Package org.apfloat

Class FixedPrecisionApcomplexHelper

java.lang.Object

org.apfloat.FixedPrecisionApcomplexHelper

Direct Known Subclasses:

FixedPrecisionApfloatHelper

public class FixedPrecisionApcomplexHelper
extends Object

Fixed-precision mathematical functions for complex numbers.

All results of the mathematical operations are set to have the specified precision. Also all input arguments are set to the specified precision before the operation. If the specified precision is not infinite, this helper class also avoids InfiniteExpansionException e.g. in case where it would happen with ApcomplexMath.acos(Apcomplex.ZERO).

Since:

1.5

Version:

1.10.1

Author:

Mikko Tommila

Constructor Summary

Constructors

Constructor	Description
FixedPrecisionApcomplexHelper(long precision)	Constructs an apcomplex fixed-precison helper with the specified precision.

Method Summary

Modifier and Type	Method	Description
Apfloat	abs(Apcomplex z)	Absolute value.
Apcomplex	acos(Apcomplex z)	Arc cosine.
Apcomplex	acosh(Apcomplex z)	Hyperbolic arc cosine.
Apcomplex	add(Apcomplex z, Apcomplex w)	Addition.
Apcomplex	agm(Apcomplex a, Apcomplex b)	Arithmetic-geometric mean.
Apcomplex[]	allRoots(Apcomplex z, int n)	All branches of a root.
Apfloat	arg(Apcomplex z)	Complex angle.
Apcomplex	asin(Apcomplex z)	Arc sine.
Apcomplex	asinh(Apcomplex z)	Hyperbolic arc sine.
Apcomplex	atan(Apcomplex z)	Arc tangent.
Apcomplex	atanh(Apcomplex z)	Hyperbolic arc tangent.
Apcomplex	cbrt(Apcomplex z)	Cube root.
Apcomplex	conj(Apcomplex z)	Complex conjugate.
Apcomplex	cos(Apcomplex z)	Cosine.
Apcomplex	cosh(Apcomplex z)	Hyperbolic cosine.
Apcomplex	divide(Apcomplex z, Apcomplex w)	Division.
Apcomplex	exp(Apcomplex z)	Exponential function.
Apcomplex	gamma(Apcomplex z)	Gamma function.
Apcomplex	gamma(Apcomplex a, Apcomplex z)	Incomplete gamma function.
Apcomplex	gamma(Apcomplex a, Apcomplex z0, Apcomplex z1)	Generalized incomplete gamma function.
Apfloat	imag(Apcomplex z)	Imaginary part.
Apcomplex	inverseRoot(Apcomplex z, long n)	Inverse root.
Apcomplex	inverseRoot(Apcomplex z, long n, long k)	Inverse root with branch.
Apcomplex	log(Apcomplex z)	Natural logarithm.
Apcomplex	log(Apcomplex z, Apcomplex w)	Logarithm in specified base.
Apcomplex	multiply(Apcomplex z, Apcomplex w)	Multiplication.
Apcomplex	negate(Apcomplex z)	Negation.
Apfloat	norm(Apcomplex z)	Norm.
Apcomplex	pow(Apcomplex z, long n)	Integer power.
Apcomplex	pow(Apcomplex z, Apcomplex w)	Power.
long	precision()	Returns the precision, which is used for the results.
Apcomplex	product(Apcomplex... z)	Product.
Apfloat	real(Apcomplex z)	Real part.
Apcomplex	root(Apcomplex z, long n)	Root.
Apcomplex	root(Apcomplex z, long n, long k)	Root with branch.
Apcomplex	scale(Apcomplex z, long scale)	Move the radix point.
Apcomplex	sin(Apcomplex z)	Sine.
Apcomplex	sinh(Apcomplex z)	Hyperbolic sine.
Apcomplex	sqrt(Apcomplex z)	Square root.
Apcomplex	subtract(Apcomplex z, Apcomplex w)	Subtraction.
Apcomplex	sum(Apcomplex... z)	Sum.
Apcomplex	tan(Apcomplex z)	Tangent.
Apcomplex	tanh(Apcomplex z)	Hyperbolic tangent.
Apfloat	ulp(Apcomplex z)	Unit in the last place.
Apcomplex	valueOf(Apcomplex z)	Returns the value with the specified precision.
Apcomplex	w(Apcomplex z)	Lambert W function.
Apcomplex	w(Apcomplex z, long k)	Lambert W function for the specified branch.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

FixedPrecisionApcomplexHelper

public FixedPrecisionApcomplexHelper(long precision)
                              throws IllegalArgumentException

Constructs an apcomplex fixed-precison helper with the specified precision. The results of all mathematical operations are set to the specified precision.

Parameters:

precision - The precision of the results.

Throws:

IllegalArgumentException - In case the precision is invalid.

Method Details

valueOf

public Apcomplex valueOf(Apcomplex z)
                  throws ApfloatRuntimeException

Returns the value with the specified precision.

Parameters:

z - The value.

Returns:

The value with to the specified precision.

Throws:

ApfloatRuntimeException

negate

public Apcomplex negate(Apcomplex z)
                 throws ApfloatRuntimeException

Negation.

Parameters:

z - The value to negate.

Returns:

-z.

Throws:

ApfloatRuntimeException

conj

public Apcomplex conj(Apcomplex z)
               throws ApfloatRuntimeException

Complex conjugate.

Parameters:

z - The operand.

Returns:

x - i y where z is x + i y.

Throws:

ApfloatRuntimeException

add

public Apcomplex add(Apcomplex z,
 Apcomplex w)
              throws ApfloatRuntimeException

Addition.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z + w.

Throws:

ApfloatRuntimeException

subtract

public Apcomplex subtract(Apcomplex z,
 Apcomplex w)
                   throws ApfloatRuntimeException

Subtraction.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z - w.

Throws:

ApfloatRuntimeException

multiply

public Apcomplex multiply(Apcomplex z,
 Apcomplex w)
                   throws ApfloatRuntimeException

Multiplication.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z * w.

Throws:

ApfloatRuntimeException

divide

public Apcomplex divide(Apcomplex z,
 Apcomplex w)
                 throws ArithmeticException,
ApfloatRuntimeException

Division.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z / w.

Throws:

ArithmeticException - If w is zero.

ApfloatRuntimeException

pow

public Apcomplex pow(Apcomplex z,
 Apcomplex w)
              throws ArithmeticException,
ApfloatRuntimeException

Power.

Parameters:

z - The first operand.

w - The second operand.

Returns:

zw.

Throws:

ArithmeticException - If z and w are zero.

ApfloatRuntimeException

pow

public Apcomplex pow(Apcomplex z,
 long n)
              throws ArithmeticException,
ApfloatRuntimeException

Integer power.

Parameters:

z - The first operand.

n - The first operand.

Returns:

zn.

Throws:

ArithmeticException - If z and n are zero, or z is zero and n is negative.

ApfloatRuntimeException

arg

public Apfloat arg(Apcomplex z)
            throws ArithmeticException,
ApfloatRuntimeException

Complex angle.

Parameters:

z - The operand.

Returns:

The angle of z on the complex plane.

Throws:

ArithmeticException - If z is zero.

ApfloatRuntimeException

imag

public Apfloat imag(Apcomplex z)

Imaginary part.

Parameters:

z - The operand.

Returns:

The imaginary part of z.

real

public Apfloat real(Apcomplex z)

Real part.

Parameters:

z - The operand.

Returns:

The real part of z.

abs

public Apfloat abs(Apcomplex z)
            throws ApfloatRuntimeException

Absolute value.

Parameters:

z - The operand.

Returns:

The absolute value of z.

Throws:

ApfloatRuntimeException

norm

public Apfloat norm(Apcomplex z)
             throws ApfloatRuntimeException

Norm.

Parameters:

z - The operand.

Returns:

x2 + y2 where z is x + i y.

Throws:

ApfloatRuntimeException

acos

public Apcomplex acos(Apcomplex z)
               throws ApfloatRuntimeException

Arc cosine.

Parameters:

z - The operand.

Returns:

The arc cosine of z.

Throws:

ApfloatRuntimeException

acosh

public Apcomplex acosh(Apcomplex z)
                throws ApfloatRuntimeException

Hyperbolic arc cosine.

Parameters:

z - The operand.

Returns:

The hyperbolic arc cosine of z.

Throws:

ApfloatRuntimeException

asin

public Apcomplex asin(Apcomplex z)
               throws ApfloatRuntimeException

Arc sine.

Parameters:

z - The operand.

Returns:

The arc sine of z.

Throws:

ApfloatRuntimeException

asinh

public Apcomplex asinh(Apcomplex z)
                throws ApfloatRuntimeException

Hyperbolic arc sine.

Parameters:

z - The operand.

Returns:

The hyperbolic arc sine of z.

Throws:

ApfloatRuntimeException

atan

public Apcomplex atan(Apcomplex z)
               throws ApfloatRuntimeException

Arc tangent.

Parameters:

z - The operand.

Returns:

The arc tangent of z.

Throws:

ArithmeticException - If z is i.

ApfloatRuntimeException

atanh

public Apcomplex atanh(Apcomplex z)
                throws ArithmeticException,
ApfloatRuntimeException

Hyperbolic arc tangent.

Parameters:

z - The operand.

Returns:

The hyperbolic arc tangent of z.

Throws:

ArithmeticException - If z is 1 or -1.

ApfloatRuntimeException

cbrt

public Apcomplex cbrt(Apcomplex z)
               throws ApfloatRuntimeException

Cube root.

Parameters:

z - The operand.

Returns:

The cube root of z.

Throws:

ApfloatRuntimeException

cos

public Apcomplex cos(Apcomplex z)
              throws ApfloatRuntimeException

Cosine.

Parameters:

z - The operand.

Returns:

The cosine of z.

Throws:

ApfloatRuntimeException

cosh

public Apcomplex cosh(Apcomplex z)
               throws ApfloatRuntimeException

Hyperbolic cosine.

Parameters:

z - The operand.

Returns:

The hyperbolic cosine of z.

Throws:

ApfloatRuntimeException

exp

public Apcomplex exp(Apcomplex z)
              throws ApfloatRuntimeException

Exponential function.

Parameters:

z - The operand.

Returns:

ez.

Throws:

ApfloatRuntimeException

log

public Apcomplex log(Apcomplex z)
              throws ArithmeticException,
ApfloatRuntimeException

Natural logarithm.

Parameters:

z - The operand.

Returns:

The natural logarithm of z.

Throws:

ArithmeticException - If z is zero.

ApfloatRuntimeException

log

public Apcomplex log(Apcomplex z,
 Apcomplex w)
              throws ArithmeticException,
ApfloatRuntimeException

Logarithm in specified base.

Parameters:

z - The operand.

w - The base.

Returns:

The base-w logarithm of z.

Throws:

ArithmeticException - If z or w is zero.

ApfloatRuntimeException

Since:

1.6

sin

public Apcomplex sin(Apcomplex z)
              throws ApfloatRuntimeException

Sine.

Parameters:

z - The operand.

Returns:

The sine of z.

Throws:

ApfloatRuntimeException

sinh

public Apcomplex sinh(Apcomplex z)
               throws ApfloatRuntimeException

Hyperbolic sine.

Parameters:

z - The operand.

Returns:

The hyperbolic sine of z.

Throws:

ApfloatRuntimeException

sqrt

public Apcomplex sqrt(Apcomplex z)
               throws ApfloatRuntimeException

Square root.

Parameters:

z - The operand.

Returns:

The square root of z.

Throws:

ApfloatRuntimeException

tan

public Apcomplex tan(Apcomplex z)
              throws ArithmeticException,
ApfloatRuntimeException

Tangent.

Parameters:

z - The operand.

Returns:

The tangent of z.

Throws:

ArithmeticException - If z is π/2 + n π where n is an integer.

ApfloatRuntimeException

tanh

public Apcomplex tanh(Apcomplex z)
               throws ArithmeticException,
ApfloatRuntimeException

Hyperbolic tangent.

Parameters:

z - The operand.

Returns:

The hyperbolic tangent of z.

Throws:

ArithmeticException - If z is i (π/2 + n π) where n is an integer.

ApfloatRuntimeException

agm

public Apcomplex agm(Apcomplex a,
 Apcomplex b)
              throws ApfloatRuntimeException

Arithmetic-geometric mean.

Parameters:

a - The first operand.

b - The first operand.

Returns:

The arithmetic-geometric mean of a and b.

Throws:

ApfloatRuntimeException

inverseRoot

public Apcomplex inverseRoot(Apcomplex z,
 long n)
                      throws ArithmeticException,
ApfloatRuntimeException

Inverse root.

Parameters:

z - The operand.

n - Which inverse root to take.

Returns:

z-1/n.

Throws:

ArithmeticException - If z or n is zero.

ApfloatRuntimeException

inverseRoot

public Apcomplex inverseRoot(Apcomplex z,
 long n,
 long k)
                      throws ArithmeticException,
ApfloatRuntimeException

Inverse root with branch.

Parameters:

z - The operand.

n - Which inverse root to take.

k - Which branch to take.

Returns:

z-1/ne-i2πk/n.

Throws:

ArithmeticException - If z or n is zero.

ApfloatRuntimeException

root

public Apcomplex root(Apcomplex z,
 long n)
               throws ArithmeticException,
ApfloatRuntimeException

Root.

Parameters:

z - The operand.

n - Which root to take.

Returns:

z1/n.

Throws:

ArithmeticException - If n is zero, or z is zero and n is negative.

ApfloatRuntimeException

root

public Apcomplex root(Apcomplex z,
 long n,
 long k)
               throws ArithmeticException,
ApfloatRuntimeException

Root with branch.

Parameters:

z - The operand.

n - Which root to take.

k - Which branch to take.

Returns:

z1/nei2πsk/n where s is the signum of the imaginary part of z.

Throws:

ArithmeticException - If n is zero, or z is zero and n is negative.

ApfloatRuntimeException

allRoots

public Apcomplex[] allRoots(Apcomplex z,
 int n)
                     throws ArithmeticException,
ApfloatRuntimeException

All branches of a root.

Parameters:

z - The operand.

n - Which root to take.

Returns:

z1/n.

Throws:

ArithmeticException - If n is zero, or z is zero and n is negative.

ApfloatRuntimeException

scale

public Apcomplex scale(Apcomplex z,
 long scale)
                throws ApfloatRuntimeException

Move the radix point.

Parameters:

z - The operand.

scale - The amount to move the radix point.

Returns:

z * z.radix()scale.

Throws:

ApfloatRuntimeException

w

public Apcomplex w(Apcomplex z)
            throws ApfloatRuntimeException

Lambert W function.

Parameters:

z - The operand.

Returns:

W0(z).

Throws:

ApfloatRuntimeException

Since:

1.8.0

w

public Apcomplex w(Apcomplex z,
 long k)
            throws ApfloatRuntimeException

Lambert W function for the specified branch.

Parameters:

z - The operand.

k - The branch.

Returns:

Wk(z).

Throws:

ApfloatRuntimeException

Since:

1.8.0

product

public Apcomplex product(Apcomplex... z)
                  throws ApfloatRuntimeException

Product.

Parameters:

z - The operand(s).

Returns:

The product of the operands.

Throws:

ApfloatRuntimeException

sum

public Apcomplex sum(Apcomplex... z)
              throws ApfloatRuntimeException

Sum.

Parameters:

z - The operand(s).

Returns:

The sum of the operands.

Throws:

ApfloatRuntimeException

gamma

public Apcomplex gamma(Apcomplex z)
                throws ArithmeticException,
ApfloatRuntimeException

Gamma function.

Parameters:

z - The operand.

Returns:

Γ(z).

Throws:

ArithmeticException - If z is a nonpositive integer.

ApfloatRuntimeException

Since:

1.9.0

gamma

public Apcomplex gamma(Apcomplex a,
 Apcomplex z)
                throws ArithmeticException,
ApfloatRuntimeException

Incomplete gamma function.

Parameters:

a - The first operand.

z - The second operand.

Returns:

Γ(a, z).

Throws:

ArithmeticException - If a is a nonpositive integer and z is zero.

ApfloatRuntimeException

Since:

1.10.0

gamma

public Apcomplex gamma(Apcomplex a,
 Apcomplex z0,
 Apcomplex z1)
                throws ArithmeticException,
ApfloatRuntimeException

Generalized incomplete gamma function.

Parameters:

a - The first operand.

z0 - The second operand.

z1 - The third operand.

Returns:

Γ(a, z0) - Γ(a, z1).

Throws:

ArithmeticException - If a is a nonpositive integer and either z0 or z1 is zero.

ApfloatRuntimeException

Since:

1.10.0

ulp

public Apfloat ulp(Apcomplex z)
            throws ApfloatRuntimeException

Unit in the last place.

Parameters:

z - The operand.

Returns:

The unit in the last place.

Throws:

ApfloatRuntimeException

Since:

1.10.0

precision

public long precision()

Returns the precision, which is used for the results.

Returns:

The precision of the results.