Современные методы численного моделирования теплофизических процессов

MATLAB Basics CS 111 Introduction to Computing in Engineering and Science

CS 111 * MATLAB BASICS Variables and Arrays Array: A collection of data values organized into rows and columns, and known by a single name. Row 1 Row 2 Row 3 Row 4 Col 1 Col 2 Col 3 Col 4 Col 5 arr(3,2)

CS 111 * MATLAB BASICS Arrays The fundamental unit of data in MATLAB Scalars are also treated as arrays by MATLAB (1 row and 1 column). Row and column indices of an array start from 1. Arrays can be classified as vectors and matrices.

CS 111 * MATLAB BASICS Vector: Array with one dimension Matrix: Array with more than one dimension Size of an array is specified by the number of rows and the number of columns, with the number of rows mentioned first (For example: n x m array). Total number of elements in an array is the product of the number of rows and the number of columns.

CS 111 * MATLAB BASICS 1 2 3 4 5 6 a= 3x2 matrix  6 elements b=[1 2 3 4] 1x4 array  4 elements, row vector c= 1 3 5 3x1 array  3 elements, column vector a(2,1)=3 b(3)=3 c(2)=3 Row # Column #

CS 111 * MATLAB BASICS Variables A region of memory containing an array, which is known by a user-specified name. Contents can be used or modified at any time. Variable names must begin with a letter, followed by any combination of letters, numbers and the underscore (_) character. Only the first 31 characters are significant. The MATLAB language is Case Sensitive. NAME, name and Name are all different variables. Give meaningful (descriptive and easy-to-remember) names for the variables. Never define a variable with the same name as a MATLAB function or command.

CS 111 * MATLAB BASICS Common types of MATLAB variables double: 64-bit double-precision floating-point numbers They can hold real, imaginary or complex numbers in the range from ±10-308 to ±10308 with 15 or 16 decimal digits. >> var = 1 + i ; char: 16-bit values, each representing a single character The char arrays are used to hold character strings. >> comment = ‘This is a character string’ ; The type of data assigned to a variable determines the type of variable that is created.

CS 111 * Initializing Variables in Assignment Statements An assignment statement has the general form var = expression Examples: >> var = 40 * i; >> a2 = [0 1+8]; >> var2 = var / 5; >> b2 = [a2(2) 7 a]; >> array = [1 2 3 4]; >> c2(2,3) = 5; >> x = 1; y = 2; >> d2 = [1 2]; >> a = [3.4]; >> d2(4) = 4; >> b = [1.0 2.0 3.0 4.0]; >> c = [1.0; 2.0; 3.0]; >> d = [1, 2, 3; 4, 5, 6]; ‘;’ semicolon suppresses the >> e = [1, 2, 3 automatic echoing of values but 4, 5, 6]; it slows down the execution. MATLAB BASICS

CS 111 * MATLAB BASICS Initializing Variables in Assignment Statements Arrays are constructed using brackets and semicolons. All of the elements of an array are listed in row order. The values in each row are listed from left to right and they are separated by blank spaces or commas. The rows are separated by semicolons or new lines. The number of elements in every row of an array must be the same. The expressions used to initialize arrays can include algebraic operations and all or portions of previously defined arrays.

CS 111 * MATLAB BASICS Initializing with Shortcut Expressions first: increment: last Colon operator: a shortcut notation used to initialize arrays with thousands of elements >> x = 1 : 2 : 10; >> angles = (0.01 : 0.01 : 1) * pi; Transpose operator: (′) swaps the rows and columns of an array >> f = [1:4]′; >> g = 1:4; >> h = [ g′ g′ ]; 1 1 2 2 3 4 4 h=

CS 111 * Initializing with Built-in Functions zeros(n) >> a = zeros(2); zeros(n,m) >> b = zeros(2, 3); zeros(size(arr)) >> c = [1, 2; 3, 4]; ones(n) >> d = zeros(size(c)); ones(n,m) ones(size(arr)) eye(n) eye(n,m) length(arr) size(arr) MATLAB BASICS

CS 111 * Initializing with Keyboard Input The input function displays a prompt string in the Command Window and then waits for the user to respond. my_val = input( ‘Enter an input value: ’ ); in1 = input( ‘Enter data: ’ ); in2 = input( ‘Enter data: ’ ,`s`); MATLAB BASICS

CS 111 * 3 2 5 4 7 6 1 10 8 9 11 12 4 7 1 10 2 5 MATLAB BASICS 8 11 Multidimensional Arrays A two dimensional array with m rows and n columns will occupy mxn successive locations in the computer’s memory. MATLAB always allocates array elements in column major order. a= [1 2 3; 4 5 6; 7 8 9; 10 11 12]; a(5) = a(1,2) = 2 A 2x3x2 array of three dimensions c(:, :, 1) = [1 2 3; 4 5 6 ]; c(:, :, 2) = [7 8 9; 10 11 12];

CS 111 * Subarrays It is possible to select and use subsets of MATLAB arrays. arr1 = [1.1 -2.2 3.3 -4.4 5.5]; arr1(3) is 3.3 arr1([1 4]) is the array [1.1 -4.4] arr1(1 : 2 : 5) is the array [1.1 3.3 5.5] For two-dimensional arrays, a colon can be used in a subscript to select all of the values of that subscript. arr2 = [1 2 3; -2 -3 -4; 3 4 5]; arr2(1, :) arr2(:, 1:2:3) MATLAB BASICS

CS 111 * Subarrays The end function: When used in an array subscript, it returns the highest value taken on by that subscript. arr3 = [1 2 3 4 5 6 7 8]; arr3(5:end) is the array [5 6 7 8] arr4 = [1 2 3 4; 5 6 7 8; 9 10 11 12]; arr4(2:end, 2:end) Using subarrays on the left hand-side of an assignment statement: arr4(1:2, [1 4]) = [20 21; 22 23]; (1,1) (1,4) (2,1) and (2,4) are updated. arr4 = [20 21; 22 23]; all of the array is changed. MATLAB BASICS

CS 111 * Subarrays Assigning a Scalar to a Subarray: A scalar value on the right-hand side of an assignment statement is copied into every element specified on the left-hand side. >> arr4 = [1 2 3 4; 5 6 7 8; 9 10 11 12]; >> arr4(1:2, 1:2) = 1 arr4 = 1 1 3 4 1 1 7 8 9 10 11 12 MATLAB BASICS

CS 111 * Special Values MATLAB includes a number of predefined special values. These values can be used at any time without initializing them. These predefined values are stored in ordinary variables. They can be overwritten or modified by a user. If a new value is assigned to one of these variables, then that new value will replace the default one in all later calculations. >> circ1 = 2 * pi * 10; >> pi = 3; >> circ2 = 2 * pi * 10; Never change the values of predefined variables. MATLAB BASICS

CS 111 * Special Values pi:  value up to 15 significant digits i, j: sqrt(-1) Inf: infinity (such as division by 0) NaN: Not-a-Number (division of zero by zero) clock: current date and time in the form of a 6-element row vector containing the year, month, day, hour, minute, and second date: current date as a string such as 16-Feb-2004 eps: epsilon is the smallest difference between two numbers ans: stores the result of an expression MATLAB BASICS

CS 111 * Changing the data format >> value = 12.345678901234567; format short  12.3457 format long  12.34567890123457 format short e  1.2346e+001 format long e  1.234567890123457e+001 format short g  12.346 format long g  12.3456789012346 format rat  1000/81 MATLAB BASICS

CS 111 * MATLAB BASICS The disp( array ) function >> disp( 'Hello' ) Hello >> disp(5) 5 >> disp( [ 'Bilkent ' 'University' ] ) Bilkent University >> name = 'Alper'; >> disp( [ 'Hello ' name ] ) Hello Alper

CS 111 * MATLAB BASICS The num2str() and int2str() functions >> d = [ num2str(16) '-Feb-' num2str(2004) ]; >> disp(d) 16-Feb-2004 >> x = 23.11; >> disp( [ 'answer = ' num2str(x) ] ) answer = 23.11 >> disp( [ 'answer = ' int2str(x) ] ) answer = 23

CS 111 * MATLAB BASICS The fprintf( format, data ) function %d integer %f floating point format %e exponential format %g either floating point or exponential format, whichever is shorter \n new line character \t tab character

CS 111 * MATLAB BASICS >> fprintf( 'Result is %d', 3 ) Result is 3 >> fprintf( 'Area of a circle with radius %d is %f', 3, pi*3^2 ) Area of a circle with radius 3 is 28.274334 >> x = 5; >> fprintf( 'x = %3d', x ) x = 5 >> x = pi; >> fprintf( 'x = %0.2f', x ) x = 3.14 >> fprintf( 'x = %6.2f', x ) x = 3.14 >> fprintf( 'x = %d\ny = %d\n', 3, 13 ) x = 3 y = 13

CS 111 * MATLAB BASICS Data files save filename var1 var2 … >> save myfile.mat x y  binary >> save myfile.dat x –ascii  ascii load filename >> load myfile.mat  binary >> load myfile.dat –ascii  ascii

CS 111 * MATLAB BASICS variable_name = expression; addition a + b  a + b subtraction a - b  a - b multiplication a x b  a * b division a / b  a / b exponent ab  a ^ b

CS 111 * MATLAB BASICS Hierarchy of operations x = 3 * 2 + 6 / 2 Processing order of operations is important parentheses (starting from the innermost) exponentials (from left to right) multiplications and divisions (from left to right) additions and subtractions (from left to right) >> x = 3 * 2 + 6 / 2 x = 9

CS 111 * MATLAB BASICS Built-in MATLAB Functions result = function_name( input ); abs, sign log, log10, log2 exp sqrt sin, cos, tan asin, acos, atan max, min round, floor, ceil, fix mod, rem help elfun  help for elementary math functions

CS 111 * MATLAB BASICS Types of errors in MATLAB programs Syntax errors Check spelling and punctuation Run-time errors Check input data Can remove “;” or add “disp” statements Logical errors Use shorter statements Check typos Check units Ask your friends, assistants, instructor, …

CS 111 * MATLAB BASICS Summary help command  Online help lookfor keyword  Lists related commands which  Version and location info clear  Clears the workspace clc  Clears the command window diary filename  Sends output to file diary on/off  Turns diary on/off who, whos  Lists content of the workspace more on/off  Enables/disables paged output Ctrl+c  Aborts operation …  Continuation %  Comments