mirror of
https://github.com/TREX-CoE/Sherman-Morrison.git
synced 2024-07-03 09:56:09 +02:00
72 lines
2.5 KiB
Mathematica
72 lines
2.5 KiB
Mathematica
## Based on Algorithm 3 from P. Maponi,
|
|
## p. 283, doi:10.1016/j.laa.2006.07.007
|
|
|
|
clc ## Clear the screen
|
|
## Define the matrix to be inverted. This is example 8 from the paper
|
|
## In the future this matrix needs to be read from the function call arguments
|
|
#A=[1,1,-1; ...
|
|
# 1,1,0; ...
|
|
# -1,0,-1];
|
|
#A0=diag(diag(A)); ## The diagonal part of A
|
|
|
|
### The modified example that gives all singular updates at some point
|
|
#A=[1,1,1; ...
|
|
# 1,1,0; ...
|
|
# -1,0,-1];
|
|
#A0=diag(diag(A)); ## The diagonal part of A
|
|
|
|
## A uniform distributed random square (5x5) integer matrix with entries in [-1,1]
|
|
do
|
|
A=randi([-1,1],5,5);
|
|
#A=rand(5);
|
|
A0=diag(diag(A)); ## The diagonal part of A
|
|
until (det(A)!=0 && det(A0)!=0) ## We need both matrices to be simultaniously non-singular
|
|
A
|
|
printf("Determinant of A is: %d\n",det(A))
|
|
printf("Determinant of A0 is: %d\n\n",det(A0))
|
|
|
|
Ar=A-A0; ## The remainder of A
|
|
nCols=columns(Ar); ## The number of coluns of A (M in accompanying PDF)
|
|
Id=eye(nCols); ## Identity matrix, used for the Cartesian basis vectors
|
|
Ainv=zeros(nCols,nCols,nCols+1); ## 3d matrix to store intermediate inverse of A
|
|
U=zeros(nCols,nCols,nCols); ## 3d matrix to store the nCols rank-1 updates
|
|
a=zeros(1,nCols); ## Vector containing the break-down values
|
|
used=zeros(1,nCols); ## Vector to keep track of which updates have been used
|
|
|
|
## Loop to calculate A0_inv and the rank-1 updates and store in U
|
|
Ainv(:,:,1)=eye(nCols);
|
|
for i=1:nCols
|
|
Ainv(i,i,1)=1/A0(i,i);
|
|
U(:,:,i)=Ar(:,i)*transpose(Id(:,i));
|
|
endfor
|
|
|
|
## Here starts the calculation of the inverse of A
|
|
for i=1:nCols ## Outer loop iterated over the intermediates A_l^-1, M times in total
|
|
|
|
## Here the break-down values are calculated for each intermediate inverse
|
|
for j=1:nCols
|
|
a(j)=1 + transpose(Id(:,j)) * Ainv(:,:,i) * Ar(:,j); ## First time all elmts 1 because A0_inv is diagonal
|
|
printf("a(%d) = %f\n",j,a(j))
|
|
## Select next update ONLY if break-down value != 0 AND not yet used
|
|
if (a(j)!=0 && used(j)!=1);
|
|
k=j;
|
|
break;
|
|
endif
|
|
endfor
|
|
|
|
## Do the actual S-M update
|
|
Ainv(:,:,i+1) = Ainv(:,:,i) - Ainv(:,:,i) * U(:,:,k) * Ainv(:,:,i) / a(k);
|
|
used(k)=1; ## Mark this update as used
|
|
endfor
|
|
|
|
## Test if the inverse found is really an inverse (does not work if values are floats)
|
|
if (A*Ainv(:,:,nCols+1)==eye(nCols))
|
|
printf("\n");
|
|
printf("Inverse found. A^{-1}:\n");
|
|
Ainv(:,:,nCols+1)
|
|
else
|
|
printf("\n");
|
|
printf("Inverse NOT found! A*A^{-1}:\n");
|
|
A*Ainv(:,:,nCols+1)
|
|
endif
|