dT/dt=(1.344-1.025T)/h (1)
dh/dt=0.025-(3.5*10^-4)*sqrt(h) (2)
h(0)=1
T(0)=1
I have to solve this system of equations in fortran. I solved the problem in matlab but I dont know fortran programming so guys if somebody can help me or somebody have the fortran code for this help me please please please
thanks a lot
Try it with Euler integration. Do something simple first. You have one advantage: you've solved this once, so you know what the answer looks like when you get it.
Since the moderators are insisting this is a low quality answer because of the short length, I'll provide a working one in Java that should spark some thoughts for you. I used the Apache Commons math library; it has several different ODE integration schemes, including Euler and Runge Kutta.
I ran this on a Windows 7 machine using JDK 8. You can switch between Euler and Runge-Kutta using the command line:
package math.ode;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math3.ode.FirstOrderIntegrator;
import org.apache.commons.math3.ode.nonstiff.ClassicalRungeKuttaIntegrator;
import org.apache.commons.math3.ode.nonstiff.EulerIntegrator;
/**
* IntegrationExample solves coupled ODEs using Euler and Runge Kutta
* Created by Michael
* Creation date 12/20/2015.
* #link https://stackoverflow.com/questions/20065521/dependencies-for-jama-in-maven
*/
public class IntegrationExample {
public static final double DEFAULT_STEP_SIZE = 0.001;
private static final double DEFAULT_MAX_TIME = 2.0;
public static void main(String[] args) {
// Problem set up
double step = (args.length > 0) ? Double.valueOf(args[0]) : DEFAULT_STEP_SIZE;
double maxTime = (args.length > 1) ? Double.valueOf(args[1]) : DEFAULT_MAX_TIME;
String integratorName = (args.length > 2) ? args[2] : "euler";
// Choose different integration schemes here.
FirstOrderIntegrator firstOrderIntegrator = getFirstOrderIntegrator(step, integratorName);
// Equations to solve here; see class below
FirstOrderDifferentialEquations odes = new CoupledOdes();
double [] y = ((CoupledOdes) odes).getInitialConditions();
double t = 0.0;
int i = 0;
while (t <= maxTime) {
System.out.println(String.format("%5d %10.6f %10.6f %10.6f", i, t, y[0], y[1]));
firstOrderIntegrator.integrate(odes, t, y, t+step, y);
t += step;
++i;
}
}
private static FirstOrderIntegrator getFirstOrderIntegrator(double step, String integratorName) {
FirstOrderIntegrator firstOrderIntegrator;
if ("runge-kutta".equalsIgnoreCase(integratorName)) {
firstOrderIntegrator = new ClassicalRungeKuttaIntegrator(step);
} else {
firstOrderIntegrator = new EulerIntegrator(step);
}
return firstOrderIntegrator;
}
}
class CoupledOdes implements FirstOrderDifferentialEquations {
public double [] getInitialConditions() {
return new double [] { 1.0, 1.0 };
}
#Override
public int getDimension() {
return 2;
}
#Override
public void computeDerivatives(double t, double[] y, double[] yDot) throws MaxCountExceededException, DimensionMismatchException {
yDot[0] = (1.344-1.025*y[0])/y[1];
yDot[1] = 0.025-3.5e-4*Math.sqrt(y[1]);
}
}
You didn't say how far out you needed to integrate in time, so I assumed 2.0 as the max time. You can change this on the command line, too.
Here's the plot of results versus time from Excel. As you can see, the responses are smooth and well behaved. Euler has no problem with systems of equations like this.
Related
I am working on training an agents thanks to ml-agents with Unity. When I changed the number of stacked vector, the observation vectors and the hyperparameters I can not resume the training from the last training because tensorflow tells me there is a problem for the lhs rhs shape that are not the same.
I would like to be able to change the agent scripts and config scripts and resume the training with this new parameters not to loose the past progress the agent made...Because for the moment I must restart a new training or not change the number of observations vectors etc.
How to do so ?
Thank you very much.
EDIT : Here an example of what I want to test and what errors I got with RollerBall ML-agents tutorial. See here https://github.com/Unity-Technologies/ml-agents/blob/master/docs/Learning-Environment-Create-New.md
GOAL : I want to see the impact of the observations vector choice on the agent's training.
I ran a learning with the basic script for the agent given in the tutorial. Here it is :
using System.Collections.Generic;
using UnityEngine;
using Unity.MLAgents;
using Unity.MLAgents.Sensors;
public class RollerAgent : Agent
{
Rigidbody rBody;
void Start()
{
rBody = GetComponent();
}
public Transform Target;
public override void OnEpisodeBegin()
{
if (this.transform.localPosition.y < 0)
{
// If the Agent fell, zero its momentum
this.rBody.angularVelocity = Vector3.zero;
this.rBody.velocity = Vector3.zero;
this.transform.localPosition = new Vector3(0, 0.5f, 0);
}
// Move the target to a new spot
Target.localPosition = new Vector3(Random.value * 8 - 4,
0.5f,
Random.value * 8 - 4);
}
public override void CollectObservations(VectorSensor sensor)
{
// Target and Agent positions
sensor.AddObservation(Target.localPosition);
sensor.AddObservation(this.transform.localPosition);
// Agent velocity
sensor.AddObservation(rBody.velocity.x);
sensor.AddObservation(rBody.velocity.z);
}
public float speed = 10;
public override void OnActionReceived(float[] vectorAction)
{
// Actions, size = 2
Vector3 controlSignal = Vector3.zero;
controlSignal.x = vectorAction[0];
controlSignal.z = vectorAction[1];
rBody.AddForce(controlSignal * speed);
// Rewards
float distanceToTarget = Vector3.Distance(this.transform.localPosition, Target.localPosition);
// Reached target
if (distanceToTarget < 1.42f)
{
SetReward(1.0f);
EndEpisode();
}
// Fell off platform
if (this.transform.localPosition.y < 0)
{
EndEpisode();
}
}
public override void Heuristic(float[] actionsOut)
{
actionsOut[0] = Input.GetAxis("Horizontal");
actionsOut[1] = Input.GetAxis("Vertical");
}
}
I stopped the training before the agent hit the benchmark.
I suppressed the observation vectors concerning the velocity observation of the agent and adjusted the number of observation vector in unity from 8 to 6. Here is the new code :
using System.Collections.Generic;
using UnityEngine;
using Unity.MLAgents;
using Unity.MLAgents.Sensors;
public class RollerAgent : Agent
{
Rigidbody rBody;
void Start()
{
rBody = GetComponent();
}
public Transform Target;
public override void OnEpisodeBegin()
{
if (this.transform.localPosition.y < 0)
{
// If the Agent fell, zero its momentum
this.rBody.angularVelocity = Vector3.zero;
this.rBody.velocity = Vector3.zero;
this.transform.localPosition = new Vector3(0, 0.5f, 0);
}
// Move the target to a new spot
Target.localPosition = new Vector3(Random.value * 8 - 4,
0.5f,
Random.value * 8 - 4);
}
public override void CollectObservations(VectorSensor sensor)
{
// Target and Agent positions
sensor.AddObservation(Target.localPosition);
sensor.AddObservation(this.transform.localPosition);
// Agent velocity
//sensor.AddObservation(rBody.velocity.x);
//sensor.AddObservation(rBody.velocity.z);
}
public float speed = 10;
public override void OnActionReceived(float[] vectorAction)
{
// Actions, size = 2
Vector3 controlSignal = Vector3.zero;
controlSignal.x = vectorAction[0];
controlSignal.z = vectorAction[1];
rBody.AddForce(controlSignal * speed);
// Rewards
float distanceToTarget = Vector3.Distance(this.transform.localPosition, Target.localPosition);
// Reached target
if (distanceToTarget < 1.42f)
{
SetReward(1.0f);
EndEpisode();
}
// Fell off platform
if (this.transform.localPosition.y < 0)
{
EndEpisode();
}
}
public override void Heuristic(float[] actionsOut)
{
actionsOut[0] = Input.GetAxis("Horizontal");
actionsOut[1] = Input.GetAxis("Vertical");
}
}
I ran again with the same ID and I RESUMED the training so as to keep the advancement made during the last training. But when I pressed the play button on the Unity editor I got this error :
tensorflow.python.framework.errors_impl.InvalidArgumentError:
Restoring from checkpoint failed. This is most likely due to a
mismatch between the current graph and the graph from the checkpoint.
Please ensure that you have not altered the graph expected based on
the checkpoint. Original error:
Assign requires shapes of both tensors to match. lhs shape= [6,128]
rhs shape= [8,128]
[[node save_1/Assign_26 (defined at c:\users\jeann\anaconda3\envs\ml-agents-1.0.2\lib\site-packages\mlagents\trainers\policy\tf_policy.py:115)
]]
Errors may have originated from an input operation.
I know that it makes non-sense to use the advancement of the last training whereas I use a new brain configuration for the agent, but in the project I am currently working on, I need to keep the improvement made by the agent before even if we change the observation vectors. Is there a way to do so or it is impossible ?
Thank you :)
recently working on a task and I encountered a problem which I am stuck on, the matter is with switch statement as follows:
private static final Double FIRST_HOUR_COST = 1.0;
private static final Double SECOND_HOUR_COST = 2.0;
private static final Double CONVERSION_RATE = 1.5
#Override
public double calculateReservationCost(Reservation reservation)
{
int hours = DateUtils.hoursDifference(reservation.getStartTime(), reservation.getStopTime()) + 1;
switch(hours)
{
case 1:
return FIRST_HOUR_COST;
case 2:
return FIRST_HOUR_COST + SECOND_HOUR_COST;
default:
return FIRST_HOUR_COST +
SECOND_HOUR_COST +
countEachNextHour(SECOND_HOUR_COST, 2, hours);
}
}
I tried probably every solution I could find on stack but wasn't able to adjust it to my needs (map with functions as values, single equation etc). Hoping there is any other way to replace it in an efficient way without breaking any OOP rules.
I would replace the Switch Statement with the Strategy pattern. This will allow you to add new strategies in the future without having a long switch statement.
I have a situation where I want to execute some methods in different threads but want to pass the result of one thread to another. I have following methods in my class.
public static int addition(int a, int b){
System.out.println((a+b));
return (a+b);
}
public static int subtract(int a, int b){
System.out.println((a-b));
return (a-b);
}
public static int multiply(int a, int b){
System.out.println((a*b));
return (a*b);
}
public static String convert(Integer a){
System.out.println((a));
return a.toString();
}
here is main method:
public static void main(String[] args) {
int a = 10;
int b = 5;
CompletableFuture<String> cf = new CompletableFuture<>();
cf.supplyAsync(() -> addition(a, b))
.thenApply(r ->subtract(20,r)
.thenApply(r1 ->multiply(r1, 10))
.thenApply(r2 ->convert(r2))
.thenApply(finalResult ->{
System.out.println(cf.complete(finalResult));
}));
System.out.println(cf.complete("Done"));
}
I am trying to pass result of addition to subtraction to multiplication to printing result. But I am getting compilation error. Looks like we can't do nested thenApply(). Is there any way we can do this? Searched it over google and found one helpful link- http://kennethjorgensen.com/blog/2016/introduction-to-completablefutures But didn't find much help.
A couple of things are wrong with your snippet:
Parenthesis: you have to start the next thenApply after the end of the one before, not after the substract method.
supplyAsync() is a static method. Use it as such.
If you just want to print out the result in the last operation, use thenAccept instead of thenApply
You do not need to complete the CF in thenAccept (neither you would have to do it in thenApply before.
This piece of code compiles, and it may be close to what you want to achieve:
CompletableFuture<Void> cf = CompletableFuture
.supplyAsync(() -> addition(a, b))
.thenApply(r -> subtract(20, r))
.thenApply(r1 -> multiply(r1, 10))
.thenApply(r2 -> convert(r2))
.thenAccept(finalResult -> {
System.out.println("this is the final result: " + finalResult);
});
//just to wait until the cf is completed - do not use it on your program
cf.join();
I have a problem that I am unwilling to believe hasn't been solved before in Sage.
Given a pair of integers (d,n) as input, I'd like to receive a list (or set, or whatever) of all nondecreasing sequences of length d all of whose entries are no greater than n.
Similarly, I'd like another function which returns all strictly increasing sequences of length d whose entries are no greater than n.
For example, for d = 2 n=3, I'd receive the output:
[[1,2], [1,3], [2,3]]
or
[[1,1], [1,2], [1,3], [2,2], [2,3], [3,3]]
depending on whether I'm using increasing or nondecreasing.
Does anyone know of such a function?
Edit Of course, if there is such a method for nonincreasing or decreasing sequences, I can modify that to fit my purposes. Just something to iterate over sequences
I needed this algorithm too and I finally managed to write one today. I will share the code here, but I only started to learn coding last week, so it is not pretty.
Idea Input=(r,d). Step 1) Create a class "ListAndPosition" that has a list L of arrays Integer[r+1]'s, and an integer q between 0 and r. Step 2) Create a method that receives a ListAndPosition (L,q) and screens sequentially the arrays in L checking if the integer at position q is less than the one at position q+1, if so, it adds a new array at the bottom of the list with that entry ++. When done, the Method calls itself again with the new list and q-1 as input.
The code for Step 1)
import java.util.ArrayList;
public class ListAndPosition {
public static Integer r=5;
public final ArrayList<Integer[]> L;
public int q;
public ListAndPosition(ArrayList<Integer[]> L, int q) {
this.L = L;
this.q = q;
}
public ArrayList<Integer[]> getList(){
return L;
}
public int getPosition() {
return q;
}
public void decreasePosition() {
q--;
}
public void showList() {
for(int i=0;i<L.size();i++){
for(int j=0; j<r+1 ; j++){
System.out.print(""+L.get(i)[j]);
}
System.out.println("");
}
}
}
The code for Step 2)
import java.util.ArrayList;
public class NonDecreasingSeqs {
public static Integer r=5;
public static Integer d=3;
public static void main(String[] args) {
//Creating the first array
Integer[] firstArray;
firstArray = new Integer[r+1];
for(int i=0;i<r;i++){
firstArray[i] = 0;
}
firstArray[r] = d;
//Creating the starting listAndDim
ArrayList<Integer[]> L = new ArrayList<Integer[]>();
L.add(firstArray);
ListAndPosition Lq = new ListAndPosition(L,r-1);
System.out.println(""+nonDecSeqs(Lq).size());
}
public static ArrayList<Integer[]> nonDecSeqs(ListAndPosition Lq){
int iterations = r-1-Lq.getPosition();
System.out.println("How many arrays in the list after "+iterations+" iterations? "+Lq.getList().size());
System.out.print("Should we stop the iteration?");
if(0<Lq.getPosition()){
System.out.println(" No, position = "+Lq.getPosition());
for(int i=0;i<Lq.getList().size();i++){
//Showing particular array
System.out.println("Array of L #"+i+":");
for(int j=0;j<r+1;j++){
System.out.print(""+Lq.getList().get(i)[j]);
}
System.out.print("\nCan it be modified at position "+Lq.getPosition()+"?");
if(Lq.getList().get(i)[Lq.getPosition()]<Lq.getList().get(i)[Lq.getPosition()+1]){
System.out.println(" Yes, "+Lq.getList().get(i)[Lq.getPosition()]+"<"+Lq.getList().get(i)[Lq.getPosition()+1]);
{
Integer[] tempArray = new Integer[r+1];
for(int j=0;j<r+1;j++){
if(j==Lq.getPosition()){
tempArray[j] = new Integer(Lq.getList().get(i)[j])+1;
}
else{
tempArray[j] = new Integer(Lq.getList().get(i)[j]);
}
}
Lq.getList().add(tempArray);
}
System.out.println("New list");Lq.showList();
}
else{
System.out.println(" No, "+Lq.getList().get(i)[Lq.getPosition()]+"="+Lq.getList().get(i)[Lq.getPosition()+1]);
}
}
System.out.print("Old position = "+Lq.getPosition());
Lq.decreasePosition();
System.out.println(", new position = "+Lq.getPosition());
nonDecSeqs(Lq);
}
else{
System.out.println(" Yes, position = "+Lq.getPosition());
}
return Lq.getList();
}
}
Remark: I needed my sequences to start at 0 and end at d.
This is probably not a very good answer to your question. But you could, in principle, use Partitions and the max_slope=-1 argument. Messing around with filtering lists of IntegerVectors sounds equally inefficient and depressing for other reasons.
If this has a canonical name, it might be in the list of sage-combinat functionality, and there is even a base class you could perhaps use for integer lists, which is basically what you are asking about. Maybe you could actually get what you want using IntegerListsLex? Hope this proves helpful.
This question can be solved by using the class "UnorderedTuples" described here:
http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/tuple.html
To return all all nondecreasing sequences with entries between 0 and n-1 of length d, you may type:
UnorderedTuples(range(n),d)
This returns the nondecreasing sequence as a list. I needed an immutable object (because the sequences would become keys of a dictionary). So I used the "tuple" method to turn the lists into tuples:
immutables = []
for s in UnorderedTuples(range(n),d):
immutables.append(tuple(s))
return immutables
And I also wrote a method which picks out only the increasing sequences:
def isIncreasing(list):
for i in range(len(list) - 1):
if list[i] >= list[i+1]:
return false
return true
The method that returns only strictly increasing sequences would look like
immutables = []
for s in UnorderedTuples(range(n),d):
if isIncreasing(s):
immutables.append(tuple(s))
return immutables
I recently started codeing java, so this question might be a little, well, stupid, but i created a small program that averages 5 numbers. I know the program is very over complicated, i have just been trying out some of the new things i've learned.My problem is i would like to get the variable "Answer" up in my main program. I dont want to change around the program if i dont have to.I have returned the value in the average method, and set this answer to the variable Answer, but how can i use System.out.print(Answer) or print the return. Heres the code! Sorry if its not in a code block, i indented 4 spaces, but it doesnt say anything.
package Tests;
import java.util.*;
public class average_Test {
static double Total=0;
public static void main(String[] args){
Scanner scan = new Scanner(System.in);
int temp;
int count[]={5,1,2,3,4};
for(int x:count){
System.out.print("Please enter 5 numbers: ");
temp=scan.nextInt();
average(temp);
}
}
public static double average(int n){
for(int c=0;c<1;c++){
Total+=n;
}
double average=Total/5;
System.out.println(average);
double Answer = Total/5;
return Total/5;
}
}
You can use variable binding, or print result of function:
double a = average(temp);
System.out.println(a);
or:
System.out.println(average(temp));
At the end it will look like this:
double result = 0;
System.out.print("Please enter 5 numbers: ");
for (int x : count) {
temp = scan.nextInt();
result = average(temp);
}
System.out.println(result);
P.S. code looks weird, consider implementing double average(int[] numbers)