Numpy Get Indices Where True

Regarding indices_or_sections, if it is an integer N, the array will be divided into N equal arrays along the axis. Instead, it is common to import under the briefer name np:. NumPy has a nice function that returns the indices where your criteria are met in some arrays: condition_1 = (a == 1) condition_2 = (b == 1) Now we can combine the operation by saying "and" - the binary operator version: &. Python NumPy: Array Object Exercise-31 with Solution. A way to overcome this is to duplicate the smaller array so that it is the dimensionality and size as the larger array. The reason it doesn’t work is because np. In this case, rows are the least rapidly changing index, hence the slice is made on the row. If it is a 1-D array of sorted integers, the entries indicate where along the axis the array is split. The three types of indexing methods that are followed in numpy − field access, basic slicing, and advanced indexing. where ¶ numpy. multiplication. Numpy For Beginners. The numpy array has many useful properties for example vector addition, we can add the two arrays as follows: z=u+v z:array([1,1]) Example 2: add numpy arrays u and v to form a new numpy array z. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. This is called array broadcasting and is available in NumPy when performing array. x, y and condition need to be broadcastable to some shape. By voting up you can indicate which examples are most useful and appropriate. NumPy Array Object Exercises, Practice and Solution: Write a NumPy program to select indices satisfying multiple conditions in a numpy array. casting=None, subok=None, copy=True. In general fruits[start:stop] will get the elements in start, start+1, , stop-1. In this part, I go into the details of the advanced features of numpy that are essential for data analysis and manipulations. x, y and condition need to be broadcastable to some shape. Fork me on GitHub. index = a > 0. Counting: Easy as 1, 2, 3… As an illustration, consider a 1-dimensional vector of True and False for which you want to count the number of “False to True” transitions in the sequence: >>>. Indexing in two-dimensional array is represented by a pair of values, where the first value is the index of the row and the second is the index of the column. It is an open source module of Python which provides fast mathematical computation on arrays and matrices. mean) group a 6. Arrays of Ones and of Zeros. + Save to library. Values from which to choose. You are not concerned about the sequence of indices in the output, you can use numpy's in1d and nonzero functions. Creating such an array is highly useful because of its immense potential just like simply checking for an element in the array 2 in integerArray returns True. where() function returns an array with indices where the specified condition is true. As we can see from the output, we were able to get 0th, 1st, 1st, 2nd, and 3rd elements of the random array. 00000000e+01] [False True True] [ True True True] It can be useful to confirm there should be a solution, e. In the case above condition is a boolean array. You can create an array of booleans and then use that to index into your array. index)) We can use frac to get 200 randomly selected rows also. NumPy stands for 'Numerical Python' or 'Numeric Python'. In other words, we can define a ndarray as the collection of the data type (dtype) objects. timeit( 'np. Indicate which axis or axes should be reduced. NumPy tries to guess a datatype when you create an array, but functions that construct arrays usually also include an optional argument to explicitly specify the datatype. How to create and initialize numpy arrays? There are many ways to create and initialize numpy arrays. Suppose, if we want to select the fifth column, then its index will be 4, or if we want to select third row data, then its index will be 2, and so on. NumPy is a Python Library/ module which is used for scientific calculations in Python programming. If you want to get anywhere, go implement that object and come back. combine_slices (slice_datasets, rescale=None) ¶ Given a list of pydicom datasets for an image series, stitch them together into a three-dimensional numpy array. import scipy. **Data type** **Description** bool_ Boolean (True or False) stored as a byte int_ Default integer type (same as C long; normally either int64 or int32) intc Identical to C int (normally int32 or int64) intp Integer used for indexing (same as C ssize_t; normally either int32 or int64) int8 Byte (-128 to 127) int16 Integer (-32768 to 32767) int32 Integer (-2147483648 to 2147483647) int64 Integer. Docstring Standard¶. Ask Question Are there any rules around when something can be described as "based on a true story"?. Join Stack Overflow to learn, share knowledge, and build your career. This tutorial was contributed by Justin Johnson. pivot_table (values = 'ounces', index = 'group', aggfunc = np. If you have some knowledge of Cython you may want to skip to the ''Efficient indexing'' section. In this tutorial, you will discover how to. This module demonstrates documentation as specified by the `NumPy Documentation HOWTO`_. For example, you can get a 4 by 4 array of samples from the standard normal distribution using normal:. Getting started with NumPy. Let's get further into this Python NumPy tutorial and learn about that as well. You will use them when you would like to work with a subset of the array. Different retailers and brands will implement indices differently. a[index] = b Printing index will show an array of True and False that mask the original array. Parameters. This is implemented as a layer rather than an activation primarily because it requires retaining the layer input in order to compute the softmax gradients properly. NumPy Array: Numpy array is a powerful N-dimensional array object which is in the form of rows and columns. You can vote up the examples you like or vote down the ones you don't like. Arrays of Ones and of Zeros. It aims to build a model with predictive power. Immutable ndarray implementing an ordered, sliceable set. sparse or list of numpy arrays) - Data source of Dataset. label (list, numpy 1-D array, pandas Series / one-column DataFrame or None, optional (default=None)) - Label of the data. linalg , as detailed in section Linear algebra operations: scipy. array(['a','e','i','o','u']) Note: Select the elements from the second array corresponding to elements in the first array that are greater than 100 and less than 110. According to documentation of numpy. Getting started with NumPy. Understanding the internals of NumPy to avoid unnecessary array copying. 666667 Name: ounces, dtype: float64 #calc. nd_grid` which returns an open (i. Will be converted to an array of characters (datatype 'S1' or 'U1') of shape a. argsort(axis=0). cross_validation` module includes utilities for cross-validation and performanc. Matrix multiplication in non-commutative and only requires that the number of columns of the matrix on the left match the number of rows of the matrix. 14 Manual Here, the following contents will be described. Encode categorical integer features as a one-hot numeric array. x, y array_like. NumPy (acronym for 'Numerical Python' or 'Numeric Python') is one of the most essential package for speedy mathematical computation on arrays and matrices in Python. NumPy's basic data type is the multidimensional array. For NumPy dtypes, this will be a reference to the actual data stored in this Series or Index (assuming copy=False). For each element in the calling DataFrame, if cond is True the element is used; otherwise the corresponding element from the DataFrame other is used. Numpy For Beginners. Boolean numpy arrays A boolean array is a numpy array with boolean (True/False) values. It provides a high-performance multidimensional array object, and tools for working with these arrays. If you don't supply enough indices to an array, an ellipsis is silently appended. NumPy (Numerical Python) is a linear algebra library in Python. You can vote up the examples you like or vote down the ones you don't like. Get the index of an item Count an item Append an item at a time Remove an item Remove an item Reverse the list Append an item Remove an item Insert an item Sort the list Index starts at 0 Select item at index 1 Select 3rd last item Select items at index 1 and 2 Select items after index 0 Select items before index 3 Copy my_list my_list[list. I have a NumPy array ‘boolarr’ of boolean type. The reason it doesn't work is because np. Masking comes up when you want to extract, modify, count, or otherwise manipulate values in an array based on some criterion: for example, you might wish to count all values greater than a certain value, or perhaps remove all outliers that are above some threshold. If a and b are both True values, then a and b returns b. Using Numpy. Where True, yield x, otherwise yield y. where creates a 2x2 array (ie the size of the array of the first param), it then checks through the entries of the array in the first param, at whatever position the entry it true, it looks over to the second param and gets the value. nonzero and where. Now if we provide this as an indexing parameter to another NumPy array (which has the same dimensions) we filter out the values to a vector (1 dimensional matrix) where the index contains True. As mentioned earlier, items in numpy array object follow zero-based index. pivot_table (values = 'ounces', index = 'group', aggfunc = np. Docstring Standard¶. For example, get the indices of elements with value less than 16 and greater than 12 i. If string, it represents the path to txt file. Given an array a, the condition a > 3 is a boolean array and since False is interpreted as 0, np. 这是一篇翻译。原文:Python Numpy Tutorial翻译:我如果有什么问题欢迎留言私信指正探讨。正文:这篇教程是由Justin Johnson. This function returns an array of unique elements in the input array. Want to learn more such tricks? Get your “Coffee Break NumPy“! The book is full of tips, tricks, and NumPy puzzles to lift you to an expert NumPy level. If you are new to Python, you may be confused by some of the pythonic ways of accessing data, such as negative indexing and array slicing. NumPy creates an appropriate scale index at the time of array creation. Create histograms and scatter plots for basic exploratory data analysis; This lab maps on to lecture 1, lecture 2, lecture 3 and to parts of homework 1. The following are code examples for showing how to use numpy. out : ndarray or tuple of ndarrays. As we can see from the output, we were able to get 0th, 1st, 1st, 2nd, and 3rd elements of the random array. I would suggest though making sure you have the basics down before you dig into numpy. They are extracted from open source Python projects. Example: you have exhange rates for a year, you want GBDT to predict next exchange rate based on the previous 10. There are different kinds of datatypes provided by NumPy for different applications but we'll mostly be working with the default integer type numpy. where(condition[, x, y]) function returns the indices of elements in an input array where the given condition is satisfied. If string, it represents the path to txt file. The corresponding non-zero values can be obtained with ``a[a. Write a Python program to get the values and indices of the elements that are bigger than 10 in a given array. Numpy Cheat Sheet Python Package Created By: arianne Colton and Sean Chen SCN NDNSUBSN numPy (numerical Python) What is NumPy? Foundation package for scientific computing in Python Why NumPy? • Numpy 'ndarray' is a much more efficient way of storing and manipulating "numerical data" than the built-in Python data structures. If only condition is given, return the tuple condition. Introduction to NumPy. Here are the examples of the python api numpy. insert(arr, 3, [1,2,3])` to insert multiple items at a single position. Transforming Indices from NumPy Array to Sliced Array, then Back. Use fancy indexing on the left and array creation on the right to assign values into an array, for instance by setting parts of the array in the diagram above to zero. In parallel, data visualization aims to present the data graphically for you to easily understanding their meaning. Values from which to choose. In combination with numpy's array-wise operations, this means that functions written for one-dimensional arrays can often just work for two-dimensional arrays. We can initialize numpy arrays from nested Python lists and access it elements. Create histograms and scatter plots for basic exploratory data analysis; This lab maps on to lecture 1, lecture 2, lecture 3 and to parts of homework 1. >>> import numpy as np. Want to learn more such tricks? Get your “Coffee Break NumPy“! The book is full of tips, tricks, and NumPy puzzles to lift you to an expert NumPy level. The following are code examples for showing how to use numpy. A sparse tensor can be uncoalesced, in that case, there are duplicate coordinates in the indices, and the value at that index is the sum of all duplicate value entries: torch. array([10, 15, 25, 35, 45, 55, 65]) arr arr[0] arr[2] arr[5] arr[7] arr[2:5] OUTPUT. Indices are grouped by element. What is Numpy? Numpy is a Python library that supports multi-dimensional arrays and matrix. float64) ' \ 'my_val = 1. The given condition is a>5. mean) group a 6. NumPy (Numerical Python) is a linear algebra library in Python. The input to this transformer should be an array-like of integers or strings, denoting the values taken on by categorical (discrete) features. We can also define a range such as [:2] which prints all values at indices 0 to 1. The reason it doesn’t work is because np. In this release, they raise a FutureWarning warning of this coming change. This document describes the current community consensus for such a standard. Installation; Documentation; Examples; Tutorials; Contributing. In other words, we can define a ndarray as the collection of the data type (dtype) objects. The goal of the numpy exercises is to serve as a reference as well as to get you to apply numpy beyond the basics. We can also do fruits[start:] which returns all elements starting from the start index. However, it is not guaranteed to be compiled using efficient routines, and thus we recommend the use of scipy. Regarding indices_or_sections, if it is an integer N, the array will be divided into N equal arrays along the axis. Numpy library can also be used to integrate C/C++ and Fortran code. For example, you can get a 4 by 4 array of samples from the standard normal distribution using normal:. indices (array_like) - Initial data for the tensor. The features are encoded using a one-hot (aka 'one-of-K' or 'dummy') encoding scheme. Returns out ndarray. where()这个函数,看了官方文件,不太明白,比如下面这段[xv if c else yv for (c,xv,yv…. A sparse tensor can be uncoalesced, in that case, there are duplicate coordinates in the indices, and the value at that index is the sum of all duplicate value entries: torch. NumPy Array Object Exercises, Practice and Solution: Write a NumPy program to get the values and indices of the elements that are bigger than 10 in a given array. insert(arr, [3], [1, 2, 3])`. I think shlok's answer is correct as you are trying to index a numpy array with float that is not correct change that and i think you are good to go commented Aug 16 by kodee ( 42. Since, arrays and matrices are an essential part of the Machine Learning ecosystem, NumPy along with Machine Learning modules like Scikit-learn, Pandas, Matplotlib. csv',delimiter=',',dtype=None)[1:] Next we will make two arrays. I need to find the rows that have true or rows in e whose value are more than 15. combine_slices (slice_datasets, rescale=None) ¶ Given a list of pydicom datasets for an image series, stitch them together into a three-dimensional numpy array. According to documentation of numpy. The matrix rank will tell us that. We can create an array of the same shape but with a dtype of bool, where each entry is True or False. The reason it doesn’t work is because np. This file can be downloaded as eg6-a-student-data. It contains a collection of tools and techniques that can be used to solve on a computer mathematical models of problems in Science and Engineering. argmax() * => Find the first True element * argmax() can be used to find the index of the maximum element. More specifically, we will permute the datframe using the indices: df_shuffled = df. Well, numpy supports another indexing syntax. I know I could do this using for loops, but is there a fast way to do this with numpy?. False to fall back to Sphinx’s default behavior, which considers the __init___ docstring as part of the class documentation. For an ndarray a both numpy. Numpy: Fastest way to insert value into array such that array's in order. data (string, numpy array, pandas DataFrame, H2O DataTable's Frame, scipy. 00000000e+01 8. Return the indices of the elements of a that are not zero nor masked, as a tuple of arrays. I think shlok's answer is correct as you are trying to index a numpy array with float that is not correct change that and i think you are good to go commented Aug 16 by kodee ( 42. A numpy array is a grid of values, all of the same type, and is indexed by a tuple of nonnegative integers. data (numpy. Create histograms and scatter plots for basic exploratory data analysis; This lab maps on to lecture 1, lecture 2, lecture 3 and to parts of homework 1. Get the SourceForge newsletter. Strides and training on sequences ¶. axis: {0 or 'index', 1 or 'columns', None}, default 0. optional kwarg encoding can be used to specify character encoding (default utf-8). float64) ' \ 'my_val = 1. MATLAB/Octave Python Description; doc help -i % browse with Info: help() Sort, return indices: a. In NumPy, the index for the first row and the first column starts with 0. If it is a 1-D array of sorted integers, the entries indicate where along the axis the array is split. This tutorial was contributed by Justin Johnson. So saying something like [0,1,2] and [2,3,4] will just give you. In the following code snippet a slice from array a is stored in b. Arrays with different sizes cannot be added, subtracted, or generally be used in arithmetic. Python Numpy: how to count the number of true elements in a bool array. uniform( size=(5,5)). The difference comes in the fact that NumPy uses C style arrays, where the most rapidly changing index comes last. axis: {0 or 'index', 1 or 'columns', None}, default 0. Numpy Cheat Sheet Python Package Created By: arianne Colton and Sean Chen SCN NDNSUBSN numPy (numerical Python) What is NumPy? Foundation package for scientific computing in Python Why NumPy? • Numpy 'ndarray' is a much more efficient way of storing and manipulating "numerical data" than the built-in Python data structures. Here, float64 is a numeric type that NumPy uses to store double-precision (8-byte) real numbers, similar to the float type in Python. The function can be able to return a tuple of array of unique vales and an array of associated indices. where(condition[, x, y]) function returns the indices of elements in an input array where the given condition is satisfied. Indexing in two-dimensional array is represented by a pair of values, where the first value is the index of the row and the second is the index of the column. If x & y arguments are not passed and only condition argument is passed then it returns a tuple of arrays (one for each axis) containing the indices of the elements that are True in bool numpy array returned by condition. The reason it doesn’t work is because np. where() Multiple conditions Replace the elements that satisfy the con. Sections are created with a section header followed by an underline of equal length. Roughly df1. While you can achieve the same results of certain pandas methods using NumPy, the result would require more lines of code. To get the value at index 1 from simple_array, you can use the following syntax: # Retrieve the value at index 1 simple_array[1] Which returns the value 19. They are extracted from open source Python projects. The three types of indexing methods that are followed in numpy − field access, basic slicing, and advanced indexing. Getting started. Then you can apply index in any other array, for example, x. this is also possible for `np. We can create an array of the same shape but with a dtype of bool, where each entry is True or False. int64 and the default float type numpy. The difference comes in the fact that NumPy uses C style arrays, where the most rapidly changing index comes last. where function to replace for loops with if-else statements. NumPy creates an appropriate scale index at the time of array creation. A numpy array is a grid of values, all of the same type, and is indexed by a tuple of nonnegative integers. optional kwarg encoding can be used to specify character encoding (default utf-8). NumPy stands for ‘Numerical Python’ or ‘Numeric Python’. Vectorized operations in NumPy delegate the looping internally to highly optimized C and Fortran functions, making for cleaner and faster Python code. To get the old and incorrect behaviour simply pass -point instead of point or -numpy. When we have something concrete to look at instead of vague assertions, then we can start tackling the issues of integrating it into the core such that 'g[idx] += 1' works like you want it to. The [1:] at the end tells numpy to ignore the first line and take everything after - effectively removing the title row of the spreadsheet and just leaving the real data. The index is used again, to put modified elements back into the original array. Softmax (dim=-1, optimizer=None) [source] ¶ Bases: numpy_ml. Encode categorical integer features as a one-hot numeric array. If you don't supply enough indices to an array, an ellipsis is silently appended. A note on the time dimension ¶ Although scikit-image does not currently provide functions to work specifically with time-varying 3D data, its compatibility with NumPy arrays allows us to work quite naturally with a 5D array of the shape (t, pln, row, col, ch):. NumPy arrays are a collection of elements of the same data type; this fundamental restriction allows NumPy to pack the data in an efficient way. This indices array is used to construct the sorted array. NumPy (Numerical Python) is a linear algebra library in Python. In this Numpy Tutorial, we will learn how to install numpy library in python, numpy multidimensional arrays, numpy datatypes, numpy mathematical operation on these multidimensional arrays, and different functionalities of Numpy library. Above, we created the NumPy array simple_array. In this tutorial, you will learn how to perform many operations on NumPy arrays such as adding, removing, sorting, and manipulating elements in many ways. It is also used to return an array with indices of this array in the condtion, where the condition is true. But I had rarely needed to use for loops on a numpy array, grab the index of a particular element based on satisfaction of boolean statements, or any numpy problem that required strained attention. If you have some knowledge of Cython you may want to skip to the ''Efficient indexing'' section. Docstring Standard¶. The array b will only have those elements that satisified the condition used to make the index. This is an example to access the items from one dimensional array. names : {None, True, str, sequence}, optional If `names` is True, the field names are read from the first line after the first `skip_header` lines. Also, our random generator is now guaranteed to be thread-safe and fork-safe. In this video, we will learn some basic numpy operations and functions. This gives me indices of the n. Matrix and Vector Math in NumPy. Returns out ndarray. In this Numpy Tutorial, we will learn how to install numpy library in python, numpy multidimensional arrays, numpy datatypes, numpy mathematical operation on these multidimensional arrays, and different functionalities of Numpy library. nonzero(a > 3) yields the indices of the a where the condition is true. linalg module. timeit( 'np. NumPy slices are like views into an array. Ndarray is the n-dimensional array object defined in the numpy which stores the collection of the similar type of elements. NumPy operations perform complex computations on entire arrays without the need for Python for loops. Parameters: axis ( numpy. They are extracted from open source Python projects. Indexing and Slicing are two of the most common operations that you need to be familiar with when working with Numpy arrays. The indices i, j where there is a True value mean that b[i] == a[j]. a: Input numpy string array with numpy datatype 'SN' or 'UN', where N is the number of characters in each string. I know I could do this using for loops, but is there a fast way to do this with numpy?. The reason it doesn’t work is because np. Modifying the result in place will modify the data stored in the Series or Index (not that we recommend doing. As mentioned earlier, items in numpy array object follow zero-based index. NumPy is an extension to the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large library of high-level mathematical functions to operate on these arrays. insert(arr, [3], [1, 2, 3])`. By voting up you can indicate which examples are most useful and appropriate. where() function can be used to yeild quick array operations based on a condition. Python is a great general-purpose programming lang. The ndarray stands for N-dimensional array where N is any number. To get the value at index 1 from simple_array, you can use the following syntax: # Retrieve the value at index 1 simple_array[1] Which returns the value 19. find_duplicates(a, key=None, ignoremask=True, return_index=False) Find the duplicates in a structured array along a given key Parameters-----a : array-like Input array key : {string, None}, optional Name of the fields along which to check the duplicates. nonzero(a) and a. Suppose, if we want to select the fifth column, then its index will be 4, or if we want to select third row data, then its index will be 2, and so on. The following aims to familiarize you with the basic functionality of quaternions in pyquaternion. argmin(a,axis=None) returns the indices to the minimum value of the 1-D arrays along the given axis. To compile without numpy, pyfasttext has a USE_NUMPY environment variable. get (k [, d]) → D[k] if k in D, else d. numpy get index where value is true. The given condition is a>5. When we have something concrete to look at instead of vague assertions, then we can start tackling the issues of integrating it into the core such that 'g[idx] += 1' works like you want it to. where() kind of oriented for two dimensional arrays. com NumPy DataCamp Learn Python for Data Science Interactively The NumPy library is the core library for scientific computing in Python. In Python, data is almost universally represented as NumPy arrays. In the example above, the *= numpy operator iterates over all remaining dimensions. multiplication. where function to replace for loops with if-else statements (though now I get it well), so I had to spend additional 2 hours playing with few examples to grasp the concept. Why using NumPy. and values being counts of those """ self. A note on the time dimension ¶ Although scikit-image does not currently provide functions to work specifically with time-varying 3D data, its compatibility with NumPy arrays allows us to work quite naturally with a 5D array of the shape (t, pln, row, col, ch):. We first defined NumPy index array, indxArr, and then use it to access elements of random NumPy array, rnd. Here, float64 is a numeric type that NumPy uses to store double-precision (8-byte) real numbers, similar to the float type in Python. Again, reproduce the fancy indexing shown in the diagram above. In this Numpy Tutorial, we will learn how to install numpy library in python, numpy multidimensional arrays, numpy datatypes, numpy mathematical operation on these multidimensional arrays, and different functionalities of Numpy library. Use fancy indexing on the left and array creation on the right to assign values into an array, for instance by setting parts of the array in the diagram above to zero. Array elements are extracted from the Indices having True value. For NumPy dtypes, this will be a reference to the actual data stored in this Series or Index (assuming copy=False). pyfasttext can export word vectors as numpy ndarrays, however this feature can be disabled at compile time. Using Numpy. Given an array a, the condition a > 3 is a boolean array and since False is interpreted as 0, np. Although the technique was developed for NumPy, it has also been adopted more broadly in other numerical computational libraries, such as Theano, TensorFlow, and Octave. NumPy is a Python Library/ module which is used for scientific calculations in Python programming. Python Code:. In other words, we can define a ndarray as the collection of the data type (dtype) objects. This function returns an array of unique elements in the input array. Similarly, you get L2, a list of elements satisfying condition 2; Then you find intersection using intersect(L1,L2). But I had rarely needed to use for loops on a numpy array, grab the index of a particular element based on satisfaction of boolean statements, or any numpy problem that required strained attention. This is part 2 of a mega numpy tutorial. Amongst other improvements, this version improves again the level of support for linear algebra - functions from the numpy. One of these tools is a high-performance multidimensional array. Encode categorical integer features as a one-hot numeric array. In the following code snippet a slice from array a is stored in b. We can create an array of the same shape but with a dtype of bool, where each entry is True or False. I need to find the rows that have true or rows in e whose value are more than 15. array([i for i in range(1000)], dtype=np. If False, the returned value is tuple of 2 numpy arrays as it is in numpy. If you don't supply enough indices to an array, an ellipsis is silently appended. You can vote up the examples you like or vote down the ones you don't like. ind == TRUE and x is an array (has a dim attribute), the result is arrayInd(which(x), dim(x), dimnames(x)), namely a matrix whose rows each are the indices of one element of x; see Examples below. Here are the examples of the python api numpy. NumPy axes are one of the hardest things to understand in the NumPy system. NumPy operations perform complex computations on entire arrays without the need for Python for loops. true and false are functions which return matrices of ones and zeros. Home Python numpy get column indices. In this part, I go into the details of the advanced features of numpy that are essential for data analysis and manipulations. insert(arr, 3, [1,2,3])` to insert multiple items at a single position. Returns: out: ndarray. Nature of the indices depend upon the type of return parameter in the function call. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under  Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over $1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: