Презентация, доклад на тему Современные методы численного моделирования теплофизических процессов

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)

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.

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.

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 #

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.

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.

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

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.

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=

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

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

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];

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

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

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

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

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

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

5
>> disp( [ 'Bilkent ' 'University' ] )
Bilkent University
>> name = 'Alper';
>> disp( [ 'Hello ' name ] )
Hello Alper

'-Feb-' num2str(2004) ];
>> disp(d)
16-Feb-2004
>> x = 23.11;
>> disp( [ 'answer = ' num2str(x) ] )
answer = 23.11
>> disp( [ 'answer = ' int2str(x) ] )
answer = 23

floating point or exponential format, whichever is shorter
\n new line character
\t tab character

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

y → binary
>> save myfile.dat x –ascii → ascii
load filename
>> load myfile.mat → binary
>> load myfile.dat –ascii → ascii

b → a - b
multiplication a x b → a * b
division a / b → a / b
exponent ab → a ^ b

/ 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

log2
exp
sqrt
sin, cos, tan
asin, acos, atan
max, min
round, floor, ceil, fix
mod, rem
help elfun → help for elementary math functions

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, …

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