update docstring to readme (#9)

* update docstring to readme

* Update Project.toml

---------

Co-authored-by: youdongguo <[email protected]>

Author: youdongguo

README.md

@@ -64,26 +64,31 @@ Here are the new components:
 
 ## Functions
 
-W, H = **gsvdnmf**(X::AbstractMatrix, ncomponents::Pair{Int,Int}; tol_final=1e-4, tol_intermediate=1e-4, kwargs...)
+W, H = **gsvdnmf**(X::AbstractMatrix, ncomponents::Pair{Int,Int}; 
+                   tol_final=1e-4, 
+                   tol_intermediate=1e-4, 
+                   kwargs...)
 
-This function performs "GSVD-NMF" on 2D data matrix ``X``.
+Perform "GSVD-NMF" on the data matrix `X`.
 
 Arguments:
 
-``X``: non-nagetive 2D data matrix
+- `X`: non-negative data matrix
 
-``ncomponents::Pair{Int,Int}``: in the form of ``n1 => n2``, augments from ``n1`` components to ``n2``components, where ``n1`` is the number of components for initial NMF (under-complete NMF), and ``n2`` is the number of components for final NMF.
+- `ncomponents`: in the form of `n1 => n2`, augments from `n1` components to `n2`components,
+  where `n1` is the number of components for initial NMF (under-complete NMF), and `n2` is the number of
+  components for final NMF.
 
-Alternatively, ``ncomponents`` can be an integer denoting the number of components for final NMF.
-In this case, ``gsvdnmf`` defaults to augment components on initial NMF solution by 1.
+Alternatively, `ncomponents` can be an integer denoting the number of components for final NMF.
+In this case, `gsvdnmf` defaults to augment components on initial NMF solution by 1.
 
 Keyword arguments:
 
-``tol_final``： The tolerence of final NMF, default:``10^{-4}``
+- `tol_final`: The tolerence of final NMF, default:`10^{-4}`
 
-``tol_intermediate``: The tolerence of initial NMF (under-complete NMF), default: $\mathrm{tol\\_final}$
+- `tol_intermediate`: The tolerence of initial NMF (under-complete NMF), default: tol_final
 
-Other keyword arguments are passed to ``NMF.nnmf``.
+Other keyword arguments are passed to `NMF.nnmf`.
 
 -----
 
@@ -92,51 +97,49 @@ W, H = **gsvdnmf**(X::AbstractMatrix, W::AbstractMatrix, H::AbstractMatrix, f;
                    tol_nmf=1e-4,
                    kwargs...)
 
-This funtion augments components for ``W`` and ``H``, and subsequently polishs new ``W`` and ``H`` by NMF.
+Augment `W` and `H` to have `n2` components, subsequently polished by NMF.
 
 Arguments:
 
-``X``: non-nagetive 2D data matrix
-
-``W``: initialization of initial NMF
+- `X`: non-negative data matrix
 
-``H``: initialization of initial NMF
+- `W` and `H`: initial NMF factorization
 
-``n2``: the number of components in augmented matrix
+- `n2`: the number of components in augmented factorization
 
-``f``: SVD (or Truncated SVD) of ``X``, ``f`` needs to be explicitly writen in ``Tuple`` form.
+- `f`: SVD (or Truncated SVD) of `X`
 
-Keyword arguments
+Keyword arguments:
 
-``tol_nmf``: the tolerance of  NMF polishing step, default: $10^{-4}$
+- `tol_nmf`: the tolerance of  NMF polishing step, default: 1e-4
 
-Other keyword arguments are passed to ``NMF.nnmf``.
+Other keyword arguments are passed to `NMF.nnmf`.
 
 -----
 
 Wadd, Hadd, S = **gsvdrecover**(X, W0, H0, kadd, f)
 
-This funtion augments components for ``W`` and ``H`` without polishing NMF step.
+Augment components for `W` and `H` without polishing by NMF.
 
 Outputs:
 
-``Wadd``: augmented NMF solution
+`Wadd`: augmented NMF solution
 
-``Hadd``: augmented NMF solution
+`Hadd`: augmented NMF solution
 
-``S``: related generalized singular value
+`S`: generalized singular values for the `kadd` augmented components
 
 Arguments:
 
-``X``: non-nagetive 2D data matrix
+`X`: non-nagetive 2D data matrix
 
-``W0``: NMF solution
+`W0`: NMF solution
 
-``H0``: NMF solution
+`H0`: NMF solution
 
-``kadd``: number of new components
+`kadd`: number of new components
 
-``f``: SVD (or Truncated SVD) of ``X``, ``f`` needs to be indexable.
+`f`: SVD (or Truncated SVD) of `X`
 
 -----