ACCEPTED SOLUTION
Accepted Solutions
First: The loop with j as upper limit seems to be a bit useless. At least its not necessary to calculate pi 100 times with increasing precision. Calculate it once with max precision and then do your num2str thing.
The reason for the error is, that you are limited to numerical precison in a program, too.
So no matter how large you choose N1 to be, you will only get a result for pi with approx. 14 or 15 digits.
This result is then converted to a string with just 16 or 17 entries.
The error is when you demand to take element with indes number j+1 and j+1 is bigger than the last index in the array (max 16).
To get more decimals of pi you have a couple of choces:
Use a different algorithm which allows you to calculate specific decimals without calculating the decimals before it (spigot algorithm).
Implement your own long number arithmetic.
or use Mathcads symbolics to do the job:
Regards
Werner
Sorry, but thats nonsense!
You stop the calculation the first time the loop is executed and return an approximated value (the value you would get originally with N1=10) which is completely independend of N1.
What you suggest is exactly the same as
Sure not, what the OP had in mind!
First: The loop with j as upper limit seems to be a bit useless. At least its not necessary to calculate pi 100 times with increasing precision. Calculate it once with max precision and then do your num2str thing.
The reason for the error is, that you are limited to numerical precison in a program, too.
So no matter how large you choose N1 to be, you will only get a result for pi with approx. 14 or 15 digits.
This result is then converted to a string with just 16 or 17 entries.
The error is when you demand to take element with indes number j+1 and j+1 is bigger than the last index in the array (max 16).
To get more decimals of pi you have a couple of choces:
Use a different algorithm which allows you to calculate specific decimals without calculating the decimals before it (spigot algorithm).
Implement your own long number arithmetic.
or use Mathcads symbolics to do the job:
Regards
Werner
Can you "cheat" by copy/pasting the symbolic result into a new string variable?
You could then easily isolate each digit by using the "substr" function.
Okay, took some looking:
The num2str function has a limit--it creates a string of only a certain length. (note num2str(pi) stops at ...79 while pi goes on ...793)
So regardless of how big N1 is, the substr function will fail when it tries to go past the last character in string c.
One fix:
This solves that problem, but it doesn't get you past the basic numerical precision issue.
The main problem is that you are trying to calculate using the numeric calculation engine. Its accuracy is very limited (17 decimal places , showing 15/16).
if you want more accuracy , the only way as I understand is to use the symbolic calculation engine.
Example shows N1-10, this can continue up to approx. N1=80 after that the symbolic engine fails to generate a result.
This is also possible:
I'm not sure how far you can take this ,1000 places appears to be OK.
But as soon as you convert it to a numeric result, the 17 places limit will apply again.
If you want to create a digit by digit array, the numer and denom function will be useful.
The first steps in a manual version are attached, whether it is possible to automate this , I don't know.
Regards
Andy
Following is a numerical procedure to get decimals for Pi. But Mathcad, as numerical tool, can get more than 47. If you want more digits, guess must to take them from other software, and read digits from a file. Attached, also first million of pi digits as plain text.
Best regards.
Alvaro.
