int
main (int argc, char *argv[])
{
const int ARRAY_SIZE = argc - 1;
double TV[ARRAY_SIZE];
int i;
int check = 0;
/*
* Expecting XSIZE arguments
*/
if (argc != (XSIZE + 1))
{
return 1;
}
for (i = 0; i < argc - 1; ++i)
{
TV[i] = atof (argv[i + 1]);
}
newtonMethod(TV, &check);
/*
printf("Check value = %i\n", check);
for (i = 0; i < argc - 1; ++i)
{
printf("%lf ", TV[i]);
}
printf("\n");
*/
return 0;
}
int main()
{
const int MAX_STEP = 1000; // 最大迭代次数
double EP = 1.0E-12; // 牛顿迭代精度
double sigmaEP = 1.0E-7; // 最小二乘拟合精度
double x[11], y[21], t[11][21], u[11][21], v[11][21], w[11][21];
// 初始化变量x, y
for (int i = 0; i < 11; i++)
{
x[i] = 0.08 * i;
}
for (int i = 0; i < 21; i++)
{
y[i] = 0.5 + 0.05 * i;
}
/* 步骤一：Newton法解非线性方程组F(t,u,v,w) = 0 */
for (int i = 0; i < 11; i++)
{
for (int j = 0; j < 21; j++)
{
newtonMethod(x + i, y + j, t[i] + j, u[i] + j, v[i] + j, w[i] + j, MAX_STEP, EP);
}
}
/* 步骤二：分片二次代数插值求z = f(ti,ui) */
double * * z = new double *[11];
for (int i = 0; i < 11; i++)
{
z[i] = new double[21];
}
double p, q;
for (int i = 1; i < 5; i++)
{
for (int j = 1; j < 5; j++)
{
// 在片上遍历搜索满足插值条件的(t,u)点
for (int k = 0; k < 11; k++)
{
for (int l = 0; l < 21; l++)
{
p = min(max(t[k][l], 0.11), 0.9);
q = min(max(u[k][l], 0.21), 1.8);
if (0.2 * i - 0.1 < p && p <= 0.2 * i + 0.1 && 0.4 * j - 0.2 < q && q <= 0.4 * j + 0.2)
{
// 由(x[i], y[j]) 得到的(t[i][j], u[i][j]) , 插值得到z[i][j]
z[k][l] = pieceInterp(i, j, t[k][l], u[k][l]);
}
}
}
}
}
// 输出数表（x, y, f(x,y))
printf("\n数表（ x, y, f(x,y) ):\n");
for (int i = 0; i < 11; i++)
{
for (int j = 0; j < 21; j++)
{
printf("( %f\t,\t%f\t,\t%.12e )\n",x[i], y[j], z[i][j]);
}
}
/* 步骤三：遍历k=2,3,...,将（xi,yj,zij)代入最小二乘曲面拟合得到z = p(x,y),当满足精度要求时，迭代结束，返回k和sigma*/
double sigma;
double * * C = NULL;
int N = 0;
printf("\nk和相应sigma的值：\n");
for (int k = 1; k < 10; k++)
{
// 动态创建k+1 * k+1 的二维数组
C = new double *[k + 1];
for (int i = 0; i < k + 1; i++)
{
C[i] = new double[k + 1];
}
// 最小二乘曲面拟合，得到系数矩阵C
computeC(C, 11, 21, k + 1, x, y, z);
// 计算sigma
sigma = computeSigma(C, k + 1, x, y, z);
// 打印k和sigma的值
printf("k = %d , sigma = %.12e\n", k, sigma);
// 判断sigma是否符合精度要求
if (sigma <= sigmaEP)
{
N = k;
// 输出系数矩阵
printf("\nk = %d时, 系数矩阵为:\n", N);
for (int i = 0; i < k + 1; i++)
{
for (int j = 0; j < k + 1; j++)
{
printf("%.12e\t", C[i][j]);
}
printf("\n");
}
break;
}
// 释放矩阵C的内存
for (int i = 0; i < k + 1; i++)
{
delete[] C[i];
}
delete[] C;
}
/* 观察效果*/
#if DEBUG
double xstar[8], ystar[5], tstar[8][5], ustar[8][5], vstar[8][5], wstar[8][5];
for (int i = 1; i < 9; i++)
{
xstar[i - 1] = 0.1 * i;
}
for (int j = 1; j < 6; j++)
{
ystar[j - 1] = 0.5 + 0.2 * j;
}
for (int i = 0; i < 8; i++)
{
for (int j = 0; j < 5; j++)
{
newtonMethod(xstar + i, ystar + j, tstar[i] + j, ustar[i] + j, vstar[i] + j, wstar[i] + j, MAX_STEP, EP);
}
}
double * * zstar = new double *[8];
for (int i = 0; i < 11; i++)
{
zstar[i] = new double[5];
}
double pstar, qstar;
for (int i = 1; i < 5; i++)
{
for (int j = 1; j < 5; j++)
{
for (int k = 0; k < 8; k++)
{
for (int l = 0; l < 5; l++)
{
pstar = min(max(tstar[k][l], 0.11), 0.9);
qstar = min(max(ustar[k][l], 0.21), 1.8);
if (0.2 * i - 0.1 < pstar && pstar <= 0.2 * i + 0.1 && 0.4 * j - 0.2 < qstar && qstar <= 0.4 * j + 0.2)
{
zstar[k][l] = pieceInterp(i, j, tstar[k][l], ustar[k][l]);
}
}
}
}
}
printf("\n数表（ x*, y*, f(x*,y*), p(x*,y*) ):\n");
for (int i = 0; i < 8; i++)
{
for (int j = 0; j < 5; j++)
{
printf("( %f\t,\t%f\t,\t%.12e\t,\t%.12e )\n", xstar[i], ystar[j], zstar[i][j], computePxy(C, N + 1, xstar[i], ystar[j]));
}
}
#endif
/* 释放内存*/
for (int i = 0; i < 11; i++)
{
delete[] z[i];
}
delete[] z;
for (int i = 0; i < N + 1; i++)
{
delete[] C[i];
}
delete[] C;
// end
getchar();
return 0;
}