Introduction to Matlab Entering Commands Constants and Functions

Introduction to Matlab

Entering Commands

Constants and Functions >> pi ans = 3. 1416 >> eps ans = 2. 2204 e-016 >> sin(pi/2) ans = 1 >> log(1000) ans = 6. 9078 >> log 10(1000) ans = 3

Some Constants • bitmax: Largest usable positive integer • eps: Smallest number that changes the value of 1 when added to it. • realmin: Smallest usable positive real number • realmax: Largest usable positive real number • ans: Default variable names used for results • i or j: sqrt(-1) • inf : Stands for infinity, e. g. , 1/0 • Na. N or nan : Stands for not a number, e. g. , 0/0.

Constants … >> bitmax ans = 9. 0072 e+015 >> eps ans = 2. 2204 e-016 >> realmin ans = 2. 2251 e-308 >> realmax ans = 1. 7977 e+308 >> i ans = 0 + 1. 0000 i >> inf ans = Inf >> Na. N ans = Na. N

Elementary Math Functions >> help elfun Elementary math functions. Trigonometric. sin - Sine. sinh - Hyperbolic sine. asin - Inverse sine. asinh - Inverse hyperbolic sine. cos - Cosine. cosh - Hyperbolic cosine. acos - Inverse cosine. acosh - Inverse hyperbolic cosine. tan - Tangent. tanh - Hyperbolic tangent. atan - Inverse tangent. atan 2 - Four quadrant inverse tangent. atanh sech asech csch acsch coth acoth - Inverse hyperbolic tangent. - Secant. - Hyperbolic secant. - Inverse hyperbolic secant. - Cosecant. - Hyperbolic cosecant. - Inverse hyperbolic cosecant. - Cotangent. - Hyperbolic cotangent. - Inverse hyperbolic cotangent.

Elementary Math Functions Exponential. exp - Exponential (e^x). log - Natural logarithm. log 10 - Common (base 10) logarithm. log 2 - Base 2 logarithm and dissect floating point number. pow 2 - Base 2 power and scale floating point number. realpow - Power that will error out on complex result. reallog - Natural logarithm of real number. realsqrt - Square root of number greater than or equal to zero. sqrt - Square root. nextpow 2 - Next higher power of 2.

Exponential Function Examples >> exp(log(3)) ans = 3. 0000 >> log(exp(3)) ans = 3 >> log 2(32) ans = 5 >> log 2(pow 2(5)) ans = 5 >> nextpow 2(27) ans = 5

Elementary Math Functions Complex. abs - Absolute value. angle - Phase angle. complex - Construct complex data from real and imaginary parts. conj - Complex conjugate. imag - Complex imaginary part. real - Complex real part. unwrap - Unwrap phase angle. isreal - True for real array. cplxpair - Sort numbers into complex conjugate pairs.

Elementary Math Functions Rounding and remainder. fix - Round towards zero. floor - Round towards minus infinity. ceil - Round towards plus infinity. round - Round towards nearest integer. mod - Modulus (signed remainder after division). rem - Remainder after division. sign - Signum.

Remainder Examples >> mod( 12, 7) ans = 5 >> mod(-12, 7) ans = 2 >> rem(12, 7) ans = 5 >> rem(-12, 7) ans = -5

Rounding Examples round(2. 7) 3, round(2. 3) 2 round(-2. 7) -3, round(-2. 3) -2 fix(2. 3) 2, fix(2. 7) 2 fix(-2. 3) -2, fix(-2. 7) -2 ceil(2. 3) 3, ceil(2. 7) 3 ceil(-2. 3) -2, ceil(-2. 7) -2 floor(2. 3) 2, floor(2. 7) 2 floor(-2. 3) -3, floor(-2. 7) -3

Getting Help >> cotangent(pi/2) ? ? ? Undefined function or variable 'cotangent'. >> help cotangent. m not found. >> lookfor cotangent ACOT Inverse cotangent. ACOTH Inverse hyperbolic cotangent. COT Cotangent. COTH Hyperbolic cotangent. ACOT Symbolic inverse cotangent. ACOTH Symbolic inverse hyperbolic cotangent. COT Symbolic cotangent. COTH Symbolic hyperbolic cotangent. >> help cot COT Cotangent. COT(X) is the cotangent of the elements of X.

Variables Let’s evaluate the following expression in matlab : Now let’s do the following: What if we need to evaluate the same expression for 2. 1, 2. 2, 2. 3, … and lots of other values?

Variables Lets evaluate: It looks like the term appears 3 times in our expression. It would be nice if we evaluated it once and “remembered” the result for other occurrences of the term in the formula.

Variables • Variables are named memory locations that can be assigned a value by the user or programmer • The system can retrieve , or “remember” the value of a variable. • Variables typically reside in main memory.

Variable Examples >> a ? ? ? Undefined function or variable 'a'. >> a=2 a= 2 >> a+3 ans = 5 >> sqrt(a+14) ans = 4 >> a=a+12 a = 14

Variables • Given: Rather than : >>cot(3)*sqrt(log(3)^3) + cos(3)*sin(log(3)), >>cot(2. 7)*sqrt(log(2. 7)^3) + cos(2. 7)*sin(log(2. 7)), … Use a variable: >>x=3 >>cot(x)*sqrt(log(x)^3) + cos(x)*sin(log(x)) >>x=2. 7 >>cot(x)*sqrt(log(x)^3) + cos(x)*sin(log(x))

Variables Rather than evaluating : >> x=0. 5 x = 0. 5000 >> term=sin(x)+cos(x)^2 term = 1. 2496 >> log(term) + realpow(term, 0. 25) - term^2 ans = -0. 2814

Who and Clear >> who Your variables are: a ans term x >> whos Name Size a 1 x 1 ans 1 x 1 term 1 x 1 x 1 x 1 Bytes Class 8 double array Grand total is 4 elements using 32 bytes >> clear a >> who Your variables are: ans term x >> clear >> who >>

Variable Names • Only first 31 characters significant • Matlab variables case sensitive • Use meaningful names rather than shorter ones ! • Avoid using existing function names !

Variable Name Examples >> log(5) ans = 1. 6094 >> log = 4 >> log(5) ? ? ? Index exceeds matrix dimensions. >> clear log >> log(5) ans = 1. 6094 >> Abc=123 Abc = 123 >> ABc ? ? ? Undefined function or variable 'ABc'.

Getting User Input >> age=input('Please enter your age : ') Please enter your age : 29 age = 29 >> age + 2 ans = 31

String variables >> a = 'This is a string' a =This is a string >> b= 'Another string' b =Another string >> a + b ? ? ? Error using ==> + Array dimensions must match for binary array op. >> whos Name Size Bytes Class a 1 x 16 32 char array b 1 x 14 28 char array Grand total is 30 elements using 60 bytes >> c = [a b 'Yet another string'] c =This is a string. Another string. Yet another string

String variables • Variables can change types based on the values assigned to them : >> a a =This is a string >> a=3; >> whos Name Size a b c 1 x 14 1 x 48 Bytes Class 8 double array 28 char array 96 char array Grand total is 63 elements using 132 bytes

Converting Numbers to Strings • You can use the function num 2 str and int 2 str: >> s = 'The number ' + 3 s = 87 104 35 113 120 112 101 104 117 >> s = ['The number ' 3] s =The number � >> s = ['The number ' num 2 str(3)] s =The number 3 >> int 2 str(2. 3) ans =2 35

Converting Strings to Numbers >> x = ['123' '789'] x =123789 >> x 2 = str 2 num(x) x 2 = 123789 >> x 2 + 1 ans = 123790 >> str 2 int('1. 2') ? ? ? Undefined function or variable 'str 2 int'.

Display Format • The values displayed at the screen doesn’t necessarily include all the information. • It is possible to change the display format. >> 1234567890 ans = 1. 2346 e+019 >> format long >> 1234567890 ans = 1. 234567890123457 e+019

Operator Precedence 1 The contents of all bracketed expressions are evaluated, starting from the innermost brackets and working out. 2 All exponentials are evaluated, working from left to right. 3 All multiplications and divisions are evaluated, working from left to right. 4 All additions and subtractions are evaluated, working from left to right.

Operator Precedence >> 2 + 3 * 4 ans = 14 >> 2 * 3 ^ 2 ans = 18 >> (2 + 3) * 4 ans = 20 >> (2^(2 + 3)) * 4 ans = 128