100 numpy exercises (with solutions)

Classification - Machine Learning This is ‘Classification’ tutorial which is a part of the Machine Learning course offered by Simplilearn. We will learn Classification algorithms, types of classification algorithms, support vector machines(SVM), Naive Bayes, Decision Tree and Random Forest Classifier in this tutorial. Objectives Let us look at some of the objectives covered under this section of Machine Learning tutorial. Define Classification and list its algorithms Describe Logistic Regression and Sigmoid Probability Explain K-Nearest Neighbors and KNN classification Understand Support Vector Machines, Polynomial Kernel, and Kernel Trick Analyze Kernel Support Vector Machines with an example Implement the Naïve Bayes Classifier Demonstrate Decision Tree Classifier Describe Random Forest Classifier Classification: Meaning Classification is a type of supervised learning. It specifies the class to which data elements belong to and is best used when the output has finite and discrete values. It predicts a class for an input variable as well. There are 2 types of Classification: Binomial Multi-Class Classification: Use Cases Some of the key areas where classification cases are being used: To find whether an email received is a spam or ham To identify customer segments To find if a bank loan is granted To identify if a kid will pass or fail in an examination Classification: Example Social media sentiment analysis has two potential outcomes, positive or negative, as displayed by the chart given below. https://www.simplilearn.com/ice9/free_resources_article_thumb/classification-example-machine-learning.JPG This chart shows the classification of the Iris flower dataset into its three sub-species indicated by codes 0, 1, and 2. https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-flower-dataset-graph.JPG The test set dots represent the assignment of new test data points to one class or the other based on the trained classifier model. Types of Classification Algorithms Let’s have a quick look into the types of Classification Algorithm below. Linear Models Logistic Regression Support Vector Machines Nonlinear models K-nearest Neighbors (KNN) Kernel Support Vector Machines (SVM) Naïve Bayes Decision Tree Classification Random Forest Classification Logistic Regression: Meaning Let us understand the Logistic Regression model below. This refers to a regression model that is used for classification. This method is widely used for binary classification problems. It can also be extended to multi-class classification problems. Here, the dependent variable is categorical: y ϵ {0, 1} A binary dependent variable can have only two values, like 0 or 1, win or lose, pass or fail, healthy or sick, etc In this case, you model the probability distribution of output y as 1 or 0. This is called the sigmoid probability (σ). If σ(θ Tx) > 0.5, set y = 1, else set y = 0 Unlike Linear Regression (and its Normal Equation solution), there is no closed form solution for finding optimal weights of Logistic Regression. Instead, you must solve this with maximum likelihood estimation (a probability model to detect the maximum likelihood of something happening). It can be used to calculate the probability of a given outcome in a binary model, like the probability of being classified as sick or passing an exam. https://www.simplilearn.com/ice9/free_resources_article_thumb/logistic-regression-example-graph.JPG Sigmoid Probability The probability in the logistic regression is often represented by the Sigmoid function (also called the logistic function or the S-curve): https://www.simplilearn.com/ice9/free_resources_article_thumb/sigmoid-function-machine-learning.JPG In this equation, t represents data values * the number of hours studied and S(t) represents the probability of passing the exam. Assume sigmoid function: https://www.simplilearn.com/ice9/free_resources_article_thumb/sigmoid-probability-machine-learning.JPG g(z) tends toward 1 as z -> infinity , and g(z) tends toward 0 as z -> infinity K-nearest Neighbors (KNN) K-nearest Neighbors algorithm is used to assign a data point to clusters based on similarity measurement. It uses a supervised method for classification. The steps to writing a k-means algorithm are as given below: https://www.simplilearn.com/ice9/free_resources_article_thumb/knn-distribution-graph-machine-learning.JPG Choose the number of k and a distance metric. (k = 5 is common) Find k-nearest neighbors of the sample that you want to classify Assign the class label by majority vote. KNN Classification A new input point is classified in the category such that it has the most number of neighbors from that category. For example: https://www.simplilearn.com/ice9/free_resources_article_thumb/knn-classification-machine-learning.JPG Classify a patient as high risk or low risk. Mark email as spam or ham. Keen on learning about Classification Algorithms in Machine Learning? Click here! Support Vector Machine (SVM) Let us understand Support Vector Machine (SVM) in detail below. SVMs are classification algorithms used to assign data to various classes. They involve detecting hyperplanes which segregate data into classes. SVMs are very versatile and are also capable of performing linear or nonlinear classification, regression, and outlier detection. Once ideal hyperplanes are discovered, new data points can be easily classified. https://www.simplilearn.com/ice9/free_resources_article_thumb/support-vector-machines-graph-machine-learning.JPG The optimization objective is to find “maximum margin hyperplane” that is farthest from the closest points in the two classes (these points are called support vectors). In the given figure, the middle line represents the hyperplane. SVM Example Let’s look at this image below and have an idea about SVM in general. Hyperplanes with larger margins have lower generalization error. The positive and negative hyperplanes are represented by: https://www.simplilearn.com/ice9/free_resources_article_thumb/positive-negative-hyperplanes-machine-learning.JPG Classification of any new input sample xtest : If w0 + wTxtest > 1, the sample xtest is said to be in the class toward the right of the positive hyperplane. If w0 + wTxtest < -1, the sample xtest is said to be in the class toward the left of the negative hyperplane. When you subtract the two equations, you get: https://www.simplilearn.com/ice9/free_resources_article_thumb/equation-subtraction-machine-learning.JPG Length of vector w is (L2 norm length): https://www.simplilearn.com/ice9/free_resources_article_thumb/length-of-vector-machine-learning.JPG You normalize with the length of w to arrive at: https://www.simplilearn.com/ice9/free_resources_article_thumb/normalize-equation-machine-learning.JPG SVM: Hard Margin Classification Given below are some points to understand Hard Margin Classification. The left side of equation SVM-1 given above can be interpreted as the distance between the positive (+ve) and negative (-ve) hyperplanes; in other words, it is the margin that can be maximized. Hence the objective of the function is to maximize with the constraint that the samples are classified correctly, which is represented as : https://www.simplilearn.com/ice9/free_resources_article_thumb/hard-margin-classification-machine-learning.JPG This means that you are minimizing ‖w‖. This also means that all positive samples are on one side of the positive hyperplane and all negative samples are on the other side of the negative hyperplane. This can be written concisely as : https://www.simplilearn.com/ice9/free_resources_article_thumb/hard-margin-classification-formula.JPG Minimizing ‖w‖ is the same as minimizing. This figure is better as it is differentiable even at w = 0. The approach listed above is called “hard margin linear SVM classifier.” SVM: Soft Margin Classification Given below are some points to understand Soft Margin Classification. To allow for linear constraints to be relaxed for nonlinearly separable data, a slack variable is introduced. (i) measures how much ith instance is allowed to violate the margin. The slack variable is simply added to the linear constraints. https://www.simplilearn.com/ice9/free_resources_article_thumb/soft-margin-calculation-machine-learning.JPG Subject to the above constraints, the new objective to be minimized becomes: https://www.simplilearn.com/ice9/free_resources_article_thumb/soft-margin-calculation-formula.JPG You have two conflicting objectives now—minimizing slack variable to reduce margin violations and minimizing to increase the margin. The hyperparameter C allows us to define this trade-off. Large values of C correspond to larger error penalties (so smaller margins), whereas smaller values of C allow for higher misclassification errors and larger margins. https://www.simplilearn.com/ice9/free_resources_article_thumb/machine-learning-certification-video-preview.jpg SVM: Regularization The concept of C is the reverse of regularization. Higher C means lower regularization, which increases bias and lowers the variance (causing overfitting). https://www.simplilearn.com/ice9/free_resources_article_thumb/concept-of-c-graph-machine-learning.JPG IRIS Data Set The Iris dataset contains measurements of 150 IRIS flowers from three different species: Setosa Versicolor Viriginica Each row represents one sample. Flower measurements in centimeters are stored as columns. These are called features. IRIS Data Set: SVM Let’s train an SVM model using sci-kit-learn for the Iris dataset: https://www.simplilearn.com/ice9/free_resources_article_thumb/svm-model-graph-machine-learning.JPG Nonlinear SVM Classification There are two ways to solve nonlinear SVMs: by adding polynomial features by adding similarity features Polynomial features can be added to datasets; in some cases, this can create a linearly separable dataset. https://www.simplilearn.com/ice9/free_resources_article_thumb/nonlinear-classification-svm-machine-learning.JPG In the figure on the left, there is only 1 feature x1. This dataset is not linearly separable. If you add x2 = (x1)2 (figure on the right), the data becomes linearly separable. Polynomial Kernel In sci-kit-learn, one can use a Pipeline class for creating polynomial features. Classification results for the Moons dataset are shown in the figure. https://www.simplilearn.com/ice9/free_resources_article_thumb/polynomial-kernel-machine-learning.JPG Polynomial Kernel with Kernel Trick Let us look at the image below and understand Kernel Trick in detail. https://www.simplilearn.com/ice9/free_resources_article_thumb/polynomial-kernel-with-kernel-trick.JPG For large dimensional datasets, adding too many polynomial features can slow down the model. You can apply a kernel trick with the effect of polynomial features without actually adding them. The code is shown (SVC class) below trains an SVM classifier using a 3rd-degree polynomial kernel but with a kernel trick. https://www.simplilearn.com/ice9/free_resources_article_thumb/polynomial-kernel-equation-machine-learning.JPG The hyperparameter coefθ controls the influence of high-degree polynomials. Kernel SVM Let us understand in detail about Kernel SVM. Kernel SVMs are used for classification of nonlinear data. In the chart, nonlinear data is projected into a higher dimensional space via a mapping function where it becomes linearly separable. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-machine-learning.JPG In the higher dimension, a linear separating hyperplane can be derived and used for classification. A reverse projection of the higher dimension back to original feature space takes it back to nonlinear shape. As mentioned previously, SVMs can be kernelized to solve nonlinear classification problems. You can create a sample dataset for XOR gate (nonlinear problem) from NumPy. 100 samples will be assigned the class sample 1, and 100 samples will be assigned the class label -1. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-graph-machine-learning.JPG As you can see, this data is not linearly separable. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-non-separable.JPG You now use the kernel trick to classify XOR dataset created earlier. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-xor-machine-learning.JPG Naïve Bayes Classifier What is Naive Bayes Classifier? Have you ever wondered how your mail provider implements spam filtering or how online news channels perform news text classification or even how companies perform sentiment analysis of their audience on social media? All of this and more are done through a machine learning algorithm called Naive Bayes Classifier. Naive Bayes Named after Thomas Bayes from the 1700s who first coined this in the Western literature. Naive Bayes classifier works on the principle of conditional probability as given by the Bayes theorem. Advantages of Naive Bayes Classifier Listed below are six benefits of Naive Bayes Classifier. Very simple and easy to implement Needs less training data Handles both continuous and discrete data Highly scalable with the number of predictors and data points As it is fast, it can be used in real-time predictions Not sensitive to irrelevant features Bayes Theorem We will understand Bayes Theorem in detail from the points mentioned below. According to the Bayes model, the conditional probability P(Y|X) can be calculated as: P(Y|X) = P(X|Y)P(Y) / P(X) This means you have to estimate a very large number of P(X|Y) probabilities for a relatively small vector space X. For example, for a Boolean Y and 30 possible Boolean attributes in the X vector, you will have to estimate 3 billion probabilities P(X|Y). To make it practical, a Naïve Bayes classifier is used, which assumes conditional independence of P(X) to each other, with a given value of Y. This reduces the number of probability estimates to 2*30=60 in the above example. Naïve Bayes Classifier for SMS Spam Detection Consider a labeled SMS database having 5574 messages. It has messages as given below: https://www.simplilearn.com/ice9/free_resources_article_thumb/naive-bayes-spam-machine-learning.JPG Each message is marked as spam or ham in the data set. Let’s train a model with Naïve Bayes algorithm to detect spam from ham. The message lengths and their frequency (in the training dataset) are as shown below: https://www.simplilearn.com/ice9/free_resources_article_thumb/naive-bayes-spam-spam-detection.JPG Analyze the logic you use to train an algorithm to detect spam: Split each message into individual words/tokens (bag of words). Lemmatize the data (each word takes its base form, like “walking” or “walked” is replaced with “walk”). Convert data to vectors using scikit-learn module CountVectorizer. Run TFIDF to remove common words like “is,” “are,” “and.” Now apply scikit-learn module for Naïve Bayes MultinomialNB to get the Spam Detector. This spam detector can then be used to classify a random new message as spam or ham. Next, the accuracy of the spam detector is checked using the Confusion Matrix. For the SMS spam example above, the confusion matrix is shown on the right. Accuracy Rate = Correct / Total = (4827 + 592)/5574 = 97.21% Error Rate = Wrong / Total = (155 + 0)/5574 = 2.78% https://www.simplilearn.com/ice9/free_resources_article_thumb/confusion-matrix-machine-learning.JPG Although confusion Matrix is useful, some more precise metrics are provided by Precision and Recall. https://www.simplilearn.com/ice9/free_resources_article_thumb/precision-recall-matrix-machine-learning.JPG Precision refers to the accuracy of positive predictions. https://www.simplilearn.com/ice9/free_resources_article_thumb/precision-formula-machine-learning.JPG Recall refers to the ratio of positive instances that are correctly detected by the classifier (also known as True positive rate or TPR). https://www.simplilearn.com/ice9/free_resources_article_thumb/recall-formula-machine-learning.JPG Precision/Recall Trade-off To detect age-appropriate videos for kids, you need high precision (low recall) to ensure that only safe videos make the cut (even though a few safe videos may be left out). The high recall is needed (low precision is acceptable) in-store surveillance to catch shoplifters; a few false alarms are acceptable, but all shoplifters must be caught. Learn about Naive Bayes in detail. Click here! Decision Tree Classifier Some aspects of the Decision Tree Classifier mentioned below are. Decision Trees (DT) can be used both for classification and regression. The advantage of decision trees is that they require very little data preparation. They do not require feature scaling or centering at all. They are also the fundamental components of Random Forests, one of the most powerful ML algorithms. Unlike Random Forests and Neural Networks (which do black-box modeling), Decision Trees are white box models, which means that inner workings of these models are clearly understood. In the case of classification, the data is segregated based on a series of questions. Any new data point is assigned to the selected leaf node. https://www.simplilearn.com/ice9/free_resources_article_thumb/decision-tree-classifier-machine-learning.JPG Start at the tree root and split the data on the feature using the decision algorithm, resulting in the largest information gain (IG). This splitting procedure is then repeated in an iterative process at each child node until the leaves are pure. This means that the samples at each node belonging to the same class. In practice, you can set a limit on the depth of the tree to prevent overfitting. The purity is compromised here as the final leaves may still have some impurity. The figure shows the classification of the Iris dataset. https://www.simplilearn.com/ice9/free_resources_article_thumb/decision-tree-classifier-graph.JPG IRIS Decision Tree Let’s build a Decision Tree using scikit-learn for the Iris flower dataset and also visualize it using export_graphviz API. https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-decision-tree-machine-learning.JPG The output of export_graphviz can be converted into png format: https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-decision-tree-output.JPG Sample attribute stands for the number of training instances the node applies to. Value attribute stands for the number of training instances of each class the node applies to. Gini impurity measures the node’s impurity. A node is “pure” (gini=0) if all training instances it applies to belong to the same class. https://www.simplilearn.com/ice9/free_resources_article_thumb/impurity-formula-machine-learning.JPG For example, for Versicolor (green color node), the Gini is 1-(0/54)2 -(49/54)2 -(5/54) 2 ≈ 0.168 https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-decision-tree-sample.JPG Decision Boundaries Let us learn to create decision boundaries below. For the first node (depth 0), the solid line splits the data (Iris-Setosa on left). Gini is 0 for Setosa node, so no further split is possible. The second node (depth 1) splits the data into Versicolor and Virginica. If max_depth were set as 3, a third split would happen (vertical dotted line). https://www.simplilearn.com/ice9/free_resources_article_thumb/decision-tree-boundaries.JPG For a sample with petal length 5 cm and petal width 1.5 cm, the tree traverses to depth 2 left node, so the probability predictions for this sample are 0% for Iris-Setosa (0/54), 90.7% for Iris-Versicolor (49/54), and 9.3% for Iris-Virginica (5/54) CART Training Algorithm Scikit-learn uses Classification and Regression Trees (CART) algorithm to train Decision Trees. CART algorithm: Split the data into two subsets using a single feature k and threshold tk (example, petal length < “2.45 cm”). This is done recursively for each node. k and tk are chosen such that they produce the purest subsets (weighted by their size). The objective is to minimize the cost function as given below: https://www.simplilearn.com/ice9/free_resources_article_thumb/cart-training-algorithm-machine-learning.JPG The algorithm stops executing if one of the following situations occurs: max_depth is reached No further splits are found for each node Other hyperparameters may be used to stop the tree: min_samples_split min_samples_leaf min_weight_fraction_leaf max_leaf_nodes Gini Impurity or Entropy Entropy is one more measure of impurity and can be used in place of Gini. https://www.simplilearn.com/ice9/free_resources_article_thumb/gini-impurity-entrophy.JPG It is a degree of uncertainty, and Information Gain is the reduction that occurs in entropy as one traverses down the tree. Entropy is zero for a DT node when the node contains instances of only one class. Entropy for depth 2 left node in the example given above is: https://www.simplilearn.com/ice9/free_resources_article_thumb/entrophy-for-depth-2.JPG Gini and Entropy both lead to similar trees. DT: Regularization The following figure shows two decision trees on the moons dataset. https://www.simplilearn.com/ice9/free_resources_article_thumb/dt-regularization-machine-learning.JPG The decision tree on the right is restricted by min_samples_leaf = 4. The model on the left is overfitting, while the model on the right generalizes better. Random Forest Classifier Let us have an understanding of Random Forest Classifier below. A random forest can be considered an ensemble of decision trees (Ensemble learning). Random Forest algorithm: Draw a random bootstrap sample of size n (randomly choose n samples from the training set). Grow a decision tree from the bootstrap sample. At each node, randomly select d features. Split the node using the feature that provides the best split according to the objective function, for instance by maximizing the information gain. Repeat the steps 1 to 2 k times. (k is the number of trees you want to create, using a subset of samples) Aggregate the prediction by each tree for a new data point to assign the class label by majority vote (pick the group selected by the most number of trees and assign new data point to that group). Random Forests are opaque, which means it is difficult to visualize their inner workings. https://www.simplilearn.com/ice9/free_resources_article_thumb/random-forest-classifier-graph.JPG However, the advantages outweigh their limitations since you do not have to worry about hyperparameters except k, which stands for the number of decision trees to be created from a subset of samples. RF is quite robust to noise from the individual decision trees. Hence, you need not prune individual decision trees. The larger the number of decision trees, the more accurate the Random Forest prediction is. (This, however, comes with higher computation cost). Key Takeaways Let us quickly run through what we have learned so far in this Classification tutorial. Classification algorithms are supervised learning methods to split data into classes. They can work on Linear Data as well as Nonlinear Data. Logistic Regression can classify data based on weighted parameters and sigmoid conversion to calculate the probability of classes. K-nearest Neighbors (KNN) algorithm uses similar features to classify data. Support Vector Machines (SVMs) classify data by detecting the maximum margin hyperplane between data classes. Naïve Bayes, a simplified Bayes Model, can help classify data using conditional probability models. Decision Trees are powerful classifiers and use tree splitting logic until pure or somewhat pure leaf node classes are attained. Random Forests apply Ensemble Learning to Decision Trees for more accurate classification predictions. Conclusion This completes ‘Classification’ tutorial. In the next tutorial, we will learn 'Unsupervised Learning with Clustering.'

100 упражнений по NumPy (версия на русском)

A set of introductory exercises for Julia. Based on [100 NumPy Exercises](https://github.com/rougier/numpy-100).

julia version of 100 numpy exercises

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trading strategy is a fixed plan to go long or short in markets, there are two common trading strategies: the momentum strategy and the reversion strategy. Firstly, the momentum strategy is also called divergence or trend trading. When you follow this strategy, you do so because you believe the movement of a quantity will continue in its current direction. Stated differently, you believe that stocks have momentum or upward or downward trends, that you can detect and exploit. Some examples of this strategy are the moving average crossover, the dual moving average crossover, and turtle trading: The moving average crossover is when the price of an asset moves from one side of a moving average to the other. This crossover represents a change in momentum and can be used as a point of making the decision to enter or exit the market. You’ll see an example of this strategy, which is the “hello world” of quantitative trading later on in this tutorial. The dual moving average crossover occurs when a short-term average crosses a long-term average. This signal is used to identify that momentum is shifting in the direction of the short-term average. A buy signal is generated when the short-term average crosses the long-term average and rises above it, while a sell signal is triggered by a short-term average crossing long-term average and falling below it. Turtle trading is a popular trend following strategy that was initially taught by Richard Dennis. The basic strategy is to buy futures on a 20-day high and sell on a 20-day low. Secondly, the reversion strategy, which is also known as convergence or cycle trading. This strategy departs from the belief that the movement of a quantity will eventually reverse. This might seem a little bit abstract, but will not be so anymore when you take the example. Take a look at the mean reversion strategy, where you actually believe that stocks return to their mean and that you can exploit when it deviates from that mean. That already sounds a whole lot more practical, right? Another example of this strategy, besides the mean reversion strategy, is the pairs trading mean-reversion, which is similar to the mean reversion strategy. Whereas the mean reversion strategy basically stated that stocks return to their mean, the pairs trading strategy extends this and states that if two stocks can be identified that have a relatively high correlation, the change in the difference in price between the two stocks can be used to signal trading events if one of the two moves out of correlation with the other. That means that if the correlation between two stocks has decreased, the stock with the higher price can be considered to be in a short position. It should be sold because the higher-priced stock will return to the mean. The lower-priced stock, on the other hand, will be in a long position because the price will rise as the correlation will return to normal. Besides these two most frequent strategies, there are also other ones that you might come across once in a while, such as the forecasting strategy, which attempts to predict the direction or value of a stock, in this case, in subsequent future time periods based on certain historical factors. There’s also the High-Frequency Trading (HFT) strategy, which exploits the sub-millisecond market microstructure. That’s all music for the future for now; Let’s focus on developing your first trading strategy for now! A Simple Trading Strategy As you read above, you’ll start with the “hello world” of quantitative trading: the moving average crossover. The strategy that you’ll be developing is simple: you create two separate Simple Moving Averages (SMA) of a time series with differing lookback periods, let’s say, 40 days and 100 days. If the short moving average exceeds the long moving average then you go long, if the long moving average exceeds the short moving average then you exit. Remember that when you go long, you think that the stock price will go up and will sell at a higher price in the future (= buy signal); When you go short, you sell your stock, expecting that you can buy it back at a lower price and realize a profit (= sell signal). This simple strategy might seem quite complex when you’re just starting out, but let’s take this step by step: First define your two different lookback periods: a short window and a long window. You set up two variables and assign one integer per variable. Make sure that the integer that you assign to the short window is shorter than the integer that you assign to the long window variable! Next, make an empty signals DataFrame, but do make sure to copy the index of your aapl data so that you can start calculating the daily buy or sell signal for your aapl data. Create a column in your empty signals DataFrame that is named signal and initialize it by setting the value for all rows in this column to 0.0. After the preparatory work, it’s time to create the set of short and long simple moving averages over the respective long and short time windows. Make use of the rolling() function to start your rolling window calculations: within the function, specify the window and the min_period, and set the center argument. In practice, this will result in a rolling() function to which you have passed either short_window or long_window, 1 as the minimum number of observations in the window that are required to have a value, and False, so that the labels are not set at the center of the window. Next, don’t forget to also chain the mean() function so that you calculate the rolling mean. After you have calculated the mean average of the short and long windows, you should create a signal when the short moving average crosses the long moving average, but only for the period greater than the shortest moving average window. In Python, this will result in a condition: signals['short_mavg'][short_window:] > signals['long_mavg'][short_window:]. Note that you add the [short_window:] to comply with the condition “only for the period greater than the shortest moving average window”. When the condition is true, the initialized value 0.0 in the signal column will be overwritten with 1.0. A “signal” is created! If the condition is false, the original value of 0.0 will be kept and no signal is generated. You use the NumPy where() function to set up this condition. Much the same like you read just now, the variable to which you assign this result is signals['signal'][short_window], because you only want to create signals for the period greater than the shortest moving average window! Lastly, you take the difference of the signals in order to generate actual trading orders. In other words, in this column of your signals DataFrame, you’ll be able to distinguish between long and short positions, whether you’re buying or selling stock.

100 numpy exercises

100 numpy exercises(Chinese version)

你真的会使用NumPy吗？来100道题彻底搞懂Numpy

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class="w3-bar-item w3-button" href="/python/python_reference.asp">Python Reference</a> <a class="w3-bar-item w3-button" href="/java/java_ref_keywords.asp">Java Reference</a> </div> <div class="w3-col l3 m6"> <h3 class="w3-margin-top">Server Side</h3> <a class="w3-bar-item w3-button" href="/sql/sql_ref_keywords.asp">SQL Reference</a> <a class="w3-bar-item w3-button" href="/mysql/mysql_ref_functions.asp">MySQL Reference</a> <a class="w3-bar-item w3-button" href="/php/php_ref_overview.asp">PHP Reference</a> <a class="w3-bar-item w3-button" href="/asp/asp_ref_response.asp">ASP Reference</a> <h3 class="w3-margin-top">XML</h3> <a class="w3-bar-item w3-button" href="/xml/dom_nodetype.asp">XML DOM Reference</a> <a class="w3-bar-item w3-button" href="/xml/dom_http.asp">XML Http Reference</a> <a class="w3-bar-item w3-button" href="/xml/xsl_elementref.asp">XSLT Reference</a> <a class="w3-bar-item w3-button" href="/xml/schema_elements_ref.asp">XML Schema Reference</a> </div> <div class="w3-col l3 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class="active">&lt;p&gt;</a> <a target="_top" href="tag_param.asp">&lt;param&gt;</a> <a target="_top" href="tag_picture.asp">&lt;picture&gt;</a> <a target="_top" href="tag_pre.asp">&lt;pre&gt;</a> <a target="_top" href="tag_progress.asp">&lt;progress&gt;</a> <a target="_top" href="tag_q.asp">&lt;q&gt;</a> <a target="_top" href="tag_rp.asp">&lt;rp&gt;</a> <a target="_top" href="tag_rt.asp">&lt;rt&gt;</a> <a target="_top" href="tag_ruby.asp">&lt;ruby&gt;</a> <a target="_top" href="tag_s.asp">&lt;s&gt;</a> <a target="_top" href="tag_samp.asp">&lt;samp&gt;</a> <a target="_top" href="tag_script.asp">&lt;script&gt;</a> <a target="_top" href="tag_section.asp">&lt;section&gt;</a> <a target="_top" href="tag_select.asp">&lt;select&gt;</a> <a target="_top" href="tag_small.asp">&lt;small&gt;</a> <a target="_top" href="tag_source.asp">&lt;source&gt;</a> <a target="_top" href="tag_span.asp">&lt;span&gt;</a> <a target="_top" href="tag_strike.asp">&lt;strike&gt;</a> <a target="_top" href="tag_strong.asp">&lt;strong&gt;</a> <a target="_top" href="tag_style.asp">&lt;style&gt;</a> <a target="_top" href="tag_sub.asp">&lt;sub&gt;</a> <a target="_top" href="tag_summary.asp">&lt;summary&gt;</a> <a target="_top" href="tag_sup.asp">&lt;sup&gt;</a> <a target="_top" href="tag_svg.asp">&lt;svg&gt;</a> <a target="_top" href="tag_table.asp">&lt;table&gt;</a> <a target="_top" href="tag_tbody.asp">&lt;tbody&gt;</a> <a target="_top" href="tag_td.asp">&lt;td&gt;</a> <a target="_top" href="tag_template.asp">&lt;template&gt;</a> <a target="_top" href="tag_textarea.asp">&lt;textarea&gt;</a> <a target="_top" href="tag_tfoot.asp">&lt;tfoot&gt;</a> <a target="_top" href="tag_th.asp">&lt;th&gt;</a> <a target="_top" href="tag_thead.asp">&lt;thead&gt;</a> <a target="_top" href="tag_time.asp">&lt;time&gt;</a> <a target="_top" href="tag_title.asp">&lt;title&gt;</a> <a target="_top" href="tag_tr.asp">&lt;tr&gt;</a> <a target="_top" href="tag_track.asp">&lt;track&gt;</a> <a target="_top" href="tag_tt.asp">&lt;tt&gt;</a> <a target="_top" href="tag_u.asp">&lt;u&gt;</a> <a target="_top" href="tag_ul.asp">&lt;ul&gt;</a> <a target="_top" href="tag_var.asp">&lt;var&gt;</a> <a target="_top" href="tag_video.asp">&lt;video&gt;</a> <a target="_top" href="tag_wbr.asp">&lt;wbr&gt;</a> </div> <br><br> </div> </div> </div> <div class="w3-main w3-light-grey" id="belowtopnav" style="margin-left: 220px; padding-top: 44px;"> <div class="w3-row w3-white"> <div class="w3-col l10 m12" id="main"> <div id="mainLeaderboard" style="overflow:hidden;"> <!-- MainLeaderboard--> <!--<pre>main_leaderboard, all: [728,90][970,90][320,50][468,60]</pre>--> <div id="adngin-main_leaderboard-0" data-google-query-id="CJPA_sueqvcCFXiOSwUd2fYBLg"><div id="google_ads_iframe_/22152718,16833175/sws-hb//w3schools.com//main_leaderboard_1__container__" style="border: 0pt none;"><iframe id="google_ads_iframe_/22152718,16833175/sws-hb//w3schools.com//main_leaderboard_1" name="google_ads_iframe_/22152718,16833175/sws-hb//w3schools.com//main_leaderboard_1" title="3rd party ad content" width="728" height="90" scrolling="no" marginwidth="0" marginheight="0" frameborder="0" role="region" aria-label="Advertisement" tabindex="0" srcdoc="" data-google-container-id="7" style="border: 0px; vertical-align: bottom;" data-load-complete="true"><div style="position: absolute; width: 0px; height: 0px; border: 0px; padding: 0px; margin: 0px; overflow: hidden;"><button></button><a href="https://yahoo.com"></a><input></div></iframe></div></div> <!-- adspace leaderboard --> </div> <h1>HTML <span class="color_h1">&lt;p&gt;</span> Tag</h1> <div class="w3-clear w3-center nextprev"> <a class="w3-left w3-btn" href="tag_output.asp">❮<span class="w3-hide-small"> Previous</span></a> <a class="w3-btn" href="default.asp"><span class="w3-hide-small">Complete HTML </span>Reference</a> <a class="w3-right w3-btn" href="tag_param.asp"><span class="w3-hide-small">Next </span>❯</a> </div> <br> <div class="w3-example"> <h3>Example</h3> <p>A paragraph is marked up as follows:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>p<span class="tagcolor" style="color:mediumblue">&gt;</span></span>This is some text in a paragraph.<span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/p<span class="tagcolor" style="color:mediumblue">&gt;</span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_paragraphs1" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <p>More "Try it Yourself" examples below.</p> <hr> <h2>Definition and Usage</h2> <p>The <code class="w3-codespan">&lt;p&gt;</code> tag defines a paragraph.</p> <p>Browsers automatically add a single blank line before and after each <code class="w3-codespan">&lt;p&gt;</code> element.</p> <p><strong>Tip:</strong> Use CSS to <a href="/html/html_css.asp">style paragraphs</a>.</p> <hr> <h2>Browser Support</h2> <table class="browserref notranslate"> <tbody><tr> <th style="width:20%;font-size:16px;text-align:left;">Element</th> <th style="width:16%;" class="bsChrome" title="Chrome"></th> <th style="width:16%;" class="bsEdge" title="Internet Explorer / Edge"></th> <th style="width:16%;" class="bsFirefox" title="Firefox"></th> <th style="width:16%;" class="bsSafari" title="Safari"></th> <th style="width:16%;" class="bsOpera" title="Opera"></th> </tr><tr> <td style="text-align:left;">&lt;p&gt;</td> <td>Yes</td> <td>Yes</td> <td>Yes</td> <td>Yes</td> <td>Yes</td> </tr> </tbody></table> <hr> <h2>Global Attributes</h2> <p>The <code class="w3-codespan">&lt;p&gt;</code> tag also supports the <a href="ref_standardattributes.asp">Global Attributes in HTML</a>.</p> <hr> <h2>Event Attributes</h2> <p>The <code class="w3-codespan">&lt;p&gt;</code> tag also supports the <a href="ref_eventattributes.asp">Event Attributes in HTML</a>.</p> <hr> <div id="midcontentadcontainer" style="overflow:auto;text-align:center"> <!-- MidContent --> <!-- <p class="adtext">Advertisement</p> --> <div id="adngin-mid_content-0" data-google-query-id="CKfs_8ueqvcCFXiOSwUd2fYBLg"><div id="sn_ad_label_adngin-mid_content-0" class="sn_ad_label" style="color:#000000;font-size:12px;margin:0;text-align:center;">ADVERTISEMENT</div><div id="google_ads_iframe_/22152718,16833175/sws-hb//w3schools.com//mid_content_1__container__" style="border: 0pt none; display: inline-block; width: 300px; height: 250px;"><iframe frameborder="0" src="https://56d0da6c34aaa471db22bb4266aac656.safeframe.googlesyndication.com/safeframe/1-0-38/html/container.html" id="google_ads_iframe_/22152718,16833175/sws-hb//w3schools.com//mid_content_1" title="3rd party ad content" name="" scrolling="no" marginwidth="0" marginheight="0" width="300" height="250" data-is-safeframe="true" sandbox="allow-forms allow-popups allow-popups-to-escape-sandbox allow-same-origin allow-scripts allow-top-navigation-by-user-activation" role="region" aria-label="Advertisement" tabindex="0" data-google-container-id="8" style="border: 0px; vertical-align: bottom;" data-load-complete="true"></iframe></div></div> </div> <hr> <h2>More Examples</h2> <div class="w3-example"> <h3>Example</h3> <p>Align text in a paragraph (with CSS):</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>p<span class="attributecolor" style="color:red"> style<span class="attributevaluecolor" style="color:mediumblue">="text-align:right"</span></span><span class="tagcolor" style="color:mediumblue">&gt;</span></span>This is some text in a paragraph.<span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/p<span class="tagcolor" style="color:mediumblue">&gt;</span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_p_align_css" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <div class="w3-example"> <h3>Example</h3> <p>Style paragraphs with CSS:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>html<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>head<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>style<span class="tagcolor" style="color:mediumblue">&gt;</span></span><span class="cssselectorcolor" style="color:brown"><br>p <span class="cssdelimitercolor" style="color:black">{</span><span class="csspropertycolor" style="color:red"><br>&nbsp; color<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> navy<span class="cssdelimitercolor" style="color:black">;</span></span><br>&nbsp; text-indent<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 30px<span class="cssdelimitercolor" style="color:black">;</span></span><br>&nbsp; text-transform<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> uppercase<span class="cssdelimitercolor" style="color:black">;</span></span><br></span><span class="cssdelimitercolor" style="color:black">}</span><br></span><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/style<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/head<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>body<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>p<span class="tagcolor" style="color:mediumblue">&gt;</span></span>Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.<span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/p<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/body<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/html<span class="tagcolor" style="color:mediumblue">&gt;</span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_p_style_css" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <div class="w3-example"> <h3>Example</h3> <p>&nbsp;More on paragraphs:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>p<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br>This paragraph<br>contains a lot of lines<br>in the source code,<br> but the browser <br>ignores it.<br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/p<span class="tagcolor" style="color:mediumblue">&gt;</span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_paragraphs2" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <div class="w3-example"> <h3>Example</h3> <p>Poem problems in HTML:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>p<span class="tagcolor" style="color:mediumblue">&gt;</span></span><br>My Bonnie lies over the ocean.<br>My Bonnie lies over the sea.<br>My Bonnie lies over the ocean.<br>Oh, bring back my Bonnie to me.<br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue">&lt;</span>/p<span class="tagcolor" style="color:mediumblue">&gt;</span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_poem" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <hr> <h2>Related Pages</h2> <p>HTML tutorial: <a href="/html/html_paragraphs.asp">HTML Paragraphs</a></p> <p>HTML DOM reference: <a href="/jsref/dom_obj_paragraph.asp">Paragraph Object</a></p> <hr> <h2>Default CSS Settings</h2> <p>Most browsers will display the <code class="w3-codespan">&lt;p&gt;</code> element with the following default values:</p> <div class="w3-example"> <h3>Example</h3> <div class="w3-code notranslate cssHigh"><span class="cssselectorcolor" style="color:brown"> p <span class="cssdelimitercolor" style="color:black">{</span><span class="csspropertycolor" style="color:red"><br>&nbsp; display<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> block<span class="cssdelimitercolor" style="color:black">;</span></span><br>&nbsp; margin-top<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 1em<span class="cssdelimitercolor" style="color:black">;</span></span><br>&nbsp; margin-bottom<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 1em<span class="cssdelimitercolor" style="color:black">;</span></span><br>&nbsp; margin-left<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 0<span class="cssdelimitercolor" style="color:black">;</span></span><br>&nbsp;&nbsp;margin-right<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 0<span class="cssdelimitercolor" style="color:black">;</span></span><br></span><span class="cssdelimitercolor" style="color:black">}</span> 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Quickstart tutorial Prerequisites Before reading this tutorial you should know a bit of Python. If you would like to refresh your memory, take a look at the Python tutorial. If you wish to work the examples in this tutorial, you must also have some software installed on your computer. Please see https://scipy.org/install.html for instructions. Learner profile This tutorial is intended as a quick overview of algebra and arrays in NumPy and want to understand how n-dimensional (n>=2) arrays are represented and can be manipulated. In particular, if you don’t know how to apply common functions to n-dimensional arrays (without using for-loops), or if you want to understand axis and shape properties for n-dimensional arrays, this tutorial might be of help. Learning Objectives After this tutorial, you should be able to: Understand the difference between one-, two- and n-dimensional arrays in NumPy; Understand how to apply some linear algebra operations to n-dimensional arrays without using for-loops; Understand axis and shape properties for n-dimensional arrays. The Basics NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of non-negative integers. In NumPy dimensions are called axes. For example, the coordinates of a point in 3D space [1, 2, 1] has one axis. That axis has 3 elements in it, so we say it has a length of 3. In the example pictured below, the array has 2 axes. The first axis has a length of 2, the second axis has a length of 3. [[ 1., 0., 0.], [ 0., 1., 2.]] NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the same as the Standard Python Library class array.array, which only handles one-dimensional arrays and offers less functionality. The more important attributes of an ndarray object are: ndarray.ndim the number of axes (dimensions) of the array. ndarray.shape the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim. ndarray.size the total number of elements of the array. This is equal to the product of the elements of shape. ndarray.dtype an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples. ndarray.itemsize the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize. ndarray.data the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities. An example >>> import numpy as np a = np.arange(15).reshape(3, 5) a array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14]]) a.shape (3, 5) a.ndim 2 a.dtype.name 'int64' a.itemsize 8 a.size 15 type(a) <class 'numpy.ndarray'> b = np.array([6, 7, 8]) b array([6, 7, 8]) type(b) <class 'numpy.ndarray'> Array Creation There are several ways to create arrays. For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences. >>> >>> import numpy as np >>> a = np.array([2,3,4]) >>> a array([2, 3, 4]) >>> a.dtype dtype('int64') >>> b = np.array([1.2, 3.5, 5.1]) >>> b.dtype dtype('float64') A frequent error consists in calling array with multiple arguments, rather than providing a single sequence as an argument. >>> >>> a = np.array(1,2,3,4) # WRONG Traceback (most recent call last): ... TypeError: array() takes from 1 to 2 positional arguments but 4 were given >>> a = np.array([1,2,3,4]) # RIGHT array transforms sequences of sequences into two-dimensional arrays, sequences of sequences of sequences into three-dimensional arrays, and so on. >>> >>> b = np.array([(1.5,2,3), (4,5,6)]) >>> b array([[1.5, 2. , 3. ], [4. , 5. , 6. ]]) The type of the array can also be explicitly specified at creation time: >>> >>> c = np.array( [ [1,2], [3,4] ], dtype=complex ) >>> c array([[1.+0.j, 2.+0.j], [3.+0.j, 4.+0.j]]) Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation. The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64. >>> >>> np.zeros((3, 4)) array([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.]]) >>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified array([[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]], dtype=int16) >>> np.empty( (2,3) ) # uninitialized array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260], # may vary [ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]]) To create sequences of numbers, NumPy provides the arange function which is analogous to the Python built-in range, but returns an array. >>> >>> np.arange( 10, 30, 5 ) array([10, 15, 20, 25]) >>> np.arange( 0, 2, 0.3 ) # it accepts float arguments array([0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8]) When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step: >>> >>> from numpy import pi >>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2 array([0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ]) >>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points >>> f = np.sin(x) See also array, zeros, zeros_like, ones, ones_like, empty, empty_like, arange, linspace, numpy.random.Generator.rand, numpy.random.Generator.randn, fromfunction, fromfile Printing Arrays When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout: the last axis is printed from left to right, the second-to-last is printed from top to bottom, the rest are also printed from top to bottom, with each slice separated from the next by an empty line. One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices. >>> >>> a = np.arange(6) # 1d array >>> print(a) [0 1 2 3 4 5] >>> >>> b = np.arange(12).reshape(4,3) # 2d array >>> print(b) [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] >>> >>> c = np.arange(24).reshape(2,3,4) # 3d array >>> print(c) [[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] [[12 13 14 15] [16 17 18 19] [20 21 22 23]]] See below to get more details on reshape. If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners: >>> >>> print(np.arange(10000)) [ 0 1 2 ... 9997 9998 9999] >>> >>> print(np.arange(10000).reshape(100,100)) [[ 0 1 2 ... 97 98 99] [ 100 101 102 ... 197 198 199] [ 200 201 202 ... 297 298 299] ... [9700 9701 9702 ... 9797 9798 9799] [9800 9801 9802 ... 9897 9898 9899] [9900 9901 9902 ... 9997 9998 9999]] To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions. >>> >>> np.set_printoptions(threshold=sys.maxsize) # sys module should be imported Basic Operations Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result. >>> >>> a = np.array( [20,30,40,50] ) >>> b = np.arange( 4 ) >>> b array([0, 1, 2, 3]) >>> c = a-b >>> c array([20, 29, 38, 47]) >>> b**2 array([0, 1, 4, 9]) >>> 10*np.sin(a) array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854]) >>> a<35 array([ True, True, False, False]) Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the @ operator (in python >=3.5) or the dot function or method: >>> >>> A = np.array( [[1,1], ... [0,1]] ) >>> B = np.array( [[2,0], ... [3,4]] ) >>> A * B # elementwise product array([[2, 0], [0, 4]]) >>> A @ B # matrix product array([[5, 4], [3, 4]]) >>> A.dot(B) # another matrix product array([[5, 4], [3, 4]]) Some operations, such as += and *=, act in place to modify an existing array rather than create a new one. >>> >>> rg = np.random.default_rng(1) # create instance of default random number generator >>> a = np.ones((2,3), dtype=int) >>> b = rg.random((2,3)) >>> a *= 3 >>> a array([[3, 3, 3], [3, 3, 3]]) >>> b += a >>> b array([[3.51182162, 3.9504637 , 3.14415961], [3.94864945, 3.31183145, 3.42332645]]) >>> a += b # b is not automatically converted to integer type Traceback (most recent call last): ... numpy.core._exceptions.UFuncTypeError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int64') with casting rule 'same_kind' When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting). >>> >>> a = np.ones(3, dtype=np.int32) >>> b = np.linspace(0,pi,3) >>> b.dtype.name 'float64' >>> c = a+b >>> c array([1. , 2.57079633, 4.14159265]) >>> c.dtype.name 'float64' >>> d = np.exp(c*1j) >>> d array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j, -0.54030231-0.84147098j]) >>> d.dtype.name 'complex128' Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class. >>> >>> a = rg.random((2,3)) >>> a array([[0.82770259, 0.40919914, 0.54959369], [0.02755911, 0.75351311, 0.53814331]]) >>> a.sum() 3.1057109529998157 >>> a.min() 0.027559113243068367 >>> a.max() 0.8277025938204418 By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array: >>> >>> b = np.arange(12).reshape(3,4) >>> b array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> b.sum(axis=0) # sum of each column array([12, 15, 18, 21]) >>> >>> b.min(axis=1) # min of each row array([0, 4, 8]) >>> >>> b.cumsum(axis=1) # cumulative sum along each row array([[ 0, 1, 3, 6], [ 4, 9, 15, 22], [ 8, 17, 27, 38]]) Universal Functions NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions”(ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output. >>> >>> B = np.arange(3) >>> B array([0, 1, 2]) >>> np.exp(B) array([1. , 2.71828183, 7.3890561 ]) >>> np.sqrt(B) array([0. , 1. , 1.41421356]) >>> C = np.array([2., -1., 4.]) >>> np.add(B, C) array([2., 0., 6.]) See also all, any, apply_along_axis, argmax, argmin, argsort, average, bincount, ceil, clip, conj, corrcoef, cov, cross, cumprod, cumsum, diff, dot, floor, inner, invert, lexsort, max, maximum, mean, median, min, minimum, nonzero, outer, prod, re, round, sort, std, sum, trace, transpose, var, vdot, vectorize, where Indexing, Slicing and Iterating One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences. >>> >>> a = np.arange(10)**3 >>> a array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729]) >>> a[2] 8 >>> a[2:5] array([ 8, 27, 64]) # equivalent to a[0:6:2] = 1000; # from start to position 6, exclusive, set every 2nd element to 1000 >>> a[:6:2] = 1000 >>> a array([1000, 1, 1000, 27, 1000, 125, 216, 343, 512, 729]) >>> a[ : :-1] # reversed a array([ 729, 512, 343, 216, 125, 1000, 27, 1000, 1, 1000]) >>> for i in a: ... print(i**(1/3.)) ... 9.999999999999998 1.0 9.999999999999998 3.0 9.999999999999998 4.999999999999999 5.999999999999999 6.999999999999999 7.999999999999999 8.999999999999998 Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas: >>> >>> def f(x,y): ... return 10*x+y ... >>> b = np.fromfunction(f,(5,4),dtype=int) >>> b array([[ 0, 1, 2, 3], [10, 11, 12, 13], [20, 21, 22, 23], [30, 31, 32, 33], [40, 41, 42, 43]]) >>> b[2,3] 23 >>> b[0:5, 1] # each row in the second column of b array([ 1, 11, 21, 31, 41]) >>> b[ : ,1] # equivalent to the previous example array([ 1, 11, 21, 31, 41]) >>> b[1:3, : ] # each column in the second and third row of b array([[10, 11, 12, 13], [20, 21, 22, 23]]) When fewer indices are provided than the number of axes, the missing indices are considered complete slices: >>> >>> b[-1] # the last row. Equivalent to b[-1,:] array([40, 41, 42, 43]) The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent the remaining axes. NumPy also allows you to write this using dots as b[i,...]. The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is an array with 5 axes, then x[1,2,...] is equivalent to x[1,2,:,:,:], x[...,3] to x[:,:,:,:,3] and x[4,...,5,:] to x[4,:,:,5,:]. >>> >>> c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays) ... [ 10, 12, 13]], ... [[100,101,102], ... [110,112,113]]]) >>> c.shape (2, 2, 3) >>> c[1,...] # same as c[1,:,:] or c[1] array([[100, 101, 102], [110, 112, 113]]) >>> c[...,2] # same as c[:,:,2] array([[ 2, 13], [102, 113]]) Iterating over multidimensional arrays is done with respect to the first axis: >>> >>> for row in b: ... print(row) ... [0 1 2 3] [10 11 12 13] [20 21 22 23] [30 31 32 33] [40 41 42 43] However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is an iterator over all the elements of the array: >>> >>> for element in b.flat: ... print(element) ... 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 40 41 42 43 See also Indexing, Indexing (reference), newaxis, ndenumerate, indices Shape Manipulation Changing the shape of an array An array has a shape given by the number of elements along each axis: >>> >>> a = np.floor(10*rg.random((3,4))) >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.shape (3, 4) The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array: >>> >>> a.ravel() # returns the array, flattened array([3., 7., 3., 4., 1., 4., 2., 2., 7., 2., 4., 9.]) >>> a.reshape(6,2) # returns the array with a modified shape array([[3., 7.], [3., 4.], [1., 4.], [2., 2.], [7., 2.], [4., 9.]]) >>> a.T # returns the array, transposed array([[3., 1., 7.], [7., 4., 2.], [3., 2., 4.], [4., 2., 9.]]) >>> a.T.shape (4, 3) >>> a.shape (3, 4) The order of the elements in the array resulting from ravel() is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0,0] is a[0,1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. NumPy normally creates arrays stored in this order, so ravel() will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel() and reshape() can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest. The reshape function returns its argument with a modified shape, whereas the ndarray.resize method modifies the array itself: >>> >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.resize((2,6)) >>> a array([[3., 7., 3., 4., 1., 4.], [2., 2., 7., 2., 4., 9.]]) If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated: >>> >>> a.reshape(3,-1) array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) See also ndarray.shape, reshape, resize, ravel Stacking together different arrays Several arrays can be stacked together along different axes: >>> >>> a = np.floor(10*rg.random((2,2))) >>> a array([[9., 7.], [5., 2.]]) >>> b = np.floor(10*rg.random((2,2))) >>> b array([[1., 9.], [5., 1.]]) >>> np.vstack((a,b)) array([[9., 7.], [5., 2.], [1., 9.], [5., 1.]]) >>> np.hstack((a,b)) array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to hstack only for 2D arrays: >>> >>> from numpy import newaxis >>> np.column_stack((a,b)) # with 2D arrays array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) >>> a = np.array([4.,2.]) >>> b = np.array([3.,8.]) >>> np.column_stack((a,b)) # returns a 2D array array([[4., 3.], [2., 8.]]) >>> np.hstack((a,b)) # the result is different array([4., 2., 3., 8.]) >>> a[:,newaxis] # view `a` as a 2D column vector array([[4.], [2.]]) >>> np.column_stack((a[:,newaxis],b[:,newaxis])) array([[4., 3.], [2., 8.]]) >>> np.hstack((a[:,newaxis],b[:,newaxis])) # the result is the same array([[4., 3.], [2., 8.]]) On the other hand, the function row_stack is equivalent to vstack for any input arrays. In fact, row_stack is an alias for vstack: >>> >>> np.column_stack is np.hstack False >>> np.row_stack is np.vstack True In general, for arrays with more than two dimensions, hstack stacks along their second axes, vstack stacks along their first axes, and concatenate allows for an optional arguments giving the number of the axis along which the concatenation should happen. Note In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis. They allow the use of range literals (“:”) >>> >>> np.r_[1:4,0,4] array([1, 2, 3, 0, 4]) When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their default behavior, but allow for an optional argument giving the number of the axis along which to concatenate. See also hstack, vstack, column_stack, concatenate, c_, r_ Splitting one array into several smaller ones Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur: >>> >>> a = np.floor(10*rg.random((2,12))) >>> a array([[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.], [8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]]) # Split a into 3 >>> np.hsplit(a,3) [array([[6., 7., 6., 9.], [8., 5., 5., 7.]]), array([[0., 5., 4., 0.], [1., 8., 6., 7.]]), array([[6., 8., 5., 2.], [1., 8., 1., 0.]])] # Split a after the third and the fourth column >>> np.hsplit(a,(3,4)) [array([[6., 7., 6.], [8., 5., 5.]]), array([[9.], [7.]]), array([[0., 5., 4., 0., 6., 8., 5., 2.], [1., 8., 6., 7., 1., 8., 1., 0.]])] vsplit splits along the vertical axis, and array_split allows one to specify along which axis to split. Copies and Views When operating and manipulating arrays, their data is sometimes copied into a new array and sometimes not. This is often a source of confusion for beginners. There are three cases: No Copy at All Simple assignments make no copy of objects or their data. >>> >>> a = np.array([[ 0, 1, 2, 3], ... [ 4, 5, 6, 7], ... [ 8, 9, 10, 11]]) >>> b = a # no new object is created >>> b is a # a and b are two names for the same ndarray object True Python passes mutable objects as references, so function calls make no copy. >>> >>> def f(x): ... print(id(x)) ... >>> id(a) # id is a unique identifier of an object 148293216 # may vary >>> f(a) 148293216 # may vary View or Shallow Copy Different array objects can share the same data. The view method creates a new array object that looks at the same data. >>> >>> c = a.view() >>> c is a False >>> c.base is a # c is a view of the data owned by a True >>> c.flags.owndata False >>> >>> c = c.reshape((2, 6)) # a's shape doesn't change >>> a.shape (3, 4) >>> c[0, 4] = 1234 # a's data changes >>> a array([[ 0, 1, 2, 3], [1234, 5, 6, 7], [ 8, 9, 10, 11]]) Slicing an array returns a view of it: >>> >>> s = a[ : , 1:3] # spaces added for clarity; could also be written "s = a[:, 1:3]" >>> s[:] = 10 # s[:] is a view of s. Note the difference between s = 10 and s[:] = 10 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Deep Copy The copy method makes a complete copy of the array and its data. >>> >>> d = a.copy() # a new array object with new data is created >>> d is a False >>> d.base is a # d doesn't share anything with a False >>> d[0,0] = 9999 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Sometimes copy should be called after slicing if the original array is not required anymore. For example, suppose a is a huge intermediate result and the final result b only contains a small fraction of a, a deep copy should be made when constructing b with slicing: >>> >>> a = np.arange(int(1e8)) >>> b = a[:100].copy() >>> del a # the memory of ``a`` can be released. If b = a[:100] is used instead, a is referenced by b and will persist in memory even if del a is executed. Functions and Methods Overview Here is a list of some useful NumPy functions and methods names ordered in categories. See Routines for the full list. Array Creation arange, array, copy, empty, empty_like, eye, fromfile, fromfunction, identity, linspace, logspace, mgrid, ogrid, ones, ones_like, r_, zeros, zeros_like Conversions ndarray.astype, atleast_1d, atleast_2d, atleast_3d, mat Manipulations array_split, column_stack, concatenate, diagonal, dsplit, dstack, hsplit, hstack, ndarray.item, newaxis, ravel, repeat, reshape, resize, squeeze, swapaxes, take, transpose, vsplit, vstack Questions all, any, nonzero, where Ordering argmax, argmin, argsort, max, min, ptp, searchsorted, sort Operations choose, compress, cumprod, cumsum, inner, ndarray.fill, imag, prod, put, putmask, real, sum Basic Statistics cov, mean, std, var Basic Linear Algebra cross, dot, outer, linalg.svd, vdot Less Basic Broadcasting rules Broadcasting allows universal functions to deal in a meaningful way with inputs that do not have exactly the same shape. The first rule of broadcasting is that if all input arrays do not have the same number of dimensions, a “1” will be repeatedly prepended to the shapes of the smaller arrays until all the arrays have the same number of dimensions. The second rule of broadcasting ensures that arrays with a size of 1 along a particular dimension act as if they had the size of the array with the largest shape along that dimension. The value of the array element is assumed to be the same along that dimension for the “broadcast” array. After application of the broadcasting rules, the sizes of all arrays must match. More details can be found in Broadcasting. Advanced indexing and index tricks NumPy offers more indexing facilities than regular Python sequences. In addition to indexing by integers and slices, as we saw before, arrays can be indexed by arrays of integers and arrays of booleans. Indexing with Arrays of Indices >>> >>> a = np.arange(12)**2 # the first 12 square numbers >>> i = np.array([1, 1, 3, 8, 5]) # an array of indices >>> a[i] # the elements of a at the positions i array([ 1, 1, 9, 64, 25]) >>> >>> j = np.array([[3, 4], [9, 7]]) # a bidimensional array of indices >>> a[j] # the same shape as j array([[ 9, 16], [81, 49]]) When the indexed array a is multidimensional, a single array of indices refers to the first dimension of a. The following example shows this behavior by converting an image of labels into a color image using a palette. >>> >>> palette = np.array([[0, 0, 0], # black ... [255, 0, 0], # red ... [0, 255, 0], # green ... [0, 0, 255], # blue ... [255, 255, 255]]) # white >>> image = np.array([[0, 1, 2, 0], # each value corresponds to a color in the palette ... [0, 3, 4, 0]]) >>> palette[image] # the (2, 4, 3) color image array([[[ 0, 0, 0], [255, 0, 0], [ 0, 255, 0], [ 0, 0, 0]], [[ 0, 0, 0], [ 0, 0, 255], [255, 255, 255], [ 0, 0, 0]]]) We can also give indexes for more than one dimension. The arrays of indices for each dimension must have the same shape. >>> >>> a = np.arange(12).reshape(3,4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> i = np.array([[0, 1], # indices for the first dim of a ... [1, 2]]) >>> j = np.array([[2, 1], # indices for the second dim ... [3, 3]]) >>> >>> a[i, j] # i and j must have equal shape array([[ 2, 5], [ 7, 11]]) >>> >>> a[i, 2] array([[ 2, 6], [ 6, 10]]) >>> >>> a[:, j] # i.e., a[ : , j] array([[[ 2, 1], [ 3, 3]], [[ 6, 5], [ 7, 7]], [[10, 9], [11, 11]]]) In Python, arr[i, j] is exactly the same as arr[(i, j)]—so we can put i and j in a tuple and then do the indexing with that. >>> >>> l = (i, j) # equivalent to a[i, j] >>> a[l] array([[ 2, 5], [ 7, 11]]) However, we can not do this by putting i and j into an array, because this array will be interpreted as indexing the first dimension of a. >>> >>> s = np.array([i, j]) # not what we want >>> a[s] Traceback (most recent call last): File "<stdin>", line 1, in <module> IndexError: index 3 is out of bounds for axis 0 with size 3 # same as a[i, j] >>> a[tuple(s)] array([[ 2, 5], [ 7, 11]]) Another common use of indexing with arrays is the search of the maximum value of time-dependent series: >>> >>> time = np.linspace(20, 145, 5) # time scale >>> data = np.sin(np.arange(20)).reshape(5,4) # 4 time-dependent series >>> time array([ 20. , 51.25, 82.5 , 113.75, 145. ]) >>> data array([[ 0. , 0.84147098, 0.90929743, 0.14112001], [-0.7568025 , -0.95892427, -0.2794155 , 0.6569866 ], [ 0.98935825, 0.41211849, -0.54402111, -0.99999021], [-0.53657292, 0.42016704, 0.99060736, 0.65028784], [-0.28790332, -0.96139749, -0.75098725, 0.14987721]]) # index of the maxima for each series >>> ind = data.argmax(axis=0) >>> ind array([2, 0, 3, 1]) # times corresponding to the maxima >>> time_max = time[ind] >>> >>> data_max = data[ind, range(data.shape[1])] # => data[ind[0],0], data[ind[1],1]... >>> time_max array([ 82.5 , 20. , 113.75, 51.25]) >>> data_max array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ]) >>> np.all(data_max == data.max(axis=0)) True You can also use indexing with arrays as a target to assign to: >>> >>> a = np.arange(5) >>> a array([0, 1, 2, 3, 4]) >>> a[[1,3,4]] = 0 >>> a array([0, 0, 2, 0, 0]) However, when the list of indices contains repetitions, the assignment is done several times, leaving behind the last value: >>> >>> a = np.arange(5) >>> a[[0,0,2]]=[1,2,3] >>> a array([2, 1, 3, 3, 4]) This is reasonable enough, but watch out if you want to use Python’s += construct, as it may not do what you expect: >>> >>> a = np.arange(5) >>> a[[0,0,2]]+=1 >>> a array([1, 1, 3, 3, 4]) Even though 0 occurs twice in the list of indices, the 0th element is only incremented once. This is because Python requires “a+=1” to be equivalent to “a = a + 1”. Indexing with Boolean Arrays When we index arrays with arrays of (integer) indices we are providing the list of indices to pick. With boolean indices the approach is different; we explicitly choose which items in the array we want and which ones we don’t. The most natural way one can think of for boolean indexing is to use boolean arrays that have the same shape as the original array: >>> >>> a = np.arange(12).reshape(3,4) >>> b = a > 4 >>> b # b is a boolean with a's shape array([[False, False, False, False], [False, True, True, True], [ True, True, True, True]]) >>> a[b] # 1d array with the selected elements array([ 5, 6, 7, 8, 9, 10, 11]) This property can be very useful in assignments: >>> >>> a[b] = 0 # All elements of 'a' higher than 4 become 0 >>> a array([[0, 1, 2, 3], [4, 0, 0, 0], [0, 0, 0, 0]]) You can look at the following example to see how to use boolean indexing to generate an image of the Mandelbrot set: >>> import numpy as np import matplotlib.pyplot as plt def mandelbrot( h,w, maxit=20 ): """Returns an image of the Mandelbrot fractal of size (h,w).""" y,x = np.ogrid[ -1.4:1.4:h*1j, -2:0.8:w*1j ] c = x+y*1j z = c divtime = maxit + np.zeros(z.shape, dtype=int) for i in range(maxit): z = z**2 + c diverge = z*np.conj(z) > 2**2 # who is diverging div_now = diverge & (divtime==maxit) # who is diverging now divtime[div_now] = i # note when z[diverge] = 2 # avoid diverging too much return divtime plt.imshow(mandelbrot(400,400)) ../_images/quickstart-1.png The second way of indexing with booleans is more similar to integer indexing; for each dimension of the array we give a 1D boolean array selecting the slices we want: >>> >>> a = np.arange(12).reshape(3,4) >>> b1 = np.array([False,True,True]) # first dim selection >>> b2 = np.array([True,False,True,False]) # second dim selection >>> >>> a[b1,:] # selecting rows array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[b1] # same thing array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[:,b2] # selecting columns array([[ 0, 2], [ 4, 6], [ 8, 10]]) >>> >>> a[b1,b2] # a weird thing to do array([ 4, 10]) Note that the length of the 1D boolean array must coincide with the length of the dimension (or axis) you want to slice. In the previous example, b1 has length 3 (the number of rows in a), and b2 (of length 4) is suitable to index the 2nd axis (columns) of a. The ix_() function The ix_ function can be used to combine different vectors so as to obtain the result for each n-uplet. For example, if you want to compute all the a+b*c for all the triplets taken from each of the vectors a, b and c: >>> >>> a = np.array([2,3,4,5]) >>> b = np.array([8,5,4]) >>> c = np.array([5,4,6,8,3]) >>> ax,bx,cx = np.ix_(a,b,c) >>> ax array([[[2]], [[3]], [[4]], [[5]]]) >>> bx array([[[8], [5], [4]]]) >>> cx array([[[5, 4, 6, 8, 3]]]) >>> ax.shape, bx.shape, cx.shape ((4, 1, 1), (1, 3, 1), (1, 1, 5)) >>> result = ax+bx*cx >>> result array([[[42, 34, 50, 66, 26], [27, 22, 32, 42, 17], [22, 18, 26, 34, 14]], [[43, 35, 51, 67, 27], [28, 23, 33, 43, 18], [23, 19, 27, 35, 15]], [[44, 36, 52, 68, 28], [29, 24, 34, 44, 19], [24, 20, 28, 36, 16]], [[45, 37, 53, 69, 29], [30, 25, 35, 45, 20], [25, 21, 29, 37, 17]]]) >>> result[3,2,4] 17 >>> a[3]+b[2]*c[4] 17 You could also implement the reduce as follows: >>> >>> def ufunc_reduce(ufct, *vectors): ... vs = np.ix_(*vectors) ... r = ufct.identity ... for v in vs: ... r = ufct(r,v) ... return r and then use it as: >>> >>> ufunc_reduce(np.add,a,b,c) array([[[15, 14, 16, 18, 13], [12, 11, 13, 15, 10], [11, 10, 12, 14, 9]], [[16, 15, 17, 19, 14], [13, 12, 14, 16, 11], [12, 11, 13, 15, 10]], [[17, 16, 18, 20, 15], [14, 13, 15, 17, 12], [13, 12, 14, 16, 11]], [[18, 17, 19, 21, 16], [15, 14, 16, 18, 13], [14, 13, 15, 17, 12]]]) The advantage of this version of reduce compared to the normal ufunc.reduce is that it makes use of the Broadcasting Rules in order to avoid creating an argument array the size of the output times the number of vectors. Indexing with strings See Structured arrays. Linear Algebra Work in progress. Basic linear algebra to be included here. Simple Array Operations See linalg.py in numpy folder for more. >>> >>> import numpy as np >>> a = np.array([[1.0, 2.0], [3.0, 4.0]]) >>> print(a) [[1. 2.] [3. 4.]] >>> a.transpose() array([[1., 3.], [2., 4.]]) >>> np.linalg.inv(a) array([[-2. , 1. ], [ 1.5, -0.5]]) >>> u = np.eye(2) # unit 2x2 matrix; "eye" represents "I" >>> u array([[1., 0.], [0., 1.]]) >>> j = np.array([[0.0, -1.0], [1.0, 0.0]]) >>> j @ j # matrix product array([[-1., 0.], [ 0., -1.]]) >>> np.trace(u) # trace 2.0 >>> y = np.array([[5.], [7.]]) >>> np.linalg.solve(a, y) array([[-3.], [ 4.]]) >>> np.linalg.eig(j) (array([0.+1.j, 0.-1.j]), array([[0.70710678+0.j , 0.70710678-0.j ], [0. -0.70710678j, 0. +0.70710678j]])) Parameters: square matrix Returns The eigenvalues, each repeated according to its multiplicity. The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]`` . Tricks and Tips Here we give a list of short and useful tips. “Automatic” Reshaping To change the dimensions of an array, you can omit one of the sizes which will then be deduced automatically: >>> >>> a = np.arange(30) >>> b = a.reshape((2, -1, 3)) # -1 means "whatever is needed" >>> b.shape (2, 5, 3) >>> b array([[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11], [12, 13, 14]], [[15, 16, 17], [18, 19, 20], [21, 22, 23], [24, 25, 26], [27, 28, 29]]]) Vector Stacking How do we construct a 2D array from a list of equally-sized row vectors? In MATLAB this is quite easy: if x and y are two vectors of the same length you only need do m=[x;y]. In NumPy this works via the functions column_stack, dstack, hstack and vstack, depending on the dimension in which the stacking is to be done. For example: >>> >>> x = np.arange(0,10,2) >>> y = np.arange(5) >>> m = np.vstack([x,y]) >>> m array([[0, 2, 4, 6, 8], [0, 1, 2, 3, 4]]) >>> xy = np.hstack([x,y]) >>> xy array([0, 2, 4, 6, 8, 0, 1, 2, 3, 4]) The logic behind those functions in more than two dimensions can be strange. See also NumPy for Matlab users Histograms The NumPy histogram function applied to an array returns a pair of vectors: the histogram of the array and a vector of the bin edges. Beware: matplotlib also has a function to build histograms (called hist, as in Matlab) that differs from the one in NumPy. The main difference is that pylab.hist plots the histogram automatically, while numpy.histogram only generates the data. >>> import numpy as np rg = np.random.default_rng(1) import matplotlib.pyplot as plt # Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2 mu, sigma = 2, 0.5 v = rg.normal(mu,sigma,10000) # Plot a normalized histogram with 50 bins plt.hist(v, bins=50, density=1) # matplotlib version (plot) # Compute the histogram with numpy and then plot it (n, bins) = np.histogram(v, bins=50, density=True) # NumPy version (no plot) plt.plot(.5*(bins[1:]+bins[:-1]), n) ../_images/quickstart-2.png Further reading The Python tutorial NumPy Reference SciPy Tutorial SciPy Lecture Notes A matlab, R, IDL, NumPy/SciPy dictionary © Copyright 2008-2020, The SciPy community. Last updated on Jun 29, 2020. Created using Sphinx 2.4.4.

Jupyter中文集成版(Python整合版)，是把python3.8和jupyter notebook高度集成，jupyter傻瓜式安装，用最简洁友好的纯中文方式(jupyter汉化100%)展现出来的优秀Jupyter绿色使用工具。本工具，把Jupyter的复杂操作简单化，集成pandas、numpy、matplotlib等常用三方库，并附带一些python的基础语法、pandas使用、股票分析实例，让您能最快的开始Jupyter的编写。

The famous Cats-vs-Dogs dataset. I have used a self laid ConvNet to classify the image into 2 classes either a Dog or a Cat. The images used are of 100*100 pixels each. The images are first converted to the numpy array of pixel values using the python ZipFile module. The images are then divided into the training ,cross-validation,testing set containing 20000 , 5000 , 12500 images respectively. Also I have used data augmentation technique to avoid chances of overfitting the model. Finally I achieved a decent accuracy of about 88 % on the validation set.

Machine-learning approach In this work, author has developed data-driven models that accurately predict the cycle life of commercial lithium iron phosphate (LFP)/ graphite cells using early-cycle data, with no prior knowledge of degradation mechanisms. To build an early-prediction model, a feature-based approach is used. Features, such as initial discharge capacity, charge time, and cell can temperature, are generated and used in a regularized linear framework and proposed from domain knowledge of lithium-ion batteries. Several features are calculated based on the discharge voltage curve to capture the electrochemical evolution of individual cells during cycling. For the Q(V), the discharge voltage curves of each cell, summary statistics such as minimum, mean, and variance are determined. The change in voltage curves between two cycles is captured by each summary statistic. Three alternative models have been studied due to the great predictive potential of features based on Q100-10(V). (1) variance of ΔQ100-10(V), (2) additional candidate features obtained during discharge and (3) features from additional data streams such as temperature and internal resistance. Data is collected from the first 100 cycles in every case. These three models are proposed to examine the cost–benefit of collecting more data streams as well as the accuracy limits of prediction. The training data (41 cells) are used to choose model features and coefficient values, while the primary testing data (43 cells) are used to evaluate model performance. The model is then tested using a secondary testing dataset (40 cells) that has been generated after the development of the model. The prediction performance is measured using two metrics: root-mean-square error (RMSE), which is measured in cycles, and average percentage error, which is explained in the ‘Machine-Learning model creation’ selection. In short, the data is first separated into training and test sets. The elastic net is then used to train the model on the training set, resulting in a linear model with downselected features and coefficients. The model is then applied to both the primary and secondary test sets. The elastic net prediction and data processing are done in MATLAB, while the classification is done in Python with the NumPy, pandas, and sklearn tools.

A collection of 100 NumPy exercises (created by user rougier) that I completed at Byte Academy.

The PyTorch solutions for numpy-100 exercises.

100 numpy exercise to brush up the skills with numpy library and to get familier with

Forked from rougier/numpy-100 numpy-100日本語バージョン

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I propose an original solution to one of the most well-known machine learning problems - Iris Species using a spiking neural network (SNN), with a test accuracy of 100%. In my work, I will not use well-known ready-made solutions in python related to SNN. All the code is written by me from scratch, using only NumPy and Pandas.

An emerging prototypical clone of https://github.com/deeplook/numpy-100, but for pandas.

100 numpy exercises by https://github.com/rougier/numpy-100

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中文版Numpy100

# Copyright 2015 Google Inc. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== """Multi-threaded word2vec mini-batched skip-gram model. Trains the model described in: (Mikolov, et. al.) Efficient Estimation of Word Representations in Vector Space ICLR 2013. http://arxiv.org/abs/1301.3781 This model does traditional minibatching. The key ops used are: * placeholder for feeding in tensors for each example. * embedding_lookup for fetching rows from the embedding matrix. * sigmoid_cross_entropy_with_logits to calculate the loss. * GradientDescentOptimizer for optimizing the loss. * skipgram custom op that does input processing. """ from __future__ import absolute_import from __future__ import division from __future__ import print_function import os import sys import threading import time from six.moves import xrange # pylint: disable=redefined-builtin import numpy as np import tensorflow as tf from tensorflow.models.embedding import gen_word2vec as word2vec flags = tf.app.flags flags.DEFINE_string("save_path", None, "Directory to write the model and " "training summaries.") flags.DEFINE_string("train_data", None, "Training text file. " "E.g., unzipped file http://mattmahoney.net/dc/text8.zip.") flags.DEFINE_string( "eval_data", None, "File consisting of analogies of four tokens." "embedding 2 - embedding 1 + embedding 3 should be close " "to embedding 4." "E.g. https://word2vec.googlecode.com/svn/trunk/questions-words.txt.") flags.DEFINE_integer("embedding_size", 200, "The embedding dimension size.") flags.DEFINE_integer( "epochs_to_train", 15, "Number of epochs to train. Each epoch processes the training data once " "completely.") flags.DEFINE_float("learning_rate", 0.2, "Initial learning rate.") flags.DEFINE_integer("num_neg_samples", 100, "Negative samples per training example.") flags.DEFINE_integer("batch_size", 16, "Number of training examples processed per step " "(size of a minibatch).") flags.DEFINE_integer("concurrent_steps", 12, "The number of concurrent training steps.") flags.DEFINE_integer("window_size", 5, "The number of words to predict to the left and right " "of the target word.") flags.DEFINE_integer("min_count", 5, "The minimum number of word occurrences for it to be " "included in the vocabulary.") flags.DEFINE_float("subsample", 1e-3, "Subsample threshold for word occurrence. Words that appear " "with higher frequency will be randomly down-sampled. Set " "to 0 to disable.") flags.DEFINE_boolean( "interactive", False, "If true, enters an IPython interactive session to play with the trained " "model. E.g., try model.analogy('france', 'paris', 'russia') and " "model.nearby(['proton', 'elephant', 'maxwell']") flags.DEFINE_integer("statistics_interval", 5, "Print statistics every n seconds.") flags.DEFINE_integer("summary_interval", 5, "Save training summary to file every n seconds (rounded " "up to statistics interval.") flags.DEFINE_integer("checkpoint_interval", 600, "Checkpoint the model (i.e. save the parameters) every n " "seconds (rounded up to statistics interval.") FLAGS = flags.FLAGS class Options(object): """Options used by our word2vec model.""" def __init__(self): # Model options. # Embedding dimension. self.emb_dim = FLAGS.embedding_size # Training options. # The training text file. self.train_data = FLAGS.train_data # Number of negative samples per example. self.num_samples = FLAGS.num_neg_samples # The initial learning rate. self.learning_rate = FLAGS.learning_rate # Number of epochs to train. After these many epochs, the learning # rate decays linearly to zero and the training stops. self.epochs_to_train = FLAGS.epochs_to_train # Concurrent training steps. self.concurrent_steps = FLAGS.concurrent_steps # Number of examples for one training step. self.batch_size = FLAGS.batch_size # The number of words to predict to the left and right of the target word. self.window_size = FLAGS.window_size # The minimum number of word occurrences for it to be included in the # vocabulary. self.min_count = FLAGS.min_count # Subsampling threshold for word occurrence. self.subsample = FLAGS.subsample # How often to print statistics. self.statistics_interval = FLAGS.statistics_interval # How often to write to the summary file (rounds up to the nearest # statistics_interval). self.summary_interval = FLAGS.summary_interval # How often to write checkpoints (rounds up to the nearest statistics # interval). self.checkpoint_interval = FLAGS.checkpoint_interval # Where to write out summaries. self.save_path = FLAGS.save_path # Eval options. # The text file for eval. self.eval_data = FLAGS.eval_data class Word2Vec(object): """Word2Vec model (Skipgram).""" def __init__(self, options, session): self._options = options self._session = session self._word2id = {} self._id2word = [] self.build_graph() self.build_eval_graph() self.save_vocab() self._read_analogies() def _read_analogies(self): """Reads through the analogy question file. Returns: questions: a [n, 4] numpy array containing the analogy question's word ids. questions_skipped: questions skipped due to unknown words. """ questions = [] questions_skipped = 0 with open(self._options.eval_data, "rb") as analogy_f: for line in analogy_f: if line.startswith(b":"): # Skip comments. continue words = line.strip().lower().split(b" ") ids = [self._word2id.get(w.strip()) for w in words] if None in ids or len(ids) != 4: questions_skipped += 1 else: questions.append(np.array(ids)) print("Eval analogy file: ", self._options.eval_data) print("Questions: ", len(questions)) print("Skipped: ", questions_skipped) self._analogy_questions = np.array(questions, dtype=np.int32) def forward(self, examples, labels): """Build the graph for the forward pass.""" opts = self._options # Declare all variables we need. # Embedding: [vocab_size, emb_dim] init_width = 0.5 / opts.emb_dim emb = tf.Variable( tf.random_uniform( [opts.vocab_size, opts.emb_dim], -init_width, init_width), name="emb") self._emb = emb # Softmax weight: [vocab_size, emb_dim]. Transposed. sm_w_t = tf.Variable( tf.zeros([opts.vocab_size, opts.emb_dim]), name="sm_w_t") # Softmax bias: [emb_dim]. sm_b = tf.Variable(tf.zeros([opts.vocab_size]), name="sm_b") # Global step: scalar, i.e., shape []. self.global_step = tf.Variable(0, name="global_step") # Nodes to compute the nce loss w/ candidate sampling. labels_matrix = tf.reshape( tf.cast(labels, dtype=tf.int64), [opts.batch_size, 1]) # Negative sampling. sampled_ids, _, _ = (tf.nn.fixed_unigram_candidate_sampler( true_classes=labels_matrix, num_true=1, num_sampled=opts.num_samples, unique=True, range_max=opts.vocab_size, distortion=0.75, unigrams=opts.vocab_counts.tolist())) # Embeddings for examples: [batch_size, emb_dim] example_emb = tf.nn.embedding_lookup(emb, examples) # Weights for labels: [batch_size, emb_dim] true_w = tf.nn.embedding_lookup(sm_w_t, labels) # Biases for labels: [batch_size, 1] true_b = tf.nn.embedding_lookup(sm_b, labels) # Weights for sampled ids: [num_sampled, emb_dim] sampled_w = tf.nn.embedding_lookup(sm_w_t, sampled_ids) # Biases for sampled ids: [num_sampled, 1] sampled_b = tf.nn.embedding_lookup(sm_b, sampled_ids) # True logits: [batch_size, 1] true_logits = tf.reduce_sum(tf.mul(example_emb, true_w), 1) + true_b # Sampled logits: [batch_size, num_sampled] # We replicate sampled noise lables for all examples in the batch # using the matmul. sampled_b_vec = tf.reshape(sampled_b, [opts.num_samples]) sampled_logits = tf.matmul(example_emb, sampled_w, transpose_b=True) + sampled_b_vec return true_logits, sampled_logits def nce_loss(self, true_logits, sampled_logits): """Build the graph for the NCE loss.""" # cross-entropy(logits, labels) opts = self._options true_xent = tf.nn.sigmoid_cross_entropy_with_logits( true_logits, tf.ones_like(true_logits)) sampled_xent = tf.nn.sigmoid_cross_entropy_with_logits( sampled_logits, tf.zeros_like(sampled_logits)) # NCE-loss is the sum of the true and noise (sampled words) # contributions, averaged over the batch. nce_loss_tensor = (tf.reduce_sum(true_xent) + tf.reduce_sum(sampled_xent)) / opts.batch_size return nce_loss_tensor def optimize(self, loss): """Build the graph to optimize the loss function.""" # Optimizer nodes. # Linear learning rate decay. opts = self._options words_to_train = float(opts.words_per_epoch * opts.epochs_to_train) lr = opts.learning_rate * tf.maximum( 0.0001, 1.0 - tf.cast(self._words, tf.float32) / words_to_train) self._lr = lr optimizer = tf.train.GradientDescentOptimizer(lr) train = optimizer.minimize(loss, global_step=self.global_step, gate_gradients=optimizer.GATE_NONE) self._train = train def build_eval_graph(self): """Build the eval graph.""" # Eval graph # Each analogy task is to predict the 4th word (d) given three # words: a, b, c. E.g., a=italy, b=rome, c=france, we should # predict d=paris. # The eval feeds three vectors of word ids for a, b, c, each of # which is of size N, where N is the number of analogies we want to # evaluate in one batch. analogy_a = tf.placeholder(dtype=tf.int32) # [N] analogy_b = tf.placeholder(dtype=tf.int32) # [N] analogy_c = tf.placeholder(dtype=tf.int32) # [N] # Normalized word embeddings of shape [vocab_size, emb_dim]. nemb = tf.nn.l2_normalize(self._emb, 1) # Each row of a_emb, b_emb, c_emb is a word's embedding vector. # They all have the shape [N, emb_dim] a_emb = tf.gather(nemb, analogy_a) # a's embs b_emb = tf.gather(nemb, analogy_b) # b's embs c_emb = tf.gather(nemb, analogy_c) # c's embs # We expect that d's embedding vectors on the unit hyper-sphere is # near: c_emb + (b_emb - a_emb), which has the shape [N, emb_dim]. target = c_emb + (b_emb - a_emb) # Compute cosine distance between each pair of target and vocab. # dist has shape [N, vocab_size]. dist = tf.matmul(target, nemb, transpose_b=True) # For each question (row in dist), find the top 4 words. _, pred_idx = tf.nn.top_k(dist, 4) # Nodes for computing neighbors for a given word according to # their cosine distance. nearby_word = tf.placeholder(dtype=tf.int32) # word id nearby_emb = tf.gather(nemb, nearby_word) nearby_dist = tf.matmul(nearby_emb, nemb, transpose_b=True) nearby_val, nearby_idx = tf.nn.top_k(nearby_dist, min(1000, self._options.vocab_size)) # Nodes in the construct graph which are used by training and # evaluation to run/feed/fetch. self._analogy_a = analogy_a self._analogy_b = analogy_b self._analogy_c = analogy_c self._analogy_pred_idx = pred_idx self._nearby_word = nearby_word self._nearby_val = nearby_val self._nearby_idx = nearby_idx def build_graph(self): """Build the graph for the full model.""" opts = self._options # The training data. A text file. (words, counts, words_per_epoch, self._epoch, self._words, examples, labels) = word2vec.skipgram(filename=opts.train_data, batch_size=opts.batch_size, window_size=opts.window_size, min_count=opts.min_count, subsample=opts.subsample) (opts.vocab_words, opts.vocab_counts, opts.words_per_epoch) = self._session.run([words, counts, words_per_epoch]) opts.vocab_size = len(opts.vocab_words) print("Data file: ", opts.train_data) print("Vocab size: ", opts.vocab_size - 1, " + UNK") print("Words per epoch: ", opts.words_per_epoch) self._examples = examples self._labels = labels self._id2word = opts.vocab_words for i, w in enumerate(self._id2word): self._word2id[w] = i true_logits, sampled_logits = self.forward(examples, labels) loss = self.nce_loss(true_logits, sampled_logits) tf.scalar_summary("NCE loss", loss) self._loss = loss self.optimize(loss) # Properly initialize all variables. tf.initialize_all_variables().run() self.saver = tf.train.Saver() def save_vocab(self): """Save the vocabulary to a file so the model can be reloaded.""" opts = self._options with open(os.path.join(opts.save_path, "vocab.txt"), "w") as f: for i in xrange(opts.vocab_size): f.write("%s %d\n" % (tf.compat.as_text(opts.vocab_words[i]), opts.vocab_counts[i])) def _train_thread_body(self): initial_epoch, = self._session.run([self._epoch]) while True: _, epoch = self._session.run([self._train, self._epoch]) if epoch != initial_epoch: break def train(self): """Train the model.""" opts = self._options initial_epoch, initial_words = self._session.run([self._epoch, self._words]) summary_op = tf.merge_all_summaries() summary_writer = tf.train.SummaryWriter(opts.save_path, graph_def=self._session.graph_def) workers = [] for _ in xrange(opts.concurrent_steps): t = threading.Thread(target=self._train_thread_body) t.start() workers.append(t) last_words, last_time, last_summary_time = initial_words, time.time(), 0 last_checkpoint_time = 0 while True: time.sleep(opts.statistics_interval) # Reports our progress once a while. (epoch, step, loss, words, lr) = self._session.run( [self._epoch, self.global_step, self._loss, self._words, self._lr]) now = time.time() last_words, last_time, rate = words, now, (words - last_words) / ( now - last_time) print("Epoch %4d Step %8d: lr = %5.3f loss = %6.2f words/sec = %8.0f\r" % (epoch, step, lr, loss, rate), end="") sys.stdout.flush() if now - last_summary_time > opts.summary_interval: summary_str = self._session.run(summary_op) summary_writer.add_summary(summary_str, step) last_summary_time = now if now - last_checkpoint_time > opts.checkpoint_interval: self.saver.save(self._session, opts.save_path + "model", global_step=step.astype(int)) last_checkpoint_time = now if epoch != initial_epoch: break for t in workers: t.join() return epoch def _predict(self, analogy): """Predict the top 4 answers for analogy questions.""" idx, = self._session.run([self._analogy_pred_idx], { self._analogy_a: analogy[:, 0], self._analogy_b: analogy[:, 1], self._analogy_c: analogy[:, 2] }) return idx def eval(self): """Evaluate analogy questions and reports accuracy.""" # How many questions we get right at precision@1. correct = 0 total = self._analogy_questions.shape[0] start = 0 while start < total: limit = start + 2500 sub = self._analogy_questions[start:limit, :] idx = self._predict(sub) start = limit for question in xrange(sub.shape[0]): for j in xrange(4): if idx[question, j] == sub[question, 3]: # Bingo! We predicted correctly. E.g., [italy, rome, france, paris]. correct += 1 break elif idx[question, j] in sub[question, :3]: # We need to skip words already in the question. continue else: # The correct label is not the precision@1 break print() print("Eval %4d/%d accuracy = %4.1f%%" % (correct, total, correct * 100.0 / total)) def analogy(self, w0, w1, w2): """Predict word w3 as in w0:w1 vs w2:w3.""" wid = np.array([[self._word2id.get(w, 0) for w in [w0, w1, w2]]]) idx = self._predict(wid) for c in [self._id2word[i] for i in idx[0, :]]: if c not in [w0, w1, w2]: return c return "unknown" def nearby(self, words, num=20): """Prints out nearby words given a list of words.""" ids = np.array([self._word2id.get(x, 0) for x in words]) vals, idx = self._session.run( [self._nearby_val, self._nearby_idx], {self._nearby_word: ids}) for i in xrange(len(words)): print("\n%s\n=====================================" % (words[i])) for (neighbor, distance) in zip(idx[i, :num], vals[i, :num]): print("%-20s %6.4f" % (self._id2word[neighbor], distance)) def _start_shell(local_ns=None): # An interactive shell is useful for debugging/development. import IPython user_ns = {} if local_ns: user_ns.update(local_ns) user_ns.update(globals()) IPython.start_ipython(argv=[], user_ns=user_ns) def main(_): """Train a word2vec model.""" if not FLAGS.train_data or not FLAGS.eval_data or not FLAGS.save_path: print("--train_data --eval_data and --save_path must be specified.") sys.exit(1) opts = Options() with tf.Graph().as_default(), tf.Session() as session: with tf.device("/cpu:0"): model = Word2Vec(opts, session) for _ in xrange(opts.epochs_to_train): model.train() # Process one epoch model.eval() # Eval analogies. # Perform a final save. model.saver.save(session, os.path.join(opts.save_path, "model.ckpt"), global_step=model.global_step) if FLAGS.interactive: # E.g., # [0]: model.analogy('france', 'paris', 'russia') # [1]: model.nearby(['proton', 'elephant', 'maxwell']) _start_shell(locals()) if __name__ == "__main__": tf.app.run()

ユニットテストフレームワークを利用したNumPyの練習問題100

This is a collection of numpy exercises from numpy mailing list, stack overflow, and numpy documentation. I've also created some problems myself to reach the 100 limit. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach. For extended exercises, make sure to read [From Python to NumPy](http://www.labri.fr/perso/nrougier/from-python-to-numpy/).

100 narray exercises (Ruby port of numpy-100)

100道小练习带你熟练掌握数据分析神器Numpy！