I agree that the choice of quadrature rules is orthogonal to Adaptive
strategy. But, can one quadrature rule be more efficient than another by
points evaluated per digit of accuracy?
It seems like in GKQ, the G and K nodes are different points at each level
of resolution. However in CCQ, the high
On Wed, 3 Jul 2013 07:39:00 -0700, Ajo Fod wrote:
I wonder if Clenshaw-Curtis Quadrature (CCQ) is more adapted for
Adaptive
Quadrature than Gauss-Kronrod (GKQ).
As Konstantin already pointed out, the choice of a quadrature rule
is orthogonal to the choice of an adaptive strategy.
It seems l
I wonder if Clenshaw-Curtis Quadrature (CCQ) is more adapted for Adaptive
Quadrature than Gauss-Kronrod (GKQ). It seems like with CCQ the points at
one level of resolution can be reused for the next level. The error bounds
for a given level of resolution is the comparable to GKQ, so I'm guessing
t
On Tue, 2 Jul 2013 12:54:12 -0400, Konstantin Berlin wrote:
IterateiveLegendreGaussIntegrator should be replaced by adaptive
guass-kronrod. The simpson and trapezoidal methods should be replaced
by
their adaptive versions, or at least adaptive wrapper provided for
them.
[I mentioned Gauss-Kro
Hi.
Thanks for pointing out the inefficiency in AQ. I just improved the
efficiency of AQ to 1.41x that of LGQ (up from 1.05x) - measured in
digits
of accuracy per evaluation for integral of normal with sigma 1000 in
range
[-5000, 5000]
Efficiency improvement is another type of enhancement
Gauss-Kronrod is an improvement over the current AQ promise because of its
improved efficiency. That would be a good upgrade to the proposed AQ.
Also, Gauss-Kronrod will allow the elimination of the fix to the bounds of
integration problem with Simpsons rule.
-Ajo.
On Tue, Jul 2, 2013 at 9:54
IterateiveLegendreGaussIntegrator should be replaced by adaptive
guass-kronrod. The simpson and trapezoidal methods should be replaced by
their adaptive versions, or at least adaptive wrapper provided for them.
On Tue, Jul 2, 2013 at 12:51 PM, Ajo Fod wrote:
> Konstantin,
>
> In essence, we're
Konstantin,
In essence, we're both rooting for Adaptive Quadratures. IMHO
AdaptiveQuadrature (or some form of it that passes all Apache standards)
must replace IterateiveLegendreGaussIntegrator as soon as possible before
somebody else gets hit by a report of convergence to the wrong answer.
**
Ch
Phil,
Adaptive Quadrature is defined here ... Gilles mentioned this:
http://en.wikipedia.org/wiki/Adaptive_quadrature
We have discussed why AQ is better in the email chain.
The differences have been discussed in this email chain and are quite minor.
Based on the tests done so far the question sho
At first it seems you are still compute redundant points. See my example
that I posted, where I propagate 3 functional values not two.
In regards to improvement. I am not an expert of different integration
strategies but:
The concept of adaptive quadrature is separate from how you integrate the
su
On 7/1/13 8:37 PM, Ajo Fod wrote:
> Hi Konstantin,
>
> Thanks for pointing out the inefficiency in AQ. I just improved the
> efficiency of AQ to 1.41x that of LGQ (up from 1.05x) - measured in digits
> of accuracy per evaluation for integral of normal with sigma 1000 in range
> [-5000, 5000]
>
> Pl
Hi Konstantin,
Thanks for pointing out the inefficiency in AQ. I just improved the
efficiency of AQ to 1.41x that of LGQ (up from 1.05x) - measured in digits
of accuracy per evaluation for integral of normal with sigma 1000 in range
[-5000, 5000]
Please let me know if this doesn't answer your que
I am not understanding the discussion here. Adaptive integration is
designed for functions that have different behavior in different
regions. Some regions are smoother, some have higher frequeniesy. How
you integrate a divided region, Simpson rule or whatever is a separate
question.
Adaptive integ
Hi Gilles,
Your accuracy concern made me wonder. So, I dropped the
AdaptiveQuadrature.EPS to 1e-2 from 1e-9 in the code and ran the test in
the patch.
I computed the log of the error per evaluation ...i.e a measure of the
efficiency of the algorithm.
And wait for it ... AQ beats LGQ by about 5% f
private void proc(UnivariateFunction fn) {
+Calc calc = calcs.pop();// pop a calculation to be done.
+double a = calc.a;
+double b = calc.b;
+
+// back off slightly from the edges (function evaluations typically go
haywire)
+// scale for the edge a
Hi.
On Mon, 1 Jul 2013 10:50:19 -0700, Ajo Fod wrote:
If you wanted to use the Math 3 codebase in AdaptiveQuadrature, you'd
compute the calculations of Q1 and Q2 with something else. I'm not
entirely
familiar with the apache Math codebase [...]
You could file a "wish" request as a Commons Ma
1> Could you provide an example of redundant function evaluations in my
code?
2> I made the adjustment in AQ because the size of the segment that was
excluded from the integration could be determined adaptively to keep the
error arbitrarily low. Note the size of the segment that is excluded (at
th
Just a few thoughts.
It seems to me that this code suffers from redundant function evaluations. I am
not sure what to think about the movement from edges since it violates proper
behavior for well behaved functions in order to work for some special cases. In
case of infinite integrals it might
If you wanted to use the Math 3 codebase in AdaptiveQuadrature, you'd
compute the calculations of Q1 and Q2 with something else. I'm not entirely
familiar with the apache Math codebase so my guess would be that you can
replace the following line in AdaptiveQuadrature.proc():
double Q1 = delta / 6
Hi.
I just noticed your request to write the algorithm along the lines of
the
wikipedia article.
The only major difference between my code and the article on
Wikipedia is
that I found it necessary to move the recursive stack in into a data
structure to avoid a StackOverflowException when t
Gilles,
I just noticed your request to write the algorithm along the lines of the
wikipedia article.
The only major difference between my code and the article on Wikipedia is
that I found it necessary to move the recursive stack in into a data
structure to avoid a StackOverflowException when the
BTW, it is possible that I'm not using LGQ correctly. If so, please show
how to pass the tests I've added. I'd much rather use something that is
better tested than my personal code.
-Ajo.
On Fri, Jun 28, 2013 at 11:04 AM, Ajo Fod wrote:
> I just posted a patch on this issue. Feel free to edit
I just posted a patch on this issue. Feel free to edit as necessary to
match your standards. There is a clear issue with LGQ.
Cheers,
Ajo.
On Fri, Jun 28, 2013 at 10:54 AM, Gilles wrote:
> Ted,
>
>
>
>> Did you read my other (rather more lengthy) post? Is that "jumping"?
>>>
>>>
>> Yes. You
Ted,
Did you read my other (rather more lengthy) post? Is that
"jumping"?
Yes. You jumped on him rather than helped him be productive. The
general
message is "we have something in the works, don't bother us with your
ideas".
Then please read all the messages pertaining to those issu
Hey guys,
Ted/Gilles, thanks for the support and reviewing the code. I realize that
there is no Junit test with the files. I'll make a working patch to make
life easier on everyone.
Cheers,
Ajo.
On Fri, Jun 28, 2013 at 9:06 AM, Ted Dunning wrote:
> On Fri, Jun 28, 2013 at 9:05 AM, Gilles >wr
On Fri, Jun 28, 2013 at 9:05 AM, Gilles wrote:
> Did you read my other (rather more lengthy) post? Is that "jumping"?
>
Yes. You jumped on him rather than helped him be productive. The general
message is "we have something in the works, don't bother us with your
ideas".
On Fri, 28 Jun 2013 08:32:49 -0700, Ted Dunning wrote:
On Fri, Jun 28, 2013 at 8:14 AM, Gilles
wrote:
Hello.
The existing LegendreGaussQuadrature class incorrectly assumes that
it has
converged for functions where the polynomial approximation fails in
a
small
corner of the integral space.
On Fri, Jun 28, 2013 at 8:14 AM, Gilles wrote:
> Hello.
>
> The existing LegendreGaussQuadrature class incorrectly assumes that it has
>> converged for functions where the polynomial approximation fails in a
>> small
>> corner of the integral space.
>>
>> This situation is handled much better wit
Hello.
The existing LegendreGaussQuadrature class incorrectly assumes that
it has
converged for functions where the polynomial approximation fails in a
small
corner of the integral space.
This situation is handled much better with the AdaptiveQuadrature
class in
the path for MATH-995. This p
The existing LegendreGaussQuadrature class incorrectly assumes that it has
converged for functions where the polynomial approximation fails in a small
corner of the integral space.
This situation is handled much better with the AdaptiveQuadrature class in
the path for MATH-995. This problem should
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