RootMpi Demos
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Sphere
In this demonstration I pretend show you how to think a parallel problem and the power of to use RootMpi to solve it using 4 processors exactly.
I want to calculate the parallel surface and volume of a sphere.
Parallel Sphere Volume
To calculate Volume I can calculate $ V=\int\limits_{0}^{r} r^2-(x^2)\,dx. $ . I can calculate it using ROOT::Mpi::Math::TIntegratorWrapper that is RootMpi's class with parallelization ready./*********************************************************************/ /*Section to calculate volume with parallel multimensional integrator*/ /*********************************************************************/ //integrator creation root's style ROOT::Math::Functor1D function(&sphere_function); ROOT::Math::Integrator integrator; integrator.SetFunction(function); //Mpi's integrator wrapper, integrator from ROOT in one dimension ROOT::Mpi::Math::TIntegratorWrapper MpiIntegrator(&integrator); //integrate in parallel and send the result to rank zero, intervar [0,radius] MpiIntegrator.Integrate(0, 0, radius);
Parallel Sphere Surface
(wait 5 secs to render latex)To calculate the surface I can express spherical coordinates in rectangular coordinates in this way:
- $x = rcos(\theta)sin(\phi)$
- $y = rsin(\theta)sin(\phi)$
- $z = rcos(\phi)$
Range for process
Process 0 $\phi \in [0,0.5\pi] and\ \theta \in [0,\pi]$
Process 1 $\phi \in [0.5,\pi] and\ \theta \in [0,\pi]$
Process 2 $\phi \in [1,1.5\pi] and\ \theta \in [0,\pi]$
Process 3 $\phi \in [1.5,2\pi] and\ \theta \in [0,\pi]$
In every section I evaluate the intervals with delta=0.01, then I have almost 50000 points in every process.
Every color is the region calculate in different processor, the points are encapsulated in a object TPolyMarker3D and sent to root process(zero) and painted.
Reference
This is the macro for ROOT interpreter.
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SphereCode
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1 . /*******************************************************************************/
2 . /*Author: Omar Andres Zapata Mesa Ago 2012 */
3 . /*this example calculate parallel surface's regions in a sphere and the volume.*/
4 . /*need 4 process to work, beacase the sphere was splitted into four parts. */
5 . /*******************************************************************************/
6 . #include <Rtypes.h>
7 . #include <Math/Math.h>
8 . #include <Math/Functor.h>
9 . #include <Math/Integrator.h>
10 .
11 . gSystem->Load("libRMpi");
12 .
13 . Double_t delta=0.01;//delta to iterate points in the surface
14 . Double_t radius=10; //sphere radius
15 . Double_t radius2=radius*radius; //radius' square
16 . Double_t theta, phi, x,y,z;
17 . Int_t point=0;
18 . /************************************************************************************/
19 . /*this is the function for positive region of a sphere. use to integrate the volume.*/
20 . /************************************************************************************/
21 . Double_t sphere_function(const Double_t param)
22 . {
23 . Double_t x,y;
24 . x=param;//coor x
25 . return 2*M_PI*(radius2-(x*x));//funtion sphere_function(r,x)=V(r,x)= 2*pi*(r2-x2)
26 . }
27 .
28 . void sphere()
29 . {
30 . /********************/
31 . /*Mpi initialization*/
32 . /********************/
33 . ROOT::Mpi::TEnvironment env(gApplication->Argc(), gApplication->Argv());
34 . ROOT::Mpi::TIntraCommunicator world;
35 .
36 . /*********************************/
37 . /*Error control, need 4 processes*/
38 . /*********************************/
39 . if(world.Size()!=4)
40 . {
41 . std::cout<<"Error: You need run with 4 processes exactly, the sphere was spplitted in four regions. \nExample: mpirun -np 4 root -l sphere.C\n";
42 . std::cout.flush();
43 . world.Abort(6);
44 . }
45 .
46 . /*********************************************************************/
47 . /*Section to calculate volume with parallel multimensional integrator*/
48 . /*********************************************************************/
49 . //integrator creation root's style
50 . ROOT::Math::Functor1D function(&sphere_function);
51 .
52 . ROOT::Math::Integrator integrator;
53 . integrator.SetFunction(function);
54 .
55 . //Mpi's integrator wrapper, integrator from ROOT in one dimension
56 . ROOT::Mpi::Math::TIntegratorWrapper MpiIntegrator(&integrator);
57 .
58 . //integrate in parallel and send the result to rank zero, intervar [0,radius]
59 . MpiIntegrator.Integrate(0, 0, radius);
60 .
61 .
62 . /*****************************************************************************************/
63 . /*this is the root process,calculate the surface z=+qsrt(1−(x2+b2)) for x∈[−1,0],y∈[−1,1]*/
64 . /*and recv the other surface regions in TPolyMarker3D object from others ranks */
65 . /*****************************************************************************************/
66 . if (world.Rank() == 0) {
67 . gBenchmark->Start("sphere");
68 . // create and open a canvas
69 . TCanvas *canvas = new TCanvas("sphere", "sphere", 300, 10, 700, 500);
70 . canvas->SetFillColor(14);
71 . // creating view
72 . TView *view = TView::CreateView(1, 0, 0);
73 . view->RotateView(90,-10);
74 . view->SetRange(-radius*2, -radius*2, -2*radius, 2*radius, 2*radius, 2*radius);
75 . // create a PolyMarker3D for region/segment 1 calculate in rank 0(this rank)
76 . TPolyMarker3D *surfaceSeg13d = new TPolyMarker3D();
77 .
78 . for (theta = 0; theta <0.5*M_PI ; theta+= delta) {
79 . for (phi = 0; phi <M_PI; phi += delta) {
80 .
81 . x=radius*cos(theta)*sin(phi);
82 . y=radius*sin(theta)*sin(phi);
83 . z=radius*cos(phi);
84 . // set points
85 . surfaceSeg13d->SetPoint(point, x, y, z);
86 . point++;
87 . }
88 . }
89 . // set marker size, color & style
90 . surfaceSeg13d->SetMarkerSize(1);
91 . surfaceSeg13d->SetMarkerColor(world.Rank() + world.Size());
92 . surfaceSeg13d->SetMarkerStyle(1);
93 . //drawing region 1
94 . surfaceSeg13d->Draw();
95 .
96 . //getting region 2 from rank 1
97 . TPolyMarker3D *surfaceSeg23d = new TPolyMarker3D;
98 . world.RecvObject(1, 1, *surfaceSeg23d);
99 . surfaceSeg23d->Draw();
100 .
101 . //getting region 3 from rank 2
102 . TPolyMarker3D *surfaceSeg33d = new TPolyMarker3D;
103 . world.RecvObject(2, 1, *surfaceSeg33d);
104 . surfaceSeg33d->Draw();
105 .
106 . //getting region 4 from rank 3
107 . TPolyMarker3D *surfaceSeg43d = new TPolyMarker3D;
108 . world.RecvObject(3, 1, *surfaceSeg43d);
109 . surfaceSeg43d->Draw();
110 .
111 . Char_t timeStr[60];
112 . Char_t pointsStr[100];
113 . Char_t radiusStr[100];
114 . Char_t deltaStr[100];
115 . gBenchmark->Show("sphere");
116 .
117 . Float_t ct = gBenchmark->GetCpuTime("sphere");
118 . sprintf(timeStr, "Execution time: %g sec.", ct);
119 . sprintf(radiusStr, "Radius : %g", radius);
120 . sprintf(deltaStr, "Delta : %g", delta);
121 . sprintf(pointsStr, "Total surface points : %g", point*4);
122 .
123 . TPaveText *text = new TPaveText(0.1, 0.6, 0.9, 0.99);
124 . text->SetFillColor(42);
125 . text->AddText("ROOTMpi example: sphere.C");
126 . text->AddText(timeStr);
127 . text->AddText(radiusStr);
128 . text->AddText(deltaStr);
129 . text->AddText(pointsStr);
130 . text->Draw();
131 .
132 . //sphere volume V=(4/3)*pi*r3
133 . //and compare the result integration's volume
134 . Char_t volumeStr[100];
135 . Double_t volume= MpiIntegrator.Result();
136 . Double_t volumeTeo=(4/3.0)*M_PI*(radius*radius*radius);
137 .
138 . sprintf(volumeStr, "Volumen with integration = %.15g \nVolumen with (4/3)*pi*r3 = %.15g", volume,volumeTeo);
139 .
140 . TPaveText *volumeText = new TPaveText(-0.1, -0.81, -0.9, -0.97);
141 . volumeText->SetFillColor(41);
142 . volumeText->SetTextAlign(11);
143 . volumeText->AddText(volumeStr);
144 . volumeText->Draw();
145 . }
146 . /*************************************************************************/
147 . /*this rank calculate the surface for theta ∈[0.5pi,pi] and phi ∈[0,pi] */
148 . /*and send the surface regions in TPolyMarker3D object to rank root zero */
149 . /*************************************************************************/
150 . if (world.Rank() == 1) {
151 . TPolyMarker3D *surfaceSeg23d = new TPolyMarker3D();
152 .
153 . for (theta = 0.5*M_PI; theta <M_PI ; theta+= delta) {
154 . for (phi = 0; phi <M_PI; phi += delta) {
155 .
156 . x=radius*cos(theta)*sin(phi);
157 . y=radius*sin(theta)*sin(phi);
158 . z=radius*cos(phi);
159 . // set points
160 . surfaceSeg23d->SetPoint(point, x, y, z);
161 . point++;
162 . }
163 . }
164 . // set marker size, color & style
165 . surfaceSeg23d->SetMarkerSize(1);
166 . surfaceSeg23d->SetMarkerColor(world.Rank() + world.Size());
167 . surfaceSeg23d->SetMarkerStyle(1);
168 . //send surface points to root process
169 . world.SendObject(0, 1, *surfaceSeg23d);
170 . }
171 . /*************************************************************************/
172 . /*this rank calculate the surface for theta ∈[pi,1.5pi] and phi ∈[0,pi] */
173 . /*and send the surface regions in TPolyMarker3D object to rank root zero */
174 . /*************************************************************************/
175 . if (world.Rank() == 2) {
176 . TPolyMarker3D *surfaceSeg33d = new TPolyMarker3D();
177 . for (theta = M_PI; theta <1.5*M_PI ; theta+= delta) {
178 . for (phi = 0; phi <M_PI; phi += delta) {
179 .
180 . x=radius*cos(theta)*sin(phi);
181 . y=radius*sin(theta)*sin(phi);
182 . z=radius*cos(phi);
183 . // set points
184 . surfaceSeg33d->SetPoint(point, x, y, z);
185 . point++;
186 . }
187 . }
188 . // set marker size, color & style
189 . surfaceSeg33d->SetMarkerSize(1);
190 . surfaceSeg33d->SetMarkerColor(world.Rank() + world.Size());
191 . surfaceSeg33d->SetMarkerStyle(1);
192 . //send surface points to root process
193 . world.SendObject(0, 1, *surfaceSeg33d);
194 . }
195 . /*************************************************************************/
196 . /*this rank calculate the surface for theta ∈[1.5pi,2pi] and phi ∈[0,pi] */
197 . /*and send the surface regions in TPolyMarker3D object to rank root zero */
198 . /*************************************************************************/
199 . if (world.Rank() == 3) {
200 . TPolyMarker3D *surfaceSeg43d = new TPolyMarker3D();
201 . for (theta = 1.5*M_PI; theta <2*M_PI ; theta+= delta) {
202 . for (phi = 0; phi <M_PI; phi += delta) {
203 .
204 . x=radius*cos(theta)*sin(phi);
205 . y=radius*sin(theta)*sin(phi);
206 . z=radius*cos(phi);
207 . // set points
208 . surfaceSeg43d->SetPoint(point, x, y, z);
209 . point++;
210 . }
211 . }
212 . // set marker size, color & style
213 . surfaceSeg43d->SetMarkerSize(1);
214 . surfaceSeg43d->SetMarkerColor(world.Rank() + world.Size());
215 . surfaceSeg43d->SetMarkerStyle(1);
216 . //send surface points to root process
217 . world.SendObject(0, 1, *surfaceSeg43d);
218 . }
219 . }
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SphereVideo
Created by Omar Andres Zapata Mesa.
Voice by Gerardo Gutierrez. (Thanks!)
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Parallel Wave Animation
In this demonstration we are going to animate a sin wave. We split it into n-1 processes, the process root(zero) gets the points from other processes and it sends a broadcast with the new angle to calculate the height, and repeat the procedure.WARNING this animation require OpenGL support in your pc.
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WaveCode
1 . /*******************************************************************************/
2 . /*Author: Omar Andres Zapata Mesa Ago 2012 */
3 . /*this example calculate parallel wave animation */
4 . /*work with any number(n) of processes but the wave is splitted into n-1 parts */
5 . /*******************************************************************************/
6 . #include <Rtypes.h>
7 . #include <Math/Math.h>
8 . #include <TF1.h>
9 . #include <TPolyMarker3D.h>
10 . Double_t delta=0.1;
11 . Double_t min=0,max=6*M_PI;
12 . Double_t angle=M_PI;
13 . Double_t init,end;
14 . Int_t counter=0;
15 .
16 . UInt_t rep=1000;
17 . UInt_t delay=100;
18 .
19 . UInt_t MPI_SUCCESS=0;
20 . /********************/
21 . /*Mpi initialization*/
22 . /********************/
23 . ROOT::Mpi::TEnvironment env(gApplication->Argc(), gApplication->Argv());
24 . ROOT::Mpi::TIntraCommunicator world;
25 .
26 . TCanvas *canvas = NULL;
27 . TView *view = NULL;
28 .
29 .
30 . void Init()
31 . {
32 . gStyle->SetCanvasPreferGL(true);
33 . gStyle->SetFrameFillColor(42);
34 . canvas = new TCanvas("canvas", "wave", 300, 10, 700, 500);
35 . canvas->SetFillColor(14);
36 . view = TView::CreateView(1, 0, 0);
37 . view->RotateView(90,0);
38 . }
39 .
40 . void Animate()
41 . {
42 . if (!gROOT->GetListOfCanvases()->FindObject("canvas")){
43 . world.Abort(MPI_SUCCESS);
44 . };
45 . gPad->Clear();
46 . for(int i=1;i<world.Size();i++)
47 . {
48 . //getting wave sections from ranks>1
49 . TPolyMarker3D *Section = new TPolyMarker3D();
50 . world.RecvObject(i, 1, *Section);
51 . Section->Draw();
52 . }
53 . gPad->Modified();
54 . gPad->Update();
55 . angle += 0.05*M_PI;
56 . world.BcastSendScalar(angle,0);
57 . counter++;
58 . if(counter<rep) world.BcastSendScalar(true,0);
59 . else world.BcastSendScalar(false,0);
60 . }
61 .
62 .
63 . void wave()
64 . {
65 .
66 . /**************************************************/
67 . /*rank zero(root) dont calculate wave, init viewer*/
68 . /*and recv wave sections from other processes */
69 . /**************************************************/
70 . if (world.Rank() == 0) {
71 . Init();
72 . TTimer *timer = new TTimer(delay);
73 . timer->SetCommand("Animate()");
74 . Char_t timeStr[60];
75 . Char_t pointsStr[100];
76 . Char_t deltaStr[100];
77 . timer->TurnOn();
78 . }else{
79 . Double_t step = fabs(min - max) / (world.Size()-1);
80 .
81 . init = min + (world.Rank()-1) * step;
82 . end = init + step;
83 . cout<<"rank="<<world.Rank()<<" init="<<init<<" end="<<end<<"\n";
84 . Int_t flag=true;
85 . while(flag){
86 . TPolyMarker3D *Section=new TPolyMarker3D();
87 . counter=0;
88 . for(Double_t t=init;t<end;t+=delta)
89 . {
90 . Section->SetPoint(counter,t,sin(t+angle),0);
91 . counter++;
92 . }
93 . // set marker size, color & style
94 . Section->SetMarkerSize(1);
95 . Section->SetMarkerColor(world.Rank());
96 . Section->SetMarkerStyle(8);
97 . //send segment of points to root process
98 . world.SendObject(0, 1, *Section);
99 .
100 . world.BcastRecvScalar(angle,0); //recv angle to wave evolution
101 . world.BcastRecvScalar(flag,0);//recv flag to stop
102 . delete Section;
103 . }
104 . world.Abort(MPI_SUCCESS);
105 . }
106 . }
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WaveVideo
Created by Omar Andres Zapata Mesa.
Voice by Gerardo Gutierrez. (Thanks!)
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