mirror of
https://github.com/TREX-CoE/Sherman-Morrison.git
synced 2024-12-26 14:23:47 +01:00
112 lines
3.3 KiB
Matlab
112 lines
3.3 KiB
Matlab
## 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 square uniform distributed random integer matrix with entries in [-1,1]
|
|
#do
|
|
# A=randi([-1,1],3,3);
|
|
# 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 square uniform distributed random float matrix with entries in (0,1)
|
|
#do
|
|
# 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
|
|
|
|
Ar=A-A0; ## The remainder of A
|
|
nCols=columns(Ar); ## The number of coluns of A (M in accompanying PDF)
|
|
Id=eye(nCols);
|
|
A0inv=eye(nCols);
|
|
Ainv=zeros(nCols,nCols);
|
|
ylk=zeros(nCols,nCols,nCols);
|
|
p=zeros(nCols,1);
|
|
breakdown=zeros(nCols,1);
|
|
|
|
A,A0
|
|
printf("Determinant of A is: %d\n",det(A))
|
|
printf("Determinant of A0 is: %d\n",det(A0))
|
|
|
|
## Calculate the inverse of A0 and populate p-vector
|
|
for i=1:nCols
|
|
A0inv(i,i) = 1 / A0(i,i);
|
|
p(i)=i;
|
|
endfor
|
|
|
|
## Calculate all the y0k in M^2 multiplications instead of M^3
|
|
for k=1:nCols
|
|
for i=1:nCols
|
|
#printf("(i,k,1) = (%d,%d,1)\n",i,k);
|
|
ylk(i,k,1) = A0inv(i,i) * Ar(i,k);
|
|
endfor
|
|
endfor
|
|
|
|
## Calculate all the ylk from the y0k calculated previously
|
|
for l=2:nCols
|
|
## Calculate break-down conditions and put in a vector
|
|
for j=l-1:nCols
|
|
breakdown(j) = abs(1+ylk(p(j),p(j),l-1));
|
|
#printf("|1 + ylk(%d,%d,%d)|\n", p(j), p(j), l-1);
|
|
endfor
|
|
[val, lbar] = max(breakdown); ## Find the index of the max value
|
|
breakdown=zeros(nCols,1); ## Reset the entries to zero for next l-round
|
|
## Swap p(l) and p(lbar)
|
|
tmp=p(l-1);
|
|
p(l-1)=p(lbar);
|
|
p(lbar)=tmp;
|
|
for k=l:nCols
|
|
for i=1:nCols
|
|
ylk(i,p(k),l) = ylk(i,p(k),l-1) - (ylk(p(l-1),p(k),l-1)) / (1+ylk(p(l-1),p(l-1),l-1)) * (ylk(i,p(l-1),l-1));
|
|
#printf("ylk(%d,%d,%d) = ylk(%d,%d,%d) - (ylk(%d,%d,%d) / (1+ylk(%d,%d,%d) * (ylk(%d,%d,%d);\n", i,p(k),l,i,p(k),l-1,p(l-1),p(k),l-1,p(l-1),p(l-1),l-1,i,p(l-1),l-1);
|
|
endfor
|
|
endfor
|
|
endfor
|
|
|
|
## Construct A-inverse from A0-inverse and the ylk
|
|
Ainv=A0inv;
|
|
for l=1:nCols
|
|
Ainv=(Id - ylk(:,p(l),l) * transpose(Id(:,p(l))) / (1 + ylk(p(l),p(l),l))) * Ainv;
|
|
#printf("Ainv=(Id - ylk(:,%d,%d) * transpose(Id(:,%d)) / (1 + ylk(%d,%d,%d))) * Ainv\n",p(l),l,p(l),p(l),p(l),l);
|
|
endfor
|
|
|
|
## Test if the inverse found is really an inverse (does not work if values are floats)
|
|
IdTest=A*Ainv;
|
|
if (IdTest==eye(nCols))
|
|
printf("\n");
|
|
printf("Inverse of A^{-1} FOUND!\n");
|
|
Ainv
|
|
else
|
|
printf("\n");
|
|
printf("Inverse of A^{-1} NOT found yet.\nRunning another test...\n");
|
|
for i=1:nCols
|
|
for j=1:nCols
|
|
if (abs(IdTest(i,j))<cutOff)
|
|
IdTest(i,j)=0;
|
|
elseif (abs(IdTest(i,j))-1<cutOff)
|
|
IdTest(i,j)=1;
|
|
endif
|
|
endfor
|
|
endfor
|
|
if (IdTest==eye(nCols))
|
|
printf("\n");
|
|
printf("Inverse of A^{-1} FOUND!\n");
|
|
Ainv
|
|
else
|
|
printf("\n");
|
|
printf("Still not found. Giving up!\n");
|
|
IdTest
|
|
endif
|
|
endif |