下面的代码是使用MKl函数库中的gesvd进行矩阵的svd分解
运行环境: win10 + vs2013 + ivf2013
代码如下：
program svd
use lapack95
implicit none
integer :: i, m, n
real, allocatable :: A(:,:), U(:,:), S(:,:), V(:,:), s1(:)
write(*,'(g0)') '请输入矩阵的大小m,n: '
read(*,*) m, n
allocate( A(m,n), U(m,m), S(m,n), s1(min(m,n)), V(n,n) )
call random_seed()
call random_number(A)
write(*,'(g0)') 'A is...'
do i = 1, size(A,1)
write(*,'(*(f11.4))') A(i,:)
end do
call gesvd( A, s1, U, V ) !// 这里返回的V是V的转置Vt
write(*,'(g0)') 'U is...'
do i = 1, size(U,1)
write(*,'(*(f11.4))') U(i,:)
end do
write(*,'(g0)') 'S is...'
S = 0.d0
forall( i = 1:min(m,n) ) S(i,i) = s1(i)
do i = 1, size(S,1)
write(*,'(*(f11.4))') S(i,:)
end do
write(*,'(g0)') 'V is...'
do i = 1, size(V,1)
write(*,'(*(f11.4))') V(i,:)
end do
write(*,'(g0)') 'cheching, A is ...'
A = matmul( matmul(U,S), V ) !// A = U*S*V'
do i = 1, size(A,1)
write(*,'(*(f11.4))') A(i,:)
end do
deallocate( A, U, S, V, s1 )
end program svd
运行结果如下：
请输入矩阵的大小m,n:
3 3
A is...
0.4229 0.7888 0.6318
0.4695 0.8313 0.3344
0.7387 0.8524 0.5978
U is...
-0.5571 -0.7084 0.4333
-0.5130 0.7039 0.4913
-0.6530 0.0514 -0.7556
S is...
1.9437 0.0000 0.0000
0.0000 0.2064 0.0000
0.0000 0.0000 0.1796
V is...
-0.4933 -0.7318 -0.4702
0.3336 0.3401 -0.8793
-0.8034 0.5906 -0.0764
cheching, A is ...
0.4229 0.7888 0.6318
0.4695 0.8313 0.3344
0.7387 0.8524 0.5978
说明计算正确
