xtheta比特幣

① matlab 方程式表達

對於已知一變數theta范圍求另一變數x，應該這樣來實施，利用for循環語句，用vpasolve函數求x，然後用plot函數繪出theta和x的圖像。
theta0=0:0.1:2*pi;
for i=1:length(theta0)
syms x
theta=theta0(i);
x=vpasolve(x.^2-200*x*cos(pi-theta)-300==0);
x0(i,:)=x;
end
plot(theta0,x0)
xlabel(' heta');ylabel('x( heta)')

注:x值有兩組。

② 幫忙解釋一下，JDK中的demo裡面的applets.html的第一個例子，xyzapp.java

哪一個啊？
這個啊。。也太長了點吧。。
import java.applet.Applet;
import java.awt.Image;
import java.awt.Event;
import java.awt.Graphics;
import java.awt.Dimension;
import java.io.*;
import java.net.URL;
import java.util.Hashtable;
import java.awt.image.IndexColorModel;
import java.awt.image.ColorModel;
import java.awt.image.MemoryImageSource;
import java.awt.event.*;
/**上面是導入庫文件，沒什麼好解釋的，關於各個庫文件的只是你在MSDN里搜索吧，你主要弄明白各個函數的用法和返回值就行了，你把用到的函數復制一下，粘貼到MSDN里查一下，沒有MSDN就貼到網路或Google里查。*/
/** The representation of a Chemical .xyz model */
class XYZChemModel {
float vert[];
Atom atoms[];
int tvert[];
int ZsortMap[];
int nvert, maxvert;

static Hashtable atomTable = new Hashtable();
static Atom defaultAtom;
static {
atomTable.put("c", new Atom(0, 0, 0));
atomTable.put("h", new Atom(210, 210, 210));
atomTable.put("n", new Atom(0, 0, 255));
atomTable.put("o", new Atom(255, 0, 0));
atomTable.put("p", new Atom(255, 0, 255));
atomTable.put("s", new Atom(255, 255, 0));
atomTable.put("hn", new Atom(150, 255, 150)); /* !!*/
defaultAtom = new Atom(255, 100, 200);
}

boolean transformed;
Matrix3D mat;

float xmin, xmax, ymin, ymax, zmin, zmax;

XYZChemModel () {
mat = new Matrix3D();
mat.xrot(20);
mat.yrot(30);
}

/** Create a Cehmical model by parsing an input stream */
XYZChemModel (InputStream is) throws Exception
{
this();
StreamTokenizer st = new StreamTokenizer(new BufferedReader(new InputStreamReader(is)));
st.eolIsSignificant(true);
st.commentChar('#');
int slot = 0;

try
{
scan:
while (true)
{
switch ( st.nextToken() )
{
case StreamTokenizer.TT_EOF:
break scan;
default:
break;
case StreamTokenizer.TT_WORD:
String name = st.sval;
double x = 0, y = 0, z = 0;
if (st.nextToken() == StreamTokenizer.TT_NUMBER)
{
x = st.nval;
if (st.nextToken() == StreamTokenizer.TT_NUMBER)
{
y = st.nval;
if (st.nextToken() == StreamTokenizer.TT_NUMBER)
z = st.nval;
}
}
addVert(name, (float) x, (float) y, (float) z);
while( st.ttype != StreamTokenizer.TT_EOL &&
st.ttype != StreamTokenizer.TT_EOF )
st.nextToken();

} // end Switch

} // end while

is.close();

} // end Try
catch( IOException e) {}

if (st.ttype != StreamTokenizer.TT_EOF)
throw new Exception(st.toString());

} // end XYZChemModel()

/** Add a vertex to this model */
int addVert(String name, float x, float y, float z) {
int i = nvert;
if (i >= maxvert)
if (vert == null) {
maxvert = 100;
vert = new float[maxvert * 3];
atoms = new Atom[maxvert];
} else {
maxvert *= 2;
float nv[] = new float[maxvert * 3];
System.array(vert, 0, nv, 0, vert.length);
vert = nv;
Atom na[] = new Atom[maxvert];
System.array(atoms, 0, na, 0, atoms.length);
atoms = na;
}
Atom a = (Atom) atomTable.get(name.toLowerCase());
if (a == null) a = defaultAtom;
atoms[i] = a;
i *= 3;
vert[i] = x;
vert[i + 1] = y;
vert[i + 2] = z;
return nvert++;
}

/** Transform all the points in this model */
void transform() {
if (transformed || nvert <= 0)
return;
if (tvert == null || tvert.length < nvert * 3)
tvert = new int[nvert * 3];
mat.transform(vert, tvert, nvert);
transformed = true;
}

/** Paint this model to a graphics context. It uses the matrix associated
with this model to map from model space to screen space.
The next version of the browser should have double buffering,
which will make this *much* nicer */
void paint(Graphics g) {
if (vert == null || nvert <= 0)
return;
transform();
int v[] = tvert;
int zs[] = ZsortMap;
if (zs == null) {
ZsortMap = zs = new int[nvert];
for (int i = nvert; --i >= 0;)
zs[i] = i * 3;
}

/*
* I use a bubble sort since from one iteration to the next, the sort
* order is pretty stable, so I just use what I had last time as a
* "guess" of the sorted order. With luck, this reces O(N log N)
* to O(N)
*/

for (int i = nvert - 1; --i >= 0;) {
boolean flipped = false;
for (int j = 0; j <= i; j++) {
int a = zs[j];
int b = zs[j + 1];
if (v[a + 2] > v[b + 2]) {
zs[j + 1] = a;
zs[j] = b;
flipped = true;
}
}
if (!flipped)
break;
}

int lg = 0;
int lim = nvert;
Atom ls[] = atoms;
if (lim <= 0 || nvert <= 0)
return;
for (int i = 0; i < lim; i++) {
int j = zs[i];
int grey = v[j + 2];
if (grey < 0)
grey = 0;
if (grey > 15)
grey = 15;
// g.drawString(names[i], v[j], v[j+1]);
atoms[j/3].paint(g, v[j], v[j + 1], grey);
// g.drawImage(iBall, v[j] - (iBall.width >> 1), v[j + 1] -
// (iBall.height >> 1));
}
}

/** Find the bounding box of this model */
void findBB() {
if (nvert <= 0)
return;
float v[] = vert;
float xmin = v[0], xmax = xmin;
float ymin = v[1], ymax = ymin;
float zmin = v[2], zmax = zmin;
for (int i = nvert * 3; (i -= 3) > 0;) {
float x = v[i];
if (x < xmin)
xmin = x;
if (x > xmax)
xmax = x;
float y = v[i + 1];
if (y < ymin)
ymin = y;
if (y > ymax)
ymax = y;
float z = v[i + 2];
if (z < zmin)
zmin = z;
if (z > zmax)
zmax = z;
}
this.xmax = xmax;
this.xmin = xmin;
this.ymax = ymax;
this.ymin = ymin;
this.zmax = zmax;
this.zmin = zmin;
}
}

/** An applet to put a Chemical model into a page */
public class XYZApp
extends Applet
implements Runnable, MouseListener, MouseMotionListener {
XYZChemModel md;
boolean painted = true;
float xfac;
int prevx, prevy;
float xtheta, ytheta;
float scalefudge = 1;
Matrix3D amat = new Matrix3D(), tmat = new Matrix3D();
String mdname = null;
String message = null;
Image backBuffer;
Graphics backGC;
Dimension backSize;

private synchronized void newBackBuffer() {
backBuffer = createImage(getSize().width, getSize().height);
if (backGC != null) {
backGC.dispose();
}
backGC = backBuffer.getGraphics();
backSize = getSize();
}

public void init() {
mdname = getParameter("model");
try {
scalefudge = Float.valueOf(getParameter("scale")).floatValue();
} catch(Exception e) {
};
amat.yrot(20);
amat.xrot(20);
if (mdname == null)
mdname = "model.obj";
resize(getSize().width <= 20 ? 400 : getSize().width,
getSize().height <= 20 ? 400 : getSize().height);
newBackBuffer();
addMouseListener(this);
addMouseMotionListener(this);
}

public void destroy() {
removeMouseListener(this);
removeMouseMotionListener(this);
}

public void run() {
InputStream is = null;
try {
Thread.currentThread().setPriority(Thread.MIN_PRIORITY);
is = new URL(getDocumentBase(), mdname).openStream();
XYZChemModel m = new XYZChemModel (is);
Atom.setApplet(this);
md = m;
m.findBB();
float xw = m.xmax - m.xmin;
float yw = m.ymax - m.ymin;
float zw = m.zmax - m.zmin;
if (yw > xw)
xw = yw;
if (zw > xw)
xw = zw;
float f1 = getSize().width / xw;
float f2 = getSize().height / xw;
xfac = 0.7f * (f1 < f2 ? f1 : f2) * scalefudge;
} catch(Exception e) {
e.printStackTrace();
md = null;
message = e.toString();
}
try {
if (is != null)
is.close();
} catch(Exception e) {
}
repaint();
}
public void start() {
if (md == null && message == null)
new Thread(this).start();
}
public void stop() {
}
/* event handling */
public void mouseClicked(MouseEvent e) {
}
public void mousePressed(MouseEvent e) {
prevx = e.getX();
prevy = e.getY();
e.consume();
}
public void mouseReleased(MouseEvent e) {
}
public void mouseEntered(MouseEvent e) {
}
public void mouseExited(MouseEvent e) {
}
public void mouseDragged(MouseEvent e) {
int x = e.getX();
int y = e.getY();
tmat.unit();
float xtheta = (prevy - y) * (360.0f / getSize().width);
float ytheta = (x - prevx) * (360.0f / getSize().height);
tmat.xrot(xtheta);
tmat.yrot(ytheta);
amat.mult(tmat);
if (painted) {
painted = false;
repaint();
}
prevx = x;
prevy = y;
e.consume();
}
public void mouseMoved(MouseEvent e) {
}

public void update(Graphics g) {
if (backBuffer == null)
g.clearRect(0, 0, getSize().width, getSize().height);
paint(g);
}

public void paint(Graphics g) {
if (md != null) {
md.mat.unit();
md.mat.translate(-(md.xmin + md.xmax) / 2,
-(md.ymin + md.ymax) / 2,
-(md.zmin + md.zmax) / 2);
md.mat.mult(amat);
// md.mat.scale(xfac, -xfac, 8 * xfac / getSize().width);
md.mat.scale(xfac, -xfac, 16 * xfac / getSize().width);
md.mat.translate(getSize().width / 2, getSize().height / 2, 8);
md.transformed = false;
if (backBuffer != null) {
if (!backSize.equals(getSize()))
newBackBuffer();
backGC.setColor(getBackground());
backGC.fillRect(0,0,getSize().width,getSize().height);
md.paint(backGC);
g.drawImage(backBuffer, 0, 0, this);
}
else
md.paint(g);
setPainted();
} else if (message != null) {
g.drawString("Error in model:", 3, 20);
g.drawString(message, 10, 40);
}
}
private synchronized void setPainted() {
painted = true;
notifyAll();
}

private synchronized void waitPainted()
{
while (!painted)
{
try
{
wait();
}
catch (InterruptedException e) {}
}
painted = false;
}

public String getAppletInfo() {
return "Title: XYZApp \nAuthor: James Gosling \nAn applet to put a Chemical model into a page.";
}

public String[][] getParameterInfo() {
String[][] info = {
{"model", "path string", "The path to the model to be displayed in .xyz format (see http://chem.leeds.ac.uk/Project/MIME.html). Default is model.obj."},
{"scale", "float", "Scale factor. Default is 1 (i.e. no scale)."}
};
return info;
}
} // end class XYZApp

class Atom {
private static Applet applet;
private static byte[] data;
private final static int R = 40;
private final static int hx = 15;
private final static int hy = 15;
private final static int bgGrey = 192;
private final static int nBalls = 16;
private static int maxr;

private int Rl;
private int Gl;
private int Bl;
private Image balls[];

static {
data = new byte[R * 2 * R * 2];
int mr = 0;
for (int Y = 2 * R; --Y >= 0;) {
int x0 = (int) (Math.sqrt(R * R - (Y - R) * (Y - R)) + 0.5);
int p = Y * (R * 2) + R - x0;
for (int X = -x0; X < x0; X++) {
int x = X + hx;
int y = Y - R + hy;
int r = (int) (Math.sqrt(x * x + y * y) + 0.5);
if (r > mr)
mr = r;
data[p++] = r <= 0 ? 1 : (byte) r;
}
}
maxr = mr;
}
static void setApplet(Applet app) {
applet = app;
}
Atom(int Rl, int Gl, int Bl) {
this.Rl = Rl;
this.Gl = Gl;
this.Bl = Bl;
}
private final int blend(int fg, int bg, float fgfactor) {
return (int) (bg + (fg - bg) * fgfactor);
}
private void Setup() {
balls = new Image[nBalls];
byte red[] = new byte[256];
red[0] = (byte) bgGrey;
byte green[] = new byte[256];
green[0] = (byte) bgGrey;
byte blue[] = new byte[256];
blue[0] = (byte) bgGrey;
for (int r = 0; r < nBalls; r++) {
float b = (float) (r+1) / nBalls;
for (int i = maxr; i >= 1; --i) {
float d = (float) i / maxr;
red[i] = (byte) blend(blend(Rl, 255, d), bgGrey, b);
green[i] = (byte) blend(blend(Gl, 255, d), bgGrey, b);
blue[i] = (byte) blend(blend(Bl, 255, d), bgGrey, b);
}
IndexColorModel model = new IndexColorModel(8, maxr + 1,
red, green, blue, 0);
balls[r] = applet.createImage(
new MemoryImageSource(R*2, R*2, model, data, 0, R*2));
}
}
void paint(Graphics gc, int x, int y, int r) {
Image ba[] = balls;
if (ba == null) {
Setup();
ba = balls;
}
Image i = ba[r];
int size = 10 + r;
gc.drawImage(i, x - (size >> 1), y - (size >> 1), size, size, applet);
}
}

③ 用matlab實現梯度下降演算法（gradient descent）。

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
% theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by
% taking num_iters gradient steps with learning rate alpha
% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);
for iter = 1:num_iters,
% ====================== YOUR CODE HERE ======================
% Instructions: Perform a single gradient step on the parameter vector
% theta.
%
% Hint: While debugging, it can be useful to print out the values
% of the cost function (computeCost) and gradient here.

p=theta(1)-alpha*(1/m)*(sum((X*theta-y).*X(:,1)));
q=theta(2)-alpha*(1/m)*(sum((X*theta-y).*X(:,2)));
theta(1)=p;
theta(2)=q;

% ============================================================
% Save the cost J in every iteration
J_history(iter) = computeCost(X, y, theta);
end
end