public static double dnbinom_mu(double x, double size, double mu, boolean give_log) {
/* originally, just set prob := size / (size + mu) and called dbinom_raw(),
* but that suffers from cancellation when mu << size */
double ans, p;
if (DoubleVector.isNaN(x) || DoubleVector.isNaN(size) || DoubleVector.isNaN(mu)) {
return x + size + mu;
}
if (mu < 0 || size < 0) {
return DoubleVector.NaN;
}
// R_D_nonint_check(x);
if (SignRank.R_D_nonint(x, true, give_log)) {
// MATHLIB_WARNING("non-integer x = %f", x);
// How to warn??
return SignRank.R_D__0(true, give_log);
}
if (x < 0 || !DoubleVector.isFinite(x)) {
return SignRank.R_D__0(true, give_log);
}
x = SignRank.R_D_forceint(x);
if (x == 0) /* be accerate, both for n << mu, and n >> mu :*/ {
return SignRank.R_D_exp(
size * (size < mu ? Math.log(size / (size + mu)) : Math.log1p(-mu / (size + mu))),
true,
give_log);
}
if (x < 1e-10 * size) {
/* don't use dbinom_raw() but MM's formula: */
/* FIXME --- 1e-8 shows problem; rather use algdiv() from ./toms708.c */
return SignRank.R_D_exp(
x * Math.log(size * mu / (size + mu))
- mu
- org.apache.commons.math.special.Gamma.logGamma(x + 1)
+ Math.log1p(x * (x - 1) / (2 * size)),
true,
give_log);
}
/* else: no unnecessary cancellation inside dbinom_raw, when
* x_ = size and n_ = x+size are so close that n_ - x_ loses accuracy
*/
ans = dbinom_raw(size, x + size, size / (size + mu), mu / (size + mu), give_log);
p = ((double) size) / (size + x);
return ((give_log) ? Math.log(p) + ans : p * ans);
}
/** Computes the probability <SPAN CLASS="MATH"><I>p</I>(<I>x</I>)</SPAN>. */
public static double prob(double n, double p, int x) {
final int SLIM = 15; // To avoid overflow
final double MAXEXP = (Num.DBL_MAX_EXP - 1) * Num.LN2; // To avoid overflow
final double MINEXP = (Num.DBL_MIN_EXP - 1) * Num.LN2; // To avoid underflow
double y;
if (p < 0.0 || p > 1.0) throw new IllegalArgumentException("p not in [0, 1]");
if (n <= 0.0) throw new IllegalArgumentException("n <= 0.0");
if (x < 0) return 0.0;
if (p >= 1.0) { // In fact, p == 1
if (x == 0) return 1.0;
else return 0.0;
}
if (p <= 0.0) // In fact, p == 0
return 0.0;
y =
Num.lnGamma(n + x)
- (Num.lnFactorial(x) + Num.lnGamma(n))
+ n * Math.log(p)
+ x * Math.log1p(-p);
if (y >= MAXEXP) throw new IllegalArgumentException("term overflow");
return Math.exp(y);
}
/** {@inheritDoc} */
public OpenMapRealVector mapLog1pToSelf() {
Iterator iter = entries.iterator();
while (iter.hasNext()) {
iter.advance();
entries.put(iter.key(), Math.log1p(iter.value()));
}
return this;
}
private static float[] ComputeGamma(int[] lo, int[] md, int[] hi) {
float[] array = new float[3];
for (int i = 0; i < 3; i++) {
if (lo[i] < md[i] && md[i] < hi[i]) {
double log =
Math.log1p(/*0.5, */ (double) (((float) (md[i] - lo[i])) / ((float) (hi[i] - lo[i]))));
array[i] = (log > 10.0) ? ((float) 10.0) : ((log < 0.1) ? ((float) 0.1) : ((float) log));
} else {
array[i] = 1f;
}
}
return array;
}
public static double pnbeta2(
double x, double o_x, double a, double b, double ncp, boolean lower_tail, boolean log_p) {
double ans = pnbeta_raw(x, o_x, a, b, ncp);
/* return R_DT_val(ans), but we want to warn about cancellation here */
if (lower_tail) {
return log_p ? Math.log(ans) : ans;
} else {
if (ans > 1 - 1e-10) {
return (DoubleVector.NaN);
}
ans = Math.min(ans, 1.0); /* Precaution */
return log_p ? Math.log1p(-ans) : (1 - ans);
}
}
/**
* Computes the inverse of the distribution function.
*
* @param xi
* @param beta
* @param tau
* @param y
* @return
*/
public static double inverseF(double xi, double beta, double tau, double y) {
if (tau <= 0.0) throw new InvalidParameterException("tau <= 0");
if (y < 0.0 || y > 1.0) throw new InvalidParameterException("y not in [0,1]");
if (y <= 0.0) return beta;
if (y >= 1.0 && xi >= 0) {
return Double.POSITIVE_INFINITY;
}
if (y >= 1.0 && xi < 0) {
return beta - tau / xi;
}
if (xi == 0) {
return beta - tau * Math.log1p(-y);
}
return beta + tau / xi * (-1 + Math.pow(1 - y, -xi));
}
private double calculateWeight(JobInProgress job, TaskType taskType) {
if (!isRunnable(job)) {
return 0;
} else {
double weight = 1.0;
if (sizeBasedWeight) {
// Set weight based on runnable tasks
weight = Math.log1p(runnableTasks(job, taskType)) / Math.log(2);
}
weight *= getPriorityFactor(job.getPriority());
if (weightAdjuster != null) {
// Run weight through the user-supplied weightAdjuster
weight = weightAdjuster.adjustWeight(job, taskType, weight);
}
return weight;
}
}
public static void main(String[] args) {
for (int i = 0; i <= 10; i++) {
System.out.println((int) Math.pow(2, i)); // üs alma
}
System.out.println("\n1024 karekökü : " + (int) Math.sqrt(1204)); // karekö alma
System.out.println(" - 45 in mutlak deðerini alalým : " + Math.abs(-45));
System.out.println("3.55 üst deðere yuvarla : " + Math.ceil(3.55));
System.out.println("3.55 alt degerini bulalým : " + Math.floor(3.55));
System.out.println("35 ve 155 arasýndaki büyük sayi : " + Math.max(35, 155));
System.out.println("25 ve 244 arasýndaki küþük sayi : " + Math.min(25, 244));
System.out.println(
"rastgele sayi : " + Math.random()); // dönecek deðer 0 ile 1 arasýnda double deðer döner.
System.out.println(
"rastgele çýkan sayýyý 10 ile çarpýmsonucu : " + (int) (Math.random() * 100));
Random r = new Random();
int a = r.nextInt(100);
float f = r.nextFloat();
System.out.println("Sonucumuz : " + a);
System.out.println(
"randon sýnýfýnda rastgele float deðer: " + f); // 0 ile 1 arasý bir float deðer verir.
System.out.println("1.5 radyan : " + Math.toDegrees(1.5) + " derecedir");
System.out.println("45 derece : " + Math.toRadians(45) + " radyandýr.");
System.out.println("sin 90 = " + Math.sin(Math.toRadians(90)));
System.out.println("cos 55 = " + Math.cos(Math.toRadians(55)));
System.out.println("Argsin 0.47 = " + Math.toDegrees(Math.asin(0.47)));
System.out.println("ArgCos 0.57 = " + Math.toDegrees(Math.acos(0.57)));
System.out.println("ln e = " + Math.log(Math.E));
System.out.println("log10(5) = " + Math.log10(5));
System.out.println("ln(7+1) = " + Math.log1p(7));
}
/**
* Return the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @since 2.1
*/
@Override
public double density(double x) {
recomputeZ();
if (x < 0 || x > 1) {
return 0;
} else if (x == 0) {
if (alpha < 1) {
throw MathRuntimeException.createIllegalArgumentException(
"Cannot compute beta density at 0 when alpha = {0,number}", alpha);
}
return 0;
} else if (x == 1) {
if (beta < 1) {
throw MathRuntimeException.createIllegalArgumentException(
"Cannot compute beta density at 1 when beta = %.3g", beta);
}
return 0;
} else {
double logX = Math.log(x);
double log1mX = Math.log1p(-x);
return Math.exp((alpha - 1) * logX + (beta - 1) * log1mX - z);
}
}
public static double dbinom_raw(double x, double n, double p, double q, boolean give_log) {
double lf, lc;
if (p == 0) {
return ((x == 0) ? SignRank.R_D__1(true, give_log) : SignRank.R_D__0(true, give_log));
}
if (q == 0) {
return ((x == n) ? SignRank.R_D__1(true, give_log) : SignRank.R_D__0(true, give_log));
}
if (x == 0) {
if (n == 0) {
return SignRank.R_D__1(true, give_log);
}
lc = (p < 0.1) ? -bd0(n, n * q) - n * p : n * Math.log(q);
return (SignRank.R_D_exp(lc, true, give_log));
}
if (x == n) {
lc = (q < 0.1) ? -bd0(n, n * p) - n * q : n * Math.log(p);
return (SignRank.R_D_exp(lc, true, give_log));
}
if (x < 0 || x > n) {
return (SignRank.R_D__0(true, give_log));
}
/* n*p or n*q can underflow to zero if n and p or q are small. This
used to occur in dbeta, and gives NaN as from R 2.3.0. */
lc = stirlerr(n) - stirlerr(x) - stirlerr(n - x) - bd0(x, n * p) - bd0(n - x, n * q);
/* f = (M_2PI*x*(n-x))/n; could overflow or underflow */
/* Upto R 2.7.1:
* lf = log(M_2PI) + log(x) + log(n-x) - log(n);
* -- following is much better for x << n : */
lf = Math.log(2.0 * Math.PI) + Math.log(x) + Math.log1p(-x / n);
return SignRank.R_D_exp(lc - 0.5 * lf, true, give_log);
}
static {
for (int i = 0; i < 0x10000; i++) logTable[i] = (float) Math.log1p(i);
}
// To add/remove functions change evaluateOperator() and registration
public double evaluateFunction(String fncnam, ArgParser fncargs) throws ArithmeticException {
switch (Character.toLowerCase(fncnam.charAt(0))) {
case 'a':
{
if (fncnam.equalsIgnoreCase("abs")) {
return Math.abs(fncargs.next());
}
if (fncnam.equalsIgnoreCase("acos")) {
return Math.acos(fncargs.next());
}
if (fncnam.equalsIgnoreCase("asin")) {
return Math.asin(fncargs.next());
}
if (fncnam.equalsIgnoreCase("atan")) {
return Math.atan(fncargs.next());
}
}
break;
case 'c':
{
if (fncnam.equalsIgnoreCase("cbrt")) {
return Math.cbrt(fncargs.next());
}
if (fncnam.equalsIgnoreCase("ceil")) {
return Math.ceil(fncargs.next());
}
if (fncnam.equalsIgnoreCase("cos")) {
return Math.cos(fncargs.next());
}
if (fncnam.equalsIgnoreCase("cosh")) {
return Math.cosh(fncargs.next());
}
}
break;
case 'e':
{
if (fncnam.equalsIgnoreCase("exp")) {
return Math.exp(fncargs.next());
}
if (fncnam.equalsIgnoreCase("expm1")) {
return Math.expm1(fncargs.next());
}
}
break;
case 'f':
{
if (fncnam.equalsIgnoreCase("floor")) {
return Math.floor(fncargs.next());
}
}
break;
case 'g':
{
// if(fncnam.equalsIgnoreCase("getExponent" )) { return
// Math.getExponent(fncargs.next()); } needs Java 6
}
break;
case 'l':
{
if (fncnam.equalsIgnoreCase("log")) {
return Math.log(fncargs.next());
}
if (fncnam.equalsIgnoreCase("log10")) {
return Math.log10(fncargs.next());
}
if (fncnam.equalsIgnoreCase("log1p")) {
return Math.log1p(fncargs.next());
}
}
break;
case 'm':
{
if (fncnam.equalsIgnoreCase("max")) {
return Math.max(fncargs.next(), fncargs.next());
}
if (fncnam.equalsIgnoreCase("min")) {
return Math.min(fncargs.next(), fncargs.next());
}
}
break;
case 'n':
{
// if(fncnam.equalsIgnoreCase("nextUp" )) { return Math.nextUp
// (fncargs.next()); } needs Java 6
}
break;
case 'r':
{
if (fncnam.equalsIgnoreCase("random")) {
return Math.random();
} // impure
if (fncnam.equalsIgnoreCase("round")) {
return Math.round(fncargs.next());
}
if (fncnam.equalsIgnoreCase("roundHE")) {
return Math.rint(fncargs.next());
} // round half-even
}
break;
case 's':
{
if (fncnam.equalsIgnoreCase("signum")) {
return Math.signum(fncargs.next());
}
if (fncnam.equalsIgnoreCase("sin")) {
return Math.sin(fncargs.next());
}
if (fncnam.equalsIgnoreCase("sinh")) {
return Math.sinh(fncargs.next());
}
if (fncnam.equalsIgnoreCase("sqrt")) {
return Math.sqrt(fncargs.next());
}
}
break;
case 't':
{
if (fncnam.equalsIgnoreCase("tan")) {
return Math.tan(fncargs.next());
}
if (fncnam.equalsIgnoreCase("tanh")) {
return Math.tanh(fncargs.next());
}
if (fncnam.equalsIgnoreCase("toDegrees")) {
return Math.toDegrees(fncargs.next());
}
if (fncnam.equalsIgnoreCase("toRadians")) {
return Math.toRadians(fncargs.next());
}
}
break;
case 'u':
{
if (fncnam.equalsIgnoreCase("ulp")) {
return Math.ulp(fncargs.next());
}
}
break;
// no default
}
throw new UnsupportedOperationException(
"MathEval internal function setup is incorrect - internal function \""
+ fncnam
+ "\" not handled");
}
@Override
public Object visit(RealUnaryExpression n, Void arg) {
Double doubleObject = (Double) n.getOperand().accept(this, null);
double doubleVal = doubleObject.doubleValue();
Operator op = n.getOperator();
switch (op) {
case ABS:
return Math.abs(doubleVal);
case ACOS:
return Math.acos(doubleVal);
case ASIN:
return Math.asin(doubleVal);
case ATAN:
return Math.atan(doubleVal);
case CBRT:
return Math.cbrt(doubleVal);
case CEIL:
return Math.ceil(doubleVal);
case COS:
return Math.cos(doubleVal);
case COSH:
return Math.cosh(doubleVal);
case EXP:
return Math.exp(doubleVal);
case EXPM1:
return Math.expm1(doubleVal);
case FLOOR:
return Math.floor(doubleVal);
case LOG:
return Math.log(doubleVal);
case LOG10:
return Math.log10(doubleVal);
case LOG1P:
return Math.log1p(doubleVal);
case NEG:
return -doubleVal;
case NEXTUP:
return Math.nextUp(doubleVal);
case RINT:
return Math.rint(doubleVal);
case SIGNUM:
return Math.signum(doubleVal);
case SIN:
return Math.sin(doubleVal);
case SINH:
return Math.sinh(doubleVal);
case SQRT:
return Math.sqrt(doubleVal);
case TAN:
return Math.tan(doubleVal);
case TANH:
return Math.tanh(doubleVal);
case TODEGREES:
return Math.toDegrees(doubleVal);
case TORADIANS:
return Math.toRadians(doubleVal);
case ULP:
return Math.ulp(doubleVal);
default:
log.warn("RealUnaryExpression: unimplemented operator: " + op);
return null;
}
}
public static double R_Log1_Exp(double x, boolean lower_tail, boolean log_p) {
return ((x) > -Math.log(2.0) ? Math.log(-Math.expm1(x)) : Math.log1p(-Math.exp(x)));
}
public static double R_D_LExp(double x, boolean lower_tail, boolean log_p) {
return (log_p ? R_Log1_Exp(x, lower_tail, log_p) : Math.log1p(-x));
}
public static double R_D_Clog(double p, boolean lower_tail, boolean log_p) {
return (log_p ? Math.log1p(-(p)) : (0.5 - (p) + 0.5));
}
public static double pnbeta_raw(double x, double o_x, double a, double b, double ncp) {
/* o_x == 1 - x but maybe more accurate */
/* change errmax and itrmax if desired;
* original (AS 226, R84) had (errmax; itrmax) = (1e-6; 100) */
final double errmax = 1.0e-9;
final int itrmax = 10000; /* 100 is not enough for pf(ncp=200)
see PR#11277 */
double[] temp = new double[1];
double[] tmp_c = new double[1];
int[] ierr = new int[1];
double a0, ax, lbeta, c, errbd, x0;
int j;
double ans, gx, q, sumq;
if (ncp < 0. || a <= 0. || b <= 0.) {
return DoubleVector.NaN;
}
if (x < 0. || o_x > 1. || (x == 0. && o_x == 1.)) {
return 0.;
}
if (x > 1. || o_x < 0. || (x == 1. && o_x == 0.)) {
return 1.;
}
c = ncp / 2.;
/* initialize the series */
x0 = Math.floor(Math.max(c - 7. * Math.sqrt(c), 0.));
a0 = a + x0;
lbeta =
org.apache.commons.math.special.Gamma.logGamma(a0)
+ org.apache.commons.math.special.Gamma.logGamma(b)
- org.apache.commons.math.special.Gamma.logGamma(a0 + b);
/* temp = pbeta_raw(x, a0, b, TRUE, FALSE), but using (x, o_x): */
Utils.bratio(a0, b, x, o_x, temp, tmp_c, ierr, false);
gx =
Math.exp(
a0 * Math.log(x)
+ b * (x < .5 ? Math.log1p(-x) : Math.log(o_x))
- lbeta
- Math.log(a0));
if (a0 > a) {
q = Math.exp(-c + x0 * Math.log(c) - org.apache.commons.math.special.Gamma.logGamma(x0 + 1.));
} else {
q = Math.exp(-c);
}
sumq = 1. - q;
ans = ax = q * temp[0];
/* recurse over subsequent terms until convergence is achieved */
j = (int) x0;
do {
j++;
temp[0] -= gx;
gx *= x * (a + b + j - 1.) / (a + j);
q *= c / j;
sumq -= q;
ax = temp[0] * q;
ans += ax;
errbd = (temp[0] - gx) * sumq;
} while (errbd > errmax && j < itrmax + x0);
if (errbd > errmax) {
// ML_ERROR(ME_PRECISION, "pnbeta");
}
if (j >= itrmax + x0) {
// ML_ERROR(ME_NOCONV, "pnbeta");
}
return ans;
}
/**
* Calculates base e logarithm for the given value.
*
* @param d value
* @return base e logarithm for d
*/
private double ln(final double d) {
return d == 0 ? 0 : Math.log1p(Math.abs(d));
}