分子動力学を使用したイオントラップシミュレーションとOpenGLによる可視化 で行っていたシミュレーション処理のクーロン力計算部分を、前回検討したmultiprocessingを使った並列処理版に置き換えて処理を行ってみた。シングルコアで動作させていた時より、よりスムーズにイオン粒子が動いているのが目視にて確認できる。
並列数4、粒子数は128個。
並列なしのシングルコア動作版の動画が下記(粒子数は同様に128個)
並列化した計算のサンプルソースコードが下記。
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####################################### # ion trap simulation --------------- # with OpenGL/multiprocessing ------- ####################################### import random import math import itertools import time import scipy.special as scm #import scipy.misc as scm from OpenGL.GL import * from OpenGL.GLU import * from OpenGL.GLUT import * from multiprocessing import Pool #delta time Dt = 0.01 step = 0 #Define xyz index PX = 0;PY = 1;PZ = 2; VX = 3;VY = 4;VZ = 5; FX = 6;FY = 7;FZ = 8; FF = [FX, FY, FZ] PP = [PX, PY, PZ] #Coulomb's Force parameter CF = 1000.0 #mouse move mx = 0.0 my = 0.0 #lattice size lsize = 1.0 #number of particles in a line line_num = 10 #total particle num PN = line_num * line_num * line_num th = math.pi * 0.5 ph = math.pi * 0.5 #ready to 9 parameters for particle #(PX, PY, PZ, VX, VY, VZ, FX, FY, FZ) xyz = [[0 for i in range(9)] for j in range(PN)] combinum = int(scm.comb(PN, 2)) #thread number(local thread num) core = 4 def find_pair_sub(prep,pend,thread): global xyz #local results array xyzF = [[0 for i in range(3)] for j in range(PN)] fx = 0; fy = 1; fz = 2 for i in range(prep,pend): for j in range(i + 1, PN): dx = xyz[i][PX] - xyz[j][PX] dy = xyz[i][PY] - xyz[j][PY] dz = xyz[i][PZ] - xyz[j][PZ] r = math.sqrt(dx*dx + dy*dy + dz*dz) xyzF[i][fx] = xyzF[i][fx] + dx/(r*r*r) xyzF[i][fy] = xyzF[i][fy] + dy/(r*r*r) xyzF[i][fz] = xyzF[i][fz] + dz/(r*r*r) xyzF[j][fx] = xyzF[j][fx] - dx/(r*r*r) xyzF[j][fy] = xyzF[j][fy] - dy/(r*r*r) xyzF[j][fz] = xyzF[j][fz] - dz/(r*r*r) return xyzF def wrapper(args): return find_pair_sub(*args) def find_pair(): global PN global combinum pw = combinum // core pl = combinum % core localt = 0 thread = 0 pre = 0 worklist = [] ppp = pw for i in range(PN) : if core == 1: worklist.append([pre,PN,thread]) break localt = localt + (PN - i - 1) if localt >= ppp: worklist.append([pre,i,thread]) ppp += pw thread += 1 pre = i if i != pre: prep = worklist[thread-1][0] worklist[thread-1] = [prep,PN,thread-1] p = Pool(core) callback = p.map(wrapper, worklist) p.close() for j in range(core): for i in range(PN): xyz[i][FX] += callback[j][i][0] xyz[i][FY] += callback[j][i][1] xyz[i][FZ] += callback[j][i][2] def update(): global step step += 1 find_pair() pnum = 0 while pnum < PN: # set force that collects particles xyz[pnum][FX] = xyz[pnum][FX] + CF*(lsize/2.0 - xyz[pnum][PX]) xyz[pnum][FY] = xyz[pnum][FY] + CF*(lsize/2.0 - xyz[pnum][PY]) xyz[pnum][FZ] = xyz[pnum][FZ] + CF*(lsize/2.0 - xyz[pnum][PZ]) # if too large force is making , reset. CUT = 10000 for f in FF: if xyz[pnum][f] > abs(CUT): xyz[pnum][f] = 0 xyz[pnum][VX] = xyz[pnum][VX] + 0.5*Dt*xyz[pnum][FX] xyz[pnum][VY] = xyz[pnum][VY] + 0.5*Dt*xyz[pnum][FY] xyz[pnum][VZ] = xyz[pnum][VZ] + 0.5*Dt*xyz[pnum][FZ] xyz[pnum][FX] = 0.0 xyz[pnum][FY] = 0.0 xyz[pnum][FZ] = 0.0 pnum += 1 #print "- step =", step," -" pnum = 0 while pnum < PN: #update position xyz[pnum][PX] = xyz[pnum][PX] + Dt*xyz[pnum][VX] xyz[pnum][PY] = xyz[pnum][PY] + Dt*xyz[pnum][VY] xyz[pnum][PZ] = xyz[pnum][PZ] + Dt*xyz[pnum][VZ] pnum += 1 def init_lattice(): #PN = line_num^3 delt = lsize/line_num; xv_sum = 0 yv_sum = 0 zv_sum = 0 pnum = 0 k = 0 while k < line_num: j = 0 while j < line_num: i = 0 while i < line_num: xyz[pnum][PX] = delt * i xyz[pnum][PY] = delt * j xyz[pnum][PZ] = delt * k pnum += 1 i += 1 j += 1 k += 1 pnum = 0 while pnum < PN: xyz[pnum][VX] = random.uniform(-1,1) # 1 x-velocity xyz[pnum][VY] = random.uniform(-1,1) # 2 y-velocity xyz[pnum][VZ] = random.uniform(-1,1) # 3 z-velocity xv_sum += xyz[pnum][VX] yv_sum += xyz[pnum][VY] zv_sum += xyz[pnum][VZ] pnum += 1 xv_sum = xv_sum / PN yv_sum = yv_sum / PN zv_sum = zv_sum / PN pnum = 0 while pnum < PN: xyz[pnum][VX] = xyz[pnum][VX] - xv_sum xyz[pnum][VY] = xyz[pnum][VY] - yv_sum xyz[pnum][VZ] = xyz[pnum][VZ] - zv_sum pnum += 1 def draw(): cx = cy = cz = lsize * 0.5 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT) glClearColor(0.0, 0.0, 0.0, 1.0) glLoadIdentity() glColor3f(1.0,1.0,0.0) gluLookAt(5*math.sin(th)*math.cos(ph)+cx, 5*math.cos(th)+cy, 5*math.sin(th)*math.sin(ph)+cz,\ cx, cy, cz, -math.cos(th)*math.cos(ph),math.sin(th),-math.cos(th)*math.sin(ph) ) glBegin(GL_LINE_LOOP) glVertex3d(0,0,0) glVertex3d(0,lsize,0) glVertex3d(lsize,lsize,0) glVertex3d(lsize,0,0) glEnd() glBegin(GL_LINE_LOOP) glVertex3d(0,0,lsize) glVertex3d(0,lsize,lsize) glVertex3d(lsize,lsize,lsize) glVertex3d(lsize,0,lsize) glEnd() glBegin(GL_LINES) glVertex3d(0,0,0) glVertex3d(0,0,lsize) glEnd() glBegin(GL_LINES) glVertex3d(0,lsize,0) glVertex3d(0,lsize,lsize) glEnd() glBegin(GL_LINES) glVertex3d(lsize,0,0) glVertex3d(lsize,0,lsize) glEnd() glBegin(GL_LINES) glVertex3d(lsize,lsize,0) glVertex3d(lsize,lsize,lsize) glEnd() pnum = 0 while pnum < PN: glPointSize(3.0) glColor3f(0.3, 0.3, 1.0) glBegin(GL_POINTS) glVertex3d(xyz[pnum][PX], xyz[pnum][PY], xyz[pnum][PZ]) glEnd() #Reduce particle velocity xyz[pnum][VX] *= 0.99 xyz[pnum][VY] *= 0.99 xyz[pnum][VZ] *= 0.99 pnum = pnum + 1 update() glutSwapBuffers() def init(): glClearColor(0.7, 0.7, 0.7, 0.7) def idle(): glutPostRedisplay() def reshape(w, h): glViewport(0, 0,w,h) glMatrixMode(GL_PROJECTION) glLoadIdentity() gluPerspective(30.0, w/h, 1.0, 100.0) glMatrixMode (GL_MODELVIEW) def motion(x, y): global ph, th, mx, my dltx = mx -x dlty = my -y #Invalid large motion if 10 < abs(dltx): dltx = 0 if 10 < abs(dlty): dlty = 0 ph = ph - 0.01*dltx th = th + 0.01*dlty glutPostRedisplay() glutSwapBuffers() mx = x my = y if __name__ == "__main__": init_lattice() glutInitWindowPosition(50, 50); glutInitWindowSize(500, 500); glutInit(sys.argv) glutInitDisplayMode(GLUT_RGBA | GLUT_DOUBLE ) glutCreateWindow("pyOpenGL TEST") glutDisplayFunc(draw) glutReshapeFunc(reshape) glutMotionFunc(motion); init() glutIdleFunc(idle) glutMainLoop() |
I tried processing by replacing the Coulomb force calculation part of simulation processing which was done by ion trap simulation using molecular dynamics and visualization by OpenGL with a parallel processing version using multiprocessing discussed previously . It can be visually confirmed that ion particles are moving more smoothly than when operating with a single core.