Module: Math

Defined in:
lib/complex.rb

Instance Method Summary collapse

Instance Method Details

#acos(z) ⇒ Object Also known as: acos! 



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# File 'lib/complex.rb', line 562

def acos(z)
  if Complex.generic?(z) and z >= -1 and z <= 1
    acos!(z)
  else
    -1.0.im * log( z + 1.0.im * sqrt(1.0-z*z) )
  end
end

#acosh(z) ⇒ Object Also known as: acosh! 



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# File 'lib/complex.rb', line 594

def acosh(z)
  if Complex.generic?(z) and z >= 1
    acosh!(z)
  else
    log( z + sqrt(z*z-1.0) )
  end
end

#asin(z) ⇒ Object Also known as: asin! 



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# File 'lib/complex.rb', line 570

def asin(z)
  if Complex.generic?(z) and z >= -1 and z <= 1
    asin!(z)
  else
    -1.0.im * log( 1.0.im * z + sqrt(1.0-z*z) )
  end
end

#asinh(z) ⇒ Object Also known as: asinh! 



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# File 'lib/complex.rb', line 602

def asinh(z)
  if Complex.generic?(z)
    asinh!(z)
  else
    log( z + sqrt(1.0+z*z) )
  end
end

#atan(z) ⇒ Object Also known as: atan! 



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# File 'lib/complex.rb', line 578

def atan(z)
  if Complex.generic?(z)
    atan!(z)
  else
    1.0.im * log( (1.0.im+z) / (1.0.im-z) ) / 2.0
  end
end

#atan2(y, x) ⇒ Object Also known as: atan2! 



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# File 'lib/complex.rb', line 586

def atan2(y,x)
  if Complex.generic?(y) and Complex.generic?(x)
    atan2!(y,x)
  else
    -1.0.im * log( (x+1.0.im*y) / sqrt(x*x+y*y) )
  end
end

#atanh(z) ⇒ Object Also known as: atanh! 



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# File 'lib/complex.rb', line 610

def atanh(z)
  if Complex.generic?(z) and z >= -1 and z <= 1
    atanh!(z)
  else
    log( (1.0+z) / (1.0-z) ) / 2.0
  end
end

#cos(z) ⇒ Object Also known as: cos!

Redefined to handle a Complex argument.



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# File 'lib/complex.rb', line 491

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

#cosh(z) ⇒ Object Also known as: cosh! 



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# File 'lib/complex.rb', line 527

def cosh(z)
  if Complex.generic?(z)
    cosh!(z)
  else
    Complex( cosh!(z.real)*cos!(z.image), sinh!(z.real)*sin!(z.image) )
  end
end

#exp(z) ⇒ Object Also known as: exp!

Redefined to handle a Complex argument.



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# File 'lib/complex.rb', line 482

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

#log(z) ⇒ Object Also known as: log!

Redefined to handle a Complex argument.



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# File 'lib/complex.rb', line 544

def log(z)
  if Complex.generic?(z) and z >= 0
    log!(z)
  else
    r, theta = z.polar
    Complex(log!(r.abs), theta)
  end
end

#log10(z) ⇒ Object Also known as: log10!

Redefined to handle a Complex argument.



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# File 'lib/complex.rb', line 554

def log10(z)
  if Complex.generic?(z)
    log10!(z)
  else
    log(z)/log!(10)
  end
end

#sin(z) ⇒ Object Also known as: sin!

Redefined to handle a Complex argument.



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# File 'lib/complex.rb', line 501

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

#sinh(z) ⇒ Object Also known as: sinh! 



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# File 'lib/complex.rb', line 519

def sinh(z)
  if Complex.generic?(z)
    sinh!(z)
  else
    Complex( sinh!(z.real)*cos!(z.image), cosh!(z.real)*sin!(z.image) )
  end
end

#sqrt(z) ⇒ Object Also known as: sqrt!

Redefined to handle a Complex argument.



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# File 'lib/complex.rb', line 463

def sqrt(z)
  if Complex.generic?(z)
    if z >= 0
	sqrt!(z)
    else
	Complex(0,sqrt!(-z))
    end
  else
    if z.image < 0
	sqrt(z.conjugate).conjugate
    else
	r = z.abs
	x = z.real
	Complex( sqrt!((r+x)/2), sqrt!((r-x)/2) )
    end
  end
end

#tan(z) ⇒ Object Also known as: tan!

Redefined to handle a Complex argument.



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# File 'lib/complex.rb', line 511

def tan(z)
  if Complex.generic?(z)
    tan!(z)
  else
    sin(z)/cos(z)
  end
end

#tanh(z) ⇒ Object Also known as: tanh! 



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# File 'lib/complex.rb', line 535

def tanh(z)
  if Complex.generic?(z)
    tanh!(z)
  else
    sinh(z)/cosh(z)
  end
end