<<<<<<< HEAD /* * Copyright (c) 2015, Netsyms Technologies * All rights reserved. * * * CODE LICENSE ========== * Redistribution and use in source and binary forms, with or without modification, * are permitted provided that the following conditions are met: * * 1. Redistributions of source code must retain the above copyright notice, this * list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright notice, * this list of conditions and the following disclaimer in the documentation and/or * other materials provided with the distribution. * * 3. Neither the name of the copyright holder nor the names of its contributors * may be used to endorse or promote products derived from this software without * specific prior written permission. * * 4. You adhere to the Media License detailed below. If you do not, this license * is automatically revoked and you must purge all copies of the software you * possess, in source or binary form. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. * * * MEDIA LICENSE ========== * All images and other graphical files ("media") included with this * software are copyright (c) 2015 Netsyms Technologies. You may not distribute * the graphics or any program, source code repository, or other digital storage * media containing them without permission from Netsyms Technologies. * This ban on distribution only applies to publicly available systems. * A password-protected network file share, USB drive, or other storage scheme that * cannot be easily accessed by the public is generally allowed. If in doubt, * contact Netsyms Technologies. If Netsyms Technologies allows or denies * you permission, that decision is considered final and binding. * * You may only use the media for personal, * non-commercial, non-educational use unless: * 1, You have paid for the software and media via the SyMAT website, * or 2, you are using it as part of the 15-day trial period. * Other uses are prohibited without permission. * If any part of this license is deemed unenforcable, the remainder * of the license remains in full effect. */ package net.apocalypselabs.symat; import java.io.BufferedReader; import java.io.IOException; import java.io.InputStream; import java.io.InputStreamReader; import static java.lang.Math.*; import java.lang.reflect.Array; import java.math.BigInteger; import java.net.URL; import java.security.SecureRandom; import java.util.ArrayList; import java.util.Arrays; import java.util.Calendar; import java.util.Date; import java.util.HashMap; import java.util.HashSet; import java.util.Iterator; import java.util.List; import java.util.Map; import java.util.NoSuchElementException; import java.util.Set; import java.util.prefs.Preferences; import javax.swing.JFileChooser; import javax.swing.JOptionPane; import static net.apocalypselabs.symat.Main.API_URL; import net.apocalypselabs.symat.components.TextBox; import org.matheclipse.core.eval.EvalUtilities; import org.matheclipse.core.interfaces.IExpr; import org.matheclipse.parser.client.math.MathException; import org.mozilla.javascript.NativeArray; import org.python.core.PyList; /** * These functions are accessible from JavaScript. * * There are a lot of aliases in here too. * * @author Skylar */ public class Functions { public static final HashMap GLOBALS = new HashMap<>(); private final EvalUtilities util = new EvalUtilities(true, true); Graph graphwin = new Graph(true); private String lang = "py"; private final SecureRandom rng = new SecureRandom(); /* Useful interactions */ /** * Display a message dialog box. * * @param message The message to give. */ public void notify(Object message) { JOptionPane.showInternalMessageDialog(Main.mainPane, message.toString()); } /** * Display message dialog. * * This is an alias to help JavaScript programmers. * * @param message The message */ public void alert(Object message) { notify(message); } /** * Display an input dialog box with a text field. * * @param question Text to label dialog * @return The inputted text */ public String ask(String question) { return JOptionPane.showInternalInputDialog(Main.mainPane, question); } /** * Pause execution for the specified number of milliseconds. * * @param millis */ public void pause(long millis) { try { Thread.sleep(millis); } catch (InterruptedException e) { // Nothing to do. } } /** * @see pause() * @param millis */ public void sleep(long millis) { pause(millis); } /** * Quit SyMAT. */ public void quitApplication() { System.exit(0); } /* Math commands */ /** * Find the factorial (n!) of a number. * * @param n positive integer * @return n! as String * @throws net.apocalypselabs.symat.BadInputException */ public String factorial(long n) throws BadInputException { if (n <= 0) { throw new BadInputException("Input must be greater than zero!"); } BigInteger inc = new BigInteger("1"); BigInteger fact = new BigInteger("1"); for (long c = 1; c <= n; c++) { fact = fact.multiply(inc); inc = inc.add(BigInteger.ONE); } return fact.toString(); } /** * Take (a^b) mod m. If b is -1, finds the modular inverse of a mod m. * * @param a Number * @param b Exponent * @param m Modulus * @return pow(a,b)%m. */ public double powermod(double a, double b, double m) { if (b == -1) { BigInteger in = new BigInteger(String.valueOf((int) a)); return in.modInverse(new BigInteger(String.valueOf((int) m))).doubleValue(); } return (pow(a, b) % m + m) % m; } /** * Take (a^b) mod m. If b is -1, finds the modular inverse of a mod m. * * @param a Number * @param b Exponent * @param m Modulus * @return pow(a,b)%m. */ public String powermod(String a, String b, String m) { BigInteger in = new BigInteger(a); if (b.equals("-1")) { return in.modInverse(new BigInteger(m)).toString(); } return in.modPow(new BigInteger(b), new BigInteger(m)).toString(); } public long gcd(long a, long b) { if (b == 0) { return a; } return gcd(b, a % b); } public String gcd(String a, String b) { return (new BigInteger(a).gcd(new BigInteger(b)).toString()); } /** * Differentiate the function with respect to idv. * * @param function Function * @param idv independent variable * @return Differentiated function */ public String diff(String function, String idv) { return util.evaluate("diff(" + function + "," + idv + ")").toString(); } /** * Differentiate the function with respect to x. * * @param function Function * @return Differentiated function */ public String diff(String function) { // Assume "x" as var return diff(function, "x"); } @Deprecated public String D(String function, String idv) { return diff(function, idv); } public double[] solve(String function, String idv, int eq) { String res = $("Solve[" + function + "==" + eq + ", " + idv + "]"); res = res.substring(1, res.length() - 1); String[] cmp = res.split(","); for (int i = 0; i < cmp.length; i++) { cmp[i] = cmp[i].replace("{" + idv + "->", ""); cmp[i] = cmp[i].replace("}", ""); } double[] out = new double[cmp.length]; for (int i = 0; i < cmp.length; i++) { try { if (cmp[i].contains("I")) { if (cmp[i].contains("-I")) { out[i] = Double.NEGATIVE_INFINITY; } else { out[i] = Double.POSITIVE_INFINITY; } } else { out[i] = Double.parseDouble(cmp[i]); } } catch (Exception ex) { return new double[]{Double.NaN}; } } return out; } public double[] solve(String function, String idv) { return solve(function, idv, 0); } public double[] solve(String function) { return solve(function, "x"); } private String printa(double[] o) { String out = "["; for (int i = 0; i < o.length; i++) { out += o[i] + (i == o.length - 1 ? "" : ", "); } out += "]"; return out; } private String printa(int[] o) { String out = "["; for (int i = 0; i < o.length; i++) { out += o[i] + (i == o.length - 1 ? "" : ", "); } out += "]"; return out; } private String printa(boolean[] o) { String out = "["; for (int i = 0; i < o.length; i++) { out += (o[i] ? "true" : "false") + (i == o.length - 1 ? "" : ", "); } out += "]"; return out; } public String printa(Object o) { String out = "["; if (o instanceof int[]) { int[] arr = (int[]) o; for (int i = 0; i < arr.length; i++) { out += arr[i] + (i == arr.length - 1 ? "" : ", "); } } else if (o instanceof double[]) { double[] arr = (double[]) o; for (int i = 0; i < arr.length; i++) { out += arr[i] + (i == arr.length - 1 ? "" : ", "); } } else if (o instanceof boolean[]) { double[] arr = (double[]) o; for (int i = 0; i < arr.length; i++) { out += arr[i] + (i == arr.length - 1 ? "" : ", "); } } else if (o instanceof int[][]) { int[][] arr = (int[][]) o; for (int i = 0; i < arr.length; i++) { out += printa(arr[i]) + (i == arr.length - 1 ? "" : ", "); } } else if (o instanceof double[][]) { double[][] arr = (double[][]) o; for (int i = 0; i < arr.length; i++) { out += printa(arr[i]) + (i == arr.length - 1 ? "" : ", "); } } else if (o instanceof boolean[][]) { boolean[][] arr = (boolean[][]) o; for (int i = 0; i < arr.length; i++) { out += printa(arr[i]) + (i == arr.length - 1 ? "" : ", "); } } else if (o instanceof NativeArray) { NativeArray arr = (NativeArray) o; for (long i = 0; i < arr.getLength(); i++) { out += (arr.get(i) instanceof NativeArray ? printa(arr.get(i)) : arr.get(i).toString()) + (i == arr.getLength() - 1 ? "" : ", "); } } else if (o instanceof PyList) { PyList arr = (PyList) o; Object[] oo = arr.toArray(); for (int i = 0; i < oo.length; i++) { out += (oo[i] instanceof Object[] ? printa(oo[i]) : oo[i].toString()) + (i == oo.length - 1 ? "" : ", "); } } else { Object[] arr = (Object[]) o; for (int i = 0; i < arr.length; i++) { out += (arr[i] instanceof Object[] ? printa(arr[i]) : arr[i].toString()) + (i == arr.length - 1 ? "" : ", "); } } out += "]"; return out; } /** * Integrate the function with respect to idv. * * @param function Function * @param idv independent variable * @return Integrated function */ public String integrate(String function, String idv) { return util.evaluate("integrate(" + function + "," + idv + ")").toString(); } /** * Integrate the function with respect to x. * * @param function Function * @return Integrated function */ public String integrate(String function) { return integrate(function, "x"); } public String factor(String function) { return sym("Factor(" + function + ")"); } /** * Simplify the given expression. * * @param expr expression * @return simplified expression */ public String simplify(String expr) { return sym("Simplify(" + expr + ")"); } public Object vpa(String expr) { IExpr ans = util.evaluate("N(" + expr + ")"); if (ans.isNumber()) { return Double.parseDouble(ans.toString()); } return ans.toString(); } public int[] primes(int in) { boolean[] prime = new boolean[in]; for (int i = 0; i < prime.length; i++) { prime[i] = true; } for (int i = 2; i < sqrt(in); i++) { if (prime[i]) { int x = 0; for (int j = i * i; j < in; j = i * i + x * i) { prime[j] = false; x++; } } } List arr = new ArrayList<>(); for (int i = 2; i < prime.length; i++) { if (prime[i]) { arr.add(i); } } int[] out = new int[arr.size()]; for (int i = 0; i < arr.size(); i++) { out[i] = arr.get(i); } return out; } public double sec(double d) { return 1.0 / Math.cos(d); } public double csc(double d) { return 1.0 / Math.sin(d); } public double cot(double d) { return 1.0 / Math.tan(d); } public double asec(double d) { return Math.acos(1.0 / d); } public double acsc(double d) { return Math.asin(1.0 / d); } public double acot(double d) { return Math.atan(1.0 / d); } public double sinh(double d) { return Math.sinh(d); } public double cosh(double d) { return Math.cosh(d); } public double tanh(double d) { return Math.tanh(d); } public double sech(double d) { return pow(Math.cosh(d), -1); } public double csch(double d) { return pow(Math.sinh(d), -1); } public double coth(double d) { return Math.cosh(d) / Math.sinh(d); } /** * Multiplies the given numbers together. * * @param a numbers. Calculates first * second * third, etc. * @return The product of the numbers or the value of input if there is only * one input. */ public double times(double... a) { double ans = 0; for (int i = 0; i < a.length; i++) { if (i == 0) { ans = a[i]; } else { ans *= a[i]; } } return ans; } /** * Multiplies the given numbers together. * * @param a * @param b * @return The product of the numbers or the value of input if there is only * one input. */ public String times(String a, String b) { return (new BigInteger(a).multiply(new BigInteger(b))).toString(); } /** * Divide the given numbers. * * @param a numbers. Calculates (first / second) / third, etc. * @return The quotient of the numbers or the value of input if there is * only one input. */ public double divide(double... a) { double ans = 0; for (int i = 0; i < a.length; i++) { if (i == 0) { ans = a[i]; } else { ans /= a[i]; } } return ans; } /** * Divide the given numbers. * * @param a * @param b * @return The quotient of the numbers or the value of input if there is * only one input. */ public String divide(String a, String b) { return (new BigInteger(a).divide(new BigInteger(b))).toString(); } /** * Divide the first number by the second and return the remainder. * * @param a numbers. Calculates (first mod second) mod third, etc. * @return The modulus of the numbers or the value of input if there is only * one input. */ public double mod(double... a) { double ans = 0; for (int i = 0; i < a.length; i++) { if (i == 0) { ans = a[i]; } else { ans %= a[i]; } } return ans; } /** * Divide the first number by the second and return the remainder. * * @param a * @param b * @return The modulus of the numbers or the value of input if there is only * one input. */ public String mod(String a, String b) { return (new BigInteger(a).mod(new BigInteger(b))).toString(); } /** * Add the given numbers together. * * @param a numbers. Calculates first + second + third, etc. * @return The sum of the numbers or the value of input if there is only one * input. */ public double add(double... a) { double ans = 0; for (double d : a) { ans += d; } return ans; } /** * Add the given numbers together. * * @param a numbers. Calculates first + second + third, etc. * @return The sum of the numbers or the value of input if there is only one * input. */ public String add(String a, String b) { return (new BigInteger(a).subtract(new BigInteger(b))).toString(); } /** * Subtract the given numbers. * * @param a numbers. Calculates (first - second) - third, etc. * @return The difference of the numbers or the value of input if there is * only one input. */ public double subtract(double... a) { double ans = 0; for (int i = 0; i < a.length; i++) { if (i == 0) { ans = a[i]; } else { ans -= a[i]; } } return ans; } /** * Subtract the given numbers. * * @param a numbers. Calculates (first - second) - third, etc. * @return The difference of the numbers or the value of input if there is * only one input. */ public String subtract(String a, String b) { BigInteger ans = new BigInteger(a); ans = ans.subtract(new BigInteger(b)); return ans.toString(); } public double[][] minvert(double a[][]) { int n = a.length; double x[][] = new double[n][n]; double b[][] = new double[n][n]; int index[] = new int[n]; for (int i = 0; i < n; ++i) { b[i][i] = 1; } // Transform the matrix into an upper triangle gaussian(a, index); // Update the matrix b[i][j] with the ratios stored for (int i = 0; i < n - 1; ++i) { for (int j = i + 1; j < n; ++j) { for (int k = 0; k < n; ++k) { b[index[j]][k] -= a[index[j]][i] * b[index[i]][k]; } } } // Perform backward substitutions for (int i = 0; i < n; ++i) { x[n - 1][i] = b[index[n - 1]][i] / a[index[n - 1]][n - 1]; for (int j = n - 2; j >= 0; --j) { x[j][i] = b[index[j]][i]; for (int k = j + 1; k < n; ++k) { x[j][i] -= a[index[j]][k] * x[k][i]; } x[j][i] /= a[index[j]][j]; } } return x; } // Method to carry out the partial-pivoting Gaussian // elimination. Here index[] stores pivoting order. private void gaussian(double a[][], int index[]) { int n = index.length; double c[] = new double[n]; // Initialize the index for (int i = 0; i < n; ++i) { index[i] = i; } // Find the rescaling factors, one from each row for (int i = 0; i < n; ++i) { double c1 = 0; for (int j = 0; j < n; ++j) { double c0 = Math.abs(a[i][j]); if (c0 > c1) { c1 = c0; } } c[i] = c1; } // Search the pivoting element from each column int k = 0; for (int j = 0; j < n - 1; ++j) { double pi1 = 0; for (int i = j; i < n; ++i) { double pi0 = Math.abs(a[index[i]][j]); pi0 /= c[index[i]]; if (pi0 > pi1) { pi1 = pi0; k = i; } } // Interchange rows according to the pivoting order int itmp = index[j]; index[j] = index[k]; index[k] = itmp; for (int i = j + 1; i < n; ++i) { double pj = a[index[i]][j] / a[index[j]][j]; // Record pivoting ratios below the diagonal a[index[i]][j] = pj; // Modify other elements accordingly for (int l = j + 1; l < n; ++l) { a[index[i]][l] -= pj * a[index[j]][l]; } } } } /** * Get all prime factors of input number. * * @param n An integer number. * @return Array of primes. * * Thanks to * http://www.javacodegeeks.com/2014/05/how-to-find-prime-factors-of-integer-numbers-in-java-factorization.html * and http://stackoverflow.com/a/2451219/2534036 */ public long[] factor(long n) { long i; Set primes = new HashSet<>(); long copyOfInput = n; for (i = 2; i <= copyOfInput; i++) { if (copyOfInput % i == 0) { primes.add(i); // prime factor copyOfInput /= i; i--; } } long[] a = new long[primes.size()]; int j = 0; for (Object val : primes) { a[j++] = (long) val; } return a; } public boolean isprime(long n) { int i = 2; while (i <= sqrt(n)) { if (n % i == 0) { return false; } i++; } return true; } public boolean isprime(String nn) { BigInteger n = new BigInteger(nn); BigInteger i = new BigInteger("2"); BigInteger ns = bigIntSqRootCeil(n); while (i.compareTo(ns) <= 0) { if (n.mod(i).toString().equals("0")) { return false; } i = i.add(BigInteger.ONE); } return true; } /** * Thanks to http://stackoverflow.com/a/11962756/2534036 * * @param x * @return * @throws IllegalArgumentException */ private BigInteger bigIntSqRootCeil(BigInteger x) throws IllegalArgumentException { if (x.compareTo(BigInteger.ZERO) < 0) { throw new IllegalArgumentException("Negative argument."); } // square roots of 0 and 1 are trivial and // y == 0 will cause a divide-by-zero exception if (x == BigInteger.ZERO || x == BigInteger.ONE) { return x; } // end if BigInteger two = BigInteger.valueOf(2L); BigInteger y; // starting with y = x / 2 avoids magnitude issues with x squared for (y = x.divide(two); y.compareTo(x.divide(y)) > 0; y = ((x.divide(y)).add(y)).divide(two)) { } if (x.compareTo(y.multiply(y)) == 0) { return y; } else { return y.add(BigInteger.ONE); } } // end bigIntSqRootCeil /** * Get all unique permutations of the given array. * * @param objs Array of items. * @return Matrix */ public Object[] perms(Object... objs) { Permutations