将u = M*x; q = sqrt(x’*u); x = x/q; u = u/q; v = A*x; rho = x’*v; k = 0; g = x; gnorm = 1; log=[]; % Initialisierungen while gnorm > tol, k = k + 1; galt = g; if exist(’C’), g = 2*(C\(C’\(v - rho*u))); % vorkonditionierter Gradient else g = 2*(v - rho*u); % Gradient end if k == 1, p = -g; else p = -g + (g’*M*g)/(galt’*M*galt)*p; end [qq,ll] = eig([x p]’*[v A*p],[x p]’*[u M*p]); [rho,ii] = min(diag(ll)); delta = qq(2,ii)/qq(1,ii); x = x + delta*p; u = M*x; q = sqrt(x’*u); x = x/q; u = u/q; v = A*x; gnorm = norm(g); if nargout>2, log = [log; [k,rho,gnorm]]; end end转换成Fortran程序
时间: 2024-03-20 13:40:21 浏览: 23
下面是将MATLAB代码转换为Fortran的程序示例:
```
PROGRAM Rayleigh_quotient_iteration
IMPLICIT NONE
INTEGER :: k, ii, n, kmax, iter
REAL :: tol, rho, delta, q, gnorm, gnorm_old
REAL, DIMENSION(:,:), ALLOCATABLE :: A, M, x, u, v, g, galt, p
REAL, DIMENSION(:), ALLOCATABLE :: ll, qq, log
LOGICAL :: C_exist
! Read in the size of the matrices
READ(*,*) n
! Read in the matrices A and M
ALLOCATE(A(n,n), M(n,n))
DO i = 1, n
READ(*,*) (A(i,j), j = 1, n)
END DO
DO i = 1, n
READ(*,*) (M(i,j), j = 1, n)
END DO
! Set up the initial guess for x
ALLOCATE(x(n))
x = 1.0
! Set up the other variables
kmax = 100
tol = 1E-6
iter = 0
! Main loop
DO
! Compute u = M*x and q = sqrt(x'u)
ALLOCATE(u(n))
u = MATMUL(M, x)
q = SQRT(DOT_PRODUCT(x, u))
x = x / q
u = u / q
! Compute v = A*x and rho = x'v
ALLOCATE(v(n))
v = MATMUL(A, x)
rho = DOT_PRODUCT(x, v)
! Compute the initial gradient g
ALLOCATE(g(n))
g = 2.0 * (v - rho*u)
gnorm = NORM2(g)
gnorm_old = gnorm
! Initialize the log array
ALLOCATE(log(3, kmax))
log(:,1) = [0, rho, gnorm]
! Main iteration loop
DO k = 1, kmax
! Compute the search direction p
IF (k == 1) THEN
p = -g
ELSE
p = -g + DOT_PRODUCT(g, MATMUL(M, g)) / DOT_PRODUCT(galt, MATMUL(M, galt)) * p
END IF
! Compute the eigenvalues and eigenvectors of [x p]'[v A*p] / [x p]'[u M*p]
ALLOCATE(qq(2,2), ll(2))
qq(1,:) = x
qq(2,:) = p
ll = EIG(MATMUL(TRANSPOSE(qq),MATMUL([v,A*p],qq)), MATMUL(TRANSPOSE(qq),MATMUL([u,M*p],qq)))
! Update x and u
ii = INDEX(MINVAL(ll))
delta = qq(2,ii) / qq(1,ii)
x = x + delta * p
u = MATMUL(M, x)
! Compute the new gradient g
galt = g
v = MATMUL(A, x)
rho = DOT_PRODUCT(x, v)
g = 2.0 * (v - rho*u)
gnorm_old = gnorm
gnorm = NORM2(g)
! Check for convergence
IF (gnorm <= tol) EXIT
! Update the log array
iter = iter + 1
log(:,iter+1) = [k, rho, gnorm]
END DO
! Print the final result
WRITE(*,*) "Lambda = ", rho
WRITE(*,*) "Number of iterations = ", k
! Deallocate the arrays
DEALLOCATE(A, M, x, u, v, g, galt, p, ll, qq, log)
! Exit the program
EXIT
END DO
END PROGRAM Rayleigh_quotient_iteration
```
请注意,这只是一个简单的程序示例,可能需要进行调整才能适合您的特定情况。此外,该程序还假定您已经了解Rayleigh quotient iteration算法,因此不包括该算法的详细解释。
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