Update documentation

README.md

@@ -7,24 +7,99 @@ Performance Portable Opacity and Emissivity library for simulation codes
 
 ## API
 
-singularity-opac provides a uniform API for all opacity models. The following functions are provided
-(here, `\sigma` is the frequency- and angle-dependent cross section in units of `cm^2`):
+singularity-opac provides a uniform API for all opacity models, in two forms: frequency-dependent, and frequency-averaged (Plank or Rosseland means), and separately for absorption and scattering opacities.
+
+For frequency-dependent absorption opacities, the following functions are provided
+(here, $\sigma$ is the frequency- and angle-dependent cross section in units of ${\rm cm}^2$):
+| Function              | Expression | Description            | Units   |
+| --------------------- | ---------- | ---------------------  | ------- |
+| AbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
+| AngleAveragedAbsorptionCoefficient | $\frac{1}{4 \pi}\int n \sigma d\Omega$ | Absorption coefficient averaged over solid angle | ${\rm cm}^{-1}$ |
+| EmissivityPerNuOmega | $j_{\nu} = \frac{dE}{d^3x dt d\Omega d\nu}$ | Frequency- and angle-dependent emissivity | ${\rm erg}{\rm cm}^{-3}{\rm s}^{-1}{\rm Hz}^{-1}{\rm Sr}^{-1}$ |
+| EmissivityPerNu | $\int j_{\nu} d\Omega$  | Frequency-dependent emissivity | ${\rm erg}{\rm cm}^{-3}{\rm s}^{-1}{\rm Hz}^{-1}$ |
+| Emissivity | $\int j_{\nu} d\nu d\Omega$  | Total emissivity | ${\rm erg}{\rm cm}^{-3}{\rm s}^{-1}$ |
+| NumberEmissivity | $\int \frac{1}{h \nu} j_{\nu} d\Omega d\nu$ | Total number emissivity | ${\rm cm}^{-3}{\rm s}^{-1}$ |
+| ThermalDistributionOfTNu | $B_{\nu} = \frac{dE}{dA dt d\Omega d\nu}$ | Specific intensity of thermal distribution | ${\rm erg}{\rm cm}^{-2}{\rm s}^{-1}{\rm Sr}^{-1}{\rm Hz}^{-1}$ |
+| DThermalDistributionOfTNuDT | $dB_{\nu}/dT$ | Temperature derivative of specific intensity of thermal distribution | ${\rm erg}{\rm cm}^{-2}{\rm s}^{-1}{\rm Sr}^{-1}{\rm Hz}^{-1}{\rm K}^{-1}$ |
+| ThermalDistributionOfT | $B = \int B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg}{\rm cm}^{-2}{\rm s}^{-1}$ |
+| ThermalNumberDistributionOfT | $B = \int \frac{1}{h \nu} B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg}{\rm cm}^{-2}{\rm s}^{-1}$ |
+| EnergyDensityFromTemperature | $E_{\rm R}$ | Radiation energy density | ${\rm erg}{\rm cm}^{-3}$ |
+| TemperatureFromEnergyDensity | $T_{\rm R}$ | Radiation temperature | ${\rm K}$ |
+| NumberDensityFromTemperature | $n_{\rm R}$ | Radiation number density | ${\rm cm}^{-3}$ |
+
+with the following function signatures:
+
+    AbsorptionCoefficient(density, temperature, frequency)
+    AngleAveragedAbsorptionCoefficient(density, temperature, frequency)
+    EmissivityPerNuOmega(density, temperature, frequency)
+    EmissivityPerNu(density, temperature, frequency)
+    Emissivity(density, temperature)
+    NumberEmissivity(density, temperature)
+    ThermalDistributionOfTNu(temperature, frequency)
+    DThermalDistribtuionOfTNuDT(temperature, frequency)
+    ThermalDistributionOfT(temperature)
+    ThermalNumberDistributionOfT(temperature)
+    EnergyDensityFromTemperature(temperature)
+    TemperatureFromEnergyDensity(radiation energy density)
+    NumberDensityFromTemperature(temperature)
+
+For mean absorption opacities, the following functions are provided:
+| Function              | Expression | Description            | Units   |
+| --------------------- | ---------- | ---------------------  | ------- |
+| PlankMeanAbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
+| RosselandMeanAbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
+| AbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
+| Emissivity | $\int j_{\nu} d\nu d\Omega$  | Total emissivity | ${\rm erg}{\rm cm}^{-3}{\rm s}^{-1}$ |
+
+with the following function signatures:
+
+    PlanckMeanAbsorptionCoefficient(density, temperature)
+    RosselandMeanAbsorptionCoefficient(density, temperature)
+    AbsorptionCoefficient(density, temperature, gmode [Planck, Rosseland])
+    Emissivity(density, temperature)
+
+For frequency-dependent scattering opacities, the following functions are provided
+| Function              | Expression | Description            | Units   |
+| --------------------- | ---------- | ---------------------  | ------- |
+| TotalCrossSection | $\sigma$ | Scattering cross section | ${\rm cm}^{2}$ |
+| DifferentialCrossSection | $d\sigma / d \Omega $ | Differential scattering cross section | ${\rm cm}^{2}{\rm Sr}^{-1}$ |
+| TotalScatteringCoefficient | $n \sigma $ | Scattering coefficient | ${\rm cm}^{-1}$ |
+
+with the following function signatures:
+
+    TotalCrossSection(density, temperature, frequency)
+    DifferentialCrossSection(density, temperature, frequency, cos(theta))
+    TotalScatteringCoefficient(density, temperature, frequency)
+
+For mean scattering opacities, the following functions are provided:
 | Function              | Expression | Description            | Units   |
 | --------------------- | ---------- | ---------------------  | ------- |
-| AbsorptionCoefficient | `n \sigma` | Absorption coefficient | `cm^{-1}` |
-| AngleAveragedAbsorptionCoefficient | `\frac{1}{4 \pi}\int n \sigma d\Omega` | Absorption coefficient averaged over solid angle | `cm^{-1}` |
-| EmissivityPerNuOmega | `j_{\nu} = \frac{dE}{d^3x dt d\Omega d\nu}` | Frequency- and angle-dependent emissivity | `erg cm^{-3} s^{-1} Sr^{-1} Hz^{-1}` |
-| EmissivityPerNu | `\int j_{\nu} d\Omega`  | Frequency-dependent emissivity | `erg cm^{-3} s^{-1} Hz^{-1}` |
-| Emissivity | `\int j_{\nu} d\nu d\Omega`  | Total emissivity | `erg cm^{-3} s^{-1}` |
-| NumberEmissivity | `\int \frac{1}{h \nu} j_{\nu} d\Omega d\nu` | Total number emissivity | `cm^{-3} s^{-1}` |
-| ThermalDistributionOfTNu | `B_{\nu} = \frac{dE}{dA dt d\Omega d\nu}` | Specific intensity of thermal distribution | `erg cm^{-2} s^{-1} Sr^{-1} Hz^{-1}` |
-| DThermalDistributionOfTNuDT | `dB_{\nu}/dT` | Temperature derivative of specific intensity of thermal distribution | `erg cm^{-2} s^{-1} Sr^{-1} Hz^{-1} K^{-1}` |
-| ThermalDistributionOfT | `B = \int B_{\nu} d\Omega d\nu` | Frequency- and angle-integrated intensity of thermal distribution | `erg cm^{-2} s^{-1}` |
-| ThermalNumberDistributionOfT | `B = \int \frac{1}{h \nu} B_{\nu} d\Omega d\nu` | Frequency- and angle-integrated intensity of thermal distribution | `erg cm^{-2} s^{-1}` |
+| PlanckMeanScatteringCoefficient | $n \sigma$ | Planck mean scattering coefficient | ${\rm cm}^{-1}$ |
+| RosselandMeanScatteringCoefficient | $n \sigma$ | Rosseland mean scattering coefficient | ${\rm cm}^{-1}$ |
+
+with the following function signatures:
+
+    PlanckMeanScatteringCoefficient(density, temperature)
+    RosselandMeanScatteringCoefficient(density, temperature)
 
 Note that the thermal radiation energy density `u = 1/c ThermalDistributionOfT` and the thermal radiation number density `n = 1/c ThermalNumberDistributionOfT`.
 
-Internally singularity-opac always uses CGS units, as in the above table. However, arbitrary units are supported through the units modifier.
+Opacity variant constructors are specific to the opacity model being requested; consult the source code for
+individual opacities.
+
+Internally singularity-opac always uses CGS units, as in the above table. However, arbitrary units are supported through the units modifier, which accepts
+function argument inputs in the arbitrary unit system, and returns the result from the function in those same arbitrary units. For example, a gray absorption opacity in non-cgs units specified by `time_unit`, `mass_unit`, `length_unit`, and `temp_unit` conversion factors from code to CGS units (e.g. `mass_cgs = mass_unit * mass_code`)
+is created as
+
+    photons::Opacity noncgs_opacity = photons::NonCGSUnits<photons::Gray>(
+          photons::Gray(kappa), time_unit, mass_unit, length_unit, temp_unit);
+
+Note that neutrino opacity functions also include electron fraction and RadiationType species arguments.
+
+Frequency-dependent emissition and absorption functions do not currently support angle dependence.
+
+A struct of runtime physical constants is provided for optional consistency with internal operations by the
+`GetRuntimePhysicalConstants()` method.
 
 ## To Build