Examples of org.jamesii.core.math.complex.Complex

org.jamesii.core.math.complex.Complex
This class represents a complex number. It has two parts, real and imaginary. Polar coordinates are represented by modulus and argument.
This class is immutable and all arithmetic operations do not alter the object but instead return a new object with the result to allow chaining of operations. If this presents too large a performance impact it could be changed, however all of Java's numeric classes are immutable so this was done out of conformance.
This class inherits from {@link Number} although it does not strictly for thepurpose of it. {@link Number} essentially seems to be a class intended for avery small subset of numbers which does not include complex or hypercomplex numbers. Thus the methods {@link #doubleValue()}, {@link #floatValue()}, {@link #intValue()}, {@link #byteValue()}, {@link #shortValue()} and{@link #longValue()} are defined and implemented but only return the possiblytruncated or rounded real part of the complex number. This is only of limited value but done to allow subclassing {@link Number} as an indication that thisclass represents numbers. @author Johannes Rössel

        -503d / 25, -43d / 10, 20.57436269, -2.931042466);
  }


  /** Tests the {@link Complex#divide(double)} method. */
  public void testDivideReal() {
    checkFields(new Complex(1, 2).divide(2), .5, 1, 1.118033989, 1.107148718);
  }

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    checkFields(new Complex(1, 2).divide(2), .5, 1, 1.118033989, 1.107148718);
  }


  /** Tests the {@link Complex#divide(Complex)} method. */
  public void testDivideComplex() {
    checkFields(new Complex(5, 4).divide(new Complex(-1, 2)), 3d / 5, -14d / 5,
        2.863564213, -1.359702994);
  }

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        2.863564213, -1.359702994);
  }


  /** Tests the {@link Complex#isReal()} method. */
  public void testIsReal() {
    assertTrue(new Complex(1, 0).isReal());
    assertFalse(new Complex(0, 1).isReal());
    assertFalse(new Complex(1, 1).isReal());
  }

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    assertFalse(new Complex(1, 1).isReal());
  }


  /** Tests the {@link Complex#isImaginary()} method. */
  public void testIsImaginary() {
    assertTrue(new Complex(0, 1).isImaginary());
    assertFalse(new Complex(1, 0).isImaginary());
    assertFalse(new Complex(1, 1).isImaginary());
  }

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   * @param b
   *          A second complex number.
   */
  private void checkProperties(Complex a, Complex b) {
    // tests for absolute value
    if (a.equals(new Complex(0, 0))) {
      assertTrue(a.getModulus() == 0);
    }
    if (a.getModulus() == 0) {
      assertTrue(a.equals(new Complex(0, 0)));
    }
    assertTrue(a.add(b).getModulus() <= a.getModulus() + b.getModulus());
    assertTrue(Double.compare(a.multiply(b).getModulus(),
        a.getModulus() * b.getModulus()) == 0);


    // complex conjugates
    assertTrue(approximatelyEqual(a.add(b).conjugate(),
        a.conjugate().add(b.conjugate())));
    assertTrue(approximatelyEqual(a.multiply(b).conjugate(), a.conjugate()
        .multiply(b.conjugate())));
    if (!b.equals(new Complex(0, 0))) {
      assertTrue(approximatelyEqual(a.divide(b).conjugate(), a.conjugate()
          .divide(b.conjugate())));
    }
    assertTrue(a.conjugate().conjugate().equals(a));
    if (a.isReal()) {
      assertTrue(a.conjugate().equals(a));
    }
    if (a.conjugate().equals(a)) {
      assertTrue(a.isReal());
    }
    if (a.isImaginary()) {
      assertTrue(a.conjugate().equals(a.negate()));
    }
    if (a.conjugate().equals(a.negate())) {
      assertTrue(a.isImaginary());
    }
    assertTrue(a.getModulus() == a.conjugate().getModulus());
    assertTrue(a.multiply(a.conjugate()).isReal());
    assertTrue(a.multiply(a.conjugate()).getReal() - pow(a.getModulus(), 2) < 1e-10);
    if (!a.equals(new Complex(0, 0))) {
      assertTrue(approximatelyEqual(ComplexMath.pow(a, -1), a.conjugate()
          .multiply(pow(a.getModulus(), -2))));
    }
  }

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  public void testProperties() {
    // Tests various properties of calculations with complex numbers. Some
    // special cases are tested here.


    // both numbers are 0.
    checkProperties(new Complex(0, 0), new Complex(0, 0));
    // one number is zero, the other an arbitrary real number
    checkProperties(new Complex(15, 0), new Complex(0, 0));
    checkProperties(new Complex(0, 0), new Complex(2, 0));
    // one number is zero, the other an arbitrary imaginary number
    checkProperties(new Complex(0, 0), new Complex(0, 3));
    checkProperties(new Complex(0, 5), new Complex(0, 0));
    // one number is zero, the other an arbitrary complex number
    checkProperties(new Complex(0, 0), new Complex(2, 6));
    checkProperties(new Complex(8, 13), new Complex(0, 0));
    // one number is one, the other zero
    checkProperties(new Complex(1, 0), new Complex(0, 0));
    checkProperties(new Complex(0, 0), new Complex(1, 0));
    // both numbers are one
    checkProperties(new Complex(1, 0), new Complex(1, 0));
    checkProperties(new Complex(1, 0), new Complex(1, 0));
    // one number is one, the other an arbitrary real number
    checkProperties(new Complex(1, 0), new Complex(46, 0));
    checkProperties(new Complex(-98, 0), new Complex(1, 0));
    // one number is one, the other an arbitrary imaginary number
    checkProperties(new Complex(1, 0), new Complex(0, 211));
    checkProperties(new Complex(0, -32), new Complex(1, 0));
    // one number is one, the other an arbitrary complex number
    checkProperties(new Complex(1, 0), new Complex(2, -7));
    checkProperties(new Complex(-1, 5), new Complex(1, 0));
    // one number is i, the other zero
    checkProperties(new Complex(0, 1), new Complex(0, 0));
    checkProperties(new Complex(0, 0), new Complex(0, 1));
    // both numbers are i
    checkProperties(new Complex(0, 1), new Complex(0, 1));
    checkProperties(new Complex(0, 1), new Complex(0, 1));
    // one number is i, the other an arbitrary real number
    checkProperties(new Complex(0, 1), new Complex(42, 0));
    checkProperties(new Complex(-23, 0), new Complex(0, 1));
    // one number is i, the other an arbitrary imaginary number
    checkProperties(new Complex(0, 1), new Complex(0, 15));
    checkProperties(new Complex(0, -8), new Complex(0, 1));
    // one number is i, the other an arbitrary complex number
    checkProperties(new Complex(0, 1), new Complex(-6, 48));
    checkProperties(new Complex(19, -1), new Complex(0, 1));
  }

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    checkProperties(new Complex(19, -1), new Complex(0, 1));
  }


  /** Tests the {@link Complex#equals(Object)} method. */
  public void testEquals() {
    assertTrue(new Complex(1, 1).equals(new Complex(1, 1)));
    assertFalse(new Complex(1, 1).equals(null));
    assertFalse(new Complex(1, 1).equals("blah"));
    assertFalse(new Complex(1, 1).equals(new Complex(2, 2)));
  }

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    assertFalse(new Complex(1, 1).equals(new Complex(2, 2)));
  }


  /** Tests the {@link Complex#hashCode()} method. */
  public void testHashCode() {
    Complex a = new Complex(1, 1);
    Complex b = new Complex(1, 0);
    b = b.add(new Complex(0, 1));
    assertTrue(a.hashCode() == a.hashCode());
    assertTrue(a.hashCode() == b.hashCode());
  }

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    assertTrue(a.hashCode() == b.hashCode());
  }


  /** Tests the {@link Complex#toString()} method. */
  public void testToString() {
    assertTrue(new Complex(0, 0).toString().equals("0"));
    assertTrue(new Complex(1, 1).toString().equals("1.0 + 1.0i"));
    assertTrue(new Complex(-5, 1).toString().equals("-5.0 + 1.0i"));
    assertTrue(new Complex(-5, -2).toString().equals("-5.0 - 2.0i"));
    assertTrue(new Complex(-5, 0).toString().equals("-5.0"));
    assertTrue(new Complex(0, 1).toString().equals("1.0i"));
    assertTrue(new Complex(0, -7.5).toString().equals("-7.5i"));
  }

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    assertTrue(new Complex(0, -7.5).toString().equals("-7.5i"));
  }


  /** Tests the {@link Complex#doubleValue()} method. */
  public void testDoubleValue() {
    Complex c = new Complex(Math.random() * 100, Math.random() * 100);
    assertEquals(c.doubleValue(), c.getReal());
  }

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org.jamesii.core.math.complex.TestComplexMath

org.jamesii.core.math.FFT

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