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Re: For loop problem in mathematica
*To*: mathgroup at smc.vnet.net
*Subject*: [mg90237] Re: [mg90163] For loop problem in mathematica
*From*: DrMajorBob <drmajorbob at att.net>
*Date*: Thu, 3 Jul 2008 06:10:22 -0400 (EDT)
*References*: <11203311.1214991822381.JavaMail.root@m08>
*Reply-to*: drmajorbob at longhorns.com
I see nothing "catastrophic" about a 10-million-long For taking
considerable time to complete.
(x = 0; For[i = 1, i < 10000000, i++, x = N[x + 1/(i^2), 53]];
N[Sqrt[6*x], 25]) // Timing
{67.2293, 3.141592558096821157357751}
(x = Sum[1/i^2, {i, 1, n}];
N[Sqrt[6 x /. n -> Infinity], 25]) // Timing
{0.004447, 3.141592653589793238462643}
N[Pi, 25] // Timing
{0.000024, 3.141592653589793238462643}
As written, your code created Rational numbers with very large
denominators. For instance:
(x = 0; For[i = 1, i < 100, i++, x = x + 1/(i^2)];
N[Sqrt[6*x], 25]) // Timing
{0.002248, 3.131980747244362801857815}
N@Log[10, #] &@Through[{Numerator, Denominator}@x]
{81.9002, 81.6867}
or
(x = 0; For[i = 1, i < 1000, i++, x = x + 1/(i^2)];
N[Sqrt[6*x], 25]) // Timing
{0.015289, 3.140637100985938301795880}
N@Log[10, #] &@Through[{Numerator, Denominator}@x]
{865.922, 865.706}
and
(x = 0; For[i = 1, i < 10000, i++, x = x + 1/(i^2)];
N[Sqrt[6*x], 25]) // Timing
{0.211607, 3.141497154397622340592830}
N@Log[10, #] &@Through[{Numerator, Denominator}@x]
{8692.74, 8692.52}
Notice that almost 9 thousand digit in the denominator isn't enough to get
25-digit accuracy in Pi.
Bobby
On Tue, 01 Jul 2008 05:59:02 -0500, PhysNova <skhoshbinfar at gmail.com>
wrote:
> Hi,
> i wrote a simple program of evaluating Pi number in M6 to test cpu
> computation timing, to do this a simple for loop
>
> was used:
>
> x=0;For[i = 1, i < 10,000,000, i++, x = x + 1/(i^2)];N[Sqrt(6*x),25]//
> Timing
>
> the result was catastrophe! it take few minuates. but i first expect
> to do this very simple job in few
>
> seconds.computation time is just satisfactory up to 100000 cycle.
>
> could anyone interperet this falut?
> our get an idea to improve the result?
>
> Tanks
>
>
--
DrMajorBob at longhorns.com
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