# Matlab Definition

For example, x=0 creates a variable named x and assigns the scalar value 0 to it. 1 Suppose, for example, that we want to solve the ﬁrst order diﬀerential equation y′(x) = xy. It is best if you learn to avoid scripts anyway. MATLAB Cell Vector. Introduction to Matrices in Matlab¶. An example of its application is shown below: the vector yc (line 6) represents a noisy rectangular pulse (y) convoluted with a transfer function c before being measured. The real power of Matlab is the ease in which you can manipulate your vectors and matrices. Note that the description MATLAB returns about the command you requested help on contains the command name in ALL CAPS. Updated October 2019. Matlab allows you to create symbolic math expressions. Structures are created and accessed in a manner familiar for those accustomed to programming in C. Introduction to MATLAB What is MATLAB? MATLAB ("MATrix LABoratory") is a tool for numerical computation and visualization. MATLAB will print up until a blank line or an executable statement, whichever comes first. By integrating the visualization, and programming, MATLAB creates an easy-to-use environment where understandable mathematical notations are used to express the problems and solutions. matlab_kmeans, programs which illustrate the use of Matlab's kmeans() function for clustering N sets of M-dimensional data into K clusters. 72 degree longitude. The Matlab programming language supports it, so a function can call itself during its own execution. The first thing to know is that you can separate rows by semi-colons (;) and that you define rows by just placing elements next to one another. 0a, Version 4. B = sqrt(X) returns the square root of each element of the array X. Consistent with the Boltzmann definition, the second law of thermodynamics needs to be re-worded as such that entropy increases over time, though the underlying principle remains the same. O MATLAB integra análise numérica, cálculo com matrizes, processamento de sinais e construção de gráficos em ambiente fácil de usar onde problemas e soluções são expressos somente como eles são escritos matematicamente, ao contrário da programação tradicional. Recent Examples on the Web. Moreover, the fundamental operators (e. Matlab Vectors. MATLAB permet de faire du calcul matriciel, de développer et d'exécuter des algorithmes, de créer des interfaces utilisateur (IU) et de visualiser des données. MATLAB Function Reference : find. In the case of a singular matrix, Matlab returns the result given by the LU decomposition, even though the underlying solver has flagged the result as erroneous. The unwrap is included to ensure that the phonse does jump from +180 t o-180 degrees. Es ist als kurze Einführung gedacht, die an Hand von Beispielen die Arbeitsweise von MATLAB demonstriert. 32 g/cm^3)? Also, can I do this in an output box displayed to the user?. Define data in MATLAB ® code intended for code generation. We need to do shifting and scaling after defining the function. Subclasses can modify inherited methods. Since the angle() command gives the angle in radians, we multiply it by 180. Round ceil and floor matlab datenumbers file exchange solved given two positive integers a and b write the use convert code containing global variables to fixed point matlab configure blocks with fixed point output matlab simulink. The notation used in the first statement is much faster than the loop. In other plotting programs a lot of this is taken for granted, but in Matlab you nust define plots with a little more care. Entire courses in computer science are devoted to extolling OOPs many virtues and we will not have space to mention them all here. Matlab allows you to create symbolic math expressions. A vector in MATLAB is a list of scalar values. This is known as short format. Note that the description MATLAB returns about the command you requested help on contains the command name in ALL CAPS. I want the bar colors to be such that if the value of 'mydata' is between [0, 0. Vectors In MATLAB a vector is a matrix with either one row or one column. Practical FIR Filter Design in MATLAB R Revision 1. The declaration starts with the function keyword, and to remind you that it's a keyword, MATLAB highlights it for you in blue. There is a variable in the file called decision. By default, MATLAB displays numbers with four decimal place values. Define methods as MATLAB ® functions within a methods block, inside the classdef block. Add spaces if necessary to align the decimal points of tables. The format long command displays 16 digits after decimal. Definition of Variables. The idea behind these tutorials is that you can view them in one window while running MATLAB in another window. - Definition of mass, momentum and energy balance equations for HVAC systems and CHP plants; - Development of Matlab models for HVAC systems and CHP plants by implementation of working principles and control logic algorithms based on Object Oriented Programming language; - Technical reports. Its syntax shares similarities with C, with some notable differences. By integrating the visualization, and programming, MATLAB creates an easy-to-use environment where understandable mathematical notations are used to express the problems and solutions. It uses the programming system and language called MATLAB to do so because it is. Matlab and Octave have a built-in function for Fourier deconvolution: deconv. Depending on the size of figure, MATLAB may or may not choose tick marks to your liking. fprintf Performs formatted writes to screen or file. 6, 1] then the corresponding bars are red. With functions, you can make your applications do anything you want. Learn more about symbolic, vector MATLAB Answers. So here first we define a sine and a cosine wave, then plotting a circle in MATLAB becomes so simple, just plot the sine Vs. MATLAB definition: (MATrix LABoratory) A programming language for technical computing from The MathWorks, Natick, MA (www. Tous les ans entre vingt et trente pour cent des etudiants du DESS utilisent Matlab pendant leur stage. Launching GitHub Desktop If nothing happens, download GitHub Desktop and try again. 32 g/cm^3)? Also, can I do this in an output box displayed to the user?. The Octave interpreter can be run in GUI mode, as a console, or invoked as part of a shell script. Syntax Examples. MATLAB Tutorial on ordinary differential equation solver (Example 12-1) Solve the following differential equation for co-current heat exchange case and plot X, Xe, T, Ta, and -rA down the length of the reactor (Refer LEP 12-1, Elements of chemical reaction engineering, 5th edition) Differential equations. MATLAB (MATrix LABoratory) A programming language for technical computing from The MathWorks, Natick, MA (www. Its syntax shares similarities with C, with some notable differences. Matlab does scientific computing very well, but many other languages can take on a variety of tasks including web development, back end, and rich GUIs. 6), the bars are blue, and if the value of my data is between [0. In C we WILL have to worry about this. 38 degree North latitude and 90. Logical Indexing. It is best if you learn to avoid scripts anyway. Data Definition for Code Generation. It is defined by and. Here is a simple example of recursion, let's elaborate Example of recursive code: function y = ten_exp(n) % This is a recursive program for computing y = 10^n. Vectors In MATLAB a vector is a matrix with either one row or one column. function Creates a user-defined function M-file. MATLAB permet de faire du calcul matriciel, de développer et d'exécuter des algorithmes, de créer des interfaces utilisateur (IU) et de visualiser des données. The RTL-SDR radio support package enables you to design wireless receivers using real world signals. Only blank lines and comments can precede classdef. Specify the point in Axes coordinates. MATLAB variable names are case sensitive so x and X are different variables. MATLAB Fast Automation: Step-by-step Action Plan to Automate Your Work With MATLAB. Computing Fourier Series and Power Spectrum with MATLAB By Brian D. MATLAB functions need to have a defined value for the case where none of the conditions hold. x-axis definition. Creating interfaces in Matlab is extremely easy. Learn more about matlab function, matlab MATLAB. xml, the name of the data file created by the clibgen. Conditionally execute statements. An array is the most fundamental data type in MATLAB. One of Matlab's best kept secrets is its comprehensive support for Object Oriented Programming, (OOP). The file is called by Matlab, and it constructs a second derivative finite difference matrix with boundary conditions. Suppose is equal to on the interval and on the interval and you want to define it as a MATLAB function. Note: Structure field names must begin with a letter, and are case-sensitive. Variables Definition for Code Generation. This MATLAB function returns the piecewise expression or function pw whose value is val1 when condition cond1 is true, is val2 when cond2 is true, and so on. How to use normalize in a sentence. As of MATLAB 7. There is NO way to define a function inside a script, unless you are talking about an anonymous function or an inline function. The Current Folder in MATLAB. MATLAB permet de faire du calcul matriciel, de développer et d'exécuter des algorithmes, de créer des interfaces utilisateur (IU) et de visualiser des données. addition, multiplication) are programmed to deal with matrices when required. And the MATLAB environment handles much of the bothersome housekeeping that makes all this possible. To include these constructs in the interface, edit the definitions in defineschool. 1) We can use MATLAB’s built-in dsolve(). 1 11 Replies. Losada The MathWorks, Inc. x is based on Matlab scripts and, for Windows. Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. This tutorial video teaches about fractional order transfer function. Many programming errors are caused by using a row vector where a column vector is required, and vice versa. , printed) version. Script files can only operate on the variables that are hard-coded into their m-file. Preventing MATLAB from putting a new plot on top of an old one. How to make a histogram in MATLAB ®. Matlab ist vor allem für numerische Berechnungen mithilfe von Matrizen ausgelegt, woher sich auch der Name ableitet: MATrix LABoratory. In the preceding example the first directory I add to my MATLAB path is /u/gerry/MATLAB/local. matlab_map , programs which illustrate the use of MATLAB's mapping toolbox to draw maps of the world, countries, the US, or individual states. The string and number data type formerly presented are particular cases of arrays. Designing a function to accept input arguments and plot relation using MATLAB. To create a cell array with a specified size, use the cell function, described below. It is defined by and. Piecewise function - separate ranges in Matlab In math, a piecewise function (or piecewise-defined function) is a function whose definition changes depending on the value of the independent variable. Matlab R2010b) this can even happen when it easy to find by hand the solution in implicit form. By default, MATLAB displays numbers with four decimal place values. Create individual snapshots showing how the technology will work based on the model. An array is the most fundamental data type in MATLAB. A matrix is a two-dimensional array of numbers. Introduction to Matrices in Matlab¶. You can perform most Simulink ® modeling basics programmatically at the MATLAB ® command prompt. Define a Matrix 3x3 using matlab. The Dirac delta is not strictly a function, because any real function that is equal to zero everywhere but at a single point must have a total integral equal to zero, but for many purposes this definition can be manipulated as a function. The RTL-SDR radio support package enables you to design wireless receivers using real world signals. MATLAB (matrix laboratory) is a multi-paradigm numerical computin environment an fowert-generation programmin leid. MATLAB is a very powerful program. Whats people lookup in this blog: Matlab Define Floor Function. In MATLAB version 7. By: Rachel Hager This lab is an introduction to audio processing with MatLab. Here's how to define and access elements in a cell vector: Defining a cell vector: cells vectors are essential in MATLAB if you want to manipulate strings. MATLAB puede llamar funciones y subrutinas escritas en C o Fortran. Subclassing Multiple Classes. MATLAB is an abbreviation for "matrix laboratory. m file and you save the file in that location, then you will be able to use it. Children vector of handles. This line is displayed when the user types help functionName in the Command line. We’ve seen how to define an array in a structure, but you’ll often need to define an array of structure (matrix or vector). If you are using a version of MATLAB prior to version 7. You can assign a new key to your Matlab. Es ist als kurze Einführung gedacht, die an Hand von Beispielen die Arbeitsweise von MATLAB demonstriert. If you want to just define a simple variable that is seen in your workspace, then. Consistent with the Boltzmann definition, the second law of thermodynamics needs to be re-worded as such that entropy increases over time, though the underlying principle remains the same. The format long command displays 16 digits after decimal. Audio Processing with MatLab. Learn more about matlab function, matlab MATLAB. MATLAB is a scientific computing software product which scientists and engineers use for complex technical computations and simulations. Matlab ist vor allem für numerische Berechnungen mithilfe von Matrizen ausgelegt, woher sich auch der Name ableitet: MATrix LABoratory. Entire courses in computer science are devoted to extolling OOPs many virtues and we will not have space to mention them all here. Supports arbitrary weak learners that you can define. MATLAB is started by clicking the mouse on the appropriate icon and is ended by typing exit or by using the menu option. MATLAB is one of the high-performance languages that is generally used for the purpose of technical computing. It consists of a single MATLAB expression and any number of input and output arguments. It means that you cannot define a function in that part of the code. The unwrap is included to ensure that the phonse does jump from +180 t o-180 degrees. You can assign a new key to your Matlab. You can just simply deactivate your license from the “HELP” button on the Matlab and choose “Deactivate”. The distinction between row vectors and column vectors is essential. An email has been sent to verify your new profile. Students will complete tasks that demonstrate the advantages of using MATLAB in engineering modeling, testing, and analysis. Creating Arrays The basic data structure in Matlab is the two-dimensional array. Basic interface, operations, functions, and programming techniques are covered. 38 degree North latitude and 90. We can easily define our own variables in MATLAB. NET, and Python ® data structures to cell arrays of equivalent MATLAB ® objects. It can be run both under interactive sessions and as a batch job. We will start by defining some vectors and some matrices. How to use normalize in a sentence. Try it with the addtwo function. Interactively label rectangular ROIs for object detection, pixels for semantic segmentation, and scenes for image classification. Use this property to create a relationship between a parent label and its children. If the variable already exists, then MATLAB replaces the original content with new content and allocates new storage space, where necessary. Requirement Types. In C we WILL have to worry about this. Variables are assigned numerical values by typing the expression directly, for example, typing. Note that the description MATLAB returns about the command you requested help on contains the command name in ALL CAPS. I will followup on this latter. The expression executes in the MATLAB workspace. In this case Matlab was unable to find the solution in implicit form. You can assign a callback to the property of a specific object or you can define a default callback for all objects of that type. Often poorly taught by graduate students to undergrads in science and engineering fields of study, usually under the false pretense that it is usefull for something other than bringing about the end of time. MATLAB Cell Vector. Square root. The declaration starts with the function keyword, and to remind you that it's a keyword, MATLAB highlights it for you in blue. As a consequence, functions have mechanisms for passing arguments into the functions, and for returning the results. Top MATLAB acronym meaning: Matrix Laboratory. To practice these commands, either cut and paste or type something similar in you Matlab window. A2A Apparently, there are no predefined lists of scientific constants in MATLAB that you can use, and as Sahil Juneja has said you can use physconst if, by chance, there is the constant that you need. Consistent with the Boltzmann definition, the second law of thermodynamics needs to be re-worded as such that entropy increases over time, though the underlying principle remains the same. Get the inside view on MATLAB and Simulink Insights and information from the engineers who design, build and support MathWorks products Subscribe to All Blogs Meet the Bloggers. The file itself will determine how many inputs the function can accept, what they are called locally, how many outputs can be returned, and what they are called locally. Variables in MATLAB. Creating Arrays The basic data structure in Matlab is the two-dimensional array. addition, multiplication) are programmed to deal with matrices when required. For example, here is the WeekDays class with a method called isMeetingDay added: classdef WeekDays enumeration Monday, Tuesday, Wednesday, Thursday, Friday end methods function tf = isMeetingDay(obj) tf = ~(WeekDays. Create requirements and define hierarchy. So either turn your script file into a function file itself, or copy your function code to a new file (with the name ff. x is based on Matlab scripts and, for Windows. Valid class names begin with an. Suppose is equal to on the interval and on the interval and you want to define it as a MATLAB function. Define the parent-child hierarchy for the requirements you associate with your model. Recent Examples on the Web. This is a problem if you have a java object that is trying to run a matlab command. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. MATLAB Functions What is a MATLAB function? A MATLAB "function" is a MATLAB program that performs a sequence of operations specified in a text file (called an m-file because it must be saved with a file extension of *. variable a in its workspace until you exit MATLAB or tell MATLAB to delete the variable. Specify the point in Axes coordinates. For anything in a computer more complicated than a list of numbers, structures can be used. 0) and the Signal Processing Toolbox (ver. MATLAB is supported on Unix, Macintosh, and Windows environments; a student version of MATLAB is available for personal computers. Fuzzy Logic Examples using Matlab Consider a very simple example: We need to control the speed of a motor by changing the input voltage. Also notice how the time had to be redefined. A version of the tutorial that is suitable for printing can be accessed by viewing the tutorial. generateLibraryDefinition command. jpg and demo2. MATLAB (MATrix LABoratory) trata-se de um software interativo de alta performance voltado para o cálculo numérico. This course teaches computer programming to those with little to no previous experience. With it, you can perform everything from basic mathematical operations to high-end programming. In this published M-file, we will use MATLAB to solve problems about lines and planes in three-dimensional space. Let us plot the simple function y = x for the range of values for x from 0 to 100, with an increment of 5. Implementation of MATLAB You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. )See Templates for C S-Functions for a complete skeleton implementation of a C MEX S-function that you can use as a starting point for creating your own S-functions. MATLAB functions need to have a defined value for the case where none of the conditions hold. Before performing any calculations with a numeric variable, MATLAB prods and pokes into its contents. having an uninterrupted series of steps : graduated; capable of being represented by a point on a scale…. Volume Slices and Isosurfaces. Audio Processing with MatLab. As a consequence, functions have mechanisms for passing arguments into the functions, and for returning the results. Programmatic Modeling Basics. Seven examples of colored, horizontal, and normal histogram bar charts. Structure Definition for Code Generation. mlx and data file 'schoolData. The Dirac delta is not strictly a function, because any real function that is equal to zero everywhere but at a single point must have a total integral equal to zero, but for many purposes this definition can be manipulated as a function. You don't have to pre-declare x to be a variable; MATLAB figures it out by virtue of the name appearing on the left-hand side of an assignment statement. We begin with the problem of finding the equation of a plane through three points. MATLAB – Eine Einführung, S. MATLAB functions to manipulate complex values 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. , printed) version. Note the use of both nested selective structures and the use of compound relational operators (that is, relational operators joined by logical operators). This is known as short format. Class File Organization Class syntax, attributes, and organization in files and folders. The distinction between row vectors and column vectors is essential. Learn more about barplot, axis definition. One of Matlab's best kept secrets is its comprehensive support for Object Oriented Programming, (OOP). One matlab function provided in the toolbox computes that direct pixel projection map. MATLAB is an incredibly powerful tool, but in order to use it safely you need to be able to understand how it works and to be very precise when you enter commands. Distributions known to package Octave include Debian, Ubuntu, Fedora, Gentoo, and openSUSE. How to Write a Function and Call It in MATLAB. uint8 variables use the integer math rules! UINT8 Overflow. See Declaring Structures for more details. Matlab allows you to create symbolic math expressions. This is known as short format. Defining functions in MATLAB, Projects and practicals using MATLAB. What does MATLAB mean? Information and translations of MATLAB in the most comprehensive dictionary definitions resource on the web. As easy as starting the GUIDE in the command line, dragging a button on a window and populating the button callback with you code. Natick, MA 01760, USA March 31, 2003 Abstract This tutorial white-paper illustrates practical aspects of FIR ﬁlter design and ﬁxed-point implementation along with the algorithms available in the Filter Design Toolbox and the. First, the independent variable and its range must be defined. MATLAB is a very powerful program. Variables are assigned numerical values by typing the expression directly, for example, typing. Object Oriented Programming in Matlab: basics. Often poorly taught by graduate students to undergrads in science and engineering fields of study, usually under the false pretense that it is usefull for something other than bringing about the end of time. (MATrix LABoratory) A programming language for technical computing from The MathWorks, Natick, MA (www. Structures are created and accessed in a manner familiar for those accustomed to programming in C. The Far-Reaching Impact of MATLAB and Simulink Explore the wide range of product capabilities, and find the solution that is right for your application or industry System Design and Simulation. Usually, the numerical solvers in Matlab work well with the standard settings. Functions are the basis of all scripting and programming languages. It is not the case in every programming language (nor is it always true in Matlab). 1 constructs require additional definition. An anonymous function is like an inline function in traditional programming languages, defined within a single MATLAB statement. Uses for MATLAB include matrix calculations, developing and running algorithms, creating user interfaces and data visualization. Modify Inherited Properties. Move interior nodes to obtain force equilibirum. Later, when integrating it with other non-matlab generated code, we may decide that we don't want things sized in exactly the same way -- say, we had a function that operated on a 100 element array, but decide we instead want 200. Time-frequency decompositions. Introduction Fourierseriesprovidesanalternatewayofrepresentingdata:insteadofrepresent-. This set of information is called the "header", and it is all the information that someone should need to run your function correctly (i. A Structure is a named collection of data representing a single idea or "object". To ensure MATLAB uses exactly the colors you define in the Figure colormap, set MinColorMap. Code at the MATLAB ® command line and in other functions cannot change persistent variables. Its syntax shares similarities with C, with some notable differences. MATLAB permet de faire du calcul matriciel, de développer et d'exécuter des algorithmes, de créer des interfaces utilisateur (IU) et de visualiser des données. It may not always provide a complete solution, but you can use it to perform these kinds of tasks: Define the original math model used to define the technology and therefore the simulation. all the bars in my bar graph have the color blue. MATLAB (MATrix LABoratory) A programming language for technical computing from The MathWorks, Natick, MA (www. hello dear sixww thanks for your answer , but i think i couldn't express clearly. Learn more about matlab function, matlab MATLAB. State Space Simulation in Matlab. What I want is to set each individual arrow color to be relative to its direction, e. global Define global variables. Clipping {on} | off. In writing a function definition, an input variable can be recycled as an output, providing preallocated space. Functions, however, define a separate ( local ) scope. MATLAB developer Loren Shure shows you how to turn your ideas into MATLAB code — Loren on the Art of MATLAB in MATLAB Central Blogs. An example of its application is shown below: the vector yc (line 6) represents a noisy rectangular pulse (y) convoluted with a transfer function c before being measured. Indeed, when you want to define a vector of strings, you have to use cells to separate the different strings from each. Children vector of handles. In particular we assume that you know how to create vectors and matrices and know how to index into them. So you could define it as a global variable, but then you need to declare each variable as global inside every function that will need it. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. - Definition of mass, momentum and energy balance equations for HVAC systems and CHP plants; - Development of Matlab models for HVAC systems and CHP plants by implementation of working principles and control logic algorithms based on Object Oriented Programming language; - Technical reports. For anything in a computer more complicated than a list of numbers, structures can be used. " While other programming languages mostly work with numbers one at a time, MATLAB® is designed to operate primarily on whole matrices and arrays. Matlab is an interpreted language and looping through a vector like this is the slowest possible way to change a vector. ^ means exponentiation. 32 g/cm^3)? Also, can I do this in an output box displayed to the user?. A basic introduction to defining and manipulating matrices is given here. Fuzzy Logic Examples using Matlab Consider a very simple example: We need to control the speed of a motor by changing the input voltage. MATLAB variable names are case sensitive so x and X are different variables. Note: You can execute the code from this tutorial by highlighting them, right-clicking, and selecting "Evaluate Selection" (or hit F9). Define a Callback as a Default. Logical indexing will allow us to select and manipulate only those subsets of data that satisfy particular logical conditions. Introduction to Matrices in Matlab¶. To ensure MATLAB uses exactly the colors you define in the Figure colormap, set MinColorMap. Consistent with the Boltzmann definition, the second law of thermodynamics needs to be re-worded as such that entropy increases over time, though the underlying principle remains the same. It is defined by and. MATLAB uses the the at-symbol (@) to indicate that what follows is the definition of an anonymous function. Computing the gist descriptor: To compute the gist descriptor on an image use the function LMgist. Create individual snapshots showing how the technology will work based on the model. The unwrap is included to ensure that the phonse does jump from +180 t o-180 degrees. An anonymous function is like an inline function in traditional programming languages, defined within a single MATLAB statement. The format long command displays 16 digits after decimal. Then, use square brackets to mark the beginning and the end of your matrix. One of Matlab's best kept secrets is its comprehensive support for Object Oriented Programming, (OOP). However, if you want more precision, you need to use the format command. This tutorial video teaches about fractional order transfer function. So please consider it while answering. It is useful in general for event-based programming in matlab, which you might be doing if you are using matlab to interact with anything, like Java apps or the real world via the serial port. 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: