R 语言 教育测评可视化 李克特量表雷达图 fmsb 包多维展示

R 语言教育测评可视化：李克特量表雷达图（fmsb 包多维展示）

在教育测评领域，李克特量表（Likert Scale）是一种常用的量化评估方法，用于衡量人们对某个主题或问题的态度、意见或感受。雷达图（Radar Chart）是一种有效的可视化工具，可以直观地展示多维数据之间的关系。本文将介绍如何使用 R 语言和 fmsb 包来创建李克特量表数据的雷达图，以实现教育测评的可视化展示。

环境准备

在开始之前，请确保您的 R 环境中已安装以下包：

R
install.packages("fmsb")
install.packages("ggplot2")
install.packages("dplyr")


数据准备

我们需要准备一些李克特量表的数据。以下是一个简单的示例数据框，包含学生的姓名和他们在不同问题上的李克特量表评分。

R
library(dplyr)

创建示例数据
data <- data.frame(
Name = c("Alice", "Bob", "Charlie", "David"),
Q1 = c(5, 4, 3, 2),
Q2 = c(4, 5, 2, 3),
Q3 = c(3, 2, 5, 4),
Q4 = c(2, 3, 4, 5)
)

添加总分列
data$Total <- rowSums(data[, -1])

添加问题标签
colnames(data) <- c("Name", "Q1", "Q2", "Q3", "Q4", "Total", "Q1 Label", "Q2 Label", "Q3 Label", "Q4 Label")
data$Q1 Label <- rep("Q1", nrow(data))
data$Q2 Label <- rep("Q2", nrow(data))
data$Q3 Label <- rep("Q3", nrow(data))
data$Q4 Label <- rep("Q4", nrow(data))

打印数据
print(data)


创建雷达图

接下来，我们将使用 fmsb 包中的 `radar()` 函数来创建雷达图。我们需要定义雷达图的参数，包括数据框、问题标签、颜色、标题等。

```R
library(fmsb)

定义雷达图参数
radar_params <- list(
data = data,
labels = c("Q1 Label", "Q2 Label", "Q3 Label", "Q4 Label"),
color = "blue",
title = "Educational Assessment Radar Chart",
title.size = 1.5,
title.position = "top",
legend.title = "Students",
legend.position = "right",
legend.size = 0.8,
angle = 45,
angle.labels = TRUE,
angle.labels.size = 0.8,
angle.labels.position = "right",
angle.labels.angle = 90,
angle.labels.offset = 0.5,
angle.labels.color = "black",
angle.labels.font = "bold",
angle.labels.hjust = 0.5,
angle.labels.vjust = 0.5,
angle.labels.box.padding = 0.5,
angle.labels.box.size = 0.5,
angle.labels.box.border = TRUE,
angle.labels.box.border.color = "black",
angle.labels.box.border.size = 0.5,
angle.labels.box.fill = "white",
angle.labels.box.fill.color = "white",
angle.labels.box.fill.alpha = 1,
angle.labels.box.fill.alpha.color = "white",
angle.labels.box.fill.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.color = "white",
angle.labels.box.fill.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha.alpha = 1,
angle_labels_box_fill_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha_alpha