/*******************************************************
* ch8, p193, 9. 编写程序：
* (1)初始化一个矩阵A(5*5),元素值取自随机函数，并输出；
* (2)将其传递给函数，实现矩阵转置；
* (3)在主函数中输出结果。
*******************************************************/
void ch8_9()
{
//(1)初始化矩阵：
int a[5][5];
int i,j;
// void srand(unsigned int seed)是随机数发生器的初始化函数，其参数是发生器的种子，使用系统当前时间作为种子，time(0)
// int rand(void)函数返回随机数，范围0~RAND_MAX,至少是双字节,32767。
// 用"int x = rand() % 100;"来生成 0 到 100 之间的随机数这种方法是不或取的，
// 比较好的做法是： j=(int)(n*rand()/(RAND_MAX+1.0))产生一个0到n之间的随机数
srand(time(0));
for(i=0;i<5;i++)
{
for(j=0;j<5;j++)
{
a[i][j] = (int) (100.0*rand())/(RAND_MAX+1.0); // 0~100的随机数
}
}
printf("随机5*5矩阵：\n");
matrixPrint(&a[0][0],5,5); // 打印输出
// （2）转置
printf("转置后：\n");
NmatrixTranspose(&a[0][0],5); // 方阵转置
matrixPrint(&a[0][0],5,5); // 打印输出
}
// LLSQ Approx. Trilateration
void locateLLSQ(int numantennas, double* antennas, double* distances, double* x)
{
// function saves triangulated position in vector x
// input *antennas holds
// x1, y1, z1,
// x2, y2, z2,
// x3, y3, z3,
// x4, y4, z4;
// numantennas holds integer number of antennas (min 5)
// double *distances holds pointer to array holding distances from each antenna
// Theory used:
// http://inside.mines.edu/~whereman/talks/TurgutOzal-11-Trilateration.pdf
// define some locals
int m = (numantennas - 1); // Number of rows in A
int n = 3; // Number of columns in A (always three)
if (m >= 4)n = 4; // Number of columns in A: three coordinates plus K
double A[m * n];
double b[m * 1];
double r;
double Atranspose[n * m];
double AtAinA[n * m];
double AtA[n * n];
//Calculating b vector
for (int i = 0; i < m; i++)
{
r = dist(antennas[0], antennas[1], antennas[2], antennas[(i + 1) * 3], antennas[(i + 1) * 3 + 1], antennas[(i + 1) * 3 + 2]);
b[i] = 0.5*(distances[0] * distances[0] - distances[i + 1] * distances[i + 1] + r * r); // If given exact distances
if (n == 4)b[i] = 0.5 * r*r; // For the case when we calculate K, overwrite b
}
#ifdef VERBOSE
matrixPrint(b, m, 1, "b");
#endif // DEBUG
//Calculating A matrix
for (int i = 0; i < m; i++)
{
A[i * n] = antennas[(i + 1) * 3] - antennas[0]; //xi-x1
A[i * n + 1] = antennas[(i + 1) * 3 + 1] - antennas[1]; //yi-y1
A[i * n + 2] = antennas[(i + 1) * 3 + 2] - antennas[2]; //zi-z1
if (n == 4) A[i * n + 3] = -0.5 * (distances[0] * distances[0] - distances[i + 1] * distances[i + 1]); // for K
}
#ifdef VERBOSE
matrixPrint(A, m, n, "A");
#endif // DEBUG
matrixTranspose(A, m, n, Atranspose);
matrixMult(Atranspose, A, n, m, n, AtA);
if (matrixInvert(AtA, n) == 1) //well behaved
{
matrixMult(AtA, Atranspose, n, n, m, AtAinA);
matrixMult(AtAinA, b, n, m, 1, x);
}
else // Ill-behaved A
{
double Q[m * m], Qtranspose[m * m], Qtransposeb[m * 1];
double R[m * m];
QR(A, m, n, Q, R);
matrixTranspose(Q, m, m, Qtranspose);
matrixMult(Qtranspose, b, m, m, 1, Qtransposeb);
matrixInvert(R, m);
matrixMult(R, Qtransposeb, m, m, 1, x);
}
// Adding back the reference point
x[0] = x[0] + antennas[0];
x[1] = x[1] + antennas[1];
x[2] = x[2] + antennas[2];
if (n == 4)x[3] = 1 / sqrt(x[3]); // Calculate K
}
void ch8()
{
printf("==========ch8()\n");
/**************************************************************************/
/*********************通用函数测试*****************************************/
// 通用函数，m*n矩阵打印输出
printf("void matrixPrint(int a[],int m,int n),通用函数,m*n矩阵打印输出.\n");
int matrix1[3][3] = {{1,2,3},{4,5,6},{7,8,9}};
printf("-----maxtrix1,3行3列\n");
//matrixPrint(matrix1,3,3); // [Warning] passing arg 1 of `matrixPrint' from incompatible pointer type
//matrixPrint(matrix1[],3,3); // [Warning] passing arg 1 of `matrixPrint' from incompatible pointer type
matrixPrint(&matrix1[0][0],3,3); // ok
// matrixPrint(*matrix1,3,3); // ok
printf("-----maxtrix2,3行2列\n");
int matrix2[3][2] = {{1,2},{3,4},{5,6}};
matrixPrint(&matrix2[0][0],3,2);
printf("-----maxtrix3,2行3列\n");
int matrix3[2][3] = {{1,2,3},{4,5,6}};
matrixPrint(&matrix3[0][0],2,3);
printf("-----maxtrix4,1行3列\n");
int matrix4[3] = {1,2,3};
matrixPrint(matrix4,1,3);
// 通用函数，n*n矩阵转置
printf("-----maxtrix1方阵转置\n");
NmatrixTranspose(&matrix1[0][0],3);
matrixPrint(&matrix1[0][0],3,3);
// 通用函数，m*n矩阵转置，即n*m矩阵，m行n列数组转为n行m列
printf("-----maxtrix2转置\n");
int matrix2_T[2][3];
MNmatrixTranspose(&matrix2[0][0],3,2,*matrix2_T);
matrixPrint(&matrix2_T[0][0],2,3);
printf("-----maxtrix3转置\n");
int matrix3_T[3][2];
MNmatrixTranspose(&matrix3[0][0],2,3,*matrix3_T);
matrixPrint(&matrix3_T[0][0],3,2);
printf("-----maxtrix4转置\n");
int matrix4_T[3][1];
MNmatrixTranspose(matrix4,1,3,*matrix4_T);
matrixPrint(&matrix4_T[0][0],3,1);
/*********************通用函数测试, 结束***********************************/
/**************************************************************************/
// int ch8_1(char *s)
printf("int ch8_1(char *s),求字符串的长度。\n");
printf("\"12345\"字符串长度为：%d\n",ch8_1("12345"));
// ch8_2(const char *s1, char *s2, int m)
printf("ch8_2(const char *s1, char *s2, int m),从s1的第m个字符开始复制成s2\n");
char s1[]="123456",s2[80]; //s2[0]='\0',注意，一定给字符串初始化为以'\0'结束，
ch8_2(s1,s2,3);
printf("从%s的第%d个字符开始复制成%s\n",s1,3,s2);
// char *ch8_2_1(const char *s1, char *s2, int m)
strcpy(s1,"123456");
printf("函数返回字符串=%s\n",ch8_2_1(s1,s2,3));
// ch8_3(char *s),统计s中字母、数字、空格和其它字符的个数;
printf("ch8_3(char *s),统计s中字母、数字、空格和其它字符的个数\n");
int Letter,Number,Space,Other;
ch8_3("123 d1 --- ",&Letter, &Number, &Space, &Other);
printf("字母、数字、空格和其它字符的个数=%d,%d,%d,%d\n",Letter,Number,Space,Other);
/**************************************************/
// ch8_4(int a[][],int n) 矩阵转置。
printf("ch8_4(int a[][],int n),矩阵转置。\n");
int a[3][3] = {{1,2,3},{4,5,6},{7,8,9}};
ch8_4(a,3);
int i,j;
for(i=0;i<3;i++)
{
for(j=0;j<3;j++) printf("%3d",a[i][j]);
printf("\n");
}
/*****************************************************/
// ch8_5(),5*5矩阵元素排列
printf("ch8_5(),5*5矩阵元素排列\n");
ch8_5();
// int ch8_6(char *str1,char *str2),自定义版的strcmp
printf("int ch8_6(const char *str1,const char *str2),自定义版的strcmp. \n");
printf("123和1234比较=%d,%d\n",ch8_6("123","1234"),strcmp("123","1234"));
printf("123和123比较=%d,%d\n",ch8_6("123","123"),strcmp("123","123"));
printf("12a和123比较=%d,%d\n",ch8_6("12a","123"),strcmp("12a","123"));
// char* ch8_7(char *dest,const char *source)，自定义版的strcpy
char dest[80]="";
char source[] = "abcd";
printf("copy %s to dest,%s\n",source,ch8_7(dest,source));
// int ch8_8(int argc, char *argv[]),模拟main函数，接收命令行参数
printf("int ch8_8(int argc, char *argv[]),模拟main函数，接收命令行参数\n");
char *argv[] = {"parameter1","parameter2"};
ch8_8(2,argv);
// void ch8_9(),产生一个随机5*5矩阵，并转置
printf("void ch8_9(),产生一个随机5*5矩阵，并转置.\n");
ch8_9();
// void ch8_10(),指针数组测试
printf("void ch8_10(),指针数组测试.\n");
ch8_10();
// 学习指导，p60,指针
exercise();
}
