Java Code Examples for org.apache.commons.math.util.MathUtils#sinh()

/**
 * Compute the 
 * <a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top">
 * cosine</a>
 * for the given complex argument.
 * <p>
 * Implements the formula: <pre>
 * <code> cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i</code></pre>
 * where the (real) functions on the right-hand side are
 * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, 
 * {@link MathUtils#cosh} and {@link MathUtils#sinh}.
 * <p>
 * Returns {@link Complex#NaN} if either real or imaginary part of the 
 * input argument is <code>NaN</code>.
 * <p>
 * Infinite values in real or imaginary parts of the input may result in
 * infinite or NaN values returned in parts of the result.<pre>
 * Examples: 
 * <code>
 * cos(1 &plusmn; INFINITY i) = 1 &#x2213; INFINITY i
 * cos(&plusmn;INFINITY + i) = NaN + NaN i
 * cos(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre>
 * 
 * @param z the value whose cosine is to be returned
 * @return the cosine of <code>z</code>
 * @throws NullPointerException if <code>z</code> is null
 */
public static Complex cos(Complex z) {
    if (z.isNaN()) {
        return Complex.NaN;
    }
    
    double a = z.getReal();
    double b = z.getImaginary();
    
    return new Complex(Math.cos(a) * MathUtils.cosh(b),
        -Math.sin(a) * MathUtils.sinh(b));
}
 

/**
 * Compute the 
 * <a href="http://mathworld.wolfram.com/HyperbolicCosine.html" TARGET="_top">
 * hyperbolic cosine</a> for the given complex argument.
 * <p>
 * Implements the formula: <pre>
 * <code> cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i</code></pre>
 * where the (real) functions on the right-hand side are
 * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, 
 * {@link MathUtils#cosh} and {@link MathUtils#sinh}.
 * <p>
 * Returns {@link Complex#NaN} if either real or imaginary part of the 
 * input argument is <code>NaN</code>.
 * <p>
 * Infinite values in real or imaginary parts of the input may result in
 * infinite or NaN values returned in parts of the result.<pre>
 * Examples: 
 * <code>
 * cosh(1 &plusmn; INFINITY i) = NaN + NaN i
 * cosh(&plusmn;INFINITY + i) = INFINITY &plusmn; INFINITY i
 * cosh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre>
 * <p>
 * Throws <code>NullPointerException</code> if z is null.
 * 
 * @param z the value whose hyperbolic cosine is to be returned.
 * @return the hyperbolic cosine of <code>z</code>.
 */
public static Complex cosh(Complex z) {
    if (z.isNaN()) {
        return Complex.NaN;
    }
    
    double a = z.getReal();
    double b = z.getImaginary();
    
    return new Complex(MathUtils.cosh(a) * Math.cos(b),
        MathUtils.sinh(a) * Math.sin(b));
}
 

/**
 * Compute the 
 * <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top">
 * sine</a>
 * for the given complex argument.
 * <p>
  * Implements the formula: <pre>
 * <code> sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i</code></pre>
 * where the (real) functions on the right-hand side are
 * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, 
 * {@link MathUtils#cosh} and {@link MathUtils#sinh}.
 * <p>
 * Returns {@link Complex#NaN} if either real or imaginary part of the 
 * input argument is <code>NaN</code>.
 * <p>
 * Infinite values in real or imaginary parts of the input may result in
 * infinite or NaN values returned in parts of the result.<pre>
 * Examples: 
 * <code>
 * sin(1 &plusmn; INFINITY i) = 1 &plusmn; INFINITY i
 * sin(&plusmn;INFINITY + i) = NaN + NaN i
 * sin(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre>
 * 
 * Throws <code>NullPointerException</code> if z is null. 
 * 
 * @param z the value whose sine is to be returned.
 * @return the sine of <code>z</code>.
 */
public static Complex sin(Complex z) {
    if (z.isNaN()) {
        return Complex.NaN;
    }
    
    double a = z.getReal();
    double b = z.getImaginary();
    
    return new Complex(Math.sin(a) * MathUtils.cosh(b),
        Math.cos(a) * MathUtils.sinh(b));
}
 

/**
 * Compute the 
 * <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top">
 * hyperbolic sine</a> for the given complex argument.
 * <p>
 * Implements the formula: <pre>
 * <code> sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i</code></pre>
 * where the (real) functions on the right-hand side are
 * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, 
 * {@link MathUtils#cosh} and {@link MathUtils#sinh}.
 * <p>
 * Returns {@link Complex#NaN} if either real or imaginary part of the 
 * input argument is <code>NaN</code>.
 * <p>
 * Infinite values in real or imaginary parts of the input may result in
 * infinite or NaN values returned in parts of the result.<pre>
 * Examples: 
 * <code>
 * sinh(1 &plusmn; INFINITY i) = NaN + NaN i
 * sinh(&plusmn;INFINITY + i) = &plusmn; INFINITY + INFINITY i
 * sinh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre
 * 
 * @param z the value whose hyperbolic sine is to be returned
 * @return the hyperbolic sine of <code>z</code>
 * @throws NullPointerException if <code>z</code> is null
 */
public static Complex sinh(Complex z) {
    if (z.isNaN()) {
        return Complex.NaN;
    }
    
    double a = z.getReal();
    double b = z.getImaginary();
    
    return new Complex(MathUtils.sinh(a) * Math.cos(b),
        MathUtils.cosh(a) * Math.sin(b));
}
 

/**
 * Compute the 
 * <a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top">
 * tangent</a> for the given complex argument.
 * <p>
 * Implements the formula: <pre>
 * <code>tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i</code></pre>
 * where the (real) functions on the right-hand side are
 * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, 
 * {@link MathUtils#cosh} and {@link MathUtils#sinh}.
 * <p>
 * Returns {@link Complex#NaN} if either real or imaginary part of the 
 * input argument is <code>NaN</code>.
 * <p>
 * Infinite (or critical) values in real or imaginary parts of the input may
 * result in infinite or NaN values returned in parts of the result.<pre>
 * Examples: 
 * <code>
 * tan(1 &plusmn; INFINITY i) = 0 + NaN i
 * tan(&plusmn;INFINITY + i) = NaN + NaN i
 * tan(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
 * tan(&plusmn;&pi/2 + 0 i) = &plusmn;INFINITY + NaN i</code></pre>
 * 
 * @param z the value whose tangent is to be returned
 * @return the tangent of <code>z</code>
 * @throws NullPointerException if <code>z</code> is null
 */
public static Complex tan(Complex z) {
    if (z.isNaN()) {
        return Complex.NaN;
    }
    
    double a2 = 2.0 * z.getReal();
    double b2 = 2.0 * z.getImaginary();
    double d = Math.cos(a2) + MathUtils.cosh(b2);
    
    return new Complex(Math.sin(a2) / d, MathUtils.sinh(b2) / d);
}
 

/**
 * Compute the
 * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top">
 * hyperbolic tangent</a> for the given complex argument.
* <p>
 * Implements the formula: <pre>
 * <code>tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i</code></pre>
 * where the (real) functions on the right-hand side are
 * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, 
 * {@link MathUtils#cosh} and {@link MathUtils#sinh}.
 * <p>
 * Returns {@link Complex#NaN} if either real or imaginary part of the 
 * input argument is <code>NaN</code>.
 * <p>
 * Infinite values in real or imaginary parts of the input may result in
 * infinite or NaN values returned in parts of the result.<pre>
 * Examples: 
 * <code>
 * tanh(1 &plusmn; INFINITY i) = NaN + NaN i
 * tanh(&plusmn;INFINITY + i) = NaN + 0 i
 * tanh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
 * tanh(0 + (&pi/2)i) = NaN + INFINITY i</code></pre>
 *
 * @param z the value whose hyperbolic tangent is to be returned
 * @return the hyperbolic tangent of <code>z</code>
 * @throws NullPointerException if <code>z</code> is null
 */
public static Complex tanh(Complex z) {
    if (z.isNaN()) {
        return Complex.NaN;
    }
    
    double a2 = 2.0 * z.getReal();
    double b2 = 2.0 * z.getImaginary();
    double d = MathUtils.cosh(a2) + Math.cos(b2);
    
    return new Complex(MathUtils.sinh(a2) / d, Math.sin(b2) / d);
}