def test_integrate():
x = symbols('x')
R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 2, 3))
q = '0.166270406994788'
assert sstr(p) == q
p = expr_to_holonomic(sin(x)).integrate((x, 0, x)).to_expr()
q = 1 - cos(x)
assert p == q
p = expr_to_holonomic(sin(x)).integrate((x, 0, 3))
q = 1 - cos(3)
assert p == q
p = expr_to_holonomic(sin(x)/x, x0=1).integrate((x, 1, 2))
q = '0.659329913368450'
assert sstr(p) == q
p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 1, 0))
q = '-0.423690480850035'
assert sstr(p) == q
p = expr_to_holonomic(sin(x)/x)
assert p.integrate(x).to_expr() == Si(x)
assert p.integrate((x, 0, 2)) == Si(2)
p = expr_to_holonomic(sin(x)**2/x)
q = p.to_expr()
assert p.integrate(x).to_expr() == q.integrate((x, 0, x))
assert p.integrate((x, 0, 1)) == q.integrate((x, 0, 1))
assert expr_to_holonomic(1/x).integrate(x).to_expr() == log(x)
p = expr_to_holonomic((x + 1)**3*exp(-x), x0=-1, lenics=4).integrate(x).to_expr()
q = (-x**3 - 6*x**2 - 15*x + 6*exp(x + 1) - 16)*exp(-x)
assert p == q
def given():
a = 1
b = R(randrange(3, 6))
c = R('0.6') + randrange(5) * R(1, 10)
e = c + randrange(4) * R(1, 10)
d = a + randrange(5, 9)
f = e + randrange(4, 7)
j = f - R(1, 2)
g = d + R(1, 2)
h = d + randrange(4, 9)
k = R(b - c, a * a)
u = -k * x ** 2 + b
v = (e - c) / (d - a) * (x - a) + c
l = (f - e) / (h - d) ** R(1, 2)
w = l * (x - d) ** R(1, 2) + e
z = l * (x - d) ** R(1, 2)
dc = Struct(
u=sympy.sstr(u),
v=sympy.sstr(v),
w=sympy.sstr(w),
z=sympy.sstr(z),
d=d,
g=g,
h=h)
return dc
def test_evalf():
x = symbols('x')
R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
# a straight line on real axis
r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]
p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1])
s = '0.699525841805253'
assert sstr(p.evalf(r)[-1]) == s
# a traingle with vertices (0, 1+i, 2)
r = [0.1 + 0.1*I]
for i in range(9):
r.append(r[-1]+0.1+0.1*I)
for i in range(10):
r.append(r[-1]+0.1-0.1*I)
s = '1.07530466271334 - 0.0251200594793912*I'
assert sstr(p.evalf(r)[-1]) == s
p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1])
s = '0.905546532085401 - 6.93889390390723e-18*I'
assert sstr(p.evalf(r)[-1]) == s
# a rectangular path (0 -> i -> 2+i -> 2)
r = [0.1*I]
for i in range(9):
r.append(r[-1]+0.1*I)
for i in range(20):
r.append(r[-1]+0.1)
for i in range(10):
r.append(r[-1]-0.1*I)
p = HolonomicFunction(Dx**2 + 1, x, 0, [1,1]).evalf(r)
s = '0.501421652861245 - 3.88578058618805e-16*I'
assert sstr(p[-1]) == s
def test_extended_domain_in_expr_to_holonomic():
x = symbols('x')
p = expr_to_holonomic(1.2*cos(3.1*x))
assert p.to_expr() == 1.2*cos(3.1*x)
assert sstr(p.integrate(x).to_expr()) == '0.387096774193548*sin(3.1*x)'
_, Dx = DifferentialOperators(RR.old_poly_ring(x), 'Dx')
p = expr_to_holonomic(1.1329138213*x)
q = HolonomicFunction((-1.1329138213) + (1.1329138213*x)*Dx, x, 0, {1: [1.1329138213]})
assert p == q
assert p.to_expr() == 1.1329138213*x
assert sstr(p.integrate((x, 1, 2))) == sstr((1.1329138213*x).integrate((x, 1, 2)))
y, z = symbols('y, z')
p = expr_to_holonomic(sin(x*y*z), x=x)
assert p.to_expr() == sin(x*y*z)
assert p.integrate(x).to_expr() == (-cos(x*y*z) + 1)/(y*z)
p = expr_to_holonomic(sin(x*y + z), x=x).integrate(x).to_expr()
q = (cos(z) - cos(x*y + z))/y
assert p == q
a = symbols('a')
p = expr_to_holonomic(a*x, x)
assert p.to_expr() == a*x
assert p.integrate(x).to_expr() == a*x**2/2
D_2, C_1 = symbols("D_2, C_1")
p = expr_to_holonomic(x) + expr_to_holonomic(1.2*cos(x))
p = p.to_expr().subs(D_2, 0)
assert p - x - 1.2*cos(1.0*x) == 0
p = expr_to_holonomic(x) * expr_to_holonomic(1.2*cos(x))
p = p.to_expr().subs(C_1, 0)
assert p - 1.2*x*cos(1.0*x) == 0
def description(self):
from sympy import sstr
s = 'RobotDef instance: ' + self.name + '\n'
s += ' DH parameters - ' + str(self.dh_convention) + ' convention:\n'
s += ' joint - alpha, a, d, theta\n'
for i, dh in enumerate(self.dh_parms):
s += ' %2i - ' % (i+1) + \
sstr(dh).replace('(', '').replace(')', '') + '\n'
s += ' gravity acceleration: ' + sstr(list(self.gravityacc)) + '^T\n'
s += ' friction model: ' + str(self.frictionmodel) + '\n'
return s
def test_complex_space():
c1 = ComplexSpace(2)
assert isinstance(c1, ComplexSpace)
assert c1.dimension == 2
assert sstr(c1) == "C(2)"
assert srepr(c1) == "ComplexSpace(Integer(2))"
n = Symbol("n")
c2 = ComplexSpace(n)
assert isinstance(c2, ComplexSpace)
assert c2.dimension == n
assert sstr(c2) == "C(n)"
assert srepr(c2) == "ComplexSpace(Symbol('n'))"
assert c2.subs(n, 2) == ComplexSpace(2)
def polyrs(self, uhat):
"Compute the polynomial for the response surface."
import sympy
dim = len(self.params)
var = []
for i, p in enumerate(self.params):
var.append(sympy.Symbol(str(p.name)))
chaos = chaos_sequence(dim, self.level)
chaos = np.int_(chaos)
for d in range(0, dim):
poly = np.array(map(lambda x: sympy.legendre(x, var[d]), chaos[:, d]))
if d == 0:
s = poly
else:
s *= poly
eqn = np.sum(uhat * s)
for i, p in enumerate(self.params):
pmin, pmax = p.pdf.srange
c = (pmax + pmin) / 2.0
s = (pmax - pmin) / 2.0
eqn = eqn.subs(var[i], (var[i] - c)/s)
return sympy.sstr(eqn.expand().evalf())
def calc(g):
nm = 1
for i, ae in enumerate(g.en):
nm = nm * simplify(g.bn[i]) ** ae
for i, ae in enumerate(g.ed):
nm = nm / simplify(g.bd[i]) ** ae
return [sstr(simplify(nm))]
def given():
a, b, c, d, e, f = random.sample(range(-9, -1) + range(1, 9), 6)
#x = a/b
rs = a - c
ls = b * x - c
rs = d * rs / ls
ls = 1 - e * x / (d + e * x)
rs = rs / (d + e * x)
rs = apart(rs)
ls = ls / f
rs = rs / f
ls1, ls2 = ls.as_two_terms()
rs1, rs2 = rs.as_two_terms()
g = Struct()
g.sls = sstr(S(ls1) + S(ls2))
g.srs = sstr(S(rs1) + S(rs2))
return g
def given():
n, d = 2, -2
while n / d == -1:
n, d = sample(range(1, 9) + range(-9, -2), 2)
a, b = sample(range(2, 9), 2)
ee = (a * x + b) ** R(n, d)
g = Struct(ee=sympy.sstr(ee))
return g
def test_extended_domain_in_expr_to_holonomic():
x = symbols('x')
p = expr_to_holonomic(1.2*cos(3.1*x), domain=RR)
assert p.to_expr() == 1.2*cos(3.1*x)
assert sstr(p.integrate(x).to_expr()) == '0.387096774193548*sin(3.1*x)'
_, Dx = DifferentialOperators(RR.old_poly_ring(x), 'Dx')
p = expr_to_holonomic(1.1329138213*x, domain=RR, lenics=2)
q = HolonomicFunction((-1.1329138213) + (1.1329138213*x)*Dx, x, 0, [0, 1.1329138213])
assert p == q
assert p.to_expr() == 1.1329138213*x
assert sstr(p.integrate((x, 1, 2))) == sstr((1.1329138213*x).integrate((x, 1, 2)))
y, z = symbols('y, z')
p = expr_to_holonomic(sin(x*y*z), x=x, domain=ZZ[y, z])
assert p.to_expr() == sin(x*y*z)
assert p.integrate(x).to_expr() == (-cos(x*y*z) + 1)/(y*z)
p = expr_to_holonomic(sin(x*y + z), x=x, domain=ZZ[y, z]).integrate(x).to_expr()
q = (cos(z) - cos(x*y + z))/y
assert p == q
def test_integrate():
x = symbols('x')
R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
p = from_sympy(sin(x)**2/x, x0=1).integrate((x, 2, 3))
q = '0.166270406994788'
assert sstr(p) == q
p = from_sympy(sin(x)).integrate((x, 0, x)).to_sympy()
q = 1 - cos(x)
assert p == q
p = from_sympy(sin(x)).integrate((x, 0, 3))
q = '1.98999246812687'
assert sstr(p) == q
p = from_sympy(sin(x)/x, x0=1).integrate((x, 1, 2))
q = '0.659329913368450'
assert sstr(p) == q
p = from_sympy(sin(x)**2/x, x0=1).integrate((x, 1, 0))
q = '-0.423690480850035'
assert sstr(p) == q
def test_integrate():
x = symbols('x')
R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx')
p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 2, 3))
q = '0.166270406994788'
assert sstr(p) == q
p = expr_to_holonomic(sin(x)).integrate((x, 0, x)).to_expr()
q = 1 - cos(x)
assert p == q
p = expr_to_holonomic(sin(x)).integrate((x, 0, 3))
q = 1 - cos(3)
assert p == q
p = expr_to_holonomic(sin(x)/x, x0=1).integrate((x, 1, 2))
q = '0.659329913368450'
assert sstr(p) == q
p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 1, 0))
q = '-0.423690480850035'
assert sstr(p) == q
p = expr_to_holonomic(sin(x)/x)
assert p.integrate(x).to_expr() == Si(x)
assert p.integrate((x, 0, 2)) == Si(2)
p = expr_to_holonomic(sin(x)**2/x)
q = p.to_expr()
assert p.integrate(x).to_expr() == q.integrate((x, 0, x))
assert p.integrate((x, 0, 1)) == q.integrate((x, 0, 1))
assert expr_to_holonomic(1/x, x0=1).integrate(x).to_expr() == log(x)
p = expr_to_holonomic((x + 1)**3*exp(-x), x0=-1).integrate(x).to_expr()
q = (-x**3 - 6*x**2 - 15*x + 6*exp(x + 1) - 16)*exp(-x)
assert p == q
p = expr_to_holonomic(cos(x)**2/x**2, y0={-2: [1, 0, -1]}).integrate(x).to_expr()
q = -Si(2*x) - cos(x)**2/x
assert p == q
p = expr_to_holonomic(sqrt(x**2+x)).integrate(x).to_expr()
q = (x**(3/2)*(2*x**2 + 3*x + 1) - x*sqrt(x + 1)*asinh(sqrt(x)))/(4*x*sqrt(x + 1))
assert p == q
p = expr_to_holonomic(sqrt(x**2+1)).integrate(x).to_expr()
q = (sqrt(x**2+1)).integrate(x)
assert (p-q).simplify() == 0
p = expr_to_holonomic(1/x**2, y0={-2:[1, 0, 0]})
r = expr_to_holonomic(1/x**2, lenics=3)
assert p == r
q = expr_to_holonomic(cos(x)**2)
assert (r*q).integrate(x).to_expr() == -Si(2*x) - cos(x)**2/x
def given():
b = randrange(3, 6)
c = b + randrange(4, 9)
d = c + randrange(3, 6)
u = randrange(1, 4)
v = u + randrange(1, 4)
w = v + randrange(1, 4)
l = w / b ** R(1, 2)
ff = l * x ** R(1, 2)
gg = (u - w) * (x - b) / (c - b) + w
hh = (v - u) * (x - c) / (d - c) + u
t = randrange(3, 9)
g = Struct(
f=sympy.sstr(ff),
g=sympy.sstr(gg),
h=sympy.sstr(hh),
b=b,
c=c,
d=d,
t=t)
return g
def test_from_hyper():
x = symbols('x')
R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
p = hyper([1, 1], [S(3)/2], x**2/4)
q = HolonomicFunction((4*x) + (5*x**2 - 8)*Dx + (x**3 - 4*x)*Dx**2, x, 1, [2*sqrt(3)*pi/9, -4*sqrt(3)*pi/27 + 4/3])
r = from_hyper(p)
assert r == q
p = from_hyper(hyper([1], [S(3)/2], x**2/4))
q = HolonomicFunction(-x + (-x**2/2 + 2)*Dx + x*Dx**2, x)
x0 = 1
y0 = '[sqrt(pi)*exp(1/4)*erf(1/2), -sqrt(pi)*exp(1/4)*erf(1/2)/2 + 1]'
assert sstr(p.y0) == y0
assert q.annihilator == p.annihilator
def generate_equations(self):
self.emit("EQUATION")
self.indent()
obs_names = self.model.observable_groups.keys()
obs_exprs = [' + '.join('%g * s%s' % g for g in self.model.observable_groups[name]) for name in obs_names]
for obs in zip(obs_names, obs_exprs):
self.emit('%s = %s;' % obs)
var_names = ['s%d' % i for i in range(len(self.model.species))]
for (name, ode) in zip(var_names, self.model.odes):
expression = sympy.sstr(ode)
expression = re.sub(r'\*\*', '^', expression)
self.emit('$%s = %s;' % (name, expression))
self.outdent()
def calc(g):
Kp = S(g.Kp)
Ep = R(-g.pmax, g.xp0) * x + g.pmax
E = sympy.integrate(Ep, x)
K = sympy.integrate(Kp, x) + S(g.Ko)
Gp = Ep - Kp
rG = [r.n() for r in sympy.roots(Gp) if r > 0][0]
G = E - K
mG = G.subs(x, rG)
kk = sympy.Wild('kk')
dd = sympy.Wild('dd')
kd = Ep.match(kk * x + dd)
p = kd[kk] * x / 2 + kd[dd]
mp = p.subs(x, rG)
el = S(1 + kd[dd] / (kd[kk] * x / 2))
return [
sympy.sstr(Ep),
sympy.sstr(E),
sympy.sstr(K),
sympy.sstr(p),
sympy.sstr(el),
rG,
mp]
def norm_expr(a):
'''
>>> a = '1/4*e^(4x+4)'
>>> norm_expr(a)
'exp(4*x + 4)/4'
'''
try:
from sympy.parsing.sympy_parser import (
parse_expr,
standard_transformations,
convert_xor,
implicit_multiplication_application)
res = parse_expr(a, transformations=(
standard_transformations + (convert_xor, implicit_multiplication_application,)))
res = sstr(res.subs('e', E))
except:
res = a
return res
def given():
xp0 = randrange(7, 10)
pmax = randrange(7, 10)
Ep = R(-pmax, xp0) * x + pmax
E = sympy.integrate(Ep, x)
b = randrange(2, xp0 - 2)
cmax = int(Ep.subs(x, b).n())
c = randrange(1, cmax)
a = R(randrange(1, pmax - c), b * b)
Kp = a * (x - b) ** 2 + c
Gp = Ep - Kp
rG = [r.n() for r in sympy.roots(Gp) if r > 0][0]
G = sympy.integrate(Gp, x)
mG = G.subs(x, rG)
Ko = int(mG - 1) / 2
#K = sympy.integrate(Kp,x)+Ko
#G = E.n()-K.n()
#rts = sorted([r.n() for r in sympy.roots(G) if r > 0])
g = Struct(pmax=pmax, xp0=xp0, Ko=Ko, Kp=sympy.sstr(Kp))
return g
def driver1(spinfile,interactionfile):
"""generates Hsave"""
atom_list, jnums, jmats,N_atoms_uc=readfiles.readFiles(interactionfile,spinfile)
N_atoms=len(atom_list)
print 'N_atoms',N_atoms,'Natoms_uc',N_atoms_uc
for atom in atom_list:
print atom.neighbors
print atom.interactions
Hsave = calculate_dispersion(atom_list,N_atoms_uc,N_atoms,jmats,showEigs=False)
print 'driver1: complete'
print Hsave
Hamfile = open('Hsave.txt','w')
Hamfile.write(sympy.sstr(Hsave))
Hamfile.close()
return Hsave
def test_evalf_rk4():
x = symbols('x')
R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
# log(1+x)
p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1])
# path taken is a straight line from 0 to 1, on the real axis
r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]
s = '0.693146363174626' # approx. equal to log(2) i.e. 0.693147180559945
assert sstr(p.evalf(r)[-1]) == s
# path taken is a traingle 0-->1+i-->2
r = [0.1 + 0.1*I]
for i in range(9):
r.append(r[-1]+0.1+0.1*I)
for i in range(10):
r.append(r[-1]+0.1-0.1*I)
# close to the exact solution 1.09861228866811
# imaginary part also close to zero
s = '1.09861574485151 + 1.36082967699958e-7*I'
assert sstr(p.evalf(r)[-1]) == s
# sin(x)
p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1])
s = '0.90929463522785 + 1.52655665885959e-16*I'
assert sstr(p.evalf(r)[-1]) == s
# computing sin(pi/2) using this method
# using a linear path from 0 to pi/2
r = [0.1]
for i in range(14):
r.append(r[-1] + 0.1)
r.append(pi/2)
s = '0.999999895088917' # close to 1.0 (exact solution)
assert sstr(p.evalf(r)[-1]) == s
# trying different path, a rectangle (0-->i-->pi/2 + i-->pi/2)
# computing the same value sin(pi/2) using different path
r = [0.1*I]
for i in range(9):
r.append(r[-1]+0.1*I)
for i in range(15):
r.append(r[-1]+0.1)
r.append(pi/2+I)
for i in range(10):
r.append(r[-1]-0.1*I)
# close to 1.0
s = '1.00000003415141 + 6.11940487991086e-16*I'
assert sstr(p.evalf(r)[-1]) == s
# cos(x)
p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0])
# compute cos(pi) along 0-->pi
r = [0.05]
for i in range(61):
r.append(r[-1]+0.05)
r.append(pi)
# close to -1 (exact answer)
s = '-0.999999993238714'
assert sstr(p.evalf(r)[-1]) == s
# a rectangular path (0 -> i -> 2+i -> 2)
r = [0.1*I]
for i in range(9):
r.append(r[-1]+0.1*I)
for i in range(20):
r.append(r[-1]+0.1)
for i in range(10):
r.append(r[-1]-0.1*I)
p = HolonomicFunction(Dx**2 + 1, x, 0, [1,1]).evalf(r)
s = '0.493152791638442 - 1.41553435639707e-15*I'
assert sstr(p[-1]) == s
def test_evalf_euler():
x = symbols('x')
R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
# log(1+x)
p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1])
# path taken is a straight line from 0 to 1, on the real axis
r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]
s = '0.699525841805253' # approx. equal to log(2) i.e. 0.693147180559945
assert sstr(p.evalf(r, method='Euler')[-1]) == s
# path taken is a traingle 0-->1+i-->2
r = [0.1 + 0.1*I]
for i in range(9):
r.append(r[-1]+0.1+0.1*I)
for i in range(10):
r.append(r[-1]+0.1-0.1*I)
# close to the exact solution 1.09861228866811
# imaginary part also close to zero
s = '1.07530466271334 - 0.0251200594793912*I'
assert sstr(p.evalf(r, method='Euler')[-1]) == s
# sin(x)
p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1])
s = '0.905546532085401 - 6.93889390390723e-18*I'
assert sstr(p.evalf(r, method='Euler')[-1]) == s
# computing sin(pi/2) using this method
# using a linear path from 0 to pi/2
r = [0.1]
for i in range(14):
r.append(r[-1] + 0.1)
r.append(pi/2)
s = '1.08016557252834' # close to 1.0 (exact solution)
assert sstr(p.evalf(r, method='Euler')[-1]) == s
# trying different path, a rectangle (0-->i-->pi/2 + i-->pi/2)
# computing the same value sin(pi/2) using different path
r = [0.1*I]
for i in range(9):
r.append(r[-1]+0.1*I)
for i in range(15):
r.append(r[-1]+0.1)
r.append(pi/2+I)
for i in range(10):
r.append(r[-1]-0.1*I)
# close to 1.0
s = '0.976882381836257 - 1.65557671738537e-16*I'
assert sstr(p.evalf(r, method='Euler')[-1]) == s
# cos(x)
p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0])
# compute cos(pi) along 0-->pi
r = [0.05]
for i in range(61):
r.append(r[-1]+0.05)
r.append(pi)
# close to -1 (exact answer)
s = '-1.08140824719196'
assert sstr(p.evalf(r, method='Euler')[-1]) == s
# a rectangular path (0 -> i -> 2+i -> 2)
r = [0.1*I]
for i in range(9):
r.append(r[-1]+0.1*I)
for i in range(20):
r.append(r[-1]+0.1)
for i in range(10):
r.append(r[-1]-0.1*I)
p = HolonomicFunction(Dx**2 + 1, x, 0, [1,1]).evalf(r, method='Euler')
s = '0.501421652861245 - 3.88578058618805e-16*I'
assert sstr(p[-1]) == s
def __str__(self):
from sympy import sstr
return sstr(self.data) + " + " + str(self.ring.base_ideal)
def __repr__(self):
from sympy import sstr
return "[" + ", ".join(sstr(x) for x in self.data) + "]"
def symbolic_analysis(circ,
source=None,
ac_enable=True,
r0s=False,
subs=None,
outfile=None,
verbose=3):
"""Attempt a symbolic, small-signal solution of the circuit.
**Parameters:**
circ : circuit instance
the circuit instance to be simulated.
source : string, optional
the ``part_id`` of the source to be used as input for the transfer
function. If ``None``, no transfer function is evaluated.
ac_enable : bool, optional
take frequency dependency into consideration (default: True).
r0s : bool, optional
take transistors' output impedance into consideration (default: False)
subs: dict, optional
a dictionary of part IDs to be substituted. It makes solving the circuit
easier. Eg. ``subs={'R1':'R2'}`` - replace the resistor R1 with R2.
outfile : string, optional
output filename - ``'stdout'`` means print to stdout, the default.
verbose: int, optional
verbosity level 0 (silent) to 6 (painful).
**Returns:**
sol : symbolic solution
The solutions.
tfs : symbolic solution
The transfer functions, only if requested. Otherwise ``tfs`` is a
``None`` object.
"""
if subs is None:
subs = {} # no subs by default
else:
subs = _parse_substitutions(subs)
if not ac_enable:
printing.print_info_line(
("Starting symbolic small-signal DC analysis...", 1), verbose)
else:
printing.print_info_line(("Starting symbolic AC analysis...", 1),
verbose)
printing.print_info_line(("Building symbolic MNA, N and x...", 3),
verbose,
print_nl=False)
mna, N, subs_g = generate_mna_and_N(circ,
opts={'r0s': r0s},
ac=ac_enable,
subs=subs,
verbose=verbose)
x = get_variables(circ)
mna = mna[1:, 1:]
N = N[1:, :]
printing.print_info_line((" done.", 3), verbose)
printing.print_info_line(("MNA matrix (reduced):", 5), verbose)
printing.print_info_line((sympy.sstr(mna), 5), verbose)
printing.print_info_line(("N matrix (reduced):", 5), verbose)
printing.print_info_line((sympy.sstr(N), 5), verbose)
printing.print_info_line(("Building equations...", 3), verbose)
eq = []
for i in _to_real_list(mna * x + N):
eq.append(sympy.Eq(i, 0))
x = _to_real_list(x)
if verbose > 3:
printing.print_symbolic_equations(eq)
printing.print_info_line(("To be solved for:", 4), verbose)
printing.print_info_line((str(x), 4), verbose)
printing.print_info_line(("Solving...", 1), verbose)
sol = sympy.solve(eq,
x,
manual=options.symb_sympy_manual_solver,
simplify=True)
for ks in list(sol.keys()):
sol.update({ks: sol[ks].subs(subs_g)})
if sol == {}:
printing.print_warning("No solutions. Check the netlist.")
else:
printing.print_info_line(("Success!", 2), verbose)
printing.print_info_line(("Results:", 1), verbose)
if options.cli:
printing.print_symbolic_results(sol)
if source is not None:
src = _symbol_factory(source.upper())
printing.print_info_line(
("Calculating small-signal symbolic transfer functions (%s))..." %
(str(src), ), 2),
verbose,
print_nl=False)
tfs = calculate_gains(sol, src)
printing.print_info_line(("done.", 2), verbose)
printing.print_info_line(
("Small-signal symbolic transfer functions:", 1), verbose)
if options.cli:
printing.print_symbolic_transfer_functions(tfs)
else:
tfs = None
# convert to a results instance
sol = results.symbolic_solution(sol, subs, circ, outfile)
if tfs:
if outfile and outfile != 'stdout':
outfile += ".tfs"
tfs = results.symbolic_solution(tfs, subs, circ, outfile, tf=True)
return sol, tfs
def symbolic_analysis(circ, source=None, ac_enable=True, r0s=False, subs=None, outfile=None, verbose=3):
"""Attempt a symbolic solution of the circuit.
**Parameters:**
circ : circuit instance
the circuit instance to be simulated.
source : string, optional
the ``part_id`` of the source to be used as input for the transfer
function. If ``None``, no transfer function is evaluated.
ac_enable : bool, optional
take frequency dependency into consideration (default: True).
r0s : bool, optional
take transistors' output impedance into consideration (default: False)
subs: dict, optional
a dictionary of ``sympy.Symbol`` to be substituted. It makes solving the circuit
easier. Eg. ``subs={R1:R2}`` - replace R1 with R2. It can be generated with
:func:`parse_substitutions()`
outfile : string, optional
output filename - ``'stdout'`` means print to stdout, the default.
verbose: int, optional
verbosity level 0 (silent) to 6 (painful).
**Returns:**
sol : dict
a dictionary with the solutions.
"""
if subs is None:
subs = {} # no subs by default
if not ac_enable:
printing.print_info_line(
("Starting symbolic DC analysis...", 1), verbose)
else:
printing.print_info_line(
("Starting symbolic AC analysis...", 1), verbose)
printing.print_info_line(
("Building symbolic MNA, N and x...", 3), verbose, print_nl=False)
mna, N, subs_g = generate_mna_and_N(
circ, opts={'r0s': r0s}, ac=ac_enable, verbose=verbose)
x = get_variables(circ)
mna = mna[1:, 1:]
N = N[1:, :]
printing.print_info_line((" done.", 3), verbose)
printing.print_info_line(
("Performing variable substitutions...", 5), verbose)
mna, N = apply_substitutions(mna, N, subs)
printing.print_info_line(("MNA matrix (reduced):", 5), verbose)
printing.print_info_line((sympy.sstr(mna), 5), verbose)
printing.print_info_line(("N matrix (reduced):", 5), verbose)
printing.print_info_line((sympy.sstr(N), 5), verbose)
printing.print_info_line(("Building equations...", 3), verbose)
eq = []
for i in _to_real_list(mna * x + N):
eq.append(sympy.Eq(i, 0))
x = _to_real_list(x)
if verbose > 3:
printing.print_symbolic_equations(eq)
printing.print_info_line(("To be solved for:", 4), verbose)
printing.print_info_line((str(x), 4), verbose)
printing.print_info_line(("Solving...", 1), verbose)
sol = sympy.solve(
eq, x, manual=options.symb_sympy_manual_solver, simplify=True)
for ks in sol.keys():
sol.update({ks: sol[ks].subs(subs_g)})
# sol = sol_to_dict(sol, x)
if sol == {}:
printing.print_warning("No solutions. Check the netlist.")
else:
printing.print_info_line(("Success!", 2), verbose)
printing.print_info_line(("Results:", 1), verbose)
if options.cli:
printing.print_symbolic_results(sol)
if source is not None:
src = _symbol_factory(source.upper())
printing.print_info_line(("Calculating small-signal symbolic transfer functions (%s))..." %
(str(src),), 2), verbose, print_nl=False)
tfs = calculate_gains(sol, src)
printing.print_info_line(("done.", 2), verbose)
printing.print_info_line(
("Small-signal symbolic transfer functions:", 1), verbose)
if options.cli:
printing.print_symbolic_transfer_functions(tfs)
else:
tfs = None
# convert to a results instance
sol = results.symbolic_solution(sol, subs, circ, outfile)
if tfs:
if outfile and outfile != 'stdout':
outfile += ".tfs"
tfs = results.symbolic_solution(tfs, subs, circ, outfile, tf=True)
return sol, tfs
def __repr__(self):
from sympy import sstr
return '[' + ', '.join(sstr(x) for x in self.data) + ']'
def calc(g):
res = sympy.sstr(S(sympy.integrate(S(g.ee), x)))
return [res]
def symbolic_analysis(circ, source=None, ac_enable=True, r0s=False, subs=None, outfile=None, verbose=3):
"""Attempt a symbolic solution of the circuit.
circ: the circuit instance to be simulated.
source: the name (string) of the source to be used as input for the transfer
function. If None, no transfer function is evaluated.
ac_enable: take frequency dependency into consideration (default: True)
r0s: take transistors' output impedance into consideration (default: False)
subs: a dictionary of sympy Symbols to be substituted. It makes solving the circuit
easier. Eg. {R1:R2} - replace R1 with R2. It can be generated with
parse_substitutions()
outfile: output filename ('stdout' means print to stdout).
verbose: verbosity level 0 (silent) to 6 (painful).
Returns: a dictionary with the solutions.
"""
if subs is None:
subs = {} # no subs by default
if not ac_enable:
printing.print_info_line(
("Starting symbolic DC analysis...", 1), verbose)
else:
printing.print_info_line(
("Starting symbolic AC analysis...", 1), verbose)
printing.print_info_line(
("Building symbolic MNA, N and x...", 3), verbose, print_nl=False)
mna, N, subs_g = generate_mna_and_N(
circ, opts={'r0s': r0s}, ac=ac_enable, verbose=verbose)
x = get_variables(circ)
mna = mna[1:, 1:]
N = N[1:, :]
printing.print_info_line((" done.", 3), verbose)
printing.print_info_line(
("Performing variable substitutions...", 5), verbose)
mna, N = apply_substitutions(mna, N, subs)
printing.print_info_line(("MNA matrix (reduced):", 5), verbose)
printing.print_info_line((sympy.sstr(mna), 5), verbose)
printing.print_info_line(("N matrix (reduced):", 5), verbose)
printing.print_info_line((sympy.sstr(N), 5), verbose)
printing.print_info_line(("Building equations...", 3), verbose)
eq = []
for i in to_real_list(mna * x + N):
eq.append(sympy.Eq(i, 0))
x = to_real_list(x)
if verbose > 4:
printing.print_symbolic_equations(eq)
print "To be solved for:"
print x
# print "Matrix is singular: ", (mna.det() == 0)
# print -1.0*mna.inv()*N #too heavy
# print sympy.solve_linear_system(mna.row_join(-N), x)
printing.print_info_line(
("Performing auxiliary simplification...", 3), verbose)
eq, x, sol_h = help_the_solver(eq, x)
if len(eq):
printing.print_info_line(("Symplified sytem:", 3), verbose)
if verbose > 3:
printing.print_symbolic_equations(eq)
printing.print_info_line(("To be solved for:", 3), verbose)
printing.print_info_line((str(x), 3), verbose)
printing.print_info_line(("Solving...", 1), verbose)
if options.symb_internal_solver:
sol = local_solve(eq, x)
else:
sol = sympy.solve(
eq, x, manual=options.symb_sympy_manual_solver, simplify=True)
if sol is not None:
sol.update(sol_h)
else:
sol = sol_h
else:
printing.print_info_line(
("Auxiliary simplification solved the problem.", 3), verbose)
sol = sol_h
for ks in sol.keys():
sol.update({ks: sol[ks].subs(subs_g)})
# sol = sol_to_dict(sol, x)
if sol == {}:
printing.print_warning("No solutions. Check the netlist.")
else:
printing.print_info_line(("Success!", 2), verbose)
printing.print_info_line(("Results:", 1), verbose)
if options.cli:
printing.print_symbolic_results(sol)
if source is not None:
src = sympy.Symbol(source.upper(), real=True)
printing.print_info_line(("Calculating small-signal symbolic transfer functions (%s))..." %
(str(src),), 2), verbose, print_nl=False)
tfs = calculate_gains(sol, src)
printing.print_info_line(("done.", 2), verbose)
printing.print_info_line(
("Small-signal symbolic transfer functions:", 1), verbose)
if options.cli:
printing.print_symbolic_transfer_functions(tfs)
else:
tfs = None
# convert to a results instance
sol = results.symbolic_solution(sol, subs, circ, outfile)
if tfs:
if outfile and outfile != 'stdout':
outfile += ".tfs"
tfs = results.symbolic_solution(tfs, subs, circ, outfile, tf=True)
return sol, tfs
def NS(e, n=15, **options):
return sstr(sympify(e).evalf(n, **options), full_prec=True)
def given():
ff1 = random.sample(funs1, 1)[0]
f1 = ff1 - random.sample(crange, 1)[0]
f2 = random.sample(funs2, 1)[0]
g = Struct(f1=sstr(f1), f2=sstr(f2))
return g
def __repr__(self):
from sympy import sstr
return '[' + ', '.join(sstr(x) for x in self.data) + ']'
def __repr__(self):
from sympy import sstr
return '<' + ','.join(sstr(x) for [x] in self._module.gens) + '>'
def __str__(self):
from sympy import sstr
return sstr(self.data) + " + " + str(self.ring.base_ideal)
def NS(e, n=15, **options):
return sstr(sympify(e).evalf(n, **options), full_prec=True)
def __str__(self):
from sympy import sympify, sstr
return sstr(sympify(self._symbol_expr), full_prec=False)
