Extracts the diagonal terms of a matrix.
Array containing the diagonal terms of matrix A. It is rank-1 or rank-2 depending on the rank of A. When A is a rank-3 array, the result is a rank-2 array consisting of each separate set of diagonals. (Output)
A — Matrix from which to extract the diagonal. This is a rank-2 or rank-3 array of type real, double, complex, or double complex. The output is a rank-1 or rank-2 array, respectively. (Input)
DIAGONALS (A)
Extracts a rank-1 array whose values are the diagonal terms of the rank-2 array A. The size of the array is the smaller of the two dimensions of the rank-2 array.
Dense Matrix Example (operator_ex32.f90)
use linear_operators
implicit none
! This is the equivalent of Example 4 (using operators) for LIN_EIG_GEN.
integer, parameter :: n=17
real(kind(1d0)), parameter :: one=1d0
real(kind(1d0)), dimension(n,n) :: A, C
real(kind(1d0)) variation(n), eta
complex(kind(1d0)), dimension(n,n) :: U, V, e(n), d(n)
! Generate a random matrix.
A = rand(A)
! Compute the eigenvalues, left- and right- eigenvectors.
D = EIG(A, W=V); E = EIG(.t.A, W=U)
! Compute condition numbers and variations of eigenvalues.
variation = norm(A)/abs(diagonals( U .hx. V))
! Now perturb the data in the matrix by the relative factors
! eta=sqrt(epsilon) and solve for values again. Check the
! differences compared to the estimates. They should not exceed
! the bounds.
eta = sqrt(epsilon(one))
C = A + eta*(2*rand(A)-1)*A
D = EIG(C)
! Looking at the differences of absolute values accounts for
! switching signs on the imaginary parts.
if (count(abs(d)-abs(e) > eta*variation) == 0) then
write (*,*) 'Example 4 for LIN_EIG_GEN (operators) is correct.'
end if
end
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