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2.350000 5897.751519 -3.100000 2.400000 6913.863713 -3.100000 2.450000 8100.919712 -3.100000 2.500000 9488.269223 -3.100000 2.550000 11110.214166 -3.100000 2.600000 13006.856784 -3.100000 2.650000 15225.091161 -3.100000 2.700000 17819.762668 -3.100000 2.750000 20855.024006 -3.100000 2.800000 24405.921363 -3.100000 2.850000 28560.249918 -3.100000 2.900000 33420.724560 -3.100000 2.950000 39107.519486 -3.100000 3.000000 45761.239487 -3.100000 3.050000 53546.396372 -3.100000 3.100000 62655.476482 diff --git a/header.h b/header.h index ef5cc3e315ddbac7ba0b642a47cda3e22fb31811..35b5c42602c384a89050fae8d468e6b40d757082 100644 --- a/header.h +++ b/header.h @@ -14,8 +14,5 @@ double Pipi = M_PI * M_PI; // Pipi = Pi * Pi void print_errno(void); void getParams(int argc, char* argv[], FILE **fp); -//double f(double x, double y); -//void u(int i, int j, double **u, double **f); double residueNorm(double *r); double timestamp(void); -//void sor(double *A, double *b, double *x, double w); diff --git a/interface.c b/interface.c deleted file mode 100644 index 0b6f0fc6ac011b13ae872c3893a9d98ff00f8966..0000000000000000000000000000000000000000 --- a/interface.c +++ /dev/null @@ -1,40 +0,0 @@ -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <errno.h> - -#define ARGS_NUM 9 - -double Hx,Hy; -int MaxIter; -FILE *fp; - -void print_errno(void) { - printf("%s",strerror(errno)); -} - -void getParams(int argc, char* argv[]) { - if(argc != ARGS_NUM) { - fprintf(stderr,"Wrong number of arguments.\n"); - exit(-1); - } - int i; - for(i=1; i<ARGS_NUM; i+=2) { - if(strcmp(argv[i],"-hx") == 0) { - Hx = atof(argv[i+1]); - } else if(strcmp(argv[i],"-hy") == 0) { - Hy = atof(argv[i+1]); - } else if(strcmp(argv[i],"-i") == 0) { - MaxIter = atoi(argv[i+1]); - } else if(strcmp(argv[i],"-o") == 0) { - fp = fopen(argv[i+1],"w"); - } else { - fprintf(stderr,"Incorrect parameter.\n"); - exit(-1); - } - } -} - -int main(int argc, char* argv[]) { - getParams(argc,argv); -} \ No newline at end of file diff --git a/makefile b/makefile index 07f59f2c0c7e9fb12211763a334a0eaface32792..9467dc8f22779b30e9f2205e96e28b790e2f70d2 100644 --- a/makefile +++ b/makefile @@ -41,7 +41,7 @@ $(TEST).o: $(TEST).c clean: - @rm -f *% *.bak *~ + @rm -f *% *.bak *~ *.o $(TEST) core distclean: limpa @rm -rf *.o lib$(LIBNOME).* lib$(LIBNOME2).* $(TEST) diff --git a/pdeSolver.c b/pdeSolver.c index 71242cd5ee38c8191d4781c2b3541eb2fd2d98cc..d7ad95bc28bfba7343fb6ff3b07207a966cfeb2b 100644 --- a/pdeSolver.c +++ b/pdeSolver.c @@ -4,7 +4,7 @@ u(i,j) = f(x,y) + (u(i+1,j) + u(i-1,j))/Δx² + (u(i,j+1) + u(i,j-1))/Δy² + (-u(i+1,j)+u(i-1,j))/2Δx + (-u(i,j+1)+u(i,j-1))/2Δy -------------------------------------------------------------------------------------------------------------------- 2/Δx² + 2/Δy² + 4π² -Resíduo: +Residue: f(x,y) = (2/Δx² + 2/Δy² + 4π²) * u(i,j) - ((u(i+1,j) + u(i-1,j))/Δx² + (u(i,j+1) + u(i,j-1))/Δy² + (-u(i+1,j)+u(i-1,j))/2Δx + (-u(i,j+1)+u(i,j-1))/2Δy) */ @@ -33,10 +33,6 @@ double timestamp(void) { return((double)(tp.tv_sec + tp.tv_usec/1000000.0)); } -void print_errno(void) { - printf("%s",strerror(errno)); -} - void getParams(int argc, char* argv[], FILE **fp) { if(argc != ARGS_NUM) { fprintf(stderr,"Wrong number of arguments.\n"); @@ -59,14 +55,13 @@ void getParams(int argc, char* argv[], FILE **fp) { } } -double f(int n) { // If stored in memory, it will need Nx * Ny * 8 bytes of memory. Should we do it? +double f(int n) { int i = n / Nx, j = n % Nx; double x = i * Hx, y = j * Hy; - return 4 * M_PI * ( ( sin(2 * M_PI * x) ) * ( sinh(M_PI * y) ) + ( sin(2 * Pipi - M_PI * x) ) * ( sinh(Pipi - M_PI * y) )); + return (4 * M_PI * ( ( sin(2 * M_PI * x) ) * ( sinh(M_PI * y) ) + ( sin(2 * Pipi - M_PI * x) ) * ( sinh(Pipi - M_PI * y) ))); } -inline int in(int i, int j) { -// Calculate vector index, like its a matrix. +inline int in(int i, int j) { // Calculate vector index, like its a matrix. return i*Ny + j; } @@ -92,29 +87,27 @@ double subsRow(int n, double *u) { } void sor(double *b, double *x, double *r, double *timeSor, double *timeResNorm) { - int i,j,k; // Ax = b -> ?u = f + int i,j,k; double sigma, now, fxy, res, maxRes = 0, tRes = 0; // maxRes is the biggest residue, tRes is total residue in this iteration. - for(k=0; k<MaxI; k++) { - now = timestamp(); - for(i = 1 + Ny; i < Nx * Ny - Ny - 1; ++i) { // Start at u[1][1], which means u[Ny+1] + for(k=0; k<MaxI; k++) { // Iterate MaxI times. + now = timestamp(); // Starting iteration time counter. + for(i = 1 + Ny; i < Nx * Ny - Ny - 1; ++i) { // Start at u[1][1], which means u[Ny+1] and do not calculate last row/column (they are borders) x[i] = x[i] + W * (calcU(i,x) - x[i]); } - *timeSor += timestamp() - now; - now = timestamp(); - printf("Res = %lf - ",res); + *timeSor += timestamp() - now; // Get iteration time. + now = timestamp(); // Start residue norm time counter. for(i = 1 + Ny; i < Nx * Ny - Ny - 1; ++i) { - res = f(i); - res -= subsRow(i,x); + res = f(i); // res = f(x,y) + res -= subsRow(i,x); // res = f(x,y) - (a0 * x0 + a1 * x1 + ... + an * xn) if(res > maxRes) maxRes = res; - tRes += res * res; + tRes += res * res; // Adds res² to the total residue of this iteration. } - printf("Res = %lf\n",res); - r[k] = sqrt(tRes); + r[k] = sqrt(tRes); // Store the norm of the residue in a vector (r). tRes = 0; - *timeResNorm += timestamp() - now; + *timeResNorm += timestamp() - now; // Get residue norm time. } - *timeSor = *timeSor / MaxI; + *timeSor = *timeSor / MaxI; // Get average values. *timeResNorm = *timeResNorm / MaxI; } @@ -124,109 +117,63 @@ int main(int argc, char *argv[]) { getParams(argc,argv,&fpExit); - Nx = (M_PI/Hx); - Ny = (M_PI/Hy); - Nx++; - Ny++; + //Nx = (M_PI/Hx); + //Ny = (M_PI/Hy); + //Nx++; + //Ny++; + Nx = (round(M_PI/Hx)) + 1; + Ny = (round(M_PI/Hy)) + 1; W = 2 - ((Hx + Hy) / 2); UDivisor = (2 / Hx * Hx) + (2 / Hy * Hy) + 4 * Pipi; double sigma; double *b, *x, *r, *timeSor, *timeResNorm; - b = malloc((Nx + 2) * (Ny + 2) * sizeof(double)); - x = malloc((Nx + 2) * (Ny + 2) * sizeof(double)); + b = malloc(Nx * Ny * sizeof(double)); + x = malloc(Nx * Ny * sizeof(double)); r = malloc(MaxI * sizeof(double)); timeSor = calloc(1,sizeof(double)); timeResNorm = calloc(1,sizeof(double)); - sigma = sinh(M_PI * M_PI); + sigma = sinh(Pipi); - // Creating borders - for(i=0; i<Nx; i++) { + for(i=0; i<Nx; i++) { // Creating borders x[ in(i,0) ] = sin(2 * M_PI * (M_PI - (i * Hx))) * sigma; - x[ in(i,Nx+1) ] = sin(2 * M_PI * (i * Hx)); + x[ in(i,Nx) ] = sin(2 * M_PI * (i * Hx)); } - //printf("Starting sor...\n"); - sor(b,x,r,timeSor,timeResNorm); - //print_vector(x); - printf("TimeSor: %lf\nTimeResNorm: %lf\n\nNorma do Resíduo\n",*timeSor,*timeResNorm); for(i=0; i<MaxI; ++i) { printf("# i=%d: %lf\n",i,r[i]); } - fprintf(fpExit,"# TimeSor: %lf\n# TimeResNorm: %lf\n\n# Norma do Resíduo\n",*timeSor,*timeResNorm); + fprintf(fpExit,"###########\n# Tempo Método SOR: %lf\n# Tempo Resíduo: %lf\n\n# Norma do Resíduo\n",*timeSor,*timeResNorm); for(i=0; i<MaxI; ++i) { fprintf(fpExit,"# i=%d: %lf\n",i,r[i]); } - fprintf(fpExit,"\n"); - FILE *expected = fopen("expected.txt","w"); + fprintf(fpExit,"###########\n"); + //FILE *expected = fopen("expected.txt","w"); for(i=0; i<Ny; i++) { // Print bottom border. - fprintf(fpExit, "%lf %lf %lf\n", 0.0f, i*Hy, x[i*Hx]); - fprintf(expected, "%lf %lf %lf\n", 0.0f, i*Hy, f[i*Hx]); + fprintf(fpExit, "%lf %lf %lf\n", 0.0f, i*Hy, subsRow(i, x)); + //fprintf(expected, "%lf %lf %lf\n", 0.0f, i*Hy, f(i)); } for(i=1; i<Nx; i++) { // Since im using subsRow, I cant start at position 0. - fprintf(fpExit,"%lf %lf %lf\n", i*Hx, 0.0f, x[i*Hx]) // Border. - fprintf(expected,"%lf %lf %lf\n", i*Hx, 0.0f, f[i*Hx]) // Border. + fprintf(fpExit,"%lf %lf %lf\n", i*Hx, 0.0f, subsRow(i*Ny,x)); // Border. + //fprintf(expected,"%lf %lf %lf\n", i*Hx, 0.0f, f(i)); // Border. for(j=1; j<Ny; j++) { fprintf(fpExit,"%lf %lf %lf\n",i*Hx,j*Hy,subsRow(i*Ny+j, x)); // Should we change i*Hx with j*Hy? (Columns by rows?) - fprintf(expected,"%lf %lf %lf\n",i*Hx,j*Hy,f(i*Ny+j)); + //fprintf(expected,"%lf %lf %lf\n",i*Hx,j*Hy,f(i*Ny+j)); } } - for(i=0; i<Ny; i++) { // Print bottom border. - fprintf(fpExit, "%lf %lf %lf\n", Nx*Hx, i*Hy, x[i*Hx]); - fprintf(expected, "%lf %lf %lf\n", Nx*Hx, i*Hy, f[i*Hx]); + for(i=0; i<Ny; i++) { // Print top border. We should check it. + fprintf(fpExit, "%lf %lf %lf\n", Nx*Hx, i*Hy, subsRow(Nx*Ny - Ny + i,x)); + //fprintf(expected, "%lf %lf %lf\n", Nx*Hx, i*Hy, f(Nx*Ny - Ny + i)); } // Nx columns and Ny rows. fclose(fpExit); + //fclose(expected); return 0; } - -/* -u(i,j) = f(x,y) + (u(i+1,j) + u(i-1,j))/Δx² + (u(i,j+1) + u(i,j-1))/Δy² + (-u(i+1,j)+u(i-1,j))/2Δx + (-u(i,j+1)+u(i,j-1))/2Δy - -------------------------------------------------------------------------------------------------------------------- - 2/Δx² + 2/Δy² + 4π² - - -Formato: - -Ax = B - -A [a11 a12 a13] * X [x1] = B [b1] -> a11*x1 + a12*x2 + a13*x3 = b1 -> x1 = (b1 - a12*x2 - a13*x3)/a11 - [a21 a22 a23] [x2] [b2] -> a11*x1 + a12*x2 + a13*x3 = b2 -> x2 = (b2 - a11*x1 - a13*x3)/a12 - [a31 a32 a33] [x3] [b3] -> a11*x1 + a12*x2 + a13*x3 = b3 -> x3 = (b3 - a11*x1 - a12*x2)/a13 - -se x1 = u(1,1), sei calcular x1 da forma double u(int i, int j) {} -Mesmo vale pra x2 e x3. E valeria pra x4, x5, x6, etc. - - -Se u for uma matriz de 6 elementos. Ou seja, Hx = 0.25 e Hy = 0.3 - -u u u u -u x5 x6 u -u x3 x4 u -u x1 x2 u -u u u u - -5 linhas, 4 colunas. -Ny = 3, Nx = 2. - -x1 = u11 -x2 = u12 -x3 = u13 -x4 = u21 -x5 = u22 -x6 = u23 - -Matriz A, olhando pela equação u(i,j) obtida, seria algo assim: -A = [1 ] - [ 1 ] - [ 1 ] - [ 1 ] - [ 1] -*/ diff --git a/sor.c b/sor.c deleted file mode 100644 index 779bf5aa0bf5b38f3199e87b8a9d5d801bec22f3..0000000000000000000000000000000000000000 --- a/sor.c +++ /dev/null @@ -1,124 +0,0 @@ -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <errno.h> - -#define SIZE 9 - -int N = SIZE; -int MaxI = 10; - -inline int in(int i, int j) { - return i*N + j; -} - -void generate_matrix(double *A, double *b) { -/* A[in(0,0)] = 10; - A[in(0,1)] = 4; - A[in(0,2)] = 2; - A[in(1,0)] = -2; - A[in(1,1)] = 15; - A[in(1,2)] = 3; - A[in(2,0)] = 2; - A[in(2,1)] = -2; - A[in(2,2)] = 13; - b[0] = 5; - b[1] = 3; - b[2] = 4;*/ - int i,j; - for(i=0; i<N*N; ++i) { - A[i] = 0; - } - for(i=0; i<N; ++i) { - for(j=0; j<N; ++j) { - if(i == j) - A[in(i,j)] = -4; - } - } - A[in(0,1)] = 1; - A[in(0,3)] = 1; - A[in(1,0)] = 1; - A[in(1,2)] = 1; - A[in(1,4)] = 1; - A[in(2,1)] = 1; - A[in(2,5)] = 1; - A[in(3,0)] = 1; - A[in(3,4)] = 1; - A[in(3,6)] = 1; - A[in(4,1)] = 1; - A[in(4,3)] = 1; - A[in(4,5)] = 1; - A[in(4,7)] = 1; - A[in(5,2)] = 1; - A[in(5,4)] = 1; - A[in(5,8)] = 1; - A[in(6,3)] = 1; - A[in(6,7)] = 1; - A[in(7,4)] = 1; - A[in(7,6)] = 1; - A[in(7,8)] = 1; - A[in(8,5)] = 1; - A[in(8,7)] = 1; - b[0] = -100; - b[1] = -20; - b[2] = -20; - b[3] = -80; - b[4] = 0; - b[5] = 0; - b[6] = -260; - b[7] = -180; - b[8] = -180; -} - -void print_vector(double *x) { - int i; - for(i=0; i<N; ++i) { - printf("%f ", x[i]); - } - printf("\n"); -} - -void print_matrix(double *A) { - int i,j; - for(i=0; i<N; ++i) { - for(j=0; j<N; ++j) { - printf("%.0f ", A[in(i,j)]); - } - printf("\n"); - } - printf("\n\n\n"); -} - -void sor(double *A, double *b, double *x, double w) { - int i,j,k; - double sigma; - for(k=0; k<MaxI; k++) { - for(i=0; i<N; ++i) { - sigma = 0; - for(j=0; j<N; ++j) { - sigma = sigma + A[in(i,j)] * x[j]; - } - sigma = sigma - A[in(i,i)] * x[i]; - x[i] = x[i] + w * ((b[i] - sigma)/A[in(i,i)] - x[i]); - } - } -} - -int main(int argc, char* argv[]) { - double *A,*b,*x,w; - int i,j; - A = malloc(N * N * sizeof(double)); - b = malloc(N * sizeof(double)); - x = malloc(N * sizeof(double)); - generate_matrix(A,b); - for(i=0; i<N; ++i) { - x[i] = 1; - } - print_vector(x); - print_matrix(A); - print_vector(b); - w = 1.25; - sor(A,b,x,w); - - print_vector(x); -} \ No newline at end of file