Contents
- Index
Resident functions and variables in MODELS
1. Resident functions
This example illustrates all built-in functions in MODELS
MODEL numfun
VAR a1, a2
EXEC
IF t=timestep THEN -- letting contents execute only at the first time step
write("*** Begin results of model 'numfun' ***")
a1:=1; a2:=-2
write('abs(2) =2 :', abs(a2))
write('sqrt(2) =1.414... :', sqrt(2*a1))
write('exp(1) =e :', exp(1))
write('ln(e) =1 :', ln(exp(1)))
write('log10(100) =2 :', log10(100))
write('log2(4) =2 :', log2(4))
write('recip(-2) =-0.5 :', recip(a2))
write('factorial(5) =120 :', factorial(5))
write('trunc(5.5) =5 :', trunc(5.5))
write('fract(5.5) =0.5 :', fract(5.5))
write('round(5.5) =6 :', round(5.5))
write('sign(-1) =-1 :', sign(a2+3-2))
write('rad(90) =pi/2 :', rad(90))
write('deg(pi) =180 :', deg(pi))
write('random :', random())
write('sin(pi/2) =1 :', sin(rad(90)))
write('cos(-pi/4) =0.707... :', cos(-pi/4))
write('tan(pi/4) =1 :', tan(pi/4))
write('asin(sin(pi/2)) =pi/2 :', asin(sin(pi/2)))
write('acos(cos(pi/2)) =pi/2 :', acos(cos(pi/2)))
write('atan(0.5) =0.4636...:', atan(0.5))
write('sinh(pi/2) =2.3012...:', sinh(pi/2))
write('cosh(pi/2) =2.5091...:', cosh(pi/2))
write('tanh(pi/2) =0.9171...:', tanh(pi/2))
--write(' :', asinh(xpr1))
--write(' :', acosh(xpr1))
--write(' :', atanh(xpr1))
write('atan2(-1,1) =-pi/4 :', atan2(-1,1))
write('binom(5,3) =10 :', binom(5,3))
write('permut(5,3) =60 :', permut(5,3))
write('min(1,-2,-2,-8) =-8 :', min(a1,a2,a2,-8))
write('max(9,8,7) =9 :', max(9,8,7))
write('norm(2,2,sqrt(8))=4 :', norm(2,-2,sqrt(8)))
write('bool(-4) =0 :', bool(-4))
write('1 :', and(1,1,1))
write('0 :', and(-1,1,1))
write('0 :', and(1,-2,1))
write('0 :', and(1,1,-3))
write('0 :', and(-4,-5,1))
write('0 :', and(-4,1,-3))
write('0 :', and(1,-2,-1))
write('0 :', and(0,0,0))
write('1 :', or(1,1,1))
write('1 :', or(-1,1,1))
write('1 :', or(1,-2,1))
write('1 :', or(1,1,-3))
write('1 :', or(-4,-5,1))
write('1 :', or(-4,1,-3))
write('1 :', or(1,-2,-1))
write('0 :', or(0,0,0))
write('0 :', nand(1,1,1))
write('1 :', nand(-1,1,1))
write('1 :', nand(1,-2,1))
write('1 :', nand(1,1,-3))
write('1 :', nand(-4,-5,1))
write('1 :', nand(-4,1,-3))
write('1 :', nand(1,-2,-1))
write('1 :', nand(0,0,0))
write('0 :', nor(1,1,1))
write('0 :', nor(-1,1,1))
write('0 :', nor(1,-2,1))
write('0 :', nor(1,1,-3))
write('0 :', nor(-4,-5,1))
write('0 :', nor(-4,1,-3))
write('0 :', nor(1,-2,-1))
write('1 :', nor(0,0,0))
write('0 :', xor(1,1,1))
write('0 :', xor(-1,1,1))
write('0 :', xor(1,-2,1))
write('0 :', xor(1,1,-3))
write('1 :', xor(-4,-5,1))
write('1 :', xor(-4,1,-3))
write('1 :', xor(1,-2,-1))
write('0 :', xor(0,0,0))
write("*** End results of model 'numfun' ***")
ENDIF
ENDEXEC
ENDMODEL
2. Resident time variables
This example illustrates the value of the simulation variables in MODELS.
MODEL simvar
VAR x -- a model expects at least one variable
EXEC
write(' ')
write("*** In model 'simvar' at t=", t, " ***")
write("'prevtime'= time of previous execution of this model : ", prevtime)
write("'simtime' = present time inside this model : ", simtime)
write("'endtime' = present time outside this model : ", endtime)
write("'fullstep'= interval since last call to this model : ", fullstep)
write("'timestep'= present size of time step in this model : ", timestep)
write("'minstep' = limit on minimum size of time step : ", minstep)
write("'maxstep' = limit on maximum size of time step : ", maxstep)
write("'starttime'= time of beginning of simulation : ", starttime)
write("'stoptime' = time of end of simulation : ", stoptime)
write("'startstep'= outermost time step of simulation : ", startstep)
ENDEXEC
ENDMODEL
2. Resident time functions
The last example illustrates the time-dependent functions in MODELS.
MODEL simul_functions
VAR y, y1, y2, y3, y4, y5, t1, t2, t3, t4, t5
y11, y22, y33, y55, t11, t22, t33, t55
HISTORY y {dflt:t*t +10*t +16} -- default history of y
EXEC
y:=t*t +10*t +16
IF t=timestep THEN
t1:=t-timestep/2
t2:=t1-timestep
t3:=t2-timestep
t4:=t3-timestep
t5:=t1+timestep
t11:=prevtime
t22:=t11-timestep
t33:=t22-timestep
t55:=t+timestep
y4:=histval(y, t4) -- always uses history function
y3:=histval(y, t3)
y2:=histval(y, t2)
y1:=histval(y, t1)
y5:=histval(y, t5)
y11:=prevval(y)
y22:=histval(y, t22)
y33:=histval(y, t33)
y55:=histval(y, t55)
write("*** In model simul_functions at t= ", t, ' ***')
write(" ")
write("y(t) = t*t +10*t +16")
write(" y(", t4, ")=", y4)
write(" y(", t33, " )=", y33)
write(" y(", t3, ")=", y3)
write(" y(", t22, " )=", y22)
write(" y(", t2, ")=", y2)
write(" y(", t11, " )=", y11)
write(" y(", t1, ")=", y1)
write(" y(", t , " )=", y)
write(" y(", t5, ")=", y5)
write(" y(", t55, " )=", y55)
write(" ")
write("backval(y, ", t4, ", 0) : ", backval(y, t4, 0)) -- no interpol.
write("backval(y, ", t3, ", 0) : ", backval(y, t3, 0)) -- no interpol.
write("backval(y, ", t22, ", 0) : ", backval(y, t22, 0)) -- no interpol.
write("backval(y, ", t2, ", 0) : ", backval(y, t2, 0)) -- no interpol.
write("backval(y, ", t11, ", 0) : ", backval(y, t11, 0)) -- no interpol.
write("backval(y, ", t1, ", 0) : ", backval(y, t1, 0)) -- no interpol.
write("backval(y, ", t, ", 0) : ", backval(y, t , 0)) -- no interpol.
write("backval(y, ", t5, ", 0) : ", backval(y, t5, 0)) -- no interpol.
write(" ")
write("backval(y, ", t4, ") : ", backval(y, t4 )) -- linear " "
write("backval(y, ", t3, ") : ", backval(y, t3 )) -- linear " "
write("backval(y, ", t22, ") : ", backval(y, t22)) -- linear " "
write("backval(y, ", t2, ") : ", backval(y, t2 )) -- linear " "
write("backval(y, ", t11, ") : ", backval(y, t11)) -- linear " "
write("backval(y, ", t1, ") : ", backval(y, t1 )) -- linear " "
write("backval(y, ", t , ") : ", backval(y, t )) -- linear " "
write("backval(y, ", t5, ") : ", backval(y, t5 )) -- linear " "
write(" ")
write("backval(y, ", t4, ", 2) : ", backval(y, t4, 2)) -- quadratic " "
write("backval(y, ", t3, ", 2) : ", backval(y, t3, 2)) -- quadratic " "
write("backval(y, ", t22, ", 2) : ", backval(y, t22, 2)) -- quadratic " "
write("backval(y, ", t2, ", 2) : ", backval(y, t2, 2)) -- quadratic " "
write("backval(y, ", t11, ", 2) : ", backval(y, t11, 2)) -- quadratic " "
write("backval(y, ", t1, ", 2) : ", backval(y, t1, 2)) -- quadratic " "
write("backval(y, ", t , ", 2) : ", backval(y, t , 2)) -- quadratic " "
write("backval(y, ", t5, ", 2) : ", backval(y, t5, 2)) -- quadratic " "
write(" ")
write("predval(y, ", t1, ", 0) : ", predval(y, t1, 0))
write("predval(y, ", t , ", 0) : ", predval(y, t , 0))
write("predval(y, ", t5, ", 0) : ", predval(y, t5, 0))
write("predval(y, ", t55, ", 0) : ", predval(y, t55, 0))
write(" ")
write("predval(y, ", t1, ") : ", predval(y, t1) )
write("predval(y, ", t , ") : ", predval(y, t ) )
write("predval(y, ", t5, ") : ", predval(y, t5) )
write("predval(y, ", t55, ") : ", predval(y, t55))
write(" ")
write("predval(y, ", t1, ", 2) : ", predval(y, t1, 2))
write("predval(y, ", t , ", 2) : ", predval(y, t , 2))
write("predval(y, ", t5, ", 2) : ", predval(y, t5, 2))
write("predval(y, ", t55, ", 2) : ", predval(y, t55, 2))
write(" ")
write("backtime(y, ", y4, ", 0) : ", backtime(y, y4, 0))
write("backtime(y, ", y33, ", 0) : ", backtime(y, y33, 0))
write("backtime(y, ", y3, ", 0) : ", backtime(y, y3, 0))
write("backtime(y, ", y22, ", 0) : ", backtime(y, y22, 0))
write("backtime(y, ", y2, ", 0) : ", backtime(y, y2, 0))
write("backtime(y, ", y11, ", 0) : ", backtime(y, y11, 0))
write("backtime(y, ", y1, ", 0) : ", backtime(y, y1, 0))
write("backtime(y, ", y , ", 0) : ", backtime(y, y , 0))
write("backtime(y, ", y5, ", 0) : ", backtime(y, y5, 0))
write(" ")
write("backtime(y, ", y4, ") : ", backtime(y, y4) )
write("backtime(y, ", y33, ") : ", backtime(y, y33))
write("backtime(y, ", y3, ") : ", backtime(y, y3) )
write("backtime(y, ", y22, ") : ", backtime(y, y22))
write("backtime(y, ", y2, ") : ", backtime(y, y2) )
write("backtime(y, ", y11, ") : ", backtime(y, y11))
write("backtime(y, ", y1, ") : ", backtime(y, y1) )
write("backtime(y, ", y , ") : ", backtime(y, y ) )
write("backtime(y, ", y5, ") : ", backtime(y, y5) )
write(" ")
write("backtime(y, ", y4, ", 2) : ", backtime(y, y4, 2))
write("backtime(y, ", y33, ", 2) : ", backtime(y, y33, 2))
write("backtime(y, ", y3, ", 2) : ", backtime(y, y3, 2))
write("backtime(y, ", y22, ", 2) : ", backtime(y, y22, 2))
write("backtime(y, ", y2, ", 2) : ", backtime(y, y2, 2))
write("backtime(y, ", y11, ", 2) : ", backtime(y, y11, 2))
write("backtime(y, ", y1, ", 2) : ", backtime(y, y1, 2))
write("backtime(y, ", y , ", 2) : ", backtime(y, y , 2))
write("backtime(y, ", y5, ", 2) : ", backtime(y, y5, 2))
write(" ")
write("predtime(y, ", y1, ", 0) : ", predtime(y, y1, 0))
write("predtime(y, ", y , ", 0) : ", predtime(y, y , 0))
write("predtime(y, ", y5, ", 0) : ", predtime(y, y5, 0))
write("predtime(y, ", y55, ", 0) : ", predtime(y, y55, 0))
write(" ")
write("predtime(y, ", y1, ") : ", predtime(y, y1) )
write("predtime(y, ", y , ") : ", predtime(y, y ) )
write("predtime(y, ", y5, ") : ", predtime(y, y5) )
write("predtime(y, ", y55, ") : ", predtime(y, y55))
write(" ")
write("predtime(y, ", y1, ", 2) : ", predtime(y, y1, 2))
write("predtime(y, ", y , ", 2) : ", predtime(y, y , 2))
write("predtime(y, ", y5, ", 2) : ", predtime(y, y5, 2))
write("predtime(y, ", y55, ", 2) : ", predtime(y, y55, 2))
ENDIF
ENDEXEC
ENDMODEL