fortran 90牛顿法.c

Fortran 90

Fortran 90牛顿法！  
 

<P>   !!!本程序适用于求解形如f(x)=1/2*x'Ax+bx+c二次函数的稳定点；
    !!!输入函数信息，输出函数的稳定点及迭代次数；
    !!!iter整型变量，存放迭代次数；
    !!!x为n维变量，初始值由用户输入；gradt实型变量，存放函数梯度;
    !!!dir实型变量，存放搜索方向；x0实型变量，存放步长
    program main
    real,dimension(:),allocatable::x,gradt,dir,b
    real,dimension(:,:),allocatable::hessin
    real::x0,tol
    integer::n ,iter 
    print*,'请输入变量的维数'
    read*,n
    allocate(x(n),gradt(n),dir(n),b(n))
    allocate(hessin(n,n))
    print*,'请输入初始向量x'
    read*,x
    print*,'请输入hessin矩阵'
    read*,hessin
    print*,'请输入矩阵b'
    read*,b
tol=0.000001
    iter=0
100 gradt=matmul(hessin,x)+b
    if(sqrt(dot_product(gradt,gradt))&lt;tol)then
        !print*,'极小值点为：',x
     !print*,'迭代次数:',iter 
     goto 101
    endif
    call gaussj(hessin,n,gradt)
    x0=golden(x,(-1)*gradt,hessin,b)
    x=x+x0*(-1)*gradt 
    iter=iter+1
if(iter&gt;10*n)then
    print*,"out"
    goto 101
endif
print*,"第",iter,"次运行结果为","direction",(-1)*gradt,"step length",x0
print*,x,"f(x)=",f(x,hessin,b)  
    goto 100
    contains</P>
<P>    !!!子程序，返回函数值    
    function f(x,A,b) result(f_result)
    real,dimension(:),intent(in)::x,b
    real,dimension(:,:),intent(in)::A
    real::f_result
    f_result=0.5*dot_product(matmul(x,A),x)+dot_product(b,x)
    end function f

    !!!子程序gaussj(hessin,n,gradt)
    !!!a为二维数组，返回值为的a逆;b为一维数组，返回值为方程ax=b的解
    subroutine gaussj(a,n,b)
    integer n,nmax
    real a(n,n),b(n)
    parameter(nmax=50)
    integer i,icol,irow,j,k,l,ll,indxc(nmax),indxr(nmax),ipiv(nmax)
    real big,dum,pivinv
    do j=1,n
       ipiv(j)=0
    enddo
    do i=1,n
       big=0.
       do j=1,n
       if(ipiv(j)/=1)then
          do k=1,n
          if(ipiv(k)==0)then
          if(abs(a(j,k))&gt;=big)then
           big=abs(a(j,k))
           irow=j
           icol=k
       endif
       else if(ipiv(k)&gt;1)then
          pause'singular matrix in gaussj'
       endif
       enddo
    endif
    enddo
    ipiv(icol)=ipiv(icol)+1
    if(irow/=icol)then
       do l=1,n
          dum=a(irow,l)
       a(irow,l)=a(icol,l)
       a(icol,l)=dum
       enddo
       dum=b(irow)
       b(irow)=b(icol)
       b(icol)=dum
    endif
    indxr(i)=irow
    indxc(i)=icol
    if(a(icol,icol)==0.)pause'singular matrix in gaussj'
    pivinv=1./a(icol,icol)
    a(icol,icol)=1.
    do l=1,n
        a(icol,l)=a(icol,l)*pivinv
    enddo
    b(icol)=b(icol)*pivinv
    do ll=1,n
       if(ll/=icol)then
          dum=a(ll,icol)
       a(ll,icol)=0
       do l=1,n
          a(ll,l)=a(ll,l)-a(icol,l)*dum
       enddo
       b(ll)=b(ll)-b(icol)*dum
       endif
    enddo
    enddo
    do l=n,1,-1
       if(indxr(l)/=indxc(l))then
       do k=1,n
          dum=a(k,indxr(l))
       a(k,indxr(l))=a(k,indxc(l))
       a(k,indxc(l))=dum
       enddo
    endif
    enddo
    end subroutine gaussj</P>
<P> !!!精确线搜索0.618法子程序 ，返回步长；
    function golden(x,d,A,b) result(golden_n)
    real::golden_n
    real::x0
    real,dimension(:),intent(in)::x,d
    real,dimension(:),intent(in)::b
    real,dimension(:,:),intent(in)::A
    real::x1,x2,a1,b1,f0,f1,f2,r,tol,dx
    parameter(r=0.618)
    tol=0.0001
    dx=0.1
    x0=1
    x1=x0+dx
    f0=f(x+x0*d,A,b)
    f1=f(x+x1*d,A,b)
    if(f0&lt;f1)then
4       dx=dx+dx
        x2=x0-dx
        f2=f(x+x2*d,A,b)
        if(f2&lt;f0)then
           x1=x0
        x0=x2
        f1=f0
        f0=f2
        goto 4
        else
           a1=x2
        b1=x1
        endif
    else
2       dx=dx+dx
        x2=x1+dx
        f2=f(x+x2*d,A,b)
        if(f2&gt;=f1)then
           b1=x2
        a1=x0
        else
           x0=x1
        x1=x2
        f0=f1
        f1=f2
        goto 2
        endif
    endif
    x1=a1+(1-r)*(b1-a1)
    x2=a1+r*(b1-a1)
    f1=f(x+x1*d,A,b)
    f2=f(x+x2*d,A,b)
3   if(abs(b1-a1)&lt;=tol)then
        x0=(a1+b1)/2
    else
        if(f1&gt;f2)then
        a1=x1
        x1=x2
        f1=f2
        x2=a1+r*(b1-a1)
        f2=f(x+x2*d,A,b)
        goto 3
     else
        b1=x2
        x2=x1
        f2=f1
        x1=a1+(1-r)*(b1-a1)
        f1=f(x+x1*d,A,b)
        goto 3
     endif
    endif
    golden_n=x0
    end  function golden
  
101 end
</P>
<P>本程序由Fortran 90语言编写，在Vistual Fortran 5下编译通过，本程序由沙沙提供！</P>