Update README.md based on the reviews

README.md

@@ -4,10 +4,8 @@
 
 UNOFFICIAL FFT interfaces for Kokkos C++ Performance Portability Programming EcoSystem
 
-KokkosFFT implements local interfaces Kokkos and de facto standard FFT libraries, including [fftw](http://www.fftw.org), [cufft](https://developer.nvidia.com/cufft) and [hipfft](https://github.com/ROCm/hipFFT). 
-"Local" means not using MPI, or running within a
-single MPI process without knowing about MPI. We are inclined to implement the [numpy.fft](https://numpy.org/doc/stable/reference/routines.fft.html)-like interfaces adapted for [Kokkos](https://github.com/kokkos/kokkos). 
-A key concept is that "As easy as numpy, as fast as vendor libraries". Accordingly, our API follows the API by [numpy.fft](https://numpy.org/doc/stable/reference/routines.fft.html) with minor differences. If something is wrong with runtime values (say ```View``` extents), it will raise runtime errors (C++ exceptions or assertions). Here is the example for 1D real to complex transform with ```rfft``` in python and KokkosFFT.
+KokkosFFT implements local interfaces Kokkos and de facto standard FFT libraries, including [fftw](http://www.fftw.org), [cufft](https://developer.nvidia.com/cufft) and [hipfft](https://github.com/ROCm/hipFFT). "Local" means not using MPI, or running within a single MPI process without knowing about MPI. We are inclined to implement the [numpy.fft](https://numpy.org/doc/stable/reference/routines.fft.html)-like interfaces adapted for [Kokkos](https://github.com/kokkos/kokkos).
+A key concept is that "As easy as numpy, as fast as vendor libraries". Accordingly, our API follows the API by [numpy.fft](https://numpy.org/doc/stable/reference/routines.fft.html) with minor differences. A fft library dedicated to Kokkos Device backend (e.g. [cufft](https://developer.nvidia.com/cufft) for CUDA backend) is automatically used. If something is wrong with runtime values (say `View` extents), it will raise runtime errors (C++ exceptions or assertions). Here is an example for 1D real to complex transform with `rfft` in python and KokkosFFT.
 ```python3
 import numpy as np
 x = np.random.rand(4)
@@ -33,9 +31,9 @@ Kokkos::fence();
 KokkosFFT::rfft(execution_space(), x, x_hat);
 ```
 
-There are two major differences: [```execution_space```](https://kokkos.org/kokkos-core-wiki/API/core/execution_spaces.html) argument and output value (```x_hat```) is an argument of API (not returned from API). As imagined, KokkosFFT only accepts [Kokkos Views](https://kokkos.org/kokkos-core-wiki/API/core/View.html) as input data. The accessibilities of Views from ```execution_space``` is statically checked (compilation errors if not accessible). 
+There are two major differences: [`execution_space`](https://kokkos.org/kokkos-core-wiki/API/core/execution_spaces.html) argument and output value (`x_hat`) is an argument of API (not returned value from API). As imagined, KokkosFFT only accepts [Kokkos Views](https://kokkos.org/kokkos-core-wiki/API/core/View.html) as input data. The accessibilities of Views from `execution_space` are statically checked (compilation errors if not accessible).
 
-Depending on the View dimension, it automatically uses the batched plans as follows
+Depending on a View dimension, it automatically uses the batched plans as follows
 ```python3
 import numpy as np
 x = np.random.rand(4, 8)
@@ -62,10 +60,10 @@ int axis = -1;
 KokkosFFT::rfft(execution_space(), x, x_hat, KokkosFFT::FFT_Normalization::BACKWARD, axis); // FFT along -1 axis and batched along 0th axis
 ```
 
-In this example, the 1D batched ```rfft``` over 2D View along ```axis -1``` is executed. Some basic examples are found in [examples](https://github.com/CExA-project/kokkos-fft/tree/main/examples).
+In this example, the 1D batched `rfft` over 2D View along `axis -1` is executed. Some basic examples are found in [examples](https://github.com/CExA-project/kokkos-fft/tree/main/examples).
 
 ## Disclaimer
-KokkosFFT is under development and subject to change without warning. The authors do not guarantee that this code runs correctly in all the environments.
+**KokkosFFT is under development and subject to change without warning. The authors do not guarantee that this code runs correctly in all the environments.**
 
 ## Using KokkosFFT
 For the moment, there are two ways to use KokkosFFT: including as a subdirectory in CMake project or installing as a library. First of all, you need to clone this repo.
@@ -74,8 +72,9 @@ git clone --recursive https://github.com/CExA-project/kokkos-fft.git
 ```
 
 ### CMake
-Since KokkosFFT is a header-only library, it is enough to simply add as a subdirectory. It is assumed that kokkos and kokkosFFT are placed under ```<project_directory>/tpls```.
-Here is an example to use KokkosFFT in the following CMake project. 
+Since KokkosFFT is a header-only library, it is enough to simply add as a subdirectory. It is assumed that kokkos and kokkosFFT are placed under `<project_directory>/tpls`.
+
+Here is an example to use KokkosFFT in the following CMake project.
 ```
 ---/
  |
@@ -87,10 +86,10 @@ Here is an example to use KokkosFFT in the following CMake project.
     └──hello.cpp
 ```
 
-The ```CMakeLists.txt``` would be 
+The `CMakeLists.txt` would be
 ```CMake
 cmake_minimum_required(VERSION 3.23)
-project(kokkos-fft LANGUAGES CXX)
+project(kokkos-fft-as-subdirectory LANGUAGES CXX)
 
 add_subdirectory(tpls/kokkos)
 add_subdirectory(tpls/kokkos-fft)
@@ -99,7 +98,7 @@ add_executable(hello-kokkos-fft hello.cpp)
 target_link_libraries(hello-kokkos-fft PUBLIC Kokkos::kokkos KokkosFFT::fft)
 ```
 
-For the compilation, we basically rely on the CMake options for Kokkos. For example, the configure options for A100 GPU is as follows.
+For compilation, we basically rely on the CMake options for Kokkos. For example, the configure options for A100 GPU is as follows.
 ```
 cmake -DBUILD_TESTING=ON \
       -DCMAKE_CXX_COMPILER=<project_directory>/tpls/kokkos/bin/nvcc_wrapper \
@@ -112,7 +111,7 @@ cmake -DBUILD_TESTING=ON \
 This way, all the functionalities are executed on A100 GPUs.
 
 ### Install as a library
-Is is assumed that the Kokkos is installed under ```<lib_dir>/kokkos``` targeting Icelake with OpenMP backend. ```Kokkos_dir``` also needs to be set appropriately. Here is a recipe to install KokkosFFT under ```<lib_dir>/kokkosFFT```.
+Is is assumed that the Kokkos is installed under `<install_dir>/kokkos` with OpenMP backend. Here is a recipe to install KokkosFFT under `<install_dir>/kokkos_fft`.
 
 ```bash
 export KOKKOSFFT_INSTALL_PREFIX=<lib_dir>/kokkosFFT
@@ -121,14 +120,12 @@ export KokkosFFT_DIR=<lib_dir>/kokkosFFT/lib64/cmake/kokkos-fft
 mkdir build_KokkosFFT && cd build_KokkosFFT
 cmake -DBUILD_TESTING=OFF \
       -DCMAKE_CXX_COMPILER=icpx \
-      -DKokkos_ENABLE_OPENMP=ON \
-      -DKokkos_ARCH_SKX=ON \
       -DCMAKE_INSTALL_PREFIX=${KOKKOSFFT_INSTALL_PREFIX} ..
 cmake --build . -j 8
 cmake --install .
 ```
 
-Here is an example to use KokkosFFT in the following CMake project. 
+Here is an example to use KokkosFFT in the following CMake project.
 ```
 ---/
  |
@@ -137,10 +134,10 @@ Here is an example to use KokkosFFT in the following CMake project.
     └──hello.cpp
 ```
 
-The ```CMakeLists.txt``` would be 
+The `CMakeLists.txt` would be
 ```CMake
 cmake_minimum_required(VERSION 3.23)
-project(kokkos-fft LANGUAGES CXX)
+project(kokkos-fft-as-library LANGUAGES CXX)
 
 find_package(Kokkos CONFIG REQUIRED)
 find_package(KokkosFFT CONFIG REQUIRED)
@@ -151,17 +148,11 @@ target_link_libraries(hello-kokkos-fft PUBLIC Kokkos::kokkos KokkosFFT::fft)
 
 The code can be built as
 ```bash
-export KOKKOSFFT_INSTALL_PREFIX=<lib_dir>/kokkosFFT
-export KokkosFFT_DIR=<lib_dir>/kokkosFFT/lib64/cmake/kokkos-fft
-
 mkdir build && cd build
-cmake -DCMAKE_CXX_COMPILER=icpx \
-      -DCMAKE_BUILD_TYPE=Release \
-      -DKokkos_ENABLE_OPENMP=ON \
-      -DKokkos_ARCH_SKX=ON ..
+cmake -DCMAKE_PREFIX_PATH="<install_dir>/kokkos;<install_dir>/kokkos_fft" ..
 cmake --build . -j 8
 ```
 
 ## LICENCE
 [![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)  
-KokkosFFT is licensed under the MIT License.
+KokkosFFT is licensed under the MIT License.