Quarto incontro

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Cirdans-Home 10 months ago
parent 078ce47958
commit ec6c598012

@ -0,0 +1,21 @@
MPICC = mpicc #The wrapper for the compiler
CC = gcc
CFLAGS += -g #Useful for debug symbols
LDLIBS += -lm
all: sequentialderiv parallelderiv
sequentialderiv: sequentialderiv.c
$(CC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
parallelderiv: parallelderiv.c
$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
midpointintegral: midpointintegral.c
$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
montecarlostyle: montecarlostyle.c
$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
clean:
rm -f easysendrecv nonblockingsendrecv sequentialderiv

@ -0,0 +1,18 @@
MPICC = mpicc #The wrapper for the compiler
CC = gcc
CFLAGS += -g #Useful for debug symbols
LDLIBS += -lm
all: parallelderiv midpointintegral montecarlostyle
parallelderiv: parallelderiv.c
$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
midpointintegral: midpointintegral.c
$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
montecarlostyle: montecarlostyle.c
$(MPICC) $(CFLAGS) $(LDFLAGS) $? $(LDLIBS) -o $@
clean:
rm -f parallelderiv midpointintegral montecarlostyle

@ -0,0 +1,43 @@
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mpi.h>
double f( double x);
int main( int argc, char *argv[]){
int n, mynode, totalnodes, i;
double PI25DT = 3.141592653589793238462643;
double mypi, pi, h, sum, x;
MPI_Init(&argc,&argv);
MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
if(mynode == 0){
if(argc != 2){
n = 20;
}else{
n = atoi(argv[1]);
}
}
MPI_Bcast(&n, 1, MPI_INT, 0, MPI_COMM_WORLD);
h = 1.0 / ((double) n*totalnodes);
sum = 0.0;
for (i = 1+mynode*n; i <= n*(mynode+1); i++){
x = h * ((double)i - 0.5);
sum += f(x);
}
mypi = h*sum;
MPI_Reduce(&mypi, &pi, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
if (mynode == 0){
printf("pi is approximately %.16f, Error is %e\n",pi, fabs(pi - PI25DT));
}
MPI_Finalize();
return 0;
}
double f( double x )
{
return (4.0 / (1.0 + x*x));
}

@ -0,0 +1,58 @@
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mpi.h>
#include <time.h>
int main( int argc, char *argv[]){
int n, mynode, totalnodes, i;
double PI25DT = 3.141592653589793238462643;
double mypi, pi, h;
double x, y, x1, x2, y1, y2;
int SqPoints, CiPoints, my_SqPoints, my_CiPoints;
unsigned int seed = (unsigned) time(NULL);
MPI_Init(&argc,&argv);
MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
if(mynode == 0){
if(argc != 2){
n = 20;
}else{
n = atoi(argv[1]);
}
}
MPI_Bcast(&n, 1, MPI_INT, 0, MPI_COMM_WORLD);
h = 2.0 / (double) totalnodes ;
x1 = -1.0 + mynode * h;
x2 = x1 + h;
y1 = -1.0;
y2 = 1.0;
my_SqPoints = 0;
my_CiPoints = 0;
for (i = 1; i <= n; i++)
{
srand(seed + mynode);
x = rand_r(&seed); x = x / RAND_MAX; x = x1 + x * (x2 - x1);
y = rand_r(&seed); y = y / RAND_MAX; y = y1 + y * (y2 - y1);
my_SqPoints++;
if ( ( x*x + y*y ) <= 1.0 ) my_CiPoints++;
}
SqPoints = 0;
CiPoints = 0;
MPI_Reduce(&my_SqPoints, &SqPoints, 1, MPI_INT, MPI_SUM, 0, MPI_COMM_WORLD);
MPI_Reduce(&my_CiPoints, &CiPoints, 1, MPI_INT, MPI_SUM, 0, MPI_COMM_WORLD);
if (mynode == 0)
{
pi = 4.0 * (double)CiPoints / (double)SqPoints;
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) );
}
MPI_Finalize();
return 0;
}

@ -0,0 +1,98 @@
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "mpi.h"
void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes);
double fun(double x);
double funprime( double x);
int main(int argc, char **argv){
double globala,globalb,a,b,dx,*f,*fx, error;
int n, mynode, totalnodes;
MPI_Status status;
MPI_Init( &argc, &argv );
MPI_Comm_rank( MPI_COMM_WORLD, &mynode );
MPI_Comm_size( MPI_COMM_WORLD, &totalnodes );
n = 20;
globala = 0;
globalb = 1;
a = globala + ((double) mynode)*(globalb - globala)/( (double) totalnodes);
b = globala + ((double) mynode+1)*(globalb - globala)/( (double) totalnodes);
f = (double *) malloc(sizeof(double)*(n));
fx = (double *) malloc(sizeof(double)*(n));
dx = (b-a)/((double) n);
for( int i = 0; i < n; i++){
f[i] = fun(a+((double) i)*dx);
}
firstderiv1Dp_vec( n, dx, f, fx, mynode, totalnodes);
error = 0.0;
for(int i = 0; i < n; i++){
error += pow( fx[i]-funprime(a+((b-a)*((double) i))/((double) n)),2.0);
}
error = sqrt(dx*error);
printf("Node %d ||f' - fx||_2 = %e\n",mynode,error);
free(f);
free(fx);
MPI_Finalize();
return 0;
}
void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes){
double scale = 1.0/(2.0*dx);
double mpitemp;
MPI_Status status;
if(mynode == 0){
fx[0] = (-3.0*f[0] + 4.0*f[1] - f[2])*scale;
}
if(mynode == (totalnodes-1)){
fx[n-1] = (3.0*f[n-1] - 4.0*f[n-2] + f[n-3])*scale;
}
for(int i=1;i<n-1;i++){
fx[i] = (f[i+1]-f[i-1])*scale;
}
if(mynode == 0){
mpitemp = f[n-1];
MPI_Send(&mpitemp,1,MPI_DOUBLE,1,1,MPI_COMM_WORLD);
MPI_Recv(&mpitemp,1,MPI_DOUBLE,1,1,MPI_COMM_WORLD,&status);
fx[n-1] = (mpitemp - f[n-2])*scale;
}
else if(mynode == (totalnodes-1)){
MPI_Recv(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD, &status);
fx[0] = (f[1]-mpitemp)*scale;
mpitemp = f[0];
MPI_Send(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD);
}
else{
MPI_Recv(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD, &status);
fx[0] = (f[1]-mpitemp)*scale;
mpitemp = f[0];
MPI_Send(&mpitemp,1,MPI_DOUBLE,mynode-1,1,MPI_COMM_WORLD);
mpitemp = f[n-1];
MPI_Send(&mpitemp,1,MPI_DOUBLE,mynode+1,1,MPI_COMM_WORLD);
MPI_Recv(&mpitemp,1,MPI_DOUBLE,mynode+1,1,MPI_COMM_WORLD, &status);
fx[n-1] = (mpitemp-f[n-2])*scale;
}
return;
}
double fun(double x){
return(sin(x));
}
double funprime( double x){
return(cos(x));
}

@ -0,0 +1,45 @@
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mpi.h>
double f( double x);
int main( int argc, char *argv[]){
int n, mynode, totalnodes, i;
double PI25DT = 3.141592653589793238462643;
double mypi, pi, h, sum, x;
MPI_Init(&argc,&argv);
MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
if(mynode == 0){
if(argc != 2){
n = 20;
}else{
n = atoi(argv[1]);
}
}
// Broadcast the value to every process
h = 1.0 / ((double) n*totalnodes);
sum = 0.0;
for (i = 1+mynode*n; i <= n*(mynode+1); i++){
// compute the local quadrature rule
}
mypi = h * sum;
// sum all the local sums via reduction
if (mynode == 0){
printf("pi is approximately %.16f, Error is %e\n",pi, fabs(pi - PI25DT));
}
MPI_Finalize();
return 0;
}
double f( double x )
{
return (4.0 / (1.0 + x*x));
}

@ -0,0 +1,58 @@
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mpi.h>
#include <time.h>
int main( int argc, char *argv[]){
int n, mynode, totalnodes, i;
double PI25DT = 3.141592653589793238462643;
double mypi, pi, h;
double x, y, x1, x2, y1, y2;
int SqPoints, CiPoints, my_SqPoints, my_CiPoints;
unsigned int seed = (unsigned) time(NULL);
MPI_Init(&argc,&argv);
MPI_Comm_size(MPI_COMM_WORLD,&totalnodes);
MPI_Comm_rank(MPI_COMM_WORLD,&mynode);
if(mynode == 0){
if(argc != 2){
n = 20;
}else{
n = atoi(argv[1]);
}
}
// Broadcast the number of intervals everywhere
h = 2.0 / (double) totalnodes;
x1 = -1.0 + mynode * h;
x2 = x1 + h;
y1 = -1.0;
y2 = 1.0;
my_SqPoints = 0;
my_CiPoints = 0;
for (i = 1; i <= n; i++)
{
srand(seed + mynode);
x = rand(&seed); x = x / RAND_MAX; x = x1 + x * (x2 - x1);
y = rand(&seed); y = y / RAND_MAX; y = y1 + y * (y2 - y1);
// do the check on the local Montecarlo Integration : my_SqPoints, my_CiPoints should store
// the number of points into the square, and into the circle (respectively)
}
SqPoints = 0;
CiPoints = 0;
// Perform reduce operation to put into SqPoints and CiPoints the values
if (mynode == 0)
{
pi = 4.0 * (double)CiPoints / (double)SqPoints;
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) );
}
MPI_Finalize();
return 0;
}

@ -0,0 +1,98 @@
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "mpi.h"
void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes);
double fun(double x);
double funprime( double x);
int main(int argc, char **argv){
double globala,globalb,a,b,dx,*f,*fx, error;
int n, mynode, totalnodes;
MPI_Status status;
MPI_Init( &argc, &argv );
MPI_Comm_rank( MPI_COMM_WORLD, &mynode );
MPI_Comm_size( MPI_COMM_WORLD, &totalnodes );
n = 20;
globala = 0;
globalb = 1;
a = globala + ((double) mynode)*(globalb - globala)/( (double) totalnodes);
b = globala + ((double) mynode+1)*(globalb - globala)/( (double) totalnodes);
f = (double *) malloc(sizeof(double)*(n));
fx = (double *) malloc(sizeof(double)*(n));
dx = (b-a)/((double) n);
for( int i = 0; i < n; i++){
f[i] = fun(a+((double) i)*dx);
}
firstderiv1Dp_vec( n, dx, f, fx, mynode, totalnodes);
error = 0.0;
for(int i = 0; i < n; i++){
error += pow( fx[i]-funprime(a+((b-a)*((double) i))/((double) n)),2.0);
}
error = sqrt(dx*error);
printf("Node %d ||f' - fx||_2 = %e\n",mynode,error);
free(f);
free(fx);
MPI_Finalize();
return 0;
}
void firstderiv1Dp_vec(int n, double dx, double *f,double *fx, int mynode, int totalnodes){
double scale = 1.0/(2.0*dx);
double mpitemp;
MPI_Status status;
if(mynode == 0){
fx[0] = (-3.0*f[0] + 4.0*f[1] - f[2])*scale;
}
if(mynode == (totalnodes-1)){
fx[n-1] = (3.0*f[n-1] - 4.0*f[n-2] + f[n-3])*scale;
}
for(int i=1;i<n-1;i++){
fx[i] = (f[i+1]-f[i-1])*scale;
}
if(mynode == 0){
mpitemp = f[n-1];
MPI_Send();
MPI_Recv();
fx[n-1] = (mpitemp - f[n-2])*scale;
}
else if(mynode == (totalnodes-1)){
MPI_Recv();
fx[0] = (f[1]-mpitemp)*scale;
mpitemp = f[0];
MPI_Send();
}
else{
MPI_Recv();
fx[0] = (f[1]-mpitemp)*scale;
mpitemp = f[0];
MPI_Send();
mpitemp = f[n-1];
MPI_Send();
MPI_Recv();
fx[n-1] = (mpitemp-f[n-2])*scale;
}
return;
}
double fun(double x){
return(sin(x));
}
double funprime( double x){
return(cos(x));
}

@ -0,0 +1,65 @@
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
void firstderiv1D(int n, double a, double b, double *fx);
void firstderiv1D_vec(int n, double dx, double *f, double *fx);
double fun(double x);
double funprime( double x);
int main(int argc, char **argv){
double a,b,dx,*f,*fx;
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);
}

@ -6,7 +6,9 @@ Progetto speciale per la didattica dell'Università di Pisa, a.a. 2022/23.
- Giovedì 30 Marzo 2023, ore 16.00: Introduzione e uso di GIT
- Giovedì 20 Aprile 2023, ore 11.00: Introduzione ad MPI
- Venerdì 28 Aprile 2023, ore 11.00: Assemblaggio e prime configurazioni
- Giovedì 4 Maggio 2023, ore 16.00: Configurazione cluster (Slurm&GlusterFS: prime run)
- Giovedì 4 Maggio 2023, ore 16.00: Comunicazioni collettive
- Giovedì 18 Maggio 2023, ore 16.00: Test con il cluster Steffé e uso di Slurm
- Giovedì 25 Maggio 2023, ore 16.00: *Guest lecture*: Prof. S. Filippone
Il materiale si trova nella cartella `Slides` del `repository`.

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