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

#%, #[email protected], #<=>, #__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.


26
27
28
29
# File 'opal/opal/corelib/complex.rb', line 26

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

Instance Attribute Details

#imagObject (readonly) Also known as: imaginary

Returns the value of attribute imag.


24
25
26
# File 'opal/opal/corelib/complex.rb', line 24

def imag
  @imag
end

#realObject (readonly)

Returns the value of attribute real.


24
25
26
# File 'opal/opal/corelib/complex.rb', line 24

def real
  @real
end

Class Method Details

.polar(r, theta = 0) ⇒ Object


16
17
18
19
20
21
22
# File 'opal/opal/corelib/complex.rb', line 16

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

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

.rect(real, imag = 0) ⇒ Object


4
5
6
7
8
9
10
# File 'opal/opal/corelib/complex.rb', line 4

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

  new(real, imag)
end

.rectangularObject


13
14
15
16
17
18
19
# File 'opal/opal/corelib/complex.rb', line 13

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

  new(real, imag)
end

Instance Method Details

#*(other) ⇒ Object


75
76
77
78
79
80
81
82
83
84
85
# File 'opal/opal/corelib/complex.rb', line 75

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

#**(other) ⇒ Object


102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
# File 'opal/opal/corelib/complex.rb', line 102

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 = 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


55
56
57
58
59
60
61
62
63
# File 'opal/opal/corelib/complex.rb', line 55

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

#-(other) ⇒ Object


65
66
67
68
69
70
71
72
73
# File 'opal/opal/corelib/complex.rb', line 65

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

#[email protected]Object


51
52
53
# File 'opal/opal/corelib/complex.rb', line 51

def [email protected]
  Complex(-@real, -@imag)
end

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


87
88
89
90
91
92
93
94
95
96
97
98
99
100
# File 'opal/opal/corelib/complex.rb', line 87

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?
    Complex(@real.quo(other), @imag.quo(other))
  else
    __coerced__ :/, other
  end
end

#==(other) ⇒ Object


41
42
43
44
45
46
47
48
49
# File 'opal/opal/corelib/complex.rb', line 41

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

#absObject Also known as: magnitude


146
147
148
# File 'opal/opal/corelib/complex.rb', line 146

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

#abs2Object


150
151
152
# File 'opal/opal/corelib/complex.rb', line 150

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

#angleObject Also known as: arg


154
155
156
# File 'opal/opal/corelib/complex.rb', line 154

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

#coerce(other) ⇒ Object


31
32
33
34
35
36
37
38
39
# File 'opal/opal/corelib/complex.rb', line 31

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

#conjObject Also known as: conjugate


160
161
162
# File 'opal/opal/corelib/complex.rb', line 160

def conj
  Complex(@real, -@imag)
end

#denominatorObject


166
167
168
# File 'opal/opal/corelib/complex.rb', line 166

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

#eql?(other) ⇒ Boolean

Returns:


172
173
174
# File 'opal/opal/corelib/complex.rb', line 172

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

#fdiv(other) ⇒ Object


176
177
178
179
180
181
182
# File 'opal/opal/corelib/complex.rb', line 176

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

  self / other
end

#finite?Boolean

Returns:


184
185
186
# File 'opal/opal/corelib/complex.rb', line 184

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

#hashObject


188
189
190
# File 'opal/opal/corelib/complex.rb', line 188

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

#infinite?Boolean

Returns:


194
195
196
# File 'opal/opal/corelib/complex.rb', line 194

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

#inspectObject


198
199
200
# File 'opal/opal/corelib/complex.rb', line 198

def inspect
  "(#{self})"
end

#numeratorObject


206
207
208
209
210
211
212
# File 'opal/opal/corelib/complex.rb', line 206

def numerator
  d = denominator

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

#polarObject


216
217
218
# File 'opal/opal/corelib/complex.rb', line 216

def polar
  [abs, arg]
end

#rationalize(eps = undefined) ⇒ Object


224
225
226
227
228
229
230
231
232
233
234
235
236
# File 'opal/opal/corelib/complex.rb', line 224

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

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

  real.rationalize(eps)
end

#real?Boolean

Returns:


238
239
240
# File 'opal/opal/corelib/complex.rb', line 238

def real?
  false
end

#rectObject Also known as: rectangular


242
243
244
# File 'opal/opal/corelib/complex.rb', line 242

def rect
  [@real, @imag]
end

#to_fObject


250
251
252
253
254
255
256
# File 'opal/opal/corelib/complex.rb', line 250

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

  @real.to_f
end

#to_iObject


258
259
260
261
262
263
264
# File 'opal/opal/corelib/complex.rb', line 258

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

  @real.to_i
end

#to_rObject


266
267
268
269
270
271
272
# File 'opal/opal/corelib/complex.rb', line 266

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

  @real.to_r
end

#to_sObject


274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
# File 'opal/opal/corelib/complex.rb', line 274

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