SuanShu, a Java numerical and statistical library



com.numericalmethod.suanshu.number.complex
Class ElementaryFunction

java.lang.Object
  extended by com.numericalmethod.suanshu.number.complex.ElementaryFunction

public class ElementaryFunction
extends Object

This class contains some elementary functions for complex number, Complex. The references for the formulae can be found in the following.

See Also:

Constructor Summary
ElementaryFunction()
           
 
Method Summary
static Complex acos(Complex z)
          Inverse of cosine.
static Complex asin(Complex z)
          Inverse of sine.
static Complex atan(Complex z)
          Inverse of tangent.
static Complex cos(Complex z)
          Cosine of a complex number.
static Complex cosh(Complex z)
          Hyperbolic cosine of a complex number.
static Complex exp(Complex z)
          Exponential of a complex number.
static Complex log(Complex z)
          Natural logarithm of a complex number.
static Complex pow(Complex z1, Complex z2)
          z1 to the power z2.
static Complex sin(Complex z)
          Sine of a complex number.
static Complex sinh(Complex z)
          Hyperbolic sine of a complex number.
static Complex sqrt(Complex z)
          Square root of a complex number.
static Complex tan(Complex z)
          Tangent of a complex number.
static Complex tanh(Complex z)
          Hyperbolic tangent of a complex number.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

ElementaryFunction

public ElementaryFunction()
Method Detail

sqrt

public static Complex sqrt(Complex z)
Square root of a complex number.

Parameters:
z - a complex number
Returns:
the square root of the number
Throws:
IllegalArgumentException - if z is a NaN or
See Also:
Wikipedia: Square roots of negative and complex numbers

log

public static Complex log(Complex z)
Natural logarithm of a complex number.
ln(a + bi) = ln(r exp(i θ)) = ln(r) + i θ

Parameters:
z - a complex number
Returns:
ln(z)
Throws:
IllegalArgumentException - if z is a NaN or

exp

public static Complex exp(Complex z)
Exponential of a complex number.

 exp(a + bi) = exp(a) * [cos(b) + i sin(b)]
             = exp(b)cos(b) + i exp(a)sin(b)
 

Parameters:
z - a complex number
Returns:
ez
Throws:
IllegalArgumentException - if z is a NaN or

pow

public static Complex pow(Complex z1,
                          Complex z2)
z1 to the power z2.
(r exp(i θ)) ^ (a + bi) = r^a exp(-b θ) (cos(b ln(r) + a θ) + i sin(b ln(r) + a θ))

Parameters:
z1 - a complex number
z2 - a complex number
Returns:
z1z2
Throws:
IllegalArgumentException - if z is a NaN or

sin

public static Complex sin(Complex z)
Sine of a complex number.
sin(a + bi) = sin(a)cosh(b) + i cos(a)sinh(b)

Parameters:
z - a complex number
Returns:
sin(z)
Throws:
IllegalArgumentException - if z is a NaN or

cos

public static Complex cos(Complex z)
Cosine of a complex number.
cos(a + bi) = cos(a)cosh(b) - i sin(a)sinh(b)

Parameters:
z - a complex number
Returns:
cos(z)
Throws:
IllegalArgumentException - if z is a NaN or

tan

public static Complex tan(Complex z)
Tangent of a complex number.

 tan(a + bi) = [sin(2a) + i sinh(2a)] / [cos(2a) + cosh(2b)]
 

Parameters:
z - a complex number
Returns:
tan(z)
Throws:
IllegalArgumentException - if z is a NaN or

asin

public static Complex asin(Complex z)
Inverse of sine.
arcsin(z) = -i ln(iz + sqrt(1 - z2))

Parameters:
z - a complex number
Returns:
sin-1(z)
Throws:
IllegalArgumentException - if z is a NaN or
See Also:
Inverse Sine from Wolfram MathWorld

acos

public static Complex acos(Complex z)
Inverse of cosine.
arccos(z) = pi / 2 + i ln(iz + sqrt(1 - z2)) = pi / 2 - arcsin(z)

Parameters:
z - a complex number
Returns:
cos-1(z)
Throws:
IllegalArgumentException - if z is a NaN or
See Also:
Inverse Cosine from Wolfram MathWorld

atan

public static Complex atan(Complex z)
Inverse of tangent.
arctan(z) = i * ( ln ( 1 - iz ) - ln ( 1 + iz) ) / 2

Parameters:
z - a complex number
Returns:
tan-1(z)
Throws:
IllegalArgumentException - if z is a NaN or
See Also:
Inverse Tangent from Wolfram MathWorld

sinh

public static Complex sinh(Complex z)
Hyperbolic sine of a complex number.
sinh(a + bi) = sinh(a)cos(b) + i cosh(a)sin(b)

Parameters:
z - a complex number
Returns:
sinh(z)
Throws:
IllegalArgumentException - if z is a NaN or

cosh

public static Complex cosh(Complex z)
Hyperbolic cosine of a complex number.
cosh(a + bi) = cosh(a)cos(b) + i sinh(a)sin(b)

Parameters:
z - a complex number
Returns:
cosh(z)
Throws:
IllegalArgumentException - if z is a NaN or

tanh

public static Complex tanh(Complex z)
Hyperbolic tangent of a complex number.
tanh(a + bi) = [sinh(2a) + i sin(2b)] / [cosh(2a) + cos(2b)]

Parameters:
z - a complex number
Returns:
tanh(z)
Throws:
IllegalArgumentException - if z is a NaN or


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