scopman3

SCoP Language Summary

A text-based language to define a simulation model

General Modeling Functions

hyperbol(x, max, K) – compute an hyperbolic function
: This function computes the value of an hyperbolic function, given the values of two constant parameters.
Inputs:
$x$
the independent variable (a double-precision floating point value)
$max$
the maximum value of the hyperbolic function (a double-precision floating point value)
$K$
the value of $x$ for which the function value is $max/2$ (a double-precision floating point value)
Return Value:
• hyperbol() returns the value of the hyperbolic function (a double-precision floating point value).

revhyperbol(x, max, K) – compute a reverse hyperbolic function
: This function computes the value of a reverse hyperbolic function, given the values of two constant parameters.
Inputs:
$x$
the independent variable (a double-precision floating point value)
$max$
the maximum value of the hyperbolic function (a double-precision floating point value)
$K$
the value of $x$ for which the function value is $max/2$ (a double-precision floating point value)
Return Value:
• revhyperbol() returns the value of the reverse hyperbolic function (a double-precision floating point value).

sigmoid(x, max, K, n) – compute a sigmoidal function
: This function computes the value of a sigmoidal function of one variable, given the values of three constants in the function.
Inputs:
$x$
the independent variable (a double-precision floating point value)
$max$
the maximum value of the sigmoidal function (a double-precision floating point value)
$K$
the value of $x$ for which the function value is $max/2$ (a double-precision floating point value)
$n$
parameter controlling the steepness of the sigmoid curve (a double-precision floating point value); it is the power to which $x$ and $K$ are raised
Return Value:
• sigmoid() returns the value of the sigmoidal function (a double-precision floating point value).

revsigmoid(x, max, K, n) – compute a reverse sigmoidal function
: This function computes the value of a reverse sigmoidal function of one variable, given the values of three constants in the function.
Inputs:
$x$
the independent variable (a double-precision floating point value)
$max$
the maximum value of the sigmoidal function (a double-precision floating point value)
$K$
the value of $x$ for which the function value is $max/2$ (a double-precision floating point value)
$n$
parameter controlling the steepness of the sigmoid curve (a double-precision floating point value); it is the power to which $x$ and $K$ are raised
Return Value:
• revsigmoid() returns the value of the reverse sigmoidal function (a double-precision floating point value).

lag(var, curt, lagt, vsize) – generalized lag function
: This function provides a generalized lag facility for the SCoP modeler, but use of it requires more than a passing knowledge of C language syntax (this `limitation’ will be addressed in a future version of SCoP). The lag() function has two independent variables, $var$ and $curt$, where $curt$ is the current value of the monotonically increasing independent variable of the model (usually time) and $var$ is a pointer to an independent variable whose value at $curt\; –\; lagt$ is desired. lag() is currently able to handle up to 50 lagged model variables.
Inputs:
$var$
pointer to the independent variable whose value at $curt\; –\; lagt$ is desired (a pointer to a double-precision floating point value)
$curt$
current value of the monotonically increasing independent variable of the model [usually time] (a double-precision floating point value)
$lagt$
difference between $curt$ and the previous value of $curt$ for which we desire the value of $var$ (a double-precision floating point value)
$vsize$
the dimension of $var$ if $var$ is a vector; otherwise $\le 1$ (an integer value)
Return Value:
• lag() returns a pointer to the double-precision floating point value of the variable $var$ at $curt-lagt$ if $curt\; \ge lagt$, or the NULL pointer if .

Forcing Functions

threshold(x, limit, mode) – threshold function
: This function provides a switch between active and inactive state, based on a threshold value.
Inputs:
$x$
the variable to be tested (a double-precision floating point value)
$limit$
the threshold switch point (a double-precision floating point value)
$mode$
a string containing either "min" or "max", indicating whether $limit$ is to be treated as a minimum or a maximum value for switching to the active state
Return Value:
The return from threshold() is an integer value. If $mode$ is "min", threshold() returns 0 (inactive state) if , and returns 1 (active state) if $x\; \ge limit$. If $mode$ is "max", threshold() returns 0 (inactive state) if $x\; >\; limit$, and returns 1 (active state) if $x\; \le limit$. threshold() returns -1 if there is an error in its arguments.

harmonic(t, period, amplitude, phase) – harmonic function
: This function generates a sine wave of specified period, amplitude, and phase.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$period$
the length of each cycle (a double-precision floating point value)
$amplitude$
the positive amplitude of the waveform (a double-precision floating point value)
$phase$
the phase shift of the waveform, in periods (a period is 360 degrees or $2\pi$ radians; a double-precision floating point value)
Return Value:
• harmonic() returns the value of the harmonic function (a double-precision floating point value).

squarewave(t, period, amplitude) – square wave function
: This function generates a square wave of specified period and amplitude.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$period$
the length of each cycle, including positive and negative phases (a double-precision floating point value)
$amplitude$
the positive amplitude of the waveform (a double-precision floating point value)
Return Value:
• squarewave() returns the value of the squarewave function (a double-precision floating point value), which is positive $amplitude$ for the first half of the cycle and negative $amplitude$ for the second half of the cycle.

sawtooth(t, period, amplitude) – sawtooth function
: This function generates a sawtooth wave (periodic ramp) of specified period and amplitude.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$period$
the duration of the ramp incline for each cycle (a double-precision floating point value)
$amplitude$
the ramp height for each cycle (a double-precision floating point value)
Return Value:
• sawtooth() returns the value of the sawtooth function (a double-precision floating point value).

revsawtooth(t, period, amplitude) – revsawtooth function
: This function generates a reverse sawtooth wave (periodic declining ramp) of specified period and amplitude.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$period$
the duration of the ramp decline for each cycle (a double-precision floating point value)
$amplitude$
the ramp height for each cycle (a double-precision floating point value)
Return Value:
• revsawtooth() returns the value of the reverse sawtooth function (a double-precision floating point value).

ramp(t, lag, height, duration) – ramp function
: This function generates a ramp function of specified height and duration.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$lag$
value of $t$ at which ramp begins (a double-precision floating point value)
$height$
the ramp height (a double-precision floating point value)
$duration$
the duration of the ramp incline (a double-precision floating point value)
Return Value:
• ramp() returns the value of the ramp function (a double-precision floating point value).

pulse(t, lag, height, duration) – pulse function
: This function generates a single pulse of specified height and duration.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$lag$
the value of $t$ at which pulse begins (a double-precision floating point value)
$height$
the pulse height (a double-precision floating point value)
$duration$
the duration of the pulse (a double-precision floating point value)
Return Value:
• pulse() returns $height$ during the pulse interval and zero otherwise (a double-precision floating point value).

perpulse(t, lag, height, duration, delay) – periodic pulse function
: This function generates periodic pulses of specified height, duration, and delay between pulses.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$lag$
the value of $t$ at which first pulse begins (a double-precision floating point value)
$height$
the pulse height (a double-precision floating point value)
$duration$
the duration of the pulse (a double-precision floating point value)
$delay$
the delay between pulses (a double-precision floating point value)
Return Value:
• perpulse() returns $height$ during the pulse interval and zero otherwise (a double-precision floating point value).

step(t, jumpt, jump) – step function
: This function generates a single jump of specified height in a constant function.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$jumpt$
the value of $t$ at which the step occurs (a double-precision floating point value)
$jump$
the step height (a double-precision floating point value)
Return Value:
• step() returns zero before the step is taken () and it returns $jump$ after the step is taken ($t\; \ge jumpt$). The return from step() is a double-precision floating point value.

perstep(t, lag, period, jump) – periodic step function
: This function generates periodic jumps of specified height and duration in a constant function.
Inputs:
$t$
the independent variable [usually time] (a double-precision floating point value)
$lag$
the value of $t$ at which stepping starts (a double-precision floating point value)
$period$
the duration of each step (a double-precision floating point value)
$jump$
the step height (a double-precision floating point value)
Return Value:
• perstep() returns zero before the first step is taken () and thereafter it returns the cumulative sum of the heights of the steps already taken. The return from perstep() is a double-precision floating point value.

Probability Functions

erf(z) – normalized error function
: This function computes the normalized error function.
$erf(z)\; =\; \{2\pi \}\; \int$₀^z exp(-t²)&sp; dt
Inputs:
$z$
the value of an independent variable (a double-precision floating point value)
Return Value:
• erf() returns the value of the normalized error function. This will lie in the interval between -1.0 and 1.0 and is a double-precision floating point value.

exprand() – random number from exponential distribution
: This function computes a random sample from the exponential distribution.
Return Value:
• exprand() returns a random number from the exponential distribution (a double-precision floating point value).

factorial(n) – factorial function
: This function computes the factorial of an integer argument.
Inputs:
$n$
the number whose factorial is desired (an integer value)
Return Value:
• factorial() returns the value of the factorial ($n!$) (a double-precision floating point value).

gauss(x, mean, std_dev) – Gaussian probability density function
: This function computes the value of a Gaussian probability density function at a particular $x$ value, given the $mean$ and standard deviation ($std\_dev$).
Inputs:
$x$
the value of an independent variable (a double-precision floating point value)
$mean$
the mean of the Gaussian distribution (a double-precision floating point value)
$std\_dev$
the standard deviation of the distribution (a double-precision floating point value)
Return Value:
• gauss() returns the value of the probability (a double-precision floating point value).

normrand(mean, std_dev) – random number from normal distribution
: This function selects a random number from the normal distribution with the specified $mean$ and standard deviation ($std\_dev$).
Inputs:
$mean$
the mean of the distribution (a double-precision floating point value)
$std\_dev$
the standard deviation of the distribution (a double-precision floating point value)
Return Value:
• normrand() returns a random number from the normal distribution (a double-precision floating point value).

poisrand(mean) – random number from Poisson distribution
: This function computes a random number from the Poisson distribution with the specified $mean$.
Inputs:
$mean$
the mean of the distribution (a double-precision floating point value)
Return Value:
• poisrand() returns an integer from the Poisson distribution (an integer value).

poisson(x, mean) – Poisson probability density function
: This function computes the value of a Poisson probability density function at a particular $x$ value, given the $mean$. Inputs:
$x$
the value of an independent variable (an integer value)
$mean$
the mean of the Poisson distribution (a double-precision floating point value)
Return Value:
• poisson() returns the value of the probability (a double-precision floating point value).

scop_random() – random number generator
: This function selects a random number from the uniform distribution on the interval between 0 and 1. A seed can be specified for the function (see set_seed() below); otherwise a seed of 1 will be used.
Return Value:
• scop_random() returns the random number (a double-precision floating point value). Note: this function is used by the other distribution generators such as poisrand.

set_seed(n) – seed the random number function (random())
: This function sets the seed of the SCoP Library random number generator (see scop_random() above).
Inputs:
$n$
the value of the seed (an integer value)
Return Value: None

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