BigDecimalMath (nd4j-common 1.0.0-beta API)

java.lang.Object
- org.nd4j.linalg.util.BigDecimalMath

public class BigDecimalMath
extends java.lang.Object

BigDecimal special functions.

Field Summary

Fields
Modifier and Type	Field and Description
`static java.math.BigDecimal`	`E` The base of the natural logarithm in a predefined accuracy.
`static java.math.BigDecimal`	`GAMMA` Euler-Mascheroni constant lower-case gamma.
`static java.math.BigDecimal`	`LOG2` Natural logarithm of 2.
`static java.math.BigDecimal`	`PI` Euler’s constant Pi.

Constructor Summary

Constructors
Constructor and Description

BigDecimalMath()

Constructors
Constructor and Description
`BigDecimalMath()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static java.math.BigDecimal`	`acosh(java.math.BigDecimal x)` The inverse hyperbolic cosine.
`static java.math.BigDecimal`	`addRound(java.math.BigDecimal x, java.math.BigDecimal y)` Add and round according to the larger of the two ulp’s.
`static java.math.BigDecimal`	`asin(java.math.BigDecimal x)` The inverse trigonometric sine.
`static java.math.BigDecimal`	`asinh(java.math.BigDecimal x)` The inverse hyperbolic sine.
`static java.math.BigDecimal`	`atan(java.math.BigDecimal x)` The inverse trigonometric tangent.
`protected static java.math.BigDecimal`	`broadhurstBBP(int n, int p, int[] a, java.math.MathContext mc)` Broadhurst ladder sequence.
`static java.math.BigDecimal`	`cbrt(java.math.BigDecimal x)` The cube root.
`static java.math.BigDecimal`	`cos(java.math.BigDecimal x)` Trigonometric cosine.
`static java.math.BigDecimal`	`cosh(java.math.BigDecimal x)` The hyperbolic cosine.
`static java.math.BigDecimal`	`cot(java.math.BigDecimal x)` The trigonometric co-tangent.
`static java.math.BigDecimal`	`divideRound(java.math.BigDecimal x, java.math.BigDecimal y)` Divide and round.
`static java.math.BigDecimal`	`divideRound(java.math.BigDecimal x, java.math.BigInteger n)` Divide and round.
`static java.math.BigDecimal`	`divideRound(java.math.BigDecimal x, int n)` Divide and round.
`static java.math.BigDecimal`	`divideRound(java.math.BigInteger n, java.math.BigDecimal x)` Divide and round.
`static java.math.BigDecimal`	`divideRound(int n, java.math.BigDecimal x)` Divide and round.
`static int`	`err2prec(java.math.BigDecimal x, java.math.BigDecimal xerr)` Convert an absolute error to a precision.
`static int`	`err2prec(double xerr)` Convert a relative error to a precision.
`static int`	`err2prec(double x, double xerr)` Convert an absolute error to a precision.
`static java.math.BigDecimal`	`exp(java.math.BigDecimal x)` The exponential function.
`static java.math.BigDecimal`	`exp(java.math.MathContext mc)` The base of the natural logarithm.
`static java.math.BigDecimal`	`Gamma(java.math.BigDecimal x)` The Gamma function.
`static java.math.BigDecimal`	`gamma(java.math.MathContext mc)` Euler-Mascheroni constant.
`static java.math.BigDecimal`	`hypot(java.math.BigDecimal x, java.math.BigDecimal y)` The hypotenuse.
`static java.math.BigDecimal`	`hypot(int n, java.math.BigDecimal x)` The hypotenuse.
`static java.math.BigDecimal`	`log(java.math.BigDecimal x)` The natural logarithm.
`static java.math.BigDecimal`	`log(int n, java.math.MathContext mc)` The natural logarithm.
`static java.math.BigDecimal`	`log(org.nd4j.linalg.util.Rational r, java.math.MathContext mc)` The natural logarithm.
`static java.math.BigDecimal`	`mod2pi(java.math.BigDecimal x)` Reduce value to the interval [0,2*Pi].
`static java.math.BigDecimal`	`modpi(java.math.BigDecimal x)` Reduce value to the interval [-Pi/2,Pi/2].
`static java.math.BigDecimal`	`multiplyRound(java.math.BigDecimal x, java.math.BigDecimal y)` Multiply and round.
`static java.math.BigDecimal`	`multiplyRound(java.math.BigDecimal x, java.math.BigInteger n)` Multiply and round.
`static java.math.BigDecimal`	`multiplyRound(java.math.BigDecimal x, int n)` Multiply and round.
`static java.math.BigDecimal`	`multiplyRound(java.math.BigDecimal x, org.nd4j.linalg.util.Rational f)` Multiply and round.
`static java.math.BigDecimal`	`pi(java.math.MathContext mc)` Euler’s constant.
`static java.math.BigDecimal`	`pochhammer(java.math.BigDecimal x, int n)` Pochhammer’s function.
`static java.math.BigDecimal`	`pow(java.math.BigDecimal x, java.math.BigDecimal y)` Power function.
`static java.math.BigDecimal`	`powRound(java.math.BigDecimal x, int n)` Raise to an integer power and round.
`static double`	`prec2err(double x, int prec)` Convert a precision (relative error) to an absolute error.
`static java.math.BigDecimal`	`root(int n, java.math.BigDecimal x)` The integer root.
`static java.math.BigDecimal`	`scalePrec(java.math.BigDecimal x, int d)` Append decimal zeros to the value.
`static java.math.BigDecimal`	`scalePrec(java.math.BigDecimal x, java.math.MathContext mc)` Boost the precision by appending decimal zeros to the value.
`static java.math.BigDecimal`	`sin(java.math.BigDecimal x)` Trigonometric sine.
`static java.math.BigDecimal`	`sinh(java.math.BigDecimal x)` The hyperbolic sine.
`static java.math.BigDecimal`	`sqrt(java.math.BigDecimal x)` The square root.
`static java.math.BigDecimal`	`subtractRound(java.math.BigDecimal x, java.math.BigDecimal y)` Subtract and round according to the larger of the two ulp’s.
`static java.math.BigDecimal`	`tan(java.math.BigDecimal x)` The trigonometric tangent.
`static java.math.BigDecimal`	`tanh(java.math.BigDecimal x)` The hyperbolic tangent.
`static java.math.BigDecimal`	`zeta(int n, java.math.MathContext mc)` Riemann zeta function.
`static double`	`zeta1(int n)` Riemann zeta function.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - E
```
public static final java.math.BigDecimal E
```
    The base of the natural logarithm in a predefined accuracy. \protect\vrule width0pt\protect\href{http://www.cs.arizona.edu/icon/oddsends/e.htm}{http://www.cs.arizona.edu/icon/oddsends/e.htm} The precision of the predefined constant is one less than the string’s length, taking into account the decimal dot. static int E_PRECISION = E.length()-1 ;
  - PI
```
public static final java.math.BigDecimal PI
```
    Euler’s constant Pi. \protect\vrule width0pt\protect\href{http://www.cs.arizona.edu/icon/oddsends/pi.htm}{http://www.cs.arizona.edu/icon/oddsends/pi.htm}
  - GAMMA
```
public static final java.math.BigDecimal GAMMA
```
    Euler-Mascheroni constant lower-case gamma. 13 \protect\vrule width0pt\protect\href{http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap35.html}{http:/
  - LOG2
```
public static final java.math.BigDecimal LOG2
```
    Natural logarithm of 2. \protect\vrule width0pt\protect\href{http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap58.html}{http:/
- Constructor Detail
  - BigDecimalMath
```
public BigDecimalMath()
```
- Method Detail
  - pi
```
public static java.math.BigDecimal pi(java.math.MathContext mc)
```
    Euler’s constant.
    
    Parameters:
    
    mc - The required precision of the result.
    
    Returns:
    
    3.14159...
  - gamma
```
public static java.math.BigDecimal gamma(java.math.MathContext mc)
```
    Euler-Mascheroni constant.
    
    Parameters:
    
    mc - The required precision of the result.
    
    Returns:
    
    0.577...
  - sqrt
```
public static java.math.BigDecimal sqrt(java.math.BigDecimal x)
```
    The square root.
    
    Parameters:
    
    x - the non-negative argument.
    
    Returns:
    
    the square root of the BigDecimal rounded to the precision implied by x.
  - cbrt
```
public static java.math.BigDecimal cbrt(java.math.BigDecimal x)
```
    The cube root.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    The cubic root of the BigDecimal rounded to the precision implied by x. The sign of the result is the sign of the argument.
  - root
```
public static java.math.BigDecimal root(int n,
                                        java.math.BigDecimal x)
```
    The integer root.
    
    Parameters:
    
    n - the positive argument.
    
    x - the non-negative argument.
    
    Returns:
    
    The n-th root of the BigDecimal rounded to the precision implied by x, x^(1/n).
  - hypot
```
public static java.math.BigDecimal hypot(java.math.BigDecimal x,
                                         java.math.BigDecimal y)
```
    The hypotenuse.
    
    Parameters:
    
    x - the first argument.
    
    y - the second argument.
    
    Returns:
    
    the square root of the sum of the squares of the two arguments, sqrt(x^2+y^2).
  - hypot
```
public static java.math.BigDecimal hypot(int n,
                                         java.math.BigDecimal x)
```
    The hypotenuse.
    
    Parameters:
    
    n - the first argument.
    
    x - the second argument.
    
    Returns:
    
    the square root of the sum of the squares of the two arguments, sqrt(n^2+x^2).
  - exp
```
public static java.math.BigDecimal exp(java.math.BigDecimal x)
```
    The exponential function.
    
    Parameters:
    
    x - the argument.
    
    Returns:
    
    exp(x). The precision of the result is implicitly defined by the precision in the argument. 16 In particular this means that "Invalid Operation" errors are thrown if catastrophic cancellation of digits causes the result to have no valid digits left.
  - exp
```
public static java.math.BigDecimal exp(java.math.MathContext mc)
```
    The base of the natural logarithm.
    
    Parameters:
    
    mc - the required precision of the result
    
    Returns:
    
    exp(1) = 2.71828....
  - log
```
public static java.math.BigDecimal log(java.math.BigDecimal x)
```
    The natural logarithm.
    
    Parameters:
    
    x - the argument.
    
    Returns:
    
    ln(x). The precision of the result is implicitly defined by the precision in the argument.
  - log
```
public static java.math.BigDecimal log(int n,
                                       java.math.MathContext mc)
```
    The natural logarithm.
    
    Parameters:
    
    n - The main argument, a strictly positive integer.
    
    mc - The requirements on the precision.
    
    Returns:
    
    ln(n).
  - log
```
public static java.math.BigDecimal log(org.nd4j.linalg.util.Rational r,
                                       java.math.MathContext mc)
```
    The natural logarithm.
    
    Parameters:
    
    r - The main argument, a strictly positive value.
    
    mc - The requirements on the precision.
    
    Returns:
    
    ln(r).
  - pow
```
public static java.math.BigDecimal pow(java.math.BigDecimal x,
                                       java.math.BigDecimal y)
```
    Power function.
    
    Parameters:
    
    x - Base of the power.
    
    y - Exponent of the power.
    
    Returns:
    
    x^y. The estimation of the relative error in the result is |log(x)*err(y)|+|y*err(x)/x|
  - powRound
```
public static java.math.BigDecimal powRound(java.math.BigDecimal x,
                                            int n)
```
    Raise to an integer power and round.
    
    Parameters:
    
    x - The base.
    
    n - The exponent.
    
    Returns:
    
    x^n.
  - sin
```
public static java.math.BigDecimal sin(java.math.BigDecimal x)
```
    Trigonometric sine.
    
    Parameters:
    
    x - The argument in radians.
    
    Returns:
    
    sin(x) in the range -1 to 1.
  - cos
```
public static java.math.BigDecimal cos(java.math.BigDecimal x)
```
    Trigonometric cosine.
    
    Parameters:
    
    x - The argument in radians.
    
    Returns:
    
    cos(x) in the range -1 to 1.
  - tan
```
public static java.math.BigDecimal tan(java.math.BigDecimal x)
```
    The trigonometric tangent.
    
    Parameters:
    
    x - the argument in radians.
    
    Returns:
    
    the tan(x)
  - cot
```
public static java.math.BigDecimal cot(java.math.BigDecimal x)
```
    The trigonometric co-tangent.
    
    Parameters:
    
    x - the argument in radians.
    
    Returns:
    
    the cot(x)
  - asin
```
public static java.math.BigDecimal asin(java.math.BigDecimal x)
```
    The inverse trigonometric sine.
    
    Parameters:
    
    x - the argument.
    
    Returns:
    
    the arcsin(x) in radians.
  - atan
```
public static java.math.BigDecimal atan(java.math.BigDecimal x)
```
    The inverse trigonometric tangent.
    
    Parameters:
    
    x - the argument.
    
    Returns:
    
    the principal value of arctan(x) in radians in the range -pi/2 to +pi/2.
  - cosh
```
public static java.math.BigDecimal cosh(java.math.BigDecimal x)
```
    The hyperbolic cosine.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    The cosh(x) = (exp(x)+exp(-x))/2 .
  - sinh
```
public static java.math.BigDecimal sinh(java.math.BigDecimal x)
```
    The hyperbolic sine.
    
    Parameters:
    
    x - the argument.
    
    Returns:
    
    the sinh(x) = (exp(x)-exp(-x))/2 .
  - tanh
```
public static java.math.BigDecimal tanh(java.math.BigDecimal x)
```
    The hyperbolic tangent.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    The tanh(x) = sinh(x)/cosh(x).
  - asinh
```
public static java.math.BigDecimal asinh(java.math.BigDecimal x)
```
    The inverse hyperbolic sine.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    The arcsinh(x) .
  - acosh
```
public static java.math.BigDecimal acosh(java.math.BigDecimal x)
```
    The inverse hyperbolic cosine.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    The arccosh(x) .
  - Gamma
```
public static java.math.BigDecimal Gamma(java.math.BigDecimal x)
```
    The Gamma function.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    Gamma(x).
  - pochhammer
```
public static java.math.BigDecimal pochhammer(java.math.BigDecimal x,
                                              int n)
```
    Pochhammer’s function.
    
    Parameters:
    
    x - The main argument.
    
    n - The non-negative index.
    
    Returns:
    
    (x)_n = x(x+1)(x+2)*...*(x+n-1).
  - mod2pi
```
public static java.math.BigDecimal mod2pi(java.math.BigDecimal x)
```
    Reduce value to the interval [0,2*Pi].
    
    Parameters:
    
    x - the original value
    
    Returns:
    
    the value modulo 2*pi in the interval from 0 to 2*pi.
  - modpi
```
public static java.math.BigDecimal modpi(java.math.BigDecimal x)
```
    Reduce value to the interval [-Pi/2,Pi/2].
    
    Parameters:
    
    x - The original value
    
    Returns:
    
    The value modulo pi, shifted to the interval from -Pi/2 to Pi/2.
  - zeta
```
public static java.math.BigDecimal zeta(int n,
                                        java.math.MathContext mc)
```
    Riemann zeta function.
    
    Parameters:
    
    n - The positive integer argument. 32
    
    mc - Specification of the accuracy of the result.
    
    Returns:
    
    zeta(n).
  - zeta1
```
public static double zeta1(int n)
```
    Riemann zeta function.
    
    Parameters:
    
    n - The positive integer argument.
    
    Returns:
    
    zeta(n)-1.
  - broadhurstBBP
```
protected static java.math.BigDecimal broadhurstBBP(int n,
                                                    int p,
                                                    int[] a,
                                                    java.math.MathContext mc)
```
    Broadhurst ladder sequence.
    
    Parameters:
    
    a - The vector of 8 integer arguments
    
    mc - Specification of the accuracy of the result
    
    Returns:
    
    S_(n, p)(a)
    
    See Also:
    
    width0pt\protect\href{http://arxiv.org/abs/math/9803067}{arXiv:math/9803067}
  - addRound
```
public static java.math.BigDecimal addRound(java.math.BigDecimal x,
                                            java.math.BigDecimal y)
```
    Add and round according to the larger of the two ulp’s.
    
    Parameters:
    
    x - The left summand
    
    y - The right summand
    
    Returns:
    
    The sum x+y.
  - subtractRound
```
public static java.math.BigDecimal subtractRound(java.math.BigDecimal x,
                                                 java.math.BigDecimal y)
```
    Subtract and round according to the larger of the two ulp’s.
    
    Parameters:
    
    x - The left term.
    
    y - The right term.
    
    Returns:
    
    The difference x-y.
  - multiplyRound
```
public static java.math.BigDecimal multiplyRound(java.math.BigDecimal x,
                                                 java.math.BigDecimal y)
```
    Multiply and round.
    
    Parameters:
    
    x - The left factor.
    
    y - The right factor.
    
    Returns:
    
    The product x*y.
  - multiplyRound
```
public static java.math.BigDecimal multiplyRound(java.math.BigDecimal x,
                                                 org.nd4j.linalg.util.Rational f)
```
    Multiply and round.
    
    Parameters:
    
    x - The left factor.
    
    f - The right factor.
    
    Returns:
    
    The product x*f.
  - multiplyRound
```
public static java.math.BigDecimal multiplyRound(java.math.BigDecimal x,
                                                 int n)
```
    Multiply and round.
    
    Parameters:
    
    x - The left factor.
    
    n - The right factor.
    
    Returns:
    
    The product x*n.
  - multiplyRound
```
public static java.math.BigDecimal multiplyRound(java.math.BigDecimal x,
                                                 java.math.BigInteger n)
```
    Multiply and round.
    
    Parameters:
    
    x - The left factor.
    
    n - The right factor.
    
    Returns:
    
    the product x*n
  - divideRound
```
public static java.math.BigDecimal divideRound(java.math.BigDecimal x,
                                               java.math.BigDecimal y)
```
    Divide and round.
    
    Parameters:
    
    x - The numerator
    
    y - The denominator
    
    Returns:
    
    the divided x/y
  - divideRound
```
public static java.math.BigDecimal divideRound(java.math.BigDecimal x,
                                               int n)
```
    Divide and round.
    
    Parameters:
    
    x - The numerator
    
    n - The denominator
    
    Returns:
    
    the divided x/n
  - divideRound
```
public static java.math.BigDecimal divideRound(java.math.BigDecimal x,
                                               java.math.BigInteger n)
```
    Divide and round.
    
    Parameters:
    
    x - The numerator
    
    n - The denominator
    
    Returns:
    
    the divided x/n
  - divideRound
```
public static java.math.BigDecimal divideRound(java.math.BigInteger n,
                                               java.math.BigDecimal x)
```
    Divide and round.
    
    Parameters:
    
    n - The numerator
    
    x - The denominator
    
    Returns:
    
    the divided n/x
  - divideRound
```
public static java.math.BigDecimal divideRound(int n,
                                               java.math.BigDecimal x)
```
    Divide and round.
    
    Parameters:
    
    n - The numerator.
    
    x - The denominator.
    
    Returns:
    
    the divided n/x.
  - scalePrec
```
public static java.math.BigDecimal scalePrec(java.math.BigDecimal x,
                                             int d)
```
    Append decimal zeros to the value. This returns a value which appears to have a higher precision than the input.
    
    Parameters:
    
    x - The input value
    
    d - The (positive) value of zeros to be added as least significant digits.
    
    Returns:
    
    The same value as the input but with increased (pseudo) precision.
  - scalePrec
```
public static java.math.BigDecimal scalePrec(java.math.BigDecimal x,
                                             java.math.MathContext mc)
```
    Boost the precision by appending decimal zeros to the value. This returns a value which appears to have a higher precision than the input.
    
    Parameters:
    
    x - The input value
    
    mc - The requirement on the minimum precision on return.
    
    Returns:
    
    The same value as the input but with increased (pseudo) precision.
  - err2prec
```
public static int err2prec(java.math.BigDecimal x,
                           java.math.BigDecimal xerr)
```
    Convert an absolute error to a precision.
    
    Parameters:
    
    x - The value of the variable
    
    xerr - The absolute error in the variable
    
    Returns:
    
    The number of valid digits in x. The value is rounded down, and on the pessimistic side for that reason.
  - err2prec
```
public static int err2prec(double x,
                           double xerr)
```
    Convert an absolute error to a precision.
    
    Parameters:
    
    x - The value of the variable The value returned depends only on the absolute value, not on the sign.
    
    xerr - The absolute error in the variable The value returned depends only on the absolute value, not on the sign.
    
    Returns:
    
    The number of valid digits in x. Derived from the representation x+- xerr, as if the error was represented 38 in a "half width" (half of the error bar) form. The value is rounded down, and on the pessimistic side for that reason.
  - err2prec
```
public static int err2prec(double xerr)
```
    Convert a relative error to a precision.
    
    Parameters:
    
    xerr - The relative error in the variable. The value returned depends only on the absolute value, not on the sign.
    
    Returns:
    
    The number of valid digits in x. The value is rounded down, and on the pessimistic side for that reason.
  - prec2err
```
public static double prec2err(double x,
                              int prec)
```
    Convert a precision (relative error) to an absolute error. The is the inverse functionality of err2prec().
    
    Parameters:
    
    x - The value of the variable The value returned depends only on the absolute value, not on the sign.
    
    prec - The number of valid digits of the variable.
    
    Returns:
    
    the absolute error in x. Derived from the an accuracy of one half of the ulp.

Class BigDecimalMath

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

E

PI

GAMMA

LOG2

Constructor Detail

BigDecimalMath

Method Detail

pi

gamma

sqrt

cbrt

root

hypot

hypot

exp

exp

log

log

log

pow

powRound

sin

cos

tan

cot

asin

atan

cosh

sinh

tanh

asinh

acosh

Gamma

pochhammer

mod2pi

modpi

zeta

zeta1

broadhurstBBP

addRound

subtractRound

multiplyRound

multiplyRound

multiplyRound

multiplyRound

divideRound

divideRound

divideRound

divideRound

divideRound

scalePrec

scalePrec

err2prec

err2prec

err2prec

prec2err