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.
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.
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 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
Ruby Core © 1993–2016 Yukihiro Matsumoto
Licensed under the Ruby License.
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Licensed under their own licenses.