complex.java

Apache的common math数学软件包

     * Compute the 
     * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top">
     * natural logarithm</a> of this complex number.
     * <p>
     * Implements the formula: <pre>
     * <code> log(a + bi) = ln(|a + bi|) + arg(a + bi)i</code></pre>
     * where ln on the right hand side is {@link java.lang.Math#log},
     * <code>|a + bi|</code> is the modulus, {@link Complex#abs},  and
     * <code>arg(a + bi) = {@link java.lang.Math#atan2}(b, a)</code></p>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code>.</p>
     * <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>
     * log(1 &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/2)i
     * log(INFINITY + i) = INFINITY + 0i
     * log(-INFINITY + i) = INFINITY + &pi;i
     * log(INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/4)i
     * log(-INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (3&pi;/4)i
     * log(0 + 0i) = -INFINITY + 0i
     * </code></pre></p>
     * 
     * @return ln of this complex number.
     * @since 1.2
     */
    public Complex log() {
        if (isNaN()) {
            return Complex.NaN;
        }

        return createComplex(Math.log(abs()),
            Math.atan2(imaginary, real));        
    }
    
    /**
     * Returns of value of this complex number raised to the power of <code>x</code>.
     * <p>
     * Implements the formula: <pre>
     * <code> y<sup>x</sup> = exp(x&middot;log(y))</code></pre> 
     * where <code>exp</code> and <code>log</code> are {@link #exp} and
     * {@link #log}, respectively.</p>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code> or infinite, or if <code>y</code>
     * equals {@link Complex#ZERO}.</p>
     * 
     * @param x the exponent.
     * @return <code>this</code><sup><code>x</code></sup>
     * @throws NullPointerException if x is null
     * @since 1.2
     */
    public Complex pow(Complex x) {
        if (x == null) {
            throw new NullPointerException();
        }
        return this.log().multiply(x).exp();
    }
    
    /**
     * Compute the 
     * <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top">
     * sine</a>
     * of this complex number.
     * <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>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code>.</p>
     * <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></p>
     * 
     * @return the sine of this complex number.
     * @since 1.2
     */
    public Complex sin() {
        if (isNaN()) {
            return Complex.NaN;
        }
        
        return createComplex(Math.sin(real) * MathUtils.cosh(imaginary),
            Math.cos(real) * MathUtils.sinh(imaginary));
    }
    
    /**
     * Compute the 
     * <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top">
     * hyperbolic sine</a> of this complex number.
     * <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>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code>.</p>
     * <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></p>
     * 
     * @return the hyperbolic sine of this complex number
     * @since 1.2
     */
    public Complex sinh() {
        if (isNaN()) {
            return Complex.NaN;
        }
        
        return createComplex(MathUtils.sinh(real) * Math.cos(imaginary),
            MathUtils.cosh(real) * Math.sin(imaginary));
    }
    
    /**
     * Compute the 
     * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
     * square root</a> of this complex number.
     * <p>
     * Implements the following algorithm to compute <code>sqrt(a + bi)</code>: 
     * <ol><li>Let <code>t = sqrt((|a| + |a + bi|) / 2)</code></li>
     * <li><pre>if <code> a &#8805; 0</code> return <code>t + (b/2t)i</code>
     *  else return <code>|b|/2t + sign(b)t i </code></pre></li>
     * </ol>
     * where <ul>
     * <li><code>|a| = {@link Math#abs}(a)</code></li>
     * <li><code>|a + bi| = {@link Complex#abs}(a + bi) </code></li>
     * <li><code>sign(b) =  {@link MathUtils#indicator}(b) </code>
     * </ul></p>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code>.</p>
     * <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>
     * sqrt(1 &plusmn; INFINITY i) = INFINITY + NaN i
     * sqrt(INFINITY + i) = INFINITY + 0i
     * sqrt(-INFINITY + i) = 0 + INFINITY i
     * sqrt(INFINITY &plusmn; INFINITY i) = INFINITY + NaN i
     * sqrt(-INFINITY &plusmn; INFINITY i) = NaN &plusmn; INFINITY i
     * </code></pre></p>
     * 
     * @return the square root of this complex number
     * @since 1.2
     */
    public Complex sqrt() {
        if (isNaN()) {
            return Complex.NaN;
        }
        
        if (real == 0.0 && imaginary == 0.0) {
            return createComplex(0.0, 0.0);
        }
        
        double t = Math.sqrt((Math.abs(real) + abs()) / 2.0);
        if (real >= 0.0) {
            return createComplex(t, imaginary / (2.0 * t));
        } else {
            return createComplex(Math.abs(imaginary) / (2.0 * t),
                MathUtils.indicator(imaginary) * t);
        }
    }
    
    /**
     * Compute the 
     * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
     * square root</a> of 1 - <code>this</code><sup>2</sup> for this complex
     * number.
     * <p>
     * Computes the result directly as 
     * <code>sqrt(Complex.ONE.subtract(z.multiply(z)))</code>.</p>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code>.</p>
     * <p>
     * Infinite values in real or imaginary parts of the input may result in
     * infinite or NaN values returned in parts of the result.</p>
     * 
     * @return the square root of 1 - <code>this</code><sup>2</sup>
     * @since 1.2
     */
    public Complex sqrt1z() {
        return createComplex(1.0, 0.0).subtract(this.multiply(this)).sqrt();
    }
    
    /**
     * Compute the 
     * <a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top">
     * tangent</a> of this complex number.
     * <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>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code>.</p>
     * <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></p>
     * 
     * @return the tangent of this complex number
     * @since 1.2
     */
    public Complex tan() {
        if (isNaN()) {
            return Complex.NaN;
        }
        
        double real2 = 2.0 * real;
        double imaginary2 = 2.0 * imaginary;
        double d = Math.cos(real2) + MathUtils.cosh(imaginary2);
        
        return createComplex(Math.sin(real2) / d, MathUtils.sinh(imaginary2) / d);
    }
    
    /**
     * Compute the
     * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top">
     * hyperbolic tangent</a> of this complex number.
     * <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>
     * <p>
     * Returns {@link Complex#NaN} if either real or imaginary part of the 
     * input argument is <code>NaN</code>.</p>
     * <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></p>
     *
     * @return the hyperbolic tangent of this complex number
     * @since 1.2
     */
    public Complex tanh() {
        if (isNaN()) {
            return Complex.NaN;
        }
        
        double real2 = 2.0 * real;
        double imaginary2 = 2.0 * imaginary;
        double d = MathUtils.cosh(real2) + Math.cos(imaginary2);
        
        return createComplex(MathUtils.sinh(real2) / d, Math.sin(imaginary2) / d);
    }

    /**
     * Create a complex number given the real and imaginary parts.
     *
     * @param real the real part
     * @param imaginary the imaginary part
     * @return a new complex number instance
     * @since 1.2
     */
    protected Complex createComplex(double real, double imaginary) {
        return new Complex(real, imaginary);
    }
}