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 raise an exception than return a complex number.
Usage¶ ↑
To start using this library, simply require cmath library:
require "cmath"
And after call any CMath function. For example:
CMath.sqrt(-9) #=> 0+3.0i CMath.exp(0 + 0i) #=> 1.0+0.0i CMath.log10(-5.to_c) #=> (0.6989700043360187+1.3643763538418412i)
For more information you can see Complec class.
Public Class Methods
returns the arc cosine of z
CMath.acos(1 + 1i) #=> (0.9045568943023813-1.0612750619050357i)
# File lib/cmath.rb, line 288 def acos(z) begin if z.real? and z >= -1 and z <= 1 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 inverse hyperbolic cosine of z
CMath.acosh(1 + 1i) #=> (1.0612750619050357+0.9045568943023813i)
# File lib/cmath.rb, line 353 def acosh(z) begin if z.real? and z >= 1 acosh!(z) else log(z + sqrt(z * z - 1.0)) end rescue NoMethodError handle_no_method_error end end
returns the arc sine of z
CMath.asin(1 + 1i) #=> (0.6662394324925153+1.0612750619050355i)
# File lib/cmath.rb, line 272 def asin(z) begin if z.real? and z >= -1 and z <= 1 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 inverse hyperbolic sine of z
CMath.asinh(1 + 1i) #=> (1.0612750619050357+0.6662394324925153i)
# File lib/cmath.rb, line 337 def asinh(z) begin if z.real? asinh!(z) else log(z + sqrt(1.0 + z * z)) end rescue NoMethodError handle_no_method_error end end
returns the arc tangent of z
CMath.atan(1 + 1i) #=> (1.0172219678978514+0.4023594781085251i)
# File lib/cmath.rb, line 304 def atan(z) begin if z.real? 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 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 321 def atan2(y,x) begin if y.real? and x.real? 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 inverse hyperbolic tangent of z
CMath.atanh(1 + 1i) #=> (0.4023594781085251+1.0172219678978514i)
# File lib/cmath.rb, line 369 def atanh(z) begin if z.real? and z >= -1 and z <= 1 atanh!(z) else log((1.0 + z) / (1.0 - z)) / 2.0 end rescue NoMethodError handle_no_method_error end end
returns the principal value of the cube root of z
CMath.cbrt(1 + 4i) #=> (1.449461632813119+0.6858152562177092i)
# File lib/cmath.rb, line 164 def cbrt(z) z ** (1.0/3) end
returns the cosine of z
, where z
is given in
radians
CMath.cos(1 + 1i) #=> (0.8337300251311491-0.9888977057628651i)
# File lib/cmath.rb, line 189 def cos(z) begin if z.real? cos!(z) else Complex(cos!(z.real) * cosh!(z.imag), -sin!(z.real) * sinh!(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)
# File lib/cmath.rb, line 239 def cosh(z) begin if z.real? cosh!(z) else Complex(cosh!(z.real) * cos!(z.imag), sinh!(z.real) * sin!(z.imag)) end rescue NoMethodError handle_no_method_error end end
Math::E raised to the z
power
CMath.exp(2i) #=> (-0.4161468365471424+0.9092974268256817i)
# File lib/cmath.rb, line 61 def exp(z) begin if z.real? exp!(z) else ere = exp!(z.real) Complex(ere * cos!(z.imag), ere * sin!(z.imag)) 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)
# File lib/cmath.rb, line 81 def log(*args) begin z, b = args unless b.nil? || b.kind_of?(Numeric) raise TypeError, "Numeric Number required" end if z.real? and z >= 0 and (b.nil? or b >= 0) log!(*args) else a = Complex(log!(z.abs), z.arg) if b a /= log(b) end a end rescue NoMethodError handle_no_method_error end end
returns the base 10 logarithm of z
CMath.log10(-1) #=> (0.0+1.3643763538418412i)
# File lib/cmath.rb, line 121 def log10(z) begin if z.real? and z >= 0 log10!(z) else log(z) / log!(10) end rescue NoMethodError handle_no_method_error end end
returns the base 2 logarithm of z
CMath.log2(-1) => (0.0+4.532360141827194i)
# File lib/cmath.rb, line 105 def log2(z) begin if z.real? and z >= 0 log2!(z) else log(z) / log!(2) 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)
# File lib/cmath.rb, line 172 def sin(z) begin if z.real? sin!(z) else Complex(sin!(z.real) * cosh!(z.imag), cos!(z.real) * sinh!(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)
# File lib/cmath.rb, line 222 def sinh(z) begin if z.real? sinh!(z) else Complex(sinh!(z.real) * cos!(z.imag), cosh!(z.real) * sin!(z.imag)) 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
# File lib/cmath.rb, line 137 def sqrt(z) begin if z.real? if z < 0 Complex(0, sqrt!(-z)) else 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(sqrt!((r + x) / 2.0), sqrt!((r - x) / 2.0)) end 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)
# File lib/cmath.rb, line 206 def tan(z) begin if z.real? tan!(z) else sin(z) / cos(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)
# File lib/cmath.rb, line 256 def tanh(z) begin if z.real? tanh!(z) else sinh(z) / cosh(z) end rescue NoMethodError handle_no_method_error end end
Private Instance Methods
returns the arc cosine of z
CMath.acos(1 + 1i) #=> (0.9045568943023813-1.0612750619050357i)
# File lib/cmath.rb, line 288 def acos(z) begin if z.real? and z >= -1 and z <= 1 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 inverse hyperbolic cosine of z
CMath.acosh(1 + 1i) #=> (1.0612750619050357+0.9045568943023813i)
# File lib/cmath.rb, line 353 def acosh(z) begin if z.real? and z >= 1 acosh!(z) else log(z + sqrt(z * z - 1.0)) end rescue NoMethodError handle_no_method_error end end
returns the arc sine of z
CMath.asin(1 + 1i) #=> (0.6662394324925153+1.0612750619050355i)
# File lib/cmath.rb, line 272 def asin(z) begin if z.real? and z >= -1 and z <= 1 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 inverse hyperbolic sine of z
CMath.asinh(1 + 1i) #=> (1.0612750619050357+0.6662394324925153i)
# File lib/cmath.rb, line 337 def asinh(z) begin if z.real? asinh!(z) else log(z + sqrt(1.0 + z * z)) end rescue NoMethodError handle_no_method_error end end
returns the arc tangent of z
CMath.atan(1 + 1i) #=> (1.0172219678978514+0.4023594781085251i)
# File lib/cmath.rb, line 304 def atan(z) begin if z.real? 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 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 321 def atan2(y,x) begin if y.real? and x.real? 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 inverse hyperbolic tangent of z
CMath.atanh(1 + 1i) #=> (0.4023594781085251+1.0172219678978514i)
# File lib/cmath.rb, line 369 def atanh(z) begin if z.real? and z >= -1 and z <= 1 atanh!(z) else log((1.0 + z) / (1.0 - z)) / 2.0 end rescue NoMethodError handle_no_method_error end end
returns the principal value of the cube root of z
CMath.cbrt(1 + 4i) #=> (1.449461632813119+0.6858152562177092i)
# File lib/cmath.rb, line 164 def cbrt(z) z ** (1.0/3) end
returns the cosine of z
, where z
is given in
radians
CMath.cos(1 + 1i) #=> (0.8337300251311491-0.9888977057628651i)
# File lib/cmath.rb, line 189 def cos(z) begin if z.real? cos!(z) else Complex(cos!(z.real) * cosh!(z.imag), -sin!(z.real) * sinh!(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)
# File lib/cmath.rb, line 239 def cosh(z) begin if z.real? cosh!(z) else Complex(cosh!(z.real) * cos!(z.imag), sinh!(z.real) * sin!(z.imag)) end rescue NoMethodError handle_no_method_error end end
Math::E raised to the z
power
CMath.exp(2i) #=> (-0.4161468365471424+0.9092974268256817i)
# File lib/cmath.rb, line 61 def exp(z) begin if z.real? exp!(z) else ere = exp!(z.real) Complex(ere * cos!(z.imag), ere * sin!(z.imag)) 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)
# File lib/cmath.rb, line 81 def log(*args) begin z, b = args unless b.nil? || b.kind_of?(Numeric) raise TypeError, "Numeric Number required" end if z.real? and z >= 0 and (b.nil? or b >= 0) log!(*args) else a = Complex(log!(z.abs), z.arg) if b a /= log(b) end a end rescue NoMethodError handle_no_method_error end end
returns the base 10 logarithm of z
CMath.log10(-1) #=> (0.0+1.3643763538418412i)
# File lib/cmath.rb, line 121 def log10(z) begin if z.real? and z >= 0 log10!(z) else log(z) / log!(10) end rescue NoMethodError handle_no_method_error end end
returns the base 2 logarithm of z
CMath.log2(-1) => (0.0+4.532360141827194i)
# File lib/cmath.rb, line 105 def log2(z) begin if z.real? and z >= 0 log2!(z) else log(z) / log!(2) 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)
# File lib/cmath.rb, line 172 def sin(z) begin if z.real? sin!(z) else Complex(sin!(z.real) * cosh!(z.imag), cos!(z.real) * sinh!(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)
# File lib/cmath.rb, line 222 def sinh(z) begin if z.real? sinh!(z) else Complex(sinh!(z.real) * cos!(z.imag), cosh!(z.real) * sin!(z.imag)) 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
# File lib/cmath.rb, line 137 def sqrt(z) begin if z.real? if z < 0 Complex(0, sqrt!(-z)) else 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(sqrt!((r + x) / 2.0), sqrt!((r - x) / 2.0)) end 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)
# File lib/cmath.rb, line 206 def tan(z) begin if z.real? tan!(z) else sin(z) / cos(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)
# File lib/cmath.rb, line 256 def tanh(z) begin if z.real? tanh!(z) else sinh(z) / cosh(z) end rescue NoMethodError handle_no_method_error end end