/**
* Trims the double to the specified number of digits in the number format.
*
* @param x the number to trim the string representation.
* @param numDigits number of digits to limits the string representation to.
* @return the string representation of the double limited to the specified number of digits in
* the number format.
*/
public static String trimDouble(double x, int numDigits) {
if (defaultNumDigits != numDigits) {
MNF.setMaximumFractionDigits(defaultNumDigits = numDigits);
MNF.setMinimumFractionDigits(0);
MNF.setGroupingUsed(false);
} // end if
return MNF.format(x);
} // end trimDouble
/**
* <code>MathUtil</code> is a math utility class.
*
* @author Dan Dexter
* @author Dr. Robert Shelton
* @version 1.0
* @since 1.0
*/
public class MathUtil {
private static final double[] inverseFactorials = {
1.0,
1.0,
0.5,
0.16666666666666666,
0.041666666666666664,
0.008333333333333333,
0.001388888888888889,
1.984126984126984E-4,
2.48015873015873E-5,
2.7557319223985893E-6,
2.755731922398589E-7,
2.505210838544172E-8,
2.08767569878681E-9,
1.6059043836821613E-10,
1.1470745597729725E-11,
7.647163731819816E-13,
4.779477332387385E-14,
2.8114572543455206E-15,
1.5619206968586225E-16,
8.22063524662433E-18
};
private static final int MAX_TERMS = inverseFactorials.length;
private static final double[] terms = new double[MAX_TERMS];
private static MdeNumberFormat MNF = MdeNumberFormat.getInstance();
private static int defaultNumDigits = -1;
private static final double INV_LOG2 = 1.0 / Math.log(2.0);
private static final double INV_LOG10 = 1.0 / Math.log(10.0);
/**
* Calculates Log base 2 of a given number.
*
* @param a the number to calculate the Log base 2 of.
* @return the Log base 2 of the number <code>a</code>
*/
public static final double log2(double a) {
return INV_LOG2 * Math.log(a);
} // end log2
/**
* Calculates Log base 10 of a given number.
*
* @param a the number to calculate the Log base 10 of.
* @return the Log base 10 of the number <code>a</code>
*/
public static final double log10(double a) {
return INV_LOG10 * Math.log(a);
} // end log10
/**
* Calculates Log of a given number for the specified base.
*
* @param a the number to calculate the Log of.
* @param base the base for calculationg the log.
* @return the Log of the number for the given <code>base</code>
*/
public static final double logBaseX(double a, double base) {
return Math.log(a) / Math.log(base);
}
/**
* Calculates <code>log( 1 + x )</code>.
*
* @param x the number to calculate the function over.
* @return the value of <code>log( 1 + x )</code>.
*/
public static double logOnePlusX(double x) {
if (Math.abs(x) > 0.1) {
return Math.log(1.0 + x);
}
if (x == 0.0) {
return 0.0;
}
double r = 0.0, t = x;
int i, l;
for (l = 0; l < MAX_TERMS; l++, t *= (-x)) {
if (Math.abs(terms[l] = t / (l + 1)) < 1.0e-16 * Math.abs(x)) {
break;
}
}
if (l >= MAX_TERMS) {
throw new IllegalStateException("logOnePlusX needed too many terms");
}
for (i = l; i >= 0; i--) {
r += terms[i];
}
return r;
} // end logOnePlusX
/**
* Determines the factor of a number for a given order.
*
* @param x the number to stump
* @param n the order
* @return the stump of the number.
*/
public static double stump(double x, int n) {
if (x == 0.0) {
return (n <= 0) ? 1.0 : 0.0;
}
int i, l;
double r = 0.0, t = 1.0;
if (Math.abs(x) < 0.1) {
for (i = 0; i < n; i++, t *= x) {
terms[i] = t * inverseFactorials[i];
}
for (l = n; l < MAX_TERMS; l++, t *= x) {
if (Math.abs(terms[l] = t * inverseFactorials[l]) < 1.0e-16 * Math.abs(terms[n])) {
break;
}
}
if (l >= MAX_TERMS) {
throw new IllegalArgumentException("Stump index limit exceeded.");
}
for (i = l; i >= n; i--) {
r += terms[i];
}
return r;
} // end if
for (i = 0; i < n; i++, t *= x) {
terms[i] = inverseFactorials[i] * t;
}
for (i = n - 1; i >= 0; i--) {
r -= terms[i];
}
return r + Math.exp(x);
} // end stump
/**
* Returns a delta floating point number that represents a whole number division of the specified
* number.
*
* @param d the number to find the delta for.
* @return a small delta (range) that represents a while number division of the specified number.
*/
public static final double findDelta(double d) {
double z = Math.pow(10.0, Math.ceil(log10(d)));
double d_div_7 = d / 7.0;
while (d_div_7 < z) {
z *= 0.5;
if (d_div_7 > z) {
return z;
}
z *= 0.2;
} // end for
double d_div_15 = d / 15.0;
while (d_div_15 > z) {
z *= 2.0;
}
return z;
} // end findDelta
/**
* Trims the double to the specified number of digits in the number format.
*
* @param x the number to trim the string representation.
* @param numDigits number of digits to limits the string representation to.
* @return the string representation of the double limited to the specified number of digits in
* the number format.
*/
public static String trimDouble(double x, int numDigits) {
if (defaultNumDigits != numDigits) {
MNF.setMaximumFractionDigits(defaultNumDigits = numDigits);
MNF.setMinimumFractionDigits(0);
MNF.setGroupingUsed(false);
} // end if
return MNF.format(x);
} // end trimDouble
/**
* Returns the equivalent rational string of a number.
*
* @param x the number.
* @param lim the limit.
* @return the equivalent rational string, or null if one does not exist.
*/
public static String getEquivalentRationalString(double x, int lim) {
long startTime = MdeSettings.DEBUG ? System.currentTimeMillis() : 0;
RationalExpression r = new RationalExpression.ContinuedFraction(x, 20).iterate();
if (MdeSettings.DEBUG) {
long endTime = System.currentTimeMillis();
System.out.println(
"Call to \"RationalExpression.ContinuedFraction.iterate\" on x = "
+ x
+ " took "
+ (endTime - startTime)
+ " milliseconds");
} // end if
if (r == null) {
return null;
}
double d = r.getDenominator().toExpression().theValue.doubleValue();
double n = r.getNumerator().toExpression().theValue.doubleValue();
if (Math.abs(n) > lim || Math.abs(d) > lim) {
return null;
}
if (d == 1.0) {
return "" + (int) n;
}
return (int) n + "/" + (int) d;
} // end getEquivalentRationalString
/**
* Returns the quadratic representation of a number.
*
* @param x the number.
* @param lim the limit.
* @return the quadratic representation of the number.
*/
public static String getQuadraticRepresentationString(double x, int lim) {
Object s = getRationalObject(x, lim);
if (s == null) {
return null;
}
if (s instanceof String) {
return (String) s;
}
double[] r = (double[]) s;
if (r.length != 3) {
return null;
}
int d = GCD(r);
for (int i = 0; i < r.length; i++) {
r[i] /= d;
}
if (Math.abs(r[0]) > lim || Math.abs(r[1]) > lim || Math.abs(r[2]) > lim) {
return null;
}
Roots.RootFactor rf = new Roots.RootFactor(r[2] / r[0], r[1] / r[0]);
if (Math.abs(x - rf.rootValues[0]) < Math.abs(x - rf.rootValues[1])) {
return prettyPrintQRoot((int) r[0], (int) r[1], (int) r[2], 0, lim);
}
return prettyPrintQRoot((int) r[0], (int) r[1], (int) r[2], 1, lim);
} // end getQuadraticRepresentationString
/**
* Returns the rational equivalent of a number.
*
* @param x the number.
* @param lim the limit.
* @return the rational equivalent of a number.
*/
public static String getRationalEquivalent(double x, int lim) {
String s = getEquivalentRationalString(x, lim);
if (s == null) {
return "approx. " + trimDouble(x, 4);
}
return s;
} // end getRationalEquivalent
/**
* A printable version of the Quadratic root.
*
* @param a the <code>a</code> value of the quadratic.
* @param b the <code>b</code> value of the quadratic.
* @param c the <code>c</code> value of the quadratic.
* @param whichRoot either the <code>0</code> or <code>1</code> root.
* @param lim the limit.
* @return printable version of the quadratic root, or null if one does not exist.
*/
public static String prettyPrintQRoot(double a, double b, double c, int whichRoot, int lim) {
String[] sign = {" - ", " + "};
if (a == 0.0) {
return getEquivalentRationalString(-b / c, lim);
}
if (b == 0.0) {
switch (whichRoot) {
case 1:
return "sqrt(" + getEquivalentRationalString(-c / a, lim) + ")";
case 0:
return "-sqrt(" + getEquivalentRationalString(-c / a, lim) + ")";
default:
throw new IllegalArgumentException("whichRoot must bbe 0 or 1");
} // end switch
}
double h = -0.5 * b / a;
double d = h * h - c / a;
String hString = getEquivalentRationalString(h, lim);
String dString = getEquivalentRationalString(d, lim);
if (hString == null || dString == null) {
return null;
}
return hString + sign[whichRoot] + "sqrt(" + dString + ")";
} // end prettyPrintQRoot
/**
* Returns the greatest common divisor.
*
* @param c the first integer.
* @param d the second integer.
* @return the greatest common divisor of the two integer numbers.
*/
public static int GCD(int c, int d) {
int c1 = Math.abs(c);
int d1 = Math.abs(d);
int big = Math.max(c1, d1);
int little = Math.min(c1, d1);
if (little == 0) {
return big;
}
return getGCD(big, little);
} // end GCD
/**
* Returns the greatest common divisor of an array of numbers.
*
* @param r array of numbers.
* @return the the greatest common divisor of an array of numbers.
*/
public static int GCD(double[] r) {
int i, n = r.length, z;
for (i = 0; i < n; i++) {
if (Math.abs(r[i]) > Integer.MAX_VALUE) {
return 1;
}
}
switch (n) {
case 1:
return (int) r[0];
case 0:
throw new IllegalArgumentException("Can't find GCD of empty array.");
default:
z = (int) r[0];
for (i = 1; i < n; i++) {
z = GCD(z, (int) r[i]);
}
return z;
} // end switch
} // end GCD
private static int getGCD(int big, int little) {
int r = big % little;
if (r == 0) {
return little;
}
return getGCD(little, r);
} // end getGCD
// // A utility method to translate between ragged arrays and MultiPoints --
// // probably should eventually be private to discourage use of ragged arrays
// static MultiPointXY[] raggedToMulti(double[][] r) {
// int d, i, j, n = r.length;
// MultiPointXY[] m = new MultiPointXY[n];
//
// for (i = 0; i < n; i++) {
// m[i] = new MultiPointXY(r[i][0]);
// m[i].yArray = new double[d = (r[i].length - 1)];
//
// for (j = 0; j < d; j++) {
// m[i].yArray[j] = r[i][j + 1];
// }
// } // end for i
//
// return m;
// } // end raggedToMulti
/**
* Utility to translate from MultiPoints to a ragged array.
*
* @param m the multipoint array.
* @return the ragged array.
*/
static double[][] multiToRagged(MultiPointXY[] m) {
int d, i, j, n = m.length;
double[][] r = new double[n][1];
for (i = 0; i < n; i++) {
if (m[i] != null) {
if ((d = 1 + m[i].yArray.length) > 1) {
r[i] = new double[d];
}
r[i][0] = m[i].x;
for (j = 1; j < d; j++) {
r[i][j] = m[i].yArray[j - 1];
}
}
} // end for i
return r;
} // end multiToRagged
private static Object getRationalObject(double x, int lim) {
if (x == 0) return "0";
double[] r = new RationalExpression.ContinuedFraction(x, 20).getPolynomialCoefficients();
if (r.length != 2) {
return r;
}
if (Math.abs(r[0]) > lim || Math.abs(r[1]) > lim) {
return null;
}
r[1] = -r[1];
if (r[0] < 0) {
r[0] = -r[0];
r[1] = -r[1];
} // end if
if (r[0] == 1.0) {
return "" + (int) r[1];
}
return "" + (int) r[1] + "/" + (int) r[0];
} // end getRationalObject
// public static void main(String[] args) {
// gov.nasa.ial.mde.solver.symbolic.Expression e =
// new gov.nasa.ial.mde.solver.symbolic.Expression(MathUtil.combineArgs(args));
//
// if (e.theValue == null)
// return;
//
// String s = MathUtil.getQuadraticRepresentationString(e.theValue.doubleValue(), 1000);
//
// System.out.println("The value = " + s);
// } // end main
}