# Matlab Array Operations

” The result of a relational comparison is a logical array indicating the locations where the relation is true. com Web comp. 1 Vector and Matrix Notation> A matrix is a rectangular array, which is arranged as horizontal row and vertical column elements and is shown in brackets. A matrix is a two-dimensional array often used for linear algebra. To have a deeper explanation of arrays and their operations, see Arrays and matrices. Perform arithmetic operations between two scalars. It can be seen that v_tank in the operation is an array of 100 random numbers. The identity IDENTITY MATRIX matrix is a square matrix whose diagonal elements are all equal to one, with the remaining elements equal to zero. txt) or view presentation slides online. The operators <, >, <=, and >= use only the real part of their. Matrices are often referred to by their sizes. These are the relational operators in MATLAB ®. size Determine the number of rows & columns linspace Build a vector containing equally spaced entries zeros Build an array with given # of rows & columns ﬁlled with zeros. Unfortunately, many of these matrix operations so time and memory expensive that they are prohibitive when the scale of data is large. • Vectors and matrices are fundamental to Matlab –Matlab is designed specifically for vector and matrix operations. Transpose of a Matrix octave: AT = A' AT = 2 3 -2 1 2 2 octave: ATT = AT' ATT = 2 1 3 2 -2 2 Common Vectors Unit Vector octave: U = ones(3,1) U = 1 1 1 Common Matrices Unit Matrix Using Stata octave: U = ones(3,2) U = 1 1 1 1 1 1 Diagonal Matrix. In-Class Activity - M-File 4. Generate a vector x=[5, -4, 6 ] with three. Transpose of a Matrix. This example shows how to use the any and all functions to reduce an entire array to a single logical value. A large array of engineering and science disciplines can use MATLAB to meet specific needs in their environment. The chapter covers six basic topics: it starts with some of the built-in statistical and set operations in MATLAB, then curve fitting, complex numbers, solving systems of linear algebraic equations, and integration and differentiation in calculus. MATLAB has some convenient vector-based tools for working with polynomials, which are used in many advanced courses and applications in engineering. Addition and subtraction are relatively simple operations and are covered first, in Section 3. I have a signal $\mathbf x$, and I need to know how to obtain the matrix which is the corresponding sparsity basis $\mathbf\Psi$ such that $\mathbf x = \mathbf{\Psi\theta}$, where $\mathbf\theta$ is. I wonder why following vectorization syntax is not implemented in MATLAB, what speaks against it:. Assignment: Read and complete the suggested commands. We’ve seen the matrix before in Lecture 1 as a 2-D array. ppt), PDF File (. Welcome to this course ( Matlab keystone skills for mathematics matrices & arrays ) , my name is ABSAR and i will accompany you along the course. The result of calculating the determinant of a 9-order square matrix is far greater than zero. Many times, logical operators are used to link together the results of several relational operators. Note that + will not renumber numeric array keys. No need to retain everything, but have the reflex to search in the documentation (online docs, help(), lookfor())!! For advanced use: master the indexing with arrays of integers, as well as broadcasting. Division operators in Matlab= There are (at least) four different division functions in Matlab:. Array Addition and Subtraction. Using the MATLAB Meshgrid Command and Array Operators to Implement One-and Two-Variable Functions By Omur Bas, MathWorks and Seth Popinchalk, MathWorks One of the more difficult topics covered in our MATLAB Fundamentals course is the use of array operators on matrices to implement functions of one and two variables. If x were, for example, a 5 by 3 matrix, then y = sin(3*x) would create a 5 by 3 matrix, y. You can think of a matrix as a collection of row vectors with the rows stacked on top of each other or a collection of column vectors with the columns side by side. Abstract: Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. In addition to differences in the types of data values they store, uint8 arrays and double arrays differ in the operations that MATLAB supports. Advanced Array Operations. MATLAB works with essentially only one kind of object, a rectangular matrix with complex elements. To indicate an array (element-by-element) operation, precede a standard operator with a period (dot). Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. LECTURE02 ARRAYS AND MATRICES Shameer A Koya 1 2. Explain Arrays operations. It is often much faster without. Operations on matrices. There are many times where we want to do an operation to every entry in a vector or matrix. A matrix can be thought as a table consisting of rows and columns. However, the && and || operators actually return the value of one of the specified operands, so if these operators are used with non-Boolean values, they will return a non-Boolean value. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. Relational operators. MATLAB allows two different types of arithmetic operations − Matrix arithmetic operations; Array arithmetic operations; Matrix arithmetic operations are same as defined in linear algebra. The transpose of matrix A is written A T. For more information, see Compatible Array Sizes for Basic Operations. Matrices are often referred to by their sizes. func can correspond to more than one function file and therefore can represent a set of overloaded functions. Most of the methods on this website actually describe the programming of matrices. /B Content you might like: Matlab Matrix Operations; Write a Matlab function that rotate a Matrix by 90 degrees. I prefer to tell you the basic difference between matrix operations and array operations in general and let's go to the question you asked. 2 or later with Compat v1. In the Python code we assume that you have already run import numpy as np. This algorithm comes from the Numerical Recipes algorithm via the Lightspeed Matlab library of Tom Minka. Legal Variable Names. MATLAB is an abbreviation for "matrix laboratory. The four "basic operations" on numbers are addition, subtraction, multiplication, and division. Arithmetic Operators. MATLAB vectorization, and other tips 7/36. To this point we’ve only looked at vectors, which are one dimensional arrays of numbers. 62x Experimental Projects. Still you can do many things to manipulate this element. Type help polyfun for more information on this category of commands. An uninitialized array produces warnings when passed to MATLAB C++ Math Library functions. The interface follows a language that is designed to look a lot like the notation use in linear algebra. Examples - M-File 3. CME 102 Matlab Workbook 2008-2009 3/55 1 Matlab Basics 1. Matlab provides two types of Arithmetic operators. See Introduction to array operations for more information on the operations MATLAB can perform on arrays. A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). If the size of any dimension is negative, then it is treated as 0. How to Contact The MathWorks: www. Braun Department of Mathematical Sciences University of Delaware 1 Introduction This collection of exercises is intended to help you start learning Matlab. Division operators in Matlab= There are (at least) four different division functions in Matlab:. MATLAB/Octave and Mathematica have their own strengths, but the former is more popular due to its current widespread use, similarity to modern programming languages, and wealth of third-party libraries. > These operations want to call a carefully written C function. Educational Technology Consultant MIT Academic Computing [email protected] Array Comparison with Relational Operators. First of all, it is helpful to tell whether a given matrix is real or complex when programming, since certain operations can only be done on real numbers. To create an empty double matrix that corresponds to [] in MATLAB, use the. Defining Matrices; Matrix Functions; Matrix Operations; Vector Functions; Loops. It integrates computation, visualization, and programming. The result of calculating the determinant of a 9-order square matrix is far greater than zero. Notice how MATLAB requires no special handling of vector or matrix math. 0 or later and have run using LinearAlgebra, Statistics, Compat. 2, and 1 to represent a logical true, for example 2 3. Solving Systems of Linear Equations; Row Reduction is to take an augmented matrix for a system and carry it by means of elementary row operations to an equivalent. The zyBooks Approach Less text doesn't mean less learning. The matrix operators and array operators are. Why are the results inconsistent? Calculating determinants of large. This tutorial covers data analysis and statistics using Matlab. They work element-wise on arrays, with 0 representing logical false (F), and anything nonzero representing logical true (T). These relational tests, when used with Matlab arrays, produce another array whose entries are '0' where the relational test is false, and '1' where the relational statement is true. Logical operators are typically used with Boolean (logical) values. This MATLAB function tests along the first array dimension of A whose size does not equal 1, and determines if any element is a nonzero number or logical 1 (true). A = rand(20, 4, 2); B = exp(A) Most numeric functions have this behavior. Whereas in other languages, you might need a loop to carry out simple mathematical operations on each entry of an array, in Matlab, these operations can be carried out in a single line of code. View Abhilash Suresh Tankasali’s profile on LinkedIn, the world's largest professional community. In this brief tutorial we discuss and illustrate a number of ways used to. It is often much faster without. Matrix Operations Using Mathcad Charles Nippert These notes describe how to use Mathcad to perform matrix operations. Like computations, MATLAB's logic operators are vectorized: >> [1,5,3] < [2,2,4] ans = 1 0 1 Two three-element arrays are compared per-element. When you want to access selected elements of an array, use indexing. Defining a Vector; Accessing elements within a vector; Basic operations on vectors; Introduction to Matrices in Matlab. MATLAB uses 0 to represent a logical false, for example 3. octave:3> A = [1, 1, 2; 3, 5, 8; 13, 21, 34] A 1 1 2 3 5 8 13 21 34. MATLAB - Arrays and Matrices 1. ©F 2j0 b131 W IK su ytxa r QS6o0f 7tqw Jakr 1ey DLvLaC8. It was originally designed for solving linear algebra type problems using matrices. MATLAB MATLAB is a software package for doing numerical computation. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). size Determine the number of rows & columns linspace Build a vector containing equally spaced entries zeros Build an array with given # of rows & columns ﬁlled with zeros. This example shows how to use the any and all functions to reduce an entire array to a single logical value. On this page, we will discuss these type of operations. Assignment: Read and complete the suggested commands. 2, and 1 to represent a logical true, for example 2 3. The size of a Matrix is its number of rows and columns. Some Undocumented Operations Work on Optimization Variables and Expressions. Multidimensional arrays in MATLAB are an extension of the normal two-dimensional matrix. It integrates computation, visualization, and programming. Compatible Array Sizes for Basic Operations. Element-wise logical operators operate element-by-element on logical arrays. Or you can type in the big output area and press "to A" or "to B" (the calculator will try its best to interpret your data). For example, consider the. The distinction between row vectors and column vectors is essential. This section will simply cover operators and functions specifically suited to linear algebra. Most operations in MATLAB can be performed on either the transfer function, the state-space model, or the zero-pole-gain form. Lately we have learned some basics about Matlab matrix operations. Many programming errors are caused by using a row vector where a column vector is required, and vice versa. Introduction. Please also note that when used without a dot, the multiplication symbol * denotes matrix multiplication. Matrix Calculator. We thought it will be also necessary you have a grip on the element-by-element Matrix division in Matlab. The numbers n and m are called the dimensions of the matrix. ” The result of a relational comparison is a logical array indicating the locations where the relation is true. This example shows how to filter the elements of an array by applying conditions to the array. Chidiogo Egbuna’s Activity. A=[1 1 -2;2 2 1;2 1 1] after pressing ENTER, here is how it will look in Matlab window. Array arithmetic operations are carried out element by element, and can be used with multidimensional arrays. When you add, subtract, multiply or divide a matrix by a number, this is called the scalar operation. Explain Arrays operations. Here, ﬁmanipu-. The basic data element of Matlab is a matrix and it is used to manipulate array-based data. Selecting data based on its values is often useful. and subtraction: > >A B. Hi, I did some tests with MATLAB and Julia: Matlab & Julia Matrix Operations Benchmark I think they (At least to some part) reflect OpenBLAS vs. Chidiogo Egbuna’s Activity. To avoid distracting implementation details, however, we would like to accomplish this implementation in the simplest. MATLAB has two different types of arithmetic operations. They work element-wise on arrays, with 0 representing logical false (F), and anything nonzero representing logical true (T). size(A) Note A here is the matrix we created in the. Enter your matrix in the cells below "A" or "B". Give ourselves some more room to work. Matlab Tutorial 4: Data Analysis and Statistics with Matlab. The size of a Matrix is its number of rows and columns. Element-by-element right divide. If you have two numeric arrays, and their indices overlap, + will use the first array's values for each numeric key, adding the 2nd array's values only where the first doesn't already have a value for that index. 2 Finding Inverses. I think that you have misunderstood a few things about arrays in python. Array Comparison with Relational Operators. The following array and matrix operations support fixed-point data types in MATLAB ®. Relational Operators These operations result in a vector or matrix of the same size as the operands, with 1 where the relation is true and 0 where it’s false. MATLAB/Octave and Mathematica have their own strengths, but the former is more popular due to its current widespread use, similarity to modern programming languages, and wealth of third-party libraries. For more information, see Compatible Array Sizes for Basic Operations. Furthermore, it is simple to transfer between these forms if the other representation is required. Create Matrices 1. import numpy as np. In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. When you index a string array with parentheses you get back a new string array. Cell arrays of Strings. View Abhilash Suresh Tankasali’s profile on LinkedIn, the world's largest professional community. This enables you to perform a wider range of operations on the array without running out of memory. In the Python code we assume that you have already run import numpy as np. Common operations. Operations on matrices. Matrix Operations Introduction. In this section we introduce one form, called array operations, which are also called element-by-element operations. You can think of a matrix as a collection of row vectors with the rows stacked on top of each other or a collection of column vectors with the columns side by side. "Operations" is mathematician-ese for "procedures". It is not clear what is your field F_3. Row Replication, Column Replication, and Tiling. INTRODUCTION INTO MATLAB COMPUTING. If the sizes. 36 LECTURE 8. These four symbols are shorthand for the Matlab functions: rdivide, ldivide, mrdivide, and mldivide, respectively. Datetime arrays — isequal ignores display format when it compares points in time. The four basic operations of addition, subtraction, multiplication and division are performed using the symbols +,-,* and /, respectively. For example, suppose you want to multiply each entry in vector v with its cooresponding entry in vector b. For loop in Matlab. The basic data element of Matlab is a matrix and it is used to manipulate array-based data. Not surprisingly, matrices, vectors and multidimensional arrays are at the heart of the language. I have a signal $\mathbf x$, and I need to know how to obtain the matrix which is the corresponding sparsity basis $\mathbf\Psi$ such that $\mathbf x = \mathbf{\Psi\theta}$, where $\mathbf\theta$ is. size Determine the number of rows & columns linspace Build a vector containing equally spaced entries zeros Build an array with given # of rows & columns ﬁlled with zeros. as can be seen by working through the operations involved in matrix multiplication. I'm going to call it M1 and let's set that equal to our matrix here. Array Addition and Subtraction. ones Build an array with the speciﬁed number of rows/columns ﬁlled with ones. Matrix Operations and Manipulation. As opposed to Python, which is an expert at string, Matlab could look sort of limited in this domain. Operations for vectors still hold here. Once up and running, the MATLAB desktop appears containing tools and graphical user interfaces for managing files, variables, and applications associated with MATLAB. Short-circuit − these operators operate on scalar, logical expressions. pdf), Text File (. Matrix operations calculator This solver can performs operations with matrices i. To enter an array function into a Microsoft Excel worksheet, you must hold down the CTRL and SHIFT keys while pressing the ENTER key:. Here, ﬁmanipu-. Multidimensional arrays in MATLAB are an extension of the normal two-dimensional matrix. Type help polyfun for more information on this category of commands. This example shows how to filter the elements of an array by applying conditions to the array. Let’s start this complete tutorial about MATLAB matrix operations. INTRODUCTION TO FOR AND WHILE LOOPS IN MATLAB For loops and while loops allow the computer to run through a series of commands, repeatedly. Exponentiation is performed by means of the symbol ^. When they are, they return a Boolean value. eye(m,n) Creates an m n matrix with ones on the main diagonal and ze-ros elsewhere (the main diagonal consists of the elements with equal row and column numbers). Reduce Logical Arrays to Single Value. This logical indexing capability allows you to do a lot of efficient things with large matrices because you very rarely have to loop through a whole matrix in order to get only specific parts of it. When doing MATLAB element by element operations, rather than explicitly iterating in a loop, MATLAB will repeat a process or evaluation on each element in a vector automatically. The unique function performs exact comparisons and determines that some values in x are not exactly equal to values in y. Quiz - Carmen In-class: Topic: Array Operations 1. One of the most powerful aspects of Matlab is that many expressions can be vectorized. A matrix is a two-dimensional array often used for linear algebra. Simulink Basics Tutorial. Hence I think they might be information worth knowing for the developers. For more information, see Compatible Array Sizes for Basic Operations. He is former director, Laser Science and Technology Centre, a premier laser and optoelectronics R&D laboratory of DRDO of Ministry of Defence &, Varsha Agrawal. For example, maybe we want to know what number is in the third row and fourth column, or maybe we want to view the whole fifth row. Matrix multiplication, array operations, polynomial fitting Array and Matrix Mathematics. Matlab has also a lot of routines related to matrix operations (i. 5 Polynomial Operations Using Arrays. MATLAB Tutorial Chapter 5. Using Vectors: utilizing Matlab's powerful vector abilities. In matrix arithmetic addition and subtraction is easy but multiplication is challenging task MatLab makes it simple and MatLab is specially designed for matrix manipulations. In the case of a for loop, the commands are executed a fixed number of times, whereas in a while loop the commands are executed until some specified condition is met. Data Entry. for a student project, I work with the "Parallel Computing Toolbox". Examples - M-File 3. Array Addition and Subtraction. Often for loops can be eliminated using Matlab’s vectorized addressing. It can be helpful to group your data by anything from color or shape to age and race. In the case of an array, a "bunch of buckets" exist. MATLAB/Octave and Mathematica have their own strengths, but the former is more popular due to its current widespread use, similarity to modern programming languages, and wealth of third-party libraries. All the basic operations on matrices, addition, subtraction, multiplication, division, and exponentiation, can be done in MATLAB. ers the students the opportunity to develop their con-. This algorithm comes from the Numerical Recipes algorithm via the Lightspeed Matlab library of Tom Minka. Explain Arrays operations. The following table shows the order in which MATLAB evaluates various operators. Compatible Array Sizes for Basic Operations. Basic MATLAB Programming MATLAB is a matrix-based language. When you index a string array with parentheses you get back a new string array. Peet Abstract—In this paper, we present PIETOOLS, a MATLAB toolbox for the construction and handling of Partial Integral (PI) operators. Click the button below to return to the English version of the page. Like standard array deletion, use vector subscripting when deleting a row or column of cells and assign the empty matrix to the dimension: A(cell_subscripts) = [] When deleting cells, curly braces do not appear in the assignment statement at all. expand all. txt) or read online for free. A matrix is a two-dimensional array of numbers. logspace Creates logarithmically spaced vector. Abhilash Suresh has 5 jobs listed on their profile. Inside the function, I concatenated the input vector in order to get two matrices, and multiplied them. MATLAB provides two notations for "matrix division" that provide rapid solutions to simultaneous equation or linear regression problems. expand all. Matrix operations are discussed in the appendix. import numpy as np. If the sizes. Type: A-B : to subtract matrix B from the matrix A. This tutorial covers data analysis and statistics using Matlab. Short-circuit − these operators operate on scalar, logical expressions. It's not pseudocode like you asked for but I hope my answer helps you to some degree. For loop in Matlab. Often for loops can be eliminated using Matlab’s vectorized addressing. Not surprisingly, matrices, vectors and multidimensional arrays are at the heart of the language. Array Creation and Concatenation. Operator Precedence. Relational Operators There are six relational operators in Matlab: Symbol Meaning < less than <= less than or equal > lreater than >= greater than or equal == equal ~= not equal 12. Notice how MATLAB requires no special handling of vector or matrix math. Python is newer to this arena but is becoming increasingly popular for similar tasks. Still you can do many things to manipulate this element. To replicate a columns, rows, or to create tiles repmat. An element of the output array is set to logical 1 (true) if both A and B contain a nonzero element at that same array location. However, there is a special matrix type for doing linear algebra, which is just a subclass of the array class. Relational operators perform element-by-element comparisons between two arrays. Division operators in Matlab= There are (at least) four different division functions in Matlab:. size(A) Note A here is the matrix we created in the. returns 1 if S is a character array and 0. MATLAB is an abbreviation for "matrix laboratory. Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are either the same or one of them is 1. Operations on two struct arrays in matlab. Exercise 1: Vectors in Matlab. 5 Polynomial Operations Using Arrays. prod Product of each column. Program (1): To perform addition, subtraction, multiplication, right division, left division and exponentiation operations on x and y given as x = 2; y = 3, in MATLAB. Another type of matrix is the transposed matrix. In this section, we are going to verify this using MATLAB, and we are also going to see what happens if we attempt this on a matrix which is not invertible. The function xor(A,B) implements the exclusive or operation. The notes begin with an introduction to MATLAB are written for students with no prior programming. ppt), PDF File (. Vector operations in Matlab allow you to apply a "single" command to an entire array. In these cases, MATLAB ® determines which function to call based on the class of the input arguments. MATLAB is an abbreviation for "matrix laboratory. These operations may be rare; however, a use may arise in specialized situations. Operator Precedence. Cell arrays of Strings. Sort Vector in Ascending Order; Sort Matrix Rows in Ascending Order; Sort Matrix Columns in Descending Order; Sort String Array; Sort and Index datetime Array; Sort 3-D Array; Complex Vector; Input Arguments. Numeric inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). In the case of a for loop, the commands are executed a fixed number of times, whereas in a while loop the commands are executed until some specified condition is met. MATLAB Vector-Vector Operations Up: MATLAB Matrices Previous: Creating Matrices from Submatrices Contents Diagonal Matrices Diagonal matrices are matrices that seem to have their elements aligned along the diagonals of the matrix. Given two arrays of the same size, one may add or subtract these as follows:. Use help in MATLAB for more information on how to use any of these commands. Symbolic Math Toolbox™ provides functions to solve systems of linear equations. هذا الدرس سوف يكون عبارة عن شرح اجراء العمليات الحسابية على المصفوفات الجزء الأول ببرنامج الماتلاب. As you’ll see in this article, Python has all of the computational power of MATLAB for. m code for rather than all functions that come with the Matlab software. Scalar Operations • Scalar operations are the most obvious if you have pro-grammed in C, Fortran, Basic, etc. Boolean logic has many applications in electronics, hardware and software, and is the basis of modern digital electronics. In these cases you can obtain sensible results from the functions or operations. LAPACK provides a foundation of routines for linear algebra functions and matrix computations in MATLAB. The inverse of a matrix is sometimes written with a "-1" superscript. Once up and running, the MATLAB desktop appears containing tools and graphical user interfaces for managing files, variables, and applications associated with MATLAB. Generally to generate a multidimensional array, we first create a two-dimensional array and extend it. The logical operators return a logical array with elements set to true (1) or false (0), as appropriate. He is former director, Laser Science and Technology Centre, a premier laser and optoelectronics R&D laboratory of DRDO of Ministry of Defence &, Varsha Agrawal. as can be seen by working through the operations involved in matrix multiplication. Generate the 3-by-3 Hilbert matrix. It is important to observe that these other operations, *, ^, \, and /, can be made to operate entry-wise by preceding them by a period. If the imaginary parts of the elements are all zero, they are not printed, but they still occupy storage. Boolean and Relational operators Summary In Matlab, there are four logical (aka boolean) operators. MATLAB has two forms of arithmetic operations on arrays. I need to remove the entries in the matrix that are greater than 1 until the number of values that are 0 and 1 outnumber the number of values that are greater than 1. This architecture is the foundation of our successful history within the paper and plastic film industries for the last 45 years. Educational Technology Consultant MIT Academic Computing [email protected] txt) or view presentation slides online. File input/output 5. MATLAB allows two different types of arithmetic operations − Matrix arithmetic operations; Array arithmetic operations; Matrix arithmetic operations are same as defined in linear algebra. Counts the number of floating point operations used to solve for X in the matrix equation AX = B where A is possibly symmetric positive definite. XD, feel free to leave any comments in the comment section. The distinction between row vectors and column vectors is essential. The & operator does a logical AND, the | operator does a logical OR, and ~A complements the elements of A. The name MATLAB stands for MATrix LABoratory. The zyBooks Approach Less text doesn't mean less learning. When they are, they return a Boolean value. Let's start this complete tutorial about MATLAB matrix operations. I will followup on this latter. An array having more than two dimensions is called a multidimensional array in MATLAB. One of the most powerful aspects of Matlab is that many expressions can be vectorized. Furthermore, it is simple to transfer between these forms if the other representation is required. 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: