In <49hrq8$92b at astor.urv.es> Santi Garcia Vallve <vallve at argo.urv.es> writes:
>I am trying to make my own programs with fortran77 to predict protein
>folding types by distances functions that make allowances for amino acid
>interactions (Chou and Zhang, 1994 JBC). I need to calculate the inverse
>of a matrix 19*19 (19 rows and 19 columns), how can I make it? It is
>possible to do it with fortran?
Using Matlab conventions:
inv(A)= Adj(A)/abs(A)
% inv(A) is read as: inverse of A
% Adj(A) is the adjoint of A which is a matrix defined by the transpose
% matrix of cofactors. For a 3x3 matrix:
Adj(A) = [c11 c12 c13
c21 c22 c23
c31 c32 c33]' % the ' stands for transpose
% abs(A) is the absolute value of A or all eigenvalues multiplied together.
Cofactors:
Cij=(-1)^(i+j)*mij
where mij is the minor for rows i and j. You can find the minor by crossing
out rows i and j in your matrix and taking the determinant of the matrix
left (18x18).
Lets say you have a 3x3 matrix A = [2 1 1
1 1 -1
2 1 3]
You need the matrix of cofactors but to find that you need to find the minors.
As an example lets find m31. To do that you cross out row 3 and column 1
which leaves you with the matrix [1 1
1 -1]
Take the determinant: 1*(-1) - 1*1=-2. So minor m31 = -2
Calculate cofactor c31=(-1)^(i+j)*m31=(-1)^(3+1)*(-2)=-2. So you now have
one of 9 cofactors. Fill out the cofactor matrix:
C = [c11 c12 c13] = [4 -5 -1]
[c21 c22 c23] [-2 4 0]
[-2 c32 c33] [-2 3 1]
abs(A)=2 so
inv(A)=Adj(A)/abs(A) = C'/abs(A) = [4 -5 -1]T / = [2 -1 -1
[-2 4 0] /-2 -5/2 2 3/2
[-2 3 1]/ -1/2 0 1/2]
Just scale it up for a 19x19 matrix :)
BTW There are other ways to do it that are more efficient but hey, this one
works and is fairly simple.
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| Hordur Kvaran | |
| University of Iceland | "I can resist everything |
| Mechanical Engineering | except temptation" |
|hordurk at rhi.hi.is | -Oscar Wilde |
| URL: http://www.rhi.hi.is/~hordurk/ | |
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PS. I know. Nothing better to do. I dread going back to work on the
project I'm working on.