Hello.
I got a few questions about the initialisation of mp-numbers and the used precision.

A short example:

mp.Digits(34);

%cuts the number at 34 decimal digits
number34digits = mp('0.123456789123456789123456789123456789') ;

%number with lower precision
number9digits = mp('0.123456789',9);

%Some calculations
number9digits-mp('10^-20')
ans = 0.123456789

number9digits-mp('10^-9')
ans = 0.123456788

number9digits-mp('10^-20',34)
ans = 0.123456789

mp('10^-20')-number9digits
ans = -0.12345678894780576228095458984375

Interestingly this works as well:
number9digits-'10^-9'
ans = 0.123456788

Obviously the calculations are done with the precision of the first number, even the global precision is 34 digits.

%Another calculation

number34digits-number9digits
ans = 1.756510268325021992797067835708226e-10

number9digits-number34digits
ans = -1.75651027e-10

I assume the calculation is done with 34 digits precision and the number9digits is converted to 34 digits. The converted version of number9digits in 34 digits is not 0.1234567890000000000000000000000000.

mp(number9digits,34)
ans = 0.12345678894780576229095458984375

I guess the reason for that is, that the binary number is converted and not the decimal one.

If I define:
number9digits_ = mp('0.123456789',34);

number34digits-number9digits_
ans = 1.23456789123456789123456781439154e-10

The result is different of course, since the number9digits_ was defined with 34 digits precision.

Could you provide a more detailed documentation on this matter? Which precision is acctually used in calculations when numbers with different precision are used?

I was wondering if it is possible to make a function which simply converts a low precision number like

numberlowprecision = mp('1.234',9);

to a higher precision number like

numberhighprecision = mp(numberlowprecision,34)

which is acctually

numberhighprecision = mp('1.234',34);

For double numbers I am able to do that with an work around:

doublenumber = 1.234;

mpnumber = (num2str(doublenumber),34);

I did not find a mp2str function but maybe I missed it.

A question on another matter is the initialisation of mp-arrays. I did not get the syntax yet. I tried:

mparray = mp('[1.23456,1.23456]');
mparray = mp({'1.23456','1.23456'})

Thank you for your answer.

Hi Pavel,

how are you doing? We are now in the last stage of preparing the next release of the Rational Krylov Toolbox. When updating the guide I was wondering what would be the best way to cite your toolbox? I looked at several papers in the literature which referred to the toolbox, and there doesn't seem to be any agreement. For example, I've seen

- Advanpix. Multiple Precision Toolbox. www.advanpix.com

- www.advanpic.com MP toolbox.

- MATLAB Multiple Precision Toolbox.

I think it would be very useful to many authors if you could add to your website how to cite the toolbox, perhaps even providing a bibitem? Perhaps you can even create an EPrint from the documentation? Or perhaps there already is one?

As promised, I will let you know about our release in due course.

Greetings from Manchester,

Stefan

Hello.

There is a bug in the display of arrays after a vertical concatenation. (Matlab 2014b)

Example:

mp.Digits(34)
a=(1:100)';
b=mp(a(1:50));
c=mp(a(51:100));
d=[b;c];

If you view the variable d in the variable editor it shows the wrong numbers after the 65th entry. If you check it in the command window it is correct.

Hi Pavel,

we have observed the following "bug" (or rather inconsistency) in the formatting of the output via DISP:

Mario Berljafa & Stefan Guettel

Hello Pavel.

I was wondering if you updated the software to use multiple cores in case of matrix multiplication. I read something about it in the change log, but it seems to me it still uses 1 core all the time.

Thank you.

Best regards,

Michael

Hello.

Following example:

Double values:
A=zeros(6000,6000);
tic
for ii = 1:6000
for jj = 1:6000
A(ii,jj)=1.234;
end
end
toc
Elapsed time is 2.038870 seconds

Now without defining A before the for-loop
tic
for ii = 1:6000
for jj= 1:6000
A(ii,jj)=1.234;
end
end
toc
Elapsed time is 120.038870 seconds

Of course the performance is better if I define the array in advance.

Now the same for an mp array with 34 digits:
A=mp(zeros(200,200));
tic
for ii =1:200
for jj = 1:200
A(ii,jj)=mp('1.234');
end
end
toc
Elapsed time is 22.309700 seconds.

Now without defining A before the for-loop
tic
for ii =1:200
for jj = 1:200
A(ii,jj)=mp('1.234');
end
end
toc
Elapsed time is 14.581011 seconds.

How is this possible? This even becomes worse if the matrix is bigger.

Thanks for your answer.