#include <vector>
#include <qdebug.h>
//多数据点拟合曲线
bool calmatchline(const std::vector<int>&xValue ,const vector<float>&yValues)
{
using namespace std;
int cloth = 4;//次幂
int matlength = cloth +1;
std::vector<float> xvalues;
//模拟数值
xvalues.push_back(-65);
xvalues.push_back(-35);
xvalues.push_back(-5);
xvalues.push_back(0);
xvalues.push_back(5);
xvalues.push_back(10);
xvalues.push_back(15);
xvalues.push_back(20);
xvalues.push_back(25);
xvalues.push_back(37);
vector<float> yvalues;
yvalues.push_back(0.26749875);
yvalues.push_back(0.40583125);
yvalues.push_back(0.85247625);
yvalues.push_back(1.001101299);
yvalues.push_back(0.97136125);
yvalues.push_back(1.1904425);
yvalues.push_back(1.017414286);
yvalues.push_back(0.839881818);
yvalues.push_back(0.759257143);
yvalues.push_back(0.511851948);
CvMat *A=cvCreateMat(matlength,matlength,CV_32FC1);
CvMat *X=cvCreateMat(matlength,1,CV_32FC1);
CvMat *b=cvCreateMat(matlength,1,CV_32FC1);
//
float onevalue = 0;
for (int i = 0; i < matlength; i++)
{
for (int j = 0; j < matlength; j++)
{
onevalue = sumxvalue(xvalues,i+j);
cvmSet(A,i,j,onevalue);
}
}
for (int i = 0; i < matlength; i++)
{
onevalue = sumxyvalue(xvalues,yvalues,i);
cvmSet(b,i,0,onevalue);
}
cvSolve(A,b,X,CV_LU);
vector<float> value;
for (int i = 0; i < matlength; i++)
{
value.push_back(cvmGet(X,i,0));
qDebug()<<QString::fromLocal8Bit("系数%1:").arg(QString::number(i))<<QString::number(value.at(i))+" ";
}
float *y = new float[20];
float *ptr = y;
for (int i = 0; i < yvalues.size(); i++)
{
float tmp = 0;
for (int j = 0; j < matlength; j++)
{
tmp += pow(xvalues.at(i),j)*value.at(j);
}
*ptr = tmp;
ptr++;
}
ptr = y;
for (int i = 0; i < xvalues.size(); i++)
{
qDebug()<<"x:"<<QString::number(xvalues.at(i))<<" y:"<<QString::number(*ptr);
ptr++;
}
std::complex<double> x[4];
x[4] = Ferrari(x,value[1],value[2],value[3],value[4],value[0]-0.5);
std::cout<<"root1: "<<x[0]<<std::endl
<<"root2: "<<x[1]<<std::endl
<<"root3: "<<x[2]<<std::endl
<<"root4: "<<x[3]<<std::endl;
return true;
//范德蒙化简方式
CvMat *A1=cvCreateMat(xvalues.size(),matlength,CV_32FC1);
CvMat *tA1=cvCreateMat(matlength,xvalues.size(),CV_32FC1);
CvMat *sumA=cvCreateMat(xvalues.size(),xvalues.size(),CV_32FC1);
CvMat *nA=cvCreateMat(xvalues.size(),xvalues.size(),CV_32FC1);
CvMat *X1=cvCreateMat(xvalues.size(),1,CV_32FC1);
CvMat *b1=cvCreateMat(xvalues.size(),1,CV_32FC1);
//
//Mat A1;
//Mat tA1;
//Mat X1;
//Mat b1;
for (int i = 0; i < xvalues.size(); i++)
{
for (int j = 0; j < matlength; j++)
{
onevalue = pow(xvalues.at(i),j);
cvmSet(A1,i,j,onevalue);
}
}
for (int i = 0; i < xvalues.size(); i++)
{
onevalue = yvalues.at(i);
cvmSet(b1,i,0,onevalue);
}
cvTranspose(A1,tA1);
cvmMul(A1,tA1,sumA);
cvInvert(sumA,nA);
CvMat *sum2=cvCreateMat(xvalues.size(),matlength,CV_32FC1);
cvMul(nA,tA1,sum2);//这里有异常,下次再处理
//invert(A1*tA1,nA,DECOMP_SVD);
float tmpvalue;
for (int i = 0; i < matlength; i++)
{
tmpvalue = cvmGet(X,i,0);
qDebug()<<QString::number(i)+":";
qDebug()<<QString::number(tmpvalue)+" ";
}
return true;
}
float sumxvalue(std::vector<float> value,int cloth)
{
float sumvalue = 0;
for (int i = 0; i < value.size(); i++)
{
sumvalue += pow(value.at(i),cloth);
}
return sumvalue;
}
float sumxyvalue(std::vector<float> xvalue,std::vector<float> yvalue,int cloth)
{
float sumvalue = 0;
for (int i = 0; i < xvalue.size(); i++)
{
sumvalue += pow(xvalue.at(i),cloth) * yvalue.at(i);
}
return sumvalue;
}
std::complex<double> sqrtn(const std::complex<double>&x,double n)
{
double r = hypot(x.real(),x.imag()); //模
if(r > 0.0)
{
double a = atan2(x.imag(),x.real()); //辐角
n = 1.0 / n;
r = pow(r,n);
a *= n;
return std::complex<double>(r * cos(a),r * sin(a));
}
return std::complex<double>();
}
//费法拉求解一元四次方程
std::complex<double> Ferrari(std::complex<double> x[4]
,std::complex<double> a
,std::complex<double> b
,std::complex<double> c
,std::complex<double> d
,std::complex<double> e)
{
a = 1.0 / a;
b *= a;
c *= a;
d *= a;
e *= a;
std::complex<double> P = (c * c + 12.0 * e - 3.0 * b * d) / 9.0;
std::complex<double> Q = (27.0 * d * d + 2.0 * c * c * c + 27.0 * b * b * e - 72.0 * c * e - 9.0 * b * c * d) / 54.0;
std::complex<double> D = sqrtn(Q * Q - P * P * P,2.0);
std::complex<double> u = Q + D;
std::complex<double> v = Q - D;
if(v.real() * v.real() + v.imag() * v.imag() > u.real() * u.real() + u.imag() * u.imag())
{
u = sqrtn(v,3.0);
}
else
{
u = sqrtn(u,3.0);
}
std::complex<double> y;
if(u.real() * u.real() + u.imag() * u.imag() > 0.0)
{
v = P / u;
std::complex<double> o1(-0.5,+0.86602540378443864676372317075294);
std::complex<double> o2(-0.5,-0.86602540378443864676372317075294);
std::complex<double>&yMax = x[0];
double m2 = 0.0;
double m2Max = 0.0;
int iMax = -1;
for(int i = 0;i < 3;++i)
{
y = u + v + c / 3.0;
u *= o1;
v *= o2;
a = b * b + 4.0 * (y - c);
m2 = a.real() * a.real() + a.imag() * a.imag();
if(0 == i || m2Max < m2)
{
m2Max = m2;
yMax = y;
iMax = i;
}
}
y = yMax;
}
else
{//一元三次方程，三重根
y = c / 3.0;
}
std::complex<double> m = sqrtn(b * b + 4.0 * (y - c),2.0);
if(m.real() * m.real() + m.imag() * m.imag() >= DBL_MIN)
{
std::complex<double> n = (b * y - 2.0 * d) / m;
a = sqrtn((b + m) * (b + m) - 8.0 * (y + n),2.0);
x[0] = (-(b + m) + a) / 4.0;
x[1] = (-(b + m) - a) / 4.0;
a = sqrtn((b - m) * (b - m) - 8.0 * (y - n),2.0);
x[2] = (-(b - m) + a) / 4.0;
x[3] = (-(b - m) - a) / 4.0;
}
else
{
a = sqrtn(b * b - 8.0 * y,2.0);
x[0] =
x[1] = (-b + a) / 4.0;
x[2] =
x[3] = (-b - a) / 4.0;
}
return x[4];
}
转载自http://blog.csdn.net/pipisorry/article/details/49804441
https://blog.csdn.net/i_chaoren/article/details/79822574
https://blog.csdn.net/qq_38222947/article/details/118212408?utm_medium=distribute.pc_aggpage_search_result.none-task-blog-2aggregatepagefirst_rank_ecpm_v1~rank_aggregation-1-118212408.pc_agg_rank_aggregation&utm_term=%E5%A4%9A%E9%A1%B9%E5%BC%8F%E6%8B%9F%E5%90%88%E5%8E%9F%E7%90%86&spm=1000.2123.3001.4430
