/**
* <u>Berechnen des Kotangens der komplexen Zahl</u><br>
*
* @return Rückgabe eines Objektes vom Typ Complex mit Lösung aus cot(<u>z</u>)
*/
public Complex cot() {
double nn =
Math.pow(Math.sin(this.real) * Math.cosh(this.imag), 2)
+ Math.pow(Math.cos(this.real) * Math.sinh(this.imag), 2);
return new Complex(
(Math.cos(this.real) * Math.sin(this.real)) / nn,
(Math.cosh(this.imag) * Math.sinh(this.imag)) / nn);
}
/**
* <u>Berechnen des Kotangens der komplexen Zahl</u><br>
*
* @param comp Komplexe Zahl
* @return Rückgabe eines Objektes vom Typ Complex mit Lösung aus cot(<u>z</u>)
*/
public static Complex cot(Complex comp) {
double nn =
Math.pow(Math.sin(comp.real) * Math.cosh(comp.imag), 2)
+ Math.pow(Math.cos(comp.real) * Math.sinh(comp.imag), 2);
return new Complex(
(Math.cos(comp.real) * Math.sin(comp.real)) / nn,
(Math.cosh(comp.imag) * Math.sinh(comp.imag)) / nn);
}
@Test
public void testCosh() {
for (double doubleValue : DOUBLE_VALUES) {
assertFunction("cosh(" + doubleValue + ")", DOUBLE, Math.cosh(doubleValue));
}
assertFunction("cosh(NULL)", DOUBLE, null);
}
/**
* @param args the function arguments which must be either one object of type Double or Long
* @return the result of the function evaluation which is the natural logarithm of the first
* argument
*/
public Object evaluateFunction(final Object[] args) {
final double angleInRadians;
try {
angleInRadians = FunctionUtil.getArgAsDouble(args[0]);
} catch (final Exception e) {
throw new IllegalArgumentException(
"can't convert \"" + args[0] + "\" to an angle in radians in a call to TANH().");
}
return Math.sinh(angleInRadians) / Math.cosh(angleInRadians);
}
/**
* draws the inside of the hyperobola part
*
* @param center center
* @param v1 1st eigenvector
* @param v2 2nd eigenvector
* @param a 1st eigenvalue
* @param b 2nd eigenvalue
* @param tMin t min
* @param tMax t max
*/
public void hyperbolaPart(
Coords center, Coords v1, Coords v2, double a, double b, double tMin, double tMax) {
manager.startGeometry(Manager.Type.TRIANGLE_FAN);
manager.texture(0, 0);
manager.normal(v1.crossProduct(v2));
int longitude = manager.getLongitudeDefault();
Coords m;
float dt = (float) (tMax - tMin) / longitude;
float u, v;
// first point on the branch
u = (float) Math.cosh(tMin);
v = (float) Math.sinh(tMin);
m = v1.mul(a * u).add(v2.mul(b * v));
// center of the fan is midpoint of branch ends
u = (float) Math.cosh(tMax);
v = (float) Math.sinh(tMax);
manager.triangleFanApex(center.add((m.add(v1.mul(a * u).add(v2.mul(b * v)))).mul(0.5)));
// first point
manager.triangleFanVertex(center.add(m));
for (int i = 1; i <= longitude; i++) {
u = (float) Math.cosh(tMin + i * dt);
v = (float) Math.sinh(tMin + i * dt);
m = v1.mul(a * u).add(v2.mul(b * v));
manager.triangleFanVertex(center.add(m));
}
manager.endGeometry();
}
public LuaValue call(LuaValue arg) {
switch (opcode) {
case 0:
return valueOf(Math.acos(arg.checkdouble()));
case 1:
return valueOf(Math.asin(arg.checkdouble()));
case 2:
return valueOf(Math.atan(arg.checkdouble()));
case 3:
return valueOf(Math.cosh(arg.checkdouble()));
case 4:
return valueOf(Math.exp(arg.checkdouble()));
case 5:
return valueOf(Math.log(arg.checkdouble()));
case 6:
return valueOf(Math.log10(arg.checkdouble()));
case 7:
return valueOf(Math.sinh(arg.checkdouble()));
case 8:
return valueOf(Math.tanh(arg.checkdouble()));
}
return NIL;
}
protected double call(double d) {
return Math.cosh(d);
}
public RealNumber cosh() {
return new RealNumber(Math.cosh(this.value));
}
@Description("hyperbolic cosine")
@ScalarFunction
@SqlType(DoubleType.NAME)
public static double cosh(@SqlType(DoubleType.NAME) double num) {
return Math.cosh(num);
}
// return a new Complex object whose value is the complex cosine of this
public Complex cos() {
return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
}
/**
* Evaluates this function. The child node is evaluated, the result of which must be a numeric
* type (one of Double, Float, Long, Integer). The hyperbolic cosine of this value becomes the
* result of this method as a double value.
*
* @return hyperbolic cosine of the value returned by the child
*/
@Override
public Double evaluate() {
Object c = getChild(0).evaluate();
return Math.cosh(NumericUtils.asDouble(c));
}
@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;
}
}
// 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");
}
/**
* Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m), and dn(u|m) of parameter m between
* 0 and 1, and real argument u. (based on the function from the Cephes Math Library)
*
* @param u
* @param m
* @return an array containing the values of the functions sn(u|m), cn(u|m), dn(u|m) and phi, the
* amplitude of u
*/
public static double[] calculateJacobianEllipticFunctionsValues(double u, double m) {
double ai, b, phi, t, twon;
double sn, cn, ph, dn;
double[] a = new double[9];
double[] c = new double[9];
int i;
// Check for special cases
if (m < 0.0 || m > 1.0 || Double.isNaN(m))
throw new IllegalArgumentException("m should be in <0,1>");
if (m < 1.0e-9) {
t = Math.sin(u);
b = Math.cos(u);
ai = 0.25 * m * (u - t * b);
sn = t - ai * b;
cn = b + ai * t;
ph = u - ai;
dn = 1.0 - 0.5 * m * t * t;
return new double[] {sn, cn, dn, ph};
}
if (m >= 0.9999999999) {
ai = 0.25 * (1.0 - m);
b = Math.cosh(u);
t = Math.tanh(u);
phi = 1.0 / b;
twon = b * Math.sinh(u);
sn = t + ai * (twon - u) / (b * b);
ph = 2.0 * Math.atan(Math.exp(u)) - Math.PI / 2 + ai * (twon - u) / b;
ai *= t * phi;
cn = phi - ai * (twon - u);
dn = phi + ai * (twon + u);
return new double[] {sn, cn, dn, ph};
}
// A. G. M. scale
a[0] = 1.0;
b = Math.sqrt(1.0 - m);
c[0] = Math.sqrt(m);
twon = 1.0;
i = 0;
while (Math.abs(c[i] / a[i]) > getMachineEpsilon()) {
if (i > 7)
throw new IllegalArgumentException(
"Jacobian elliptic functions cannot be calculated due to overflow range error");
ai = a[i];
i++;
c[i] = (ai - b) / 2.0;
t = Math.sqrt(ai * b);
a[i] = (ai + b) / 2.0;
b = t;
twon *= 2.0;
}
// backward recurrence
phi = twon * a[i] * u;
do {
t = c[i] * Math.sin(phi) / a[i];
b = phi;
phi = (Math.asin(t) + phi) / 2.0;
i--;
} while (i > 0);
sn = Math.sin(phi);
t = Math.cos(phi);
cn = t;
dn = t / Math.cos(phi - b);
ph = phi;
return new double[] {sn, cn, dn, ph};
}
public static IntervalDouble math_cosh(IntervalDouble a) {
IntervalDouble res =
new IntervalDouble(Math.cosh(a.value), DoubleInterval.cosh(a.interval), a.isUnStable);
return res;
}
/**
* <u>Berechnen der e-Funktion der komplexen Zahl</u><br>
*
* @return Rückgabe eines Objektes vom Typ Complex mit Lösung aus exp(<u>z</u>)
*/
public Complex exp() {
return new Complex(
Math.cos(this.getImag()) * (Math.sinh(this.getReal()) + Math.cosh(this.getReal())),
Math.sin(this.getImag()) * (Math.cosh(this.getReal()) + Math.sinh(this.getReal())));
}
/** {@inheritDoc} */
public OpenMapRealVector mapCoshToSelf() {
for (int i = 0; i < virtualSize; i++) {
setEntry(i, Math.cosh(getEntry(i)));
}
return this;
}
/**
* <u>Berechnen der e-Funktion der komplexen Zahl</u><br>
*
* @param comp Komplexe Zahl
* @return Rückgabe eines Objektes vom Typ Complex mit Lösung aus exp(<u>z</u>)
*/
public static Complex exp(Complex comp) {
return new Complex(
Math.cos(comp.getImag()) * (Math.sinh(comp.getReal()) + Math.cosh(comp.getReal())),
Math.sin(comp.getImag()) * (Math.cosh(comp.getReal()) + Math.sinh(comp.getReal())));
}
public static double besselI(double nu, double x) {
double next, sum, next1, next2, sum1, sum2, int1, int2, yp, y, yn, h;
long m, N;
if (x < 0) return Double.NaN;
if ((nu < 0) && (Math.round(nu) == nu))
if (((int) Math.round(nu)) % 2 == 1) return -besselI(-nu, x);
else return besselI(-nu, x);
if ((nu == 0.0) && (x == 0.0)) return 1.0;
if (x == 0.0) return 0.0;
// power series
if ((x <= 15) || (x * x < 15 * nu)) {
next = Math.pow(x / 2, nu) / eulergamma(nu + 1);
sum = next;
int max = (int) (40 * x);
for (m = 1; m < 200; m++) {
next *= (x * x / 4) / (m * (m + nu));
sum += next;
}
return sum;
} else if (8 * x > (nu * nu)) {
// asymptotic expansion
// if((x>30)&&(x>(3*(nu*nu-0.25)))){
next1 = 1;
sum1 = next1;
// next2=(4*nu*nu-1)/(8*x);
// sum2=next2;
int max = 10 > nu ? 10 : (int) nu;
for (m = 1; m <= max; m++) {
next1 *= -(4 * nu * nu - (2 * m - 1) * (2 * m - 1)) / (m * 8 * x);
sum1 += next1;
// next2*=-(4*nu*nu-(4*m-1)*(4*m-1))*(4*nu*nu-(4*m+1)*(4*m+1))/(2*m*(2*m+1)*8*x*8*x);
// sum2+=next2;
}
return Math.exp(x) / Math.sqrt(2 * pi * x) * sum1;
}
// integral
N = (long) 40 * Math.round(x);
h = pi / N;
yp = Math.exp(x);
y = Math.exp(x * Math.cos(h)) * Math.cos(nu * h);
yn = Math.exp(x * Math.cos(2 * h)) * Math.cos(nu * 2 * h);
int1 = h / 3 * (yp + 4 * y + yn);
for (m = 3; m < N; m += 2) {
yp = yn;
y = Math.exp(x * Math.cos(m * h)) * Math.cos(nu * m * h);
yn = Math.exp(x * Math.cos((m + 1) * h)) * Math.cos(nu * (m + 1) * h);
int1 += h / 3 * (yp + 4 * y + yn);
}
if (nu == Math.round(nu)) return int1 / pi;
h = 0.0004;
yp = 1;
y = Math.exp(-x * Math.cosh(h) - nu * h);
yn = Math.exp(-x * Math.cosh(2 * h) - nu * h);
int2 = h / 3 * (yp + 4 * y + yn);
for (m = 3; m < 5000; m += 2) {
yp = yn;
y = Math.exp(-x * Math.cosh(m * h) - nu * m * h);
yn = Math.exp(-x * Math.cosh((m + 1) * h) - nu * (m + 1) * h);
int2 += h / 3 * (yp + 4 * y + yn);
}
return int1 / pi - Math.sin(nu * pi) * int2 / pi;
}