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demo_nnls

于 2011-08-26 发布文件大小:639KB

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PLS - DN是一个有限的牛顿为解决非退化的分段线性系统的算法。 PLS - DN的展品可证明半迭代财产即在全球范围内的精确解在有限数量的迭代算法收敛。被证明是收敛速度至少前终止线性。广泛的算法是在我们的AISTATS 2011纸描述：“一个非退化的分段线性系统的有限牛顿算法”。此演示包重新运行在解决非负最小二乘法（NNLS）问题上的三个稀疏的设计矩阵，从哈威尔波音收集（达夫等人，1989年）第4.2节的实验。随着PLS - DN，此演示包建议实施五其他NNLS求解：LCP_Fisher_Newton，LCP_Lemke，PQN，TRESNEI，和SCD (PLS- DN is a finite non-degenerate Newton to solve the piecewise linear system algorithms. PLS- DN exhibits semi-iterative property to prove that the exact solutions worldwide in a limited number of iterative convergence. Proved to be terminated before the linear convergence rate at least. A wide range of algorithms in our AISTATS 2011 paper describes: " a non-degenerate sub-linear systems with limited Newton algorithm." This demo package to re-run in the settlement of non-negative least squares (NNLS) on the design of the three sparse matrices from the Harwell Boeing collection (Duff et al, 1989) Section 4.2 of the experiment. With PLS- DN, this demonstrates the implementation of five other NNLS package proposed solution: LCP_Fisher_Newton, LCP_Lemke, PQN, TRESNEI, and SCD)

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function dg=gplus(x,y,z,x1,x2,y1,y2,z1,z2,p) G=6.67e-11 t222=myfun(x,y,z,x2,y2,z2) t122=myfun(x,y,z,x1,y2,z2) t212=myfun(x,y,z,x2,y1,z2) t221=myfun(x,y,z,x2,y2,z1) t211=myfun(x,y,z,x2,y1,z1) t121=myfun(x,y,z,x1,y2,z1) t112=myfun(x,y,z,x1,y1,z2) t111=myfun(x,y,z,x1,y1,z1) dg=-G*p*1e6*(t222-t122-t212-t221+t211+t121+t112-t111) 转化为g.u. function y=myfun(x,y,z,xi,eta,zeta) R=sqrt((xi-x).^2+(eta-y).^2+(zeta-z).^2) temp1=(xi-x).*log((eta-y)+R) temp2=(eta-y).*log((xi-x)+R) temp3=(zeta-z).*atan((zeta-z).*R/((xi-x).*(eta-y))) 书中所给公式 temp3=-(zeta-z).*atan((xi-x).*(eta-y)./(zeta-z)./R) 上式变换 y=temp1+temp2+temp3 (function dg = gplus (x, y, z, x1, x2, y1, y2, z1, z2, p) G = 6.67e-11 t222 = myfun (x, y, z, x2, y2, z2) t122 = myfun (x, y, z, x1, y2, z2) t212 = myfun (x, y, z, x2, y1, z2) t221 = myfun (x, y, z, x2, y2, z1) t211 = myfun (x, y, z, x2, y1, z1) t121 = myfun (x, y, z, x1, y2, z1) t112 = myfun (x, y, z, x1, y1, z2) t111 = myfun (x, y, z, x1, y1, z1) dg =-G* p* 1e6* (t222-t122-t212-t221+t211+t121+t112-t111) converted the Gu function y = myfun, (x y, z, xi, eta, zeta) R = sqrt ((xi-x). ^ 2+ (eta-y). ^ 2+ (zeta-z). ^ 2) temp1 = (xi-x).* log ((eta-y)+R) temp2 = (eta-y).* log ((xi-x)+R) temp3 = (zeta-z).* atan ((zeta-z).* R/( (xi-x).* (eta-y))) book given formula Temp3 =- (Zeta-z)* ATAN ((Xi-X)* (ETA-y)/(Zeta- Z)/R) the above formula transform Y = temp1+temp2+temp3 )

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积分：1

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