Class: Complex

Inherits:
Numeric show all
Defined in:
opal/opal/corelib/complex.rb

Constant Summary collapse

I = 
new(0, 1)

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Numeric

#%, #+@, #<=>, #__coerced__, #ceil, #clone, #div, #divmod, #dup, #floor, #i, #integer?, #negative?, #nonzero?, #positive?, #round, #step, #to_c, #to_int, #truncate, #zero?

Methods included from Comparable

#<, #<=, #>, #>=, #between?, #clamp

Constructor Details

#initialize(real, imag = 0) ⇒ Complex

Returns a new instance of Complex.

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# File 'opal/opal/corelib/complex.rb', line 23

def initialize(real, imag = 0)
  @real = real
  @imag = imag
  freeze
end

Instance Attribute Details

#imag ⇒ Object (readonly) Also known as: imaginary

Returns the value of attribute imag.


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# File 'opal/opal/corelib/complex.rb', line 21

def imag
  @imag
end

#real ⇒ Object (readonly)

Returns the value of attribute real.


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# File 'opal/opal/corelib/complex.rb', line 21

def real
  @real
end

Class Method Details

.from_string(str) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 271

def self.from_string(str)
  %x{
    var re = /[+-]?[\d_]+(\.[\d_]+)?(e\d+)?/,
        match = str.match(re),
        real, imag, denominator;

    function isFloat() {
      return re.test(str);
    }

    function cutFloat() {
      var match = str.match(re);
      var number = match[0];
      str = str.slice(number.length);
      return number.replace(/_/g, '');
    }

    // handles both floats and rationals
    function cutNumber() {
      if (isFloat()) {
        var numerator = parseFloat(cutFloat());

        if (str[0] === '/') {
          // rational real part
          str = str.slice(1);

          if (isFloat()) {
            var denominator = parseFloat(cutFloat());
            return #{::Kernel.Rational(`numerator`, `denominator`)};
          } else {
            // reverting '/'
            str = '/' + str;
            return numerator;
          }
        } else {
          // float real part, no denominator
          return numerator;
        }
      } else {
        return null;
      }
    }

    real = cutNumber();

    if (!real) {
      if (str[0] === 'i') {
        // i => Complex(0, 1)
        return #{::Kernel.Complex(0, 1)};
      }
      if (str[0] === '-' && str[1] === 'i') {
        // -i => Complex(0, -1)
        return #{::Kernel.Complex(0, -1)};
      }
      if (str[0] === '+' && str[1] === 'i') {
        // +i => Complex(0, 1)
        return #{::Kernel.Complex(0, 1)};
      }
      // anything => Complex(0, 0)
      return #{::Kernel.Complex(0, 0)};
    }

    imag = cutNumber();
    if (!imag) {
      if (str[0] === 'i') {
        // 3i => Complex(0, 3)
        return #{::Kernel.Complex(0, `real`)};
      } else {
        // 3 => Complex(3, 0)
        return #{::Kernel.Complex(`real`, 0)};
      }
    } else {
      // 3+2i => Complex(3, 2)
      return #{::Kernel.Complex(`real`, `imag`)};
    }
  }
end

.polar(r, theta = 0) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 13

def self.polar(r, theta = 0)
  unless ::Numeric === r && r.real? && ::Numeric === theta && theta.real?
    ::Kernel.raise ::TypeError, 'not a real'
  end

  new(r * ::Math.cos(theta), r * ::Math.sin(theta))
end

.rect(real, imag = 0) ⇒ Object Also known as: rectangular

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# File 'opal/opal/corelib/complex.rb', line 5

def self.rect(real, imag = 0)
  unless ::Numeric === real && real.real? && ::Numeric === imag && imag.real?
    ::Kernel.raise ::TypeError, 'not a real'
  end

  new(real, imag)
end

Instance Method Details

#*(other) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 73

def *(other)
  if ::Complex === other
    ::Kernel.Complex(@real * other.real - @imag * other.imag,
      @real * other.imag + @imag * other.real,
    )
  elsif ::Numeric === other && other.real?
    ::Kernel.Complex(@real * other, @imag * other)
  else
    __coerced__ :*, other
  end
end

#**(other) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 100

def **(other)
  if other == 0
    return ::Complex.new(1, 0)
  end

  if ::Complex === other
    r, theta = polar
    ore      = other.real
    oim      = other.imag
    nr       = ::Math.exp(ore * ::Math.log(r) - oim * theta)
    ntheta   = theta * ore + oim * ::Math.log(r)

    ::Complex.polar(nr, ntheta)
  elsif ::Integer === other
    if other > 0
      x = self
      z = x
      n = other - 1

      while n != 0
        div, mod = n.divmod(2)
        while mod == 0
          x = ::Kernel.Complex(x.real * x.real - x.imag * x.imag, 2 * x.real * x.imag)
          n = div
          div, mod = n.divmod(2)
        end

        z *= x
        n -= 1
      end

      z
    else
      (::Rational.new(1, 1) / self)**-other
    end
  elsif ::Float === other || ::Rational === other
    r, theta = polar

    ::Complex.polar(r**other, theta * other)
  else
    __coerced__ :**, other
  end
end

#+(other) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 53

def +(other)
  if ::Complex === other
    ::Kernel.Complex(@real + other.real, @imag + other.imag)
  elsif ::Numeric === other && other.real?
    ::Kernel.Complex(@real + other, @imag)
  else
    __coerced__ :+, other
  end
end

#-(other) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 63

def -(other)
  if ::Complex === other
    ::Kernel.Complex(@real - other.real, @imag - other.imag)
  elsif ::Numeric === other && other.real?
    ::Kernel.Complex(@real - other, @imag)
  else
    __coerced__ :-, other
  end
end

#-@ ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 49

def -@
  ::Kernel.Complex(-@real, -@imag)
end

#/(other) ⇒ Object Also known as: divide, quo

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# File 'opal/opal/corelib/complex.rb', line 85

def /(other)
  if ::Complex === other
    if (::Number === @real && @real.nan?) || (::Number === @imag && @imag.nan?) ||
       (::Number === other.real && other.real.nan?) || (::Number === other.imag && other.imag.nan?)
      ::Complex.new(::Float::NAN, ::Float::NAN)
    else
      self * other.conj / other.abs2
    end
  elsif ::Numeric === other && other.real?
    ::Kernel.Complex(@real.quo(other), @imag.quo(other))
  else
    __coerced__ :/, other
  end
end

#==(other) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 39

def ==(other)
  if ::Complex === other
    @real == other.real && @imag == other.imag
  elsif ::Numeric === other && other.real?
    @real == other && @imag == 0
  else
    other == self
  end
end

#abs ⇒ Object Also known as: magnitude

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# File 'opal/opal/corelib/complex.rb', line 144

def abs
  ::Math.hypot(@real, @imag)
end

#abs2 ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 148

def abs2
  @real * @real + @imag * @imag
end

#angle ⇒ Object Also known as: arg

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# File 'opal/opal/corelib/complex.rb', line 152

def angle
  ::Math.atan2(@imag, @real)
end

#coerce(other) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 29

def coerce(other)
  if ::Complex === other
    [other, self]
  elsif ::Numeric === other && other.real?
    [::Complex.new(other, 0), self]
  else
    ::Kernel.raise ::TypeError, "#{other.class} can't be coerced into Complex"
  end
end

#conj ⇒ Object Also known as: conjugate

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# File 'opal/opal/corelib/complex.rb', line 156

def conj
  ::Kernel.Complex(@real, -@imag)
end

#denominator ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 160

def denominator
  @real.denominator.lcm(@imag.denominator)
end

#eql?(other) ⇒ Boolean

Returns:

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# File 'opal/opal/corelib/complex.rb', line 164

def eql?(other)
  Complex === other && @real.class == @imag.class && self == other
end

#fdiv(other) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 168

def fdiv(other)
  unless ::Numeric === other
    ::Kernel.raise ::TypeError, "#{other.class} can't be coerced into Complex"
  end

  self / other
end

#finite? ⇒ Boolean

Returns:

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# File 'opal/opal/corelib/complex.rb', line 176

def finite?
  @real.finite? && @imag.finite?
end

#hash ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 180

def hash
  "Complex:#{@real}:#{@imag}"
end

#infinite? ⇒ Boolean

Returns:

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# File 'opal/opal/corelib/complex.rb', line 184

def infinite?
  @real.infinite? || @imag.infinite?
end

#inspect ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 188

def inspect
  "(#{self})"
end

#numerator ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 192

def numerator
  d = denominator

  ::Kernel.Complex(@real.numerator * (d / @real.denominator),
    @imag.numerator * (d / @imag.denominator),
  )
end

#polar ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 200

def polar
  [abs, arg]
end

#rationalize(eps = undefined) ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 204

def rationalize(eps = undefined)
  %x{
    if (arguments.length > 1) {
      #{::Kernel.raise ::ArgumentError, "wrong number of arguments (#{`arguments.length`} for 0..1)"};
    }
  }

  if @imag != 0
    ::Kernel.raise ::RangeError, "can't convert #{self} into Rational"
  end

  real.rationalize(eps)
end

#real? ⇒ Boolean

Returns:

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# File 'opal/opal/corelib/complex.rb', line 218

def real?
  false
end

#rect ⇒ Object Also known as: rectangular

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# File 'opal/opal/corelib/complex.rb', line 222

def rect
  [@real, @imag]
end

#to_f ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 226

def to_f
  unless @imag == 0
    ::Kernel.raise ::RangeError, "can't convert #{self} into Float"
  end

  @real.to_f
end

#to_i ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 234

def to_i
  unless @imag == 0
    ::Kernel.raise ::RangeError, "can't convert #{self} into Integer"
  end

  @real.to_i
end

#to_r ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 242

def to_r
  unless @imag == 0
    ::Kernel.raise ::RangeError, "can't convert #{self} into Rational"
  end

  @real.to_r
end

#to_s ⇒ Object

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# File 'opal/opal/corelib/complex.rb', line 250

def to_s
  result = @real.inspect

  result +=
    if (::Number === @imag && @imag.nan?) || @imag.positive? || @imag.zero?
      '+'
    else
      '-'
    end

  result += @imag.abs.inspect

  if ::Number === @imag && (@imag.nan? || @imag.infinite?)
    result += '*'
  end

  result + 'i'
end