{"Function":"gamma(x)","Description":"The Gamma function","Aliases":"gammafn"}
{"Function":"lgamma(x)","Description":"Natural logarithm of absolute value of gamma function","Aliases":"digamma"}
{"Function":"digamma(x)","Description":"First derivative of lgamma","Aliases":""}
{"Function":"trigamma(x)","Description":"Second derivative of lgamma","Aliases":""}
{"Function":"tetragamma(x)","Description":"Third derivative of lgamma","Aliases":""}
{"Function":"pentagamma(x)","Description":"Fourth derivative of lgamma","Aliases":""}
{"Function":"psigamma(x, deriv)","Description":"n-th derivative of Psi, the digamma function, which is the derivative of lgammafn. In other words, digamma(x) is the same as psigamma(x,0), trigamma(x) == psigamma(x,1), etc. ","Aliases":""}
{"Function":"cospi(x)","Description":"cos(pi*x)","Aliases":""}
{"Function":"sinpi(x)","Description":"sin(pi*x)","Aliases":""}
{"Function":"tanpi(x)","Description":"tan(pi*x)","Aliases":""}
{"Function":"beta(a, b)","Description":"Beta function","Aliases":""}
{"Function":"lbeta(a, b)","Description":"log Beta function","Aliases":""}
{"Function":"bessel_i(x, nu, expo)","Description":"Bessel function type I with index nu","Aliases":" expo==1 is unscaled expo==2 is scaled by exp(-x)"}
{"Function":"bessel_j(x, nu)","Description":"Bessel function type J with index nu","Aliases":""}
{"Function":"bessel_k(x, ku, expo)","Description":"Bessel function type K with index nu","Aliases":" expo==1 is unscaled expo==2 is scaled by exp(x)"}
{"Function":"bessel_y(x, nu)","Description":"Bessel function type Y with index nu","Aliases":""}
{"Function":"R_pow(x, y)","Description":"x^y","Aliases":""}
{"Function":"R_pow_di(x, I)","Description":"x^y","Aliases":" y is an integer"}
{"Function":"log1pmx","Description":"log(1+x) - x ","Aliases":""}
{"Function":"log1pexp","Description":"log(1+exp(x))","Aliases":""}
{"Function":"expm1(x)","Description":"exp(x)-1","Aliases":""}
{"Function":"lgamma1p(x)","Description":"log(gamma(x+1))","Aliases":""}
{"Function":"sign(x)","Description":"Compute the signum function where sign(x) is 1, 0 -1","Aliases":""}
{"Function":"fsign(x, y)","Description":"abs(x)*sign(y)","Aliases":""}
{"Function":"fprec(x, digits)","Description":"x rounded to digits (after the decimal point, used by signif()","Aliases":""}
{"Function":"fround(x, digits)","Description":"Round, used by R's round()","Aliases":""}
{"Function":"ftrunc(x)","Description":"Truncated towards zero","Aliases":""}
{"Function":"abs(x)","Description":"absolute value of x","Aliases":"fabs"}
{"Function":"sin(x)","Description":"sine of x","Aliases":""}
{"Function":"cos(x)","Description":"cos of x","Aliases":""}
{"Function":"tan(x)","Description":"tan of x","Aliases":""}
{"Function":"factorial(x)","Description":"factorial of x","Aliases":""}
{"Function":"lfactorial(x)","Description":"log(factorial(x))","Aliases":""}
{"Function":"log10(x)","Description":"log base 10","Aliases":""}
{"Function":"log2(x)","Description":"log base 2","Aliases":""}
{"Function":"pnorm(x)","Description":"Normal CDF of x","Aliases":"normcdf, phi"}
{"Function":"qnorm(x)","Description":"Normal pdf of x","Aliases":"norminv"}
{"Function":"probit(x, low=0, hi=1)","Description":"Probit (normal pdf) of x transforming into a range","Aliases":""}
{"Function":"probitInv(q, low=0, hi=1)","Description":"Inverse probit of x transforming into a range","Aliases":""}
{"Function":"acos(x)","Description":"Inverse cosine","Aliases":""}
{"Function":"asin(x)","Description":"Inverse sine","Aliases":""}
{"Function":"atan(x)","Description":"Inverse tangent","Aliases":""}
{"Function":"atan2(a, b)","Description":"Four quadrant inverse tangent","Aliases":""}
{"Function":"sinh(x)","Description":"Hyperbolic sine","Aliases":""}
{"Function":"cosh(x)","Description":"Hyperbolic cosine","Aliases":""}
{"Function":"tanh(x)","Description":"Hyperbolic tangent","Aliases":""}
{"Function":"floor(x)","Description":"Downward rounding","Aliases":""}
{"Function":"ceil(x)","Description":"Upward rounding","Aliases":""}
{"Function":"logit(x, low=0, hi=1)","Description":"Logit transformation of x transforming into a range","Aliases":""}
{"Function":"expit(x, low=0, hi=1)","Description":"expit transofmration in range","Aliases":"invLogit, logitInv"}
{"Function":"gammaq(a, z)","Description":"Normalized incomplete gamma from boost","Aliases":""}
{"Function":"gammaqInv(a, q)","Description":"Normalized incomplete gamma inverse from boost","Aliases":""}
{"Function":"ifelse(cond, trueValue, falseValue)","Description":"if else function","Aliases":""}
{"Function":"gammap(a, z)","Description":"Normalized lower incomplete gamma from boost","Aliases":""}
{"Function":"gammapInv(a, p)","Description":"Inverse of Normalized lower incomplete gamma from boost","Aliases":""}
{"Function":"gammapInva(x, p)","Description":"Inverse of Normalized lower incomplete gamma from boost","Aliases":""}
{"Function":"rxnorm(x)","Description":"Generate one deviate of from a normal distribution for each observation scale","Aliases":""}
{"Function":"rxnormV(x)","Description":"Generate one deviate from low discrepancy normal for each observation","Aliases":""}
{"Function":"rxcauchy","Description":"Generate one deviate from the cauchy distribution for each observation","Aliases":""}
{"Function":"rxchisq","Description":"Generate one deviate from the chisq distribution for each observation","Aliases":""}
{"Function":"rxexp","Description":"Generate one deviate from the exponential distribution for each observation","Aliases":""}
{"Function":"rxf","Description":"Generate one deviate from low discrepancy normal for each observation","Aliases":""}
{"Function":"rxgamma","Description":"Generate one deviate from the gamma distribution for each observation","Aliases":""}
{"Function":"rxbeta","Description":"Generate one deviate from the beta distribution for each observation","Aliases":""}
{"Function":"rxgeom","Description":"Generate one deviate from the geometric distribution for each observation","Aliases":""}
{"Function":"rxpois","Description":"Generate one deviate from the poission distribution for each observation","Aliases":""}
{"Function":"rxt","Description":"Generate one deviate from the t distribtuion for each observation","Aliases":""}
{"Function":"tad() or tad(x)","Description":"Time after dose (tad()) or time after dose for a compartment tad(cmt); no dose=NA","Aliases":""}
{"Function":"tad0() or tad0(x)","Description":"Time after dose (tad0()) or time after dose for a compartment tad0(cmt); no dose=0","Aliases":""}
{"Function":"tafd() or tafd(x)","Description":"Time after first dose (tafd()) or time after first dose for a compartment tafd(cmt); no dose=NA","Aliases":""}
{"Function":"tafd0() or tafd0(x)","Description":"Time after first dose (tafd()) or time after first dose for a compartment tafd(cmt); no dose=NA","Aliases":""}
{"Function":"dosenum()","Description":"Dose Number","Aliases":""}
{"Function":"tlast() or tlast(cmt)","Description":"Time of Last dose;  This takes into consideration any lag time, so if there is a dose at time 3 and a lag of 1, the time of last dose would be 4.  tlast(cmt) calculates the time since last dose of a compartment; no dose=NA","Aliases":""}
{"Function":"tlast0() or tlast0(cmt)","Description":"Time of Last dose;  This takes into consideration any lag time, so if there is a dose at time 3 and a lag of 1, the time of last dose would be 4.  tlast(cmt) calculates the time since last dose of a compartment; no dose=0","Aliases":""}
{"Function":"tfirst() or tfirst(cmt)","Description":"Time since first dose or time since first dose of a compartment; no dose=NA","Aliases":""}
{"Function":"tfirst0() or tfirst0(cmt)","Description":"Time since first dose or time since first dose of a compartment; no dose=0","Aliases":""}
{"Function":"prod(...)","Description":"product of terms;  This uses PreciseSums so the product will not have as much floating point errors (though it will take longer)","Aliases":""}
{"Function":"sum(...)","Description":"sum of terms;  This uses PreciseSums so the product will not have as much floating point errors (though it will take longer)","Aliases":""}
{"Function":"max(...)","Description":"maximum of a group of numbers","Aliases":""}
{"Function":"min(...)","Description":"Min of a group of numbers","Aliases":""}
{"Function":"lag(parameter, number=1)","Description":"Get the lag of an input parameter; You can specify a number of lagged observations","Aliases":""}
{"Function":"lead(parameter, number=2)","Description":"Get the lead of an input parameter; You can specify a number of lead observation","Aliases":""}
{"Function":"diff(par, number=1)","Description":"Get the difference between the current parameter and the last parameter; Can change the parameter number","Aliases":""}
{"Function":"first(par)","Description":"Get the first value of an input parameter","Aliases":""}
{"Function":"last(par)","Description":"Get the last value of an input parameter","Aliases":""}
{"Function":"transit()","Description":"The transit compartment psuedo function","Aliases":""}
{"Function":"is.na()","Description":"Determine if a value is NA","Aliases":""}
{"Function":"is.nan()","Description":"Determine if a value is NaN","Aliases":""}
{"Function":"is.infinite()","Description":"Check to see if the value is infinite","Aliases":""}
{"Function":"rinorm(x)","Description":"Generate one deviate of from a normal distribution for each individual","Aliases":""}
{"Function":"rinormV(x)","Description":"Generate one deviate from low discrepancy normal for each individual","Aliases":""}
{"Function":"ricauchy","Description":"Generate one deviate from the cauchy distribution for each individual","Aliases":""}
{"Function":"richisq","Description":"Generate one deviate from the chisq distribution for each individual","Aliases":""}
{"Function":"riexp","Description":"Generate one deviate from the exponential distribution for each individual","Aliases":""}
{"Function":"rif","Description":"Generate one deviate from low discrepancy normal for each individual","Aliases":""}
{"Function":"rigamma","Description":"Generate one deviate from the gamma distribution for each individual","Aliases":""}
{"Function":"ribeta","Description":"Generate one deviate from the beta distribution for each individual","Aliases":""}
{"Function":"rigeom","Description":"Generate one deviate from the geometric distribution for each individual","Aliases":""}
{"Function":"ropois","Description":"Generate one deviate from the poission distribution for each individual","Aliases":""}
{"Function":"rit","Description":"Generate one deviate from the t distribtuion for each individual","Aliases":""}
{"Function":"simeps","Description":"Simulate EPS from possibly truncated sigma matrix.  Will take sigma matrix from the current study. Simulated at the very last moment.","Aliases":""}
{"Function":"simeta","Description":"Simulate ETA from possibly truncated omega matrix.  Will take the omega matrix from the current study. Simulated at the initilization of the ODE system or the intialization of lhs","Aliases":""}