├── LICENSE ├── README.md ├── chemicalreactio.c ├── manto carlo.png ├── montecarlo.cpp ├── pokertext.c └── pseudorandom.c /LICENSE: -------------------------------------------------------------------------------- 1 | Creative Commons Legal Code 2 | 3 | CC0 1.0 Universal 4 | 5 | CREATIVE COMMONS CORPORATION IS NOT A LAW FIRM AND DOES NOT PROVIDE 6 | LEGAL SERVICES. DISTRIBUTION OF THIS DOCUMENT DOES NOT CREATE AN 7 | ATTORNEY-CLIENT RELATIONSHIP. CREATIVE COMMONS PROVIDES THIS 8 | INFORMATION ON AN "AS-IS" BASIS. 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Monte Carlo Pi Estimation

3 |

The Monte Carlo Pi Estimation is a simple program that uses the Monte Carlo method to estimate the value of pi. The program generates a large number of random points and determines the number of points that fall within a circle inscribed in a square. The ratio of the number of points within the circle to the total number of points generated is used to estimate the value of pi.

4 |

System Requirements

5 | 10 |

Installation and Setup

11 |
    12 |
  1. Download and install a C++ compiler on your system.
    2. 13 |
  2. Download the graphics.h library and install it on your system.
    3. 14 |
  3. Download the Monte Carlo Pi Estimation program file (montecarlo.cpp) and save it to a directory of your choice.
    4. 15 |
  4. Compile the program using the following command:
    gcc -pi montecarlo.cpp -lstdc++ -lgraph
    5. 16 |
  5. On Windows, run the compiled executable file (pi.exe) from the command prompt or double-click on it to run it.
    6. 17 |
  6. On Linux, run the compiled executable file (pi.out) from the terminal using the following command:
    ./pi.out
    7. 18 |
19 |

Usage

20 |

After running the program, you will be prompted to enter the number of iterations to perform for the pi estimation. Enter a positive integer value and press Enter.

21 |

The program will display a circle inscribed in a square on the screen, with the center of the circle at (300, 300) and a radius of 200. The program will generate random points within the square and plot them on the screen. Points that fall within the circle will be colored green, while points that fall outside the circle will be colored red.

22 |

After all the points have been generated and plotted, the program will calculate the estimated value of pi based on the ratio of the number of points within the circle to the total number of points generated. The estimated value of pi will be displayed on the screen.

23 | 24 | 25 | 26 | 27 |

Four-Digit Poker Test

28 |

The Four-Digit Poker Test is a statistical test used to determine if a set of randomly generated numbers is independent or not. The test involves generating a large number of four-digit integers and counting the frequency of certain combinations of digits. The observed frequencies are then compared to the expected frequencies, and a chi-squared test is performed to determine if the differences between the observed and expected frequencies are significant.

29 |

How to Use

30 |

To use the Four-Digit Poker Test, follow these steps:

31 |
    32 |
  1. Compile and run the program on your computer. The program requires the user to input the number of numbers generated, as well as the observed frequencies of the following combinations of digits:
    2. 33 | 40 |
  2. After the user inputs the observed frequencies, the program calculates the expected frequencies based on the probabilities of each combination of digits occurring.
    3. 41 |
  3. The program then performs a chi-squared test on the observed and expected frequencies to determine if the generated random numbers are independent or not. If the calculated chi-squared value is less than or equal to the tabulated value for chi-squared, then the numbers are considered independent. Otherwise, they are considered dependent.
    4. 42 |
43 | 44 |

Interpreting Results

45 |

If the program determines that the generated random numbers are independent, this means that the numbers are truly random and do not depend on any previous numbers generated. If the numbers are dependent, this means that there is some pattern or correlation between the generated numbers, indicating that they are not truly random.

46 |

It is important to note that the Four-Digit Poker Test is not foolproof and can only detect certain types of non-randomness. In addition, the test may produce false positives or false negatives, depending on the quality of the random number generator used and the sample size.

47 | 48 |

References

49 | 53 | 54 | 55 | 56 | 57 |

Chemical Reaction Simulation User Manual

58 |

This program simulates the chemical reaction between two reactants (C1 and C2) to produce a product (C3).

59 | less 60 | Copy code 61 |

Program Inputs

62 | 71 | 72 |

Program Outputs

73 |

The program outputs the concentration of C1, C2, and C3 at each time increment, as well as a text file ("lab01.txt") containing the same data.

74 | 75 |

Graphing the Data

76 |

To graph the data, open the "lab01.txt" file in a spreadsheet program (such as Microsoft Excel or Google Sheets) and plot the concentration of each species over time.

77 | 78 | 79 | -------------------------------------------------------------------------------- /chemicalreactio.c: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | int main() 5 | { 6 | int i=0; 7 | float c1[1000],c2[1000],c3[1000]; 8 | float k1=0.025,k2=0.01;//k1 and k2 are constant 9 | c1[0]=30,c2[0]=15,c3[0]=0; 10 | float delta=0.001; //small increment of time 11 | float t=0.0, time=100; 12 | FILE *fp; 13 | fp=fopen("lab01.txt","w"); 14 | 15 | printf("\nC1 C2 C3"); 16 | while(t<=time) 17 | { 18 | printf("\n%f %f %f",c1[i],c2[i],c3[i]); 19 | c1[i+1]=c1[i]+(k2*c3[i]-k1*c1[i]*c2[i])*delta; 20 | c2[i+1]=c2[i]+(k2*c3[i]-k1*c1[i]*c2[i])*delta; 21 | c3[i+1]=c3[i]+(2.0*k1*c1[i]*c2[i]-2.0*k2*c3[i])*delta; 22 | fprintf(fp,"\n%f %f %f",c1[i],c2[i],c3[i]); 23 | i=i+1; 24 | t=t+delta; 25 | } 26 | fclose(fp); 27 | printf("Reaction Simulated"); 28 | } -------------------------------------------------------------------------------- /manto carlo.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dyells07/Simulation-Modeling/8ff512a228b4db9aca56ad33e1cf9f783439dbd1/manto carlo.png -------------------------------------------------------------------------------- /montecarlo.cpp: -------------------------------------------------------------------------------- 1 | include 2 | #include 3 | #include 4 | #include 5 | 6 | #include 7 | using namespace std; 8 | void generate_random_points(double &x,double &y){ 9 | x= (double)rand()/RAND_MAX*2-1; 10 | y= (double) rand()/RAND_MAX *2-1; 11 | 12 | } 13 | 14 | int main(){ 15 | int gd=DETECT,gm; 16 | int i,circlepoints=0,squarepoints=0,itetration; 17 | double x,y; 18 | cout<<"Enter number of itetration"; 19 | cin>>itetration; 20 | initgraph(&gd,&gm,NULL); 21 | srand(time(0)); 22 | 23 | circle(300,300,200); 24 | rectangle(100,100,500,500); 25 | 26 | for (i=0;i 3 | //#include 4 | int main() 5 | { 6 | int x0,x1,x2,a,c,m; /*xo=seed, x1=next random number (but for arithmetic, x1 is the 7 | 2nd seed & x2 is next random number,a=constant multiplier, c=increment, m=modulus */ 8 | int i,n,num, method; 9 | int array[20]; //to store the random numbers generated 10 | printf("Choose the method:\n"); 11 | printf("\n1.Linear congruential Method"); 12 | printf("\n2.Arithmetic congruential Method\n"); 13 | scanf("%d",&method); 14 | switch(method) 15 | { 16 | case 1: 17 | printf("\nEnter the seed value x0: "); 18 | scanf("%d",&x0); 19 | printf("\nEnter the modulus m: "); 20 | scanf("%d",&m); 21 | printf("\nHow many random numbers you want to generate: "); 22 | scanf("%d",&n); 23 | printf("\nWhich method you want to perform"); 24 | printf("\n1.Mixed congruential"); 25 | printf("\n2.Additive congruential"); 26 | printf("\n3.Multiplicative congurential\n"); 27 | scanf("\n%d",&num); 28 | switch(num) 29 | { 30 | 31 | case 1: 32 | printf("\nEnter the constant multiplier a: "); 33 | scanf("%d",&a); 34 | 35 | printf("\nEnter the increment c: "); 36 | scanf("%d",&c); 37 | 38 | if(c!=0) 39 | { 40 | for(i=1;i<=n;i++) // loop to generate random numbers 41 | { 42 | x1=(a*x0+c) %m; 43 | array[i]=x1; 44 | x0=x1; 45 | } 46 | 47 | printf("\nThe generated random numbers are: "); 48 | for(i=1;i<=n;i++) 49 | { 50 | printf("\nX%d=%d",i,array[i]); 51 | printf("\t"); 52 | } 53 | } 54 | else 55 | printf("for mixed congruential value of c cannot be zero");break; 56 | case 2: 57 | printf("\nEnter the increment c: "); 58 | scanf("%d",&c); 59 | for(i=1;i<=n;i++) 60 | { 61 | x1=(1*x0+c) %m; 62 | array[i]=x1; 63 | x0=x1; 64 | } 65 | 66 | printf("\nThe generated random numbers are: "); 67 | for(i=1;i<=n;i++) 68 | { 69 | printf("\nX%d=%d",i,array[i]); 70 | printf("\t");break; 71 | } 72 | 73 | case 3: 74 | printf("\nEnter the constant multiplier a: "); 75 | scanf("%d",&a); 76 | 77 | for(i=1;i<=n;i++) 78 | { 79 | x1=(a*x0) %m; 80 | array[i]=x1; 81 | x0=x1; 82 | } 83 | 84 | printf("\nThe generated random numbers are: "); 85 | for(i=1;i<=n;i++) 86 | { 87 | printf("\nX%d=%d",i,array[i]); 88 | printf("\t"); 89 | } 90 | case 4: 91 | printf("Enter the seed value x1: "); 92 | scanf("%d",&x1); 93 | 94 | for(i=1;i<=n;i++) 95 | { 96 | x1=(a*x0) %m; 97 | array[i]=x1; 98 | x0=x1; 99 | } 100 | 101 | printf("\nThe generated random numbers are: "); 102 | for(i=1;i<=n;i++) 103 | { 104 | printf("\nX%d=%d",i,array[i]); 105 | printf("\t"); 106 | }break; 107 | default : 108 | printf("Please Enter 1-4"); 109 | } 110 | break; 111 | 112 | case 2: 113 | printf("\nEnter the seed value x0: "); 114 | scanf("%d",&x0); 115 | 116 | 117 | printf("\nEnter the seed value x1: "); 118 | scanf("%d",&x1); 119 | 120 | printf("\nEnter the modulus m: "); 121 | scanf("%d",&m); 122 | 123 | printf("\nHow many random numbers you want to generate: "); 124 | scanf("%d",&n); 125 | 126 | 127 | for(i=1;i<=n;i++) 128 | { 129 | x2=(x0+x1) %m; 130 | array[i]=x2; 131 | x0=x1; 132 | x1=x2; 133 | } 134 | 135 | printf("\nThe generated random numbers are: "); 136 | for(i=1;i<=n;i++) 137 | { 138 | printf("\nX%d=%d",i+1,array[i]); 139 | printf("\t"); 140 | } 141 | break; 142 | default: 143 | printf("Please Enter 1-2"); 144 | //return switch(method); 145 | } 146 | return 0; 147 | getch(); 148 | } --------------------------------------------------------------------------------