module CMath

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(-1) 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) click to toggle source

Returns the arc cosine of z

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

# File lib/cmath.rb, line 281
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

acosh(z) click to toggle source

returns the inverse hyperbolic cosine of z

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

# File lib/cmath.rb, line 346
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

asin(z) click to toggle source

Returns the arc sine of z

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

# File lib/cmath.rb, line 265
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

asinh(z) click to toggle source

returns the inverse hyperbolic sine of z

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

# File lib/cmath.rb, line 330
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

atan(z) click to toggle source

Returns the arc tangent of z

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

# File lib/cmath.rb, line 297
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

atan2(y,x) click to toggle source

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)

# File lib/cmath.rb, line 314
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

atanh(z) click to toggle source

returns the inverse hyperbolic tangent of z

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

# File lib/cmath.rb, line 362
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

cbrt(z) click to toggle source

Returns the principal value of the cube root of z

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

# File lib/cmath.rb, line 157
def cbrt(z)
  z ** (1.0/3)
end

cos(z) click to toggle source

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

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

# File lib/cmath.rb, line 182
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

cosh(z) click to toggle source

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

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

# File lib/cmath.rb, line 232
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

exp(z) click to toggle source

Math::E raised to the z power

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

# File lib/cmath.rb, line 62
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

log(z, b=::Math::E) click to toggle source

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)

# File lib/cmath.rb, line 82
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

log10(z) click to toggle source

Returns the base 10 logarithm of z

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

# File lib/cmath.rb, line 114
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

log2(z) click to toggle source

Returns the base 2 logarithm of z

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

# File lib/cmath.rb, line 98
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

sin(z) click to toggle source

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

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

# File lib/cmath.rb, line 165
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

sinh(z) click to toggle source

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

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

# File lib/cmath.rb, line 215
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

sqrt(z) click to toggle source

Returns the non-negative square root of Complex.

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

# File lib/cmath.rb, line 130
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

tan(z) click to toggle source

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

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

# File lib/cmath.rb, line 199
def tan(z)
  begin
    if z.real?
      RealMath.tan(z)
    else
      sin(z) / cos(z)
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

tanh(z) click to toggle source

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

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

# File lib/cmath.rb, line 249
def tanh(z)
  begin
    if z.real?
      RealMath.tanh(z)
    else
      sinh(z) / cosh(z)
    end
  rescue NoMethodError
    handle_no_method_error
  end
end

Private Instance Methods