Exam preparation materials

Appendix A

MATLAB Functions

This appendix provides you with an overview of the MATLAB functions. It would be impossible to provide a complete list of every function here, but these functions see common use for solving math problems. To see an exhaustive list of MATLAB functions, check out https://www.mathworks.com/help/matlab/referencelist.html?type=function.

Each function helps you perform a specific task within MATLAB. Tables A-1 through A-21 contain function names and a short description of the task that each function performs. If you need more information than this appendix gives you, you can obtain additional information by typing help <function_name> in the MATLAB command window and pressing Enter. Of course, you also have the information found in this book, and you can search in Help. See the “Getting additional help with MATLAB” section of Chapter 2 for some useful information on using the Help resources that MATLAB provides.

TABLE A-1 Arithmetic Functions

*Function*	*Description*
ceil	Rounds toward positive infinity
diff	Differences and approximate derivatives
fix	Rounds toward zero
floor	Rounds toward negative infinity
idivide	Integer division with rounding option
ldivide	Left-array division — comparable to .\
minus	Minus — comparable to – subtracting two objects
mldivide	Solves systems of linear equations Ax = B for x — comparable to \
mod	Modulus after division
mpower	Matrix power — comparable to ^
mrdivide	Solves systems of linear equations xA = B for x — comparable to /
mtimes	Matrix multiplication — comparable to *
plus	Plus — comparable to + adding two objects
power	Array power — comparable to .^
prod	Product of array elements
rdivide	Right-array division — comparable to ./
rem	Remainder after division
round	Rounds to nearest integer
sum	Sum of array elements
times	Array multiply — comparable to .*
uminus	Unary minus — comparable to – acting on one object
uplus	Unary plus — comparable to + acting on one object

TABLE A-2 Trigonometric Functions

*Function*	*Description*
acos	Inverse cosine; result in radians
acosd	Inverse cosine; result in degrees
acosh	Inverse hyperbolic cosine
acot	Inverse cotangent; result in radians
acotd	Inverse cotangent; result in degrees
acoth	Inverse hyperbolic cotangent
acsc	Inverse cosecant; result in radians
acscd	Inverse cosecant; result in degrees
acsch	Inverse hyperbolic cosecant
asec	Inverse secant; result in radians
asecd	Inverse secant; result in degrees
asech	Inverse hyperbolic secant
asin	Inverse sine; result in radians
asind	Inverse sine; result in degrees
asinh	Inverse hyperbolic sine
atan	Inverse tangent; result in radians
atan2	Four-quadrant inverse tangent in radians
atan2d	Four-quadrant inverse tangent; result in degrees
atand	Inverse tangent; result in degrees
atanh	Inverse hyperbolic tangent
cos	Cosine of argument in radians
cosd	Cosine of argument in degrees
cosh	Hyperbolic cosine
cot	Cotangent of argument in radians
cotd	Cotangent of argument in degrees
coth	Hyperbolic cotangent
csc	Cosecant of argument in radians
cscd	Cosecant of argument in degrees
csch	Hyperbolic cosecant
hypot	Square root of sum of squares
sec	Secant of argument in radians
secd	Secant of argument in degrees
sech	Hyperbolic secant
sin	Sine of argument in radians
sind	Sine of argument in degrees
sinh	Hyperbolic sine of argument in radians
tan	Tangent of argument in radians
tand	Tangent of argument in degrees
tanh	Hyperbolic tangent

TABLE A-3 Exponentials, Logarithms, Powers, and Roots

*Function*	*Description*
exp	Exponential
expm1	Computes exp(x)–1 accurately for small values of x
log	Natural logarithm
log10	Common (base 10) logarithm
log1p	Computes log(1+x) accurately for small values of x
log2	Determines base 2 logarithm and dissects floating-point numbers into exponent and mantissa
nextpow2	Computes the exponent of the next higher power of 2
nthroot	Real nth root of real numbers
pow2	Base 2 power and scale floating-point numbers
reallog	Natural logarithm for nonnegative real arrays
realpow	Array power for real-only output
realsqrt	Square root for nonnegative real arrays
sqrt	Square root

TABLE A-4 Complex Number Functions

*Function*	*Description*
abs	Absolute value and complex magnitude
angle	Phase angle
complex	Construct complex data from real and imaginary components
conj	Complex conjugate
cplxpair	Sorts complex numbers into complex conjugate pairs
i	Imaginary unit
imag	Imaginary part of complex number
isreal	Checks whether input is a real array
j	Imaginary unit
real	Real part of complex number
sign	The sign() (or signum) function returns 1 if the corresponding element is greater than 0, 0 if the corresponding element is zero, and –1 if the corresponding element is less than 0
unwrap	Shifts the phase angles of vector P

TABLE A-5 Discrete Math Functions

*Function*	*Description*
factor	Prime factors
factorial	Factorial function
gcd	Greatest common divisor
isprime	Array elements that are prime numbers
lcm	Least common multiple
matchpairs	Solves a linear assignment problem
nchoosek	Binomial coefficient or all combinations
perms	All possible permutations
primes	Generates list of prime numbers
rat, rats	Rational fraction approximation

TABLE A-6 Polynomial Functions

*Function*	*Description*
poly	Polynomial with specified roots
polyder	Polynomial derivative
polyeig	Polynomial eigenvalue problem
polyfit	Polynomial curve fitting
polyint	Integrates the polynomial analytically
polyval, polyvalm	Polynomial evaluation
roots	Polynomial roots

TABLE A-7 Special Functions

*Function*	*Description*
erf	Error function
erfc	Complementary error function
erfcinv	Inverse complementary error function
erfcx	Scaled complementary error function
erfinv	Inverse error function

TABLE A-8 Cartesian, Polar, and Spherical Functions

*Function*	*Description*
cart2pol	Transforms Cartesian coordinates to polar or cylindrical coordinates
cart2sph	Transforms Cartesian coordinates to spherical coordinates
pol2cart	Transforms polar or cylindrical coordinates to Cartesian coordinates
sph2cart	Transforms spherical coordinates to Cartesian coordinates

TABLE A-9 Constants and Test Matrix Functions

*Function*	*Description*
compan	Returns the corresponding companion matrix
eps	Floating-point relative accuracy
i,j	Imaginary units
Inf	Infinity
pi	Ratio of circle’s circumference to its diameter
NaN	Not-a-Number
isfinite	Array elements that are finite
isinf	Array elements that are infinite
isnan	Array elements that are NaN
gallery	Test matrices
magic	Magic square

TABLE A-10 Matrix Operation Functions

*Function*	*Description*
cross	Vectors cross product
ctranpose	Performs complex conjugate transpose
dot	Vectors dot product
funm	Evaluates a general matrix function
kron	Kronecker tensor product
transpose	Transposes

TABLE A-11 Linear Equation Functions

*Function*	*Description*
inv	Matrix inverse
linsolve	Solves linear system of equations

TABLE A-12 Eigenvalue Functions

*Function*	*Description*
eig	Eigenvalues and eigenvectors
eigs	Largest eigenvalues and eigenvectors of matrix

TABLE A-13 Matrix Analysis Functions

*Function*	*Description*
det	Matrix determinant
norm	Vector and matrix norms
rank	Rank of matrix
rref	Reduced row echelon form
trace	Sum of diagonal elements

TABLE A-14 Matrix Functions

*Function*	*Description*
arrayfun	Applies function to each element of array
expm	Matrix exponential
logm	Matrix logarithm
sqrtm	Matrix square root

TABLE A-15 Statistical Functions

*Function*	*Description*
bounds	Obtains the smallest and largest elements of an array
corrcoef	Correlation coefficients
cov	Covariance matrix
max, maxk	Largest elements in array
mean	Average or mean value of array
median	Median value of array
min, mink	Smallest elements in array
mode	Most frequent values in array
std	Standard deviation
var	Variance

TABLE A-16 Random Number Generator

*Function*	*Description*
rng	Controls random number generation
rand	Uniformly distributed pseudo-random numbers
randn	Normally distributed pseudo-random numbers
randi	Uniformly distributed pseudo-random integers

TABLE A-17 Interpolation

*Function*	*Description*
interp1	1-D data interpolation (table lookup)
interp2	2-D data interpolation (table lookup)
interp3	3-D data interpolation (table lookup)
interpn	nD data interpolation (table lookup)
griddedInterpolant	Interpolant for gridded data
griddata	Interpolates scattered data
ndgrid	Rectangular grid in nD space
meshgrid	Rectangular grid in 2D and 3D space
spline	Cubic spline data interpolation

TABLE A-18 Optimization Functions

*Function*	*Description*
fminbnd	Finds minimum of single-variable function on fixed intervals
fminsearch	Finds minimum of unconstrained multivariable function using derivative-free method
fzero	Finds root of continuous function of one variable
lsqnonneg	Solves a non-negative linear least-squares problem

TABLE A-19 Ordinary Differential Equation Functions

*Function*	*Description*
ode23, ode45, ode113	Solve nonstiff differential equations
ode15s, od23s, ode23t, od23tb	Solve stiff differential equations
ode15i, decic	Solve fully implicit differential equations

TABLE A-20 Sparse Matrix Manipulation Functions

*Function*	*Description*
spy	Visualizes a sparsity pattern
find	Finds indices and values of nonzero elements

TABLE A-21 Elementary Polygons

*Function*	*Description*
polyarea	Area of polygon
inpolygon	Determines whether points are inside or on the edges of a polygon
rectint	Rectangle intersection area

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