feat(docs): Support MathJax && Refactor HPA, crane-scheduler

docs/assets/mathjax.js

@@ -0,0 +1,16 @@
+window.MathJax = {
+  tex: {
+    inlineMath: [["\\(", "\\)"]],
+    displayMath: [["\\[", "\\]"]],
+    processEscapes: true,
+    processEnvironments: true
+  },
+  options: {
+    ignoreHtmlClass: ".*|",
+    processHtmlClass: "arithmatex"
+  }
+};
+
+document$.subscribe(() => {
+  MathJax.typesetPromise()
+})

docs/assets/util.css

@@ -1,3 +1,7 @@
 .md-nav__title {
     display: none;
-}
+}
+
+.arithmatex {
+  font-size: 0.85rem;
+}

docs/tutorials/hpa-recommendation.md

@@ -1,6 +1,6 @@
 # HPA Recommendation
 
-Using hpa recommendations, you can find resources in the cluster that are suitable for autoscaling, and use Crane's recommended result to create an autoscaling object: [Effective HorizontalPodAutoscaler](using-time-series-prediction.md).
+Using hpa recommendations, you can find resources in the cluster that are suitable for autoscaling, and use Crane's recommended result to create an autoscaling object: [Effective HorizontalPodAutoscaler](using-effective-hpa-to-scaling-with-effectiveness.md).
 
 ## Create HPA Analytics
 
@@ -178,25 +178,40 @@ In the advising phase, one EffectiveHPA Spec is recommended using the following
 
 Principle: Use Pod P99 resource utilization to recommend hpa. Because if the application can accept this utilization over P99 time, it can be inferred as a target for elasticity.
 
-1. Get the Pod P99 usage of the past seven days by Percentile algorithm: pod_cpu_usage_p99
-2. Corresponding utilization: target_pod_CPU_utilization = pod_cpu_usage_p99 / pod_cpu_request
+1. Get the Pod P99 usage of the past seven days by Percentile algorithm: $pod\_cpu\_usage\_p99$
+2. Corresponding utilization:
+
+      $target\_pod\_CPU\_utilization = \frac{pod\_cpu\_usage\_p99}{pod\_cpu\_request}$
+
 3. To prevent over-utilization or under-utilization, target_pod_cpu_utilization needs to be less than ehpa.min-cpu-target-utilization and greater than ehpa. max-cpu-target-utilization
 
+   $ehpa.max\mbox{-}cpu\mbox{-}target\mbox{-}utilization  < target\_pod\_cpu\_utilization < ehpa.min\mbox{-}cpu\mbox{-}target\mbox{-}utilization$
+
 **Recommend minReplicas**
 
 Principle: MinReplicas are recommended for the lowest hourly workload utilization for the past seven days.
 
-1. Calculate the lowest median workload cpu usage of the past seven days: workload_cpu_usage_medium_min
-2. Corresponding replicas: minReplicas = workload_cpu_usage_medium_min / pod_cpu_request / ehpa.max-cpu-target-utilization
+1. Calculate the lowest median workload cpu usage of the past seven days: $workload\_cpu\_usage\_medium\_min$
+2. Corresponding replicas: 
+
+      $minReplicas = \frac{\mathrm{workload\_cpu\_usage\_medium\_min} }{pod\_cpu\_request \times ehpa.max-cpu-target-utilization}$
+
 3. To prevent the minReplicas being too small, the minReplicas must be greater than or equal to ehpa.default-min-replicas
 
+      $minReplicas \geq ehpa.default\mbox{-}min\mbox{-}replicas$
+
 **Recommend maxReplicas**
 
 Principle: Use workload's past and future seven days load to recommend maximum replicas.
 
-1. Calculate P95 workload CPU usage for the past seven days and the next seven days: workload_cpu_usage_p95
-2. Corresponding replicas: max_replicas_origin = workload_cpu_usage_p95 / pod_cpu_request / target_cpu_utilization
-3. To handle with the peak traffic, Magnify by a certain factor: max_replicas = max_replicas_origin * ehpa.max-replicas-factor
+1. Calculate P95 workload CPU usage for the past seven days and the next seven days: $workload\_cpu\_usage\_p95$
+2. Corresponding replicas:
+
+     $max\_replicas\_origin = \frac{\mathrm{workload\_cpu\_usage\_p95} }{pod\_cpu\_request \times target\_cpu\_utilization}$
+
+3. To handle with the peak traffic, Magnify by a certain factor: 
+
+   $max\_replicas = max\_replicas\_origin \times  ehpa.max\mbox{-}replicas\mbox{-}factor$
 
 **Recommend MetricSpec(except CpuUtilization)**
 
@@ -214,15 +229,17 @@ Principle: Use workload's past and future seven days load to recommend maximum r
 
 ## Configurations for HPA Recommendation
 
-- ehpa.deployment-min-replicas: the default value is 1，hpa recommendations are not made for workloads smaller than this value
-- ehpa.statefulset-min-replicas: the default value is 1，hpa recommendations are not made for workloads smaller than this value
-- ehpa.workload-min-replicas: the default value is 1，Workload replicas smaller than this value are not recommended for hpa.
-- ehpa.pod-min-ready-seconds: the default value is 30，specifies the number of seconds in decide whether a POD is ready.
-- ehpa.pod-available-ratio: the default value is 0.5，Workloads whose Ready pod ratio is smaller than this value are not recommended for hpa.
-- ehpa.default-min-replicas: the default value is 2，the default minimum minReplicas.
-- ehpa.max-replicas-factor: the default value is 3，the factor for calculate maxReplicas.
-- ehpa.min-cpu-usage-threshold: the default value is 10, hpa recommendations are not made for workloads smaller than this value.
-- ehpa.fluctuation-threshold: the default value is 1.5, hpa recommendations are not made for workloads smaller than this value.
-- ehpa.min-cpu-target-utilization: the default value is 30
-- ehpa.max-cpu-target-utilization: the default value is 75
-- ehpa.reference-hpa: the default value is true, which means inherits the existing HPA configuration
+| Configuration | Default Value | Description |
+| ------------- | ------------- | ----------- |
+| ehpa.deployment-min-replicas | 1 | hpa recommendations are not made for workloads smaller than this value. |
+| ehpa.statefulset-min-replicas| 1 | hpa recommendations are not made for workloads smaller than this value. |
+| ehpa.workload-min-replicas| 1 | Workload replicas smaller than this value are not recommended for hpa. |
+| ehpa.pod-min-ready-seconds| 30 | specifies the number of seconds in decide whether a POD is ready. |
+| ehpa.pod-available-ratio| 0.5 | Workloads whose Ready pod ratio is smaller than this value are not recommended for hpa. |
+| ehpa.default-min-replicas| 2 | the default minimum minReplicas.|
+| ehpa.max-replicas-factor| 3 | the factor for calculate maxReplicas. |
+| ehpa.min-cpu-usage-threshold| 10| hpa recommendations are not made for workloads smaller than this value.|
+| ehpa.fluctuation-threshold| 1.5 | hpa recommendations are not made for workloads smaller than this value.|
+| ehpa.min-cpu-target-utilization| 30 | |
+| ehpa.max-cpu-target-utilization| 75 | |
+| ehpa.reference-hpa| true | inherits the existing HPA configuration |

docs/tutorials/hpa-recommendation.zh.md

@@ -1,6 +1,6 @@
 # 弹性推荐
 
-通过弹性推荐，你可以发现集群中适合弹性的资源，并使用 Crane 推荐的弹性配置创建自动弹性器: EffectiveHPA
+通过弹性推荐，你可以发现集群中适合弹性的资源，并使用 Crane 推荐的弹性配置创建自动弹性器: [Effective HorizontalPodAutoscaler](using-effective-hpa-to-scaling-with-effectiveness.md)
 
 ## 创建弹性分析
 
@@ -178,25 +178,40 @@ status:
 
 原理: 使用 Pod P99 资源利用率推荐弹性的目标。因为如果应用可以在 P99 时间内接受这个利用率，可以推断出可作为弹性的目标。
 
- 1. 通过 Percentile 算法得到 Pod 过去七天 的 P99 使用量: pod_cpu_usage_p99
- 2. 对应的利用率：target_pod_cpu_utilization = pod_cpu_usage_p99 / pod_cpu_request
+ 1. 通过 Percentile 算法得到 Pod 过去七天 的 P99 使用量: $pod\_cpu\_usage\_p99$
+ 2. 对应的利用率:
+
+      $target\_pod\_CPU\_utilization = \frac{pod\_cpu\_usage\_p99}{pod\_cpu\_request}$
+
  3. 为了防止利用率过大或过小，target_pod_cpu_utilization 需要小于 ehpa.min-cpu-target-utilization 和大于 ehpa.max-cpu-target-utilization
 
+    $ehpa.max\mbox{-}cpu\mbox{-}target\mbox{-}utilization  < target\_pod\_cpu\_utilization < ehpa.min\mbox{-}cpu\mbox{-}target\mbox{-}utilization$
+
 **推荐 minReplicas**
 
 原理: 使用 workload 过去七天内每小时负载最低的利用率推荐 minReplicas。
 
-1. 计算过去7天 workload 每小时使用量中位数的最低值: workload_cpu_usage_medium_min
-2. 对应的最低利用率对应的副本数: minReplicas = workload_cpu_usage_medium_min / pod_cpu_request / ehpa.max-cpu-target-utilization
+1. 计算过去7天 workload 每小时使用量中位数的最低值: $workload\_cpu\_usage\_medium\_min$
+2. 对应的最低利用率对应的副本数: 
+
+     $minReplicas = \frac{\mathrm{workload\_cpu\_usage\_medium\_min} }{pod\_cpu\_request \times ehpa.max-cpu-target-utilization}$
+
 3. 为了防止 minReplicas 过小，minReplicas 需要大于等于 ehpa.default-min-replicas
 
+     $minReplicas \geq ehpa.default\mbox{-}min\mbox{-}replicas$
+
 **推荐 maxReplicas**
 
 原理: 使用 workload 过去和未来七天的负载推荐最大副本数。
 
-1. 计算过去七天和未来七天 workload cpu 使用量的 P95: workload_cpu_usage_p95
-2. 对应的副本数: max_replicas_origin = workload_cpu_usage_p95 / pod_cpu_request / target_cpu_utilization
-3. 为了应对流量洪峰，放大一定倍数: max_replicas = max_replicas_origin * ehpa.max-replicas-factor
+1. 计算过去七天和未来七天 workload cpu 使用量的 P95: $workload\_cpu\_usage\_p95$
+2. 对应的副本数:
+
+     $max\_replicas\_origin = \frac{\mathrm{workload\_cpu\_usage\_p95} }{pod\_cpu\_request \times target\_cpu\_utilization}$
+
+3. 为了应对流量洪峰，放大一定倍数:
+
+     $max\_replicas = max\_replicas\_origin \times  ehpa.max\mbox{-}replicas\mbox{-}factor$
 
 **推荐CPU以外 MetricSpec**
 
@@ -214,15 +229,17 @@ status:
 
 ## 弹性分析计算配置
 
-- ehpa.deployment-min-replicas: 默认值 1，小于该值的工作负载不做弹性推荐
-- ehpa.statefulset-min-replicas: 默认值 1，小于该值的工作负载不做弹性推荐
-- ehpa.workload-min-replicas: 默认值 1，小于该值的工作负载不做弹性推荐
-- ehpa.pod-min-ready-seconds: 默认值 30，定义了 Pod 是否 Ready 的秒数
-- ehpa.pod-available-ratio: 默认值 0.5，Ready Pod 比例小于该值的工作负载不做弹性推荐
-- ehpa.default-min-replicas: 默认值 2，最小 minReplicas
-- ehpa.max-replicas-factor: 默认值 3，计算 maxReplicas 的倍数
-- ehpa.min-cpu-usage-threshold: 默认值 10, 小于该值的工作负载不做弹性推荐
-- ehpa.fluctuation-threshold: 默认值 1.5, 小于该值的工作负载不做弹性推荐
-- ehpa.min-cpu-target-utilization: 默认值 30
-- ehpa.max-cpu-target-utilization: 默认值 75
-- ehpa.reference-hpa: 默认值 true，继承现有的 HPA 配置
+| 配置项 | 默认值 | 描述|
+| ------------- | ------------- | ----------- |
+| ehpa.deployment-min-replicas | 1 | 小于该值的工作负载不做弹性推荐 |
+| ehpa.statefulset-min-replicas| 1 | 小于该值的工作负载不做弹性推荐 |
+| ehpa.workload-min-replicas| 1 | 小于该值的工作负载不做弹性推荐 |
+| ehpa.pod-min-ready-seconds| 30 | 定义了 Pod 是否 Ready 的秒数 |
+| ehpa.pod-available-ratio| 0.5 | Ready Pod 比例小于该值的工作负载不做弹性推荐 |
+| ehpa.default-min-replicas| 2 | 最小 minReplicas |
+| ehpa.max-replicas-factor| 3 | 计算 maxReplicas 的倍数 |
+| ehpa.min-cpu-usage-threshold| 10| 小于该值的工作负载不做弹性推荐 |
+| ehpa.fluctuation-threshold| 1.5 | 小于该值的工作负载不做弹性推荐 |
+| ehpa.min-cpu-target-utilization| 30 | |
+| ehpa.max-cpu-target-utilization| 75 | |
+| ehpa.reference-hpa| true | 继承现有的 HPA 配置 |