Matplotlib decision tree. However, we haven't yet put aside a validation set.

e. pyplot as plt. data, breast_cancer. from networkx. meshgrid to do this. drawing. It works by splitting the data into subsets based on the values of the input features. You can pass axe to tree. balanced_tree(2, 5) pos = graphviz_layout(T, prog="twopi") nx. I had the same problem recently and the only way I found is by trying diffent figure size (it can still be bluery with big figure. To plot Desicion boundaries you need to make a meshgrid. Fortunately it's a well-studied field, particularly for SVM machine learning. plot_tree without relying on the dot library which is a hard-to-install dependency which we will cover later on in the blog post. 3, random_state=20) from sklearn. plot_tree(sometree) plt. nx_pydot import graphviz_layout. Mar 10, 2014 · Your question is more complicated than a simple plot : you need to draw the contour which will maximize the inter-class distance. from_estimator(classifier, X, response_method May 15, 2024 · Visualize Decision Tree: Create a figure with specified size using plt. As we can see below, it’s an up-side-down tree with root at the top, and leaves at the bottom of the tree. The resulting plot places the decision tree partial dependence curves in the first row of the multi-layer perceptron in the second row. Visualizing decision trees is a tremendous aid when learning how these models work and when interpreting models. datasets import load_boston. Blind source separation using FastICA; Comparison of LDA and PCA 2D Aug 15, 2019 · import networkx as nx. from sklearn. load_iris #. However, as the documentation suggested, we need to define the grid of points Xof yin the feature space. The data file is located where you save the model/ data/. It also generates corresponding feature labels. I use scikit-learn's confusion matrix method for computing the confusion matrix. My motivation: I like to plot decision trees in tutorials, and I'd like the readers of my book to plot decision trees. In this tutorial, you discovered how to plot a decision surface for a classification machine learning algorithm. Steps to Calculate Gini impurity for a split. export_graphviz Aug 19, 2020 · Generating decision surface. """. This method is compelling in data science for its clarity in decision-making and interpretability. It creates a model in the shape of a tree structure, with each internal node standing in for a “decision” based on a feature, each branch for the decision’s result, and each leaf node for a regression value or class label. Axes with decision boundary. sometree = . decision_boundaries () that illustrates one and two-dimensional feature space for classifiers, including colors that represent probabilities, decision boundaries, and misclassified entities. Can you try it like this? # Visualizing a Decision Tree using a Classifier (discrete variables, labels, etc. predict(test) dotfile = StringIO. ipynb <-- Notebook sample from Mac. fit(train, target) # Test classifier with other, unknown feature vector test = [2,2,3] predicted = dectree. It happens like this: The DT is trained. datasets import load_iris #update. 5) and with a fair amount of free time. fit(X,iris. figsize'] = (10. Text Representation of the tree. subplots(2, 1, figsize=(10, 10)) tree_disp. fit (breast_cancer. And without anaconda it's near-impossible. At least on windows matplotlib (which is used to show the tree with tree. Plots a ete3. Aug 16, 2017 · 1. The algorithm recursively splits the data until it reaches a point where the data in each subset belongs to the same class It continues the process until it reaches the leaf node of the tree. You can probably plot a similar graph by executing something like this, assuming that you have imported other necessary dependencies: Decision trees are extremely intuitive ways to classify or label objects - you simply ask a series of questions designed to zero-in on the classification. However, we haven't yet put aside a validation set. tree. Below is a snapshot of my Jupyter Notebook and what I see: Aug 18, 2018 · (Equivalently you can use matplotlib to show images). If you want, you can use the ax parameter to plot onto a specified axes object instead; in the below example you don't really need to call the figure and axes lines, but it might be helpful depending on how you end up decorating the plot. The maximum is given by the number of instances in the training set. Classes. getvalue Dec 21, 2021 · Welcome to this crazy world of data analytics. Axe object on which the tree will be painted. Script File: Loads, normalises, and organises the Iris dataset from Sklearn package. drop ('Outcome', axis=1) y = df_cleaned ['Outcome'] # Initialize the Decision Tree Classifier with max_depth=3 for simplification dt Jul 2, 2024 · A decision tree classifier is a well-liked and adaptable machine learning approach for classification applications. But in this case I do not know how to proceed. pyplot as plt #update. Our training set has 9568 instances, so the maximum value is 9568. plot decision boundary matplotlib. 0 (roughly May 2019), Decision Trees can now be plotted with matplotlib using scikit-learn’s tree. First of all, visualizations is the Text Representation which as the name says is the Textual Representation of the Decision Tree. import pandas as pd. %matplotlib inline. The simplest idea is to plot contour plot of the decision function. The Decision Tree algorithm is a hierarchical tree-based algorithm that is used to classify or predict outcomes based on a set of rules. Confusion matrix. meshgrid requires min and max values of X and Y and a meshstep size parameter. First, import export_text: from sklearn. I prefer Jupyter Lab due to its interactive features. Plot Decision Tree with dtreeviz Package. Apr 8, 2024 · The decision tree again edges out logistic regression with a higher AUC measurement at 0. clf = DecisionTreeClassifier (max_depth=3) #max_depth is maximum number of levels in the tree. If plot_method is ‘contour’ or ‘contourf’, surface_ is a QuadContourSet. T. import pydot. plot(ax=ax1) ax1. For which the code is as below: import pandas as pd. Set filled=True to fill the decision tree nodes with colors representing majority class. subplots(nrows=5, ncols=2) ax = ax. import numpy as np. 1. DecisionTreeClassifier(criterion='gini This function will get the graph to show up in Jupyter notebooks: # Imports from sklearn. import graphviz. graph_from_dot_data(dot_data. Plot the decision surface of a decision tree trained on pairs of features of the iris dataset. T = nx. model1 = LogisticRegression() m Apr 19, 2023 · Plot Decision Boundaries Using Python and Scikit-Learn. tree import DecisionTreeClassifier, export_graphviz from sklearn. See decision tree for more information on the estimator. Dec 15, 2023 · Getting Started with Decision Trees. The diagonal elements represent the number of points for which the predicted label is equal to the true label, while off-diagonal elements are those that are mislabeled by the classifier. plot_tree into red and blue. Feb 4, 2020 · The plot in the image you posted was most likely created with the matplotlib. figure (figsize= (12, 8)). plot_tree with large figsize and set larger fontsize like below: (I can't run your code then I send an example) from sklearn. Hyper-parameters get tuned (unsatisfactorily). I want to visualize each of the Decision Tree in the Random Forest. A picture or graph is always a great way to visualize our metrics. 6. Aug 26, 2020 · Plot the decision surface of a decision tree on the iris dataset, sklearn example. The following also works fine: from sklearn. savefig("temp. tree_ also stores the entire binary tree structure, represented as a Apr 25, 2024 · use matplotlib to draw phylogenetic trees from ETE3. If you do ha Dec 21, 2021 · Many matplotlib functions follow the color cycler to assign default colors, but that doesn't seem to apply here. Natural overfitting presents. plot_tree method (matplotlib needed) plot with sklearn. Jul 25, 2021 · I'm new to matplotlib and I'm trying to plot my decision tree that was built from scratch (not with sklearn) so it's basically a Node object with left, right and other identification variables which was built recursively. The iris dataset is a classic and very easy multi-class classification dataset. tree import export_graphviz # Export as dot file Nov 28, 2023 · Introduction. iris = load_iris() X = iris. Let's start by loading a simple sample dataset from sci-kit-learn - the or write a custom (decision) tree visualization, which is 1000x easier than plotting generic graphs. target) disp = DecisionBoundaryDisplay. from_estimator: # Assuming there are 10 classifiers fig, ax = plt. Decision Tree for Classification. tree import DecisionTreeClassifier matplotlib. Jul 12, 2018 · The SVM-Decision-Boundary-Animator GitHub repo animates the SVM Decision Boundary Hyperplane on the Iris data using matplotlib. They are also the fundamental components of Random Forests, which is one of the Nov 22, 2023 · Among the trees (photo by author) Decision trees (DT) get ditched much too soon. If plot_method is ‘pcolormesh’, surface_ is a QuadMesh. Make a graph in pydot from decision tree in sklearn Python. Specifically, you learned: Decision surface is a diagnostic tool for understanding how a classification algorithm divides up the feature space. Decision trees are the fundamental building block of gradient boosting machines and Random Forests(tm), probably the two most popular machine learning models for structured data. Khác với những thuật toán khác trong học có giám sát, mô hình cây quyết định Jun 11, 2022 · plot_tree plots on the current matplotlib. Aug 21, 2019 · 0. Let’s create the ROC chart which will illustrate both the tradeoff of true positives and false positives and show the AUC for both models. clf = tree. figure to control the size of the rendering. # Load the Iris dataset. Apr 15, 2020 · How to Visualize Decision Trees using Matplotlib As of scikit-learn version 21. Custom handles (i. plt. matplotlib provides a handy function called contour(), which can insert the colors between points. # Display in jupyter notebook from IPython. In this post, we'll look at how to visualize and interpret individual trees from an XGBoost model. load_iris(*, return_X_y=False, as_frame=False) [source] #. target) The decision plot transforms the three-dimensional SHAP interaction structure to a standard two-dimensional SHAP matrix. Decision trees are versatile machine learning algorithm capable of performing both regression and classification task and even work in case of tasks which has multiple outputs. externals. plot'tree method to visualize the decision tree by using matplotlib instead of relying on the dot library that is difficult to install. datasets import load_iris iris = load_iris() # Model (can also use single decision tree) from sklearn. 0, 8. 1. figure(dpi=200) tree. The following approach loops through the generated annotation texts (artists) and the clf tree structure to assign colors depending on the majority class and the impurity (gini). plot_tree(model, num_trees=4, ax=ax) plt. Finally, the tree is replaced with Random Forest. figure(figsize=(50,30)) artists = sklearn. rcParams['figure. Tree-plots in Python How to make interactive tree-plot in Python with Plotly. data. It is sometimes prudent to make the minimal values a bit lower then the minimal value of x and y and the max value a bit higher. Aug 26, 2019 · To display the trees, we have to use the plot_tree function provided by XGBoost. While that may be a quick win for performance, the replacement prioritizes a “black box The decision classifier has an attribute called tree_ which allows access to low level attributes such as node_count, the total number of nodes, and max_depth, the maximal depth of the tree. Note: Both the classification and regression tasks were executed in a Jupyter iPython Notebook. Decision boundary is generally much more complex then just a line, and so (in 2d dimensional case) it is better to use the code for generic case, which will also work well with linear classifiers. target. y = iris. The sample counts that are shown are weighted with any sample_weights that might be present. An ensemble of randomized decision trees is known as a random forest. We would like to show you a description here but the site won’t allow us. datasets import load_breast_cancer. This file contains much of the needed meta data for the decision tree or even randomForest. arange(y_min, y_max, h)) some examples from sklearn documentation. In this example, we omit the plot by setting show=False. from sklearn import tree. Visualize the Decision Tree with graphviz. To represent your example with a line graph, just use tree. plot_tree. The proper way of choosing multiple hyperparameters of an estimator is of course grid search or similar methods (see Tuning the hyper-parameters of an estimator) that Jul 30, 2022 · matplotlib: data visualization; Step 1 – Understanding How A Decision Tree Model Works. Summary. Starting from scikit learn version 21. display import Image Image(filename = 'tree. pyplot as plt # create tree object model_gini_class = tree. New to Plotly? Plotly is a free and open-source Aug 29, 2022 · After you fit a random forest model in scikit-learn, you can visualize individual decision trees from a random forest. The visualization is fit automatically to the size of the axis. draw(T, pos) plt. model_selection import cross_val_score from sklearn. data y = iris. fit(iris. The minimum value is 1. show() If you adjust the window to make it square, the result is. show() from sklearn. ensemble import RandomForestClassifier model = RandomForestClassifier(n_estimators=10) # Train model. See Permutation feature importance as Feb 25, 2021 · 1. X_train, X_test, y_train, y_test = train_test_split(X,y, test_size=0. show() # mandatory on Windows. As a first example, we use the iris dataset. set_title("Decision Tree") mlp_disp. export_text method; plot with sklearn. load_iris () X = iris. Whether it’s representing family trees, organizational structures, or decision trees, tree plotting in Python can be a valuable tool for visualizing complex hierarchical data. load_iris. 8% Implemented decision tree accuracy - 87% Jan 3, 2023 · The model is a standard decison tree classifer as shown below. Tree-based models have become a popular choice for Machine Learning, not only due to their results, and the need for fewer transformations when working with data (due to robustness to input and scale invariance), but also because there is a way to take a peek inside of Nov 16, 2023 · In this section, we will implement the decision tree algorithm using Python's Scikit-Learn library. Getting started with decision trees in Python is made significantly easier with libraries like scikit-learn. The goal of the decision tree algorithm is to create a model, that predicts the value of the target variable by learning simple decision rules inferred from the data features, based on Decision Trees. Jun 20, 2024 · Decision Tree Go Out / Free Time. label is not None: Oct 3, 2016 · Random values are initialized with always the same random seed of value 0 # (allows reproducible results) dectree = tree. subplots(figsize=(30, 30)) xgb. . They are powerful algorithms, capable of fitting even complex datasets. For each pair of iris features, the decision tree learns decision boundaries made of combinations of simple thresholding rules inferred from the training samples. 5) have as low grades as those who go out a lot (>4. Step-2: Find the best attribute in the dataset using Attribute Selection Measure (ASM). Image by the author. Plot a decision tree. StringIO() tree. Impurity-based feature importances can be misleading for high cardinality features (many unique values). With a random forest, every tree will be built differently. data, iris. Jan 26, 2019 · There are 4 methods which I'm aware of for plotting the scikit-learn decision tree: print the text representation of the tree with sklearn. DecisionTreeClassifier(random_state=0) dectree. The goal is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features. Tree object using matploltib. The num_trees indicates the tree that should be drawn not the number of trees, so when I set the value to two, I get the second tree generated by XGBoost. The given axes will be used by the plotting function to draw the partial dependence. , labels) can then be provided via ax. decision-tree-sample. png') Considerations. display import Image, display import pydotplus def jupyter_graphviz(m, **kwargs): dot_data = StringIO() export_graphviz(m, dot_data, **kwargs) graph = pydotplus. Jun 22, 2022 · CART (Classification and Regression Tree) uses the Gini method to create binary splits. Decision Trees are a supervised learning method, used most often for classification tasks, but can also be used for regression tasks. Feb 23, 2016 · I am using scikit-learn for classification of text documents(22000) to 100 classes. Apr 19, 2020 · Step #3: Create the Decision Tree and Visualize it! Within your version of Python, copy and run the below code to plot the decision tree. Mô hình cây quyết định là một mô hình được sử dụng khá phổ biến và hiệu quả trong cả hai lớp bài toán phân loại và dự báo của học có giám sát. It is important to change the size of the plot because the default one is not readable. Samples per class. 87 vs 0. Libraries used - numpy, pandas, matplotlib Sklearn decision tree accuracy - 82. Use the figsize or dpi arguments of plt. Cássia Sampaio. ) from matplotlib import pyplot as plt from sklearn import datasets from sklearn. Mar 28, 2024 · Decision Trees are a method of data analysis that presents a hierarchical structure of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. In bL scale. # Create a decision tree classifier. cancer = load_breast_cancer() x = cancer. Jul 13, 2017 · 13. The data is already included in scikit-learn and consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris Explore the art of writing and freely express your thoughts on Zhihu's column platform. Notice that those who don’t go out frequently (< 1. export_graphviz method (graphviz needed) plot with dtreeviz package (dtreeviz and graphviz needed) Oct 10, 2016 · Installation Issue with matplotlib Python. If this was a pyplot figure I would use the command plt. References: matplotlib Documentation; DataCamp: Matplotlib Tutorial May 12, 2017 · Decision trees do not have very nice boundaries. tree import export_text. Using Scikit model dot export and covert dot to png approach with Graphviz; Using Matplotlib to visualize decision tree and export to png approach; Contents. 0, you can use scikit learn's tree. At their core, Decision Trees split data into branches Sep 7, 2021 · # Display plots inline and change default figure size %matplotlib inline from sklearn. Load and return the iris dataset (classification). Let’s visualize Decision trees… 1. The branches of the tree represent the possible outcomes of the tests. You can use np. 5. pdf") Nov 23, 2018 · You may notice those X1, X2 making up from meshgrid so as to utilize the space I'm using for coloring, however you are free to ignore if solution you propose covers plotting more than 2 features as far as it is on matplotlib. 3. show() somewhere. target) # Extract single tree estimator = model. For this answer I modified parts of that code to return a list of Oct 30, 2019 · Here is my code in which I use the iris dataset to draw the decision tree I hope it can help you. plot_tree(clf) and for view tree. I use these images to display the reasoning behind a decision tree (and subsequently a random forest) rather than for Apr 6, 2020 · 2. model_selection import train_test_split. export_graphviz method (graphviz needed) plot with dtreeviz package (dtreeviz and graphviz needed) Feb 12, 2022 · How to import predefined decision tree and use it for classification. To validate a model we need a scoring function (see Metrics and scoring: quantifying the quality of predictions ), for example accuracy for classifiers. plt. Repository consists of a script file, hyperplane generator function and the gif file. We could probably even do that with matplotlib without any graph stuff. Jul 30, 2022 · Plot Tree with plot_tree. In my implementation of Node Harvest I wrote functions that parse scikit's decision trees and extract the decision regions. flatten() i = 0 for classifier in classifiers: classifier. These structures can be retrieved from a decision plot by setting return_objects=True. 4. Figure containing the decision boundary. fit(X_train, y_train) I've tried messing with the dpi and file type, as well as saving directly from the Two approach to visualize Decision Tree in Notebook & Azure Databricks Notebook. Feature importances are provided by the fitted attribute feature_importances_ and they are computed as the mean and standard deviation of accumulation of the impurity decrease within each tree. sklearn. Apr 18, 2023 · In this Byte, learn how to plot decision trees using Python, Scikit-Learn and Matplotlib. datasets. Nov 1, 2022 · To get the decision boundaries of different classifiers in one figure, make sure to pass the argument ax in DecisionBoundaryDisplay. Apr 7, 2021 · A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resourc Jul 8, 2024 · 19. 5) and don’t have free time (<1. This type of bagging classification can be done manually using Scikit-Learn's BaggingClassifier meta-estimator, as shown here: In this example, we have randomized the data by fitting each estimator with a random subset of 80% of the training points. Warning. May 15, 2020 · Am using the following code to extract rules. They have multiple boundaries that hierarchically split the feature space into rectangular regions. six import StringIO from IPython. Oct 7, 2023 · Oct 7, 2023 1 min. My tree plot looks squished: Below are my code: from sklearn import tree from sklearn. legend. estimators_[5] from sklearn. tree import DecisionTreeClassifier. 1- (p²+q²) where p =P (Success) & q=P (Failure) Calculate Gini for Apr 9, 2023 · Decision Tree Summary. surface_ matplotlib QuadContourSet or QuadMesh. In this Matplotlib animation, I demonstrate the order in which splits are made based on the information gain while constructing a Decision Tree. figure(figsize = (12,7)) to constrain the visualization. compute_node_depths() method computes the depth of each node in the tree. import matplotlib. This is my program: def plot_tree(node, x_axis=0, y_axis=10, space=5): if node. A decision tree is usually a binary tree consisting of the root node, decision nodes, and leaf nodes. Plotting a decision tree with pydot. This powerful, easy-to-use library provides tools for data mining and data analysis and is built on NumPy, SciPy, and matplotlib. You can get the number of statistics of all the leaf nodes, like impurity, gain, gini, Array of element classified into each label by the model data file. pyplot module. plot_tree(classifier); Custom legend labels can be provided by returning the axis object (s) from the plot_decision_region function and then getting the handles and labels of the legend. datasets import load_iris. #. figure_ matplotlib Figure. model = DecisionTreeClassifier() model. tree import DecisionTreeClassifier, export_graphviz. XGBoost is a popular gradient-boosting library for building regression and classification models. Related. The core of XGBoost is an ensemble of decision trees. Mar 20, 2021 · Just increase figsize=(50,30), adjust dpi=300 and apply the code to save the image in png. tree import DecisionTreeClassifier from sklearn import tree classifier = DecisionTreeClassifier(max_depth = 3,random_state = 0) tree. In the following examples we'll solve both classification as well as regression problems using the decision tree. np. 5. Validation curve #. Example of confusion matrix usage to evaluate the quality of the output of a classifier on the iris data set. An examples of a tree-plot in Plotly. ax_ matplotlib Axes. plot_tree(. ¶. answered May 4, 2022 at 8:27. :param None name_offset: offset relative to tips to write leaf_names. The variables goout and freetime are scaled from 1= Very Low to 5 = Very High. DecisionTreeClassifier(random_state=0) Mô hình cây quyết định ( decision tree) ¶. Jan 3, 2018 · Let's first decide what training set sizes we want to use for generating the learning curves. This method is not limited to tree models, by the way, and should work with any model that answers method Dec 4, 2019 · I am trying to plot a plot_tree object from sklearn with matplotlib, but my tree plot doesn't look good. % matplotlib inline. Sklearn Decision Rules for Specific Class in Decision tree. target # Fit the May 26, 2018 · Retrieve Decision Boundary Lines (x,y coordinate format) from SKlearn Decision Tree. Calculate Gini impurity for sub-nodes, using the formula subtracting the sum of the square of probability for success and failure from one. To make the rules look more readable, use the feature_names argument and pass a list of your feature names. tree. Or, if you prefer a top-down tree, you could replace the string "twopi" in that code with "dot", and Apr 14, 2022 · The following method below should save an image of the tree: def save_image(clf_, filename, feat_names, class_names, show=True): """Plot the tree and save to file. ensemble import RandomForestClassifier. From there you can make use of matplotlib functionality. The code below first fits a random forest model. reduced by this same value. 80 for logistic regression. ) Feb 14, 2024 · With customization options, we can enhance the appearance of the tree plot to suit our specific needs. This saved image should look better. The tree_. Visualize the decision tree using Matplotlib’s plot_tree method: Pass the individual decision tree, feature names, and target names as parameters. I am using export_graph_viz to visualize a decision tree but the image spreads out of view in my Jupyter Notebook. But again all the examples I'm seeing, they are only training with 2 features so they are good to go from my understanding, they are not facing my problem with the Z shape that's not the right one. fig = plt. clf_, filled=True, feature_names=feat_names, class_names=class_names. It consists of Root Node (WINDY), Internal nodes (OUTLOOK, TEMPERATURE), which represent tests on attributes, and leaf nodes, which represent the final decisions. clf. plot_tree(decision_tree=clf, feature_names=feature_names, class_names=class_names, filled=True, rounded=True, fontsize=10, max_depth=4,dpi=300) #adjust the dpi to the parameter that fits best your output plt Mar 15, 2020 · This works for me. Decision Tree Regression; Multi-output Decision Tree Regression; Plot the decision surface of decision trees trained on the iris dataset; Post pruning decision trees with cost complexity pruning; Understanding the decision tree structure; Decomposition. The complete process can be better understood using the below algorithm: Step-1: Begin the tree with the root node, says S, which contains the complete dataset. plot(ax Oct 17, 2021 · 2. The following Python code shows how to use scikit learn to visualize the decision tree: Once you've fit your model, you just need two lines of code. metrics import accuracy_score import matplotlib. In this video, learn how to make a visualization based on a decision tree model using the Python libraries scikit-learn and Matplotlib. show() To save it, you can do. Decision-Tree-From-Scratch Coding a decision tree from scratch. . There are a number of ways to model a decision tree. Visualization of decision tree using Matplotlib. offset = max_x / 600. Aug 12, 2014 · There are 4 methods which I'm aware of for plotting the scikit-learn decision tree: print the text representation of the tree with sklearn. :param None axe: a matploltib. tree import DecisionTreeClassifier from sklearn import tree # Prepare the data data iris = datasets. plot_tree) will not show anything if you don't have plt. # Separate the features (X) and target (y) X = df_cleaned. For exemple, to plot the 4th tree, use: fig, ax = plt. Please help me plot a tree of higher resolution as the image gets blurred when I increase the tree depth. 0) # Train the Decision Jul 29, 2023 · How to change colors in decision tree plot using sklearn. As a utility function, dtreeviz provides dtreeviz. pyplot axes by default. ax = plot_decision_regions(X, y, clf=svm, legend=0) Feb 6, 2024 · In the above figure, decision tree is a flowchart-like tree structure that is used to make decisions. Second, create an object that will contain your rules. red for class Diabetes and blue for class No Diabetes. Decision Trees (DTs) are a non-parametric supervised learning method used for classification and regression. fig, (ax1, ax2) = plt. pp lh xc gb bd sf tg by qi ti