算法——纯C语言最小二乘法曲线拟合
写完，还没来得及写注释，已通过Matlab的polyfit验证(阶数高或者数据量太大会有double数据溢出的危险，低阶的都吻合)，时间有点紧，程序注释，数学推导等时间充裕一点再贴上来
// 最小二乘法拟合.cpp : Defines the entry point for the console application.
//
#include "stdafx.h"
#include "stdlib.h"
#include "math.h"
//
#define ParaBuffer(Buffer,Row,Col) (*(Buffer + (Row) * (SizeSrc + 1) + (Col)))
//
/***********************************************************************************
***********************************************************************************/
static int GetXY(const char* FileName, double* X, double* Y, int* Amount)
{
FILE* File = fopen(FileName, "r");
if (!File)
return -1;
for (*Amount = 0; !feof(File); X++, Y++, (*Amount)++)
if (2 != fscanf(File, (const char*)"%lf %lf", X, Y))
break;
fclose(File);
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int PrintPara(double* Para, int SizeSrc)
{
int i, j;
for (i = 0; i < SizeSrc; i++)
{
for (j = 0; j <= SizeSrc; j++)
printf("%10.6lf ", ParaBuffer(Para, i, j));
printf("
");
}
printf("
");
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int ParalimitRow(double* Para, int SizeSrc, int Row)
{
int i;
double Max, Min, Temp;
for (Max = abs(ParaBuffer(Para, Row, 0)), Min = Max, i = SizeSrc; i; i--)
{
Temp = abs(ParaBuffer(Para, Row, i));
if (Max < Temp)
Max = Temp;
if (Min > Temp)
Min = Temp;
}
Max = (Max + Min) * 0.000005;
for (i = SizeSrc; i >= 0; i--)
ParaBuffer(Para, Row, i) /= Max;
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int Paralimit(double* Para, int SizeSrc)
{
int i;
for (i = 0; i < SizeSrc; i++)
if (ParalimitRow(Para, SizeSrc, i))
return -1;
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int ParaPreDealA(double* Para, int SizeSrc, int Size)
{
int i, j;
for (Size -= 1, i = 0; i < Size; i++)
{
for (j = 0; j < Size; j++)
ParaBuffer(Para, i, j) = ParaBuffer(Para, i, j) * ParaBuffer(Para, Size, Size) - ParaBuffer(Para, Size, j) * ParaBuffer(Para, i, Size);
ParaBuffer(Para, i, SizeSrc) = ParaBuffer(Para, i, SizeSrc) * ParaBuffer(Para, Size, Size) - ParaBuffer(Para, Size, SizeSrc) * ParaBuffer(Para, i, Size);
ParaBuffer(Para, i, Size) = 0;
ParalimitRow(Para, SizeSrc, i);
}
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int ParaDealA(double* Para, int SizeSrc)
{
int i;
for (i = SizeSrc; i; i--)
if (ParaPreDealA(Para, SizeSrc, i))
return -1;
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int ParaPreDealB(double* Para, int SizeSrc, int OffSet)
{
int i, j;
for (i = OffSet + 1; i < SizeSrc; i++)
{
for (j = OffSet + 1; j <= i; j++)
ParaBuffer(Para, i, j) *= ParaBuffer(Para, OffSet, OffSet);
ParaBuffer(Para, i, SizeSrc) = ParaBuffer(Para, i, SizeSrc) * ParaBuffer(Para, OffSet, OffSet) - ParaBuffer(Para, i, OffSet) * ParaBuffer(Para, OffSet, SizeSrc);
ParaBuffer(Para, i, OffSet) = 0;
ParalimitRow(Para, SizeSrc, i);
}
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int ParaDealB(double* Para, int SizeSrc)
{
int i;
for (i = 0; i < SizeSrc; i++)
if (ParaPreDealB(Para, SizeSrc, i))
return -1;
for (i = 0; i < SizeSrc; i++)
{
if (ParaBuffer(Para, i, i))
{
ParaBuffer(Para, i, SizeSrc) /= ParaBuffer(Para, i, i);
ParaBuffer(Para, i, i) = 1.0;
}
}
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int ParaDeal(double* Para, int SizeSrc)
{
PrintPara(Para, SizeSrc);
Paralimit(Para, SizeSrc);
PrintPara(Para, SizeSrc);
if (ParaDealA(Para, SizeSrc))
return -1;
PrintPara(Para, SizeSrc);
if (ParaDealB(Para, SizeSrc))
return -1;
return 0;
}
/***********************************************************************************
***********************************************************************************/
static int GetParaBuffer(double* Para, const double* X, const double* Y, int Amount, int SizeSrc)
{
int i, j;
for (i = 0; i < SizeSrc; i++)
for (ParaBuffer(Para, 0, i) = 0, j = 0; j < Amount; j++)
ParaBuffer(Para, 0, i) += pow(*(X + j), 2 * (SizeSrc - 1) - i);
for (i = 1; i < SizeSrc; i++)
for (ParaBuffer(Para, i, SizeSrc - 1) = 0, j = 0; j < Amount; j++)
ParaBuffer(Para, i, SizeSrc - 1) += pow(*(X + j), SizeSrc - 1 - i);
for (i = 0; i < SizeSrc; i++)
for (ParaBuffer(Para, i, SizeSrc) = 0, j = 0; j < Amount; j++)
ParaBuffer(Para, i, SizeSrc) += (*(Y + j)) * pow(*(X + j), SizeSrc - 1 - i);
for (i = 1; i < SizeSrc; i++)
for (j = 0; j < SizeSrc - 1; j++)
ParaBuffer(Para, i, j) = ParaBuffer(Para, i - 1, j + 1);
return 0;
}
/***********************************************************************************
***********************************************************************************/
int Cal(const double* BufferX, const double* BufferY, int Amount, int SizeSrc, double* ParaResK)
{
double* ParaK = (double*)malloc(SizeSrc * (SizeSrc + 1) * sizeof(double));
GetParaBuffer(ParaK, BufferX, BufferY, Amount, SizeSrc);
ParaDeal(ParaK, SizeSrc);
for (Amount = 0; Amount < SizeSrc; Amount++, ParaResK++)
*ParaResK = ParaBuffer(ParaK, Amount, SizeSrc);
free(ParaK);
return 0;
}
/***********************************************************************************
***********************************************************************************/
int main(int argc, char* argv[])
{
int Amount;
double BufferX[1024], BufferY[1024], ParaK[6];
if (GetXY((const char*)"test.txt", (double*)BufferX, (double*)BufferY, &Amount))
return 0;
Cal((const double*)BufferX, (const double*)BufferY, Amount, sizeof(ParaK) / sizeof(double), (double*)ParaK);
for (Amount = 0; Amount < sizeof(ParaK) / sizeof(double); Amount++)
printf("ParaK[%d] = %lf!
", Amount, ParaK[Amount]);
return 0;
}
测试test.txt里的内容
0.995119 -7.620000
2.001185 -2.460000
2.999068 108.760000
4.001035 625.020000
4.999859 2170.500000
6.004461 5814.580000
6.999335 13191.840000
7.999433 26622.060000
9.002257 49230.220000
10.003888 85066.500000
11.004076139226.280000
12.001602217970.140000
13.003390328843.860000
14.001623480798.420000
15.003034684310.000000
16.002561951499.980000
17.003010 1296254.940000
18.003897 1734346.660000
19.002563 2283552.120000
20.003530 2963773.500000
matlab拟合m代码：
load test.txt;
x = test(:, 1)';
y = test(:, 2)';
para = polyfit(x, y, 5);
