Alright so this program is meant to simulate a solar system by semi-randomly generating a star, semi-randomly generating planets around the star, simulating the passing of time (using MPI to spread out the computational load), and determining habitability of resulting planets. I should have it commented for readability.
I am however having a problem with getting MPI working. As far as I can tell I'm doing something wrong that prevents it from initializing properly. Here's the errors I get.
OrbitPlus.cpp:323:50: error: invalid conversion from ‘char’ to ‘char**’ [-fpermissive]
system1 = Time( system, n , dt , argc, **argv);
^
OrbitPlus.cpp:191:33: error: initializing argument 5 of ‘std::vector<std::vector<float> > Time(std::vector<std::vector<float> >, int, float, int, char**)’ [-fpermissive]
std::vector<std::vector<float>> Time( std::vector<std::vector<float>> system , int n, float dt, int argc, char **argv){
^
I do find it interesting that both errors are considered fpermissive errors if when I compile it with -
mpic++ -std=c++11 -o OrbitPlus OrbitPlus.cpp
So it seems if I was feeling adventurous I could just run the code with -fpermissive option and roll the dice, but I don't feel like being so brave. Clearly the errors are related to each other.
Here's my code.
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <tuple>
#include <vector>
#include <stdio.h>
#include <math.h>
#include <complex>
#include <stdint.h>
#include <time.h>
#include <string.h>
#include <algorithm>
#include "mpi.h"
double MyRandom(){
//////////////////////////
//Random Number Generator
//Returns number between 0-99
//////////////////////////
double y = 0;
unsigned seed = time(0);
std::srand(seed);
uint64_t x = std::rand();
x ^= x << 13;
x ^= x >> 7;
x ^= x << 17;
x = (1070739 * x) % 2199023255530;
y = x / 21990232555.31 ;
return y;
}
////////////////////////
///////////////////////
std::tuple< char , float , float , float , int > Star(){
////////////////////////////
//Star will generate a Star
//Randomly or User Selected
//Class, Luminosity, Probability, Radius, Mass, Temperature
//Stars always take up 99% of the mass of the system.
///////////////////////////
char Class;
int choice = 8;
float L, R, M, T;
double y = 4;
std::tuple< char , float , float , float , float > star( Class , L , R , M , T) ;
std::cout << "Select Star Class (OBAFGKM) or Select 8 for Random" << std::endl;
std::cout << "1 = O, 2 = B, 3 = A, 4 = F, 5 = G, 6 = K, 7 = M : ";
std::cin >> choice;
if ( choice == 8 ) {
y = MyRandom();
if (y <= 0.003) choice = 1;
if ((y > 0.003) && (y <= 0.133)) choice = 2;
if ((y > 0.133) && (y <= 0.733)) choice = 3;
if ((y > 0.733) && (y <= 3.733)) choice = 4;
if ((y > 3.733) && (y <= 11.333)) choice = 5;
if ((y > 11.333) && (y <= 23.433)) choice = 6;
else choice = 7;
}
if (choice == 1) {
Class = 'O';
L = 30000;
R = 0.0307;
M = 16;
T = 30000;
}
if (choice == 2) {
Class = 'B';
L = 15000;
R = 0.0195;
M = 9;
T = 20000;
}
if (choice == 3) {
Class = 'A';
L = 15;
R = 0.00744;
M = 1.7;
T = 8700;
}
if (choice == 4) {
Class = 'F';
L = 3.25;
R = 0.00488;
M = 1.2;
T = 6750;
}
if (choice == 5) {
Class = 'G';
L = 1;
R = 0.00465;
M = 1;
T = 5700;
}
if (choice == 6) {
Class = 'K';
L = 0.34;
R = 0.00356;
M = 0.62;
T = 4450;
}
if (choice == 7) {
Class = 'M';
L = 0.08;
R = 0.00326;
M = 0.26;
T = 3000;
}
return star;
}
////////////
///////////
std::vector< std::vector<float> > Planet( float L, float R, float M, int T, int n){
///////////////////////////
//Planet generates the Planets
//Random 1 - 10, Random distribution 0.06 - 6 JAU unless specified by User
//Frost line Calculated, First Planet after Frost line is the Jupiter
//The Jupiter will have the most mass of all Jovian worlds
//Otherwise divided into Jovian and Terrestrial Worlds, Random Masses within groups
//Also calculates if a planet is in the Habitable Zone
////////////////////////////
float frostline, innerCHZ, outerCHZ;
float a = 0.06; // a - albedo
float m = M / 100; //Mass of the Jupiter always 1/100th mass of the Star.
std::vector<float> sys;
std::vector<std::vector <float>> system;
for (int i = 0 ; i < n ; i++){
sys.push_back( MyRandom()/10 * 3 ) ; //Distances in terms of Sol AU
}
sort(sys.begin(), sys.end() );
for (int i = 0 ; i < n ; i++){
system[i].push_back(sys[i]);
system[i].push_back(0); //system[i][0] is x, system[i][1] is y
}
frostline = (0.6 * T / 150) * (0.6 * T/150) * R / sqrt(1 - a);
innerCHZ = sqrt(L / 1.1);
outerCHZ = sqrt(L / 0.53);
for (int i = 0 ; i < n ; i++){
if (system[i][0] <= frostline) {
float tmass = m * 0.0003 * MyRandom();
system[i].push_back(tmass) ; //system[i][2] is mass, [3] is marker for the Jupiter
system[i].push_back(0) ;
}
if ((system[i][0] >= frostline) && (system[i-1][0] < frostline)){
system[i].push_back(m) ;
float J = 1;
system[i].push_back(J) ;
}
if ((system[i][0] >= frostline) && (system[i-1][0] >= frostline)) {
float jmass = m * 0.01 * MyRandom();
system[i].push_back(jmass) ;
system[i].push_back(0) ;
}
if ((system[i][0] >= innerCHZ) && (system[i][0] <= outerCHZ)){
float H = 1;
system[i].push_back(H);
}
else system[i].push_back(0); //[4] is habitable marker
}
return system;
}
////////////
////////////
std::vector<std::vector<float>> Time( std::vector<std::vector<float>> system , int n, float dt, int argc, char **argv){
#define ASIZE 3 //Setup
int MPI_Init(int *argc, char ***argv);
int rank, numtasks = n, namelen, rc;
char processor_name[MPI_MAX_PROCESSOR_NAME];
MPI_Status status;
MPI_Init( &argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &numtasks);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Get_processor_name(processor_name, &namelen);
rc = MPI_Bcast(&system, ASIZE, MPI_DOUBLE, 0, MPI_COMM_WORLD); //Master
// Broadcast computed initial values to all other processes
if (rc != MPI_SUCCESS) {
fprintf(stderr, "Oops! An error occurred in MPI_Bcast()\n");
MPI_Abort(MPI_COMM_WORLD, rc);
}
//Slaves
const float pi = 4 * atan(1.0);
const float G = 6.67 * pow(10,-11);
float a_x, a_y;
for (int i = 0 ; i < n; i++) {
if (rank != i){
a_x = G * system[i][2] * (system[i][0]-system[rank][0]) / ((system[i][0]-system[rank][0]) * (system[i][0]-system[rank][0]));
a_y = G * system[i][2] * (system[i][1]-system[rank][1]) / ((system[i][1]-system[rank][1]) * (system[i][1]-system[rank][1]));
}
if (rank == i){
a_x = G * system[i][2] * 100 * system[i][0] / (system[i][0] * system[i][0]);
a_y = G * system[i][2] * 100 * system[i][1] / (system[i][1] * system[i][1]);
}
a_x += a_x;
a_y += a_y;
}
for (int i=0; i < n; i++){
system[i][0] += system[i][5] * dt + 0.5 * a_x * dt * dt;
system[i][1] += system[i][6] * dt + 0.5 * a_y * dt * dt;
system[i][5] += a_x * dt;
system[i][6] += a_y * dt;
}
for(int i=0 ; i<n ; i++){
for(int j=0 ; j<i ; j++){
if (system[j][0] == 0 && system[j][1] == 0){
system.erase(system.begin() + j);
} // crash into star
if (system[j][0] == system[i][0] && system[j][1] == system[i][1]){
system[i][2] += system[j][2];
system.erase(system.begin() + j);
} // planet crash
} //check co-ordinates
} // planet destroy loop
for(int i = 0 ; i < n ; i++){
if (sqrt(system[i][0]*system[i][0] + system[i][1]*system[i][1]) >= 60) system.erase(system.begin() + i);
}
//Send results back to the first process
if (rank != 0){// All processes except the one of rank 0
MPI_Send(&system, 1, MPI_DOUBLE, 0, 1, MPI_COMM_WORLD);
}
else {
for (int j = 1; j < numtasks; j++) {
MPI_Recv(&system, 1, MPI_DOUBLE, MPI_ANY_SOURCE, 1,
MPI_COMM_WORLD, &status);
}
}
MPI_Finalize();
///////////////////////////
//Time advances the solar system.
//Plots the Orbits
//Uses MPI to spread it's calculations.
///////////////////////////
return system;
}
////////////
////////////
std::vector<bool> FinalCheck( std::vector<std::vector<float>> system, std::vector<bool> Water, int n){
///////////////////////////
//Final Checks
//Reports if a Planet spent the whole Time in the Habitable Zone
///////////////////////////
for (int i = 0 ; i < n ; i++){
if (system[i][4] == 1.0) Water.push_back(true);
else Water.push_back(false);
}
return Water;
}
////////////
////////////
int main(int argc, char** argv){
char Class;
float L, R, M, T;
std::tuple< char , float , float , float , float > star( Class , L , R , M , T );
star = Star();
int n = MyRandom()/10 + 1;
std::vector<std::vector <float>> system ;
std::vector<std::vector <float>> system1 ;
system = Planet( L , R , M, T, n);
float G = 6.67 * pow(10,-11), pi = 4 * atan(1.0), dt;
for (int i = 0; i < n; i++){
if (system[i][3] == 1){
dt = 2 * pi * .01 * pow(system[i][0] * 1.5 * pow(10,8), 1.5) / sqrt(G * M * 2 * pow(10,30));
}
system[i].push_back(0.0); //system[i][5] is speed in x-axis
system[i].push_back( sqrt(6.67 * pow(10,-11) * 2 * pow(10,30) * M / system[i][0])); //system[i][6] is speed in y-axis
}
std::ofstream Finder;
std::ofstream Report;
Finder.open("plotdata.dat");
Report.open("report.txt");
Finder << "# Plot Co-ordinates" << std::endl;
for (int i = 0 ; i < 1000 ; i++) {
system1 = Time( system, n , dt , argc, argv);
for (int j=0 ; j<n ; j++){
Finder << "[color " << j << "] " << system[j][0] << " " << system[j][1] << std::endl;
if((system[j][4] == 1.0) && ( (sqrt(system[j][0] * system[j][0] + system[j][1] * system[j][1]) < sqrt(L / 1.1) ) || ((sqrt(system[j][0] * system[j][0] + system[j][1] * system[j][1]) > sqrt(L / 0.53)) ))) system[j][4] = 0.0;
}
system = system1;
}
Finder.close();
int m;
m = system.size()/system[0].size();
std::vector<bool> Water;
Water = FinalCheck( system, Water, n);
//Report
for (int i = 0 ; i < n ; i++){
Report << "Planet " << i << "ends up at" << system[i][0] << " and " << system[i][1] << "has mass " << system[i][2] ;
if (system[i][3] == 1) Report << ", which is the 'Jupiter' of the system." ;
if (system[i][4] == 1) Report << ", which can have liquid water on the surface." ;
}
Report.close();
///////////////////////////
//Report cleans everything up and gives the results
//Shows the plot, lists the Planets
//Reports the Positions and Masses of all Planets
//Reports which was the Jupiter and which if any were Habitable
//////////////////////////
return 0;
}
Any thoughts the gurus here have would be appreciated, especially with getting rid of those -fpermissive errors.
EDIT 1 - Code as presented will now completely compile - but will return a Segmentation fault during the Star routine. After the user inputs the star type but before it actually makes a star as far as I can tell.
Related
Using the formula in the pic, I need to write a program that allows the user to calculate sin(x), cos(x), tan(x). The user should enter the angle in degrees, and then the program should transform it into radians before performing the three requested calculations. For each requested calculation (i.e., sin(x), cos(x), tan(x)), I only need to calculate the first 15 terms of the series.
The problem seems to be in the arrays of the last block in the code, it keeps returning wrong results of the tan(x) series; how can I fix it?
#include <iostream>
using namespace std;
//create a function to convert angles from degrees to radian
double convertToRadian(double deg)
{ //formula : radian = (degree * pi)/180
const double pi = 3.14159265359; //declaring pi's value as a constant
return (deg * (pi / 180)); //returning the radian value
}
//create a function to calculate the exponent/power
double power(double base, unsigned int exp)
{
double result = 1;
for(int i = 0; i < exp; i++){
result = result * base;
}
return result;
}
//create a function to get the factorial of a value
double factorial(int fac)
{
if(fac > 1)
return fac * factorial(fac - 1);
else
return 1;
}
//create a function to print out arrays as we will use it to print the terms in the series
void printTerms(double terms[15])
{ for (int i = 0; i < 15; i++)
{
cout<<terms[i]<<endl;
}
}
int main()
{
double degree; //declare the variables used in the program
double valueOfCos, valueOfSin, valueOfTan; //declare variables for terms of each function
cout << "Enter angle (x) in degrees: " << endl; //prompt for user to enter angle in deg
cin >> degree;
double radian = convertToRadian(degree); //first, converting from degrees to radian
//make an array for the first 15 terms of cos(x):
double cos[15];
//make a loop to insert values in the array
for (int n = 0; n < 15; n++)
{ //type the maclaurin series formula for cos(x):
valueOfCos = (( power(-1 , n)) / (factorial(2*n))) * (power(radian, (2*n)));
cos[n] = valueOfCos;
}
//print out the first 15 terms of cos(x) in the maclaurin series:
cout << "cos(x)= ";
printTerms (cos);
//make an array for the first 15 terms of sin(x):
double sin[15];
for (int n = 0; n < 15; n++)
{
valueOfSin = ((power(-1 , n)) / (factorial((2*n + 1)))) * (power(radian, (2*n + 1)));
sin[n] = valueOfSin;
}
cout << "sin(x)= ";
printTerms (sin);
double tan[15];
for (int n = 0; n < 15; n++)
{ double bernoulli[15] = {(1/6), (-1/30),(1/42), (-1/30), (5/66), (-691/2730),
(7/6), (-3617/510), (43867/798), (-174611/330), (854513/138), (-236364091/2730),
(8553103/6),(-23749461029/870),(8615841276005/14322) };
for (int i = 0; i < 15; i++)
{
double firstNum = 0, secondNum = 0 , thirdNum = 0 , denominator = 0;
firstNum = power(-1 , n);
secondNum = power(2 , 2*n + 2);
thirdNum = ((secondNum) - 1);
denominator = factorial(2*n + 2);
valueOfTan = ((firstNum * secondNum * thirdNum * (bernoulli[i])) / denominator) *
(power(radian, 2*n + 1));
tan [n] = valueOfTan;
}
}
cout << "tan(x)= ";
printTerms (tan);
return 0;
}
This loop : for (int n = 0; n < 15; n++) is not running or entire expression. You'll need to correct something like this :
double bernoulli[15] = {(1/6), (-1/30),(1/42), (-1/30), (5/66), (-691/2730),(7/6), (-3617/510), (43867/798), (-174611/330), (854513/138), (-236364091/2730),(8553103/6),(-23749461029/870),(8615841276005/14322) };
for (int n = 0; n < 15; n++){
double firstNum = 0, secondNum = 0 , thirdNum = 0 , denominator = 0;
firstNum = power(-1 , n);
secondNum = power(2 , 2*n + 2);
thirdNum = ((secondNum) - 1);
denominator = factorial(2*n + 2);
valueOfTan = ((firstNum * secondNum * thirdNum * (bernoulli[n])) / denominator) * (power(radian, 2*n + 1));
tan [n] = valueOfTan;
}
}
You are incorrectly calculating the tan value.
In valueOfTan = ((firstNum * secondNum * thirdNum * (bernoulli[i])) / denominator) * (power(radian, 2 * n + 1));
Instead of bernoulli[i], you need to have bernoulli[2*i+2] as per the formulae.
And one more suggestion please pull the double bernoulli[15] = {(1/6), (-1/30),(1/42), (-1/30), (5/66), (-691/2730), (7/6), (-3617/510), (43867/798), (-174611/330), (854513/138), (-236364091/2730), (8553103/6),(-23749461029/870),(8615841276005/14322) array initialization out of the for loop, as it's constant you don't need to initialize it every time unnecessarily. It will increase your code runtime
Long time Reader, First time Asker.
So I'm working on a coding project of which the long term goal is to make a solar system simulator. The idea is that that it whips up a randomized solar system with a few rules like 'at formation the first planet after the frostline has to be the largest gas giant' etc, and calculates the orbits to check for stability.
Obviously it's not done yet, I'm having some trouble with using the arrays in the subroutines. I know that you can't directly take arrays in and out of functions, but you can take pointers to said arrays in and out of functions if you do it right.
I apparently have not done it right below. I've tried to comment and make the code as readable as possible, here it is.
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <tuple>
#include <vector>
#include <stdio.h>
#include <math.h>
#include <complex>
#include <stdint.h>
#include <time.h>
#include <string.h>
#include <algorithm>
//#include "mpi.h"
using namespace std;
double MyRandom(){
//////////////////////////
//Random Number Generator
//Returns number between 0-99
//////////////////////////
double y = 0;
unsigned seed = time(0);
srand(seed);
uint64_t x = rand();
x ^= x << 13;
x ^= x >> 7;
x ^= x << 17;
x = (1070739 * x) % 2199023255530;
y = x / 21990232555.31 ;
return y;
}
////////////////////////
///////////////////////
tuple< char& , float& , float& , float& , int& > Star(){
////////////////////////////
//Star will generate a Star
//Randomly or User Selected
//Class, Luminosity, Probability, Radius, Mass, Temperature
//Stars always take up 99% of the mass of the system.
///////////////////////////
char Class;
string Choice;
float L, R, M;
int T;
tuple< char& , float& , float& , float& , int& > star( Class = 'i', L = 1 , R = 1 , M = 1 , T = 3000) ;
cout << "Select Star Class (OBAFGKM) or Select R for Random: ";
cin >> Choice;
if ( Choice == "R" ) {
double y;
y = MyRandom();
if (y <= 0.003) Class = 'O';
if ((y > 0.003) && (y <= 0.133)) Class = 'B';
if ((y > 0.133) && (y <= 0.733)) Class = 'A';
if ((y > 0.733) && (y <= 3.733)) Class = 'F';
if ((y > 3.733) && (y <= 11.333)) Class = 'G';
if ((y > 11.333) && (y <= 23.433)) Class = 'K';
else Class = 'M';
}
if (Class == 'O') {
L = 30000;
R = 0.0307;
M = 16;
T = 30000;
}
if (Class == 'B') {
L = 15000;
R = 0.0195;
M = 9;
T = 20000;
}
if (Class == 'A') {
L = 15;
R = 0.00744;
M = 1.7;
T = 8700;
}
if (Class == 'F') {
L = 3.25;
R = 0.00488;
M = 1.2;
T = 6750;
}
if (Class == 'G') {
L = 1;
R = 0.00465;
M = 1;
T = 5700;
}
if (Class == 'K') {
L = 0.34;
R = 0.00356;
M = 0.62;
T = 4450;
}
if (Class == 'M') {
L = 0.08;
R = 0.00326;
M = 0.26;
T = 3000;
}
return star;
}
////////////
////////////
float* Planet( float &L, float &R, float &M, int &T, int &n){
///////////////////////////
//Planet generates the Planets
//Random 1 - 10, Random distribution 0.06 - 6 JAU unless specified by User
//Frost line Calculated, First Planet after Frost line is the Jupiter
//The Jupiter will have the most mass of all Jovian worlds
//Otherwise divided into Jovian and Terrestrial Worlds, Random Masses within groups
//Also calculates if a planet is in the Habitable Zone
////////////////////////////
float frostline, innerCHZ, outerCHZ;
float a = 0.06; // a - albedo
float m = M / 100; //Mass of the Jupiter always 1/100th mass of the Star.
float sys[n];
float* system[n][5] = {{0}};
for (int i = 0 ; i < n ; i++){
sys[i] = MyRandom()/10 * 3; //Distances in terms of Sol AU
}
sort(sys, sys + n );
for (int i = 0 ; i < n ; i++){
system[i][0] = &sys[i];
system[i][1] = 0; //system[i][0] is x, system[i][1] is y
}
frostline = (0.6 * T / 150) * (0.6 * T/150) * R / sqrt(1 - a);
innerCHZ = sqrt(L / 1.1);
outerCHZ = sqrt(L / 0.53);
for (int i = 0 ; i < n ; i++){
if (system[i][0] <= &frostline) {
float tmass = m * 0.0003 * MyRandom();
system[i][2] = &tmass ; //system[i][2] is mass, [3] is marker for the Jupter
system[i][3] = 0 ;
}
if ((system[i][0] >= &frostline) && (system[i-1][0] < &frostline)){
system[i][2] = &m ;
float J = 1;
system[i][3] = &J ;
}
if ((system[i][0] >= &frostline) && (system[i-1][0] >= &frostline)) {
float jmass = m * 0.01 * MyRandom();
system[i][2] = &jmass ;
system[i][3] = 0 ;
}
if ((system[i][0] >= &innerCHZ) && (system[i][0] <= &outerCHZ)){
float H = 1;
system[i][4] = &H;
}
else system[i][4] = 0; //[4] is habitable marker
}
return system[n][5];
}
////////////
////////////
float* Time( float *system , int n){
///////////////////////////
//Time advances the solar system.
//Plots the Orbits
//Uses MPI to spread it's calculations.
///////////////////////////
return system;
}
////////////
////////////
void FinalCheck( float system){
///////////////////////////
//Final Checks
//Reports if a Planet spent the whole Time in the Habitable Zone
///////////////////////////
/*for (int i = 0 ; i < row ; i++){
if (system[i][4] == 1.0) {
cout << "Planet " << i << " in this system is Habitable." ;
}
// The Habitable stat only means liquid water can exist on the surface
// Add pi if planet enters habitable zone, minus 1 if it leaves.
// If planet was habitable but left, assuming all life was destroyed
}
*/
}
////////////
int main(){
char Class;
int T;
float L, R, M;
tuple< char , float , float , float , int > star( Class , L , R , M , T );
star = Star();
int n = MyRandom()/10 + 1;
float * system[n][5] = {{0}};
float system1[n][5] = {{0}};
system[n][5] = Planet( L , R , M, T, n);
for (int i = 0 ; i < 100 ; i++) {
system1[n][5] = Time( *system, n );
system[n][5] = &system1[n][5];
}
FinalCheck( *system[n][5]);
///////////////////////////
//Report cleans everything up and gives the results
//Shows the plot, lists the Planets
//Reports the Positions and Masses of all Planets
//Reports which was the Jupiter and which if any were Habitable
//////////////////////////
return 0;
}
The problem is when I run a compiler over this line 227 gets flagged -
system1[n][5] = Time( *system, n );
With the following error:
error: cannot convert 'float**' to 'float*' for argument '1' to 'float* Time(float*, int)
I get that this means that the compiler things I'm trying to equate a pointer-to-a-pointer with a pointer, but I'm not sure how it arrived at that conclusion or how to fix it. I'd appreciate help with this, especially the second part. I also would love to hear anything about passing arrays through subroutines as apparently I'm not doing it right, or at least not well.
Update 1 : - Got the short-term fix in and the compiler makes it through but gives a segmentation fault (core dumped) error when I try to run it. Looks like I have some reading and updates to do though with the namespace, the pointers, and possibly changing the arrays into vectors instead. Feels like if I concentrate on those first it might fix the segmentation error.
Your variable system is declared as
float * system[n][5] = {{0}};
which is a pointer to a 2D array (which will decay to float*** when passed to a function).
Your Time function is declared as
float* Time( float *system , int n);
where the 1st argument needs to be a float*.
That means this call
system1[n][5] = Time( *system, n );
should actually be something like
system1[n][5] = Time( **system, n );
That being said, there are a number of issues in your code.
To start off, don't do using namespace std;.
Also, this line float sys[n]; is not allowed. You can't have variable length arrays in c++.
float* system[n][5]
system here is a 2D array of float*s, not floats.
So, in other words, system decays to float***, *system decays to float**, **system decays to float*, and ***system decays to float.
So, the compiler is correct. You're passing what decays to a float** to Time() which expects a float*.
You're going to have to reconfigure your code to pass the right thing, whatever that is.
Side note: please be advised that the way you're creating arrays isn't valid C++ and may cause issues later.
I try to implement A* algorithm with both manhattan distance and manhattan distance + linear conflict heuristic.
but my manhattan distance works much better and I can't understand why!
manhattan distance + linear conflict in my algorithm expands much more node and i found that it's answer it not even optimal.
#include <iostream>
#include <time.h>
#include <fstream>
#include <set>
#include <vector>
#include <queue>
#include <map>
#include "node.h"
using namespace std;
const int n = 4;
const int hash_base = 23;
const long long hash_mod = 9827870924701019;
set<long long> explored;
set<pair<int , node*> > frontier;
map<string,int> database[3];
void check(int* state){
for(int j = 0 ; j < n ; j++){
for(int i = 0 ; i < n ; i++)
cerr << state[j * n + i] << " ";
cerr << endl;
}
cerr << endl;
}
bool goal_test(int* state){
if(state[n * n - 1] != 0) return 0;
for(int i = 0 ; i < (n * n - 1) ; i++){
if(state[i] != i + 1)
return 0;
}
return 1;
}
vector<node> solution(node* v){
vector<node> ans;
while((v->parent)->hash != v->hash){
ans.push_back(*v);
v = v->parent;
}
return ans;
}
//first heuristic
int manhattanDistance(int* state){
int md = 0;
for(int i = 0 ; i < (n * n) ; i++){
if(state[i] == 0) continue;
//what is the goal row and column of this tile
int gr = (state[i] - 1) / n , gc = (state[i] - 1) % n;
//what is the row and column of this tile
int r = i / n , c = i % n;
md += (max(gr - r , r - gr) + max(gc - c , c - gc));
}
return md;
}
//second heuristic
int linearConflict(int* state){
int lc = 0;
for(int i = 0 ; i < n ; i++){
for(int j = 0 ; j < n ; j++){
//jth tile in ith row = (i * n + j)th in state
int la = i * n + j;
if(state[la] == 0 || (state[la] / n) != i)
continue;
for(int k = j + 1 ; k < n ; k++){
//kth tile in ith row = (i * n + k)th in state
int lb = i * n + k;
if(state[lb] == 0 || (state[lb] / n) != i)
continue;
if(state[la] > state[lb])
lc++;
}
}
}
for(int i = 0 ; i < n ; i++){
for(int j = 0 ; j < n ; j++){
//j the tile of i th column
int la = j * 4 + i;
if(state[la] == 0 || (state[la] % n) != i)
continue;
for(int k = j + 1 ; k < n ; k++){
int lb = k * 4 + i;
if(state[lb] == 0 || (state[lb] % n) != i)
continue;
if(state[la] > state[lb])
lc++;
}
}
}
return lc * 2;
}
long long make_hash(int* v){
long long power = 1LL;
long long hash = 0 * 1LL;
for(int i = 0 ; i < (n * n) ; i++){
hash += (power * v[i] * 1LL) % hash_mod;
hash %= hash_mod;
power = (hash_base * power * 1LL) % hash_mod;
}
return hash;
}
vector<node> successor(node* parent){
vector<node> child;
int parent_empty = parent->empty_cell;
//the row and column of empty cell
int r = parent_empty / n , c = parent_empty % n;
//empty cell go down
if(r + 1 < n){
struct node down;
for(int i = 0 ; i < (n*n) ; i++)
down.state[i] = parent->state[i];
down.state[parent_empty] = parent->state[parent_empty + n];
down.state[parent_empty + n] = 0;
down.hash = make_hash(down.state);
down.empty_cell = parent_empty + n;
down.cost = parent->cost + 1;
down.parent = parent;
//first heuristic -> manhattan Distance
// down.heuristic = manhattanDistance(down.state);
//second heuristic -> manhattan distance + linear conflict
down.heuristic = linearConflict(down.state) + manhattanDistance(down.state);
//third heuristic -> disjoint pattern database
// down.heuristic = DisjointPatternDB(down.state);
child.push_back(down);
}
//empty cell go up
if(r - 1 >= 0){
struct node up;
for(int i = 0 ; i < n * n ; i++)
up.state[i] = parent->state[i];
up.state[parent_empty] = parent->state[parent_empty - n];
up.state[parent_empty - n] = 0;
up.empty_cell = parent_empty - n;
up.hash = make_hash(up.state);
up.cost = parent->cost + 1;
up.parent = parent;
//first heuristic -> manhattan Distance
// up.heuristic = manhattanDistance(up.state);
//second heuristic -> manhattan distance + linear conflict
up.heuristic = linearConflict(up.state) + manhattanDistance(up.state);
//third heuristic -> disjoint pattern database
// up.heuristic = DisjointPatternDB(up.state);
child.push_back(up);
}
//empty cell going right
if(c + 1 < n){
struct node right;
for(int i = 0 ; i < (n * n) ; i++)
right.state[i] = parent->state[i];
right.state[parent_empty] = parent->state[parent_empty + 1];
right.state[parent_empty + 1] = 0;
right.empty_cell = parent_empty + 1;
right.hash = make_hash(right.state);
right.cost = parent->cost + 1;
right.parent = parent;
//first heuristic -> manhattan Distance
// right.heuristic = manhattanDistance(right.state);
//second heuristic -> manhattan distance + linear conflict
right.heuristic = linearConflict(right.state) + manhattanDistance(right.state);
//third heuristic -> disjoint pattern database
// right.heuristic = DisjointPatternDB(right.state);
child.push_back(right);
}
//empty cell going left
if(c - 1 >= 0){
struct node left;
for (int i = 0; i < (n * n) ; i++)
left.state[i] = parent->state[i];
left.state[parent_empty] = parent->state[parent_empty - 1];
left.state[parent_empty - 1] = 0;
left.empty_cell = parent_empty - 1;
left.hash = make_hash(left.state);
left.cost = parent->cost + 1;
left.parent = parent;
//first heuristic -> manhattan Distance
// left.heuristic = manhattanDistance(left.state);
//second heuristic -> manhattan distance + linear conflict
left.heuristic = linearConflict(left.state) + manhattanDistance(left.state);
//third heuristic -> disjoint pattern database
// left.heuristic = DisjointPatternDB(left.state);
child.push_back(left);
}
return child;
}
node* nodeCopy(node child){
node* tmp = new node;
for(int i = 0 ; i < n * n; i++)
tmp->state[i] = child.state[i];
tmp->hash = child.hash;
tmp->empty_cell = child.empty_cell;
tmp->cost = child.cost;
tmp->parent = child.parent;
tmp->heuristic = child.heuristic;
return tmp;
}
vector<node> Astar(node* initNode){
if(goal_test(initNode->state)) return solution(initNode);
frontier.insert(make_pair(initNode->cost + initNode-> heuristic ,initNode));
explored.insert(initNode->hash);
while(!frontier.empty()){
node* v = (*frontier.begin()).second;
if(goal_test(v->state)) return solution(v);
frontier.erase(frontier.begin());
vector<node> childs = successor(v);
for(node child: childs){
if(explored.find(child.hash) == explored.end()){
node* tmp = nodeCopy(child);
frontier.insert(make_pair((child.cost + child.heuristic) , tmp));
explored.insert(child.hash);
}
}
}
return solution(initNode);
}
int main(){
clock_t tStart = clock();
printf("Time taken: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC);
struct node init;// {{1 , 2 , 3 , 4 , 5, 6, 7, 8, 0} , 1 , 9 , 0 , &init , 0};
for(int i = 0 ; i < (n * n) ; i++){
cin >> init.state[i];
if(init.state[i] == 0)
init.empty_cell = i;
}
init.hash = make_hash(init.state);
init.cost = 0;
init.parent = &init;
init.heuristic = manhattanDistance(init.state) ;//+ linearConflict(init.state);
vector <node> ans = Astar(&init);
//cout << 1 << " ";
for(int j = 0 ; j < n * n ; j++){
if(j == n * n - 1) cout << init.state[j];
else cout << init.state[j] << ",";
}
cout << endl;
for(int i = (ans.size() - 1) ; i >= 0 ; i--){
//cout << (ans.size() - i + 1) << " ";
cerr << linearConflict(ans[i].state) << endl;
for(int j = 0 ; j < n * n ; j++){
if(j == n * n - 1) cout << ans[i].state[j];
else cout << ans[i].state[j] << ",";
}
cout << endl;
}
cout << "path size : " << ans.size() << endl;
cout << "number of node expanded : " << explored.size() << endl;
printf("Time taken: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC);
}
#include <vector>
using namespace std;
struct node{
int state[16];
long long hash;
int empty_cell;
long cost;
node* parent;
int heuristic;
};
If its answer is not optimal it is because your heuristic is not admissible.
This means that sometimes it is overestimating the cost to reach a node in your graph.
linear conflicts heuristic should always be coupled with a distance estimated heuristic like Manhattan and it is not as simple as giving twice the number of linear conflicts in each row / column.
See Linear Conflict violating admissibility and driving me insane
and
https://cse.sc.edu/~mgv/csce580sp15/gradPres/HanssonMayerYung1992.pdf
I am trying to integrate functions, which includes changing of variables with ICDF function (gsl_cdf_gaussian_Pinv(x[1], 1)), but the results are always wrong:
#include <fstream>
#include <iostream>
#include <memory>
#include <cmath>
#include <iomanip>
#include <ctime>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <math.h>
#include <stdio.h>
#include <gaussinv.c>
#define _USE_MATH_DEFINES
using namespace std;
double f(double[], int);
double int_mcnd(double(*)(double[], int), double[], double[], int, int);
double varr[100];
int k = 0;
double hj = 0;
double mj = 1;
# include "sobol.hpp"
int DIM_NUM = 10;
int main() {
const int n = 10; /* define how many integrals */
// const int m = 1000000; /* define how many points */
double a[n] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; /* left end-points */
double b[n] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}; /* right end-points */
double result;
int i, m;
int ntimes;
cout.setf(ios::fixed | ios::showpoint);
// current time in seconds (begin calculations)
time_t seconds_i;
seconds_i = time(NULL);
m = 1; // initial number of intervals
ntimes = 20; // number of interval doublings with nmax=2^ntimes
cout << setw(12) << n << "D Integral" << endl;
for (i = 0; i <= ntimes; i = i + 1) {
result = int_mcnd(f, a, b, n, m);
cout << setw(10) << m << " " << setprecision(30) << result << endl;
m = m * 2;
}
// current time in seconds (end of calculations)
time_t seconds_f;
seconds_f = time(NULL);
cout << endl << "total elapsed time = " << seconds_f - seconds_i << " seconds" << endl << endl;
return 0;
}
double f(double x[], int n) {
double y;
int j;
y = 0.0;
/* define Multidimensional Gaussian distribution and covariance */
/* X=(x1, k=2, mu = (0, covariance matrix = (v 0 0 0
* x2 0 0 v 0 0
* x3 0 0 0 v 0
* x4) 0) 0 0 0 v) */
double v = 1;
double determinant = pow(v, 10);
double inverse = 1 / v;
double rang = gsl_cdf_gaussian_Pinv(0.99999904632568359375, 1) - gsl_cdf_gaussian_Pinv(0.00000095367431640625, 1) +
gsl_cdf_gaussian_Pinv(0.00000095367431640625, 1);
y = (1 / sqrt(pow(2 * M_PI, 10) * determinant) * exp(-0.5 * (inverse * pow(gsl_cdf_gaussian_Pinv(x[0], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[1], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[2], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[3], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[4], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[5], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[6], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[7], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[8], 1), 2) +
inverse * pow(gsl_cdf_gaussian_Pinv(x[9], 1), 2))));
return y;
}
/*==============================================================
input:
fn - a multiple argument real function (supplied by the user)
a[] - left end-points of the interval of integration
b[] - right end-points of the interval of integration
n - dimension of integral
m - number of random points
output:
r - result of integration
================================================================*/
double int_mcnd(double(*fn)(double[], int), double a[], double b[], int n, int m) {
double r, x[n], p;
int i, j;
double rarr[DIM_NUM];
long long int seed;
seed = 1;
long long int seed_in;
long long int seed_out;
srand(time(NULL)); /* initial seed value (use system time) */
r = 0.0;
p = 1.0;
// step 1: calculate the common factor p
for (j = 0; j < n; j = j + 1) {
// p = p * (b[j] - a[j]);
p=p*(gsl_cdf_gaussian_Pinv(0.99999904632568359375, 1)-gsl_cdf_gaussian_Pinv(0.00000095367431640625, 1));
}
// step 2: integration
for (i = 1; i <= m; i = i + 1) {
seed_in = seed;
i8_sobol(DIM_NUM, &seed, rarr);
seed_out = seed;
// calculate random x[] points
for (j = 0; j < n; j = j + 1) {
x[j] = a[j] + (b[j] - a[j]) * rarr[j];
}
r = r + fn(x, n);
}
cout << endl << "p = " << p << " seconds" << endl << endl;
r = r * p / m;
return r;
}
The problem is in the parametrization parameter p, which I suggest to be
p=p*(gsl_cdf_gaussian_Pinv(0.99999904632568359375, 1)-gsl_cdf_gaussian_Pinv(0.00000095367431640625, 1))
instead of standard - p = p * (b[j] - a[j]);
I want to integrate not only within [0,1]^N intervals, but also in [-20;20].
I can't define my mistake. Can somebody help, please?
I am having trouble explaining/understanding the following phenomenon:
To test fftw3 i am using the 2d poisson test case:
laplacian(f(x,y)) = - g(x,y) with periodic boundary conditions.
After applying the fourier transform to the equation we obtain : F(kx,ky) = G(kx,ky) /(kx² + ky²) (1)
if i take g(x,y) = sin (x) + sin(y) , (x,y) \in [0,2 \pi] i have immediately f(x,y) = g(x,y)
which is what i am trying to obtain with the fft :
i compute G from g with a forward Fourier transform
From this i can compute the Fourier transform of f with (1).
Finally, i compute f with the backward Fourier transform (without forgetting to normalize by 1/(nx*ny)).
In practice, the results are pretty bad?
(For instance, the amplitude for N = 256 is twice the amplitude obtained with N = 512)
Even worse, if i try g(x,y) = sin(x)*sin(y) , the curve has not even the same form of the solution.
(note that i must change the equation; i divide by two the laplacian in this case : (1) becomes F(kx,ky) = 2*G(kx,ky)/(kx²+ky²)
Here is the code:
/*
* fftw test -- double precision
*/
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <fftw3.h>
using namespace std;
int main()
{
int N = 128;
int i, j ;
double pi = 3.14159265359;
double *X, *Y ;
X = (double*) malloc(N*sizeof(double));
Y = (double*) malloc(N*sizeof(double));
fftw_complex *out1, *in2, *out2, *in1;
fftw_plan p1, p2;
double L = 2.*pi;
double dx = L/(N - 1);
in1 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
out2 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
out1 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
in2 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
p1 = fftw_plan_dft_2d(N, N, in1, out1, FFTW_FORWARD,FFTW_MEASURE );
p2 = fftw_plan_dft_2d(N, N, in2, out2, FFTW_BACKWARD,FFTW_MEASURE);
for(i = 0; i < N; i++){
X[i] = -pi + i*dx ;
for(j = 0; j < N; j++){
Y[j] = -pi + j*dx ;
in1[i*N + j][0] = sin(X[i]) + sin(Y[j]) ; // row major ordering
//in1[i*N + j][0] = sin(X[i]) * sin(Y[j]) ; // 2nd test case
in1[i*N + j][1] = 0 ;
}
}
fftw_execute(p1); // FFT forward
for ( i = 0; i < N; i++){ // f = g / ( kx² + ky² )
for( j = 0; j < N; j++){
in2[i*N + j][0] = out1[i*N + j][0]/ (i*i+j*j+1e-16);
in2[i*N + j][1] = out1[i*N + j][1]/ (i*i+j*j+1e-16);
//in2[i*N + j][0] = 2*out1[i*N + j][0]/ (i*i+j*j+1e-16); // 2nd test case
//in2[i*N + j][1] = 2*out1[i*N + j][1]/ (i*i+j*j+1e-16);
}
}
fftw_execute(p2); //FFT backward
// checking the results computed
double erl1 = 0.;
for ( i = 0; i < N; i++) {
for( j = 0; j < N; j++){
erl1 += fabs( in1[i*N + j][0] - out2[i*N + j][0]/N/N )*dx*dx;
cout<< i <<" "<< j<<" "<< sin(X[i])+sin(Y[j])<<" "<< out2[i*N+j][0]/N/N <<" "<< endl; // > output
}
}
cout<< erl1 << endl ; // L1 error
fftw_destroy_plan(p1);
fftw_destroy_plan(p2);
fftw_free(out1);
fftw_free(out2);
fftw_free(in1);
fftw_free(in2);
return 0;
}
I can't find any (more) mistakes in my code (i installed the fftw3 library last week) and i don't see a problem with the maths either but i don't think it's the fft's fault. Hence my predicament. I am all out of ideas and all out of google as well.
Any help solving this puzzle would be greatly appreciated.
note :
compiling : g++ test.cpp -lfftw3 -lm
executing : ./a.out > output
and i use gnuplot in order to plot the curves :
(in gnuplot ) splot "output" u 1:2:4 ( for the computed solution )
Here are some little points to be modified :
You need to account for all small frequencies, including the negative ones ! Index i corresponds to the frequency 2PI i/N but also to the frequency 2PI (i-N)/N. In the Fourier space, the end of the array matters as much as the beginning ! In our case, we keep the smallest frequency : it's 2PI i/N for the first half of the array, and 2PI(i-N)/N on the second half.
Of course, as Paul said, N-1 should be Nin double dx = L/(N - 1); => double dx = L/(N ); N-1 does not correspond to a continious periodic signal. It woud be hard to use it as a test case...
Scaling...I did it empirically
The result i obtain is closer to the expected one, for both cases. Here is the code :
/*
* fftw test -- double precision
*/
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <fftw3.h>
using namespace std;
int main()
{
int N = 128;
int i, j ;
double pi = 3.14159265359;
double *X, *Y ;
X = (double*) malloc(N*sizeof(double));
Y = (double*) malloc(N*sizeof(double));
fftw_complex *out1, *in2, *out2, *in1;
fftw_plan p1, p2;
double L = 2.*pi;
double dx = L/(N );
in1 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
out2 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
out1 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
in2 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*(N*N) );
p1 = fftw_plan_dft_2d(N, N, in1, out1, FFTW_FORWARD,FFTW_MEASURE );
p2 = fftw_plan_dft_2d(N, N, in2, out2, FFTW_BACKWARD,FFTW_MEASURE);
for(i = 0; i < N; i++){
X[i] = -pi + i*dx ;
for(j = 0; j < N; j++){
Y[j] = -pi + j*dx ;
in1[i*N + j][0] = sin(X[i]) + sin(Y[j]) ; // row major ordering
// in1[i*N + j][0] = sin(X[i]) * sin(Y[j]) ; // 2nd test case
in1[i*N + j][1] = 0 ;
}
}
fftw_execute(p1); // FFT forward
for ( i = 0; i < N; i++){ // f = g / ( kx² + ky² )
for( j = 0; j < N; j++){
double fact=0;
in2[i*N + j][0]=0;
in2[i*N + j][1]=0;
if(2*i<N){
fact=((double)i*i);
}else{
fact=((double)(N-i)*(N-i));
}
if(2*j<N){
fact+=((double)j*j);
}else{
fact+=((double)(N-j)*(N-j));
}
if(fact!=0){
in2[i*N + j][0] = out1[i*N + j][0]/fact;
in2[i*N + j][1] = out1[i*N + j][1]/fact;
}else{
in2[i*N + j][0] = 0;
in2[i*N + j][1] = 0;
}
//in2[i*N + j][0] = out1[i*N + j][0];
//in2[i*N + j][1] = out1[i*N + j][1];
// in2[i*N + j][0] = out1[i*N + j][0]*(1.0/(i*i+1e-16)+1.0/(j*j+1e-16)+1.0/((N-i)*(N-i)+1e-16)+1.0/((N-j)*(N-j)+1e-16))*N*N;
// in2[i*N + j][1] = out1[i*N + j][1]*(1.0/(i*i+1e-16)+1.0/(j*j+1e-16)+1.0/((N-i)*(N-i)+1e-16)+1.0/((N-j)*(N-j)+1e-16))*N*N;
//in2[i*N + j][0] = 2*out1[i*N + j][0]/ (i*i+j*j+1e-16); // 2nd test case
//in2[i*N + j][1] = 2*out1[i*N + j][1]/ (i*i+j*j+1e-16);
}
}
fftw_execute(p2); //FFT backward
// checking the results computed
double erl1 = 0.;
for ( i = 0; i < N; i++) {
for( j = 0; j < N; j++){
erl1 += fabs( in1[i*N + j][0] - out2[i*N + j][0]/(N*N))*dx*dx;
cout<< i <<" "<< j<<" "<< sin(X[i])+sin(Y[j])<<" "<< out2[i*N+j][0]/(N*N) <<" "<< endl; // > output
// cout<< i <<" "<< j<<" "<< sin(X[i])*sin(Y[j])<<" "<< out2[i*N+j][0]/(N*N) <<" "<< endl; // > output
}
}
cout<< erl1 << endl ; // L1 error
fftw_destroy_plan(p1);
fftw_destroy_plan(p2);
fftw_free(out1);
fftw_free(out2);
fftw_free(in1);
fftw_free(in2);
return 0;
}
This code is far from being perfect, it is neither optimized nor beautiful. But it gives almost what is expected.
Bye,