def setup_sinusodial():
# sinusodial test signal:
s = State()
y, my, mdy = symbols("y, my, mdy")
s[my] = dda.neg(y)
s[y] = dda.int(mdy, dt, 0)
s[mdy] = dda.int(my, dt, 1)
s[diff_in] = y # diff_in = cos(t)
s[diff_out] = dda.neg(dda.diff(diff_in, dt, 0)) # 0 = sin(0)
s[int_out] = dda.neg(dda.int(diff_in, dt, +1)) # -1 = cos(0), but negated
return s
diff_in, diff_out, diff_loop = symbols("diff_in, diff_out, diff_loop")
s = State()
dt = 0.05
t_final = 10
alpha = 0.9
ic = 0
# test signal:
#s[diff_in] = dda.int(dda.int(1, dt, 0), dt, 0) # diff_in = t^2
# sinusodial test signal:
y, my, mdy = symbols("y, my, mdy")
s[my] = dda.neg(y)
s[y] = dda.int(mdy, dt, 0)
s[mdy] = dda.int(my, dt, 1)
s[diff_in] = y # diff_in = cos(t)
s[diff_out] = dda.neg(dda.sum(diff_in, diff_loop, dda.mult(alpha, diff_out)))
s[diff_loop] = dda.int(diff_out, dt, ic)
data = s.export(to="CppSolver").run(max_iterations=t_final / dt,
rk_order=4).as_recarray()
xtime = np.arange(0, t_final, dt)
assert len(data) == len(xtime)
from matplotlib.pylab import *
ion()
clf()
#
# Random number by DDA:
#
# We can use the noise function to get randoms between [-1,1].
# Integration over such noise should give the average, i.e. 0.
#
import numpy as np
from dda import State, Symbol, dda
s = State()
dt = 0.01
t_final = 5
s["a"] = dda.noise(0)
s["i"] = dda.int(Symbol("a"), dt, 0)
data = s.export(to="CppSolver").run(max_iterations=t_final / dt,
rk_order=4).as_recarray()
xtime = np.arange(0, t_final, dt)
#assert len(data) == len(xtime)
from matplotlib.pylab import *
#ion(); clf()
#cols = data.dtype.names
cols = "a i".split()
for n in cols:
plot(xtime, data[n], label=n)
legend()
import numpy as np
from dda import State, symbols, dda
ddy, y, mdy, my, lu, ld, y2, y2ohne = symbols("ddy, y, mdy, my, lu, ld, y2, y2ohne")
s = State()
dt = 0.1
t_final = 50
err = 0.5
ic_y = 1.0
ic_mdy = 0.0
s[my] = dda.neg(y)
s[y] = dda.int(lu, mdy, ld, dda.mult(err,my), dt, ic_y)
s[mdy] = dda.int(my, dt, ic_mdy) # my = ddy
s[lu] = dda.mult(1, dda.dead_upper(y, +1))
s[ld] = dda.mult(1, dda.dead_lower(y, -1))
# count zero crossings:
ys, yd, yi = symbols("ys, yd, yi")
s[ys] = dda.sign(y)
s[yd] = dda.max(0, dda.min(1, dda.diff(ys, dt, 0)))
s[yi] = dda.neg(dda.int(dda.mult(yd,1/dt), dt, 0))
# Frequenzverdopplung ohne linearem Offset
s[y2] = dda.mult(y,y)
s[y2ohne] = dda.diff(y2, dt, 0)
# oscillator frqeuency variation
#FREQS = [ 0.95, 1.00, 1.05 ]
freqvarianz = 1.0
# oscillator gain variation
GAINS = [0.95, 1.00, 1.05]
N = len(GAINS)
ddavars = [[Symbol(f"{x}{n}") for n in range(N)]
for x in symbols("y, limu, limd, mdy, my")]
for y, limu, limd, mdy, my, gain in zip(*ddavars, GAINS):
s[y] = dda.mult(
gain,
dda.int(dda.mult(freqvarianz, mdy), dda.mult(A, my), limu, limd, dt,
ic_dy))
s[limu] = dda.mult(stabilization, dda.dead_upper(y, norm))
s[limd] = dda.mult(stabilization, dda.dead_lower(y, -norm))
s[mdy] = dda.int(dda.mult(freqvarianz, my), dda.mult(D, mdy), dt, ic_mdy)
s[my] = dda.sum(y)
runtime_args = {
'max_iterations': t_final / dt,
"rk_order": 3,
"modulo_write": modulo_write,
"modulo_progress": t_final / dt / 10,
}
fields_to_export = ["y0", "y1", "y2"]
solver = s.export(to="CppSolver", constexpr_consts=False)
# Investment in agriculture
delta_capital_investment_in_agriculture = (
CAPITAL_FRACTION_INDICATE_BY_FOOD_RATIO_TABLE(food_ratio)
* CAPITAL_INVESTMENT_FROM_QUALITY(
(
QUALITY_OF_LIFE_FROM_MATERIAL(standard_of_living)
/ QUALITY_OF_LIFE_FROM_FOOD(food_ratio)
) # life quality ratio
) # capital investment from quality ratio
- capital_investment_in_agriculture
) / capital_investment_in_agriculture_frac_adj_time
### Actual evolution
population = dda.int(delta_population, delta_t, ic_pollution)
natural_resources = dda.int(delta_natural_resources, delta_t, ic_natural_resources)
capital_investment = dda.int(delta_capital_investment, delta_t, ic_capital_investment)
pollution = dda.int(delta_pollution, delta_t, ic_pollution)
capital_investment_in_agriculture = dda.int(delta_capital_investment_in_agriculture,
delta_t, ic_capital_investment_in_agriculture)
### This is a derived quantity of interest from the solution:
### The quality of life measure
qol = (
quality_of_life_standard
* QUALITY_OF_LIFE_FROM_MATERIAL(
standard_of_living
) # material multiplier
def setup_polynomial():
s = State()
s[diff_in] = dda.mult(2,dda.int(dda.int(1, dt, 0), dt, 0)) # diff_in = 2*int(1) = t^2
s[diff_out] = dda.neg(dda.diff(diff_in, dt, 0)) # 2*t
s[int_diff] = dda.neg(dda.int(diff_out, dt, 0)) # t^2 but with increasing deviations due to dt
return s
def setup_constant():
s = State()
#s[diff_in] = dda.const(1) # TODO: Such an expression does no more work!!
s[diff_out] = dda.diff(1, dt, 0)
s[int_diff] = dda.int(diff_out, dt, 1) # integrates over 0, should do it.
return s
diff_in, diff_out, diff_loop = symbols("diff_in, diff_out, diff_loop")
s = State()
dt = 0.01
t_final = 5
alpha = 0.9
ic = 0
# test signal:
#s[diff_in] = dda.int(dda.int(1, dt, 0), dt, 0) # diff_in = t^2
# sinusodial test signal:
y, my, mdy = symbols("y, my, mdy")
s[my] = dda.neg(y)
s[y] = dda.int(mdy, dt, 0)
s[mdy] = dda.int(my, dt, 1)
s[diff_in] = y # diff_in = cos(t)
s[diff_out] = dda.diff(diff_in, dt, 0)
from dda.cpp_exporter import compile, run
compile(s.export(to="C"))
data = run(arguments={'max_iterations': t_final / dt, "rk_order": 4} )# return_recarray=True)
xtime = np.arange(0, t_final, dt)
assert len(data) == len(xtime)
from matplotlib.pylab import *