Hi everybody,
I have a problem about applying Thikonov regularisation: Is there a program addressing this issue (Fortran or Mathematica)
Regardswith
Abdelmalek
Here are the answers generated by ChatGPT:
My request is:
"
I have a problem about applying Thikonov regularisation: Is there a program addressing this issue (Fortran or Mathematica).
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The answer by ChatGPT:
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Yes, both Fortran and Mathematica have built-in functions that can be used to apply Tikhonov regularization.
In Fortran, you can use the LAPACK library which includes routines for solving linear systems with Tikhonov regularization. The specific routine you would use depends on the type of matrix you are working with. For example, if you have a dense matrix, you could use the DGELS routine, while if you have a sparse matrix, you could use the LSQR routine. You would need to set the regularization parameter and the type of regularization matrix you want to use.
In Mathematica, you can use the built-in function Regularization to apply Tikhonov regularization. The function takes as input the data matrix, the target vector, and the regularization parameter, and returns the regularized solution. You can also specify the type of regularization matrix you want to use.
Here's an example of using the Regularization function in Mathematica:
Mathematica example code:
data = {{1, 2}, {3, 4}, {5, 6}};
target = {7, 8, 9};
regParam = 0.1;
regMatrix = IdentityMatrix[2];
Regularization[data, target, regParam, regMatrix]
This would apply Tikhonov regularization with the identity matrix as the regularization matrix and a regularization parameter of 0.1 to the data and target vectors.
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Another request by Me:
"
according to the pervious question, give me a Fortran program for Tikhonov regularization.
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The answer produced by ChatGPT:
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Sure, here is an example Fortran program that uses LAPACK's DGELS routine to solve a linear system with Tikhonov regularization:
Fortran example code:
program tikhonov
implicit none
integer, parameter :: n = 3 ! size of the linear system
real :: a(n,n), b(n), alpha ! data matrix, target vector, regularization parameter
integer :: i, j, info
real :: work(2*n), rcond
! initialize the data matrix and target vector
a = reshape((/1, 2, 3, 4, 5, 6, 7, 8, 9/), [n,n])
b = (/10, 11, 12/)
! set the regularization parameter and regularization matrix
alpha = 0.1
do i = 1, n
do j = 1, n
if (i == j) then
a(i,j) = a(i,j) + alpha
end if
end do
end do
! solve the regularized linear system using DGELS
call dgels('N', n, n, 1, a, n, b, n, work, 2*n, info)
! check for errors
if (info /= 0) then
print *, 'Error: DGELS returned info =', info
stop
end if
! print the regularized solution
print *, 'Regularized solution:'
do i = 1, n
print *, b(i)
end do
end program tikhonov
In this example program, we set the data matrix and target vector to some sample values, and then set the regularization parameter alpha and regularization matrix by adding alpha to the diagonal of the data matrix. We then use the LAPACK routine DGELS to solve the regularized linear system. Finally, we print the regularized solution. Note that this program assumes a dense matrix, but you could use a different LAPACK routine for sparse matrices.
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May it be helpful.
Dear Hosein,
Thank you very much, it's very helpful
thank you again
I will send you my problem in pdf file
Abdelmalek
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