# Numpy Product

PEP 465 -- A dedicated infix operator for matrix multiplication numpy, for example, it is technically possible to switch between the conventions, because numpy provides two different types with different __mul__ methods. torch_ex_float_tensor = torch. Location: London UK. You therefore need to transpose one of your matrices. After I made this change, the naïve for-loop and NumPy were about a factor of 2 apart, not enough to write a blog post about. Below is a partial list of third-party and operating system vendor package managers containing NumPy and SciPy packages. 1BestCsharp blog. NumPy is a Python Library/ module which is used for scientific calculations in Python programming. It can handle 2D arrays but considering them as matrix and will perform matrix multiplication. dtype dtype, optional. MATLAB commands in numerical Python (NumPy) 3 Vidar Bronken Gundersen /mathesaurus. From the previous section, we know that to solve a system of linear equations, we need to perform two operations: matrix inversion and a matrix dot product. fromnumeric: transpose(a, axes=None) Permute the dimensions of an array. NumPy (short for Numerical Python) is an open source Python library for doing scientific computing with Python. NumPy's array (or ndarray) is a Python object used for storing data. Help on function transpose in module numpy. The initial values of such a numpy array are 1s and 0s. To construct a matrix in numpy we list the rows of the matrix in a list and pass that list to the numpy array constructor. NumPy is based on two earlier Python modules dealing with arrays. However NumPy is not always the most efficient system for calculating many matrices. The above function is used to make a numpy array with elements in the range between the start and stop value and num_of_elements as the size of the numpy array. For comparison “B” , things change significantly. He was appointed by Gaia (Mother Earth) to guard the oracle of Delphi, known as Pytho. Dot product is a common linear algebra matrix operation to multiply vectors and matrices. Input data. Over 90 fascinating recipes to learn and perform mathematical, scientific, and engineering Python computations with NumPy About This Book Perform high-performance calculations with clean and efficient NumPy code Simplify large data sets by. Once you have created the arrays, you can do basic Numpy operations. This course will help students to understand machine learning code as Numpy, Pandas are the building blocks for machine learning. It vastly simplifies manipulating and crunching vectors and matrices. For comparison "A" (not optimal, nested loops implementations) , Numpy performance is several times bigger than Pandas performance. Given that most of the optimization seemed to be focused on a single matrix multiplication, let's focus on speed in matrix multiplication. NumPy's array (or ndarray) is a Python object used for storing data. NumPy - Matplotlib - Matplotlib is a plotting library for Python. matlab/Octave Python R Round round(a) around(a) or math. NumPy allows for efficient operations on the data structures often used in machine learning: vectors, matrices, and tensors. Numpy itself mostly does basic matrix operations, and some linear algebra, and interfaces with BLAS and LAPACK, so is fairly fast (certainly much preferable ver number crunching in pure-python code. dot( a, b, out=None) Few specifications of numpy. I just wonder: When I have to go parallel (multi-thread, multi-core, multi-node, gpu), what. Input array. The Numpu matmul() function is used to return the matrix product of 2 arrays. You therefore need to transpose one of your matrices. Numpy arrays are much like in C - generally you create the array the size you need beforehand and then fill it. Finding eigenvalues, eigenvectors. In this code snippet, I present an implementation that creates per vertex normals from an indexed vertex array, and all without any loops. Ndarray is the n-dimensional array object defined in the numpy which stores the collection of the similar type of elements. Merging, appending is not recommended as Numpy will create one empty array in the size of arrays being merged and then just copy the contents into it. cross (a, b, axisa=-1, axisb=-1, axisc=-1, axis=None) [source] ¶ Return the cross product of two (arrays of) vectors. 13 videos Play all NumPy Tutorials Fluidic Colours Java Project Tutorial - Make Login and Register Form Step by Step Using NetBeans And MySQL Database - Duration: 3:43:32. The significant advantage of this compared to solutions like numpy. dot(column_vec) (as recommended in the numpy docs) and get the expected result. 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. - In this chapter, we're going to look at NumPy,…a third party package for Python that extends…the language with multi-dimensional arrays. Learn basic and advanced features in NumPy (Numerical Python) Get started with data analysis tools in the pandas library Use flexible tools to load, clean, transform, merge, and reshape data Create informative visualizations with matplotlib Apply the pandas groupby facility to slice, dice, and summarize datasets. This guide only gets you started with tools to iterate a NumPy array. Learn about NumPy arrays which can be in many dimensions and are used as matrices. Since much of NumPy and SciPy is implemented as C extension modules, the code may not run any faster (for most cases it's significantly slower still, however PyPy is actively working on improving this). To execute the following codes of this tutorial,. A NumPy int_ object has range -2147483648 to 2147483647 (that is -2 31 to 2 31 -1) on systems that store integers using 32 binary digits, and -9223372036854775808 to 9223372036854775807 (that is, -2 63 to 2 63 -1) on systems that store integers using 64 binary digits. array([3,2) z=u*v z:array([6,3]). Notes ----- The first argument is not conjugated. These are implemented under the hood using the same industry-standard Fortran libraries used in other languages like MATLAB and R, such as like BLAS, LAPACK, or possibly (depending on your NumPy build) the Intel MKL:. numpy documentation: Cross Product of Two Vectors. The official home of the Python Programming Language. If you like GeeksforGeeks and would like to contribute, you can also write an article using. *FREE* shipping on qualifying offers. To start a Jupyter notebook, simply click the Jupyter icon on the bottom panel of your desktop or open a Terminal window and type: jupyter notebook. DataFrames[1:n] WILL include the nth (last) element in the result. What is Numpy? Numpy is a Python library that supports multi-dimensional arrays and matrix. For Math courses using Python, Sympy, Numpy, Matplotlib, and Jupyter, the Calclab systems will have these installed for use during your weekly lab. This book uses the proven method of solving practical code puzzles and practice testing -- to make learning more fun, faster, and easier. R/S-Plus Python Description; help. We use three-day historical data and store it in the numpy array x. the total number of elements of the array. Location: London UK. stack array-joining function generalized to masked arrays. There is no "GPU backend for NumPy" (much less for any of SciPy's functionality). Always use numpy arrays, and not numpy matrices. NumPy Beginner's Guide - Second Edition - Kindle edition by Ivan Idris. ones ((5,)), np. [Numpy-discussion] numarray bug: dot product between 2x2 and 3x2x3 on Mac different from PC. numpy for matrices and vectors. For example, product(A, B) returns the same as ((x,y) for x in A for y in B). transpose()) must work on arrays of arbitrary dimension. Since NumPy's a third package, we need to first import it into Python. Second, you can create new numpy arrays of a specified shape using the functions ones() and zeros(). This book uses the proven method of solving practical code puzzles and practice testing -- to make learning more fun, faster, and easier. NOTE: third parties dispute this issue because it is a behavior that might have legitimate applications in (for example) loading serialized Python object arrays from trusted and authenticated sources. The default axis is None, it will calculate the product of all the elements in the input array. 0 and earlier. All of the NumPy array methods for operating on arrays. The Numpu matmul() function is used to return the matrix product of 2 arrays. cumprod (a, axis=None, dtype=None, out=None) [source] ¶ Return the cumulative product of elements along a given axis. Find index of a value in 1D Numpy array. Perhaps you can clean up your system with sudo pip uninstall numpy two or three times until it cannot find a version to remove, then sudo apt install python3-numpy or pip install --user numpy This comment has been minimized. While it returns a normal product for 2-D arrays, if dimensions of either argument is >2, it is treated as a stack of matrices residing in the last two indexes and is broadcast accordingly. NumPy Beginner's Guide - Second Edition - Kindle edition by Ivan Idris. You can sort of think of this as a column vector, and wherever you would need a column vector in linear algebra, you could use an array of shape (n,1). See what the numpy docs say about this. The above method is simple, however, the NumPy library makes it even easier to find the dot product via the dot method, as shown here: print(x. axis None or int or tuple of ints, optional. inner¶ numpy. You therefore need to transpose one of your matrices. , a scalar). Like the generic NumPy equivalent the product sum is over the last dimension of a and b. 1 References • The official NumPy documentation. Download it once and read it on your Kindle device, PC, phones or tablets. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of positive integers. The nditer iterator object provides a systematic way to touch each of the elements of the array. NumPy is a popular open source library for doing math and science with Python. NumPy 2019 full offline installer setup for PC 32bit/64bit NumPy (Numerical Python) is the fundamental package for scientific computing with Python. Parameters a array_like. Input array. It provides a high-performance multidimensional array object, and tools for working with these arrays. For an ndarray a both numpy. Use features like bookmarks, note taking and highlighting while reading NumPy Beginner's Guide - Second Edition. If you would like to know the different techniques to create an array, refer to my previous guide: Different Ways to Create Numpy Arrays. inner (a, b) ¶ Inner product of two arrays. We can initialize numpy arrays from nested Python lists and access it elements. 209 내적 vs 외적 구분 내적 외적 명칭 Inner product, dot product, scalar product Outer product. dot for matrix-vector multiplication but behaves differently for matrix-matrix and tensor multiplication (see Wikipedia regarding the differences between the inner product and dot product in general or see this SO answer regarding numpy's implementations). Those libraries may be provided by NumPy itself using C versions of a subset of their reference implementations but, when possible, highly optimized libraries that take. start() help() Browse help interactively: help() help: Matrix product (dot product) inner. ndarray which returns the dot product of two matrices. They are extracted from open source Python projects. In numpy, you can call the. The NumPy library is an important Python library for Data Scientists and it is one that you should be familiar with. NumPy - Data Types - NumPy supports a much greater variety of numerical types than Python does. All the elements will be spanned over logarithmic scale i. Two matrices can be multiplied using the dot() method of numpy. Instead, it is common to import under the briefer name np:. Certainly relevant to linear algebra, NumPy's ndarray lets you do dot product and inner product of two matrices as well as matrix product and raising a matrix to a power. order : {‘C’, ‘F’}, optional Row-major or column-major order. Originally, launched in 1995 as ‘Numeric,’ NumPy is the foundation on which many important Python data science libraries are built, including Pandas, SciPy and scikit-learn. products sale. It can handle 2D arrays but considering them as matrix and will perform matrix multiplication. dot for matrix-vector multiplication but behaves differently for matrix-matrix and tensor multiplication (see Wikipedia regarding the differences between the inner product and dot product in general or see this SO answer regarding numpy's implementations). We provide a brief introduction here to get the reader familiar with some broad functionality and applications. Another predecessor of NumPy is Numarray, which is a complete rewrite of Numeric but is deprecated as well. The cross product of vectors [1, 0, 0] and [0, 1, 0] is [0, 0, 1]. Appendix E: The NumPy Library. Download it once and read it on your Kindle device, PC, phones or tablets. dot function is a NumPy function. Trent Hare ([email protected] linspace (-2, 2, 5)) >>> rl array([[-2. dot(vector_a, vector_b, out = None): returns the dot product of vectors a and b. In this guide, I will use NumPy, Matplotlib, Seaborn and Pandas to perform data exploration. Arbitrary data-types can be defined. We use cookies to ensure you have the best browsing experience on our website. nonzero(a) and a. ARRAYS AND VECTORS WITH NUMPY Jos e M. This feature is not available right now. You can vote up the examples you like or vote down the ones you don't like. Here is how it works. Parameters ----- a : array_like Input array. For each official release of NumPy and SciPy, we provide source code (tarball) as well as binary wheels for several major platforms (Windows, OSX, Linux). It vastly simplifies manipulating and crunching vectors and matrices. NumPy is a first-rate library for numerical programming • Widely used in academia, finance and industry. nonzero() return the indices of the elements of a that are non-zero. dot(vector_a, vector_b, out = None) returns the dot product of vectors a and b. linalg module; Solving linear systems: A x = b with A as a matrix and x, b as vectors. It also provides simple routines for linear algebra and fft and sophisticated random-number generation. To execute the following codes of this tutorial,. When the NumPy package is loaded, ndarrays become as much a part of the Python language as standard Python data types such as lists and dictionaries. For example, you can use the DataFrame attribute. Originally, launched in 1995 as 'Numeric,' NumPy is the foundation on which many important Python data science libraries are built, including Pandas, SciPy and scikit-learn. product (*iterables [, repeat]) ¶ Cartesian product of input iterables. The array class is intended to be a general-purpose n-dimensional array for many kinds of numerical computing, while matrix is intended to facilitate linear algebra computations specifically. It is designed to be a reference that can be used by practitioners who are familiar with Python but want to learn more about NumPy and related tools. cumprod() function is used when we want to compute the cumulative product of array elements over a given axis. dtype : dtype, optional The type of the returned array, as well as of the accumulator in which the elements are multiplied. torch_ex_float_tensor = torch. These packages are not. Input data. The above function is used to make a numpy array with elements in the range between the start and stop value and num_of_elements as the size of the numpy array. You can vote up the examples you like or vote down the ones you don't like. matmul() function returns the matrix product of two arrays. Pandas works differently. If both a and b are 2-D arrays, it is matrix multiplication, but using matmul or a @ b is preferred. 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. NumPy Cookbook - Second Edition [Ivan Idris] on Amazon. We use cookies to ensure you have the best browsing experience on our website. What is Numpy? Numpy is a Python library that supports multi-dimensional arrays and matrix. These packages are not. array), an n-dimensional array that is also present in some form in array-oriented languages such as Fortran 90, R, and MATLAB, as well as predecessors APL and J. 1 (49 ratings) Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. Find index of a value in 1D Numpy array. If this seems like something unreasonable, keep in mind that many of numpy's functions (for example np. Once you have created the arrays, you can do basic Numpy operations. Arbitrary data-types can be defined. The result is returned as a NumPy array of type numpy. NumPy 2019 full offline installer setup for PC 32bit/64bit NumPy (Numerical Python) is the fundamental package for scientific computing with Python. Python NumPy Extension NumPy extension is an open source python extension for use in multi-dimensional arrays and matrices. So if you want the dot product of each column vector of A with itself, you could use ColDot = np. Return values NumPy operations return views or copies. ): these work element-wise some functions that can be applied to arrays for example a. 1) 2-D arrays, it returns normal product. Which one you transpose will determine the meaning and shape of the result. Dot Product Numpy is powerful library for matrices computation. Another predecessor of NumPy is Numarray, which is a complete rewrite of Numeric but is deprecated as well. Python has a numerical library called NumPy, which has a function called numpy. 1 Job Portal. NumPy Array Object Exercises, Practice and Solution: Write a NumPy program to sum and compute the product of a numpy array elements. Numeric is like NumPy a Python module for high-performance, numeric computing, but it is obsolete nowadays. array), an n-dimensional array that is also present in some form in array-oriented languages such as Fortran 90, R, and MATLAB, as well as predecessors APL and J. Some very basic linear algebra support (determinant, matrix hat operator, inverse, least squares, SVD, matrix power, and multi-dot product). Python NumPy Extension NumPy extension is an open source python extension for use in multi-dimensional arrays and matrices. stack, the numpy. This guide only gets you started with tools to iterate a NumPy array. Additionally NumPy provides types of its own. Find index of a value in 1D Numpy array. x and y both should. ARRAYS AND VECTORS WITH NUMPY Jos e M. Get complete instructions for manipulating, processing, cleaning, and crunching datasets in Python. ): these work element-wise some functions that can be applied to arrays for example a. An n-dimensional array is also called a tensor in the machine-learning community, so you can kind of think. Here is how it works. You will use Numpy arrays to perform logical, statistical, and Fourier transforms. Originally, launched in 1995 as ‘Numeric,’ NumPy is the foundation on which many important Python data science libraries are built, including Pandas, SciPy and scikit-learn. The initial values of such a numpy array are 1s and 0s. 1BestCsharp blog. The following are code examples for showing how to use numpy. an object describing the type of the elements in the array. NumPy is a Python library that allows you to perform numerical calculations. dot(vector_a, vector_b, out = None) returns the dot product of vectors a and b. Finding eigenvalues, eigenvectors. This guide will provide you with a set of tools that you can use to manipulate the arrays. You can vote up the examples you like or vote down the ones you don't like. gcd and numpy. Code in python. inner() - This function returns the inner product of vectors for 1-D arrays. The NumPy package is the workhorse of data analysis, machine learning, and scientific computing in the python ecosystem. Solving a System of Linear Equations with Numpy. For 1-D arrays, it is the inner product of the vectors. NumPy utilizes an optimized C API to make the array operations particularly quick. Two matrices can be multiplied using the dot() method of numpy. The NumPy array. Introduction to Stateful Property-based Testing. Numpy focuses on array, vector, and matrix computations. If arr is not an array, a conversion is attempted. For comparison "A" (not optimal, nested loops implementations) , Numpy performance is several times bigger than Pandas performance. I want to calculate the nearest cosine neighbors of a vector using the rows of a matrix, and have been testing the performance of a few Python functions for doing this. In Numpy dimensions are called axes. 13 videos Play all NumPy Tutorials Fluidic Colours Java Project Tutorial - Make Login and Register Form Step by Step Using NetBeans And MySQL Database - Duration: 3:43:32. sum() and a. While it returns a normal product for 2-D arrays, if dimensions of either argument is >2, it is treated as a stack of matrices residing in the last two indexes and is broadcast accordingly. The following are code examples for showing how to use numpy. multi_dot : Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order. In Numpy dimensions are called axes. 9 Manual NumPy is an extension to Python only, and cannot be directly used in Java. The dot product is approximately 8 and 7 times faster respectively with Theano/Tensorflow compared to NumPy for the largest matrices. In addition to the capabilities discussed in this guide, you can also perform more advanced iteration operations like Reduction Iteration, Outer Product Iteration, etc. NumPy is a package that defines a multi-dimensional array object and associated fast math functions that operate on it. A developer gives a tutorial on how to use the NumPy library for Python to work with arrays of data and perform basic mathematical operations on this data. Notes ----- The first argument is not conjugated. This guide will provide you with a set of tools that you can use to manipulate the arrays. Pandas Series and Data Frames, the program syntax: pd. Views share the underlying storage of the original array. multiply() or plain *. A NumPy int_ object has range -2147483648 to 2147483647 (that is -2 31 to 2 31 -1) on systems that store integers using 32 binary digits, and -9223372036854775808 to 9223372036854775807 (that is, -2 63 to 2 63 -1) on systems that store integers using 64 binary digits. Please read our cookie policy for more information about how we use cookies. pad function in Numpy 1. NumPy Discussion - A mailing list devoted only to the NumPy package (not the SciPy stack). However, there is a better way of working Python matrices using NumPy package. The Numpu matmul() function is used to return the matrix product of 2 arrays. and using ``numpy. First, you can specify the shape of the numpy array as a tuple (n,m) where n is the number of rows and m the number of columns. Linear transformations in Numpy jun 11, 2016 geometry geometric-transformations python numpy matplotlib. For N dimensions it is a sum product over the last axis of a and the second-to-last of b:. And I hope that with these tips and tricks, you'll also be able to much more easily write bug-free, python and numpy code. Python NumPy. Find index of a value in 1D Numpy array. This guide only gets you started with tools to iterate a NumPy array. cumprod (a, axis=None, dtype=None, out=None) [source] ¶ Return the cumulative product of elements along a given axis. MATLAB commands in numerical Python (NumPy) 3 Vidar Bronken Gundersen /mathesaurus. NumPy is a popular open source library for doing math and science with Python. Get complete instructions for manipulating, processing, cleaning, and crunching datasets in Python. For multiplying two matrices, use the dot method. With the ability to build arrays that are considerably faster than the regular lists in Python, and to make more efficient mathematical computations, NumPy’s applications range from data. • Chapter 2 provides information on testing Python, NumPy, and compiling and installing NumPy if neces-sary. Python In Greek mythology, Python is the name of a a huge serpent and sometimes a dragon. It can be simply calculated with the help of numpy. numpy comes with a large library of common functions (sin, cos, log, exp,. This course will help students to understand machine learning code as Numpy, Pandas are the building blocks for machine learning. The following table shows different scalar data types defined in NumPy. In addition to the capabilities discussed in this guide, you can also perform more advanced iteration operations like Reduction Iteration, Outer Product Iteration, etc. NumPy's array (or ndarray) is a Python object used for storing data. This forms the basis for everything else. Additionally NumPy provides types of its own. nonzero() return the indices of the elements of a that are non-zero. nanquantile function, an interface to nanpercentile without factors of 100. 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. NumPy Beginner's Guide - Second Edition - Kindle edition by Ivan Idris. If this seems like something unreasonable, keep in mind that many of numpy's functions (for example np. This post will cover what options you have in Python. matrix objects have all sorts of horrible incompatibilities with regular ndarrays. Here is how you use it do implement Dot product of two matrices using Python. Input data. I want to calculate the nearest cosine neighbors of a vector using the rows of a matrix, and have been testing the performance of a few Python functions for doing this. You can vote up the examples you like or vote down the ones you don't like. float64 are some examples. Once you have created the arrays, you can do basic Numpy operations. Python NumPy. Numpy slow at vector cross product? DFS: 11/20/16 12:47 PM: import sys, time, numpy as np. From the previous section, we know that to solve a system of linear equations, we need to perform two operations: matrix inversion and a matrix dot product. Numpy is the de facto ndarray tool for the Python scientific ecosystem. Dot Product Numpy is powerful library for matrices computation. Python Image Processing using GDAL. linalg)¶ The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient low level implementations of standard linear algebra algorithms. NumPy Beginner's Guide - Second Edition - Kindle edition by Ivan Idris. We can initialize numpy arrays from nested Python lists and access it elements. An important feature with NumPy arrays is broadcasting. You can also save this page to your account. I have a NumPy array 'boolarr' of boolean type. For example, a matrix of shape 3x2 and a matrix of shape 2x3 can be multiplied, resulting in a matrix shape of 3 x 3. The standard approach is to use a simple import statement: >>> import numpy However, for large amounts of calls to NumPy functions, it can become tedious to write numpy. Numerical Operations on Numpy Arrays. torch_ex_float_tensor = torch. This guide will provide you with a set of tools that you can use to manipulate the arrays. You therefore need to transpose one of your matrices. Here is how you use it do implement Dot product of two matrices using Python. linalg module; Solving linear systems: A x = b with A as a matrix and x, b as vectors. This post will go through an example of how to use numpy for dot product. For instance, you can compute the dot product with np. prod(a, axis=None, dtype=None, out=None, keepdims=) Parameters a : array_like Its the input data. quantile function, an interface to percentile without factors of 100. To execute the following codes of this tutorial,. 2) Dimensions > 2, the product is treated as a stack of matrix. Sebastian Haase Mon, 17 Jul 2006 09:41:33 -0700. Numpy arrays are much like in C - generally you create the array the size you need beforehand and then fill it. Axis or axes along which a product is performed. If both arguments are 2-D they are multiplied like conventional matrices. You can talk about creating arrays, using operators, reshaping and more. 5+, you can use @ for matrix multiplication with numpy arrays, which means there should be absolutely no good reason to use matrices over arrays. You will use Numpy arrays to perform logical, statistical, and Fourier transforms. This book uses the proven method of solving practical code puzzles and practice testing -- to make learning more fun, faster, and easier. stack array-joining function generalized to masked arrays. The Numpy library from Python supports both the operations. int32, numpy. Python for beginners. NumPy gives every matrix a dot() method we can use to carry-out dot product. Python often requires certain modules such as Numpy, Scipy, and Matplotlib for scientific computing or others such as Pygame for making games. Since NumPy's a third package, we need to first import it into Python. dot Syntax numpy. I can perform matrix multiplication using matrix. For higher dimensions, it returns the sum product over the last axes. 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: