// Main class // /* * Taylor Polynomial Approximation Applet * By Mike May, S.J., August 2001 * e-mail: maymk@slu.edu * * Some of the work derives from the Riemann Sum applet * by Brendon Cheves & Bill Ziemer * e-mail: brendon@csulb.edu wziemer@csulb.edu * expr package Copyright 1996 by Darius Bacon */ // Last update 8/2/2001 /* * The applet graphs a function and the specified Taylor polynomial approximation * over a specified range. The derivatives needed for the Taylor polynomial are * approximated with standard numerical techniques. The user can specify the * degree of the approximation be from 0 to 4. * * The function can be tyoed in by the user. The user can also specify the x and * y range of the graph, the base point X0, the approximated point X1, and the * dX used for the numericalderivative approxiamtions. The vlaues of X0 and X1 * can be changed by mouse click or mouse drag. * * The structure of the program has a main class AproxPoly. * The work is broken into a number of visible classes: * DrawingPanel, FeedbackPanel, HelpArea, and AboutArea. * The names of these classes are fairly self descriptive. * MultilineLabel is used by AboutArea. * The function being studied is handled by the ZFunction class. * This class uses a parser that calls on the following classes: * Expr, Parser, Syntax_error, Test, TrivialClass and Variable. */ /* * public class ApproxPoly extends Applet * public void init() * public boolean action(Event e, Object arg) * * The applet is set up in a form that can be modified for other applets. * The main applet has a title label and buttons to switch between three * cards, the main card, the help card, and the about card. * The about card provides author information. * The help card gives help that a user may need to run the applet. * The main card is what we might think of as the applet proper. It * contains a drawing panel and a feedback panel. The drawing panel * and feedback panel are separate objects where most of the real work is done. * * The init method sets up the basic interface though the most of the hard * details are in the feedback panel and the drawing panel. * * An action method is needed to deal with the buttons that switch cards. * * * public void fixMain() * public void moveFeedbackPanelValues() * * The majority of the work is done with the fixMain method. A subsidiary method * that is called is moveFeedbackPanelValues. * * * public void drawingPanelClick(double xReal) * * The method drawingPanelClick updates things in response to a mouseclick * somewhere on the drawingPanel. * */ // java packages import java.applet.*; import java.awt.*; import java.lang.Math; import expr.*; // f(x) parser by Darius Bacon public class ApproxPoly extends Applet { // Declare variables int drawingPanelWidth = 680, drawingPanelHeight = 340, leftXOffset = 40, rightXOffset = 60, areaXWidth = drawingPanelWidth - leftXOffset - rightXOffset, YOFFSET = 20; int firstIndex = 1, clickIndex = 0; double leftX, rightX; double xMin = 0.0, xMax = 1.0, x0, x1, fX1, approxX1; double zeroDeriv, firstDeriv, secondDeriv, thirdDeriv, fourthDeriv; String functionString, approxString; // GUI elements Button helpButton, aboutButton, okBtn; Label titleLabel; CardLayout theCards; Panel mainCd, mainPanel, cardChoicePanel; HelpArea helpText; AboutArea aboutText; FeedbackPanel feedbackPanel; DrawingPanel theDrawingPanel; public void init() { this.setLayout(null); resize(700,500); // Set up the pieces titleLabel = new Label("Taylor Polynomial Approximations", Label.CENTER); setLayout(new BorderLayout(3,3)); this.add(titleLabel, BorderLayout.NORTH); titleLabel.setFont(new Font("Dialog", Font.BOLD, 18)); mainPanel = new Panel(); this.add(mainPanel, BorderLayout.CENTER); // create a card layout and 3 cards theCards = new CardLayout(0,0); mainPanel.setLayout(theCards); // create the main card mainCd = new Panel(); mainPanel.add("main",mainCd); mainCd.setLayout(new BorderLayout(3,3)); // create the about card aboutText = new AboutArea(); aboutText.setBounds(0,0,600,380); mainPanel.add("about",aboutText); // create the help card helpText = new HelpArea(600, 300); helpText.setBounds(0,0,600,380); mainPanel.add("help",helpText); // create the feedback panel and add it to the main cd feedbackPanel = new FeedbackPanel(this); feedbackPanel.setSize(200,400); mainCd.add(feedbackPanel, BorderLayout.EAST); feedbackPanel.fixInputs(); feedbackPanel.resetYMinYMax(); // create the drawing panel and add it to the main cd theDrawingPanel = new DrawingPanel(this); mainCd.add(theDrawingPanel, BorderLayout.CENTER); fixMain(); /** * Add a panel to the bottom of the screen to let the user choose * between cards. */ cardChoicePanel = new Panel(); this.add(cardChoicePanel, BorderLayout.SOUTH); cardChoicePanel.setLayout(new GridLayout(1,0,10,0)); okBtn = new Button("Main Panel"); cardChoicePanel.add(okBtn); helpButton = new Button("Help Panel"); cardChoicePanel.add(helpButton); aboutButton = new Button("About Panel"); cardChoicePanel.add(aboutButton); // finally, show the main card theCards.show(mainPanel,"main"); } // init // handle GUI events public boolean action(Event e, Object arg) { double outputdx; if(e.target == aboutButton) { theCards.show(mainPanel,"about"); return true; } else if(e.target == helpButton) { theCards.show(mainPanel,"help"); return true; } else if(e.target == okBtn) { theCards.show(mainPanel,"main"); feedbackPanel.fixInputs(); fixMain(); paint(theDrawingPanel.getGraphics()); return true; } else return super.action(e,arg); } // action public void fixMain() { feedbackPanel.updateFeedbackPanelValues(); moveFeedbackPanelValues(); theDrawingPanel.updateDrawingValues(); paint(getGraphics()); theDrawingPanel.repaint(); } // fixMain public void moveFeedbackPanelValues() { theDrawingPanel.functionString = feedbackPanel.functionString; theDrawingPanel.xBase = feedbackPanel.xBase; theDrawingPanel.xDel = feedbackPanel.xDel; theDrawingPanel.x1 = feedbackPanel.x1; theDrawingPanel.xMin = feedbackPanel.xMin; theDrawingPanel.xMax = feedbackPanel.xMax; theDrawingPanel.bottomY = feedbackPanel.yMin; theDrawingPanel.topY = feedbackPanel.yMax; theDrawingPanel.firstIndex = feedbackPanel.firstIndex; clickIndex = feedbackPanel.clickIndex; theDrawingPanel.clickIndex = feedbackPanel.clickIndex; } // importfeedbackPanelValues public void drawingPanelClick() { feedbackPanel.setXBase(theDrawingPanel.xBase); feedbackPanel.setX1(theDrawingPanel.x1); if(clickIndex == 2) { feedbackPanel.yMin = theDrawingPanel.bottomY; feedbackPanel.yMax = theDrawingPanel.topY; feedbackPanel.xMin = theDrawingPanel.leftX; feedbackPanel.xMax = theDrawingPanel.rightX; feedbackPanel.postXMinXMax(); feedbackPanel.postYMinYMax(); } feedbackPanel.fixInputs(); fixMain(); } // drawingPanelClick } // ApproxPoly //// //// //// // Other pieces //// //// /* * The drawing panel is an object for the graphical display of the applet. * * *public class DrawingPanel extends Canvas implements MouseListener, MouseMotionListener * public DrawingPanel(ApproxPoly appPoly, ZFunction f) * public void updateDrawingValues() * public void repaint() * public void paint(Graphics g) * public void mouseDragged(MouseEvent e) * public void mouseMoved(MouseEvent e) * public void mousePressed(MouseEvent e) * public void mouseReleased(MouseEvent e) * public void mouseEntered(MouseEvent e) * public void mouseExited(MouseEvent e) * public void mouseClicked(MouseEvent e) * * The constructor does little more than extend canvas and identify the applet * and applet so that information can be passed back and forth. It also adds * action listeners for the mouse. The corresponding methods are included, * though all but mouse dragged and mouse releases are empty. The repaint method * simply calls paint which does all the work. The updateDrawingValues method * computes values used by the drawingPanel after data has been transferred from * the feedbackPanel. * * * public boolean mouseUp(Event e, int x, int y) * * This method listens for mouse clicks on the graph and starts appropriate action * * * public void plot(Graphics g, ZFunction f, double leftX, double rightX, Color color) * * This methods draws in the function or the appropriate approximation. * * * public void drawAxis(Graphics g) * public void drawLimits(Graphics g) * * These methods add in the axes and the text that goes on the graph. * * * public double xPixelToReal(double xPixel) * public double xPixelToReal(int xPixel) * public int xRealToPixel(double xReal) * public int xRealToPixel(int xReal) * public int yRealToPixel(double yReal) * public int yRealToPixel(int yReal) * public double yPixelToReal(double yPixel) * public double yPixelToReal(int yPixel) * * These methods switch between coordinate and pixel measurements of locations on * the graph * */ import java.awt.event.*; import java.awt.*; import java.applet.*; import MIO.*; public class DrawingPanel extends Canvas implements MouseListener, MouseMotionListener { // Declare variables // variables concerned with the size of the panel and how much is used // for the actual drawing. // The left and right offsets determine where // the Riemann approximation is done. The vertical offset is just to // make everything look nice. The panel is set up with a single offset // at the top and a double one at the bottom of the panel. int drawingPanelWidth = 680, drawingPanelHeight = 340, leftXOffset = 40, rightXOffset = 60, areaXWidth = drawingPanelWidth - leftXOffset - rightXOffset, YOFFSET = 20; // variables concerning the approximation to be graphed int firstIndex = 0, clickIndex = 0; double xBase=-1.0, x1=1.0; double leftX, rightX, bottomY, topY, halfHigh, halfWide; double xMin = 0.0, xMax = 1.0, xDel; String functionString = "x+0.1*x^2-3*sin(x)", approxString; double approxX1, fX1, zeroDeriv; ZFunction theFunction, approxFunction; ApproxPoly applet; public DrawingPanel(ApproxPoly appPoly) { super(); theFunction = new ZFunction(); approxFunction = new ZFunction(); applet = appPoly; addMouseMotionListener(this); addMouseListener(this); } // DrawingPanel constructor public void repaint() { paint(getGraphics()); } // repaint public void updateDrawingValues() { drawingPanelWidth = getSize().width; drawingPanelHeight = getSize().height; areaXWidth = drawingPanelWidth - leftXOffset - rightXOffset; theFunction.parse(functionString); fX1 = theFunction.value(x1); theFunction.xBase = xBase; theFunction.xDel = xDel; theFunction.findNumDerivs(); zeroDeriv = theFunction.zeroDeriv; leftX = xMin - (1.0*leftXOffset/areaXWidth)*(xMax-xMin); rightX = xMax + (1.0*rightXOffset/areaXWidth)*(xMax-xMin); approxString = Mio.doubleToStringNoE(theFunction.zeroDeriv); if(firstIndex >= 1) approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.firstDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")"; if(firstIndex >= 2) approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.secondDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")^2/2 "; if(firstIndex >= 3) approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.thirdDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")^3/6 "; if(firstIndex >= 4) approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.fourthDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")^4/24 "; approxFunction.parse(approxString); } public void paint(Graphics g) { updateDrawingValues(); // clear the canvas g.clearRect(0,0,drawingPanelWidth,drawingPanelHeight); // plot the function plot(g, theFunction, leftX, rightX, Color.cyan); // paint the appropriate approximation if(firstIndex == 0)plot(g, approxFunction, leftX, rightX, Color.magenta); if(firstIndex == 1)plot(g, approxFunction, leftX, rightX, Color.green); if(firstIndex == 2)plot(g, approxFunction, leftX, rightX, Color.red); if(firstIndex == 3)plot(g, approxFunction, leftX, rightX, Color.black); if(firstIndex == 4)plot(g, approxFunction, leftX, rightX, Color.blue); // add axes and limits drawAxis(g); drawLimits(g); } // paint // methods for the mouse listener and the mouse motion listener public void mouseDragged(MouseEvent e) { if(clickIndex < 2) { double xRealClick = xPixelToReal(e.getX()); double yRealClick = yPixelToReal(e.getY()); double xReal2 = ((int)(xRealClick*1000))/1000.0; double yReal2 = ((int)(yRealClick*1000))/1000.0; if (clickIndex == 0) xBase = xReal2; if (clickIndex == 1) x1 = xReal2; applet.drawingPanelClick(); } } // mouseDragged public void mouseMoved(MouseEvent e) { } //mouseMoved public void mousePressed(MouseEvent e) { } // mousePressed public void mouseReleased(MouseEvent e) { double xRealClick = xPixelToReal(e.getX()); double yRealClick = yPixelToReal(e.getY()); double xReal2 = ((int)(xRealClick*1000))/1000.0; double yReal2 = ((int)(yRealClick*1000))/1000.0; if (clickIndex == 0) xBase = xReal2; if (clickIndex == 1) x1 = xReal2; if (clickIndex == 2) { halfHigh = (topY - bottomY)/2; topY = yReal2 + halfHigh; bottomY = yReal2 - halfHigh; halfWide = (xMax - xMin)/2; rightX = xReal2 + halfWide; leftX = xReal2 - halfWide; } applet.drawingPanelClick(); } // mouseReleased public void mouseEntered(MouseEvent e) { } // mouseEntered public void mouseExited(MouseEvent e) { } // mouseExited public void mouseClicked(MouseEvent e) { } // mouseClicked // end of motion litener methods public void plot(Graphics g, ZFunction f, double leftX, double rightX, Color color) { int y1, y2, j; g.setColor(color); f.xvar.set_value(xPixelToReal(leftX)); y1 = yRealToPixel(f.expr.value()); for(int i=xRealToPixel(leftX); i < xRealToPixel(rightX); i++) { f.xvar.set_value(xPixelToReal(i+1)); y2 = yRealToPixel(f.expr.value()); // Bug in drawLine that freaks when both arguments // outside drawing area; yields spurious vertical lines if( (0 <= y2) && (y2 <= drawingPanelHeight)) { g.drawLine(i, y1, i+1, y2); } y1 = y2; } } // plot // draw the axis public void drawAxis(Graphics g) { int xAxisPixel, yAxisPixel; int x1Pixel = (int) xRealToPixel(x1); g.setColor(Color.black); xAxisPixel = yRealToPixel(0); if(xAxisPixel > drawingPanelHeight - 50) xAxisPixel = drawingPanelHeight - 50; if(xAxisPixel < 28) xAxisPixel = 28; yAxisPixel = leftXOffset; // x axis g.drawLine(0,xAxisPixel,drawingPanelWidth - 20,xAxisPixel); // y axis g.drawLine(yAxisPixel,20, yAxisPixel,drawingPanelHeight-10); g.drawString("X",drawingPanelWidth - 15,xAxisPixel + 4); g.drawString("Y",yAxisPixel-2,17); // approximating function g.setColor(Color.black); g.drawLine(x1Pixel,20, x1Pixel,drawingPanelHeight-10); } // drawAxis // draw limits in the proper places public void drawLimits(Graphics g) { int xAxisPixel, yAxisPixel, xMaxPixel, xMidPixel, yPixel; int xBasePixel, x1Pixel; double yVal; xBasePixel = (int) xRealToPixel(xBase); x1Pixel = (int) xRealToPixel(x1); xAxisPixel = (int) yRealToPixel(0); if(xAxisPixel > drawingPanelHeight - 50) xAxisPixel = drawingPanelHeight - 50; if(xAxisPixel < 28) xAxisPixel = 28; yAxisPixel = leftXOffset; xMidPixel = leftXOffset + areaXWidth/2; xMaxPixel = leftXOffset + areaXWidth; g.setColor(Color.red); // x limit g.drawString(Mio.doubleToStringSigFigures(xMin, 4), yAxisPixel + 4,xAxisPixel + 14); g.drawLine(yAxisPixel,xAxisPixel - 2, yAxisPixel,xAxisPixel + 2); g.drawString(Mio.doubleToStringSigFigures((xMin + xMax)/2.0, 4), xMidPixel + 4,xAxisPixel + 14); g.drawLine(xMidPixel,xAxisPixel - 2, xMidPixel,xAxisPixel + 2); g.drawString(Mio.doubleToStringSigFigures(xMax, 4), xMaxPixel + 4,xAxisPixel + 14); g.drawLine(xMaxPixel,xAxisPixel - 2, xMaxPixel,xAxisPixel + 2); // y limit yVal = topY; yPixel = yRealToPixel(yVal); g.drawString(Mio.doubleToStringSigFigures(yVal, 4), yAxisPixel - 40,yPixel + 3); g.drawLine(yAxisPixel - 2,yPixel, yAxisPixel + 2,yPixel); yVal = bottomY; yPixel = yRealToPixel(yVal); g.drawString(Mio.doubleToStringSigFigures(yVal, 4), yAxisPixel - 40,yPixel + 3); g.drawLine(yAxisPixel - 2,yPixel, yAxisPixel + 2,yPixel); // (X0, f(X0)) g.drawString(Mio.doubleToStringSigFigures(xBase, 4), xBasePixel + 4,xAxisPixel + 14); g.drawString("X0", xBasePixel + 4,xAxisPixel + 28); g.drawLine(xBasePixel,xAxisPixel - 2, xBasePixel,xAxisPixel + 2); yVal = theFunction.value(xBase); yPixel = yRealToPixel(yVal); g.drawString(Mio.doubleToStringSigFigures(yVal, 4), yAxisPixel - 40,yPixel + 3); g.drawLine(yAxisPixel - 2, yPixel, yAxisPixel + 2, yPixel); g.drawLine(xBasePixel - 2, yPixel, xBasePixel + 2, yPixel); g.drawLine(xBasePixel,yPixel - 2, xBasePixel,yPixel + 2); // (X1, f(X1)) g.drawString(Mio.doubleToStringSigFigures(x1, 4), x1Pixel + 4,xAxisPixel -16); g.drawString("X1", x1Pixel + 4, xAxisPixel -2); g.drawLine(x1Pixel, xAxisPixel - 2, x1Pixel, xAxisPixel + 2); yVal = theFunction.value(x1); yPixel = yRealToPixel(yVal); g.drawString(Mio.doubleToStringSigFigures(yVal, 4), yAxisPixel - 40,yPixel + 3); g.drawLine(yAxisPixel - 2, yPixel, yAxisPixel + 2, yPixel); g.drawLine(x1Pixel - 2, yPixel, x1Pixel + 2, yPixel); } // drawLimits // input pixel, output real value in interval [xMIn, xMax] public double xPixelToReal(double xPixel) { return ((xPixel - leftXOffset) * (xMax - xMin) / areaXWidth + xMin); } // xPixelToReal public double xPixelToReal(int xPixel) { return ((xPixel - leftXOffset) * (xMax - xMin) / areaXWidth + xMin); } // xPixelToReal // input real, output pixel in interval [0, XSCALE] public int xRealToPixel(double xReal) { return (int)((xReal - xMin) / (xMax - xMin) * areaXWidth + leftXOffset); } // xRealToPixel public int xRealToPixel(int xReal) { return (int)((xReal - xMin) / (xMax - xMin) * areaXWidth + leftXOffset); } // xRealToPixel // input real value, output pixel in interval [0, YSCALE] public int yRealToPixel(double yReal) { return (int)((yReal - topY) * (drawingPanelHeight - 3.0*YOFFSET) / (bottomY - topY) + YOFFSET); } // yRealToPixel public int yRealToPixel(int yReal) { return (int)((yReal - topY) * (drawingPanelHeight - 3.0*YOFFSET) / (bottomY - topY) + YOFFSET); } // yRealToPixel // input pixel, output real in interval [yMin, yMax] public double yPixelToReal(double yPixel) { return ((yPixel - YOFFSET) * (bottomY - topY) / (drawingPanelHeight - 3*YOFFSET) + topY); } // yPixelToReal public double yPixelToReal(int yPixel) { return ((yPixel - YOFFSET) * (bottomY - topY) / (drawingPanelHeight - 3*YOFFSET) + topY); } // yPixelToReal } // DrawingPanel class /* * The feedback panel is intended to contain all the inputs and text * outputs used by the applet. * * * public FeedbackPanel(ApproxPoly applet) * public void setChoices(Choice currentChoice) * class SymItem implements java.awt.event.ItemListener * public boolean action(Event e, Object arg) * * The longest method of the class is the constructor that puts the GUI * interface into place. In this case setChoices is a subsidiary method * used to set up the choices on drop down menues. * * The action method and the itemStateChanged method listen for button * pushes, return in a text field, and choosing an item from a menu. * Each button causes its own results. * * * * public void fixInputs() * public void updateFeedbackPanelValues() * public void resetYMinYMax() * public void getXBase() * public void getX1() * public void getXDel() * public void getXMinXMax() * public void getYMinYMax() * * public void postXMinYMax() * public void postYMinYMax() * * public void drawLabels() * public void setXBase(double xBase) * public void setX1(double x1) * * The two main methods fixInputs and drawLabels collect input and print * out the output. * * The subsidiary methods used in collecting data are getXminXMax, * getXBase, getX1 and getXDel. * postXMinXMax and postYMinYMax put values back in text fields. * Subsidiary methods of printing output are setXBase and setX1. * */ import java.awt.*; import java.applet.*; import MIO.*; public class FeedbackPanel extends Panel { /* * Public variables that are either inputs or outputs to be passed */ double xBase, xDel, zeroDeriv; double yMin = -5.0, yMax = 5.0; double xMin = -5.0, xMax = 5.0, x1 = 0.54, fX1, approxX1; int firstIndex, clickIndex; String functionString; double xCenter, halfWide, yCenter, halfHigh; /* * GUI elements for the panel */ Button graphfx, zoomIn, zoomOut, zSquare; Button yZoomIn, yZoomOut, yReset; Choice approxChoice, clickChoice; Panel miscPanel, domainPanel, approxPanel, evalPanel; Panel checkBoxPanel; Label zeroDerivLabel; Label fxLabel, xBaseLabel, xDelLabel, xMinLabel, xMaxLabel, yMinLabel, yMaxLabel, x1Label, fEvalLabel, approxEvalLabel, errorLabel, approx0Label, approx1Label, approx2Label, approx3Label, approx4Label; TextField functionFld, xMinField, xMaxField, yMinField, yMaxField, xBaseField, xDelField, x1Field; String approxString, approxString0, approxString1, approxString2, approxString3, approxString4; ApproxPoly approxPoly; ZFunction theFunction, approxFunction; public FeedbackPanel(ApproxPoly applet) { this.setLayout(null); approxPoly = applet; theFunction = new ZFunction(); approxFunction = new ZFunction(); /* * The feedback panel is further divided into a number of panels. * * miscPanel contains info on the function, the base point, the size of xDel * which is used for numeric approximations of the derivatives and the * graphing domain. It is 200 by 100 and on the top. * * Thee middle is the approxPanel which contains the approximation * point X1, a choice menu of types of approximation, the value of f and the * approximation evaluates at X1, along with the error. There is also * a choice menu to determine if clickiing on the graph panel moves X0 or X1. * This panel is 200 by 200. * * On the bottom is the domainPanel which contains info on x and y limits * of the graph. There are buttons for zooming in and zooming out, for * squaring the graph region, and for adjusting the graph to the function. * This panel is 200 by 60 pixels. */ miscPanel = new Panel(); miscPanel.setBounds(0,0,200,100); miscPanel.setLayout(null); this.add(miscPanel); fxLabel = new Label("f(x) = "); fxLabel.setBounds(0,0,35,20); miscPanel.add(fxLabel); functionFld = new TextField("x+0.1*x^2-3*sin(x)", 30); functionFld.setBounds(0,20,200,20); miscPanel.add(functionFld); xBaseLabel = new Label("The base point is"); xBaseLabel.setBounds(0,40,85,20); miscPanel.add(xBaseLabel); xBaseField = new TextField("1.5", 6); xBaseField.setBounds(85,40,60,20); miscPanel.add(xBaseField); xDelLabel = new Label("del X is"); xDelLabel.setBounds(0,60,35,20); miscPanel.add(xDelLabel); xDelField = new TextField("0.01", 6); xDelField.setBounds(70,60,50,20); miscPanel.add(xDelField); zeroDerivLabel = new Label("f(X0) = "); zeroDerivLabel.setBounds(0,80,120,20); miscPanel.add(zeroDerivLabel); domainPanel = new Panel(); domainPanel.setBounds(0, 300, 200, 60); domainPanel.setLayout(null); this.add(domainPanel); xMinLabel = new Label("xMin ="); xMinLabel.setBounds(0, 20, 40, 20); domainPanel.add(xMinLabel); xMinField = new TextField("-5.0", 7); xMinField.setBounds(45, 20, 50, 20); domainPanel.add(xMinField); xMaxLabel = new Label("xMax ="); xMaxLabel.setBounds(0, 0, 40, 20); domainPanel.add(xMaxLabel); xMaxField = new TextField("5.0", 7); xMaxField.setBounds(45, 0, 50, 20); domainPanel.add(xMaxField); zoomIn = new Button("Zoom In"); zoomIn.setBounds(0,42,45,18); domainPanel.add(zoomIn); zoomOut = new Button("Zoom Out"); zoomOut.setBounds(50,42,50,18); domainPanel.add(zoomOut); yReset = new Button("Reset Y"); yReset.setBounds(105,42,45,18); domainPanel.add(yReset); zSquare = new Button("Square"); zSquare.setBounds(155,42,45,18); domainPanel.add(zSquare); yMinLabel = new Label("yMin ="); yMinLabel.setBounds(100, 20, 40, 20); domainPanel.add(yMinLabel); yMinField = new TextField("-5.0", 7); yMinField.setBounds(145, 20, 50, 20); domainPanel.add(yMinField); yMaxLabel = new Label("yMax ="); yMaxLabel.setBounds(100, 0, 40, 20); domainPanel.add(yMaxLabel); yMaxField = new TextField("5.0", 7); yMaxField.setBounds(145, 0, 50, 20); domainPanel.add(yMaxField); approxPanel = new Panel(); approxPanel.setBounds(0,100,200,200); approxPanel.setLayout(null); this.add(approxPanel); x1Label = new Label("X1 = "); x1Label.setBounds(0,0,25,20); approxPanel.add(x1Label); x1Field = new TextField("2.74", 7); x1Field.setBounds(25,0,55,20); approxPanel.add(x1Field); errorLabel = new Label("error = "); errorLabel.setBounds(90,0,105,20); approxPanel.add(errorLabel); fEvalLabel = new Label("f(X1) = "); fEvalLabel.setBounds(0,20,95,20); approxPanel.add(fEvalLabel); approxEvalLabel = new Label("Apr(X1) = "); approxEvalLabel.setBounds(100,20,95,20); approxPanel.add(approxEvalLabel); approxChoice = new Choice(); approxChoice.addItem("Constant Approx"); approxChoice.addItem("Linear Approx"); approxChoice.addItem("Quadratic Approx"); approxChoice.addItem("Cubic Approx"); approxChoice.addItem("Quartic Approx"); approxChoice.select(1); approxChoice.setBounds(0,40,115,20); approxPanel.add(approxChoice); clickChoice = new Choice(); clickChoice.addItem("X0 click"); clickChoice.addItem("X1 click"); clickChoice.addItem("Center"); clickChoice.select(0); clickChoice.setBounds(120,40,75,20); approxPanel.add(clickChoice); SymItem lSymItem = new SymItem(); approxChoice.addItemListener(lSymItem); clickChoice.addItemListener(lSymItem); approx0Label = new Label(" "); approx0Label.setBounds(0,60,190,20); approxPanel.add(approx0Label); approx1Label = new Label(" "); approx1Label.setBounds(0,80,190,20); approxPanel.add(approx1Label); approx2Label = new Label(" "); approx2Label.setBounds(0,100,190,20); approxPanel.add(approx2Label); approx3Label = new Label(" "); approx3Label.setBounds(0,120,190,20); approxPanel.add(approx3Label); approx4Label = new Label(" "); approx4Label.setBounds(0,140,190,20); approxPanel.add(approx4Label); } // handle GUI events // listen for changes in menues class SymItem implements java.awt.event.ItemListener { public void itemStateChanged(java.awt.event.ItemEvent event) { fixInputs(); approxPoly.fixMain(); } } // listen for button pushes and returns in text fields public boolean action(Event e, Object arg) { if((e.target == graphfx)||(e.target == xBaseField)|| (e.target == xMinField)||(e.target == xMaxField)|| (e.target == yMinField)||(e.target == yMaxField)|| (e.target == xDelField)||(e.target == x1Field)) { fixInputs(); theFunction.yMin = yMin; theFunction.yMax = yMax; approxPoly.fixMain(); return true; } if((e.target == functionFld)||(e.target == yReset)) { fixInputs(); theFunction.parse(functionString); theFunction.determineYMinYMax(); resetYMinYMax(); approxPoly.fixMain(); return true; } if(e.target == zoomIn) { xCenter = (xMax + xMin)/2; halfWide = xMax - xCenter; xMinField.setText(Double.toString(xCenter - halfWide/2.0)); xMaxField.setText(Double.toString(xCenter + halfWide/2.0)); yCenter = (yMax + yMin)/2; halfHigh = yMax - yCenter; yMinField.setText(Double.toString(yCenter - halfHigh/2.0)); yMaxField.setText(Double.toString(yCenter + halfHigh/2.0)); fixInputs(); approxPoly.fixMain(); return true; } if(e.target == zoomOut) { xCenter = (xMax + xMin)/2; halfWide = xMax - xCenter; xMinField.setText(Double.toString(xMin - halfWide)); xMaxField.setText(Double.toString(xMax + halfWide)); yCenter = (yMax + yMin)/2; halfHigh = yMax - yCenter; yMinField.setText(Double.toString(yMin - halfHigh)); yMaxField.setText(Double.toString(yMax + halfHigh)); fixInputs(); approxPoly.fixMain(); return true; } if(e.target == zSquare) { halfWide = (xMax - xMin)/2; yCenter = (yMax + yMin)/2; yMinField.setText(Double.toString(yCenter - halfWide)); yMaxField.setText(Double.toString(yCenter + halfWide)); fixInputs(); approxPoly.fixMain(); return true; } else return super.action(e,arg); } // action // Gather the inputs - main collection method public void fixInputs() { getXBase(); getX1(); getXDel(); getXMinXMax(); getYMinYMax(); functionString = functionFld.getText(); firstIndex = approxChoice.getSelectedIndex(); clickIndex = clickChoice.getSelectedIndex(); updateFeedbackPanelValues(); } // fixInputs public void updateFeedbackPanelValues() { theFunction.parse(functionString); theFunction.xBase = xBase; theFunction.xDel = xDel; fX1 = theFunction.value(x1); theFunction.findNumDerivs(); zeroDeriv = theFunction.zeroDeriv; approxString0 = "Apr(X) = " + Mio.doubleToStringSigFigures(theFunction.zeroDeriv,5); approxString = Mio.doubleToStringNoE(theFunction.zeroDeriv); approxString1 = " "; if(firstIndex >= 1) { approxString1 = " + " + Mio.doubleToStringSigFigures(theFunction.firstDeriv,5) + "*(X - " + Mio.doubleToStringSigFigures(xBase,5) + ")"; approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.firstDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")"; } approxString2 = " "; if(firstIndex >= 2) { approxString2 = " + " + Mio.doubleToStringSigFigures(theFunction.secondDeriv,5) + "*(X - " + Mio.doubleToStringSigFigures(xBase,5) + ")^2/2 "; approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.secondDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")^2/2 "; } approxString3 = " "; if(firstIndex >= 3) { approxString3 = " + " + Mio.doubleToStringSigFigures(theFunction.thirdDeriv,5) + "*(X - " + Mio.doubleToStringSigFigures(xBase,5) + ")^3/6 "; approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.thirdDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")^3/6 "; } approxString4 = " "; if(firstIndex >= 4) { approxString4 = " + " + Mio.doubleToStringSigFigures(theFunction.fourthDeriv,5) + "*(X - " + Mio.doubleToStringSigFigures(xBase,5) + ")^4/24 "; approxString = approxString + " + " + Mio.doubleToStringNoE(theFunction.fourthDeriv) + "*(x-" + Mio.doubleToStringNoE(xBase) +")^4/24 "; } approxFunction.parse(approxString); approxX1 = approxFunction.value(x1); drawLabels(); } // updateFeedbackPanelValues public void resetYMinYMax() { theFunction.parse(functionString); theFunction.xMin = xMin; theFunction.xMax = xMax; theFunction.determineYMinYMax(); yMin = theFunction.yMin; yMax = theFunction.yMax; postYMinYMax(); } // resetYMinYMax // Subsidary methods for collecting data public void getXBase() { xBase = Mio.doubleFromTextField(xBaseField); } // getXBase public void getX1() { x1 = Mio.doubleFromTextField(x1Field); } // getX1 public void getXDel() { xDel = Mio.doubleFromTextField(xDelField); if (xDel <= 0.0) { System.out.println("Warning, del X should be positive"); System.out.println("del X reset to default."); xDel = 0.01; xDelField.setText(Double.toString(xDel)); } } // getXDel public void getXMinXMax() { // Check that xMin < xMax and set them xMin=Mio.doubleFromTextField(xMinField); xMax=Mio.doubleFromTextField(xMaxField); if (xMax <= xMin) { System.out.println("Warning, xMin should be < xMax"); System.out.println("xMin and xMax reset to defaults."); xMin = -5.0; xMax = 5.0; } xMinField.setText(Double.toString(xMin)); xMaxField.setText(Double.toString(xMax)); } // getXMinXMax public void getYMinYMax() { // Check that xMin < xMax and set them yMin=Mio.doubleFromTextField(yMinField); yMax=Mio.doubleFromTextField(yMaxField); if (yMax <= yMin) { System.out.println("Warning, yMin should be < yMax"); System.out.println("xMin and xMax reset to defaults."); yMin = -5.0; yMax = 5.0; } yMinField.setText(Double.toString(yMin)); yMaxField.setText(Double.toString(yMax)); } // getYMinYMax public void postXMinXMax() { xMinField.setText(Mio.doubleToStringSigFigures(xMin,5)); xMaxField.setText(Mio.doubleToStringSigFigures(xMax,5)); } // postYMinYMax public void postYMinYMax() { yMinField.setText(Mio.doubleToStringSigFigures(yMin,5)); yMaxField.setText(Mio.doubleToStringSigFigures(yMax,5)); } // postYMinYMax // Methods to produce output - main method public void drawLabels() { zeroDerivLabel.setText("f(X0) = " + Mio.doubleToStringSigFigures(zeroDeriv, 5)); fEvalLabel.setText("f(X1) = " + Mio.doubleToStringSigFigures(fX1, 5)); approxEvalLabel.setText("Apr(X1) = " + Mio.doubleToStringSigFigures(approxX1, 5)); errorLabel.setText("err = " + Mio.doubleToStringSigFigures(fX1 - approxX1, 5)); approx0Label.setText(approxString0); approx1Label.setText(approxString1); approx2Label.setText(approxString2); approx3Label.setText(approxString3); approx4Label.setText(approxString4); } //drawLabels // Subsidiary output methods public void setXBase(double xBase) { xBaseField.setText(Double.toString(xBase)); } // setXBase public void setX1(double x1) { x1Field.setText(Mio.doubleToStringSigFigures(x1,6)); } // setX1 } // FeedbackPanel /* * Help are is a simple object to be used for the help panel of the applet. * It is set up as a scrolling region in case the help text is made long * enough to require that, but the default is that no scrollbars are visible. */ import java.awt.TextArea; public class HelpArea extends TextArea { public HelpArea(int width, int height) { //Scrollbar visibility - 0 = both, 1= vert only, 2=horizon only, 3 = none // super(String text, int width, int height, int scrollbarVisibility) super(" ", width, height, 1); this.setText( "This applet was designed to explore how Taylor polynomials approximate\n" + "arbitrary functions. \n\n" + "The user enters a function, the range of x values that will be graphed, \n" + "a base point X0, the degree of the approximating polynomial, and the point \n" + "X1 the value is to be approximated at. The values of X0 and X1 can\n" + "either be changed by typing values in text fields or by clicking on the\n" + "graph. If the mouse is dragged rather than clicked the values will\n" + "change smoothly.\n\n" + "The applet graphs the function and the indicated approximating polynomial.\n" + "It also gives the value of the function and the approximation at X1 along \n" + "the error in the approximation. A formula for the approximating polynomial\n" + "is provided.\n\n" + "The derivatives for the taylor polynomials are approximated by standard \n" + "numeric techniques. We use balanced difference qutient formulas.\n" + "Using d for the del X term we have:\n\n" + "f'(x) = (f(x+d)-f(x-d))/(2d).\n" + "f''(x) = (f(x+2d)-2f(x)+f(x-2d))/(4d^2).\n" + "f'''(x) = (f(x+3d)-3f(x+d)+3f(x-d)-f(x-3d))/(8d^3).\n" + "f''''(x) = (f(x+4d)-4f(x+2d)+6f(x)-4f(x-2d)+f(x-4d))/(16d^4).\n\n" + "Given the derivatives, the formula for the nth degree taylor polynomial\n" + "approximation to f(x) based at X0 is:\n\n" + "Approx(x) = f(X0) + f'(X0)*(x-X0) + ... + f^(n)(X0)*(x-X0)^n/(n!)\n\n" + "where f^(n)(X0) is the nth derivative of f evaluated at X0.\n\n\n" + "The function should be an expression in x. Implicit multiplication is not allowed.\n" + "(Use 3*x rather than 3x.) Exponentiation is indicated by ^. \n" + "The mathematical constant pi can be in upper or lower case.\n" + "The constant e is indicated by either e or exp(1).\n" + "(These constants only have double precision, Thus e^x will only appoximate exp(x).\n" + "Trig functions are in radians. Use the functions toDegrees and toRadians to convert.\n\n" + "The functions understood by the parser are:\n" + "sin, cos, tan, sec, csc, acos or arccos, asin or arcsin, atan or arctan, \n" + "toDegrees, toRadians, abs, ceil, floor, round,\n" + "sqrt, exp, log or ln (for natural log), and log10.\n\n" + "Each of these functions requires one argument enclosed in parentheses."); this.setEditable(false); } } // HelpArea /* * AboutArea is an object for the About Panel. It is a multi-line label * with a fixed text message. */ import java.awt.*; public class AboutArea extends MultiLineLabel { Font theFont = new Font("TimesRoman", Font.BOLD, 18); String label = "Taylor Polynomial Approximation Applet\n \n"+ "Copyright 2001 by Mike May, S.J.\n"+ "maymk@slu.edu\n \n"+ "zFunction class inspired by class of that name\n"+ "from Riemann Sum applet by\n"+ "Bill Ziemer and Brendon Cheves\n"+ "Copyright 1996 by California State University," + " Long Beach\n \n"+ "Function Parsing Copyright 1996 by Darius Bacon"; int alignment = 1; // center int margin_width =10, margin_height = 10; public AboutArea(){ // super(label, margin_width, margin_height, alignmnet); // Possible alignment values are 0 for left, 1 for center and 2 for right. super(" ", 10,10, 1); this.setLabel(label); this.setFont(theFont); } } // AboutArea // MultiLineLabel // This example is from _Java Examples in a Nutshell_. (http://www.oreilly.com) // Copyright (c) 1997 by David Flanagan // This example is provided WITHOUT ANY WARRANTY either expressed or implied. // You may study, use, modify, and distribute it for non-commercial purposes. // For any commercial use, see http://www.davidflanagan.com/javaexamples import java.awt.*; import java.util.*; /** * A custom component that displays multiple lines of text with specified * margins and alignment. In Java 1.1, we could extend Component instead * of Canvas, making this a more efficient "Lightweight component" */ public class MultiLineLabel extends Canvas { // User-specified attributes protected String label; // The label, not broken into lines protected int margin_width; // Left and right margins protected int margin_height; // Top and bottom margins protected int alignment; // The alignment of the text. public static final int LEFT = 0, CENTER = 1, RIGHT = 2; // alignment values // Computed state values protected int num_lines; // The number of lines protected String[] lines; // The label, broken into lines protected int[] line_widths; // How wide each line is protected int max_width; // The width of the widest line protected int line_height; // Total height of the font protected int line_ascent; // Font height above baseline protected boolean measured = false; // Have the lines been measured? // Here are five versions of the constructor public MultiLineLabel(String label, int margin_width, int margin_height, int alignment) { this.label = label; // Remember all the properties this.margin_width = margin_width; this.margin_height = margin_height; this.alignment = alignment; newLabel(); // Break the label up into lines } public MultiLineLabel(String label, int margin_width, int margin_height) { this(label, margin_width, margin_height, LEFT); } public MultiLineLabel(String label, int alignment) { this(label, 10, 10, alignment); } public MultiLineLabel(String label) { this(label, 10, 10, LEFT); } public MultiLineLabel() { this(""); } // Methods to set and query the various attributes of the component // Note that some query methods are inherited from the superclass. public void setLabel(String label) { this.label = label; newLabel(); // Break the label into lines measured = false; // Note that we need to measure lines repaint(); // Request a redraw } public void setFont(Font f) { super.setFont(f); // tell our superclass about the new font measured = false; // Note that we need to remeasure lines repaint(); // Request a redraw } public void setForeground(Color c) { super.setForeground(c); // tell our superclass about the new color repaint(); // Request a redraw (size is unchanged) } public void setAlignment(int a) { alignment = a; repaint(); } public void setMarginWidth(int mw) { margin_width = mw; repaint(); } public void setMarginHeight(int mh) { margin_height = mh; repaint(); } public String getLabel() { return label; } public int getAlignment() { return alignment; } public int getMarginWidth() { return margin_width; } public int getMarginHeight() { return margin_height; } /** * This method is called by a layout manager when it wants to * know how big we'd like to be. In Java 1.1, getPreferredSize() is * the preferred version of this method. We use this deprecated version * so that this component can interoperate with 1.0 components. */ public Dimension preferredSize() { if (!measured) measure(); return new Dimension(max_width + 2*margin_width, num_lines * line_height + 2*margin_height); } /** * This method is called when the layout manager wants to know * the bare minimum amount of space we need to get by. * For Java 1.1, we'd use getMinimumSize(). */ public Dimension minimumSize() { return preferredSize(); } /** * This method draws the label (same method that applets use). * Note that it handles the margins and the alignment, but that * it doesn't have to worry about the color or font--the superclass * takes care of setting those in the Graphics object we're passed. */ public void paint(Graphics g) { int x, y; Dimension size = this.size(); // use getSize() in Java 1.1 if (!measured) measure(); y = line_ascent + (size.height - num_lines * line_height)/2; for(int i = 0; i < num_lines; i++, y += line_height) { switch(alignment) { default: case LEFT: x = margin_width; break; case CENTER: x = (size.width - line_widths[i])/2; break; case RIGHT: x = size.width - margin_width - line_widths[i]; break; } g.drawString(lines[i], x, y); } } /** This internal method breaks a specified label up into an array of lines. * It uses the StringTokenizer utility class. */ protected synchronized void newLabel() { StringTokenizer t = new StringTokenizer(label, "\n"); num_lines = t.countTokens(); lines = new String[num_lines]; line_widths = new int[num_lines]; for(int i = 0; i < num_lines; i++) lines[i] = t.nextToken(); } /** This internal method figures out how the font is, and how wide each * line of the label is, and how wide the widest line is. */ protected synchronized void measure() { FontMetrics fm = this.getToolkit().getFontMetrics(this.getFont()); line_height = fm.getHeight(); line_ascent = fm.getAscent(); max_width = 0; for(int i = 0; i < num_lines; i++) { line_widths[i] = fm.stringWidth(lines[i]); if (line_widths[i] > max_width) max_width = line_widths[i]; } measured = true; } } // MultiLineLabel // ZFunction Class /* Modified by Mike May, August 2001 * Inspired by a class witten Bill Ziemer and Brendon Cheves * that was based upon the Java Polygon class * *public class ZFunction * public ZFunction() * * public void parse( String f ) * * the parse method sends the string over to the Parser class for parsing * * * public double value(double x) * * This method evaluates the function at x. * * * public void findNumDerivs() * * Attached to Taylor polynomials is the need to find derivatives at a base * point. This method does that numerically. * * * public void determineYMinYMax() * public void setXRange(double f, double l) * * The last two methods are useful in setting finding appropriate limits * to use when graphing the function. * */ // java packages import java.applet.*; import java.awt.*; import java.lang.Math; import expr.*; // expr package Copyright 1996 by Darius Bacon public class ZFunction { //Real number bounds for the function public double yMin = -5.0, yMax = 5.0; public double xMin = -5.0, xMax = 5.0; public double xBase = 1.5, xDel = 0.01, zeroDeriv, firstDeriv, secondDeriv, thirdDeriv, fourthDeriv; // created for access to infinity constants Double doubleCheck = new Double(1.0); public Expr expr; public Variable xvar; public ZFunction() { // set up the parsing variables xvar = Variable.make("x"); Variable.make("pi").set_value (Math.PI); Variable.make("PI").set_value (Math.PI); Variable.make("Pi").set_value (Math.PI); Variable.make("e").set_value (Math.exp(1)); /* * ¼ and e are not in the parsing constructor */ } // ZFunction constructor /* * Parse the function */ public void parse( String f ) { try {expr = Parser.parse(f);} catch (Syntax_error se) { System.err.println ("Syntax error: " + se); return; } } // parse public double value(double x) { xvar.set_value(x); return expr.value(); } // value public void findNumDerivs() { zeroDeriv = value(xBase); firstDeriv = (value(xBase + xDel) - value(xBase - xDel))/(2.0*xDel); secondDeriv = (value(xBase + 2*xDel) - 2*value(xBase) + value(xBase - 2*xDel)) / (4.0*xDel*xDel); thirdDeriv = (value(xBase + 3*xDel) - 3*value(xBase + xDel) + 3*value(xBase - xDel) - value(xBase - 3*xDel))/(8.0*xDel*xDel*xDel); fourthDeriv = (value(xBase + 4*xDel) - 4*value(xBase + 2*xDel) +6*value(xBase) - 4*value(xBase - 2*xDel) + value(xBase - 4*xDel))/(16.0*xDel*xDel*xDel*xDel); } // findNumDerivs public void determineYMinYMax() { double dx = (xMax-xMin)/500.0, tempY; yMin = doubleCheck.POSITIVE_INFINITY; yMax = doubleCheck.NEGATIVE_INFINITY; for(int i=0;i<=500;i++) { tempY = value(xMin + i*dx); if(tempY > yMax) yMax = tempY; if(tempY < yMin) yMin = tempY; } // Round to three decimal places yMax = ((int)(yMax*1000))/1000.0; yMin = ((int)(yMin*1000))/1000.0; // Fudge things so that the X-axis is included if (yMin > -.5) yMin = -.5; if (yMax < 0.5) yMax = 0.5; } // determineYminYMax // set x range manually public void setXRange(double f, double l) { xMin = f; xMax = l; } // setXRange } // end of ZFunction Class //// //// // Code for the parser //// //// // Mathematical expressions. // Copyright 1996 by Darius Bacon; see the file COPYING. // 14May96: added constant folding // 07JUL1999 - version 1.0 - C. Pheatt // 05AUG2000 - Mike May, S.J. // add in SEC, CSC. ToDEG, TORAD package expr; /** * A mathematical expression, built out of literal numbers, variables, * arithmetic operators, and elementary functions. The operator names * are from java.lang.Math. */ public abstract class Expr { /** @return the value given the current variable values */ public abstract double value (); /** Binary operator. */ public static final int ADD = 0; /** Binary operator. */ public static final int SUB = 1; /** Binary operator. */ public static final int MUL = 2; /** Binary operator. */ public static final int DIV = 3; /** Binary operator. */ public static final int POW = 4; /** Binary operator. */ public static final int MOD = 5; /** Binary operator. */ public static final int LTH = 6; /** Binary operator. */ public static final int LEQ = 7; /** Binary operator. */ public static final int GTH = 8; /** Binary operator. */ public static final int GEQ = 9; /** Binary operator. */ public static final int EQU = 10; /** Binary operator. */ public static final int NEQ = 11; /** Binary operator. */ public static final int AND = 12; /** Binary operator. */ public static final int ORR = 13; /** Unary operator. */ public static final int ABS = 100; /** Unary operator. */ public static final int ACOS = 101; /** Unary operator. */ public static final int ASIN = 102; /** Unary operator. */ public static final int ATAN = 103; /** Unary operator. */ public static final int CEIL = 104; /** Unary operator. */ public static final int COS = 105; /** Unary operator. */ public static final int EXP = 106; /** Unary operator. */ public static final int FLOOR = 107; /** Unary operator. */ public static final int LOG = 108; /** Unary minus operator. */ public static final int NEG = 109; /** Unary operator. */ public static final int ROUND = 110; /** Unary operator. */ public static final int SIN = 111; /** Unary operator. */ public static final int SQRT = 112; /** Unary operator. */ public static final int TAN = 113; /** Unary operator. */ public static final int LOG10 = 114; /** Unary operator. */ public static final int SEC = 115; /** Unary operator. */ public static final int CSC = 116; /** Unary operator. */ public static final int TODEG = 117; /** Unary operator. */ public static final int TORAD = 118; /** Unary operator. */ // public static final int FACT = 115; public static Expr make_literal (double v) { return new Literal (v); } public static Expr make_var_ref (Variable var) { return new Var_ref (var); } /** * @param rator unary operator * @param rand operand */ public static Expr make_app1 (int rator, Expr rand) { Expr app = new App1 (rator, rand); return rand instanceof Literal ? new Literal (app.value ()) : app; } /** * @param rator binary operator * @param rand0 left operand * @param rand1 right operand */ public static Expr make_app2 (int rator, Expr rand0, Expr rand1) { Expr app = new App2 (rator, rand0, rand1); return rand0 instanceof Literal && rand1 instanceof Literal ? new Literal (app.value ()) : app; } } // Expr // These classes are all private to this module so that I can get rid // of them later. For applets you want to use as few classes as // possible to avoid http connections at load time; it'd be profitable // to replace all these subtypes with bytecodes for a stack machine, // or perhaps a type that's the union of all of them (see class Node // in java/demo/SpreadSheet/SpreadSheet.java). class Literal extends Expr { double v; Literal (double _v) { v = _v; } public double value () { return v; } } // Literal class Var_ref extends Expr { Variable var; Var_ref (Variable _var) { var = _var; } public double value () { return var.value (); } } // Var_ref class App1 extends Expr { int rator; Expr rand; App1 (int _rator, Expr _rand) { rator = _rator; rand = _rand; } public double value () { double arg = rand.value (); switch (rator) { case ABS: return Math.abs (arg); case ACOS: return Math.acos (arg); case ASIN: return Math.asin (arg); case ATAN: return Math.atan (arg); case CEIL: return Math.ceil (arg); case COS: return Math.cos (arg); case EXP: return Math.exp (arg); // case FACT: return MiscFunctions.fact (arg); case FLOOR: return Math.floor (arg); case LOG: return Math.log (arg); case LOG10: return Math.log (arg) * 0.434294481903251827651128918916; case NEG: return -arg; case ROUND: return Math.round (arg); case SIN: return Math.sin (arg); case SQRT: return Math.sqrt (arg); case TAN: return Math.tan (arg); case SEC: return 1/Math.cos (arg); case CSC: return 1/Math.sin (arg); case TODEG: return 180*(arg)/(3.141582653589793); case TORAD: return (Math.PI)*(arg)/180; default: throw new RuntimeException ("BUG: bad rator"); } } } // App1 class App2 extends Expr { int rator; Expr rand0, rand1; App2 (int _rator, Expr _rand0, Expr _rand1) { rator = _rator; rand0 = _rand0; rand1 = _rand1; } public double value () { double arg0 = rand0.value (); double arg1 = rand1.value (); switch (rator) { case ADD: return arg0 + arg1; case SUB: return arg0 - arg1; case MUL: return arg0 * arg1; case DIV: return arg0 / arg1; // check for division by 0? case POW: return Math.pow (arg0, arg1); case MOD: return arg0 % arg1; case LTH: if(arg0 < arg1) return 1; else return 0; case LEQ: if(arg0 <= arg1) return 1; else return 0; case GTH: if(arg0 > arg1) return 1; else return 0; case GEQ: if(arg0 >= arg1) return 1; else return 0; case EQU: if(arg0 == arg1) return 1; else return 0; case NEQ: if(arg0 != arg1) return 1; else return 0; case AND: if((arg0 != 0) && (arg1 != 0)) return 1; else return 0; case ORR: if((arg0 != 0) || (arg1 != 0)) return 1; else return 0; default: throw new RuntimeException ("BUG: bad rator"); } } } // App2 // End package Expr // Operator-precedence parser. // Copyright 1996 by Darius Bacon; see the file COPYING. // 14May96: bugfix. // StreamTokenizer treated '-' as a numeric token, not a minus // operator followed by a number. Fix: make '-' an ordinaryChar. // 12May97: Changed the precedence of unary minus to be lower than // multiplication, so -y^2 is like -(y^2), not (-y)^2. // 07JUL1999 - version 1.0 - C. Pheatt // 05AUG2000 - Mike May, S.J. // add in sec, csc, toDegrees, toRadians, ln package expr; import java.io.*; /** Parses strings representing mathematical formulas with variables. The following operators, in descending order of precedence, are defined: ^ associates right-to-left; other operators associate left-to-right.

These functions are defined: abs, acos, asin, atan, ceil, cos, exp, floor, log, round, sin, sqrt, tan. Each requires one argument enclosed in parentheses.

Whitespace outside identifiers is ignored.

The syntax-error messages aren't very informative, unfortunately. IWBNI it indicated where in the input string the parse failed, but that'd be kind of a pain since our scanner is a StreamTokenizer. A hook for that info should've been built into StreamTokenizer.

Examples: