Functions

Functions

The following functions are available. Most functions can be applied element-wise to matrices. Check each function for details on accepted arguments. Functions will turn maroon in the formula bar.

Function	Name	Description	Arguments	Accepts Matrix
abs	Absolute Value	abs(x): Returns the absolute value of x	Real number	Yes
acos	Arccosine	acos(x): Returns the arccosine of x	Real number in [-1,1]	Yes
asin	Arcsine	asin(x): Returns the arcsine of x	Real number in [-1,1]	Yes
atan	Arctangent	atan(x): Returns the arctangent of x	Real number	Yes
bound	Bounded Value	bound(x,a,b): Bounds x to be in [a,b]	x: Real number a: Lower bound (inclusive), real number b: Upper bound (inclusive), real number	Yes
cbrt	Cube Root	cbrt(x): Returns the cube root of x	Real number	Yes
ceil	Ceiling	ceil(x): Returns the nearest integer above x	Real number	Yes
choose	Binomial Coefficient	choose(n,k): Returns the Binomial Coefficient	n: Integer k: Integer	No
cos	Cosine	cos(x): Returns the cosine of x	Real number	Yes
cosh	Hyperbolic Cosine	cosh(x): Returns the hyperbolic cosine of x	Real number	Yes
erf	Error Function	erf(x): Returns the error function evaluated at x	Real number	Yes
exp	Exponential Function	exp(x): Returns Euler's number e raised to the power of x	Real number	Yes
fact	Factorial	fact(n): Returns n! (the factorial of n)	Integer ≥0	No
floor	Floor	floor(x): Returns the nearest integer below x	Real number	Yes
gamma	Gamma Function	gamma(x): Returns the gamma function evaluated at x	Real number >0	Yes
hypot	Hypotenuse	hypot(x,y): Returns sqrt(x^2+y^2) without intermediate overflow or underflow	x: Real number y: Real number	No
if	If Function	if(<expr>,a,b): Returns a if the expression is true and b if it is false	<expr>: Boolean expression to evaluate a: Object returned if true b: Object returned if false	Yes
invErf	Inverse Error Function	invErf(x): Returns the inverse error function evaluated at x	Real number in [-1,1]	Yes
log	Natural Log	log(x): Returns the natural logarithm (base e) of x	Real number >0	Yes
logb	Base-b Log	logb(x,b): Returns the base-b logarithm of x	x: Real number >0 b: Real number >0	Yes
logGamma	Log-Gamma Function	logGamma(x): Returns the log-Gamma function evaluated at x	Real number >0	Yes
log10	Base-10 Log	log10(x): Returns the base-10 logarithm of x	Real number >0	Yes
logit	Logit Function	logit(p): Returns the log odds of probability p	p: Probability in [0,1]	Yes
logistic	Logistic Function	logistic(x): Returns the standard logistic transformation: 1/(1+exp(-x))	x: Real number	Yes
max	Maximum	max(a,b): Returns the maximum of a and b	a: Real number b: Real number	No
min	Minimum	min(a,b): Returns the minimum of a and b	a: Real number b: Real number	No
probRescale	Probability Rescale	probRescale(p,t1,t2): Rescales a probability p from time interval t1 to a new time interval t2	p: Probability in [0,1] t1: Original time interval >0 t2: New time interval >0	Yes
probToRate	Probability to Rate	probToRate(p): Converts a probability p to a rate for a fixed time interval probToRate(p,t1,t2): Converts a probability p per time interval t1 to a rate per time interval t2	p: Probability in [0,1] t1: Probability time interval >0 (optional) t2: Rate time interval >0 (optional)	Yes
rateToProb	Rate to Probability	rateToProb(r): Converts a rate r to a probability for a fixed time interval rateToProb(r,t1,t2): Converts a rate r per time interval t1 to a probability per time interval t2	r: Rate ≥0 t1: Rate time interval >0 (optional) t2: Probability time interval >0 (optional)	Yes
round	Round	round(x): Rounds x to the nearest integer round(x,n): Rounds x to n decimal places	x: Real number n: Number of digits (Integer ≥0) (optional)	Yes
sin	Sine	sin(x): Returns the sine of x	Real number	Yes
sinh	Hyperbolic Sine	sinh(x): Returns the hyperbolic sine of x	Real number	Yes
sqrt	Square Root	sqrt(x): Returns the square root of x	Real number ≥0	Yes
tan	Tangent	tan(x): Returns the tangent of x	Real number	Yes
tanh	Hyperbolic Tangent	tanh(x): Returns the hyperbolic tangent of x	Real number	Yes
signum	Signum Function	signum(x): Returns the sign of x (returns -1 or 1)	Real number	Yes

The following summary functions are also available.

Function	Name	Description	Arguments	Accepts Matrix
mean	Mean	mean(x_1, x_2, ..., x_n): Returns the mean of all arguments	x_1 to x_n: Real numbers	Yes
product	Product	product(x_1, x_2, ..., x_n): Returns the product of all arguments	x_1 to x_n: Real numbers	Yes
quantile	Quantile	quantile,(q, x_1, x_2, ..., x_n): Returns the quantile q of all arguments	q: Quantile to evaluate. Real number (or row vector of real numbers) in [0,1] x_1 to x_n: Real numbers	Yes
sd	Standard Deviation	sd(x_1, x_2, ..., x_n): Returns the standard deviation of all arguments	x_1 to x_n: Real numbers	Yes
sum	Sum	sum(x_1, x_2, ..., x_n): Returns the sum of all arguments	x_1 to x_n: Real numbers	Yes
var	Variance	var(x_1, x_2, ..., x_n): Returns the variance of all arguments	x_1 to x_n: Real numbers	Yes