add use case to readme

README.md

@@ -7,11 +7,11 @@
 
 [中文版本](README_CN.md)
 
-This is a repository for the Summer 2021 of Open Source Promotion Plan. NiSparseArrays implements operations in [SparseArrays](https://docs.julialang.org/en/v1/stdlib/SparseArrays/) in a reversible way by [NiLang](https://giggleliu.github.io/NiLang.jl/dev/). 
+This is a repository for the Summer 2021 of Open Source Promotion Plan. `NiSparseArrays` implements operations in [`SparseArrays`](https://docs.julialang.org/en/v1/stdlib/SparseArrays/) in a reversible way by [`NiLang`](https://giggleliu.github.io/NiLang.jl/dev/). 
 
 ## Background 
 
-Sparse matrices are extensively used in scientific computing, however there is no automatic differentiation package in Julia yet to handle sparse matrix operations yet. This project will utilize the reversible embedded domain-specific language NiLang.jl to differentiate sparse matrix operations by re-writing the sparse functions in Julia base in a reversible style. Furthermore, the generated backward rules would be generated to ChainRules.jl as an extension.
+Sparse matrices are extensively used in scientific computing, however there is no automatic differentiation package in Julia yet to handle sparse matrix operations yet. This project will utilize the reversible embedded domain-specific language `NiLang.jl` to differentiate sparse matrix operations by re-writing the sparse functions in Julia base in a reversible style. Furthermore, the generated backward rules would be generated to `ChainRules.jl` as an extension.
 
 ## Install 
 
@@ -40,6 +40,30 @@ pkg> add NiSparseArrays
 
 More to add in the next stage...
 
+## A Simple Using Case
+
+Here we present a minimal using case to illustrate how to use `NiSparseArrays` to speed up `Zygote`'s gradient. To access for more examples, navigate to `examples` directory.
+
+``` julia 
+julia> using SparseArrays, LinearAlgebra, Random, BenchmarkTools
+
+julia> A = sprand(1000, 1000, 0.1);
+
+julia> x = rand(1000);
+
+julia> using Zygote
+
+julia> @btime Zygote.gradient((A, x) -> sum(A*x), $A, $x)
+  15.065 ms (27 allocations: 8.42 MiB)
+
+julia> using NiSparseArrays
+
+julia> @btime Zygote.gradient((A, x) -> sum(A*x), $A, $x)
+  644.035 μs (32 allocations: 3.86 MiB)
+```
+
+You will see that using `NiSparseArrays` would not only speed up the computation process but also save much memory since our implementation keeps the original type rather than dense arrays in gradient computation. 
+
 ## Contribute 
 
 Suggestions and Comments in the Issues are welcome.

README_CN.md

@@ -7,11 +7,11 @@
 
 [英文版本](README.md)
 
-这是开源软件供应链点亮计划-暑期2021仓库。NiSparseArrays 通过[NiLang](https://giggleliu.github.io/NiLang.jl/dev/)以可逆编程地形式对 [SparseArrays](https://docs.julialang.org/en/v1/stdlib/SparseArrays/)进行实现。 
+这是开源软件供应链点亮计划-暑期2021仓库。`NiSparseArrays` 通过[`NiLang`](https://giggleliu.github.io/NiLang.jl/dev/)以可逆编程地形式对 [`SparseArrays`](https://docs.julialang.org/en/v1/stdlib/SparseArrays/)进行实现。 
 
 ## 背景
 
-稀疏矩阵在科学计算中应用广泛，但是在Julia语言里面却没有很好的软件包实现对稀疏矩阵的自动微分，这个项目将会使用可逆嵌入式语言 NiLang.jl 通过对 Julia Base 里的稀疏矩阵操作的改写实现对其自动微分。我们将会把生成的自动微分规则接入到 Julia 生态中最流行的自动微分规则库 ChainRules 中。
+稀疏矩阵在科学计算中应用广泛，但是在Julia语言里面却没有很好的软件包实现对稀疏矩阵的自动微分，这个项目将会使用可逆嵌入式语言 `NiLang.jl` 通过对 Julia Base 里的稀疏矩阵操作的改写实现对其自动微分。我们将会把生成的自动微分规则接入到 Julia 生态中最流行的自动微分规则库 ChainRules 中。
 
 ## 安装 
 
@@ -41,6 +41,30 @@ pkg> add NiSparseArrays
 
 API还在不断扩充中...
 
+## 一个简单的用例
+
+这里我们用一个最小的用例去展示如何使用`NiSparseArrays`去加速`Zygote`梯度。更多测试用例，可前往`examples`文件夹查看。
+
+``` julia 
+julia> using SparseArrays, LinearAlgebra, Random, BenchmarkTools
+
+julia> A = sprand(1000, 1000, 0.1);
+
+julia> x = rand(1000);
+
+julia> using Zygote
+
+julia> @btime Zygote.gradient((A, x) -> sum(A*x), $A, $x)
+  15.065 ms (27 allocations: 8.42 MiB)
+
+julia> using NiSparseArrays
+
+julia> @btime Zygote.gradient((A, x) -> sum(A*x), $A, $x)
+  644.035 μs (32 allocations: 3.86 MiB)
+```
+
+你会发现使用`NiSparseArrays`不仅能够加速计算过程，还能够节省内存分配——这是因为我们的实现在梯度计算的过程中能够保持类型不变，而不是像`Zygote`的原始实现将其转换为`dense array`。
+
 ## 贡献
 
 欢迎提出Issue和PR👏