MODELS > Examples > Models Residents

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

Models Resident Functions and Variables

Models Resident Functions and Variables