various tiny fixes on documentations

doc/sphinx/source/tutorials/polarized_fits.rst

@@ -4,15 +4,15 @@ How to run a Polarized fit
 ==========================
 
 The user should first refer to the :ref:`detailed guide <n3fit-usage>` on how to run
-a standard unpolarized PDF fit. Most of the steps in that guide are still apply
-and in the following section we only highlight the differences.
+a standard unpolarized PDF fit. Most of the steps in that guide still apply and in
+the following section we only highlight the differences.
 
 
 Preparing a runcard and running a fit
 -------------------------------------
 
 The writing of a polarized fit runcard follows exactly the guideline described
-in :ref:`Preparing a fit runcard <prepare-fits>`. The user only need to modify 
+in :ref:`Preparing a fit runcard <prepare-fits>`. The user only need to modify
 and adjust various entries.
 
 In polarized fits, the positivity of the polarized PDFs are enforced using as
@@ -30,7 +30,7 @@ constraint is enforced is defined under the key ``positivity_bound`` as follows:
 
 where ``unpolarized_bc `` specifies the name of the unpolarized PDF set to be used as a
 boundary condition while ``n_std `` specifies the shift in terms of the standard
-deviation to be applied to the PDF central values. If ``stderr=0.0`` then the
+deviation to be applied to the PDF central values. If ``n_std=0.0`` then the
 PDF central values will be used to constrain their polarized counterparts.
 
 Given that polarized fits require different fitting bases and different theory
@@ -52,46 +52,46 @@ Specifically:
 
 where ``TSR`` specifies that only sum rules on the :math:`T_3` and :math:`T_8`
 distributions are applied. If any of these values are specified differently the program will
-raise an error.
+raise an error. Note that for polarized fits, the basis has to start with ``POLARIZED_```.
 
 .. note::
 
-   While the treatment of integrability follows exactly the same concept as in the 
-   default unpolarized fits, the treatment of positivity in the polarized case 
-   requires specific treatment. Similar to the unpolarised fits, the cost function 
+   While the treatment of integrability follows exactly the same concept as in the
+   default unpolarized fits, the treatment of positivity in the polarized case
+   requires specific treatment. Similar to the unpolarized fits, the cost function
    used to enforce the positivity is defined by the following observable:
-  
+
    .. math::
      \chi_{\mathrm{tot}}^2 \rightarrow \chi_{\mathrm{tot}}^2+ \Lambda_{\rm POS} \sum_{k=1}^8 \sum_{i=1}^{n_x} \operatorname{ReLU}\left(-\mathcal{C}_k\left(x_i, Q^2\right)\right)
 
    where:
-  
+
    .. math::
      \mathrm{ReLU}(t)= \begin{cases}t & \text { if } t>0 \\ 0 & \text { if } t \leq 0\end{cases}
 
-   with :math:`n_i=20` and :math:`Q^2=5~\mathrm{GeV}^2` chosen to be the same as in the unpolarised 
-   case. In the polarized case, omitting the :math:`Q^2`-dependence, the expression of :math:`\mathcal{C}_k` 
+   with :math:`n_i=20` and :math:`Q^2=5~\mathrm{GeV}^2` chosen to be the same as in the unpolarized
+   case. In the polarized case, omitting the :math:`Q^2`-dependence, the expression of :math:`\mathcal{C}_k`
    is rather given by:
-     
+
      .. math::
        \mathcal{C}_k(x_i) = \mathcal{F}_k(x_i) + \Sigma_k(x_i) - | \Delta \mathcal{F}_k(x_i)  |
 
-   where :math:`\Sigma_k(x_i)` represents the one standard deviation error computed at 
-   :math:`x_i` for the flavour :math:`k`. :math:`\mathcal{F}_k` can be a (p)PDF of 
+   where :math:`\Sigma_k(x_i)` represents the one standard deviation error computed at
+   :math:`x_i` for the flavour :math:`k`. :math:`\mathcal{F}_k` can be a (p)PDF of
    flavour :math:`k` or the longitudinally (polarized) structure functions :math:`(k=1)`.
-   The way in which the unpolarized prediction uncertainties are accounted for during 
-   the fit is by sampling according to a normal distribution and ought to enforce the 
+   The way in which the unpolarized prediction uncertainties are accounted for during
+   the fit is by sampling according to a normal distribution and ought to enforce the
    following inequality:
-  
+
    .. math::
      \mathcal{N}_r \left( \mathcal{F}_k, \Sigma_k^2 \right) - | \Delta \mathcal{F}_k | \geq 0
 
-   where the subscript :math:`r` indicates that the random seed per replica is always 
-   different. In practice, when imposing the positivity at the level of PDFs, we enforce 
-   the constraints on the flavor combination :math:`\left( \Delta f_i + \Delta \bar{f}_i \right)`, 
+   where the subscript :math:`r` indicates that the random seed per replica is always
+   different. In practice, when imposing the positivity at the level of PDFs, we enforce
+   the constraints on the flavor combination :math:`\left( \Delta f_i + \Delta \bar{f}_i \right)`,
    that is :math:`(\Delta) \mathcal{F}_k \equiv (\Delta) f_k + (\Delta) \bar{f}_k`.
 
-Once the runcard is ready, the user can follow the guidelines :ref:`here <run-n3fit-fits>` 
+Once the runcard is ready, the user can follow the guidelines :ref:`here <run-n3fit-fits>`
 to set up and run fits.
 
 
@@ -112,11 +112,11 @@ Comparing polarized fits
 ------------------------
 
 Additionally, a specific report template should be used when comparing two polarized
-fits. This can be done by simply using the ``--use_polarized`` when using ``vp-comparefits``: 
+fits. This can be done by simply using the ``--use_polarized`` when using ``vp-comparefits``:
 
 .. code-block:: bash
 
   vp-comparefits -i --use_polarized
 
-To read in details how to compare two fits, head to the :ref:`following <compare-fits>` 
+To read in details how to compare two fits, head to the :ref:`following <compare-fits>`
 documentation.

n3fit/runcards/examples/nnpdfpol20_dis_nnlo.yaml

@@ -39,7 +39,7 @@ datacuts:
 # Define the unpolarized PDF set to be used as BC for POS
 positivity_bound:
   unpolarized_bc: NNPDF40_nnlo_pch_as_01180
-  n_stdv: 1.00 # Standard Deviation to be added as Error
+  n_std: 1.00 # Standard Deviation to be added as Error
 
 ############################################################
 theory: