使用优化工具箱是时问题。

我用matlab的优化app来求解一个非线性最小二乘法问题主函数：

close all; clear; clc;

x=-3:1:3

y=-2:1:2

[X,Y]= meshgrid(x,y)

Z=X.^2+Y.^2

mesh(X,Y,Z)

hold on

d=1/180*pi

e=2/180*pi

f=3/180*pi

T=[1,0,0,0

0,1,0,0

0,0,1,0

0.1,0.2,0.3,1]

R1=[1,0,0,0

0,cos(d),sin(d),0

0,(-1)*sin(d),cos(d),0

0,0,0,1];

R2=[cos(e),0,(-1)*sin(e),0

0,1,0,0

sin(e),0,cos(e),0

0,0,0,1];

R3=[cos(f),sin(f),0,0

(-1)*sin(f),cos(f),0,0

0,0,1,0

0,0,0,1];

t=size(X,1)*size(X,2);

W=[X(:),Y(:),Z(:),ones(t,1)]*T*R1*R2*R3;

global X2

global Y2

global Z2

X2=W(:,1)

Y2=W(:,2)

Z2=W(:,3)

plot3(X2,Y2,Z2)

函数文件：

function [n,x1,x2,x3] = obj(a,x,y,z)

%UNTITLa(5)a(4)4 此处显示有关此函数的摘要

% 此处显示详细说明

T=[1,0,0,0

0,1,0,0

0,0,1,0

a(1),a(2),a(3),1];

R1=[1,0,0,0

0,cos(a(4)),sin(a(4)),0

0,(-1)*sin(a(4)),cos(a(4)),0

0,0,0,1];

R2=[cos(a(5)),0,(-1)*sin(a(5)),0

0,1,0,0

sin(a(5)),0,cos(a(5)),0

0,0,0,1];

R3=[cos(a(6)),sin(a(6)),0,0

(-1)*sin(a(6)),cos(a(6)),0,0

0,0,1,0

0,0,0,1];

w=[x,y,z,1]*R3*R2*R1*T;

x1=w(:,1);

x2=w(:,2);

x3=w(:,3);

n=x3-x1^2-x2^2;

使用优化app时的报错如图：我检查过没有上述说的括号的问题，实在不知道怎么回事了，请赐教！

Answer 1

[lapep]

你调用方式不太对，我修改了一下你的代码，但是有warning，选择合适的算法求吧:)

obj.M

function [n,x1,x2,x3] = obj(t)

%UNTITLa(5)a(4)4 此处显示有关此函数的摘要

% 此处显示详细说明

x=t(1);

y=t(2);

a1=t(3);

a2=t(4);

a3=t(5);

d=t(6);

e=t(7);

f=t(8);

[X,Y]= meshgrid(x,y);

z=X.^2+Y.^2;

T=[1,0,0,0

0,1,0,0

0,0,1,0

a1,a2,a3,1];

R1=[1,0,0,0

0,cos(d),sin(d),0

0,(-1)*sin(d),cos(d),0

0,0,0,1];

R2=[cos(e),0,(-1)*sin(e),0

0,1,0,0

sin(e),0,cos(e),0

0,0,0,1];

R3=[cos(f),sin(f),0,0

(-1)*sin(f),cos(f),0,0

0,0,1,0

0,0,0,1];

w=[x,y,z,1]*R3*R2*R1*T;

x1=w(:,1);

x2=w(:,2);

x3=w(:,3);

n=x3-x1^2-x2^2;

Optimization running.

Warning: Trust-region-reflective algorithm requires at least as many equations as variables; using Levenberg-Marquardt algorithm instead.

Objective function value: 7.888609052210118E-31

Local minimum found.

Optimization completed because the size of the gradient is less than

the default value of the function tolerance.