= MATLAB Built-in Functions =

Several '''functions''' are built into MATLAB.

<<TableOfContents>>

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== Numeric Functions ==

Most built-in functions operate on [[MATLAB/DataTypes#Numeric|numeric arrays]] by applying the function element-wise. These include:

=== Mathematical functions ===

||'''Name'''    ||'''Meaning'''                   ||'''Notes'''||
||`abs(x)`      ||absolute value                  ||           ||
||`ceil(x)`     ||round toward positive infinity  ||           ||
||`exp(x)`      ||exponentiation                  ||           ||
||`factorial(x)`||factorial                       ||           ||
||`fix(x)`      ||round toward 0                  ||           ||
||`floor(x)`    ||round toward negative infinity  ||           ||
||`log(x)`      ||natural logarithm               ||           ||
||`log10(x)`    ||base-10 logarithm               ||           ||
||`max(x)`      ||maximum                         ||optionally return index of maximum as well: `[m,i]=max(x)`||
||`min(x)`      ||minimum                         ||optionally return index of minimum as well: `[m,i]=min(x)`||
||`mod(x,d)`    ||modulo of ''x'' divided by ''d''||           ||
||`nthroot(x,n)`||''n''th root of ''x''           ||           ||
||`round(x)`    ||round to integer                ||           ||
||`sqrt(x)`     ||square root                     ||           ||

=== Trig functions ===

||'''Name''' ||'''Meaning'''               ||
||`sin`      ||sine                        ||
||`cos`      ||cosine                      ||
||`tan`      ||tangent                     ||
||`cot`      ||cotangent                   ||
||`sec`      ||secant                      ||
||`csc`      ||cosecant                    ||
||`asin`     ||inverse sine                ||
||`acos`     ||inverse cosine              ||
||`atan`     ||inverse tangent             ||
||`acot`     ||inverse cotangent           ||
||`asec`     ||inverse secant              ||
||`acsc`     ||inverse cosecant            ||
||`sinh`     ||hyperbolic sine             ||
||`cosh`     ||hyperbolic cosine           ||
||`tanh`     ||hyperbolic tangent          ||
||`coth`     ||hyperbolic cotangent        ||
||`sech`     ||hyperbolic secant           ||
||`csch`     ||hyperbolic cosecant         ||
||`asinh`    ||inverse hyperbolic sine     ||
||`acosh`    ||inverse hyperbolic cosine   ||
||`atanh`    ||inverse hyperbolic tangent  ||
||`acoth`    ||inverse hyperbolic cotangent||
||`asech`    ||inverse hyperbolic secant   ||
||`acsch`    ||inverse hyperbolic cosecant ||

=== Type-checking functions ===

||'''Name'''    ||'''Meaning'''                   ||
||`allfinite(x)`||are all elements finite         ||
||`anynan(x)`   ||are any elements NaN            ||
||`isfloat(x)`  ||is a floating-point array       ||
||`isinteger(x)`||is an integer array             ||
||`isnumeric(x)`||is a numeric array              ||
||`isreal(x)`   ||uses complex storage            ||

=== Array functions ===

||'''Name'''       ||'''Meaning'''                                                             ||
||`linspace(a,b,n)`||row vector of `n` evenly-spaced elements starting at `a` and ending in `b`||

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== String Functions ==

These functions operate on a [[MATLAB/DataTypes#String|string array]] and return a string scalar:

||'''Name''' ||'''Meaning'''                                             ||
||`join(s)`  ||join the elements of string matrix `s`                    ||
||`join(s,d)`||join the elements of string matrix `s` using delimiter `d`||

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== Matrix Functions ==

These functions create a matrix from other types:

||'''Name'''  ||'''Meaning'''                     ||
||`diag(v)`   ||diagonal matrix from vector `v`   ||
||`eye(n)`    ||''n x n'' identity matrix         ||
||`ones(n)`   ||''n x n'' matrix of 1s            ||
||`ones(r,c)` ||''r x c'' matrix of 1s            ||
||`rand(n)`   ||''n x n'' matrix of random numbers||
||`rand(r,c)` ||''r x c'' matrix of random numbers||
||`zeros(n)`  ||''n x n'' matrix of 0s            ||
||`zeros(r,c)`||''r x c'' matrix of 0s            ||

These functions operate on a matrix and return other types:

||'''Name''' ||'''Meaning'''                  ||
||`det(m)`   ||determinant                    ||
||`diag(m)`  ||diagonal vector from matrix `m`||
||`eig(m)`   ||vector of eigenvalues          ||
||`size(m)`  ||array of dimensions            ||

These functions transform a matrix:

||'''Name'''    ||'''Meaning'''||
||`inv(m)`      ||invert       ||
||`transpose(m)`||transpose    ||

To demonstrate how the `size` function can be used:

{{{
>> A = [12 62 93 -8];
>> sz = size(A)

sz = 1×2

     1     4
>> B = zeros(size(A))

B = 1x4

       0    0    0    0
}}}

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== Vector Functions ==

These functions operate on matrices that are specifically of sizes ''1 x n'' or ''n x 1''. MATLAB generally can work with either row or column vectors.

||'''Name'''  ||'''Meaning'''                  ||
||`cross(a,b)`||Cross product                  ||
||`dot(a,b)`  ||Dot product                    ||




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