MATLAB: Precision arithmetic

MATLABprecision

I calculate Lyapunov Exponent. I need a big precision, such as 10000. I create a simple example for verifing calculating: >> vpa(pi, 10) ans = 3.141592654 >> vpa(pi*10, 10) ans = 31.41592654

But, I need a 10 symbols after dot. But not 9 and 8 as in example. How can I achive a calculating with specified symbols after dot?

Best Answer

Increase the vpa digits much beyond what you need and do the calculations. floor() the result, abs() it, add 1, and take ceil() of the log10 of that. The result of ceil() will be the number of digits that were used before the decimal point. With that number in hand, you can vpa() the result of the calculation, this time specifying 10 + the number of digits before the decimal point as your precision. The result will be a symbolic number.

OR....

Do the calculation with more digits than you need. char() the result of the vpa. locate the '.' in the string and discard everything after the 10th character after the decimal place. The result will be a character string.

Related Solutions

MATLAB: How to get more than 49 digits of pi in a string

You could always download my HPF toolbox from the file exchange. It will provide 500100 digits of pi.

P = hpf('pi',500000);
cp = disp(P);
numel(cp)
ans =
      500001
      
cp(1:1001)
ans =
    '3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198'

So 1000 digits of pi, plus a decimal point.

As I recall, I even computed those digits using HPF itself just to test the tool, and verify it was working correctly. I'm not sure which series I used, but there are many good ones out there if you look carefully. You do need to be working with a tool that can handle high precision arithmetic. A double will not suffice.

Be careful with the last digit reported to make sure it was not rounded. For example, if you do this:

vpa(sym('pi'),1000)

the last 10 digits reported are ...9216420199

However, the true digits of pi in that vicinity run as: ...9216420198938095...

So the last digit reported by vpa is actually rounded up to a 9.

MATLAB: How to display a complex decimal result with actual precision value

The default display format, format short, displays numbers "Short, fixed-decimal format with 4 digits after the decimal point." But note that this has no impact on how the numbers are stored and computed, which is to double precision. Change your display format if you want to see more decimal places.

If you want to compute your complex number using higher precision than double precision, use Symbolic Math Toolbox.

Best Answer

Related Solutions

MATLAB: How to get more than 49 digits of pi in a string

MATLAB: How to display a complex decimal result with actual precision value

Related Question