def test_u():
theta, phi, lambd = symbols("theta phi lambd")
actual_1 = simplify(Circuit().u(theta, phi, lambd, -(phi + lambd) / 2)[0].run(backend="sympy_unitary"))
assert actual_1[0, 0] != 0
expected_1 = simplify(Circuit().rz(lambd)[0].ry(theta)[0].rz(phi)[0].run_with_sympy_unitary())
assert expected_1[0, 0] != 0
assert simplify(nfloat(actual_1)) == simplify(nfloat(expected_1))
def NR_Multivar(X0, F, kk):
J = Matrix.jacobian(F, [x, y, z]) # calculate Jacobian matrix
for i in range(kk):
Jinv = invJ(J, X0)
Fi = sp.nfloat(F.subs([(x, X0[0]), (y, X0[1]), (z, X0[2])]),
7) # 7 is numbers after the point
X0 = Iteration(X0, Jinv, Fi)
print(sp.nfloat(X0, 7))
def test_nfloat():
from sympy.core.basic import _aresame
x = Symbol("x")
eq = x**(S(4)/3) + 4*x**(S(1)/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(S(1)/3))
assert _aresame(nfloat(eq, exponent=True), x**(4.0/3) + (4.0/3)*x**(1.0/3))
eq = x**(S(4)/3) + 4*x**(x/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(x/3))
big = 12345678901234567890
Float_big = Float(big, '')
assert _aresame(nfloat(x**big, exponent=True),
x**Float_big)
assert _aresame(nfloat(big), Float_big)
def spec(f, a, b, T):
mag = [nfloat(sqrt(a[i]**2 + b[i]**2)) for i in range(len(a))]
phi = len(a) * [0]
for i in range(len(b)):
if a[i] == S.Zero:
phi[i] = 0
else:
phi[i] = nfloat(arg(a[i] - S.ImaginaryUnit * b[i]))
mag.insert(0, a0(f, T))
if mag[0] >= 0:
phi.insert(0, 0)
else:
phi.insert(0, pi)
return (mag, phi)
def test_evalf_relational():
assert Eq(x/5, y/10).evalf() == Eq(0.2*x, 0.1*y)
# if this first assertion fails it should be replaced with
# one that doesn't
assert unchanged(Eq, (3 - I)**2/2 + I, 0)
assert Eq((3 - I)**2/2 + I, 0).n() is S.false
assert nfloat(Eq((3 - I)**2 + I, 0)) == S.false
def test_evalf_relational():
assert Eq(x/5, y/10).evalf() == Eq(0.2*x, 0.1*y)
# if this first assertion fails it should be replaced with
# one that doesn't
assert unchanged(Eq, (3 - I)**2/2 + I, 0)
assert Eq((3 - I)**2/2 + I, 0).n() is S.false
# note: these don't always evaluate to Boolean
assert nfloat(Eq((3 - I)**2 + I, 0)) == Eq((3.0 - I)**2 + I, 0)
def test_nfloat():
from sympy.core.basic import _aresame
x = Symbol("x")
eq = x**(S(4)/3) + 4*x**(S(1)/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(S(1)/3))
assert _aresame(nfloat(eq, exponent=True), x**(4.0/3) + (4.0/3)*x**(1.0/3))
eq = x**(S(4)/3) + 4*x**(x/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(x/3))
big = 12345678901234567890
Float_big = Float(big, '')
assert _aresame(nfloat(x**big, exponent=True),
x**Float_big)
assert _aresame(nfloat(big), Float_big)
# issues 3243
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solve(f.subs(x, -0.139)))
def test_evalf_relational():
assert Eq(x / 5, y / 10).evalf() == Eq(0.2 * x, 0.1 * y)
# if this first assertion fails it should be replaced with
# one that doesn't
assert unchanged(Eq, (3 - I)**2 / 2 + I, 0)
assert Eq((3 - I)**2 / 2 + I, 0).n() is S.false
# note: these don't always evaluate to Boolean
assert nfloat(Eq((3 - I)**2 + I, 0)) == Eq((3.0 - I)**2 + I, 0)
def test_nfloat():
from sympy.core.basic import _aresame
x = Symbol("x")
eq = x**(S(4) / 3) + 4 * x**(S(1) / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(S(1) / 3))
assert _aresame(nfloat(eq, exponent=True),
x**(4.0 / 3) + (4.0 / 3) * x**(1.0 / 3))
eq = x**(S(4) / 3) + 4 * x**(x / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(x / 3))
big = 12345678901234567890
Float_big = Float(big, '')
assert _aresame(nfloat(x**big, exponent=True), x**Float_big)
assert _aresame(nfloat(big), Float_big)
# issues 3243
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solve(f.subs(x, -0.139)))
def sroots(self, Am, tol=None, nn=None, char=None):
#returns sympy format, python format
λ = sp.Symbol('λ')
if tol == None:
tol = 10**-15
if nn == None:
nv = 15
elif nn != None:
nv = int(nn)
if char == None:
A = sp.Matrix(Am)
M, N = np.array(Am).shape
II = sp.eye(M)
Ad = A - II*λ
Deta = Ad.det()
elif char != None:
Deta = char
Detsimp = sp.nfloat(sp.nsimplify(Deta, tolerance=tol, full=True), n=nv)
# rlist = list(sp.solve(Detsimp, λ))
rlist = list(sp.solve(Detsimp, λ, **{'set': True ,'particular': True}))
rootsd = [sp.nsimplify(i, tolerance=tol, full=True) for i in rlist]
sympl = []
numpr = []
numpi = []
for i, j in enumerate(rootsd):
sympl.append(sp.simplify(sp.nfloat(rootsd[i], n=nv), rational=False))
vals = j.as_real_imag()
vali = sp.nfloat(vals[0], n=nv)
valj = sp.nfloat(vals[1], n=nv)
numpr.append(vali)
numpi.append(valj)
reals = []
iss = []
simps = []
for i, j in zip(numpr, numpi):
reale = i
compe = j
reals.append(reale)
if compe != 0.0:
iss.append(compe)
simps.append(complex(i,j))
else:
simps.append(reale)
return rlist, simps
def test_sympy_backend_for_two_qubit_gate2():
x, y, z = symbols('x y z', real=True)
E = eye(2)
UPPER = Matrix([[1, 0], [0, 0]])
LOWER = Matrix([[0, 0], [0, 1]])
RX = Matrix([[cos(x / 2), -I * sin(x / 2)], [-I * sin(x / 2), cos(x / 2)]])
RY = Matrix([[cos(y / 2), -sin(y / 2)], [sin(y / 2), cos(y / 2)]])
RZ = Matrix([[cos(z / 2) - I * sin(z / 2), 0], [0, cos(z / 2) + I * sin(z / 2)]])
CRX_3 = reduce(TensorProduct, [E, UPPER, E]) + reduce(TensorProduct, [E, LOWER, RX])
CRY_4 = reduce(TensorProduct, [UPPER, E, E]) + reduce(TensorProduct, [LOWER, RY, E])
CRZ_3 = reduce(TensorProduct, [E, E, UPPER]) + reduce(TensorProduct, [RZ, E, LOWER])
actual_9 = Circuit().crx(x)[1, 0].i[2].run(backend="sympy_unitary")
assert simplify(actual_9 - CRX_3) == zeros(8)
actual_10 = Circuit().cry(y)[2, 1].run(backend="sympy_unitary")
assert simplify(actual_10 - CRY_4) == zeros(8)
actual_11 = Circuit().crz(z)[0, 2].run(backend="sympy_unitary")
m = simplify(nfloat(actual_11) - nfloat(CRZ_3))
def cfourreeks(f, T, N):
"""Let op! Periode tussen -T/2 en T/2!"""
N += 1
omega0 = 2 * pi / T
cp = (N - 1) * [0]
cn = (N - 1) * [0]
mag = (2 * N - 1) * [0]
phase = (2 * N - 1) * [0]
c0 = 1 / T * integrate(f, (t, -T / 2, T / 2)).nsimplify()
mag[N - 1] = Abs(nfloat(c0))
phase[N - 1] = 0
som = c0
for n in range(1, N):
cp[n - 1] = ac(f, T, n, omega0)
cn[n - 1] = conjugate(cp[n - 1])
mag[N - n - 1] = 2 * Abs(nfloat(cn[n - 1]))
mag[N + n - 1] = 2 * Abs(nfloat(cp[n - 1]))
phase[N - n - 1] = arg(cn[n - 1])
phase[N + n - 1] = arg(cp[n - 1])
som += cp[n - 1] * exp(S.ImaginaryUnit * n * omega0 * t) + cn[
n - 1] * exp(-S.ImaginaryUnit * n * omega0 * t)
cp.insert(0, c0)
return som, mag, phase
def compute_lenth(p,interval):
'''
计算多项式函数的弧长
:param p: 多项式系数的 narray
:param interval: 区间,传入一个 narray,包含上下限
:return: 长度
'''
x = sy.symbols('x')
n = len(p) # 有多少个系数
# p_1 = np.zeros(n)
# 产生多项式函数
func = 0
for i in range(n):
#p_1[i] = sy.evaluate(p[i])
func += (p[i] * (x ** (n-1-i)))
print('\n拟合得到的多项式函数为：')
sy.pprint(func)
# 用高数求弧长公式求弧长
print('\n用以下公式求弧长：')
func_compute(func)
# 对其求导
print('\n先对其求导，其导数为：')
func1 = sy.diff(func,x)
sy.pprint(func1)
func2 = sy.sqrt(1 + func1**2)
#sy.pprint(func2)
# func3 = sy.integrate(func2,x)
# sy.pprint(func3)
a = sy.integrate(func2,(x,interval[0],interval[1])) # 积分函数
b = sy.nfloat(a,5) # 积分值，保留五位有效数字
print('\n这是求解该长度定积分的函数表达式：')
sy.pprint(a)
print('\n估计长度为：')
sy.pprint(b)
def parse(string, env):
'''
Parses a value.
'''
if isinstance(string, bool): # If it is already a boolean, just edit it
return sp.nfloat(int(string))
if isinstance(string, str): # If it is a string, parse it
if '"' in string or '\'' in string:
return string.strip('"').strip(
'\'') # Strip quotes and parse strings
else:
var = env.getval(
string) # If it is a variable, try and get its value
try:
if var:
return var
except ValueError: # Numpy throws this if you try to use if on an array
return var
try:
return sp.Float(string, '') # Make it into a number
except:
return string # Give up
return string # Give up again
def test_nfloat():
from sympy.core.basic import _aresame
from sympy.polys.rootoftools import rootof
x = Symbol("x")
eq = x**(S(4)/3) + 4*x**(S(1)/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(S(1)/3))
assert _aresame(nfloat(eq, exponent=True), x**(4.0/3) + (4.0/3)*x**(1.0/3))
eq = x**(S(4)/3) + 4*x**(x/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(x/3))
big = 12345678901234567890
# specify precision to match value used in nfloat
Float_big = Float(big, 15)
assert _aresame(nfloat(big), Float_big)
assert _aresame(nfloat(big*x), Float_big*x)
assert _aresame(nfloat(x**big, exponent=True), x**Float_big)
assert nfloat({x: sqrt(2)}) == {x: nfloat(sqrt(2))}
assert nfloat({sqrt(2): x}) == {sqrt(2): x}
assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
# issue 6342
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solveset(f.subs(x, -0.139)))
# issue 6632
assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
9.99999999800000e-11
# issue 7122
eq = cos(3*x**4 + y)*rootof(x**5 + 3*x**3 + 1, 0)
assert str(nfloat(eq, exponent=False, n=1)) == '-0.7*cos(3.0*x**4 + y)'
def test_nfloat():
from sympy.core.basic import _aresame
x = Symbol("x")
eq = x**(S(4) / 3) + 4 * x**(S(1) / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(S(1) / 3))
assert _aresame(nfloat(eq, exponent=True),
x**(4.0 / 3) + (4.0 / 3) * x**(1.0 / 3))
eq = x**(S(4) / 3) + 4 * x**(x / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(x / 3))
big = 12345678901234567890
Float_big = Float(big)
assert _aresame(nfloat(x**big, exponent=True), x**Float_big)
assert _aresame(nfloat(big), Float_big)
assert nfloat({x: sqrt(2)}) == {x: nfloat(sqrt(2))}
assert nfloat({sqrt(2): x}) == {sqrt(2): x}
assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
# issues 3243
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solve(f.subs(x, -0.139)))
# issue 3533
assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
9.99999999800000e-11
def test_nfloat():
from sympy.core.basic import _aresame
from sympy.polys.rootoftools import RootOf
x = Symbol("x")
eq = x**(S(4)/3) + 4*x**(S(1)/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(S(1)/3))
assert _aresame(nfloat(eq, exponent=True), x**(4.0/3) + (4.0/3)*x**(1.0/3))
eq = x**(S(4)/3) + 4*x**(x/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(x/3))
big = 12345678901234567890
Float_big = Float(big)
assert _aresame(nfloat(x**big, exponent=True),
x**Float_big)
assert _aresame(nfloat(big), Float_big)
assert nfloat({x: sqrt(2)}) == {x: nfloat(sqrt(2))}
assert nfloat({sqrt(2): x}) == {sqrt(2): x}
assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
# issue 3243
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solve(f.subs(x, -0.139)))
# issue 3533
assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
9.99999999800000e-11
# issue 4023
eq = cos(3*x**4 + y)*RootOf(x**5 + 3*x**3 + 1, 0)
assert str(nfloat(eq, exponent=False, n=1)) == '-0.7*cos(3.0*x**4 + y)'
def test_nfloat():
from sympy.core.basic import _aresame
from sympy.polys.rootoftools import rootof
x = Symbol("x")
eq = x**(S(4) / 3) + 4 * x**(S(1) / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(S(1) / 3))
assert _aresame(nfloat(eq, exponent=True),
x**(4.0 / 3) + (4.0 / 3) * x**(1.0 / 3))
eq = x**(S(4) / 3) + 4 * x**(x / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(x / 3))
big = 12345678901234567890
# specify precision to match value used in nfloat
Float_big = Float(big, 15)
assert _aresame(nfloat(big), Float_big)
assert _aresame(nfloat(big * x), Float_big * x)
assert _aresame(nfloat(x**big, exponent=True), x**Float_big)
assert nfloat({x: sqrt(2)}) == {x: nfloat(sqrt(2))}
assert nfloat({sqrt(2): x}) == {sqrt(2): x}
assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
# issue 6342
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solveset(f.subs(x, -0.139)))
# issue 6632
assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
9.99999999800000e-11
# issue 7122
eq = cos(3 * x**4 + y) * rootof(x**5 + 3 * x**3 + 1, 0)
assert str(nfloat(eq, exponent=False, n=1)) == '-0.7*cos(3.0*x**4 + y)'
def test_nfloat():
from sympy.core.basic import _aresame
from sympy.polys.rootoftools import RootOf
x = Symbol("x")
eq = x**(S(4) / 3) + 4 * x**(S(1) / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(S(1) / 3))
assert _aresame(nfloat(eq, exponent=True),
x**(4.0 / 3) + (4.0 / 3) * x**(1.0 / 3))
eq = x**(S(4) / 3) + 4 * x**(x / 3) / 3
assert _aresame(nfloat(eq), x**(S(4) / 3) + (4.0 / 3) * x**(x / 3))
big = 12345678901234567890
Float_big = Float(big)
assert _aresame(nfloat(x**big, exponent=True), x**Float_big)
assert _aresame(nfloat(big), Float_big)
assert nfloat({x: sqrt(2)}) == {x: nfloat(sqrt(2))}
assert nfloat({sqrt(2): x}) == {sqrt(2): x}
assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
# issue 3243
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solve(f.subs(x, -0.139)))
# issue 3533
assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
9.99999999800000e-11
# issue 4023
eq = cos(3 * x**4 + y) * RootOf(x**5 + 3 * x**3 + 1, 0)
assert str(nfloat(eq, exponent=False, n=1)) == '-0.7*cos(3.0*x**4 + y)'
def test_issue_10395():
eq = x * Max(0, y)
assert nfloat(eq) == eq
eq = x * Max(y, -1.1)
assert nfloat(eq) == eq
assert Max(y, 4).n() == Max(4.0, y)
def test_issue_10395():
eq = x*Max(0, y)
assert nfloat(eq) == eq
eq = x*Max(y, -1.1)
assert nfloat(eq) == eq
assert Max(y, 4).n() == Max(4.0, y)
def test_nfloat():
from sympy.core.basic import _aresame
from sympy.polys.rootoftools import rootof
x = Symbol("x")
eq = x**Rational(4, 3) + 4 * x**(S.One / 3) / 3
assert _aresame(nfloat(eq), x**Rational(4, 3) + (4.0 / 3) * x**(S.One / 3))
assert _aresame(nfloat(eq, exponent=True),
x**(4.0 / 3) + (4.0 / 3) * x**(1.0 / 3))
eq = x**Rational(4, 3) + 4 * x**(x / 3) / 3
assert _aresame(nfloat(eq), x**Rational(4, 3) + (4.0 / 3) * x**(x / 3))
big = 12345678901234567890
# specify precision to match value used in nfloat
Float_big = Float(big, 15)
assert _aresame(nfloat(big), Float_big)
assert _aresame(nfloat(big * x), Float_big * x)
assert _aresame(nfloat(x**big, exponent=True), x**Float_big)
assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
# issue 6342
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solveset(f.subs(x, -0.139)))
# issue 6632
assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
9.99999999800000e-11
# issue 7122
eq = cos(3 * x**4 + y) * rootof(x**5 + 3 * x**3 + 1, 0)
assert str(nfloat(eq, exponent=False, n=1)) == '-0.7*cos(3.0*x**4 + y)'
# issue 10933
for ti in (dict, Dict):
d = ti({S.Half: S.Half})
n = nfloat(d)
assert isinstance(n, ti)
assert _aresame(list(n.items()).pop(), (S.Half, Float(.5)))
for ti in (dict, Dict):
d = ti({S.Half: S.Half})
n = nfloat(d, dkeys=True)
assert isinstance(n, ti)
assert _aresame(list(n.items()).pop(), (Float(.5), Float(.5)))
d = [S.Half]
n = nfloat(d)
assert type(n) is list
assert _aresame(n[0], Float(.5))
assert _aresame(nfloat(Eq(x, S.Half)).rhs, Float(.5))
assert _aresame(nfloat(S(True)), S(True))
assert _aresame(nfloat(Tuple(S.Half))[0], Float(.5))
assert nfloat(Eq((3 - I)**2 / 2 + I, 0)) == S.false
# pass along kwargs
assert nfloat([{S.Half: x}], dkeys=True) == [{Float(0.5): x}]
# Issue 17706
A = MutableMatrix([[1, 2], [3, 4]])
B = MutableMatrix(
[[Float('1.0', precision=53),
Float('2.0', precision=53)],
[Float('3.0', precision=53),
Float('4.0', precision=53)]])
assert _aresame(nfloat(A), B)
A = ImmutableMatrix([[1, 2], [3, 4]])
B = ImmutableMatrix(
[[Float('1.0', precision=53),
Float('2.0', precision=53)],
[Float('3.0', precision=53),
Float('4.0', precision=53)]])
assert _aresame(nfloat(A), B)
def test_nfloat():
from sympy.core.basic import _aresame
x = Symbol("x")
eq = x**(S(4)/3) + 4*x**(S(1)/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(S(1)/3))
assert _aresame(nfloat(eq, exponent=True), x**(4.0/3) + (4.0/3)*x**(1.0/3))
eq = x**(S(4)/3) + 4*x**(x/3)/3
assert _aresame(nfloat(eq), x**(S(4)/3) + (4.0/3)*x**(x/3))
big = 12345678901234567890
Float_big = Float(big)
assert _aresame(nfloat(x**big, exponent=True),
x**Float_big)
assert _aresame(nfloat(big), Float_big)
assert nfloat({x: sqrt(2)}) == {x: nfloat(sqrt(2))}
assert nfloat({sqrt(2): x}) == {sqrt(2): x}
assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2)))
# issues 3243
f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4')
assert not any(a.free_symbols for a in solve(f.subs(x, -0.139)))
# issue 3533
assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \
9.99999999800000e-11