struct Hisnum//直方圖結構體 進行多項式擬合
{
int gray;
int num;
};
struct Hisnum//直方圖結構體 進行多項式擬合
{
int gray;
int num;
};
struct xishu
{
double A1;
double A2;
double A3;
double A4;
};
xishu polfit2(Hisnum his[], int n)//最小二乘 二次多項式擬合 y=A1+A2*x+A3*x*x x爲灰度 y爲灰度數量
{
//-----------------公式---------------------------
//n A1 + sumX A2 + sumXX A3 = sumY
//sumX A1 + sumXX A2 + sumXXX A3 = sumXY
//sumXX A1 + sumXXX A2 + sumXXXX A3 = sumXXY
//--------------------------------------------目的：求係數A1 A2 A3
int jiange = 10;//相隔十個點選一個點進行計算
n = n / jiange + 1;
long long int sumX = 0, sumY = 0, sumXX = 0, sumXXX = 0, sumXXXX = 0, sumXY = 0, sumXXY = 0;//建立方程組
for (int i = 0; i < 256; i = i + jiange)
{
cout << "number:" << his[i].num << endl;
cout << "gray:" << his[i].gray << endl;
sumX = sumX + his[i].gray;
sumY = sumY + his[i].num;
sumXX = sumXX + his[i].gray*his[i].gray;
sumXXX = sumXXX + his[i].gray*his[i].gray*his[i].gray;
sumXXXX = sumXXXX + his[i].gray*his[i].gray*his[i].gray*his[i].gray;
sumXY = sumXY + his[i].gray*his[i].num;
sumXXY = sumXXY + his[i].gray*his[i].num*his[i].gray;
}
cout << "n:" << n << " sumX: " << sumX << " sumXX: " << sumXX << " sumXXX: " << sumXXX << " sumXXXX: " << sumXXXX << endl;
cout << " sumY: " << sumY << " sumXY: " << sumXY << " sumXXY: " << sumXXY << endl;
double a11 = n; double a12 = sumX; double a13 = sumXX; double b1 = sumY; //構造矩陣 求解方程係數 a11 第一行第一列
double a21 = sumX; double a22 = sumXX; double a23 = sumXXX; double b2 = sumXY;
double a31 = sumXX; double a32 = sumXXX; double a33 = sumXXXX; double b3 = sumXXY;
//double a11 = 2; double a12 = 4; double a13 = -2; double b1 = 2; //構造矩陣 求解方程係數 a11 第一行第一列
//double a21 = 1; double a22 = -3; double a23 = -3; double b2 = -1;
//double a31 = 4; double a32 = 2; double a33 = 2; double b3 = 3;
//R2-(a21/a11)*R1 ------------------------------------------------------------ - 進行消元 高斯消元法
double a21x, a22x, a23x, b2x;
a21x = a21 - a21 / a11*a11; a22x = a22 - a21 / a11*a12; a23x = a23 - a21 / a11*a13; b2x = b2 - a21 / a11*b1;
//R3-(a31/a11)*R1
double a31x, a32x, a33x, b3x;
a31x = a31 - a31 / a11*a11; a32x = a32 - a31 / a11*a12; a33x = a33 - a31 / a11*a13; b3x = b3 - a31 / a11*b1;
//R3-(a32/a22)*R2
double a32xx, a33xx, b3xx;
a32xx = a32x - a32x / a22x*a22x; a33xx = a33x - a32x / a22x*a23x; b3xx = b3x - a32x / a22x*b2x;
//------------------------------------------------------------求得係數矩陣未知數
double A3 = b3xx / a33xx;
double A2 = (b2x - a23x*A3) / a22x;
double A1 = (b1 - A2*a12 - A3*a13) / a11;
cout << " A1: " << A1 << " A2: " << A2 << " A3: " << A3 << endl;
xishu A;
A.A1 = A1;
A.A2 = A2;
A.A3 = A3;
return A;
}
xishu polfit3(Hisnum his[], int n)//最小二乘 三次多項式擬合 y=A1 + A2*x + A3*x*x + A4*x*x*x x爲灰度 y爲灰度數量
{
//-----------------公式---------------------------
//n A1 + sumX A2 + sumXX A3 + sumXXX A4 = sumY
//sumX A1 + sumXX A2 + sumXXX A3 + sumXXXX A4 = sumXY
//sumXX A1 + sumXXX A2 + sumXXXX A3 + sumXXXXX A4 = sumXXY
//sumXXX A1+sumXXXX A2 + sumXXXXX A3+ sumXXXXXX A4 =sumXXXY
//--------------------------------------------目的：求係數A1 A2 A3
int jiange = 10;//相隔十個點選一個點進行計算
n = n / jiange + 1;
long double sumX = 0, sumY = 0, sumXX = 0, sumXXX = 0, sumXXXX = 0, sumXXXXX = 0, sumXXXXXX = 0, sumXXXXXXX = 0, sumXY = 0, sumXXY = 0, sumXXXY = 0;//建立方程組
for (int i = 0; i < 256; i = i + jiange)
{
cout << "number:" << his[i].num << endl;
cout << "gray:" << his[i].gray << endl;
sumX = sumX + his[i].gray;
sumY = sumY + his[i].num;
sumXX = sumXX + his[i].gray*his[i].gray;
sumXXX = sumXXX + his[i].gray*his[i].gray*his[i].gray;
sumXXXX = sumXXXX + his[i].gray*his[i].gray*his[i].gray*his[i].gray;
sumXXXXX = sumXXXXX + his[i].gray*his[i].gray*his[i].gray*his[i].gray*his[i].gray;//
sumXXXXXX = sumXXXXXX + his[i].gray*his[i].gray*his[i].gray*his[i].gray*his[i].gray*his[i].gray;
// sumXXXXXXX = sumXXXXXXX + his[i].gray*his[i].gray*his[i].gray*his[i].gray*his[i].gray*his[i].gray*his[i].gray;
sumXY = sumXY + his[i].gray*his[i].num;
sumXXY = sumXXY + his[i].gray*his[i].num*his[i].gray;
sumXXXY = sumXXXY + his[i].gray*his[i].num*his[i].gray*his[i].gray;
}
cout << "n:" << n << " sumX: " << sumX << " sumXX: " << sumXX << " sumXXX: " << sumXXX << " sumXXXX: " << sumXXXX << " sumXXXXX: " << sumXXXXX << " sumXXXXXX: " << sumXXXXXX << " sumXXXXXXX: " << sumXXXXXXX << endl;
cout << " sumY: " << sumY << " sumXY: " << sumXY << " sumXXY: " << sumXXY << " sumXXXY: " << sumXXXY << endl;
double a11 = n; double a12 = sumX; double a13 = sumXX; double a14 = sumXXX; double b1 = sumY; //構造矩陣 求解方程係數 a11 第一行第一列
double a21 = sumX; double a22 = sumXX; double a23 = sumXXX; double a24 = sumXXXX; double b2 = sumXY;
double a31 = sumXX; double a32 = sumXXX; double a33 = sumXXXX; double a34 = sumXXXXX; double b3 = sumXXY;
double a41 = sumXXX; double a42 = sumXXXX; double a43 = sumXXXXX; double a44 = sumXXXXXX; double b4 = sumXXXY;
//double a11 = 2; double a12 = 4; double a13 = -2; double b1 = 2; //構造矩陣 求解方程係數 a11 第一行第一列
//double a21 = 1; double a22 = -3; double a23 = -3; double b2 = -1;
//double a31 = 4; double a32 = 2; double a33 = 2; double b3 = 3;
//R2=R2-(a21/a11)*R1 ------------------------------------------------------------ - 進行消元 高斯消元法 第一例消元
double a21x, a22x, a23x, a24x, b2x;
a21x = a21 - a21 / a11*a11; a22x = a22 - a21 / a11*a12; a23x = a23 - a21 / a11*a13; a24x = a24 - a21 / a11*a14; b2x = b2 - a21 / a11*b1;
//R3=R3-(a31/a11)*R1
double a31x, a32x, a33x, a34x, b3x;
a31x = a31 - a31 / a11*a11; a32x = a32 - a31 / a11*a12; a33x = a33 - a31 / a11*a13; a34x = a34 - a31 / a11*a14; b3x = b3 - a31 / a11*b1;
//R4=R4-(a41/a11)*R1
double a41x, a42x, a43x, a44x, b4x;
a41x = a41 - a41 / a11*a11; a42x = a42 - a41 / a11*a12; a43x = a43 - a41 / a11*a13; a44x = a44 - a41 / a11*a14; b4x = b4 - a41 / a11*b1;
//------------------------------------------------------------ - 進行消元 高斯消元法 第二例消元
//R3=R3-(a32/a22)*R2
double a32xx, a33xx, a34xx, b3xx;
a32xx = a32x - a32x / a22x*a22x; a33xx = a33x - a32x / a22x*a23x; a34xx = a34x - a32x / a22x*a24x; b3xx = b3x - a32x / a22x*b2x;
//R4=R4-(a42/a22)*R2
double a42xx, a43xx, a44xx, b4xx;
a42xx = a42x - a42x / a22x*a22x; a43xx = a43x - a42x / a22x*a23x; a44xx = a44x - a42x / a22x*a24x; b4xx = b4x - a42x / a22x*b2x;
//------------------------------------------------------------ - 進行消元 高斯消元法 第三例消元
//R4=R4-(a43/a33)R3
double a43xxx, a44xxx, b4xxx;
a43xxx = a43xx - a43xx / a33xx*a33xx; a44xxx = a44xx - a43xx / a33xx*a34xx; b4xxx = b4xx - a43xx / a33xx*b3xx;
//------------------------------------------------------------求得係數矩陣未知數
double A4 = b4xxx / a44xxx;
double A3 = (b3xx - a34xx*A4) / a33xx;
double A2 = (b2x - a23x*A3 - a24x*A4) / a22x;
double A1 = (b1 - a12*A2 - a13*A3 - a14*A4) / a11;
cout << " A1: " << A1 << " A2: " << A2 << " A3: " << A3 << " A4: " << A4 << endl;
xishu A;
A.A1 = A1;
A.A2 = A2;
A.A3 = A3;
A.A4 = A4;
return A;
}