/* emprical Heine-Abarenkov pseudopotential - real space DFT-LDA */
/* coded by Ikeuchi Mitsuru    */
/* ver 0.0.1   2004.09.12      */
/* ver 0.0.2   2004.09.18  improve setVcx() */

import java.awt.*;
import java.awt.event.*;
import java.applet.*;

public class HeineAbarenkovPP extends Applet
  implements MouseListener, MouseMotionListener,
    ItemListener, ActionListener, AdjustmentListener, Runnable {

/* -------------------------------------- set global ------ */

  Choice cvw, ch_md, ch_noe;
  Button bt_reset, bt_start, bt_stop;
  Scrollbar spx,spy,spz;
  Thread th = null;

  Dimension dim;
  Image imgOff;
  Graphics gOff;

  int sleepTime = 30;

  int dispMode = 1;
  int dispObj = 0;
  double px0 = 0.0;
  double py0 = 0.0;
  double pz0 = 0.0;
  int started = 1;
  double NOE = 3.0;
  double Znuc = 3.0;
  double Rcore = 1.377;
  double HAu = -0.453;

  int dgX, dgY, dgXb,dgYb;
  double viewTheta = -15.0*3.14/180.0;
  double viewFai = -72.0*3.14/180.0;
  double dtheta = 0.0*3.14/180.0;
  double pai = 3.1415926536;

  double cosTh = Math.cos(viewTheta); 
  double sinTh = Math.sin(viewTheta);
  double cosFi = Math.cos(viewFai);
  double sinFi = Math.sin(viewFai);


  double t = 0.0;

  double dx = 1.0/4.0;
  double dy = 1.0/4.0;
  double dz = 1.0/4.0;
  double dt = 1.0*(dx*dx);

  int NNx = 64+1;
  int NNy = 64+1;
  int NNz = 64+1;
  int NN = NNx+1; /* max(NNx,NNy,NNz)+1 */
  /*
  int NNr = 500;*/

  double vv[][][] = new double[NNx][NNy][NNz];

  double vvext[][][] = new double[NNx][NNy][NNz];
  double vvh[][][] = new double[NNx][NNy][NNz];
  double vvx[][][] = new double[NNx][NNy][NNz];
  double vvc[][][] = new double[NNx][NNy][NNz];
  
  double rho[][][] = new double[NNx][NNy][NNz];

  double sdEnergy[] = new double[20];
  double sdState[][][][] = new double[20][NNx][NNy][NNz];

/* simple metal - local Heine-Abarenkov pseudopotential */
/* F.Nogueira, C. Fiolhais and J.P.Perdew; Phys. Rev. B59 [4] p.2570-2578 (1999)          */

  double HApp[][] = {
    /*          rs , Zv ,  rc  ,   u   ,  Z,    M     */
    /* Be */ { 1.87, 2.0, 0.779,  0.416,  4,   9.012  },
    /* Al */ { 2.07, 3.0, 1.377, -0.453, 13,  26.982  },
    /* Ga */ { 2.19, 3.0, 1.481, -0.705, 31,  69.72   },
    /* Sn */ { 2.22, 4.0, 1.951, -0.898, 50, 118.6    },
    /* Pb */ { 2.30, 4.0, 2.350, -1.030, 82, 207.2    },
    /* In */ { 2.41, 3.0, 1.963, -0.876, 49, 114.82   },
    /* Tl */ { 2.48, 3.0, 2.256, -0.993, 81, 204.3    },
    /* Mg */ { 2.65, 2.0, 1.741, -0.571, 12,  24.305  },
    /* Li */ { 3.24, 1.0, 1.482, -0.127,  3,   9.012  },
    /* Ca */ { 3.27, 2.0, 2.599, -0.774, 20,  40.08   },
    /* Sr */ { 3.57, 2.0, 3.071, -0.858, 38,  87.62   },
    /* Ba */ { 3.71, 2.0, 3.425, -0.936, 56, 137.33   },
    /* Na */ { 3.93, 1.0, 2.371, -0.660, 11,  22.99   },
    /* K  */ { 4.86, 1.0, 3.362, -0.774, 19,  39.098  },
    /* Rb */ { 5.20, 1.0, 3.897, -0.870, 37,  85.467  },
    /* Cs */ { 5.62, 1.0, 4.486, -0.926, 55, 132.91   },
  };

  int pxBox[] = new int[8];
  int pyBox[] = new int[8];
  int boxp[][] = {
   {0,1},{0,2},{0,4},{1,3},{1,5},{2,3},{2,6},{4,5},{4,6},{3,7},{5,7},{6,7}
  };

  int xpts[] = new int[NN];
  int ypts[] = new int[NN];

/* ----------------------------- applet control ------ */

  public void init() {

    resize(630,320);
    setBackground(Color.white);

    dim = getSize();
    imgOff = createImage(dim.width,dim.height);
    gOff = imgOff.getGraphics();

    cvw = new Choice();
    cvw.addItem("ph-0");cvw.addItem("ph-1");cvw.addItem("ph-2");
    cvw.addItem("ph-3");
    cvw.addItemListener(this);
    cvw.select("ph-0");

    ch_md = new Choice();
    ch_md.addItem("density");ch_md.addItem("phase");ch_md.addItem("ph-grid");
    ch_md.addItem("Vext"); ch_md.addItem("VH"); ch_md.addItem("Vx");
    ch_md.addItem("Vc"); ch_md.addItem("Veff"); ch_md.addItem("rho");
    ch_md.addItemListener(this);
    ch_md.select("phase");

    ch_noe = new Choice();
    ch_noe.addItem("n=1.5(Be)");ch_noe.addItem("n=2(Be)");
    ch_noe.addItem("n=2.5(Al)");ch_noe.addItem("n=3(Al)");
    ch_noe.addItem("n=2.5(Ga)");ch_noe.addItem("n=3(Ga)");
    ch_noe.addItem("n=3.5(Sn)");ch_noe.addItem("n=4(Sn)");
    ch_noe.addItem("n=3.5(Pb)");ch_noe.addItem("n=4(Pb)");
    ch_noe.addItem("n=2.5(In)");ch_noe.addItem("n=3(In)");
    ch_noe.addItem("n=2.5(Tl)");ch_noe.addItem("n=3(Tl)");
    ch_noe.addItem("n=1.5(Mg)");ch_noe.addItem("n=2(Mg)");
    ch_noe.addItem("n=0.5(Li)");ch_noe.addItem("n=1(Li)");
    ch_noe.addItem("n=1.5(Ca)");ch_noe.addItem("n=2(Ca)");
    ch_noe.addItem("n=1.5(Sr)");ch_noe.addItem("n=2(Sr)");
    ch_noe.addItem("n=1.5(Ba)");ch_noe.addItem("n=2(Ba)");
    ch_noe.addItem("n=0.5(Na)");ch_noe.addItem("n=1(Na)");
    ch_noe.addItem("n=0.5(K)");ch_noe.addItem("n=1(K)");
    ch_noe.addItem("n=0.5(Rb)");ch_noe.addItem("n=1Rb)");
    ch_noe.addItem("n=0.5(Cs)");ch_noe.addItem("n=1(Cs)");
    ch_noe.addItemListener(this);
    ch_noe.select("n=3(Al)");

    bt_reset= new Button("reset");
    bt_reset.addActionListener(this);

    bt_start= new Button("start");
    bt_start.addActionListener(this); 

    bt_stop = new Button("stop");
    bt_stop.addActionListener(this);

    
    spx= new Scrollbar(Scrollbar.HORIZONTAL,50,10,0,110);
    spx.addAdjustmentListener(this);

    spy= new Scrollbar(Scrollbar.HORIZONTAL,0,10,0,110);
    spy.addAdjustmentListener(this);

    spz= new Scrollbar(Scrollbar.HORIZONTAL,0,10,0,110);
    spz.addAdjustmentListener(this);

    addMouseListener(this);  
    addMouseMotionListener(this);

    setLayout(new BorderLayout());
    Panel pnl = new Panel();
    pnl.setLayout(new GridLayout(1,6,5,0));
    pnl.add(bt_reset);
    pnl.add(bt_start);
    pnl.add(bt_stop);
    pnl.add(ch_noe);
    pnl.add(cvw);
    pnl.add(ch_md);
    add(pnl,"North");

    setInitialCondition();
  }

  public void start() {
    if (th == null) {
      th = new Thread(this);
      th.start();
    }
  }

  public void stop() {
    if (th != null) {
      th.stop();
      th = null;
    }
  }

  public void itemStateChanged(ItemEvent ev){
    int ic;

    if (ev.getSource() == cvw){
      dispObj = cvw.getSelectedIndex();
    } else if (ev.getSource() == ch_md){
      dispMode = ch_md.getSelectedIndex();
    } else if (ev.getSource() == ch_noe){
      ic = ch_noe.getSelectedIndex();
	  Znuc = HApp[ic/2][1];
	  NOE = Znuc - 0.5 + 0.5*(ic%2);
	  Rcore = HApp[ic/2][2];
      HAu = HApp[ic/2][3];
      setPotential();
    }
  }

  public void actionPerformed(ActionEvent ev){
    if(ev.getSource() == bt_reset){ 
      started = -1;
    } else if(ev.getSource() == bt_start){ 
      started = 1;
    } else if(ev.getSource() == bt_stop){
      started = 0;
    }
  }

  public void adjustmentValueChanged(AdjustmentEvent ev){
    if (ev.getSource() == spx) { 
      px0 = 0.1*(double)(spx.getValue());
    } else if (ev.getSource() == spy) { 
      py0 = 0.1*(double)(spy.getValue());
    } else if (ev.getSource() == spz) { 
      pz0 = 0.1*(double)(spz.getValue());
    }
  }

  public void mousePressed(MouseEvent ev){ }
  public void mouseReleased(MouseEvent ev){
    dgXb = 0; dgYb = 0;
    dgX = 0; dgY = 0;
  }
  public void mouseClicked(MouseEvent ev){ }
  public void mouseEntered(MouseEvent ev){ } 
  public void mouseExited (MouseEvent ev){ }

  public void mouseMoved  (MouseEvent ev){ }

  public void mouseDragged(MouseEvent ev){
    dgXb = dgX; dgYb = dgY;
    dgX=ev.getX();
    dgY=ev.getY();
    if (dgXb==0 && dgYb==0) {
      dgXb = dgX; dgYb = dgY;
    }
    viewTheta += 0.5*3.14/180.0*(dgX-dgXb);
    viewFai += 0.5*3.14/180.0*(dgY-dgYb);
    cosTh = Math.cos(viewTheta); 
    sinTh = Math.sin(viewTheta);
    cosFi = Math.cos(viewFai);
    sinFi = Math.sin(viewFai);
  }

  public void run() {
    while (th != null) {
      try {
        timeEvolution();
        offPaint();
        repaint();
        Thread.sleep(sleepTime);
      } catch (InterruptedException e) { }
    }
  }

  public void update(Graphics g) {
    paint(g);
  }

  public void paint(Graphics g) {
    g.drawImage(imgOff,0,0,this);
  }

/* ----------------------------- offPaint -------------------- */

  void offPaint() {
    int i,gb;
    double ev,ek;
    double g0,g1;
    double dens;

    gOff.setColor(Color.white);
    gOff.fillRect(0,0,dim.width,dim.height);

    g0 = 0.0; g1 = 0.0;
	if (NOE<=2.0) {
	  g0= NOE; g1 = 0.0;
	} else if (NOE>2.0) {
	  g0= 2.0; g1 = (NOE-2.0)/3.0;
	}

    dens = 500.0;

    if (dispMode==0 || dispMode==1) {

      boxPlot();
      dens3DPlotSD(dens,dispMode,dispObj);
      boxPlot2();

    } else if (dispMode==2) {

      gridFnPlot(sdState[dispObj], NNz/2, 50.0);

    } else if (dispMode==3) {

      gridFnPlot(vvext, NNz/2, 20.0);

    } else if (dispMode==4) {

      gridFnPlot(vvh, NNz/2, 20.0);

    } else if (dispMode==5) {

      gridFnPlot(vvx, NNz/2, 20.0);

    } else if (dispMode==6) {

      gridFnPlot(vvc, NNz/2, 20.0);

    } else if (dispMode==7) {

      gridFnPlot(vv, NNz/2, 20.0);

    } else if (dispMode==8) {

      gridFnPlot(rho, NNz/2, 100.0);

    }

    gOff.setColor(Color.black);
    gOff.drawString("Heine-Abarenkov pseudopotential",30,40);
    gOff.drawString("atom & ne",630/6*3+10,40);
    gOff.drawString("object",630/6*4+10,40);
    gOff.drawString("view",630/6*5+10,40);

    gb = 400;
    gOff.setColor(Color.black);
    gOff.drawString("box="+(int)(NNx*dx)+"x"+ +(int)(NNy*dy)+"x"+(int)(NNz*dz)+" au",gb,60);
    gOff.drawString("dx="+(int)(dx*100.0)/100.0+" au",gb,80);
    gOff.drawString("V(r)=-Zv/r (r>=Rc)",gb,100);
    gOff.drawString("		= u*Zv/Rc (r<Rc)",gb,120);
    gOff.drawString("   Zv="+Znuc+", ne="+NOE+", Rc="+Rcore+"",gb,140);
    gOff.drawString("   u="+HAu+"",gb,160);

    gOff.drawString("g0="+(float)(g0)+"",gb,200);
    gOff.drawString("g1=g2=g3="+(float)(g1)+"",gb,220);
    for (i=0; i<4; i++) {
      if (i<1 || g1>0.0) {
	    gOff.setColor(Color.red);
	  } else {
	    gOff.setColor(Color.blue);
	  }
      gOff.drawString("E["+i+"]="+(float)(sdEnergy[i])+"",gb,240+15*i);
	}
  }

/*------------------------------- plot methods  ------------*/

  void dens3DPlotSD(double weight,int mode, int istate) {
    int i,j,k,ix,iy,ir;
    int gbx,gby;
    double cxx,cyy,czz;
    double z,ppx,ppy,ppz;
    double mag,dens,col;

    gbx = 60;
    gby = 80;
    mag = 3.0;
    cxx = mag*(NNx/2.0); 
    cyy = mag*(NNy/2.0);
    czz = mag*(NNz/2.0);

    for (i=1; i<NNx-1; i+=2) {
      for(j=1; j<NNy-1; j +=2) {
        for (k=1; k<NNz-1; k+=2) {

          dens = 1.0*sdState[istate][i][j][k]*sdState[istate][i][j][k];
          ir = (int)(weight*dens+0.5);
          if (ir>0) {
            if (ir>10) {
              ir = 10;
            }
            z = k*mag;
            ppy = cosFi*(j*mag-cyy)+sinFi*(z-czz) + cyy; 
            ppz = -sinFi*(j*mag-cyy)+cosFi*(z-czz) + czz;
            ppx = cosTh*(i*mag-cxx)+sinTh*(ppz-czz) + cxx; 
            ppz = -sinTh*(i*mag-cxx)+cosTh*(ppz-czz) + czz;

            ix = (int)(ppx)+gbx;
            iy = (int)(ppy)+gby;
            col = 0.0;
            if (mode==0) {
              col = 0.66 -0.05*dens;
              if (col<0.0) {
                col = 0.0;
              }
            } else if (mode==1) {
              if (sdState[istate][i][j][k]>=0) {
                col = 0.33;
              } else {
                col = 0.01;
              }
            }
			
            gOff.setColor(Color.getHSBColor((float)col, 0.9f,0.9f));
            gOff.fillOval(ix-ir/2,iy-ir/2,ir,ir);
          }
        }
      }
    }
  }


  void gridFnPlot(double fn[][][], int zPos, double weight) {
    int i,j,k,gbx,gby;
    int cx,cy,cz;
    double z,px,py,pz,sc;
    double ph2;

    cx = NNx/2;
    cy = NNy/2;
    cz = 0;
    sc = 4.0;

    gbx = 30+(int)(cx/sc);
    gby = 20+(int)(cy/sc);
    k = zPos;

    for(j=0; j<NNy; j += 2) {
      for (i=0; i<NNx; i++) { 
        z = weight*fn[i][j][k] + cz;
        py = cosFi*(j-cy)+sinFi*(z-cz) + cy; 
        pz = -sinFi*(j-cy)+cosFi*(z-cz) + cz;
        px = cosTh*(i-cx)+sinTh*(pz-cz) + cx; 
        pz = -sinTh*(i-cx)+cosTh*(pz-cz) + cz;
        xpts[i] = (int)(sc*px)+gbx;
        ypts[i] = (int)(sc*py)+gby;
      }
      for (i=0; i<NNx-1; i++) {
        gOff.setColor(Color.getHSBColor(0.66f,0.6f,0.9f));
        gOff.drawLine(xpts[i],ypts[i],xpts[i+1],ypts[i+1]);
      }
    }

    for(i=0; i<NNx; i += 2) {
      for (j=0; j<NNy; j++) {
        z = weight*fn[i][j][k] + cz;
        py = cosFi*(j-cy)+sinFi*(z-cz) + cy; 
        pz = -sinFi*(j-cy)+cosFi*(z-cz) + cz;
        px = cosTh*(i-cx)+sinTh*(pz-cz) + cx; 
        pz = -sinTh*(i-cx)+cosTh*(pz-cz) + cz;
        xpts[j] = (int)(sc*px)+gbx;
        ypts[j] = (int)(sc*py)+gby;
      }
      for (j=0; j<NNy-1; j++) { 
        gOff.setColor(Color.getHSBColor(0.66f,0.6f,0.9f));
        gOff.drawLine(xpts[j],ypts[j],xpts[j+1],ypts[j+1]);
      }
    }
  }


  void boxPlot() {
    int i,j,k,ip,i1,i2;
    int gbx,gby;
    double cxx,cyy,czz;
    double z,ppx,ppy,ppz;
    double mag,dens;

    gbx = 60;
    gby = 80;
    mag = 3.0;
    cxx = mag*(NNx/2.0); 
    cyy = mag*(NNy/2.0);
    czz = mag*(NNz/2.0);

    ip = 0;
    for (i=0; i<NNx; i+=NNx-1) {
      for(j=0; j<NNy; j+=NNy-1) {
        for (k=0; k<NNz; k+=NNz-1) {
          z = k*mag;
          ppy = cosFi*(j*mag-cyy)+sinFi*(z-czz) + cyy; 
          ppz = -sinFi*(j*mag-cyy)+cosFi*(z-czz) + czz;
          ppx = cosTh*(i*mag-cxx)+sinTh*(ppz-czz) + cxx; 
          ppz = -sinTh*(i*mag-cxx)+cosTh*(ppz-czz) + czz;

          pxBox[ip] = (int)(ppx)+gbx;
          pyBox[ip] = (int)(ppy)+gby;
          ip += 1;
        }
      }
    }
    gOff.setColor(Color.gray);
    for (i=0; i<12; i++) {
      i1= boxp[i][0]; i2= boxp[i][1];
      if (i1==0) {
        gOff.setColor(Color.gray);
        gOff.drawLine(pxBox[i1],pyBox[i1],pxBox[i2],pyBox[i2]);
      }
    }
  }

  void boxPlot2() {
    int i,i1,i2;

    for (i=0; i<12; i++) {
      i1= boxp[i][0]; i2= boxp[i][1];
      if (i1 != 0) {
        gOff.setColor(Color.black);
        gOff.drawLine(pxBox[i1],pyBox[i1],pxBox[i2],pyBox[i2]);
      }
    }
  }

/*-------------------------- statistics ----------*/

  double meanKinetic(double ph[][][]) {
    int i,j,k;
    double p,d2ph,h2;

    h2 = dx*dx;
    p = 0.0;
    for (i=1;i<NNx-1;i++) {
      for (j=1;j<NNy-1;j++) {
        for (k=1;k<NNz-1;k++) {
          d2ph = (ph[i+1][j][k]+ph[i-1][j][k]+ph[i][j+1][k]+ph[i][j-1][k]+ph[i][j][k+1]+ph[i][j][k-1]-6.0*ph[i][j][k])/h2;
          p += ph[i][j][k]*d2ph;
        }
      }
    }
    return ( -0.5*p*dx*dy*dz );
  }

  double meanValue(double ph[][][],double a[][][]) {
    int i,j,k;
    double s;

    s = 0.0;
    for (i=1;i<NNx-1;i++) {
      for (j=1;j<NNy-1;j++) {
        for (k=1;k<NNz-1;k++) {
          s += a[i][j][k]*ph[i][j][k]*ph[i][j][k];
        }
      }
    }
    return ( s*dx*dy*dz );
  }


/*-------------------------- set initial condition ----------*/

  void setInitialCondition() {

    t = 0.0;

    setPotential();

    initSD(4);
  }

/* ----------------------------- set potential -------------- */

  void setPotential() {
    int i,j,k;
    double x0,y0,z0;
    double x,y,z,r;

    x0 = 8.0; y0 = 8.0; z0 = 8.0;
    for (i=0;i<NNx;i++) {
      for (j=0;j<NNy;j++) {
        for (k=0;k<NNz;k++) {
          x = i*dx;
          y = j*dy;
          z = k*dz;
          r = Math.sqrt((x-x0)*(x-x0)+(y-y0)*(y-y0)+(z-z0)*(z-z0));
          if (r<Rcore) {
            vvext[i][j][k] = HAu*Znuc/Rcore;
          } else {
            vvext[i][j][k] = -Znuc/r;
		   }
          if (r<2.0*Rcore) {
            vvh[i][j][k] = 0.5*NOE/Rcore;
          } else {
            vvh[i][j][k] = NOE/r;
		   }
        }
      }
    }
  }

/* ----------------------------- timeEvolution -------------- */

  void timeEvolution() {
    int i;

    if (started==-1) {
      t = 0.0;
      setInitialCondition();
      started = 0;
    } else if (started==1) {

      setVeff();
      SD(4, vv, 2, 0.03);
	  sortState(4);

    }
  }

  void sortState(int maxState){
    int ist,i,j,k;
    double w;

    for (ist=0; ist<maxState-1; ist++) {
      if (sdEnergy[ist]>sdEnergy[ist+1]+0.001) {
        for (i=1;i<NNx-1;i++) {
          for (j=1;j<NNy-1;j++) {
            for (k=1;k<NNz-1;k++) {
			   w = sdState[ist][i][j][k];
               sdState[ist][i][j][k] = sdState[ist+1][i][j][k];
			   sdState[ist+1][i][j][k] = w;
            }
          }
        }
        w = sdEnergy[ist]; sdEnergy[ist]= sdEnergy[ist+1]; sdEnergy[ist+1]= w;
      }
    }

  }


/* ----------------- effective potential <-- electron density ------- */

  void setVeff() {
    int i,j,k;

    setRho();
    poisson(5);
    setVcx();

    for (i=1;i<NNx-1;i++) {
      for (j=1;j<NNy-1;j++) {
        for (k=1;k<NNz-1;k++) {
          vv[i][j][k] = vvext[i][j][k]+vvh[i][j][k]+vvx[i][j][k]+vvc[i][j][k];
        }
      }
    }
  }

  void setRho() {
    int i,j,k,ie;
    double ne,g0,g1;

    ne = NOE;
	g0 = 2.0;
	g1 = 0.0;

	if (ne<=2.0) {
	  g0 = ne;
	  g1 = 0.0;
    } else if (ne>2.0) {
	  g0 = 2.0;
	  g1 = (ne-2.0)/3.0;
	}
    for (i=1; i<NNx-1; i++) {
      for (j=1; j<NNy-1; j++) {
        for (k=1; k<NNz-1; k++) {
          rho[i][j][k] = g0*(sdState[0][i][j][k]*sdState[0][i][j][k]);
		  if (g1>0.0) {
            for (ie=1; ie<=3; ie++) {
		      rho[i][j][k] += g1*(sdState[ie][i][j][k]*sdState[ie][i][j][k]);
            }
		  }
        }
      }
    }
  }

  void poisson(int iterMax) {
    int i,j,k,iter;
    double h2,w;

    h2 = 4.0*3.1416*dx*dx;
    w = 0.2;

	for (iter=1; iter<iterMax; iter++) {
	  for (i=1; i<NNx-1; i++) {
        for (j=1; j<NNy-1; j++) {
          for (k=1; k<NNz-1; k++) {
            vvh[i][j][k] = vvh[i][j][k]+w*(vvh[i+1][j][k]+vvh[i-1][j][k]+vvh[i][j+1][k]+vvh[i][j-1][k]+vvh[i][j][k+1]+vvh[i][j][k-1]-6.0*vvh[i][j][k] +h2*rho[i][j][k]);
          }
        }
      }
    }
  }

/* LDA :  J. P. Perdew and A. Zunger; Phys. Rev., B23, 5048 (1981) */

  void setVcx() {
    int i,j,k;
    double c1,rh,drho;

    c1 = -0.984745022;
    drho = 0.01;
    for (i=1; i<NNx-1; i++) {
      for (j=1; j<NNy-1; j++) {
        for (k=1; k<NNz-1; k++) {
          rh = rho[i][j][k];
          vvx[i][j][k] = c1*Math.pow(rh,0.33333333);
          vvc[i][j][k] = eeCorrelation(rh)+rh*(eeCorrelation(rh+drho)-eeCorrelation(rh))/drho;
        }
      }
    }
  }

  double eeCorrelation(double rh) {
    double r,ec;

    r = 0.6204/(Math.pow(rh,0.33333333)+1.0e-20);
    if (r>=1.0) {
      ec = -0.1423/(1.0+1.0529*Math.sqrt(r)+0.3334*r);
    } else {
      ec = -0.0480-0.0116*r+(0.0311+0.0020*r)*Math.log(r);
    }
    return ( ec );
  }

/* ----------------- Gram-Schmidt --------- */

  void GramSchmidt(int stateMax) {
    int i,j,k,ist,istate;
    double s;

    normalize(sdState[0]);

    for (istate=1; istate<stateMax; istate++) {
      for (ist=0; ist<istate; ist++) {
        s = innerProduct(sdState[ist],sdState[istate]);
        for (i=1; i<NNx-1; i++) {
          for (j=1; j<NNy-1; j++) {
            for (k=1; k<NNz-1; k++) {
              sdState[istate][i][j][k] -= s*sdState[ist][i][j][k];
            }
          }
        }
      }
      normalize(sdState[istate]);
    }
  }

  double innerProduct(double f[][][],double g[][][]) {
    int i,j,k;
    double s,dv;

    dv = dx*dy*dz;
    s = 0.0;
    for (i=1; i<NNx-1; i++) {
      for (j=1; j<NNy-1; j++) {
        for (k=1; k<NNz-1; k++) {
          s += f[i][j][k]*g[i][j][k]*dv;
        }
      }
    }
    return ( s );
  }

  void normalize(double ph[][][]) {
    int i,j,k;
    double s,a,dv;

    dv = dx*dy*dz;
    s = 0.0;
    for (i=1; i<NNx-1; i++) {
      for (j=1; j<NNy-1; j++) {
        for (k=1; k<NNz-1; k++) {
          s += ph[i][j][k]*ph[i][j][k]*dv;
        }
      }
    }
    a = Math.sqrt(1.0/s);
    for (i=1; i<NNx-1; i++) {
      for (j=1; j<NNy-1; j++) {
        for (k=1; k<NNz-1; k++) {
          ph[i][j][k] = a*ph[i][j][k];
        }
      }
    }
  }

/* --------------------- steepest descent method -------------- */

  void SD(int stateMax, double v[][][], int iterMax, double dump) {
    int i,ist;

    for (i=0; i<iterMax; i++) {
	  for (ist=0; ist<stateMax; ist++) {
        sdEnergy[ist] = steepestDescent(sdState[ist], v, dump);
      }
	  GramSchmidt(stateMax);
    }
  }

  void initSD(int stateMax) {
    int i,j,k,ist;
    double pai = 3.14159265;

    for (ist=0; ist<stateMax; ist++) {
      for (i=1; i<NNx-1; i++) {
        for (j=1; j<NNy-1; j++) {
          for (k=1; k<NNz-1; k++) {
            sdState[ist][i][j][k] = Math.random()-0.5;
          }
        }
      }
	  normalize(sdState[ist]);
    }
  }

  double steepestDescent(double psi[][][], double v[][][], double dump) {
    int i,j,k;
    double h2,ei,wk;

    h2 = 2.0*dx*dx;
    ei = energyOf(psi,vv);
    for (i=1; i<NNx-1; i++) {
      for (j=1; j<NNy-1; j++) {
        for (k=1; k<NNz-1; k++) {
          psi[i][j][k] -= dump*((6.0*psi[i][j][k]-psi[i+1][j][k]-psi[i-1][j][k]-psi[i][j+1][k]-psi[i][j-1][k]-psi[i][j][k+1]-psi[i][j][k-1])/h2 + (v[i][j][k]-ei)*psi[i][j][k]);
        }
      }
    }
    normalize(psi);
    return (ei);
  }

  double energyOf(double psi[][][], double v[][][]) {
    int i,j,k;
    double h2,dv,s,sn;

    h2 = 2.0*dx*dx;
    dv = dx*dy*dz;
    s = 0.0; sn=0.0;
    for (i=1; i<NNx-1; i++) {
      for (j=1; j<NNy-1; j++) {
        for (k=1; k<NNz-1; k++) {
          s += psi[i][j][k]*((6.0*psi[i][j][k]-psi[i+1][j][k]-psi[i-1][j][k]-psi[i][j+1][k]-psi[i][j-1][k]-psi[i][j][k+1]-psi[i][j][k-1])/h2 + v[i][j][k]*psi[i][j][k])*dv;
          sn += psi[i][j][k]*psi[i][j][k]*dv;
        }
      }
    }
    return ( s/sn );
  }

/* ----------------------------- end of applet -------------- */

}