1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203 | #include <assert.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
// Simulates heat transmission through a plate represented by a matrix
typedef struct
{
// Dimensions of the matrix
size_t rows;
size_t cols;
// When temperature changes are lower than epsilon, simulation stops
double epsilon;
// Matrix of temperatures representing the plate
double** matrix;
// An auxiliary matrix to store the state of the plate after an update
double** mirror;
// The starting time of the simulation
struct timespec start_time;
// Current generation of the simulation
size_t generation;
// Pointer to the matrix with the current state of the simulation
double** current;
// Pointer to the matrix that will hold the next generation
double** next;
} heat_t;
int read_matrix(heat_t* heat, const char* filename);
void simulate(heat_t* heat);
double update_generation(heat_t* heat);
double update_cell(heat_t* heat, size_t row, size_t col);
double elapsed(const struct timespec* start_time);
void** create_matrix(const size_t rows, const size_t columns, const size_t cell_size);
void** destroy_matrix(void** matrix, const size_t rows);
int main(int argc, char* argv[])
{
if ( argc != 3 )
return fprintf(stderr, "usage: heat matrix.bin epsilon\n"), 1;
heat_t heat;
memset(&heat, 0, sizeof(heat_t));
heat.epsilon = strtod(argv[2], NULL);
if ( heat.epsilon <= 0.0 )
return fprintf(stderr, "error: invalid epsilon %lg\n", heat.epsilon), 2;
int error = read_matrix(&heat, argv[1]);
if ( error == EXIT_SUCCESS )
{
clock_gettime(CLOCK_MONOTONIC, &heat.start_time);
simulate(&heat);
destroy_matrix((void**)heat.matrix, heat.rows);
destroy_matrix((void**)heat.mirror, heat.rows);
}
return error;
}
int read_matrix(heat_t* heat, const char* filename)
{
int error = EXIT_SUCCESS;
FILE* input = fopen(filename, "rb");
if ( input == NULL )
return fprintf(stderr, "error opening %s\n", filename), 11;
if ( fread(&heat->rows, sizeof(size_t), 1, input) > 0 &&
fread(&heat->cols, sizeof(size_t), 1, input) > 0 &&
heat->rows >= 2 && heat->cols >= 2 )
{
heat->matrix = (double**) create_matrix(heat->rows, heat->cols, sizeof(double));
heat->mirror = (double**) create_matrix(heat->rows, heat->cols, sizeof(double));
if ( heat->matrix && heat->mirror )
{
for ( size_t row = 0; row < heat->rows; ++row )
{
if ( fread( heat->matrix[row], sizeof(double), heat->cols, input ) > 0 )
memcpy( heat->mirror[row], heat->matrix[row], sizeof(double) * heat->cols );
else
{
fprintf(stderr, "error reading %zu row\n", row + 1);
error = 14;
break;
}
}
}
else
{
fprintf(stderr, "error allocating %zu x %zu matrixes\n", heat->rows, heat->cols);
error = 13;
}
}
else
{
fprintf(stderr, "error reading matrix dimensions\n");
error = 12;
}
if ( error )
{
heat->matrix = (double**) destroy_matrix((void**)heat->matrix, heat->rows);
heat->mirror = (double**) destroy_matrix((void**)heat->mirror, heat->rows);
}
else
printf("%zu x %zu matrix loaded (%0.3lf GiB)\n", heat->rows, heat->cols
, 2 * 8 * heat->rows * heat->cols / 1073741824.0);
fclose(input);
return error;
}
void simulate(heat_t* heat)
{
heat->current = heat->matrix;
heat->next = heat->mirror;
double delta = 0.0;
while ( (delta = update_generation(heat)) > heat->epsilon )
printf("%.9lfs: generation %zu delta=%0.6lf\n", elapsed(&heat->start_time), heat->generation, delta);
}
double update_generation(heat_t* heat)
{
// The maximum temperature change detected in this generation
double max_change = DBL_MIN;
// Update all rows
for ( size_t row = 1; row < heat->rows - 1; ++row )
{
// Upate all columns
for ( size_t col = 1; col < heat->cols - 1; ++col )
{
// Update cell from current matrix to the next matrix
double change = update_cell(heat, row, col);
// If the cell change is greater than our maximum, update the maximum
if ( change > max_change )
max_change = change;
}
}
// The next matrix is enterely updated, it is now the current matrix
// The current matrix will be used for the next generation. So swap them
double** temp = heat->current;
heat->current = heat->next;
heat->next = temp;
// A new generation was completed
++heat->generation;
// Return the max temperature change detected in this generation
return max_change;
}
double update_cell(heat_t* heat, size_t row, size_t col)
{
// The new value is the average of the neighbors in the previous generation
heat->next[row][col] = ( heat->current[row - 1][col]
+ heat->current[row][col - 1]
+ heat->current[row][col + 1]
+ heat->current[row + 1][col] ) / 4.0;
// Return the difference between the cell's new temperature and old one
return fabs( heat->next[row][col] - heat->current[row][col] );
}
double elapsed(const struct timespec* start_time)
{
struct timespec current_time;
clock_gettime(CLOCK_MONOTONIC, ¤t_time);
return current_time.tv_sec - start_time->tv_sec
+ 1e-9 * (current_time.tv_nsec - start_time->tv_nsec);
}
void** create_matrix(const size_t rows, const size_t columns, const size_t cell_size)
{
void** matrix = (void**) calloc(rows, sizeof(void*));
if ( matrix == NULL )
return NULL;
for ( size_t row = 0; row < rows; ++row )
if ( ( matrix[row] = calloc( columns, cell_size ) ) == NULL )
return destroy_matrix(matrix, rows), NULL;
return matrix;
}
void** destroy_matrix(void** matrix, const size_t rows)
{
if ( matrix )
for ( size_t row = 0; row < rows; ++row )
free( matrix[row] );
free( matrix );
return NULL;
}
|