problem_3, Fortran

problem_3

program newtoniterative
 implicit none
 real::mat(2,3),x = 2.0,y = 2.0,m,n,tol = 0.001
 integer::i
 call jacobianMatrixAtPoint(mat,x,y)
 Write(*,*)'Jacobian matrix'
 call printMatrix(mat)
 Write(*,*)''
 call guasselimination(mat,m,n)
 do i = 1,100
 call jacobianMatrixAtPoint(mat,x,y)
 call guasselimination(mat,m,n)
 x= x+m
 y = y+n
 write(*,*) x,y
 if (abs(m)<tol .or. abs(n)<tol)then
 exit
 end if
 end do
end program
Subroutine printMatrix(mat)
 Implicit none
 Real,intent (in)::mat(2,3)
 integer::i,j
 write(*,*) ""
 do i=1,2
 write(*,*) mat(i,1),mat(i,2),mat(i,3)
 end do
End Subroutine
Subroutine jacobianMatrixAtPoint(mat,x0,y0)
 Implicit none
 Real,intent (in)::x0,y0
 real::mat(2,3), dxf1, dyf1, f1, dxf2, dyf2, f2
 integer::i
 mat(1,1) = dxf1(x0,y0)
 mat(1,2) = dyf1(x0,y0)
 mat(1,3) = -f1(x0,y0)
 mat(2,1) = dxf2(x0,y0)
 mat(2,2) = dyf2(x0,y0)
 mat(2,3) = -f2(x0,y0)
End Subroutine
function f1(x,y)
 implicit none
 real::f1,x,y
 f1 = log(abs(x - y**2.0)) - sin(x*y) - sin(3.141592)
end function
function dxf1(x,y)
 implicit none
 real::dxf1,x,y
 dxf1 = (1/(x - y**2.0)) - y * cos(x*y)
end function
function dyf1(x,y)
 implicit none
 real::dyf1,x,y
 dyf1 = -x * cos(x*y) - ((2.0 * y) / (x - y**2.0))
end function
function f2(x,y)
 implicit none
 real::f2,x,y
 f2 = exp(x*y) + cos(x - y) - 2.0
end function
function dxf2(x,y)
 implicit none
 real::dxf2,x,y
 dxf2 = y * exp(x * y) - sin(x-y)
end function
function dyf2(x,y)
 implicit none
 real::dyf2,x,y
 dyf2 = x * exp (x * y) - sin(x-y)
end function
subroutine guasselimination(matx,x1,y1)
 IMPLICIT NONE
 REAL,intent(in)::matx(2,3)
 real,intent(out)::x1,y1
 real::temp,mat(2,3)
 INTEGER::i,j,k
 mat = matx
 do i =1,2
 temp = mat(i,i)
 do j = 1,3
 mat(i,j) = mat(i,j)/temp
 end do
 do k=1,2
 if (i ==k)then
 cycle
 end if
 temp = mat(k,i)
 do j=1,3
 mat(k,j) = mat(k,j) - mat(i,j)*temp
 end do
 end do
 end do
 x1 = mat(1,3)
 y1 = mat(2,3)
end subroutine


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