Module: CMath

Relationships & Source Files
Super Chains via Extension / Inclusion / Inheritance
Instance Chain: self, Math
Defined in:	lib/cmath.rb

Overview

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"

Constant Summary

RealMath = private Internal use only

Backup of Math is needed because mathn.rb replaces Math with CMath.

# File 'lib/cmath.rb', line 28
```
Math
```

Class Method Summary

.acos(z) mod_func

Returns the arc cosine of z
.acosh(z) mod_func

returns the inverse hyperbolic cosine of z
.asin(z) mod_func

Returns the arc sine of z
.asinh(z) mod_func

returns the inverse hyperbolic sine of z
.atan(z) mod_func

Returns the arc tangent of z
.atan2(y, x) mod_func

returns the arc tangent of y divided by x using the signs of y and x to determine the quadrant.
.atanh(z) mod_func

returns the inverse hyperbolic tangent of z
.cbrt(z) mod_func

Returns the principal value of the cube root of z
.cos(z) mod_func

Returns the cosine of z, where z is given in radians.
.cosh(z) mod_func

Returns the hyperbolic cosine of z, where z is given in radians.
.exp(z) mod_func

Math::E raised to the z power.
.log(z, b = ::Math::E) mod_func

Returns the natural logarithm of Complex.
.log10(z) mod_func

Returns the base 10 logarithm of z
.log2(z) mod_func

Returns the base 2 logarithm of z
.sin(z) mod_func

Returns the sine of z, where z is given in radians.
.sinh(z) mod_func

Returns the hyperbolic sine of z, where z is given in radians.
.sqrt(z) mod_func

Returns the non-negative square root of Complex.
.tan(z) mod_func

Returns the tangent of z, where z is given in radians.
.tanh(z) mod_func

Returns the hyperbolic tangent of z, where z is given in radians.
.handle_no_method_error mod_func Internal use only

Class Method Details

.acos(z) (mod_func)

Returns the arc cosine of z

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

[ GitHub ]

# 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) (mod_func)

returns the inverse hyperbolic cosine of z

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

[ GitHub ]

# 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) (mod_func)

Returns the arc sine of z

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

[ GitHub ]

# 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) (mod_func)

returns the inverse hyperbolic sine of z

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

[ GitHub ]

# 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) (mod_func)

Returns the arc tangent of z

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

[ GitHub ]

# 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) (mod_func)

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)

[ GitHub ]

# 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) (mod_func)

returns the inverse hyperbolic tangent of z

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

[ GitHub ]

# 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) (mod_func)

Returns the principal value of the cube root of z

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

[ GitHub ]

# File 'lib/cmath.rb', line 157


def cbrt(z)
  z ** (1.0/3)
end

.cos(z) (mod_func)

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

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

[ GitHub ]

# 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) (mod_func)

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

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

[ GitHub ]

# 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) (mod_func)

Math::E raised to the z power

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

[ GitHub ]

# 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

.handle_no_method_error (mod_func)

This method is for internal use only.

[ GitHub ]

# File 'lib/cmath.rb', line 426


def handle_no_method_error # :nodoc:
  if $!.name == :real?
    raise TypeError, "Numeric Number required"
  else
    raise
  end
end

.log(z, b = ::Math::E) (mod_func)

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)

[ GitHub ]

# 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) (mod_func)

Returns the base 10 logarithm of z

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

[ GitHub ]

# 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) (mod_func)

Returns the base 2 logarithm of z

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

[ GitHub ]

# 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) (mod_func)

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

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

[ GitHub ]

# 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) (mod_func)

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

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

[ GitHub ]

# 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) (mod_func)

Returns the non-negative square root of Complex.

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

[ GitHub ]

# 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) (mod_func)

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

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

[ GitHub ]

# 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) (mod_func)

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

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

[ GitHub ]

# 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