Introduction to Matlab

Entering Commands

Constants and Functions >> pi ans = >> eps ans = e-016 >> sin(pi/2) ans = 1 >> log(1000) ans = >> log10(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 NaN or nan :Stands for not a number, e.g., 0/0.

Constants … >> bitmax ans = e+015 >> eps ans = e-016 >> realmin ans = e-308 >> realmax ans = e+308 >> ans ans = e+308 >> i ans = i >> inf ans = Inf >> NaN ans = NaN

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. atan2 - Four quadrant inverse tangent. atanh - Inverse hyperbolic tangent. sec - Secant. sech - Hyperbolic secant. asec - Inverse secant. asech - Inverse hyperbolic secant. csc - Cosecant. csch - Hyperbolic cosecant. acsc - Inverse cosecant. acsch - Inverse hyperbolic cosecant. cot - Cotangent. coth - Hyperbolic cotangent. acot - Inverse cotangent. acoth - Inverse hyperbolic cotangent.

Elementary Math Functions Exponential. exp - Exponential (e^x). log - Natural logarithm. log10 - Common (base 10) logarithm. log2 - Base 2 logarithm and dissect floating point number. pow2 - 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. nextpow2 - Next higher power of 2.

Exponential Function Examples >> exp(log(3)) ans = >> log(exp(3)) ans = 3 >> log2(32) ans = 5 >> log2(pow2(5)) ans = 5 >> nextpow2(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 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 = >> term=sin(x)+cos(x)^2 term = >> log(term) + realpow(term, 0.25) - term^2 ans =

Who and Clear >> who Your variables are: a ans term x >> whos Name Size Bytes Class a 1x1 8 double array ans 1x1 8 double array term 1x1 8 double array x 1x1 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 = >> log = 4 log = 4 >> log(5) ??? Index exceeds matrix dimensions. >> clear log >> log(5) ans = >> 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 1x16 32 char array b 1x14 28 char array Grand total is 30 elements using 60 bytes >> c = [a b 'Yet another string'] c =This is a stringAnother stringYet 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 Bytes Class a 1x1 8 double array b 1x14 28 char array c 1x48 96 char array Grand total is 63 elements using 132 bytes

Converting Numbers to Strings You can use the function num2str and int2str: >> s = 'The number ' + 3 s = >> s = ['The number ' 3] s =The number >> s = ['The number ' num2str(3)] s =The number 3 >> int2str(2.3) ans =2

Converting Strings to Numbers >> x = ['123' '789'] x = >> x2 = str2num(x) x2 = >> x2 + 1 ans = >> str2int('1.2') ??? Undefined function or variable 'str2int'.

Display Format The values displayed at the screen doesn’t necessarily include all the information. It is possible to change the display format. >> ans = e+019 >> format long >> ans = 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 >> * 4 ans = 14 >> 2 * 3 ^ 2 ans = 18 >> (2 + 3) * 4 ans = 20 >> (2^(2 + 3)) * 4 ans = 128