package numerics
Contains several standard numerical functions as UFunc with MappingUFuncs,
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Type Members
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trait
Scaling extends AnyRef
Scaling utilities.
Scaling utilities.
Often, in order to avoid underflow, we can offload some of the exponent of a double into an int. To make things more efficient, we can actually share that exponent between doubles.
The scales used in this trait are in log space: they can be safely added and subtracted.
Value Members
- val Inf: Double
- val NaN: Double
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def
closeTo(a: Double, b: Double, relDiff: Double = 1E-4): Boolean
closeTo for Doubles.
- val inf: Double
- val nan: Double
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def
polyval(coefs: Array[Double], x: Double): Double
Computes the polynomial P(x) with coefficients given in the passed in array.
Computes the polynomial P(x) with coefficients given in the passed in array. coefs(i) is the coef for the x_i term.
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object
Bessel
Implementations of the Bessel functions, based on Numerical Recipes
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object
Conversions
Package for common unit conversions.
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object
I extends UFunc with ActiveMappingUFunc
The indicator function.
The indicator function. 1.0 iff b, else 0.0 For non-boolean arguments, 1.0 iff b != 0, else 0.0
- object IntMath
- object Scaling extends Scaling
- object abs extends UFunc with ActiveMappingUFunc
- object acos extends UFunc with MappingUFunc
- object acosh extends UFunc with MappingUFunc
- object asin extends UFunc with ActiveMappingUFunc
- object asinh extends UFunc with ActiveMappingUFunc
- object atan extends UFunc with ActiveMappingUFunc
- object atan2 extends UFunc with MappingUFunc
- object atanh extends UFunc with ActiveMappingUFunc
- object cbrt extends UFunc with ActiveMappingUFunc
- object ceil extends UFunc with ActiveMappingUFunc
- object cos extends UFunc with MappingUFunc
- object cosh extends UFunc with MappingUFunc
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object
digamma extends UFunc with MappingUFunc
The derivative of the log gamma function
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object
erf extends UFunc with ActiveMappingUFunc
An approximation to the error function
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object
erfc extends UFunc with MappingUFunc
An approximation to the complementary error function: erfc(x) = 1 - erfc(x)
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object
erfcinv extends UFunc with MappingUFunc
Inverse erfc
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object
erfi extends UFunc with MappingUFunc
The imaginary error function for real argument x.
The imaginary error function for real argument x.
Adapted from http://www.mathworks.com/matlabcentral/newsreader/view_thread/24120 verified against mathematica
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object
erfinv extends UFunc with MappingUFunc
Inverse erf
- object exp extends UFunc with MappingUFunc
- object expm1 extends UFunc with ActiveMappingUFunc
- object floor extends UFunc with ActiveMappingUFunc
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object
gammp extends UFunc with MappingUFunc
regularized incomplete gamma function \int_0x \exp(-t)pow(t,a-1) dt / Gamma(a)
regularized incomplete gamma function \int_0x \exp(-t)pow(t,a-1) dt / Gamma(a)
- See also
http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double)
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object
gammq extends UFunc with MappingUFunc
regularized incomplete gamma function \int_0x \exp(-t)pow(t,a-1) dt / Gamma(a)
regularized incomplete gamma function \int_0x \exp(-t)pow(t,a-1) dt / Gamma(a)
- See also
http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double)
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object
isEven extends UFunc with MappingUFunc
Whether a number is even.
Whether a number is even. For Double and Float, isEven also implies that the number is an integer, and therefore does not necessarily equal !isOdd for fractional input.
- object isFinite extends UFunc with MappingUFunc
- object isNonfinite extends UFunc with ActiveMappingUFunc
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object
isOdd extends UFunc with ActiveMappingUFunc
Whether a number is odd.
Whether a number is odd. For Double and Float, isOdd also implies that the number is an integer, and therefore does not necessarily equal !isEven for fractional input.
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object
lbeta extends UFunc
Evaluates the log of the generalized beta function.
Evaluates the log of the generalized beta function. \sum_a lgamma(c(a))- lgamma(c.sum)
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object
lgamma extends UFunc with MappingUFunc
Computes the log of the gamma function.
Computes the log of the gamma function. The two parameter version is the log Incomplete gamma function = \log \int_0x \exp(-t)pow(t,a-1) dt
- returns
an approximation of the log of the Gamma function of x.
- object log extends UFunc with MappingUFunc
- object log10 extends UFunc with MappingUFunc
- object log1p extends UFunc with MappingUFunc
- object log2 extends UFunc with MappingUFunc
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object
logI extends UFunc with MappingUFunc
The indicator function in log space: 0.0 iff b else Double.NegativeInfinity
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object
logit extends UFunc with MappingUFunc
The logit (inverse sigmoid) function: -log((1/x) - 1)
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object
multidigamma extends UFunc with MappingUFunc
Multivariate Digamma
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object
multidigammalog extends UFunc with MappingUFunc
Multivariate digamma log
- object multiloggamma extends UFunc with MappingUFunc
- object nextExponent extends UFunc with MappingUFunc
- object nextExponent10 extends UFunc with MappingUFunc
- object nextExponent2 extends UFunc with MappingUFunc
- object nextPower extends UFunc with MappingUFunc
- object nextPower10 extends UFunc with MappingUFunc
- object nextPower2 extends UFunc with MappingUFunc
- object pow extends UFunc with MappingUFunc
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object
relu extends UFunc with ActiveMappingUFunc
The Relu function: max(0, x)
The Relu function: max(0, x)
- See also
https://en.wikipedia.org/wiki/Rectifier_(neural_networks)
- object rint extends UFunc with ActiveMappingUFunc
- object round extends UFunc with ActiveMappingUFunc
- object sech extends UFunc with MappingUFunc
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object
sigmoid extends UFunc with MappingUFunc
The sigmoid function: 1/(1 + exp(-x))
- object signum extends UFunc with ActiveMappingUFunc
- object sin extends UFunc with ActiveMappingUFunc
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object
sinc extends UFunc with MappingUFunc
The sine cardinal (sinc) function, as defined by sinc(0)=1, sinc(n != 0)=sin(x)/x.
The sine cardinal (sinc) function, as defined by sinc(0)=1, sinc(n != 0)=sin(x)/x. Note that this differs from some signal analysis conventions, where sinc(n != 0) is defined by sin(Pi*x)/(Pi*x). This variant is provided for convenience as breeze.numerics.sincpi. Use it instead when translating from numpy.sinc..
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object
sincpi extends UFunc with MappingUFunc
The pi-normalized sine cardinal (sinc) function, as defined by sinc(0)=1, sinc(n != 0)=sin(Pi*x)/(Pi*x).
The pi-normalized sine cardinal (sinc) function, as defined by sinc(0)=1, sinc(n != 0)=sin(Pi*x)/(Pi*x). See also breeze.numerics.sinc.
- object sinh extends UFunc with ActiveMappingUFunc
- object sqrt extends UFunc with ActiveMappingUFunc
- object tan extends UFunc with ActiveMappingUFunc
- object tanh extends UFunc with ActiveMappingUFunc
- object toDegrees extends UFunc with ActiveMappingUFunc
- object toRadians extends UFunc with ActiveMappingUFunc
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object
trigamma extends UFunc with MappingUFunc
The second derivative of the log gamma function