如何用matlab做高精度计算？【第三辑】(完)

>> mp.Digits(34);                   % Setup default precision to 34 decimal digits (quadruple).
>> format longG                     % Toolbox shows all digits in case of 'long' formats.
% Simple expressions evaluation in quadruple precision:
>> x = mp('pi/4')                          
x = 
    0.7853981633974483096156608458198757
 
>> y = mp('sqrt(2)/2')
y = 
    0.707106781186547524400844362104849
 
>> A = repmat(x,10,10);  % Create mp-matrix by scalar replication.
>> norm(y-cos(A))        % Calculations are done with 34 digits precision.
ans = 
    9.629649721936179265279889712924637e-35
 
% Assemble matrix row by row:
% (Butcher tableau for Gauss-Legendre method: https://goo.gl/izuFWg)
>> a1 = mp('[ 5/36              2/9-sqrt(15)/15   5/36-sqrt(15)/30 ]');
>> a2 = mp('[ 5/36+sqrt(15)/24  2/9               5/36-sqrt(15)/24 ]');
>> a3 = mp('[ 5/36+sqrt(15)/30  2/9+sqrt(15)/15   5/36             ]');
>> a = [a1;a2;a3];                  % Concatenate rows into final matrix 
 
% Create mp-matrices by conversion from double
>> A = mp(rand(5));
>> B = mp(eye(5));
>> [V,D] = eig(A,B);
>> norm(A*V - B*V*D,1)/(norm(A,1) * norm(B,1))
ans = 
    8.1433805952291741154581605524001229e-34
 
% Create sparse matrix with accumulation using triplets:
>> i = [6 6 6 5 10 10 9 9]';                      
>> j = [1 1 1 2 3 3 10 10]';
>> v = mp('[100 202 173 305 410 550 323 121]')';  % Prepare vector of nonzeros
>> S = sparse(i,j,v)                              % Form quadruple precision sparse matrix
S =
    (6,1)      475
    (5,2)      305
    (10,3)     960
    (9,10)     444

gallery('grcar',8)
ans =
     1     1     1     1     0     0     0     0
    -1     1     1     1     1     0     0     0
     0    -1     1     1     1     1     0     0
     0     0    -1     1     1     1     1     0
     0     0     0    -1     1     1     1     1
     0     0     0     0    -1     1     1     1
     0     0     0     0     0    -1     1     1
     0     0     0     0     0     0    -1     1

% MATLAB浮点数精度
A = -gallery('grcar',150);
figure('Color','w');
plot(eig(A),'k.'), hold on, axis equal
plot(eig(A'),'ro')
 
% MATLAB VPA高精度计算(34位精度)
digits(34); 
A = vpa(-gallery('grcar',150));
eA = eig(A);
cA = eig(A');
figure('Color','w');
plot(eA,'k.'), hold on, axis equal
plot(cA,'ro')