Version 2.1.3 - 2014-01-13
=============================
The last (probably) in a series of very minor changes. Here only the 
documentation has been changed. There is a new section in the Tutorial 
showing how to use multiple CPUs to evaluate costly integrands in parallel. 
There is also a new section on how to use vegas to do multi-dimensional sums,
rather than integrals.

Version 2.1.2 - 2014-01-12
============================
Another very minor (backwards compatibile) modification. Internally vegas processes 
integration points in batches. These were called vectors initially but this name
has proven confusing, especially now that integrands can be array-valued.
To remove the potential confusion, collections of integration points are 
now called batches, and: VecIntegrand is now BatchIntegrand; vecintegrand is
now batchintegrand; and nhcube_vec has become nhcube_batch. The old names 
are still available, as aliases, to support legacy code.

Version 2.1.1 - 2014-01-09
==========================
This is a very minor upgrade. Missed out a couple of variable declarations 
in one of the cython routines that slowed the routine (and vegas) down
significantly (eg, 20%) in some situations. These are now fixed. This 
changes nothing other than the run time.

Version 2.1 - 2014-01-08
=========================
vegas normally uses weighted averages to combine results from different 
iterations. This is important since earlier iterations may have much larger
errors and so should carry less weight in the average. The weighted averages
mean, however, that the integral estimates are biased (see discussion of
systematic error in the Tutorial). The bias is completely negligible compared
to the statistical errors, and so unproblematic, unless the number of 
iterations (nitn) is made very large (eg, thousands). vegas does not need to,
and no longer does use weighted averages when parameter adapt=False, because
then different iterations are all the same (since there is no adaptation 
going on). Consequently the estimates for the mean and std deviation 
are unbiased when adapt=False. This is likely a non-issue for most 
and possibly all applications (since the bias vanishes so quickly with
increasing neval --- like 1/neval), but taking unweighted averages is 
more correct when adapt=False so that is what vegas does now. 

Other changes:

- Added parameter adapt to Integrator, as mentioned above. Setting alpha=False
  prevents vegas from adapting any further. See the discussion in the Tutorial.

- RWAvg and RWAvgArray have changed names to RAvg and RAvgArray. The R 
  stands for "running", since these objects keep a running total. The "W"
  used to stand for "weighted" but is inappropriate now since averages 
  may be weighted or unweighted (depending upon parameter Integrator.adapt).

- Changed the way vegas handles situations where variances
  (or diagonal elements of covariance matrices) are negative or otherwise
  afflicted by roundoff error. A small positive number is added, scaled by
  the mean**2 (roughly 1e-15 * mean**2). This helps vegas survive unusual
  situations like a constant integrand (independent of x) without generating
  nan's or divide checks. 

- Have more robust mechanisms for defining integrands for vegas's vector 
  mode. Deriving from vegas.VecIntegand but failing to define a __call__
  results in an error message (saying there is no __call__). Also there
  is now a function decorator, vegas.vecintegrand, that can be applied
  to an ordinary function to make it suitable as an integrand.

Version 2.0.1 - 2014-01-07
===========================
Tiny improvement in how vegas interacts with the gvar module. The gvar
module can now be installed by itself, without the rest of the lsqfit 
distribution: pip install gvar. Array-valued integrands work much better
with gvar installed.

Version 2.0 - 2014-01-06
==========================
This is a significant upgrade and cleanup of the code. As a result
it is not entirely backwards compatible with earlier versions (see below).

- Integrands are allowed to be array-valued now, with different elements
  of the array representing different integrands. vegas always tunes on 
  the first function in the array. vegas determines whether the 
  integrand is scalar- or array-valued automatically, and returns
  results that are either scalar or array-valued, as appropriate. 
  This functionality replaces method Integrator.multi, and is 
  implemented quite a bit differently (and better); 
  Integrator.multi has now disappeared. There is no longer a need for a 
  separate method for array-valued integrands.

- The calling conventions for integrands in vector mode have been changed
  (simplified): eg,

    class fv(vegas.VecIntegrand):
      def __call__(self, x):
        return x[:, 0] ** 2 + x[:, 1] ** 4

  See discussion in the tutorial. This is not compatible with the old
  convention. The fcntype argument to Integrator is no longer needed.

- Renamed RunningWAvg to RWAvg -- shorter name. Also introduced RWAvgArray 
  for arrays of same.

- Major reorganization of the internal code to simplify the developer's
  life. The code appears to be somewhat faster, though probably not 
  enough to be noticed by anyone other than the developer.



Version 1.3 - 2014-01-03
========================

- Introduced new method Integrator.multi for doing multiple integrals 
  simultaneously, using the same integration points for all of the 
  integrals. Integrating simultaneously can lead to very large reductions
  in the uncertainties for ratios or differences of integrals whose
  integrands are very similar. See discussion in the documentation under
  "Multiple Integrands Simultaneously."

- Introduced iterators (Integrator.random and Integrator.random_vec) 
  that return |vegas| integration points and weights
  for applications that use |vegas| as a random number generator.

- Changed the semantics concerning the memory optimization introduced in 
  v1.2. To run with minimum memory set parameter minimize_mem = True. This
  will cause vegas to use extra integrand evaluations, which can slow it by
  50-100%, but also decouples the internal memory used from neval. The 
  default value, False, is the better choice unless vegas is running out 
  of RAM. Parameter max_nhcube limits the number of h-cubes used in the
  stratification, unless beta=0 or minimize_mem=True in which case it is 
  ignored.


Version 1.2 - 2013-12-29
========================

- Memory optimization: The (new) adaptive stratified sampling algorithm
  can use a lot of memory since it must store a float (sigf = the std dev of
  the integrand) for each h-cube. When neval gets to be 1e8 or larger, 
  the memory needs start to approach typical RAM limits (in laptops, 
  anyway). To avoid exceeding these limits, which would greatly slow 
  progress, vegas now switches to a different mode of operation when
  the number of h-cubes exceeds parameter max_nhcube (set by default 
  to 5e8). Rather than store values of sigf for every h-cube for use
  in the next iteration, it recomputes sigf just before it uses it 
  to move integrand evalutions around (and then throws the sigf value away). 
  This requires extra integrand evaluations, beyond those used to estimate
  the integral. The number of extra evaluations is between 50% and 100% of
  the number used to estimate the integral, typically increasing 
  execution time by the same fractions. This is worthwhile provided the
  adaptive stratified sampling decreases errors by at least 30% 
  (since omitting it would allow up to 2x as many integration points
  for the same cost, decreasing errors by a factor of 1/sqrt(2)). The
  adaptive stratified sampling usually decreases errors by this amount,
  and frequently by much more. The new mode is in operation if (internal)
  attribute minimize_sigf_mem is True. Again the threshold for this
  new behavior is set by max_nhcube which is 5e8 by default, which 
  is sufficiently large that this new mode will be used quite 
  infrequently. 

- Refactored Integrator._integrate to prepare for future project.

- Tests for beta=0.0 mode and for the propagation of Python exceptions
  from the integrand.

- More polished documentation - still a work in progress.

- Fixed bug in pickling of Integrator. Added testing for pickling.

Version 1.1.1 - 2013-12-22
============================
Fixed a tiny typo that would not cause problems particularly, 
but needed to be fixed --- code would not import gvar from lsqfit
even if it was present.

Also made the slower examples run faster, so you don't have 
to wait so long. Added a plot to the path-integral example to 
compare the lattice path-integral result with the exact result
(provided matplotlib installed).

Version 1.1 - 2013-12-22
=========================

Original release made use of the lsqfit package in the testing. This package
is quite useful in conjunction with vegas (for the gvar module) but it is not
required. The testing and examples now work without  lsqfit present, which was
the original intent. See discussion at the  end of the Tutorial about the role
of lsqfit. 

Version 1.0 - 2013-12-21
==========================
This is the first version of a new implementation
of the vegas algorithm for adaptive multidimensional
Monte Carlo integration. It is written in Python/Cython
and features a significantly improved algorithm
relative to earlier versions of vegas. In particular
it now uses two adaptive strategies instead of one.
