Minor corrections/additions to documentation.

Author: ShrinivasJC

README.md

@@ -1,6 +1,6 @@
 # FNFT: Fast Nonlinear Fourier Transforms
 
-![Version](https://img.shields.io/github/v/release/FastNFT/FNFT) [![Documentation](https://img.shields.io/badge/-documentation-informational)](https://fastnft.github.io/FNFT/) [![Build Status](https://travis-ci.org/FastNFT/FNFT.svg?branch=master)](https://travis-ci.org/FastNFT/FNFT) [![DOI](http://joss.theoj.org/papers/10.21105/joss.00597/status.svg)](https://doi.org/10.21105/joss.00597)
+[![Version](https://img.shields.io/github/v/release/FastNFT/FNFT)](https://github.com/FastNFT/FNFT/releases) [![Documentation](https://img.shields.io/badge/-documentation-informational)](https://fastnft.github.io/FNFT/) [![Build Status](https://travis-ci.org/FastNFT/FNFT.svg?branch=master)](https://travis-ci.org/FastNFT/FNFT) [![DOI](http://joss.theoj.org/papers/10.21105/joss.00597/status.svg)](https://doi.org/10.21105/joss.00597)
 
 FNFT is a software library for the numerical computation of (inverse) nonlinear Fourier transforms, which are also known as (inverse) scattering transforms. The focus of the library is on fast algorithms, but it also contains non-fast methods. FNFT is written in C and comes with a MATLAB interface. A [Python interface](https://github.com/xmhk/FNFTpy) is available separately.
 

include/fnft.h

@@ -37,7 +37,7 @@
  * The C interface is separated into a public part ("fnft_" prefix) and a private
  * part ("fnft__" prefix).
  *
- * To get start with the public part of the C interface, study the modules
+ * To get started with the public part of the C interface, study the modules
  * \ref fnft and \ref fnft_inverse, and try the examples in the examples
  * directory.
  */

include/fnft_nsep.h

@@ -189,16 +189,38 @@ fnft_nsep_opts_t fnft_nsep_default_opts();
  *      - Prins and Wahls, <a href="https://doi.org/10.1109/ICASSP.2018.8461708">&quot;Higher order exponential splittings for the fast non-linear Fourier transform of the KdV equation,&quot;</a>in Proc.ICASSP 2018, Calgary, AB, 2018, pp. 4524-4528.
  *      - Mertsching, <a href="https://doi.org/10.1002/prop.2190350704">&quot; Quasiperiodie Solutions of the Nonlinear Schrödinger Equation,&quot;</a> Fortschr. Phys. 35:519-536, 1987.
  *
+ * * The routine supports the following discretizations of type \link fnft_nse_discretization_t \endlink:
+ *       - fnft_nse_discretization_2SPLIT1A
+ *       - fnft_nse_discretization_2SPLIT1B
+ *       - fnft_nse_discretization_2SPLIT2A
+ *       - fnft_nse_discretization_2SPLIT2B
+ *       - fnft_nse_discretization_2SPLIT2S
+ *       - fnft_nse_discretization_2SPLIT2_MODAL
+ *       - fnft_nse_discretization_2SPLIT3A
+ *       - fnft_nse_discretization_2SPLIT3B
+ *       - fnft_nse_discretization_2SPLIT3S
+ *       - fnft_nse_discretization_2SPLIT4A
+ *       - fnft_nse_discretization_2SPLIT4B
+ *       - fnft_nse_discretization_2SPLIT5A
+ *       - fnft_nse_discretization_2SPLIT5B
+ *       - fnft_nse_discretization_2SPLIT6A
+ *       - fnft_nse_discretization_2SPLIT6B
+ *       - fnft_nse_discretization_2SPLIT7A
+ *       - fnft_nse_discretization_2SPLIT7B
+ *       - fnft_nse_discretization_2SPLIT8A
+ *       - fnft_nse_discretization_2SPLIT8B
+ *       - fnft_nse_discretization_4SPLIT4A
+ *
  * @param[in] D Number of samples. Has to be even.
  * @param[in] q Array of length D, contains samples \f$ q(t_n)=q(x_0, t_n) \f$,
  *  where \f$ t_n = T[0] + n*L/D \f$, where \f$L=T[1]-T[0]\f$ is the period and
  *  \f$n=0,1,\dots,D-1\f$, of the to-be-transformed signal in ascending order
  *  (i.e., \f$ q(t_0), q(t_1), \dots, q(t_{D-1}) \f$)
  * @param[in] T Array of length 2. T[0] is the position in time of the first
- *  sample. T[2] is the beginning of the next period. (The location of the last
- *  sample is thus t_{D-1}=T[1]-L/D.) It should be T[0]<T[1].
+ *  sample. T[1] is the beginning of the next period. (The location of the last
+ *  sample is thus \f$t_{D-1}=T[1]-L/D\f$.) It should be \f$T[0]<T[1]\f$.
  * @param[in] phase_shift Real scalar constant. It is the change in the phase
- * over one quasi-period, arg(q(t+L)/q(t)). For periodic signals it will be 0.
+ * over one quasi-period,\f$ arg(q(t+L)/q(t))\f$. For periodic signals it will be 0.
  * @param[in,out] K_ptr Upon entry, *K_ptr should contain the length of the array
  *  main_spec. Upon return, *K_ptr contains the number of actually detected
  *  points in the main spectrum. If the length of the array main_spec was not

matlab/mex_fnft_nsep.m

@@ -57,7 +57,7 @@
 %                    2nd degree polynomial.
 %    'quiet'        Turns off messages generated by then FNFT C library.
 %                   (To turn off the messages generated by the mex
-%                   interface functions, use Matlab's warning and error
+%                   interface functions, use MATLAB's warning and error
 %                   commands instead.)
 %
 % OUTPUTS

matlab/mex_fnft_nsev.m

@@ -22,17 +22,17 @@
 %                   desired value, a positive integer.
 %   'bsloc_fasteigen'   Use fast eigenvalue method to locate bound states.
 %                   This method is very reliable, but requires O(D^2)
-%                   flops. This input is not followed by a value.
+%                   FLOPs. This input is not followed by a value.
 %   'bsloc_newton'  Use Newton's method to locate bound states. This method
 %                   is reliable if good intial guesses for the bound states
 %                   are known. Followed by a complex row vector of K
-%                   initial guesses. It requires O(niter KD) flops.
+%                   initial guesses. It requires O(niter KD) FLOPs.
 %   'bsloc_subsamp_refine' Use a mixed method to locate bound states. First
 %                   get initial guesses for the bound states by applying
 %                   the 'fasteigen' method to a subsampled version of the
 %                   signal. Then refine using 'Newton' based on the full
 %                   signal. This method is reliable if D is not too low.
-%                   It requires O(D log^2 D + niter K D) flops if Dsub (see
+%                   It requires O(D log^2 D + niter K D) FLOPs if Dsub (see
 %                   below) is set by the algorithm. Not followed by a
 %                   value.
 %   'bsloc_niter'   Number of iterations to be carried by Newton's method.
@@ -85,7 +85,7 @@
 %   'skip_nc'       Skip computation of the norming constants.
 %   'quiet'         Turns off messages generated by then FNFT C library.
 %                   (To turn off the messages generated by the mex
-%                   interface functions, use Matlab's warning and error
+%                   interface functions, use MATLAB's warning and error
 %                   commands instead.)
 %
 % OUTPUTS

matlab/mex_fnft_nsev_inverse.m

@@ -65,7 +65,7 @@
 %                   which q(t) is given.
 %   'quiet'         Turns off messages generated by then FNFT C library.
 %                   (To turn off the messages generated by the mex
-%                   interface functions, use Matlab's warning and error
+%                   interface functions, use MATLAB's warning and error
 %                   commands instead.)
 %
 % OUTPUTS

matlab/mex_fnft_nsev_inverse_XI.m

@@ -4,7 +4,8 @@
 %   [XI xi] = MEX_FNFT_NSEV_XI(D, T, M);
 %
 % DESCRIPTION
-%   Provides an interface to the C routine fnft_nsev_inverse.
+%   Provides an interface to the function fnft_nsev_inverse_XI
+%   in the C routine fnft_nsev_inverse.
 %
 % INPUTS
 %   D               Real scalar, must be a positive power of two