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! Singular Value Decomposition
program example_svd
use stdlib_linalg_constants, only: dp
use stdlib_linalg, only: svd
implicit none
real(dp), allocatable :: A(:,:),s(:),u(:,:),vt(:,:)
character(*), parameter :: fmt = "(a,*(1x,f12.8))"
! We want to find the singular value decomposition of matrix:
!
! A = [ 3 2 2]
! [ 2 3 -2]
!
A = transpose(reshape([ 3, 2, 2, &
2, 3,-2], [3,2]))
! Prepare arrays
allocate(s(2),u(2,2),vt(3,3))
! Get singular value decomposition
call svd(A,s,u,vt)
! Singular values: [5, 3]
print fmt, ' '
print fmt, 'S = ',s
print fmt, ' '
! Left vectors (may be flipped):
! [2/2 2/2]
! U = [2/2 -2/2]
!
print fmt, ' '
print fmt, 'U = ',u(1,:)
print fmt, ' ',u(2,:)
! Right vectors (may be flipped):
! [2/2 2/2 0]
! V = [1/18 -1/18 4/18]
! [ 2/3 -2/3 -1/3]
!
print fmt, ' '
print fmt, ' ',vt(1,:)
print fmt, 'VT= ',vt(2,:)
print fmt, ' ',vt(3,:)
print fmt, ' '
end program example_svd
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