From 23eb44534daf5874802ece28eea9d381dbe7b078 Mon Sep 17 00:00:00 2001
From: Martin Reinecke
Date: Thu, 7 Mar 2019 15:10:57 +0100
Subject: [PATCH] line breaks and small adjustments
---
docs/source/volume.rst | 12 +++++++++---
1 file changed, 9 insertions(+), 3 deletions(-)
diff --git a/docs/source/volume.rst b/docs/source/volume.rst
index 8c707d3f..e12b8b19 100644
--- a/docs/source/volume.rst
+++ b/docs/source/volume.rst
@@ -166,9 +166,15 @@ NIFTy aids you in constructing your own log-likelihood by providing methods like
An integral over a :class:`~field.Field` :code:`s` can be performed by calling :code:`s.weight(1).sum()`, which is equivalent to :code:`s.integrate()`.
Volume factors are also applied automatically in the following places:
- - :class:`~operators.harmonic_operators.FFTOperator` as well as all other harmonic operators. Here the zero mode of the transformed field is the integral over the original field, thus the whole field is weighted once.
- - Some response operators, such as the :class:`~library.los_response.LOSResponse`. In this operator a line integral is discretised, so a 1-dimensional volume factor is applied.
- - In :class:`~library.correlated_fields.CorrelatedField` as well :class:`~library.correlated_fields.MfCorrelatedField` both describing fields with a smooth, a priori unknown correlation structure specified by a power spectrum. The field is multiplied by the square root of the total volume of it domain's harmonic counterpart. This ensures that the same power spectrum can be used regardless of the chosen resolution, provided the total volume of the space remains the same. It also guarantees that the power spectra in NIFTy behave according to their definition, i.e. the power of a mode :math:`s_k` is the expectation value of that mode squared, divided by the volume of its space :math:`P(k) = \left\langle s_k^2 \right\rangle / V_k`
+ - :class:`~operators.harmonic_operators.FFTOperator` as well as all other harmonic operators.
+ Here the zero mode of the transformed field is the integral over the original field, thus the whole field is weighted once.
+ - Some response operators, such as the :class:`~library.los_response.LOSResponse`.
+ In this operator a line integral is discretised, so a 1-dimensional volume factor is applied.
+ - In :class:`~library.correlated_fields.CorrelatedField` as well as :class:`~library.correlated_fields.MfCorrelatedField`.
+ Both describe fields with a smooth, a priori unknown correlation structure specified by a power spectrum.
+ The field is multiplied by the square root of the total volume of it domain's harmonic counterpart.
+ This ensures that the same power spectrum can be used regardless of the chosen resolution, provided the total volume of the space remains the same.
+ It also guarantees that the power spectra in NIFTy behave according to their definition, i.e. the power of a mode :math:`s_k` is the expectation value of that mode squared, divided by the volume of its space :math:`P(k) = \left\langle s_k^2 \right\rangle / V_k`.
Note that in contrast to some older versions of NIFTy, the dot product :code:`s.vdot(t)` of fields does **not** apply a volume factor, but instead just sums over the field components,
--
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