Backslash, applied to an overdetermined system, is expected deterministic; i.e, no variability in solution.

But repeated calls to backslash, for data vL provided in the link, is variable and of infinite dynamic range.

clear all
load vL
% vL = double(vL);
% Amat = double(Amat);
xi = Amat\vL;  %backslash error is nonzero when differenced with same backslash later on
for i=1:10
   notabug = Amat\vL;
   sum(abs(xi - notabug))
end

ans = 0

ans = 0
ans = 0
ans = 3.312601991721914126549721394248086e-06
ans = 3.271854404182205550123018444983506e-05
ans = 0
ans = 8.904811628089073569772503832159206e-06
ans = 8.904811628089073569772503832159206e-06
ans = 8.904811628089073569772503832159206e-06
ans = 3.312601991721914126549721394248086e-06

Uncommenting the double cast always produces ans=0 but reveals Amat to be an overdetermined rank deficient matrix.

MATLAB Version: 9.14.0.2489007 (R2023a) Update 6
Operating System: Microsoft Windows 10 Pro Version 10.0 (Build 19043)

CPU: AMD 3995WX

Advanpix Multiprecision Computing Toolbox Version 5.2.8.15537

https://www.convexoptimization.com/vL.mat

%randn ignores high precision

mp.Digits(1034)

t=randn(1,'mp')
t =0.1048747160164939795645722142580780200660228729248046875

t - 0.1048747160164939795645722142580780200660228729248046875
ans = 0

MATLAB Version 9.14 (R2023a)
Advanpix Multiprecision Computing Toolbox Version 5.2.8.15537

Running your example function for fsolve I get the following error:

Not enough input arguments.

Error in validateFinDiffRelStep (line 10)
value = optimget(options,'FinDiffRelStep',defaultopt,optimgetFlag);

Error in mpfsolve

Error in mp/fsolve (line 5717)
[varargout{1:nargout}] = mpfsolve(varargin{:});

Error in test_fsolve (line 7)
[x,fval,exitflag,output] = fsolve(@myfun,x0,options)

test_fsolve is directly copied from your documentation:

function test_fsolvex0 = mp([-5; -5]);

options = optimset('Display','iter', 'TolFun', mp('eps'),... 'TolX', mp('eps'),... 'Algorithm','levenberg-marquardt'); [x,fval,exitflag,output] = fsolve(@myfun,x0,options) 

function F = myfun(x) 

F = [2*x(1) - x(2) - exp(-x(1)); -x(1) + 2*x(2) - exp(-x(2))]; 

end

end

My matlab version is 2023b version 8.

In a larger code I want to construct an mp sparse matrix in two steps - first the off-diagonal entries and then add the diagonal.

However, using mp.Digits(1) the code breaks down with the error message

" Error using mp/sparse
Index exceeds matrix dimensions.

Error in mpspdiags

Error in mp/spdiags (line 4541)
[varargout{1:nargout}] = mpspdiags(varargin{:}); "

I tried to simplify the matrix creation process and got to the following:

mp.Digits(1);

x = zeros(n,'mp');
identity = spdiags(ones(n,1,'mp'),0,x);

This runs fine for n=10, 100 but breaks down for n=101 and many others (with the error message above). Taking mp.Digits(2); and n=1311 or n = 2520 reproduces the same error message. So does mp.Digits(3); and n=4140.

Is there a quick & simple but revertible way to convert an extensive Matlab program, developed in multiprecision, back to double precision?  For example,  mp.Digits(16) ?  

This question arises because code is sometimes developed in multiprecision for the purpose of eliminating quantization artifacts (finite precision) as a possible error source.  A natural question arises as to the exact tradeoff of speed versus precision.  This information is required for coherently answering one's boss during an entire development phase, preparing talks & papers, and otherwise impressing people at Mathworks enough for them to integrate MCT into Matlab. 

Is the version 4.9.1.14792 available for linux?

I am able to download only version 4.9.0.14753

Pavel,

Doubling array size quadruples execution time.

I'm not asking for help debugging code; this is something you need to see.

Look at it under the Matlab Profiler.

Jon

______________________________________________________________________

%MP Toolbox timing anomaly: twice the array size takes four times the execution time

clearvars

Fs = mp('48000');

freq = mp('997');

NumSecs = mp('1');  %record duration in seconds

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

N = NumSecs*Fs;

disp(['generating ' num2str(double(NumSecs)) '-second D/A signal'])

y1 = zeros(N,1,'mp');

y2 = zeros(N,1,'mp');

cosom = cos(mp('2*pi')*freq/Fs);

tic

for n=2:N  %for loop necessary in production code

   y1(n) = cosom*y1(n-1);  %7.5 seconds in Matlab Profiler, AMD 3995WX CPU Windows 10

   y2(n) = cosom*y2(n-1);  %7.5 seconds in Matlab Profiler, AMD 3995WX CPU Windows 10

end

toc

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% DOUBLING number of array elements takes FOUR times the previous execution time %%%

NumSecs = mp('2');  %record duration in seconds

%%%%%%%%%%%%%%%%% EXACT DUPLICATE (cut & paste) of code block above %%%%%%%%%%%%%%%%

N = NumSecs*Fs;

disp(['generating ' num2str(double(NumSecs)) '-second D/A signal'])

y1 = zeros(N,1,'mp');

y2 = zeros(N,1,'mp');

cosom = cos(mp('2*pi')*freq/Fs);

tic

for n=2:N  %for loop necessary in production code

   y1(n) = cosom*y1(n-1);  %37 seconds in Matlab Profiler, AMD 3995WX CPU Windows 10

   y2(n) = cosom*y2(n-1);  %37 seconds in Matlab Profiler, AMD 3995WX CPU Windows 10

end

toc

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Quoting this page:

>> mp.Test

nthroot() :Error using char/eps

Too many input arguments.

Error in nthroot (line 35)

m = x ~= 0 & (abs(x) < 1./eps('like',y)) & isfinite(n);

Error in mptest (line 1298)

d = nthroot(X,Y)-nthroot(mp(X),mp(Y));

Error in mp.Test (line 300)

mptest(); % Run tests