| java.lang.Object
 org.apache.commons.math.complex.ComplexUtils
| ComplexUtils | | public class ComplexUtils (Code) | | Static implementations of common
org.apache.commons.math.complex.Complex -valued functions. Included
are trigonometric, exponential, log, power and square root functions.
Reference:
See individual method javadocs for the computational formulas used.
In general, NaN values in either real or imaginary parts of input arguments
result in
Complex.NaN returned. Otherwise, infinite or NaN values
are returned as they arise in computing the real functions specified in the
computational formulas. Null arguments result in NullPointerExceptions.
version:
$Revision: 349387 $ $Date: 2005-11-27 23:15:46 -0700 (Sun, 27 Nov 2005) $ |
| Method Summary | |
| public static Complex | acos(Complex z)
Compute the
inverse cosine for the given complex argument. | | public static Complex | asin(Complex z)
Compute the
inverse sine for the given complex argument.
Implements the formula:
asin(z) = -i (log(sqrt(1 - z2) + iz))
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN or infinite.
Parameters:
z - the value whose inverse sine is to be returned. | | public static Complex | atan(Complex z)
Compute the
inverse tangent for the given complex argument.
Implements the formula:
atan(z) = (i/2) log((i + z)/(i - z))
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN or infinite. | | public static Complex | cos(Complex z)
Compute the
cosine
for the given complex argument. | | public static Complex | cosh(Complex z)
Compute the
hyperbolic cosine for the given complex argument.
Implements the formula:
cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
cosh(1 ± INFINITY i) = NaN + NaN i
cosh(±INFINITY + i) = INFINITY ± INFINITY i
cosh(±INFINITY ± INFINITY i) = NaN + NaN i
Throws NullPointerException if z is null.
Parameters:
z - the value whose hyperbolic cosine is to be returned. | | public static Complex | exp(Complex z)
Compute the
exponential function for the given complex argument. | | public static Complex | log(Complex z)
Compute the
natural logarithm for the given complex argument.
Implements the formula:
log(a + bi) = ln(|a + bi|) + arg(a + bi)i
where ln on the right hand side is
java.lang.Math.log ,
|a + bi| is the modulus,
Complex.abs , and
arg(a + bi) =
java.lang.Math.atan2 (b, a)
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite (or critical) values in real or imaginary parts of the input may
result in infinite or NaN values returned in parts of the result.
Examples:
log(1 ± INFINITY i) = INFINITY ± (π/2)i
log(INFINITY + i) = INFINITY + 0i
log(-INFINITY + i) = INFINITY + πi
log(INFINITY ± INFINITY i) = INFINITY ± (π/4)i
log(-INFINITY ± INFINITY i) = INFINITY ± (3π/4)i
log(0 + 0i) = -INFINITY + 0i
Throws NullPointerException if z is null.
Parameters:
z - the value. | | public static Complex | polar2Complex(double r, double theta)
Creates a complex number from the given polar representation. | | public static Complex | pow(Complex y, Complex x)
Returns of value of y raised to the power of x.
Implements the formula:
yx = exp(x·log(y))
where exp and log are
ComplexUtils.exp and
ComplexUtils.log , respectively.
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN or infinite, or if y
equals
Complex.ZERO .
Parameters:
y - the base.
Parameters:
x - the exponent. | | public static Complex | sin(Complex z)
Compute the
sine
for the given complex argument.
Implements the formula:
sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
sin(1 ± INFINITY i) = 1 ± INFINITY i
sin(±INFINITY + i) = NaN + NaN i
sin(±INFINITY ± INFINITY i) = NaN + NaN i
Throws NullPointerException if z is null. | | public static Complex | sinh(Complex z)
Compute the
hyperbolic sine for the given complex argument. | | public static Complex | sqrt(Complex z)
Compute the
square root for the given complex argument. | | public static Complex | sqrt1z(Complex z)
Compute the
square root of 1 - z2 for the given complex
argument.
Computes the result directly as
sqrt(Complex.ONE.subtract(z.multiply(z))).
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result. | | public static Complex | tan(Complex z)
Compute the
tangent for the given complex argument. | | public static Complex | tanh(Complex z)
Compute the
hyperbolic tangent for the given complex argument. |
| acos | | public static Complex acos(Complex z)(Code) | | Compute the
inverse cosine for the given complex argument.
Implements the formula:
acos(z) = -i (log(z + i (sqrt(1 - z2))))
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN or infinite.
Parameters:
z - the value whose inverse cosine is to be returned the inverse cosine of z
throws:
NullPointerException - if z is null |
| asin | | public static Complex asin(Complex z)(Code) | | Compute the
inverse sine for the given complex argument.
Implements the formula:
asin(z) = -i (log(sqrt(1 - z2) + iz))
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN or infinite.
Parameters:
z - the value whose inverse sine is to be returned. the inverse sine of z.
throws:
NullPointerException - if z is null |
| atan | | public static Complex atan(Complex z)(Code) | | Compute the
inverse tangent for the given complex argument.
Implements the formula:
atan(z) = (i/2) log((i + z)/(i - z))
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN or infinite.
Parameters:
z - the value whose inverse tangent is to be returned the inverse tangent of z
throws:
NullPointerException - if z is null |
| cos | | public static Complex cos(Complex z)(Code) | | Compute the
cosine
for the given complex argument.
Implements the formula:
cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
cos(1 ± INFINITY i) = 1 ∓ INFINITY i
cos(±INFINITY + i) = NaN + NaN i
cos(±INFINITY ± INFINITY i) = NaN + NaN i
Parameters:
z - the value whose cosine is to be returned the cosine of z
throws:
NullPointerException - if z is null |
| cosh | | public static Complex cosh(Complex z)(Code) | | Compute the
hyperbolic cosine for the given complex argument.
Implements the formula:
cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
cosh(1 ± INFINITY i) = NaN + NaN i
cosh(±INFINITY + i) = INFINITY ± INFINITY i
cosh(±INFINITY ± INFINITY i) = NaN + NaN i
Throws NullPointerException if z is null.
Parameters:
z - the value whose hyperbolic cosine is to be returned. the hyperbolic cosine of z. |
| exp | | public static Complex exp(Complex z)(Code) | | Compute the
exponential function for the given complex argument.
Implements the formula:
exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i
where the (real) functions on the right-hand side are
java.lang.Math.exp ,
java.lang.Math.cos , and
java.lang.Math.sin .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
exp(1 ± INFINITY i) = NaN + NaN i
exp(INFINITY + i) = INFINITY + INFINITY i
exp(-INFINITY + i) = 0 + 0i
exp(±INFINITY ± INFINITY i) = NaN + NaN i
Throws NullPointerException if z is null.
Parameters:
z - the value ez |
| log | | public static Complex log(Complex z)(Code) | | Compute the
natural logarithm for the given complex argument.
Implements the formula:
log(a + bi) = ln(|a + bi|) + arg(a + bi)i
where ln on the right hand side is
java.lang.Math.log ,
|a + bi| is the modulus,
Complex.abs , and
arg(a + bi) =
java.lang.Math.atan2 (b, a)
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite (or critical) values in real or imaginary parts of the input may
result in infinite or NaN values returned in parts of the result.
Examples:
log(1 ± INFINITY i) = INFINITY ± (π/2)i
log(INFINITY + i) = INFINITY + 0i
log(-INFINITY + i) = INFINITY + πi
log(INFINITY ± INFINITY i) = INFINITY ± (π/4)i
log(-INFINITY ± INFINITY i) = INFINITY ± (3π/4)i
log(0 + 0i) = -INFINITY + 0i
Throws NullPointerException if z is null.
Parameters:
z - the value. ln z. |
| polar2Complex | | public static Complex polar2Complex(double r, double theta)(Code) | | Creates a complex number from the given polar representation.
The value returned is r·ei·theta,
computed as r·cos(theta) + r·sin(theta)i
If either r or theta is NaN, or
theta is infinite,
Complex.NaN is returned.
If r is infinite and theta is finite,
infinite or NaN values may be returned in parts of the result, following
the rules for double arithmetic.
Examples:
polar2Complex(INFINITY, π/4) = INFINITY + INFINITY i
polar2Complex(INFINITY, 0) = INFINITY + NaN i
polar2Complex(INFINITY, -π/4) = INFINITY - INFINITY i
polar2Complex(INFINITY, 5π/4) = -INFINITY - INFINITY i
Parameters:
r - the modulus of the complex number to create
Parameters:
theta - the argument of the complex number to create r·ei·theta
throws:
IllegalArgumentException - if r is negative
since:
1.1 |
| sin | | public static Complex sin(Complex z)(Code) | | Compute the
sine
for the given complex argument.
Implements the formula:
sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
sin(1 ± INFINITY i) = 1 ± INFINITY i
sin(±INFINITY + i) = NaN + NaN i
sin(±INFINITY ± INFINITY i) = NaN + NaN i
Throws NullPointerException if z is null.
Parameters:
z - the value whose sine is to be returned. the sine of z. |
| sinh | | public static Complex sinh(Complex z)(Code) | | Compute the
hyperbolic sine for the given complex argument.
Implements the formula:
sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
sinh(1 ± INFINITY i) = NaN + NaN i
sinh(±INFINITY + i) = ± INFINITY + INFINITY i
sinh(±INFINITY ± INFINITY i) = NaN + NaN i Parameters:
z - the value whose hyperbolic sine is to be returned the hyperbolic sine of z
throws:
NullPointerException - if z is null |
| sqrt | | public static Complex sqrt(Complex z)(Code) | | Compute the
square root for the given complex argument.
Implements the following algorithm to compute sqrt(a + bi):
- Let
t = sqrt((|a| + |a + bi|) / 2)
if a ≥ 0 return t + (b/2t)i
else return |b|/2t + sign(b)t i
where
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
sqrt(1 ± INFINITY i) = INFINITY + NaN i
sqrt(INFINITY + i) = INFINITY + 0i
sqrt(-INFINITY + i) = 0 + INFINITY i
sqrt(INFINITY ± INFINITY i) = INFINITY + NaN i
sqrt(-INFINITY ± INFINITY i) = NaN ± INFINITY i
Parameters:
z - the value whose square root is to be returned the square root of z
throws:
NullPointerException - if z is null |
| sqrt1z | | public static Complex sqrt1z(Complex z)(Code) | | Compute the
square root of 1 - z2 for the given complex
argument.
Computes the result directly as
sqrt(Complex.ONE.subtract(z.multiply(z))).
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Parameters:
z - the value the square root of 1 - z2
throws:
NullPointerException - if z is null |
| tan | | public static Complex tan(Complex z)(Code) | | Compute the
tangent for the given complex argument.
Implements the formula:
tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite (or critical) values in real or imaginary parts of the input may
result in infinite or NaN values returned in parts of the result.
Examples:
tan(1 ± INFINITY i) = 0 + NaN i
tan(±INFINITY + i) = NaN + NaN i
tan(±INFINITY ± INFINITY i) = NaN + NaN i
tan(±&pi/2 + 0 i) = ±INFINITY + NaN i
Parameters:
z - the value whose tangent is to be returned the tangent of z
throws:
NullPointerException - if z is null |
| tanh | | public static Complex tanh(Complex z)(Code) | | Compute the
hyperbolic tangent for the given complex argument.
Implements the formula:
tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i
where the (real) functions on the right-hand side are
java.lang.Math.sin ,
java.lang.Math.cos ,
MathUtils.cosh and
MathUtils.sinh .
Returns
Complex.NaN if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
tanh(1 ± INFINITY i) = NaN + NaN i
tanh(±INFINITY + i) = NaN + 0 i
tanh(±INFINITY ± INFINITY i) = NaN + NaN i
tanh(0 + (&pi/2)i) = NaN + INFINITY i
Parameters:
z - the value whose hyperbolic tangent is to be returned the hyperbolic tangent of z
throws:
NullPointerException - if z is null |
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