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Diffstat (limited to 'lib/complex.rb')
| -rw-r--r-- | lib/complex.rb | 502 |
1 files changed, 0 insertions, 502 deletions
diff --git a/lib/complex.rb b/lib/complex.rb deleted file mode 100644 index cb0a3dc564..0000000000 --- a/lib/complex.rb +++ /dev/null @@ -1,502 +0,0 @@ -# -# complex.rb - -# $Release Version: 0.5 $ -# $Revision: 1.3 $ -# $Date: 1998/07/08 10:05:28 $ -# by Keiju ISHITSUKA(SHL Japan Inc.) -# -# -- -# Usage: -# class Complex < Numeric -# -# Complex(x, y) --> x + yi -# y.im --> 0 + yi -# -# Complex::polar -# -# Complex::+ -# Complex::- -# Complex::* -# Complex::/ -# Complex::** -# Complex::% -# Complex::divmod -- obsolete -# Complex::abs -# Complex::abs2 -# Complex::arg -# Complex::polar -# Complex::conjugate -# Complex::<=> -# Complex::== -# Complex::to_i -# Complex::to_f -# Complex::to_r -# Complex::to_s -# -# Complex::I -# -# Numeric::im -# -# Math.sqrt -# Math.exp -# Math.cos -# Math.sin -# Math.tan -# Math.log -# Math.log10 -# Math.atan2 -# -# - -def Complex(a, b = 0) - if a.kind_of?(Complex) and b == 0 - a - elsif b.kind_of?(Complex) - if a.kind_of?(Complex) - Complex(a.real-b.image, a.image + b.real) - else - Complex(a-b.image, b.real) - end - elsif b == 0 and defined? Complex::Unify - a - else - Complex.new(a, b) - end -end - -class Complex < Numeric - @RCS_ID='-$Id: complex.rb,v 1.3 1998/07/08 10:05:28 keiju Exp keiju $-' - - def Complex.generic?(other) - other.kind_of?(Integer) or - other.kind_of?(Float) or - (defined?(Rational) and other.kind_of?(Rational)) - end - - def Complex.polar(r, theta) - Complex(r*Math.cos(theta), r*Math.sin(theta)) - end - - def initialize(a, b = 0) - raise "non numeric 1st arg `#{a.inspect}'" if !a.kind_of? Numeric - raise "non numeric 2nd arg `#{b.inspect}'" if !b.kind_of? Numeric - @real = a - @image = b - end - - def + (other) - if other.kind_of?(Complex) - re = @real + other.real - im = @image + other.image - Complex(re, im) - elsif Complex.generic?(other) - Complex(@real + other, @image) - else - x , y = other.coerce(self) - x + y - end - end - - def - (other) - if other.kind_of?(Complex) - re = @real - other.real - im = @image - other.image - Complex(re, im) - elsif Complex.generic?(other) - Complex(@real - other, @image) - else - x , y = other.coerce(self) - x - y - end - end - - def * (other) - if other.kind_of?(Complex) - re = @real*other.real - @image*other.image - im = @real*other.image + @image*other.real - Complex(re, im) - elsif Complex.generic?(other) - Complex(@real * other, @image * other) - else - x , y = other.coerce(self) - x * y - end - end - - def / (other) - if other.kind_of?(Complex) - self*other.conjugate/other.abs2 - elsif Complex.generic?(other) - Complex(@real/other, @image/other) - else - x, y = other.coerce(self) - x/y - end - end - - def ** (other) - if other == 0 - return Complex(1) - end - if other.kind_of?(Complex) - r, theta = polar - ore = other.real - oim = other.image - nr = Math.exp!(ore*Math.log!(r) - oim * theta) - ntheta = theta*ore + oim*Math.log!(r) - Complex.polar(nr, ntheta) - elsif other.kind_of?(Integer) - if other > 0 - x = self - z = x - n = other - 1 - while n != 0 - while (div, mod = n.divmod(2) - mod == 0) - x = Complex(x.real*x.real - x.image*x.image, 2*x.real*x.image) - n = div - end - z *= x - n -= 1 - end - z - else - if defined? Rational - (Rational(1) / self) ** -other - else - self ** Float(other) - end - end - elsif Complex.generic?(other) - r, theta = polar - Complex.polar(r.power!(other), theta * other) - else - x, y = other.coerce(self) - x/y - end - end - - def % (other) - if other.kind_of?(Complex) - Complex(@real % other.real, @image % other.image) - elsif Complex.generic?(other) - Complex(@real % other, @image % other) - else - x , y = other.coerce(self) - x % y - end - end - -# def divmod(other) -# if other.kind_of?(Complex) -# rdiv, rmod = @real.divmod(other.real) -# idiv, imod = @image.divmod(other.image) -# return Complex(rdiv, idiv), Complex(rmod, rmod) -# elsif Complex.generic?(other) -# Complex(@real.divmod(other), @image.divmod(other)) -# else -# x , y = other.coerce(self) -# x.divmod(y) -# end -# end - - def abs - Math.sqrt!((@real*@real + @image*@image).to_f) - end - - def abs2 - @real*@real + @image*@image - end - - def arg - Math.atan2(@image.to_f, @real.to_f) - end - - def polar - return abs, arg - end - - def conjugate - Complex(@real, -@image) - end - - def <=> (other) - self.abs <=> other.abs - end - - def == (other) - if other.kind_of?(Complex) - @real == other.real and @image == other.image - elsif Complex.generic?(other) - @real == other and @image == 0 - else - x , y = other.coerce(self) - x == y - end - end - - def coerce(other) - if Complex.generic?(other) - return Complex.new(other), self - else - super - end - end - - def to_i - Complex(@real.to_i, @image.to_i) - end - - def to_f - Complex(@real.to_f, @image.to_f) - end - - def to_r - Complex(@real.to_r, @image.to_r) - end - - def denominator - @real.denominator.lcm(@image.denominator) - end - - def numerator - cd = denominator - Complex(@real.numerator*(cd/@real.denominator), - @image.numerator*(cd/@image.denominator)) - end - - def to_s - if @real != 0 - if defined?(Rational) and @image.kind_of?(Rational) and @image.denominator != 1 - if @image >= 0 - @real.to_s+"+("+@image.to_s+")i" - else - @real.to_s+"-("+(-@image).to_s+")i" - end - else - if @image >= 0 - @real.to_s+"+"+@image.to_s+"i" - else - @real.to_s+"-"+(-@image).to_s+"i" - end - end - else - if defined?(Rational) and @image.kind_of?(Rational) and @image.denominator != 1 - "("+@image.to_s+")i" - else - @image.to_s+"i" - end - end - end - - def hash - @real ^ @image - end - - def inspect - sprintf("Complex(%s, %s)", @real.inspect, @image.inspect) - end - - - I = Complex(0,1) - - attr :real - attr :image - -end - -class Numeric - def im - Complex(0, self) - end - - def real - self - end - - def image - 0 - end - - def arg - if self >= 0 - return 0 - else - return Math.atan2(1,1)*4 - end - end - - def polar - return abs, arg - end - - def conjugate - self - end -end - -class Fixnum - if not defined? Rational - alias power! ** - end - - def ** (other) - if self < 0 - Complex.new(self) ** other - else - if defined? Rational - if other >= 0 - self.power!(other) - else - Rational.new!(self,1)**other - end - else - self.power!(other) - end - end - end -end - -class Bignum - if not defined? Rational - alias power! ** - end -end - -class Float - alias power! ** -end - -module Math - alias sqrt! sqrt - alias exp! exp - alias cos! cos - alias sin! sin - alias tan! tan - alias log! log - alias log10! log10 - alias atan2! atan2 - - def sqrt(z) - if Complex.generic?(z) - if z >= 0 - sqrt!(z) - else - Complex(0,sqrt!(-z)) - end - else - z**Rational(1,2) - end - end - - def exp(z) - if Complex.generic?(z) - exp!(z) - else - Complex(exp!(z.real) * cos!(z.image), exp!(z.real) * sin!(z.image)) - end - end - - def cosh!(x) - (exp!(x) + exp!(-x))/2.0 - end - - def sinh!(x) - (exp!(x) - exp!(-x))/2.0 - end - - def cos(z) - if Complex.generic?(z) - cos!(z) - else - Complex(cos!(z.real)*cosh!(z.image), - -sin!(z.real)*sinh!(z.image)) - end - end - - def sin(z) - if Complex.generic?(z) - sin!(z) - else - Complex(sin!(z.real)*cosh!(z.image), - cos!(z.real)*sinh!(z.image)) - end - end - - def tan(z) - if Complex.generic?(z) - tan!(z) - else - sin(z)/cos(z) - end - end - - def log(z) - if Complex.generic?(z) and z >= 0 - log!(z) - else - r, theta = z.polar - Complex(log!(r.abs), theta) - end - end - - def log10(z) - if Complex.generic?(z) - log10!(z) - else - log(z)/log!(10) - end - end - - def atan2(x, y) - if Complex.generic?(x) and Complex.generic?(y) - atan2!(x, y) - else - fail "Not yet implemented." - end - end - - def atanh!(x) - log((1.0 + x.to_f) / ( 1.0 - x.to_f)) / 2.0 - end - - def atan(z) - if Complex.generic?(z) - atan2!(z, 1) - elsif z.image == 0 - atan2(z.real,1) - else - a = z.real - b = z.image - - c = (a*a + b*b - 1.0) - d = (a*a + b*b + 1.0) - - Complex(atan2!((c + sqrt(c*c + 4.0*a*a)), 2.0*a), - atanh!((-d + sqrt(d*d - 4.0*b*b))/(2.0*b))) - end - end - - module_function :sqrt - module_function :sqrt! - module_function :exp! - module_function :exp - module_function :cosh! - module_function :cos! - module_function :cos - module_function :sinh! - module_function :sin! - module_function :sin - module_function :tan! - module_function :tan - module_function :log! - module_function :log - module_function :log10! - module_function :log - module_function :atan2! - module_function :atan2 -# module_function :atan! - module_function :atan - module_function :atanh! - -end |