module CMath

Included modules:: Math

Trigonometric and transcendental functions for complex numbers.

CMath is a library that provides trigonometric and transcendental functions for complex numbers. The functions in this module accept integers, floating-point numbers or complex numbers as arguments.

Note that the selection of functions is similar, but not identical, to that in module math. The reason for having two modules is that some users aren't interested in complex numbers, and perhaps don't even know what they are. They would rather have Math#sqrt raise an exception than return a complex number.

For more information you can see Complex class.

Usage

To start using this library, simply require cmath library:

require "cmath"

Public Class Methods

acos(z) Show source

# File lib/cmath.rb, line 280
def acos(z)
  begin
    if z.real? and z >= -1 and z <= 1
      RealMath.acos(z)
    else
      (-1.0).i * log(z + 1.0.i * sqrt(1.0 - z * z))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the arc cosine of z

CMath.acos(1 + 1i) #=> (0.9045568943023813-1.0612750619050357i)

acosh(z) Show source

# File lib/cmath.rb, line 345
def acosh(z)
  begin
    if z.real? and z >= 1
      RealMath.acosh(z)
    else
      log(z + sqrt(z * z - 1.0))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

returns the inverse hyperbolic cosine of z

CMath.acosh(1 + 1i) #=> (1.0612750619050357+0.9045568943023813i)

asin(z) Show source

# File lib/cmath.rb, line 264
def asin(z)
  begin
    if z.real? and z >= -1 and z <= 1
      RealMath.asin(z)
    else
      (-1.0).i * log(1.0.i * z + sqrt(1.0 - z * z))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the arc sine of z

CMath.asin(1 + 1i) #=> (0.6662394324925153+1.0612750619050355i)

asinh(z) Show source

# File lib/cmath.rb, line 329
def asinh(z)
  begin
    if z.real?
      RealMath.asinh(z)
    else
      log(z + sqrt(1.0 + z * z))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

returns the inverse hyperbolic sine of z

CMath.asinh(1 + 1i) #=> (1.0612750619050357+0.6662394324925153i)

atan(z) Show source

# File lib/cmath.rb, line 296
def atan(z)
  begin
    if z.real?
      RealMath.atan(z)
    else
      1.0.i * log((1.0.i + z) / (1.0.i - z)) / 2.0
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the arc tangent of z

CMath.atan(1 + 1i) #=> (1.0172219678978514+0.4023594781085251i)

atan2(y,x) Show source

# File lib/cmath.rb, line 313
def atan2(y,x)
  begin
    if y.real? and x.real?
      RealMath.atan2(y,x)
    else
      (-1.0).i * log((x + 1.0.i * y) / sqrt(x * x + y * y))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

returns the arc tangent of y divided by x using the signs of y and x to determine the quadrant

CMath.atan2(1 + 1i, 0) #=> (1.5707963267948966+0.0i)

atanh(z) Show source

# File lib/cmath.rb, line 361
def atanh(z)
  begin
    if z.real? and z >= -1 and z <= 1
      RealMath.atanh(z)
    else
      log((1.0 + z) / (1.0 - z)) / 2.0
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

returns the inverse hyperbolic tangent of z

CMath.atanh(1 + 1i) #=> (0.4023594781085251+1.0172219678978514i)

cbrt(z) Show source

# File lib/cmath.rb, line 156
def cbrt(z)
  z ** (1.0/3)
end

Returns the principal value of the cube root of z

CMath.cbrt(1 + 4i) #=> (1.449461632813119+0.6858152562177092i)

cos(z) Show source

# File lib/cmath.rb, line 181
def cos(z)
  begin
    if z.real?
      RealMath.cos(z)
    else
      Complex(RealMath.cos(z.real) * RealMath.cosh(z.imag),
              -RealMath.sin(z.real) * RealMath.sinh(z.imag))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the cosine of z, where z is given in radians

CMath.cos(1 + 1i) #=> (0.8337300251311491-0.9888977057628651i)

cosh(z) Show source

# File lib/cmath.rb, line 231
def cosh(z)
  begin
    if z.real?
      RealMath.cosh(z)
    else
      Complex(RealMath.cosh(z.real) * RealMath.cos(z.imag),
              RealMath.sinh(z.real) * RealMath.sin(z.imag))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the hyperbolic cosine of z, where z is given in radians

CMath.cosh(1 + 1i) #=> (0.8337300251311491+0.9888977057628651i)

exp(z) Show source

# File lib/cmath.rb, line 61
def exp(z)
  begin
    if z.real?
      RealMath.exp(z)
    else
      ere = RealMath.exp(z.real)
      Complex(ere * RealMath.cos(z.imag),
              ere * RealMath.sin(z.imag))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Math::E raised to the z power

CMath.exp(1.i * Math::PI) #=> (-1.0+1.2246467991473532e-16i)

log(z, b=::Math::E) Show source

# File lib/cmath.rb, line 81
def log(z, b=::Math::E)
  begin
    if z.real? && z >= 0 && b >= 0
      RealMath.log(z, b)
    else
      Complex(RealMath.log(z.abs), z.arg) / log(b)
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the natural logarithm of Complex. If a second argument is given, it will be the base of logarithm.

CMath.log(1 + 4i)     #=> (1.416606672028108+1.3258176636680326i)
CMath.log(1 + 4i, 10) #=> (0.6152244606891369+0.5757952953408879i)

log10(z) Show source

# File lib/cmath.rb, line 113
def log10(z)
  begin
    if z.real? and z >= 0
      RealMath.log10(z)
    else
      log(z) / RealMath.log(10)
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the base 10 logarithm of z

CMath.log10(-1) #=> (0.0+1.3643763538418412i)

log2(z) Show source

# File lib/cmath.rb, line 97
def log2(z)
  begin
    if z.real? and z >= 0
      RealMath.log2(z)
    else
      log(z) / RealMath.log(2)
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the base 2 logarithm of z

CMath.log2(-1) => (0.0+4.532360141827194i)

sin(z) Show source

# File lib/cmath.rb, line 164
def sin(z)
  begin
    if z.real?
      RealMath.sin(z)
    else
      Complex(RealMath.sin(z.real) * RealMath.cosh(z.imag),
              RealMath.cos(z.real) * RealMath.sinh(z.imag))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the sine of z, where z is given in radians

CMath.sin(1 + 1i) #=> (1.2984575814159773+0.6349639147847361i)

sinh(z) Show source

# File lib/cmath.rb, line 214
def sinh(z)
  begin
    if z.real?
      RealMath.sinh(z)
    else
      Complex(RealMath.sinh(z.real) * RealMath.cos(z.imag),
              RealMath.cosh(z.real) * RealMath.sin(z.imag))
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the hyperbolic sine of z, where z is given in radians

CMath.sinh(1 + 1i) #=> (0.6349639147847361+1.2984575814159773i)

sqrt(z) Show source

# File lib/cmath.rb, line 129
def sqrt(z)
  begin
    if z.real?
      if z < 0
        Complex(0, RealMath.sqrt(-z))
      else
        RealMath.sqrt(z)
      end
    else
      if z.imag < 0 ||
          (z.imag == 0 && z.imag.to_s[0] == '-')
        sqrt(z.conjugate).conjugate
      else
        r = z.abs
        x = z.real
        Complex(RealMath.sqrt((r + x) / 2.0), RealMath.sqrt((r - x) / 2.0))
      end
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the non-negative square root of Complex.

CMath.sqrt(-1 + 0i) #=> 0.0+1.0i

tan(z) Show source

# File lib/cmath.rb, line 198
def tan(z)
  begin
    if z.real?
      RealMath.tan(z)
    else
      sin(z) / cos(z)
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the tangent of z, where z is given in radians

CMath.tan(1 + 1i) #=> (0.27175258531951174+1.0839233273386943i)

tanh(z) Show source

# File lib/cmath.rb, line 248
def tanh(z)
  begin
    if z.real?
      RealMath.tanh(z)
    else
      sinh(z) / cosh(z)
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Returns the hyperbolic tangent of z, where z is given in radians

CMath.tanh(1 + 1i) #=> (1.0839233273386943+0.27175258531951174i)

Private Instance Methods