Quarto incontro
Cirdans-Home
2 years ago
parent
078ce47958
commit
ec6c598012
@ -0,0 +1,21 @@
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MPICC = mpicc #The wrapper for the compiler
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CC = gcc
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CFLAGS += -g #Useful for debug symbols
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LDLIBS += -lm
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all: sequentialderiv parallelderiv
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sequentialderiv: sequentialderiv.c
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$(CC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
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parallelderiv: parallelderiv.c
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$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
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midpointintegral: midpointintegral.c
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$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
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montecarlostyle: montecarlostyle.c
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$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
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clean:
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rm -f easysendrecv nonblockingsendrecv sequentialderiv
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@ -0,0 +1,18 @@
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MPICC = mpicc #The wrapper for the compiler
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CC = gcc
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CFLAGS += -g #Useful for debug symbols
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LDLIBS += -lm
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all: parallelderiv midpointintegral montecarlostyle
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parallelderiv: parallelderiv.c
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$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
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midpointintegral: midpointintegral.c
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$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
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montecarlostyle: montecarlostyle.c
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$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
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clean:
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rm -f parallelderiv midpointintegral montecarlostyle
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@ -0,0 +1,43 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <mpi.h>
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double f( double x);
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int main( int argc, char *argv[]){
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int n, mynode, totalnodes, i;
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double PI25DT = 3.141592653589793238462643;
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double mypi, pi, h, sum, x;
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MPI_Init(&argc,&argv);
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MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
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MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
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if(mynode == 0){
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if(argc != 2){
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n = 20;
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}else{
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n = atoi(argv[1]);
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}
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}
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MPI_Bcast(&n, 1, MPI_INT, 0, MPI_COMM_WORLD);
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h = 1.0 / ((double) n*totalnodes);
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sum = 0.0;
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for (i = 1+mynode*n; i <= n*(mynode+1); i++){
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x = h * ((double)i - 0.5);
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sum += f(x);
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}
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mypi = h*sum;
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MPI_Reduce(&mypi, &pi, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
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if (mynode == 0){
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printf("pi is approximately %.16f, Error is %e\n",pi, fabs(pi - PI25DT));
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}
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MPI_Finalize();
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return 0;
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}
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double f( double x )
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{
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return (4.0 / (1.0 + x*x));
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}
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@ -0,0 +1,58 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <mpi.h>
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#include <time.h>
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int main( int argc, char *argv[]){
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int n, mynode, totalnodes, i;
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double PI25DT = 3.141592653589793238462643;
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double mypi, pi, h;
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double x, y, x1, x2, y1, y2;
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int SqPoints, CiPoints, my_SqPoints, my_CiPoints;
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unsigned int seed = (unsigned) time(NULL);
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MPI_Init(&argc,&argv);
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MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
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MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
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if(mynode == 0){
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if(argc != 2){
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n = 20;
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}else{
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n = atoi(argv[1]);
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}
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}
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MPI_Bcast(&n, 1, MPI_INT, 0, MPI_COMM_WORLD);
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h = 2.0 / (double) totalnodes ;
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x1 = -1.0 + mynode * h;
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x2 = x1 + h;
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y1 = -1.0;
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y2 = 1.0;
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my_SqPoints = 0;
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my_CiPoints = 0;
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for (i = 1; i <= n; i++)
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{
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srand(seed + mynode);
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x = rand_r(&seed); x = x / RAND_MAX; x = x1 + x * (x2 - x1);
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y = rand_r(&seed); y = y / RAND_MAX; y = y1 + y * (y2 - y1);
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my_SqPoints++;
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if ( ( x*x + y*y ) <= 1.0 ) my_CiPoints++;
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}
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SqPoints = 0;
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CiPoints = 0;
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MPI_Reduce(&my_SqPoints, &SqPoints, 1, MPI_INT, MPI_SUM, 0, MPI_COMM_WORLD);
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MPI_Reduce(&my_CiPoints, &CiPoints, 1, MPI_INT, MPI_SUM, 0, MPI_COMM_WORLD);
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if (mynode == 0)
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{
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pi = 4.0 * (double)CiPoints / (double)SqPoints;
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printf("Pi is approximately %.16f = 4.0 %d/%d, Error is %e (h = %e)\n",pi,CiPoints,SqPoints,fabs(pi - PI25DT),1.0/sqrt( (double) SqPoints) );
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}
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MPI_Finalize();
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return 0;
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}
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include "mpi.h"
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void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes);
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double fun(double x);
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double funprime( double x);
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int main(int argc, char **argv){
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double globala,globalb,a,b,dx,*f,*fx, error;
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int n, mynode, totalnodes;
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MPI_Status status;
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MPI_Init( &argc, &argv );
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MPI_Comm_rank( MPI_COMM_WORLD, &mynode );
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MPI_Comm_size( MPI_COMM_WORLD, &totalnodes );
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n = 20;
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globala = 0;
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globalb = 1;
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a = globala + ((double) mynode)*(globalb - globala)/( (double) totalnodes);
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b = globala + ((double) mynode+1)*(globalb - globala)/( (double) totalnodes);
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f = (double *) malloc(sizeof(double)*(n));
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fx = (double *) malloc(sizeof(double)*(n));
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dx = (b-a)/((double) n);
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for( int i = 0; i < n; i++){
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f[i] = fun(a+((double) i)*dx);
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}
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firstderiv1Dp_vec( n, dx, f, fx, mynode, totalnodes);
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error = 0.0;
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for(int i = 0; i < n; i++){
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error += pow( fx[i]-funprime(a+((b-a)*((double) i))/((double) n)),2.0);
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}
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error = sqrt(dx*error);
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printf("Node %d ||f' - fx||_2 = %e\n",mynode,error);
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free(f);
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free(fx);
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MPI_Finalize();
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return 0;
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}
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void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes){
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double scale = 1.0/(2.0*dx);
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double mpitemp;
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MPI_Status status;
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if(mynode == 0){
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fx[0] = (-3.0*f[0] + 4.0*f[1] - f[2])*scale;
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}
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if(mynode == (totalnodes-1)){
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fx[n-1] = (3.0*f[n-1] - 4.0*f[n-2] + f[n-3])*scale;
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}
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for(int i=1;i<n-1;i++){
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fx[i] = (f[i+1]-f[i-1])*scale;
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}
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if(mynode == 0){
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mpitemp = f[n-1];
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MPI_Send(&mpitemp,1,MPI_DOUBLE,1,1,MPI_COMM_WORLD);
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MPI_Recv(&mpitemp,1,MPI_DOUBLE,1,1,MPI_COMM_WORLD,&status);
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fx[n-1] = (mpitemp - f[n-2])*scale;
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}
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else if(mynode == (totalnodes-1)){
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MPI_Recv(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD, &status);
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fx[0] = (f[1]-mpitemp)*scale;
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mpitemp = f[0];
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MPI_Send(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD);
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}
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else{
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MPI_Recv(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD, &status);
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fx[0] = (f[1]-mpitemp)*scale;
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mpitemp = f[0];
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MPI_Send(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD);
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mpitemp = f[n-1];
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MPI_Send(&mpitemp,1,MPI_DOUBLE,mynode+1,1,MPI_COMM_WORLD);
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MPI_Recv(&mpitemp,1,MPI_DOUBLE,mynode+1,1,MPI_COMM_WORLD, &status);
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fx[n-1] = (mpitemp-f[n-2])*scale;
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}
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return;
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}
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double fun(double x){
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return(sin(x));
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}
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double funprime( double x){
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return(cos(x));
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}
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@ -0,0 +1,45 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <mpi.h>
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double f( double x);
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int main( int argc, char *argv[]){
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int n, mynode, totalnodes, i;
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double PI25DT = 3.141592653589793238462643;
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double mypi, pi, h, sum, x;
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MPI_Init(&argc,&argv);
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MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
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MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
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if(mynode == 0){
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if(argc != 2){
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n = 20;
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}else{
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n = atoi(argv[1]);
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}
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}
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// Broadcast the value to every process
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h = 1.0 / ((double) n*totalnodes);
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sum = 0.0;
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for (i = 1+mynode*n; i <= n*(mynode+1); i++){
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// compute the local quadrature rule
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}
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mypi = h * sum;
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// sum all the local sums via reduction
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if (mynode == 0){
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printf("pi is approximately %.16f, Error is %e\n",pi, fabs(pi - PI25DT));
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}
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MPI_Finalize();
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return 0;
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}
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double f( double x )
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{
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return (4.0 / (1.0 + x*x));
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}
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@ -0,0 +1,58 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <mpi.h>
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#include <time.h>
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int main( int argc, char *argv[]){
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int n, mynode, totalnodes, i;
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double PI25DT = 3.141592653589793238462643;
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double mypi, pi, h;
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double x, y, x1, x2, y1, y2;
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int SqPoints, CiPoints, my_SqPoints, my_CiPoints;
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unsigned int seed = (unsigned) time(NULL);
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MPI_Init(&argc,&argv);
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MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
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MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
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if(mynode == 0){
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if(argc != 2){
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n = 20;
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}else{
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n = atoi(argv[1]);
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}
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}
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// Broadcast the number of intervals everywhere
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h = 2.0 / (double) totalnodes;
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x1 = -1.0 + mynode * h;
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x2 = x1 + h;
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y1 = -1.0;
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y2 = 1.0;
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my_SqPoints = 0;
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my_CiPoints = 0;
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for (i = 1; i <= n; i++)
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{
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srand(seed + mynode);
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x = rand(&seed); x = x / RAND_MAX; x = x1 + x * (x2 - x1);
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y = rand(&seed); y = y / RAND_MAX; y = y1 + y * (y2 - y1);
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// do the check on the local Montecarlo Integration : my_SqPoints, my_CiPoints should store
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// the number of points into the square, and into the circle (respectively)
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}
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SqPoints = 0;
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CiPoints = 0;
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// Perform reduce operation to put into SqPoints and CiPoints the values
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if (mynode == 0)
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{
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pi = 4.0 * (double)CiPoints / (double)SqPoints;
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printf("Pi is approximately %.16f = 4.0 %d/%d, Error is %e (h = %e)\n",pi,CiPoints,SqPoints,fabs(pi - PI25DT),1.0/sqrt( (double) SqPoints) );
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}
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MPI_Finalize();
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return 0;
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}
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@ -0,0 +1,98 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include "mpi.h"
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void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes);
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double fun(double x);
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double funprime( double x);
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int main(int argc, char **argv){
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double globala,globalb,a,b,dx,*f,*fx, error;
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int n, mynode, totalnodes;
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MPI_Status status;
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MPI_Init( &argc, &argv );
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MPI_Comm_rank( MPI_COMM_WORLD, &mynode );
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MPI_Comm_size( MPI_COMM_WORLD, &totalnodes );
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n = 20;
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globala = 0;
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globalb = 1;
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a = globala + ((double) mynode)*(globalb - globala)/( (double) totalnodes);
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b = globala + ((double) mynode+1)*(globalb - globala)/( (double) totalnodes);
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f = (double *) malloc(sizeof(double)*(n));
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fx = (double *) malloc(sizeof(double)*(n));
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dx = (b-a)/((double) n);
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for( int i = 0; i < n; i++){
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f[i] = fun(a+((double) i)*dx);
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}
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firstderiv1Dp_vec( n, dx, f, fx, mynode, totalnodes);
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error = 0.0;
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for(int i = 0; i < n; i++){
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error += pow( fx[i]-funprime(a+((b-a)*((double) i))/((double) n)),2.0);
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}
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error = sqrt(dx*error);
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printf("Node %d ||f' - fx||_2 = %e\n",mynode,error);
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free(f);
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free(fx);
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MPI_Finalize();
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return 0;
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}
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void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes){
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double scale = 1.0/(2.0*dx);
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double mpitemp;
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MPI_Status status;
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if(mynode == 0){
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fx[0] = (-3.0*f[0] + 4.0*f[1] - f[2])*scale;
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}
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if(mynode == (totalnodes-1)){
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fx[n-1] = (3.0*f[n-1] - 4.0*f[n-2] + f[n-3])*scale;
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}
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for(int i=1;i<n-1;i++){
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fx[i] = (f[i+1]-f[i-1])*scale;
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}
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if(mynode == 0){
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mpitemp = f[n-1];
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MPI_Send();
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MPI_Recv();
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fx[n-1] = (mpitemp - f[n-2])*scale;
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}
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else if(mynode == (totalnodes-1)){
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MPI_Recv();
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fx[0] = (f[1]-mpitemp)*scale;
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mpitemp = f[0];
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MPI_Send();
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}
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else{
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MPI_Recv();
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fx[0] = (f[1]-mpitemp)*scale;
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mpitemp = f[0];
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MPI_Send();
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mpitemp = f[n-1];
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MPI_Send();
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MPI_Recv();
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fx[n-1] = (mpitemp-f[n-2])*scale;
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}
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return;
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}
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double fun(double x){
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return(sin(x));
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}
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double funprime( double x){
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return(cos(x));
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}
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@ -0,0 +1,65 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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void firstderiv1D(int n, double a, double b, double *fx);
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void firstderiv1D_vec(int n, double dx, double *f, double *fx);
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double fun(double x);
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double funprime( double x);
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int main(int argc, char **argv){
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double a,b,dx,*f,*fx;
|
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int n;
|
||||
if(argc != 2){
|
||||
n = 20;
|
||||
}else{
|
||||
n = atoi(argv[1]);
|
||||
}
|
||||
a = 0.0;
|
||||
b = 1.0;
|
||||
f = (double *) malloc(sizeof(double)*n);
|
||||
fx = (double *) malloc(sizeof(double)*n);
|
||||
// firstderiv1D(n, a, b, fx);
|
||||
dx = (b-a)/((double) n);
|
||||
for( int i = 0; i <= n; i++){
|
||||
f[i] = fun(a+((double) i)*dx);
|
||||
}
|
||||
firstderiv1D_vec(n, dx, f, fx);
|
||||
for(int i = 0; i < n; i++){
|
||||
printf("fx[%d] = %1.2f f'[%d] = %1.2f |fx - f'| = %1.1e\n",
|
||||
i,fx[i],i,funprime(a+((b-a)*i)/n),abs(fx[i]-
|
||||
funprime(a+((b-a)*((double) i))/((double) (n-1)))));
|
||||
}
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
void firstderiv1D(int n, double a, double b, double *fx){
|
||||
double dx = (b-a)/((double) n-1);
|
||||
double scale = 1.0/(2.0*dx);
|
||||
for (int i = 1; i < n-1; i++){
|
||||
fx[i] = (fun(a + (i+1)*dx) - fun(a + (i-1)*dx))*scale;
|
||||
}
|
||||
fx[0] = (-3.0*fun(a) + 4.0*fun(a + dx) - fun(a + 2.0*dx))*scale;
|
||||
fx[n-1] = (3.0*fun(a+ (n-1)*dx) - 4.0*fun(a + (n-2)*dx) + fun(a + (n-3)*dx))*scale;
|
||||
return;
|
||||
}
|
||||
|
||||
void firstderiv1D_vec(int n, double dx, double *f, double *fx){
|
||||
double scale;
|
||||
scale = 1.0/(2.0*dx);
|
||||
for (int i = 1; i < n-1; i++){
|
||||
fx[i] = (f[i+1] - f[i-1])*scale;
|
||||
}
|
||||
fx[0] = (-3.0*f[0] + 4.0*f[1] - f[2])*scale;
|
||||
fx[n-1] = (3.0*f[n-1] - 4.0*f[n-2] + f[n-3])*scale;
|
||||
return;
|
||||
}
|
||||
|
||||
double fun(double x){
|
||||
return(x*x + 1);
|
||||
}
|
||||
|
||||
double funprime( double x){
|
||||
return(2*x);
|
||||
}
|
||||
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Reference in New Issue