EIGEN VALUE.doc - program main implicit none integer NDIM...

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program main implicit none integer NDIM real FTOL parameter(NDIM=3,FTOL=1.0E-10) integer i,iter,np,n real fret,p(NDIM),xi(NDIM,NDIM),yi(NDIM,NDIM),zi(NDIM,NDIM),np=NDIM,n=3 data xi/1,0,0,0,1,0,0,0,1/ data yi/5,0,0,0,5,0,0,0,5/ data zi/102,1004,25,-31,595,206,-67,898,-3000/ data p/1,1,1/ call powell(p,xi,n,np,ftol,iter,fret) write(*,*)" 初始 P 值: ",p write(*,'(/1x,a,i3)') ' iterations:',iter write(*,'(1x,a/1x,3f12.6)') 'Pmin : ',(p(i),i=1,NDIM) write(*,'(1x,a,f12.6)') ' 无约束最小特征值 ',fret end real function func(x) real x(*) func=-(6*x(1)**2+3*x(2)**2+x(3)**2+4*x(1)*x(2)+2*x(1)*x(3)+2*x(2)*x(3))/ (x(1)**2+x(2)**2+x(3)**2) end Powell 方法主要有基本搜索,加速搜索,调整搜索方向翻个部 分组成。基本搜索从起始点出发沿已知的 N 个搜索方向进行一 维搜索,确定一个新基点。加速搜索是沿着相邻的两个极点连 线方向进行一维搜索。最后用几点连线方向代替一直 N 个搜索 方向之一,构成新的搜索方向组,进行下一轮迭代。例如:
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下面我们直接看本题中优化的稳定性与准确性: data xi/1,0,0,0,1,0,0,0,1/ ,下面是结果 data yi/5,0,0,0,5,0,0,0,5/ data zi/12,14,25,31,55,26,67,88,0/
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所以此算法先不论准确性,至少对 X 矩阵的设定要求并不严格。 基本不随 X 的变化而变化,有良好的容错性。 下面用雅克比变换来看这个矩阵的准确特征值
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