зеркало из https://github.com/github/ruby.git
631 строка
12 KiB
Ruby
631 строка
12 KiB
Ruby
#
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# complex.rb -
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# $Release Version: 0.5 $
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# $Revision: 1.3 $
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# $Date: 1998/07/08 10:05:28 $
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# by Keiju ISHITSUKA(SHL Japan Inc.)
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#
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# ----
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#
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# complex.rb implements the Complex class for complex numbers. Additionally,
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# some methods in other Numeric classes are redefined or added to allow greater
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# interoperability with Complex numbers.
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#
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# Complex numbers can be created in the following manner:
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# - <tt>Complex(a, b)</tt>
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# - <tt>Complex.polar(radius, theta)</tt>
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#
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# Additionally, note the following:
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# - <tt>Complex::I</tt> (the mathematical constant <i>i</i>)
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# - <tt>Numeric#im</tt> (e.g. <tt>5.im -> 0+5i</tt>)
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#
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# The following +Math+ module methods are redefined to handle Complex arguments.
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# They will work as normal with non-Complex arguments.
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# sqrt exp cos sin tan log log10
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# cosh sinh tanh acos asin atan atan2 acosh asinh atanh
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#
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#
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# Numeric is a built-in class on which Fixnum, Bignum, etc., are based. Here
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# some methods are added so that all number types can be treated to some extent
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# as Complex numbers.
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#
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class Numeric
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#
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# Returns a Complex number <tt>(0,<i>self</i>)</tt>.
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#
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def im
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Complex(0, self)
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end
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#
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# The real part of a complex number, i.e. <i>self</i>.
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#
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def real
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self
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end
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#
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# The imaginary part of a complex number, i.e. 0.
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#
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def image
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0
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end
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alias imag image
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#
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# See Complex#arg.
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#
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def arg
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if self >= 0
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return 0
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else
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return Math::PI
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end
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end
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alias angle arg
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#
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# See Complex#polar.
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#
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def polar
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return abs, arg
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end
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#
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# See Complex#conjugate (short answer: returns <i>self</i>).
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#
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def conjugate
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self
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end
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alias conj conjugate
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end
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#
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# Creates a Complex number. +a+ and +b+ should be Numeric. The result will be
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# <tt>a+bi</tt>.
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#
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def Complex(a, b = 0)
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if b == 0 and (a.kind_of?(Complex) or defined? Complex::Unify)
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a
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else
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Complex.new( a.real-b.imag, a.imag+b.real )
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end
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end
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#
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# The complex number class. See complex.rb for an overview.
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#
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class Complex < Numeric
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@RCS_ID='-$Id: complex.rb,v 1.3 1998/07/08 10:05:28 keiju Exp keiju $-'
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undef step
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def scalar?
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false
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end
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def Complex.generic?(other) # :nodoc:
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other.kind_of?(Integer) or
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other.kind_of?(Float) or
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(defined?(Rational) and other.kind_of?(Rational))
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end
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#
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# Creates a +Complex+ number in terms of +r+ (radius) and +theta+ (angle).
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#
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def Complex.polar(r, theta)
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Complex(r*Math.cos(theta), r*Math.sin(theta))
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end
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#
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# Creates a +Complex+ number <tt>a</tt>+<tt>b</tt><i>i</i>.
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#
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def Complex.new!(a, b=0)
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new(a,b)
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end
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def initialize(a, b)
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raise TypeError, "non numeric 1st arg `#{a.inspect}'" if !a.kind_of? Numeric
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raise TypeError, "`#{a.inspect}' for 1st arg" if a.kind_of? Complex
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raise TypeError, "non numeric 2nd arg `#{b.inspect}'" if !b.kind_of? Numeric
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raise TypeError, "`#{b.inspect}' for 2nd arg" if b.kind_of? Complex
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@real = a
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@image = b
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end
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#
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# Addition with real or complex number.
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#
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def + (other)
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if other.kind_of?(Complex)
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re = @real + other.real
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im = @image + other.image
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Complex(re, im)
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elsif Complex.generic?(other)
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Complex(@real + other, @image)
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else
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x , y = other.coerce(self)
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x + y
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end
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end
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#
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# Subtraction with real or complex number.
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#
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def - (other)
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if other.kind_of?(Complex)
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re = @real - other.real
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im = @image - other.image
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Complex(re, im)
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elsif Complex.generic?(other)
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Complex(@real - other, @image)
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else
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x , y = other.coerce(self)
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x - y
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end
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end
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#
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# Multiplication with real or complex number.
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#
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def * (other)
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if other.kind_of?(Complex)
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re = @real*other.real - @image*other.image
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im = @real*other.image + @image*other.real
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Complex(re, im)
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elsif Complex.generic?(other)
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Complex(@real * other, @image * other)
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else
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x , y = other.coerce(self)
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x * y
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end
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end
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#
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# Division by real or complex number.
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#
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def / (other)
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if other.kind_of?(Complex)
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self*other.conjugate/other.abs2
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elsif Complex.generic?(other)
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Complex(@real/other, @image/other)
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else
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x, y = other.coerce(self)
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x/y
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end
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end
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#
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# Raise this complex number to the given (real or complex) power.
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#
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def ** (other)
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if other == 0
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return Complex(1)
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end
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if other.kind_of?(Complex)
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r, theta = polar
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ore = other.real
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oim = other.image
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nr = Math.exp!(ore*Math.log!(r) - oim * theta)
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ntheta = theta*ore + oim*Math.log!(r)
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Complex.polar(nr, ntheta)
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elsif other.kind_of?(Integer)
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if other > 0
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x = self
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z = x
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n = other - 1
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while n != 0
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while (div, mod = n.divmod(2)
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mod == 0)
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x = Complex(x.real*x.real - x.image*x.image, 2*x.real*x.image)
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n = div
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end
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z *= x
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n -= 1
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end
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z
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else
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if defined? Rational
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(Rational(1) / self) ** -other
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else
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self ** Float(other)
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end
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end
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elsif Complex.generic?(other)
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r, theta = polar
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Complex.polar(r**other, theta*other)
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else
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x, y = other.coerce(self)
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x**y
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end
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end
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#
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# Remainder after division by a real or complex number.
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#
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def % (other)
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if other.kind_of?(Complex)
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Complex(@real % other.real, @image % other.image)
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elsif Complex.generic?(other)
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Complex(@real % other, @image % other)
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else
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x , y = other.coerce(self)
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x % y
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end
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end
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#--
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# def divmod(other)
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# if other.kind_of?(Complex)
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# rdiv, rmod = @real.divmod(other.real)
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# idiv, imod = @image.divmod(other.image)
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# return Complex(rdiv, idiv), Complex(rmod, rmod)
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# elsif Complex.generic?(other)
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# Complex(@real.divmod(other), @image.divmod(other))
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# else
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# x , y = other.coerce(self)
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# x.divmod(y)
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# end
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# end
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#++
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#
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# Absolute value (aka modulus): distance from the zero point on the complex
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# plane.
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#
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def abs
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Math.hypot(@real, @image)
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end
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#
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# Square of the absolute value.
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#
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def abs2
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@real*@real + @image*@image
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end
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#
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# Argument (angle from (1,0) on the complex plane).
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#
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def arg
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Math.atan2!(@image, @real)
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end
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alias angle arg
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#
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# Returns the absolute value _and_ the argument.
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#
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def polar
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return abs, arg
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end
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#
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# Complex conjugate (<tt>z + z.conjugate = 2 * z.real</tt>).
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#
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def conjugate
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Complex(@real, -@image)
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end
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alias conj conjugate
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undef <=>
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#
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# Test for numerical equality (<tt>a == a + 0<i>i</i></tt>).
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#
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def == (other)
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if other.kind_of?(Complex)
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@real == other.real and @image == other.image
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elsif Complex.generic?(other)
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@real == other and @image == 0
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else
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other == self
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end
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end
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#
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# Attempts to coerce +other+ to a Complex number.
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#
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def coerce(other)
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if Complex.generic?(other)
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return Complex.new!(other), self
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else
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super
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end
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end
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#
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# FIXME
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#
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def denominator
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@real.denominator.lcm(@image.denominator)
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end
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#
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# FIXME
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#
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def numerator
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cd = denominator
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Complex(@real.numerator*(cd/@real.denominator),
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@image.numerator*(cd/@image.denominator))
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end
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#
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# Standard string representation of the complex number.
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#
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def to_s
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if @real != 0
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if defined?(Rational) and @image.kind_of?(Rational) and @image.denominator != 1
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if @image >= 0
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@real.to_s+"+("+@image.to_s+")i"
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else
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@real.to_s+"-("+(-@image).to_s+")i"
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end
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else
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if @image >= 0
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@real.to_s+"+"+@image.to_s+"i"
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else
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@real.to_s+"-"+(-@image).to_s+"i"
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end
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end
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else
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if defined?(Rational) and @image.kind_of?(Rational) and @image.denominator != 1
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"("+@image.to_s+")i"
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else
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@image.to_s+"i"
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end
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end
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end
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#
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# Returns a hash code for the complex number.
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#
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def hash
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@real.hash ^ @image.hash
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end
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#
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# Returns "<tt>Complex(<i>real</i>, <i>image</i>)</tt>".
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#
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def inspect
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sprintf("Complex(%s, %s)", @real.inspect, @image.inspect)
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end
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#
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# +I+ is the imaginary number. It exists at point (0,1) on the complex plane.
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#
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I = Complex(0,1)
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# The real part of a complex number.
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attr_reader :real
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# The imaginary part of a complex number.
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attr_reader :image
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alias imag image
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end
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module Math
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alias sqrt! sqrt
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alias exp! exp
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alias log! log
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alias log10! log10
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alias cos! cos
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alias sin! sin
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alias tan! tan
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alias cosh! cosh
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alias sinh! sinh
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alias tanh! tanh
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alias acos! acos
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alias asin! asin
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alias atan! atan
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alias atan2! atan2
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alias acosh! acosh
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alias asinh! asinh
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alias atanh! atanh
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# Redefined to handle a Complex argument.
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def sqrt(z)
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if Complex.generic?(z)
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if z >= 0
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sqrt!(z)
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else
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Complex(0,sqrt!(-z))
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end
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else
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if z.image < 0
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sqrt(z.conjugate).conjugate
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else
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r = z.abs
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x = z.real
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Complex( sqrt!((r+x)/2), sqrt!((r-x)/2) )
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end
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end
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end
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# Redefined to handle a Complex argument.
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def exp(z)
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if Complex.generic?(z)
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exp!(z)
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else
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Complex(exp!(z.real) * cos!(z.image), exp!(z.real) * sin!(z.image))
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end
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end
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# Redefined to handle a Complex argument.
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def cos(z)
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if Complex.generic?(z)
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cos!(z)
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else
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Complex(cos!(z.real)*cosh!(z.image),
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-sin!(z.real)*sinh!(z.image))
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end
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end
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# Redefined to handle a Complex argument.
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def sin(z)
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if Complex.generic?(z)
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sin!(z)
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else
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Complex(sin!(z.real)*cosh!(z.image),
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cos!(z.real)*sinh!(z.image))
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end
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end
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# Redefined to handle a Complex argument.
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def tan(z)
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if Complex.generic?(z)
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tan!(z)
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else
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sin(z)/cos(z)
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end
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end
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def sinh(z)
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if Complex.generic?(z)
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sinh!(z)
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else
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Complex( sinh!(z.real)*cos!(z.image), cosh!(z.real)*sin!(z.image) )
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end
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end
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def cosh(z)
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if Complex.generic?(z)
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cosh!(z)
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else
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Complex( cosh!(z.real)*cos!(z.image), sinh!(z.real)*sin!(z.image) )
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end
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end
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def tanh(z)
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if Complex.generic?(z)
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tanh!(z)
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else
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sinh(z)/cosh(z)
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end
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end
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# Redefined to handle a Complex argument.
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def log(z)
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if Complex.generic?(z) and z >= 0
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log!(z)
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else
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r, theta = z.polar
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Complex(log!(r.abs), theta)
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end
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end
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# Redefined to handle a Complex argument.
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def log10(z)
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if Complex.generic?(z)
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log10!(z)
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else
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log(z)/log!(10)
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end
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end
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def acos(z)
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if Complex.generic?(z) and z >= -1 and z <= 1
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acos!(z)
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else
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-1.0.im * log( z + 1.0.im * sqrt(1.0-z*z) )
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end
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end
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def asin(z)
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if Complex.generic?(z) and z >= -1 and z <= 1
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asin!(z)
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else
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-1.0.im * log( 1.0.im * z + sqrt(1.0-z*z) )
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end
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end
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def atan(z)
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if Complex.generic?(z)
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atan!(z)
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else
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1.0.im * log( (1.0.im+z) / (1.0.im-z) ) / 2.0
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end
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end
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def atan2(y,x)
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if Complex.generic?(y) and Complex.generic?(x)
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atan2!(y,x)
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else
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-1.0.im * log( (x+1.0.im*y) / sqrt(x*x+y*y) )
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end
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end
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def acosh(z)
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if Complex.generic?(z) and z >= 1
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acosh!(z)
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else
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log( z + sqrt(z*z-1.0) )
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end
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end
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def asinh(z)
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if Complex.generic?(z)
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asinh!(z)
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else
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log( z + sqrt(1.0+z*z) )
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end
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end
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def atanh(z)
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if Complex.generic?(z) and z >= -1 and z <= 1
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atanh!(z)
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else
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log( (1.0+z) / (1.0-z) ) / 2.0
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end
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end
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module_function :sqrt!
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module_function :sqrt
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module_function :exp!
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module_function :exp
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module_function :log!
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module_function :log
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module_function :log10!
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module_function :log10
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module_function :cosh!
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module_function :cosh
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module_function :cos!
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module_function :cos
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module_function :sinh!
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module_function :sinh
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module_function :sin!
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module_function :sin
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module_function :tan!
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module_function :tan
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module_function :tanh!
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module_function :tanh
|
|
module_function :acos!
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|
module_function :acos
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|
module_function :asin!
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module_function :asin
|
|
module_function :atan!
|
|
module_function :atan
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|
module_function :atan2!
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|
module_function :atan2
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|
module_function :acosh!
|
|
module_function :acosh
|
|
module_function :asinh!
|
|
module_function :asinh
|
|
module_function :atanh!
|
|
module_function :atanh
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|
|
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end
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# Documentation comments:
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# - source: original (researched from pickaxe)
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# - a couple of fixme's
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# - RDoc output for Bignum etc. is a bit short, with nothing but an
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# (undocumented) alias. No big deal.
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