+
+@deftypefun size_t gsl_qrng_size (const gsl_qrng * @var{q})
+@deftypefunx {void *} gsl_qrng_state (const gsl_qrng * @var{q})
+These functions return a pointer to the state of generator @var{r} and
+its size.  You can use this information to access the state directly.  For
+example, the following code will write the state of a generator to a
+stream,
+
+@example
+void * state = gsl_qrng_state (q);
+size_t n = gsl_qrng_size (q);
+fwrite (state, n, 1, stream);
+@end example
+@end deftypefun
+
+
+@node Saving and resorting quasi-random number generator state
+@section Saving and resorting quasi-random number generator state
+
+@deftypefun int gsl_qrng_memcpy (gsl_qrng * @var{dest}, const gsl_qrng * @var{src})
+This function copies the quasi-random sequence generator @var{src} into the
+pre-existing generator @var{dest}, making @var{dest} into an exact copy
+of @var{src}.  The two generators must be of the same type.
+@end deftypefun
+
+@deftypefun {gsl_qrng *} gsl_qrng_clone (const gsl_qrng * @var{q})
+This function returns a pointer to a newly created generator which is an
+exact copy of the generator @var{q}.
+@end deftypefun
+
+@node Quasi-random number generator algorithms
+@section Quasi-random number generator algorithms
+
+The following quasi-random sequence algorithms are available,
+
+@deffn {Generator} gsl_qrng_niederreiter_2
+This generator uses the algorithm described in Bratley, Fox,
+Niederreiter, @cite{ACM Trans. Model. Comp. Sim.} 2, 195 (1992). It is
+valid up to 12 dimensions.
+@end deffn
+
+@deffn {Generator} gsl_qrng_sobol
+This generator uses the Sobol sequence described in Antonov, Saleev,
+@cite{USSR Comput. Maths. Math. Phys.} 19, 252 (1980). It is valid up to
+40 dimensions.
+@end deffn
+
+@node Quasi-random number generator examples
+@section Examples
+
+The following program prints the first 1024 points of the 2-dimensional
+Sobol sequence.
+
+@example
+@verbatiminclude examples/qrng.c
+@end example
+
+@noindent
+Here is the output from the program,
+
+@example
+$ ./a.out
+0.50000 0.50000
+0.75000 0.25000
+0.25000 0.75000
+0.37500 0.37500
+0.87500 0.87500
+0.62500 0.12500
+0.12500 0.62500
+....
+@end example
+
+@noindent
+It can be seen that successive points progressively fill-in the spaces
+between previous points. 
+
+@iftex
+@need 4000
+The following plot shows the distribution in the x-y plane of the first
+1024 points from the Sobol sequence,
+@sp 1
+@center @image{qrng,3.4in}
+@sp 1
+@center Distribution of the first 1024 points 
+@center from the quasi-random Sobol sequence
+@end iftex
+
+@node Quasi-random number references
+@section References
+
+The implementations of the quasi-random sequence routines are based on
+the algorithms described in the following paper,
+
+@itemize @asis
+P. Bratley and B.L. Fox and H. Niederreiter, ``Algorithm 738: Programs
+to Generate Niederreiter's Low-discrepancy Sequences'', @cite{ACM
+Transactions on Mathematical Software}, Vol.@: 20, No.@: 4, December, 1994,
+p.@: 494--495.
+@end itemize
+