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breeze

numerics

package numerics

Contains several standard numerical functions as MappingUFuncs,

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Package Members

  1. package constants

    This package specifies standard numerical/scientific constants in SI units.

  2. package financial
  3. package units

Type Members

  1. 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

  1. val Inf: Double
  2. val NaN: Double
  3. def closeTo(a: Double, b: Double, relDiff: Double = 1E-4): Boolean

    closeTo for Doubles.

  4. val inf: Double
  5. val nan: Double
  6. 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.

  7. object Bessel

    Implementations of the Bessel functions, based on Numerical Recipes

  8. object Conversions

    Package for common unit conversions.

  9. object I extends ZeroPreservingUFunc

    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

  10. object IntMath

  11. object Scaling extends Scaling
  12. object abs extends ZeroPreservingUFunc
  13. object acos extends MappingUFunc
  14. object acosh extends MappingUFunc
  15. object asin extends ZeroPreservingUFunc
  16. object asinh extends ZeroPreservingUFunc
  17. object atan extends ZeroPreservingUFunc
  18. object atan2 extends MappingUFunc
  19. object atanh extends ZeroPreservingUFunc
  20. object cbrt extends ZeroPreservingUFunc
  21. object ceil extends ZeroPreservingUFunc
  22. object cos extends MappingUFunc
  23. object cosh extends MappingUFunc
  24. object digamma extends MappingUFunc

    The derivative of the log gamma function

  25. object erf extends ZeroPreservingUFunc

    An approximation to the error function

  26. object erfc extends MappingUFunc

    An approximation to the complementary error function: erfc(x) = 1 - erfc(x)

  27. object erfcinv extends MappingUFunc

    Inverse erfc

  28. object erfi extends 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

  29. object erfinv extends MappingUFunc

    Inverse erf

  30. object exp extends MappingUFunc
  31. object expm1 extends ZeroPreservingUFunc
  32. object floor extends ZeroPreservingUFunc
  33. object gammp extends 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)

  34. object gammq extends 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)

  35. object isEven extends 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.

  36. object isFinite extends MappingUFunc
  37. object isNonfinite extends ZeroPreservingUFunc
  38. object isOdd extends ZeroPreservingUFunc

    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.

  39. 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)

  40. object lgamma extends 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.

  41. object log extends MappingUFunc
  42. object log10 extends MappingUFunc
  43. object log1p extends MappingUFunc
  44. object log2 extends MappingUFunc
  45. object logI extends UFunc with MappingUFunc

    The indicator function in log space: 0.0 iff b else Double.NegativeInfinity

  46. object logit extends MappingUFunc

    The logit (inverse sigmoid) function: -log((1/x) - 1)

  47. object multidigamma extends MappingUFunc

    Multivariate Digamma

  48. object multidigammalog extends MappingUFunc

    Multivariate digamma log

  49. object multiloggamma extends MappingUFunc
  50. object nextExponent extends MappingUFunc
  51. object nextExponent10 extends MappingUFunc
  52. object nextExponent2 extends MappingUFunc
  53. object nextPower extends MappingUFunc
  54. object nextPower10 extends MappingUFunc
  55. object nextPower2 extends MappingUFunc
  56. object pow extends MappingUFunc
  57. object relu extends ZeroPreservingUFunc

    The Relu function: max(0, x)

    The Relu function: max(0, x)

    See also

    https://en.wikipedia.org/wiki/Rectifier_(neural_networks)

  58. object rint extends ZeroPreservingUFunc
  59. object round extends ZeroPreservingUFunc
  60. object sech extends MappingUFunc
  61. object sigmoid extends MappingUFunc

    The sigmoid function: 1/(1 + exp(-x))

  62. object signum extends ZeroPreservingUFunc
  63. object sin extends ZeroPreservingUFunc
  64. object sinc extends 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..

  65. object sincpi extends 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.

  66. object sinh extends ZeroPreservingUFunc
  67. object sqrt extends ZeroPreservingUFunc
  68. object step extends MappingUFunc

    The Step function: if (x > 0) 1 else 0

    The Step function: if (x > 0) 1 else 0

    See also

    https://en.wikipedia.org/wiki/Step_function

  69. object tan extends ZeroPreservingUFunc
  70. object tanh extends ZeroPreservingUFunc
  71. object toDegrees extends ZeroPreservingUFunc
  72. object toRadians extends ZeroPreservingUFunc
  73. object trigamma extends MappingUFunc

    The second derivative of the log gamma function

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