OBT.Maths

A library for Maths of all kinds, WIP.

1. Maths

• Extension Methods
• Constants
• Physics Constants

2. MathsF

Maths

Static class so it can be accessed anywhere in your solution.

Extension Methods

Extension methods for conversion between float, double, and decimal types. Standard value.ToType() usage. Most constants are stored as a decimal, so these extension methods make it shorter to code the return type you want.

• decimal.ToDouble()
• float.ToDouble()
• decimal.ToFloat()
• double.ToFloat()
• double.ToDecimal()
• float.ToDecimal()

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Constants

Constants not found in the standard Math or Mathf libraries, stored as decimal for high precision.

Constant Name	Symbol	Constant Name	Symbol
1. Glaisher-Kinkelin	_A_GlaisherKinkelin	15. Lieb's Square Ice	_Lieb
2. Mills'	_A_Mills	16. Meissel-Mertens	_M
3. Feigenbaum Alpha	_α	17. Ramanujan-Soldner	_μ
4. Backhouse's	_B	18. Omega	_Ω
5. Landau-Ramanujan	_b	19. Universal Parabolic	_P
6. Cahen's	_C_Cahen	20. Pi	_π
7. Porter's	_C_Porter	21. Phi	_Φ
8. Feigenbaum Delta	_δ	22. Inverse Golden Ratio	_φ
9. Erdős–Borwein	_E	23. Reciprocal Fibonacci	_ψ
10. Catalan	_G	24. Plastic Number	_ρ
11. Euler-Mascheroni	_γ	25. √2	_Root2
12. Conway's	_λ_Conway	26. √3	_Root3
13. Golomb-Dickman	_λ_GolombDickman	27. √5	_Root5
14. Khinchin's	_L	28. Apéry’s	_ζ3

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Physics Constants

Physics constants, stored as decimal for high precision, excepting Planck Temperature and Planck Time, which use float since the Exponent values are so large. Pulled from the NIST-accepted values, most of the good ones are here.

Constant Name	Symbol
1. Absolute Zero, Celsius	AbsZero_C
2. Absolute Zero, Fahrenheit	AbsZero_F
3. Absolute Entropy, STP	AbsoluteEntropy_STP
4. Absolute Entropy, 1 Atm	AbsoluteEntropy_Atm
5. Angstrom Star	AngstromStar
6. Atomic Mass	AtomicMass_mu
7. Avogadro's Number	Avogadro_NA
8. Bohr Magneton	BohrMagneton_μB
9. Bohr Magneton	BohrMagnetonIneVPerT_μB
10. Bohr Radius	BohrRadius_a0
11. Boltzmann	Boltzmann_kB
12. Classical Electron Radius	ClassicalElectronRadius_re
13. Conductance Quantum	ConductanceQuantum_G0
14. Conductance Quantum (e^2/Joule)	ConductanceQuantumIneSquaredPerJoule_G0
15. Coulomb	Coulomb_ke
16. Deuteron Mass	DeuteronMass_md
17. Efimov Factor	EfimovFactor_
18. Electron G Factor	ElectronGFactor_ge
19. Electron Magnetic Moment	ElectronMagneticMoment_μe
20. Electron Mass	ElectronMass_me
21. Electron-Proton Mass Ratio	ElectronProtonMassRatio_memp
22. Electron-Neutron Mass Ratio	ElectronNeutronMassRatio_memn
23. Elementary Charge	ElementaryCharge_e
24. Faraday Constant	Faraday_F
25. Fermi Coupling Constant	FermiCoupling_GF
26. Fine Structure Constant	FineStructure_α
27. First Radiation Constant	FirstRadiation_c1
28. First Radiation Constant (Spectral)	FirstRadiationSpectral_c1L
29. Gravitational Constant	Gravitational_G
30. Hartree Energy	HartreeEnergy_Eh
31. Hydrogen Mass	HydrogenMass_mH
32. Hyperfine Transition Frequency Cs133	HyperfineTransitionFrequencyCesium133_ΔνCs
33. Inverse Conductance Quantum	InverseConductanceQuantum_G0Inv
34. Inverse Fine Structure Constant	InverseFineStructure_αInv
35. Josephson Constant	Josephson_KJ
36. Loschmidt Constant	Loschmidt_n0
37. Luminous Efficacy (Ideal Source)	LuminousEfficacy_Kcd
38. Magnetic Flux Quantum	MagneticFluxQuantum_Φ0
39. Magnetic Flux Quantum (e^2/Joule)	MagneticFluxQuantumIneSquaredPerJoule_Φ0
40. Magnetic Moment of Electron	MagneticMomentOfElectron_μe
41. Magnetic Moment of Neutron	MagneticMomentOfNeutron_μn
42. Magnetic Moment of Proton	MagneticMomentOfProton_μp
43. Molar Gas Constant	MolarGas_R
44. Molar Mass	MolarMass_Mu
45. Molar Mass Of Carbon-12	MolarMassOfCarbon12_M12C
46. Molar Planck Constant	MolarPlanck_NAh
47. Muon Compton Wavelength	MuonComptonWavelength_λCμ
48. Muon Electron Mass Ratio	MuonElectronMassRatio_mμme
49. Muon Magnetic Moment	MuonMagneticMoment_μμ
50. Muon Mass	MuonMass_mμ
51. Muon Mass Energy Equivalent	MuonMassEnergyEquivalent_mμc2
52. Muon Mass Inu	MuonMassInu_mμu
53. Muon Molar Mass	MuonMolarMass_Mμ
54. Molar Volume Of Ideal Gas (Atm)	MolarVolumeOfIdealGas_Vm_Atm
55. Molar Volume Of Ideal Gas (STP)	MolarVolumeOfIdealGas_Vm_STP
56. Muon Proton Mass Ratio	MuonProtonMassRatio_mμmp
57. Neutron Electron Mass Ratio	NeutronElectronMassRatio_mnme
58. Neutron Magnetic Moment	NeutronMagneticMoment_μn
59. Neutron Proton Mass Ratio	NeutronProtonMassRatio_mnmp
60. Neutron Mass	NeutronMass_mn
61. Nuclear Magneton	NuclearMagneton_μN
62. Planck Constant	Planck_h
63. Planck Constant Reduced	PlanckReduced_ħ
64. Planck Length	PlanckLength_lP
65. Planck Mass	PlanckMass_mP
66. Planck Temperature	PlanckTemperature_TP
67. Planck Time	PlanckTime_tP
68. Proton Electron Mass Ratio	ProtonElectronMassRatio_mpme
69. Proton Mass	ProtonMass_mp
70. Proton Neutron Mass Ratio	ProtonNeutronMassRatio_mpmn
71. Proton Magnetic Moment	ProtonMagneticMoment_μp
72. Quantum Of Circulation	QuantumOfCirculation_Γ
73. Rydberg Constant	Rydberg_Rꚙ
74. Rydberg Constant Times C in Hz	RydbergTimesCinHz_Rꚙc
75. Rydberg Energy Equivalent	RydbergEnergyEquivalent_Rꚙhc
76. Rydberg Energy Equivalent in eV	RydbergEnergyEquivalentIneV_Rꚙhc
77. Second Radiation Constant	SecondRadiation_c2
78. Speed Of Light	SpeedOfLight_c
79. Standard Atmosphere	StandardAtmosphere_atm
80. Standard State Pressure	StandardStatePressure_Pa
81. Stefan Boltzmann Constant	StefanBoltzmannConstant_σ
82. Vacuum Impedance	VacuumImpedance_Z0
83. Vacuum Permeability	VacuumPermeability_μ0
84. Vacuum Permittivity	VacuumPermittivity_ε0
85. Von Klitzing Constant	VonKlitzingConstant_RK
86. Weak Mixing Angle	WeakMixingAngle_θW
87. Wien Displacement Constant	WienDisplacement_b

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MathsF

Library of Maths functions. Static class so it can be accessed anywhere in your solution. Most functions can return float, decimal and double.

• Derivative()

• PartialDerivative()

• Sqrt() - Custom method for Decimal Square Root. Others use standard libraries.

• Log() - Custom method for Decimal Natural Log.

• LogN() - Custom method for Decimal Log(n).

• Log10() - Custom method for Decimal Log10.

• Log2() - Custom method for Decimal Log2.

• Sigmoid()

• SigmoidMultivariate()

• Logit()

• LogitMultivariate()

• ReLU()

• ReLUMultivariate()

• LeakyReLU()

• LeakyReLUMultivariate()

• Tanh()

• TanhMultivariate()

• Softmax()

• MeanSquaredError()

• MeanBiasError()

• MeanAbsoluteError()

• CrossEntropyError()

• HingeLoss()

• HuberLoss()

• KullbackLieblerDivergence()

• LogCoshLoss()

• PoissonLoss()

• QuantileLoss()

• RootMeanSquareError()

• TripletLoss()

• CalculateLucasNumber()

• GetFibonacciNumber()

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MathsFourier

Library of functions related to Fast Fourier Transforms, frequency domain functions, methods of visualizing.

• TextureGraph2D()

• FrequencyToMel()

• InverseMelScale()

• DiscreteCosineTransform()

• CalculateMFCC()

• CalculateMelFilterBank()

• ApplyMFCCFilterBank()

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