I am using Matlab and using numbers in scientific notation, which are represented with the letter e for the exponent. An example in Matlab:
>> 2e5
ans =
200000
Now would like to work with numbers in scientific notation, but using variables to hold the values of the mantissa and the exponent (left and right side of the e respectively). I do not understand how this can be done without the variable names merging with the letter e for the exponent. Eg:
>> rr=5;
>> 2err
??? 2err
|
Error: Unexpected MATLAB operator.
Can this still be done? Or must I use the manual approach:
>> 2*10^rr
ans =
200000
You must use the manual approach; you can't use scientific notation like that with variables. You might want to use 2.*10.^rr, with the ., to enable you to use the same statement with arrays of numbers.
Related
I have a set of integer values, for example:
V = [26767559, 6022443, 9923637]; % etc.
For my application, it is convenient to represent them as <rounded_mantissa>E5 (that is, some_val*105), so for the above examples I want to get:
N = ["268E5", "60E5", "99E5"]; % I won't mind if it's E+05
At the moment, I'm using one of several conceivable workarounds to achieve this output,
N = round(V*1E-5) + "E5";
but I'd like to know if it's possible to specify the formatSpec of sprintf, num2str (etc.) such that it would output numbers with a specific value for the exponent (in this case, 5), without performing division (like in num2str(round(V/1E5).','%3uE5')).
I'm using R2018a.
You can at least remove the use of round, then I don't think there's any further short-hand because it's just a single division...
N = num2str( V/1e5, '%.0fE5' )
The .0 precision operator will force the 0 decimal place rounding for you anyway.
You can only specify the number of digits (significant or after the decimal point) using the formatSpec property, so unless you've got fixed numbers of digits (which you don't) you won't be able to use that alone.
Let's say I create some number A, of the order 10^4:
A = 81472.368639;
disp(A)
8.1472e+04
That wasn't what I wanted. Where are my decimals? There should be six decimals more. Checking the variable editor shows me this:
Again, I lost my decimals. How do I keep these for further calculations?
Scientific notation, or why you didn't lose any decimals
You didn't lose any decimals, this is just MATLAB's way of displaying large numbers. MATLAB rounds the display of numbers, both in the command window and in the variable editor, to one digit before the dot and four after that, using scientific notation. Scientific notation is the Xe+y notation, where X is some number, and y an integer. This means X times 10 to the power of y, which can be visualised as "shift the dot to the right for y places" (or to the left if y is negative).
Force MATLAB to show you all your decimals
Now that we know what MATLAB does, can we force it to show us our number? Of course, there're several options for that, the easiest is setting a longer format. The most used for displaying long numbers are format long and format longG, whose difference is apparent when we use them:
format long
A
A =
8.1472368639e+04
format longG
A
A =
81472.368639
format long displays all decimals (up to 16 total) using scientific notation, format longG tries to display numbers without scientific notation but with most available decimals, again: as many as there are or up to 16 digits, both before and after the dot, in total.
A more fancy solution is using disp(sprintf()) or fprintf if you want an exact number of decimals before the dot, after the dot, or both:
fprintf('A = %5.3f\n',A) % \n is just to force a line break
A = 81472.369
disp(sprintf('A = %5.2f\n',A))
A = 81472.37
Finally, remember the variable editor? How do we get that to show our variable completely? Simple: click on the cell containing the number:
So, in short: we didn't lose any decimals along the way, MATLAB still stores them internally, it just displays less decimals by default.
Other uses of format
format has another nice property in that you can set format compact, which gets rid of all the additional empty lines which MATLAB normally adds in the command window:
format compact
format long
A
A =
8.147236863931789e+04
format longG
A
A =
81472.3686393179
which in my opinion is very handy when you don't want to make your command window very big, but don't want to scroll a lot either.
format shortG and format longG are useful when your array has very different numbers in them:
b = 10.^(-3:3);
A.*b
ans =
1.0e+07 *
0.0000 0.0001 0.0008 0.0081 0.0815 0.8147 8.1472
format longG
A.*b
ans =
Columns 1 through 3
81.472368639 814.72368639 8147.2368639
Columns 4 through 6
81472.368639 814723.68639 8147236.8639
Column 7
81472368.639
format shortG
A.*b
ans =
81.472 814.72 8147.2 81472 8.1472e+05 8.1472e+06 8.1472e+07
i.e. they work like long and short on single numbers, but chooses the most convenient display format for each of the numbers.
There's a few more exotic options, like shortE, shortEng, hex etc, but those you can find well documented in The MathWork's own documentation on format.
what is this code meaning?
k = round(Q/12. + Q/123.)-1;
I couldn't understand why that point(.) needed.
That code is from RSA code. Part of calculating coprime number.
The decimal point does not do anything here. It is probably the result of someone porting the code from another language with different data type conventions.
As hbaderts said, in Matlab the default numeric type is double precision; other numeric types must be explicitly set. You can test this yourself:
>> x = 123;
>> whos x
Name Size Bytes Class Attributes
x 1x1 8 double
You will often see the dot (.) preceding the division, multiplication, or power sign; there it means an elementwise operation.
when I calculate a very small number, matlab gives
1.12345e-15
What is this?
I can interpret it as 1.12345*10^(-15)
or its 1.12345*e^(-15)
I am in very hurry. Sorry for the stupid question.
e represents exponential. Its the scientific notation of writing numbers.
The base is 10. For example:
1e2 =100
1e-2= 0.01
e represents scientific notation as Rahul said but it is base 10, not base e.
Run the following code to confirm.
1e1
It gives you
ans = 10
MATLAB does not satisfy matrix arithmetic for inverse, that is;
(ABC)-1 = C-1 * B-1 * A-1
in MATLAB,
if inv(A*B*C) == inv(C)*inv(B)*inv(A)
disp('satisfied')
end
It does not qualify. When I made it format long, I realized that there is difference in points, but it even does not satisfy when I make it format rat.
Why is that so?
Very likely a floating point error. Note that the format function affects only how numbers display, not how MATLAB computes or saves them. So setting it to rat won't help the inaccuracy.
I haven't tested, but you may try the Fractions Toolbox for exact rational number arithmetics, which should give an equality to above.
Consider this (MATLAB R2011a):
a = 1e10;
>> b = inv(a)*inv(a)
b =
1.0000e-020
>> c = inv(a*a)
c =
1.0000e-020
>> b==c
ans =
0
>> format hex
>> b
b =
3bc79ca10c924224
>> c
c =
3bc79ca10c924223
When MATLAB calculates the intermediate quantities inv(a), or a*a (whether a is a scalar or a matrix), it by default stores them as the closest double precision floating point number - which is not exact. So when these slightly inaccurate intermediate results are used in subsequent calculations, there will be round off error.
Instead of comparing floating point numbers for direct equality, such as inv(A*B*C) == inv(C)*inv(B)*inv(A), it's often better to compare the absolute difference to a threshold, such as abs(inv(A*B*C) - inv(C)*inv(B)*inv(A)) < thresh. Here thresh can be an arbitrary small number, or some expression involving eps, which gives you the smallest difference between two numbers at the precision at which you're working.
The format command only controls the display of results at the command line, not the way in which results are internally stored. In particular, format rat does not make MATLAB do calculations symbolically. For this, you might take a look at the Symbolic Math Toolbox. format hex is often even more useful than format long for diagnosing floating point precision issues such as the one you've come across.