[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);举个例子

这段代码是在MATLAB中使用特征值分解（eig）函数对矩阵[x p]'*[v A*p]和[x p]'*[u M*p]进行分解。分解后得到的特征向量存储在qq中，特征值存储在ll中。接下来，通过min函数找到ll的对角线元素中的最小值和对应的索引ii。最后，计算delta值，即qq(2,ii)/qq(1,ii)。

相关问题

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

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。

[qq,ll] = eig([x p]’*[v A*p],[x p]’*[u M*p]);

这是一个MATLAB中求解矩阵特征值和特征向量的示例代码，其中：

- 输入矩阵为[x p]'*[v A*p]和[x p]'*[u M*p]的组合，其中x、p、v、A、u和M均为已知矩阵或向量。
- 输出矩阵qq和向量ll分别为输入矩阵的特征向量和特征值。

具体代码如下：

x = rand(10,1);
p = rand(10,1);
v = rand(10,1);
A = rand(10,10);
u = rand(10,1);
M = rand(10,10);

M_inv = inv(M);
[V,D] = eig([x p]'*[v A*p], [x p]'*[u M*p]);

qq = [v A*p]*V*M_inv;
ll = diag(D);

该代码中，首先定义了矩阵x、p、v、A、u和M，并通过inv函数求出M的逆矩阵M_inv。然后调用eig函数求解[x p]'*[v A*p]和[x p]'*[u M*p]的特征向量和特征值，分别存储在V和D中。最后，根据特征向量和特征值计算出qq和ll。

需要注意的是，该代码中使用了MATLAB内置函数inv和eig，因此在使用前需要确保这两个函数已经被正确加载。此外，由于特征值和特征向量的计算涉及到矩阵的求逆和对角化，因此对于较大的矩阵，计算时间可能会比较长。