eval.java

此程序是用来计算高等数学里的微积分运算的

		if (expression.indexOf("rint") >= 0) {
			return "rint";
		}
		if (expression.indexOf("round") >= 0) {
			return "round";
		}
		if (expression.indexOf("signum") >= 0) {
			return "signum";
		}
		if (expression.indexOf("sin") >= 0) {
			return "sin";
		}
		if (expression.indexOf("sinh") >= 0) {
			return "sinh";
		}
		if (expression.indexOf("sqrt") >= 0) {
			return "sqrt";
		}
		if (expression.indexOf("tan") >= 0) {
			return "tan";
		}
		if (expression.indexOf("tanh") >= 0) {
			return "tanh";
		}
		if (expression.indexOf("todegrees") >= 0) {
			return "todegrees";
		}
		if (expression.indexOf("toradians") >= 0) {
			return "toradians";
		}
		if (expression.indexOf("ulp") >= 0) {
			return "ulp";
		}

		// 两个参数的函数
		if (expression.indexOf("atan2") >= 0) {
			return "atan2";
		}
		if (expression.indexOf("hypot") >= 0) {
			return "hypot";
		}
		if (expression.indexOf("ieeeremainder") >= 0) {
			return "ieeeremainder";
		}
		if (expression.indexOf("max") >= 0) {
			return "max";
		}
		if (expression.indexOf("min") >= 0) {
			return "min";
		}
		if (expression.indexOf("pow") >= 0) {
			return "pow";
		}
		return null;
	}

	/**
	 * 计算表达式
	 * 
	 * @author 北大青鸟--杜永耀
	 * @param expression
	 *            表达式。可以包含数学函数（以 java.util.Math 里的函数为准）
	 * @return 表达式计算后的结果
	 * @throws Exception
	 */
	public double eval2(String expression) throws Exception {
		expression = "(" + expression.toLowerCase().replace(" ", "") + ")";
		String currentExpression = expression;
		String functionName = null;
		String[] temp = null;
		while (getMathFunctionName(currentExpression) != null) {// 如果存在数学函数
			functionName = getMathFunctionName(currentExpression);
			temp = splitStr(currentExpression, functionName);
			if (getMathFunctionName(temp[1]) == null) {// 如果参数中不包含数学函数
				if (temp[1].indexOf(",") < 0) {// 一个参数
					currentExpression = temp[0]
							+ getPartResultWithOneParameter("" + eval(temp[1]),
									functionName) + temp[2];
				} else {// 两个参数
					String[] temp2 = temp[1].split(",");
					currentExpression = temp[0]
							+ getPartResultWithTwoParameter(eval(temp2[0])
									+ "," + eval(temp2[1]), functionName)
							+ temp[2];
				}
			} else {// 如果参数中包含数学函数
				temp[1] = functionName + "(" + eval2(temp[1]) + ")";
				currentExpression = temp[0] + "(" + eval2(temp[1]) + ")"
						+ temp[2];
			}
		}
		return eval(currentExpression);
	}

	/**
	 * 求导 
	 * <br/> 
	 * 理论依据--三点公式 
	 * <br/> 
	 * 公式的详细证明见： 
	 * <br/> 
	 * 《数值分析》 重庆大学出版社--杨大地、涂光裕 1998年1月第1版 第97页 
	 * <br/> 
	 * <br/> 
	 * 注意：该方法不适用于不可导点，或不可导函数
	 * 
	 * @author 北大青鸟--杜永耀
	 * @param expression
	 *            表达式。变量由小写 x 表示，可以包含数学函数（以 java.util.Math 里的函数为准）
	 * @param value
	 *            在何处求导。
	 * @return 当前表达式在某点的导数
	 * @throws Exception
	 */
	public double differentiate(String expression, String value)
			throws Exception {
		double result = 0.0;
		expression = "0+" + expression.toLowerCase();
		expression = expression.replace("expm1", "ewpm1").replace("exp", "ewp")
				.replace("max", "maw");
		String firstExpression = expression.replace("x", "(" + value + ")")
				.replace("ewpm1", "expm1").replace("ewp", "exp").replace("maw",
						"max");
		String secondExpression = expression.replace("x",
				"(" + value + "+0.00000001)").replace("ewpm1", "expm1")
				.replace("ewp", "exp").replace("maw", "max");
		String thirdExpression = expression.replace("x",
				"(" + value + "+0.00000002)").replace("ewpm1", "expm1")
				.replace("ewp", "exp").replace("maw", "max");
		result = (-3 * eval2(firstExpression) + 4 * eval2(secondExpression) - eval2(thirdExpression)) * 1e8 / 2;
		return result;
	}

	/**
	 * 积分 
	 * <br/> 
	 * 理论依据--复化抛物形公式 
	 * <br/> 
	 * 公式的详细证明见： 
	 * <br/> 
	 * 《数值分析》 重庆大学出版社--杨大地、涂光裕 1998年1月第1版 第132页
	 * 
	 * @author 北大青鸟--杜永耀
	 * @param expression
	 *            表达式。变量由小写 x 表示，可以包含数学函数（以 java.util.Math 里的函数为准）
	 * @param beginValue
	 *            初始值，即定积分的开始值
	 * @param endValue
	 *            结束值，定积分的结束值
	 * 
	 * @param partNumber
	 *            分块数量。分块越多，精度越高，但是消耗时间更多
	 * @return 当前表达式在某个范围的定积分。积分范围由 beginValue 和 endValue 确定
	 * @throws Exception
	 */
	public double integral(String expression, String beginValue,
			String endValue, int partNumber) throws Exception {
		double result = 0.0;
		double h = (Double.parseDouble(endValue) - Double
				.parseDouble(beginValue))
				/ partNumber;

		expression = expression.toLowerCase();
		expression = expression.replace("expm1", "ewpm1").replace("exp", "ewp")
				.replace("max", "maw");
		partNumber = partNumber % 2 == 1 ? (partNumber + 1) : partNumber;
		int m = partNumber / 2;

		result += eval2(expression.replace("x", "(" + beginValue + ")")
				.replace("ewpm1", "expm1").replace("ewp", "exp").replace("maw",
						"max"))
				+ eval2(expression.replace("x", "(" + endValue + ")").replace(
						"ewpm1", "expm1").replace("ewp", "exp").replace("maw",
						"max"))
				+ 4
				* eval2(expression.replace("x",
						"(" + beginValue + "+" + h + ")").replace("ewpm1",
						"expm1").replace("ewp", "exp").replace("maw", "max"));
		for (int k = 1; k < m; k++) {
			result += 2
					* eval2(expression.replace("x",
							"(" + beginValue + "+" + 2 * k * h + ")").replace(
							"ewpm1", "expm1").replace("ewp", "exp").replace(
							"maw", "max"))
					+ 4
					* eval2(expression.replace("x",
							"(" + beginValue + "+" + (2 * k + 1) * h + ")")
							.replace("ewpm1", "expm1").replace("ewp", "exp")
							.replace("maw", "max"));
		}
		result *= (h / 3);
		return result;
	}

	/**
	 * 将科学计数转换为普通计数
	 * 
	 * @author 北大青鸟--杜永耀
	 * @param scientificNumber
	 *            科学计数
	 * @return 普通计数
	 * @throws Exception
	 */
	public String scientificExpressionToNormal(String scientificNumber) {
		String result = scientificNumber.toLowerCase().replace(" ", "");
		int currentLocationOfE = -1;
		int beginLocation = -1;
		int endLocation = -1;
		String[] temp = new String[2];

		// 负
		while ((currentLocationOfE = result.indexOf("e-")) >= 0) {
			int i = currentLocationOfE - 1;
			char currentChar = result.charAt(i);
			temp[0] = "";
			while (currentChar >= '0' && currentChar <= '9'
					|| currentChar == '.') {
				temp[0] = currentChar + temp[0];
				i--;
				if (i < 0) {
					beginLocation = i + 1;
					break;
				}
				currentChar = result.charAt(i);
				if (!(currentChar >= '0' && currentChar <= '9' || currentChar == '.')) {
					beginLocation = i + 1;
					break;
				}
			}

			i = currentLocationOfE + 2;
			currentChar = result.charAt(i);
			temp[1] = "";
			while (currentChar >= '0' && currentChar <= '9') {
				temp[1] = temp[1] + currentChar;
				i++;
				if (i >= result.length()) {
					endLocation = i - 1;
					break;
				}
				currentChar = result.charAt(i);
				if (!(currentChar >= '0' && currentChar <= '9')) {
					endLocation = i - 1;
					break;
				}
			}
			result = result.substring(0, beginLocation)
					+ scientificNumberToNormal(temp[0] + "e-" + temp[1])
					+ result.substring(endLocation + 1);
		}

		// 正
		while ((currentLocationOfE = result.indexOf("e")) >= 0) {
			int i = currentLocationOfE - 1;
			char currentChar = result.charAt(i);
			temp[0] = "";
			while (currentChar >= '0' && currentChar <= '9'
					|| currentChar == '.') {
				temp[0] = currentChar + temp[0];
				i--;
				if (i < 0) {
					beginLocation = i + 1;
					break;
				}
				currentChar = result.charAt(i);
				if (!(currentChar >= '0' && currentChar <= '9' || currentChar == '.')) {
					beginLocation = i + 1;
					break;
				}
			}

			i = currentLocationOfE + 1;
			currentChar = result.charAt(i);
			temp[1] = "";
			while (currentChar >= '0' && currentChar <= '9') {
				temp[1] = temp[1] + currentChar;
				i++;
				if (i >= result.length()) {
					endLocation = i - 1;
					break;
				}
				currentChar = result.charAt(i);
				if (!(currentChar >= '0' && currentChar <= '9')) {
					endLocation = i - 1;
					break;
				}
			}
			result = result.substring(0, beginLocation)
					+ scientificNumberToNormal(temp[0] + "e" + temp[1])
					+ result.substring(endLocation + 1);
		}

		return result;
	}

	private String scientificNumberToNormal(String scientificNumber) {
		String result = scientificNumber;
		String temp[] = result.split("e");
		String[] temp2 = new String[2];
		String sign = temp[0].startsWith("-") ? "-" : "";
		int secondPart = Integer.parseInt(temp[1]);
		while (secondPart > 0) {
			int dot = temp[0].indexOf(".");
			temp2[0] = temp[0].substring(0, dot);
			temp2[1] = temp[0].substring(dot + 1);
			temp[0] = temp2[0]
					+ (temp2[1].length() > 0 && !temp2[1].equals("0") ? (temp2[1]
							.charAt(0)
							+ "." + temp2[1].substring(1))
							: "0.0");
			secondPart--;
		}
		while (secondPart < 0) {
			int dot = temp[0].indexOf(".");
			temp2[0] = temp[0].substring(0, dot);
			temp2[1] = temp[0].substring(dot + 1);
			temp[0] = "0." + temp2[0] + temp2[1];
			secondPart++;
		}
		result = sign + temp[0];
		return result;
	}

//	public static void main(String[] args) {
//		try {
//			Eval eval = new Eval();
//			System.out.println(eval.eval2("-0.105*(tan(123)+sin(cos(-3*4)))"));
//			System.out.println("---------------------------------------------");
//			System.out.println(eval
//					.eval2("-0.105*abs(tan(123)+sin(cos(-3*4)))"));
//
//			System.out.println("导数："
//					+ eval.differentiate("pow(x,2)+pow(x,3)", "2"));
//			System.out.println(eval.eval2("2*2+3*pow(2,2)"));
//			System.out.println(eval.integral("pow(x,2)+sin(x)", "0", "1", 100));
//			System.out.println(eval
//					.scientificExpressionToNormal("-1.23e-1+4.21312e3"));
//			System.out.println(eval.eval2("pow(1,3)/3-cos(1)")
//					- eval.eval2("pow(0,3)/3-cos(0)"));
//			System.out.println(eval.integral("tan(pow(x,x))", "0", "1", 5000));
//			System.out.println("运算结果：" + eval.eval2("tan(pow(1,2))"));
//			System.out.println(eval.eval2("sin(-1*acos(0))"));
//
//			System.out.println(eval.integral("tan(pow(x,2))", "-3", "3", 3000));
//			System.out.println(eval.differentiate("tan(pow(x,2))", "3.14"));
//			System.out.println(eval.eval2("tan(pow(1,2))"));
//			System.out.println(eval.eval2("tan(pow(-1,2))"));
//			System.out.println(eval.eval2("4*tan(pow(0.75,2))"));
//			System.out.println(eval.eval2("4*tan(pow(0.5,2))"));
//			System.out.println(eval.eval2("4*tan(pow(0.25,2))"));
//			System.out.println(eval.eval2("2*tan(pow(0,2))"));
//
//			System.out.println("--------------------------");
//			System.out
//					.println(eval
//							.eval("(1.5574077246549023+1.5574077246549023+2.521750695343539+1.021367684884145+0.2503260302651001+0)/9"));
//			System.out
//					.println(eval
//							.eval2("tan(pow(1,2))+tan(pow(-1,2))+4*tan(pow(0.75,2))+4*tan(pow(0.5,2))+4*tan(pow(0.25,2))+2*tan(pow(0,2))"));
//
//			System.out.println(eval.eval2("tan(pow(3,2))"));
//			System.out.println(eval.eval2("tan(pow(-3,2))"));
//			System.out.println(eval.eval2("4*tan(pow(2.25,2))"));
//			System.out.println(eval.eval2("4*tan(pow(1.5,2))"));
//			System.out.println(eval.eval2("4*tan(pow(0.75,2))"));
//			System.out.println(eval.eval2("2*tan(pow(0,2))"));
//			System.out
//					.println(eval
//							.eval2("(tan(pow(3,2))+tan(pow(-3,2))+4*tan(pow(2.9,2))+4*tan(pow(2.8,2))+4*tan(pow(2.7,2))+4*tan(pow(2.6,2))+4*tan(pow(2.5,2))+4*tan(pow(2.4,2))+4*tan(pow(2.3,2))+4*tan(pow(2.2,2))+4*tan(pow(2.1,2))+4*tan(pow(2.0,2))+4*tan(pow(1.9,2))+4*tan(pow(1.8,2))+4*tan(pow(1.7,2))+4*tan(pow(1.6,2))+4*tan(pow(1.5,2))+4*tan(pow(1.4,2))+4*tan(pow(1.3,2))+4*tan(pow(1.2,2))+4*tan(pow(1.1,2))+4*tan(pow(1.0,2))+4*tan(pow(0.9,2))+4*tan(pow(0.8,2))+4*tan(pow(0.7,2))+4*tan(pow(0.6,2))+4*tan(pow(0.5,2))+4*tan(pow(0.4,2))+4*tan(pow(0.3,2))+4*tan(pow(0.2,2))+4*tan(pow(0.1,2)))/60"));
//
//			System.out.println("--------------------------");
//			System.out
//					.println(eval
//							.eval("(1.5574077246549023+1.5574077246549023+2.521750695343539+1.021367684884145+0.2503260302651001+0)/9"));
//
//			System.out.println(eval.scientificExpressionToNormal("1.2345e10"));
//
//			System.out.println(eval
//					.scientificExpressionToNormal("-5.307179586686775E-6"));
//			System.out.println(eval.eval2("sin(sin(3.14159+3.14159))"));
//			System.out.println(eval.eval2("sin(-5.307179586686775E-6)"));
//
//			System.out.println(eval.eval2("sin(pow(2,2)-2*3.1415926)"));
//			System.out.println(eval.eval2("sin(4)"));
//			System.out.println(eval
//					.differentiate("max((sin(x)+x)*10/x,2)", "1"));
//			System.out.println(eval.eval("-(1)"));
//		} catch (Exception e) {
//			e.printStackTrace();
//		}
//	}
}