Precision (decimal digits) are very low and digits(32) does not help.

Hi everyone,

I searched everywhere but cant find a solution. The problem seems so simple! I am using the code below. See that my numbers have many digits (are precise).

The following code returns m4m5 = 1.010 while I know from my calculator / wolframalpha that the solution is closer to 1.0095....

How can I achieve a higher level of precision?

• Changing to solve instead of vpasolve did not help.
• Changing line one to syms m4m5 'double' did not help.

I also have this problem when multiplying later: a is very precise and then for b I cannot see more digits (I need them.)

    syms m4m5
    Breguet1 = 1852*1500 == (230.1330/(1.466*10^-4))*(18.4)*log(m4m5);
    solvem4m5 = vpasolve(Breguet1, m4m5);
    m4m5 = solvem4m5(1,1)
   
    a = 62826.3402201552
    b = a * m4m5

[MalteMan]

My current code, which still does not reveal more digits:

clear
clc

format longG
digits 50

syms m4m5
    Breguet1 = 1852*1500 == (230.1330/(1.466*10^-4))*(18.4)*log(m4m5);
    solvem4m5 = vpasolve(Breguet1, m4m5);
    m4m5 = solvem4m5(1,1)
   
    a = sym(62826.3402201552)
    b = a * m4m5

The result is:

    m4m5 =
 
1.1010
 
 
a =
 
6.2826e+04
 
 
b =
 
6.9169e+04
 

Answer 1

[MalteMan]

sympref('FloatingPointOutput',false)  

%was the solution! Must have changed it sometime

Answer 2

[James Tursa]

This is likely just a display issue and you don't need the Symbolic Toolbox. MATLAB does regular calculations in full double precision, but only displays four digits beyond the decimal point using the default format, so what you see displayed is a rounded version of the actual number stored. Try this

format longG

and then run your code as a regular expression and examine the result again.

https://www.mathworks.com/help/matlab/ref/format.html?searchHighlight=format&s_tid=srchtitle

E.g.,

>> m4m5 = exp(1852*1500/((230.1330/(1.466*10^-4))*(18.4)))
m4m5 =
    1.1010   <-- The rounded version of the number for display purposes only
>> format longG
>> m4m5
m4m5 =
          1.10095349222101  <-- the longer decimal version of the actual number stored

[MalteMan]

Thanks for the reply, however it does not seem to work for me still. See my other reply.

Very strange.

[James Tursa]

What doesn't work for you? I just showed you code that displays the full digits and should agree pretty well with your calculator etc. If you have an m4m5 that is symbolic then you can do this:

m4m5 = double(m4m5)

E.g.,

>> syms m4m5
>> Breguet1 = 1852*1500 == (230.1330/(1.466*10^-4))*(18.4)*log(m4m5);
>> solvem4m5 = vpasolve(Breguet1, m4m5);
>> m4m5 = solvem4m5(1,1)
m4m5 =
1.100953492221007152713645627688375978171968089947806639541560572250312809929508272188194937733533164
>> m4m5 = double(m4m5)
m4m5 =
    1.1010
>> format longG
>> m4m5
m4m5 =
          1.10095349222101

[MalteMan]

Alright, when using the expression

m4m5 = exp(1852*1500/((230.1330/(1.466*10^-4))*(18.4)))

it does in fact work! I can also inspect m4m5 in the workspace and see the full digits there (and its not a 1x1 sym anymore).

However, when using solve (which I would like to do/need to do) m4m5 is a 1x1 sym and does not reveal more digits, even after longG.

See here:

>> syms m4m5
    Breguet1 = 1852*1500 == (230.1330/(1.466*10^-4))*(18.4)*log(m4m5);
    solvem4m5 = vpasolve(Breguet1, m4m5);
    m4m5 = solvem4m5(1,1)
 
m4m5 =
 
1.1010
 
>> format longG
>> m4m5
 
m4m5 =
 
1.1010

To add to your edit (using double(m4m5)):

Still does not work.... It really seems like m4m5, as a 1x1 sym, only contains the four digits, since thats also what I see when double clicking etc on it in the Workspace.

[James Tursa]

What version of MATLAB are you using?

And setting the digits prior to your symbolic stuff doesn't help? E.g.,

digits 50
syms m4m5
  :
etc.

[MalteMan]

I just copied (again) each line of your reply.

It still only gives me the 1.1010

The 1x1 sym solvem4m5 as well as m4m5 only contain:

 
val =
 
1.1010
 

Further: m4m5 = double(m4m5) results in

>> m4m5 = double(m4m5)

m4m5 =

   1.101000000000000

[MalteMan]

I am using

R2020b Update 3 (9.9.0.1538559)

64-bit (maci64)

Nov 23, 2020

on Mac OS Catalina

[MalteMan]

I added my "latest" code as a direct comment to my question above, still does not help!

This is so strange. Thanks so much for your time and suggestions already...

Answer 3

[John D'Errico]

Of course, asking for 32 or more digits of precision is a bit on the side of the ridiculous, when the numbers going into the computation are themselves only accurate to 4 significant digits. Even worse, numbers like this:

230.1330

are not exactly the numbers you want them to be when converted to symbolic form.

vpa(sym(230.1330),32)
ans =
230.13300000000000977706804405898

vpa(sym(1.466*10^-4),32)
ans =
0.00014660000000000001263607274371026

That is, each of these numbers are stored as a double precision number, then converted into symbolic form. And that ratio is FIRST computed as a double precision number.

So you don't have exactly the numbers you think you have. Then asking for more digits is asking MATLAB to generate what are virtually garbage results.