% Generate 100-by-4-by-4 amat object symmetric positive definite matrices:
A=fc_amat.random.randnsympd(100,4);
% determinants computation:
D=det(A); % D: 100-by-1-by-1 amat object,  det(A(k))=D(k),    for all k
% LU factorizations:
[L,U,P]=lu(A);
E1=abs(L*U-P*A);
fprintf('max of E1 elements: %.6e\n',max(E1(:)))
% Cholesky factorizations:
R=chol(A);
E2=abs(R'*R-A);
fprintf('max of E2 elements: %.6e\n',max(E2(:)))
% Solving linear systems:
b=ones(4,1); % RHS
X=A\b;   % X: 100-by-4-by-1, X(k)=A(k)\b,    for all k
E3=abs(A*X-b);
fprintf('max of E3 elements: %.6e\n',max(E3(:)))
B=fc_amat.random.randn(100,4,1); % RHS
Y=A\B;   % Y: 100-by-4-by-1, Y(k)=A(k)\B(k), for all k
E4=abs(A*Y-B);
fprintf('max of E4 elements: %.6e\n',max(E4(:)))
whos

max of E1 elements: 3.552714e-15
max of E2 elements: 7.105427e-15
max of E3 elements: 4.884981e-15
max of E4 elements: 1.398881e-14
  Name            Size             Bytes  Class     Attributes

  A             100x4x4            12832  amat                
  B             100x4x1             3232  amat                
  C               4x5                160  double              
  D             100x1x1              832  amat                
  D1            100x3x2             4832  amat                
  D2            100x3x5            12032  amat                
  D3            100x3x4             9632  amat                
  E1            100x4x4            12832  amat                
  E2            100x4x4            12832  amat                
  E3            100x4x1             3232  amat                
  E4            100x4x1             3232  amat                
  L             100x4x4            12832  amat                
  P             100x4x4            12832  amat                
  R             100x4x4            12832  amat                
  U             100x4x4            12832  amat                
  X             100x4x1             3232  amat                
  Y             100x4x1             3232  amat                
  ans             1x71               142  char                
  b               4x1                 32  double              
  codes           1x6                840  cell                
  demo            1x32                64  char                
  demofile        1x16                32  char                
  i               1x1                  8  double              

Published with MATLAB® R2022a