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## Homework Statement

I try to run this program, but there are still some errors, please help me to solve this problems

## Homework Equations

## The Attempt at a Solution

Code:

```
Program Main
!====================================================================
! eigenvalues and eigenvectors of a real symmetric matrix
! Method: calls Jacobi
!====================================================================
implicit none
integer, parameter :: n=3
double precision :: a(n,n), x(n,n)
double precision, parameter:: abserr=1.0e-09
integer i, j
! matrix A
data (a(1,i), i=1,3) / 1.0, 2.0, 3.0 /
data (a(2,i), i=1,3) / 2.0, 2.0, -2.0 /
data (a(3,i), i=1,3) / 3.0, -2.0, 4.0 /
! print a header and the original matrix
write (*,200)
do i=1,n
write (*,201) (a(i,j),j=1,n)
end do
call Jacobi(a,x,abserr,n)
! print solutions
write (*,202)
write (*,201) (a(i,i),i=1,n)
write (*,203)
do i = 1,n
write (*,201) (x(i,j),j=1,n)
end do
200 format (' Eigenvalues and eigenvectors (Jacobi method) ',/, &
' Matrix A')
201 format (6f12.6)
202 format (/,' Eigenvalues')
203 format (/,' Eigenvectors')
end program main
subroutine Jacobi(a,x,abserr,n)
!===========================================================
! Evaluate eigenvalues and eigenvectors
! of a real symmetric matrix a(n,n): a*x = lambda*x
! method: Jacoby method for symmetric matrices
! Alex G. (December 2009)
!-----------------------------------------------------------
! input ...
! a(n,n) - array of coefficients for matrix A
! n - number of equations
! abserr - abs tolerance [sum of (off-diagonal elements)^2]
! output ...
! a(i,i) - eigenvalues
! x(i,j) - eigenvectors
! comments ...
!===========================================================
implicit none
integer i, j, k, n
double precision a(n,n),x(n,n)
double precision abserr, b2, bar
double precision beta, coeff, c, s, cs, sc
! initialize x(i,j)=0, x(i,i)=1
! *** the array operation x=0.0 is specific for Fortran 90/95
x = 0.0
do i=1,n
x(i,i) = 1.0
end do
! find the sum of all off-diagonal elements (squared)
b2 = 0.0
do i=1,n
do j=1,n
if (i.ne.j) b2 = b2 + a(i,j)**2
end do
end do
if (b2 <= abserr) return
! average for off-diagonal elements /2
bar = 0.5*b2/float(n*n)
do while (b2.gt.abserr)
do i=1,n-1
do j=i+1,n
if (a(j,i)**2 <= bar) cycle ! do not touch small elements
b2 = b2 - 2.0*a(j,i)**2
bar = 0.5*b2/float(n*n)
! calculate coefficient c and s for Givens matrix
beta = (a(j,j)-a(i,i))/(2.0*a(j,i))
coeff = 0.5*beta/sqrt(1.0+beta**2)
s = sqrt(max(0.5+coeff,0.0))
c = sqrt(max(0.5-coeff,0.0))
! recalculate rows i and j
do k=1,n
cs = c*a(i,k)+s*a(j,k)
sc = -s*a(i,k)+c*a(j,k)
a(i,k) = cs
a(j,k) = sc
end do
! new matrix a_{k+1} from a_{k}, and eigenvectors
do k=1,n
cs = c*a(k,i)+s*a(k,j)
sc = -s*a(k,i)+c*a(k,j)
a(k,i) = cs
a(k,j) = sc
cs = c*x(k,i)+s*x(k,j)
sc = -s*x(k,i)+c*x(k,j)
x(k,i) = cs
x(k,j) = sc
end do
end do
end do
end do
return
end
```

200 format (' Eigenvalues and eigenvectors (Jacobi method) ',/, &

1

Error: Unexpected element '&' in format string at (1)

C:\Users\TOSHIBA\AppData\Local\Temp\~Source7.f:34.13:

' Matrix A')

1

Error: Invalid character in name at (1)

C:\Users\TOSHIBA\AppData\Local\Temp\~Source7.f:18.20:

write (*,200)

1

Error: FORMAT label 200 at (1) not defined

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