/* ---------------------------------------------------------------------- * * A Monte Carlo simulation to estimate the probability that the          * * determinant of a 3 by 3 matrix of random numbers is positive.          *  *                                                                        * * Name              : det.c                                              * * Author            : Larry Leemis                                       * * Language          : ANSI C                              * Latest Revision   : 8-8-02                                             * * Compile with      : gcc det.c rng.c                                    * *                     if math functions needed, add #include <math.h>    * *                     and compile with gcc -lm det.c rng.c               * * ---------------------------------------------------------------------- */#include <stdio.h>#include "rng.h"#define N 200000000L                     /* number of replications        *//* ============= */  int main(void)/* ============= */{  int    i;                              /* replication index             */  int    j;                              /* row index                     */  int    k;                              /* column index                  */  double a[4][4];                        /* matrix (only 9 elements used) */  double temp1;                          /* first 2 by 2 determinant      */  double temp2;                          /* second 2 by 2 determinant     */  double temp3;                          /* third 2 by 2 determinant      */  double x;                              /* determinant                   */  int    count = 0;                      /* counts number of pos det      */    PutSeed(0);  for (i = 0; i < N; i++) {    for (j = 1; j <= 3; j++) {      for (k = 1; k <= 3; k++) {        a[j][k] = Random();        if (j != k)          a[j][k] = -a[j][k];      }    }    temp1 = a[2][2] * a[3][3] - a[3][2] * a[2][3];    temp2 = a[2][1] * a[3][3] - a[3][1] * a[2][3];    temp3 = a[2][1] * a[3][2] - a[3][1] * a[2][2];    x = a[1][1] * temp1 - a[1][2] * temp2 + a[1][3] * temp3;    if (x > 0)      count++;  }  printf("\nbased on %ld replications ", N);  printf("the estimated probability of a positive determinant is:\n");  printf("%11.9f", (double) count / N);  printf("\n");  return (0);}