def _contains(self, other): from sympy.functions import arg, Abs from sympy.core.containers import Tuple other = sympify(other) isTuple = isinstance(other, Tuple) if isTuple and len(other) != 2: raise ValueError('expecting Tuple of length 2') # If the other is not an Expression, and neither a Tuple if not isinstance(other, Expr) and not isinstance(other, Tuple): return S.false # self in rectangular form if not self.polar: re, im = other if isTuple else other.as_real_imag() for element in self.psets: if And(element.args[0]._contains(re), element.args[1]._contains(im)): return True return False # self in polar form elif self.polar: if isTuple: r, theta = other elif other.is_zero: r, theta = S.Zero, S.Zero else: r, theta = Abs(other), arg(other) for element in self.psets: if And(element.args[0]._contains(r), element.args[1]._contains(theta)): return True return False
def _contains(self, other): from sympy.functions import arg, Abs other = sympify(other) isTuple = isinstance(other, Tuple) if isTuple and len(other) != 2: raise ValueError('expecting Tuple of length 2') # If the other is not an Expression, and neither a Tuple if not isinstance(other, (Expr, Tuple)): return S.false # self in rectangular form if not self.polar: re, im = other if isTuple else other.as_real_imag() return fuzzy_or(fuzzy_and([ pset.args[0]._contains(re), pset.args[1]._contains(im)]) for pset in self.psets) # self in polar form elif self.polar: if other.is_zero: # ignore undefined complex argument return fuzzy_or(pset.args[0]._contains(S.Zero) for pset in self.psets) if isTuple: r, theta = other else: r, theta = Abs(other), arg(other) if theta.is_real and theta.is_number: # angles in psets are normalized to [0, 2pi) theta %= 2*S.Pi return fuzzy_or(fuzzy_and([ pset.args[0]._contains(r), pset.args[1]._contains(theta)]) for pset in self.psets)
def computeSpinWeightCoeff(self,l): fname="Lebedev/lebedev_" +"{:03d}".format(self.qprec)+".txt" lebedev_theata=[] lebedev_phi=[] lebedev_w=[] # read lebedev points with open(fname,'r') as f: for row in f: row=row.strip().split() lebedev_theata.append(float(row[0])) lebedev_phi.append(float(row[1])) lebedev_w.append(float(row[2])) #print(lebedev_w) numQuadPts=len(lebedev_theata); #print(numQuadPts) cReal=[] cImg=[] cArg=[] for m in range(-l,l+1): self.psi4_lm=0 for q in range(0,numQuadPts): self.psi4_lm=self.psi4_lm + self.psi4_s2*lebedev_w[q]*self.swsh(self.spin,l,m,lebedev_theata[q],lebedev_phi[q]) cReal.append(re(self.psi4_lm)) cImg.append(im(self.psi4_lm)) cArg.append(arg(self.psi4_lm)) return [cReal,cImg,cArg]
def test_Function(): assert mcode(sin(x) ** cos(x)) == "sin(x).^cos(x)" assert mcode(abs(x)) == "abs(x)" assert mcode(ceiling(x)) == "ceil(x)" assert mcode(arg(x)) == "angle(x)" assert mcode(im(x)) == "imag(x)" assert mcode(re(x)) == "real(x)" assert mcode(Max(x, y) + Min(x, y)) == "max(x, y) + min(x, y)" assert mcode(Max(x, y, z)) == "max(x, max(y, z))" assert mcode(Min(x, y, z)) == "min(x, min(y, z))"
def test_Function(): assert mcode(sin(x)**cos(x)) == "sin(x).^cos(x)" assert mcode(abs(x)) == "abs(x)" assert mcode(ceiling(x)) == "ceil(x)" assert mcode(arg(x)) == "angle(x)" assert mcode(im(x)) == "imag(x)" assert mcode(re(x)) == "real(x)" assert mcode(Max(x, y) + Min(x, y)) == "max(x, y) + min(x, y)" assert mcode(Max(x, y, z)) == "max(x, max(y, z))" assert mcode(Min(x, y, z)) == "min(x, min(y, z))"
def _invert_complex(f, g_ys, symbol): """ Helper function for invert_complex """ if not f.has(symbol): raise ValueError("Inverse of constant function doesn't exist") if f is symbol: return (f, g_ys) n = Dummy('n') if f.is_Add: # f = g + h g, h = f.as_independent(symbol) if g != S.Zero: return _invert_complex(h, imageset(Lambda(n, n - g), g_ys), symbol) if f.is_Mul: # f = g*h g, h = f.as_independent(symbol) if g != S.One: return _invert_complex(h, imageset(Lambda(n, n / g), g_ys), symbol) if hasattr(f, 'inverse') and \ not isinstance(f, TrigonometricFunction) and \ not isinstance(f, exp): if len(f.args) > 1: raise ValueError("Only functions with one argument are supported.") return _invert_complex(f.args[0], imageset(Lambda(n, f.inverse()(n)), g_ys), symbol) if isinstance(f, exp): if isinstance(g_ys, FiniteSet): exp_invs = Union(*[ imageset( Lambda(n, I * (2 * n * pi + arg(g_y)) + log(Abs(g_y))), S.Integers) for g_y in g_ys if g_y != 0 ]) return _invert_complex(f.args[0], exp_invs, symbol) return (f, g_ys)
def _contains(self, other): from sympy.functions import arg, Abs # self in rectangular form if not self.polar: re, im = other.as_real_imag() for element in self.psets: if And(element.args[0]._contains(re), element.args[1]._contains(im)): return True return False # self in polar form elif self.polar: if S(other).is_zero: r, theta = S(0), S(0) else: r, theta = Abs(other), arg(other) for element in self.psets: if And(element.args[0]._contains(r), element.args[1]._contains(theta)): return True return False
def test_Function_change_name(): assert mcode(abs(x)) == "abs(x)" assert mcode(ceiling(x)) == "ceil(x)" assert mcode(arg(x)) == "angle(x)" assert mcode(im(x)) == "imag(x)" assert mcode(re(x)) == "real(x)" assert mcode(conjugate(x)) == "conj(x)" assert mcode(chebyshevt(y, x)) == "chebyshevT(y, x)" assert mcode(chebyshevu(y, x)) == "chebyshevU(y, x)" assert mcode(laguerre(x, y)) == "laguerreL(x, y)" assert mcode(Chi(x)) == "coshint(x)" assert mcode(Shi(x)) == "sinhint(x)" assert mcode(Ci(x)) == "cosint(x)" assert mcode(Si(x)) == "sinint(x)" assert mcode(li(x)) == "logint(x)" assert mcode(loggamma(x)) == "gammaln(x)" assert mcode(polygamma(x, y)) == "psi(x, y)" assert mcode(RisingFactorial(x, y)) == "pochhammer(x, y)" assert mcode(DiracDelta(x)) == "dirac(x)" assert mcode(DiracDelta(x, 3)) == "dirac(3, x)" assert mcode(Heaviside(x)) == "heaviside(x)" assert mcode(Heaviside(x, y)) == "heaviside(x, y)"
def _invert_complex(f, g_ys, symbol): """ Helper function for invert_complex """ if not f.has(symbol): raise ValueError("Inverse of constant function doesn't exist") if f is symbol: return (f, g_ys) n = Dummy('n') if f.is_Add: # f = g + h g, h = f.as_independent(symbol) if g != S.Zero: return _invert_complex(h, imageset(Lambda(n, n - g), g_ys), symbol) if f.is_Mul: # f = g*h g, h = f.as_independent(symbol) if g != S.One: return _invert_complex(h, imageset(Lambda(n, n/g), g_ys), symbol) if hasattr(f, 'inverse') and \ not isinstance(f, C.TrigonometricFunction) and \ not isinstance(f, exp): if len(f.args) > 1: raise ValueError("Only functions with one argument are supported.") return _invert_complex(f.args[0], imageset(Lambda(n, f.inverse()(n)), g_ys), symbol) if isinstance(f, exp): if isinstance(g_ys, FiniteSet): exp_invs = Union(*[imageset(Lambda(n, I*(2*n*pi + arg(g_y)) + log(Abs(g_y))), S.Integers) for g_y in g_ys]) return _invert_complex(f.args[0], exp_invs, symbol) return (f, g_ys)
def _invert_complex(f, g_ys, symbol): """Helper function for _invert.""" if f == symbol: return (f, g_ys) n = Dummy("n") if f.is_Add: # f = g + h g, h = f.as_independent(symbol) if g is not S.Zero: return _invert_complex(h, imageset(Lambda(n, n - g), g_ys), symbol) if f.is_Mul: # f = g*h g, h = f.as_independent(symbol) if g is not S.One: return _invert_complex(h, imageset(Lambda(n, n / g), g_ys), symbol) if hasattr(f, "inverse") and not isinstance(f, TrigonometricFunction) and not isinstance(f, exp): if len(f.args) > 1: raise ValueError("Only functions with one argument are supported.") return _invert_complex(f.args[0], imageset(Lambda(n, f.inverse()(n)), g_ys), symbol) if isinstance(f, exp): if isinstance(g_ys, FiniteSet): exp_invs = Union( *[ imageset(Lambda(n, I * (2 * n * pi + arg(g_y)) + log(Abs(g_y))), S.Integers) for g_y in g_ys if g_y != 0 ] ) return _invert_complex(f.args[0], exp_invs, symbol) return (f, g_ys)
def _contains(self, other): from sympy.functions import arg, Abs # self in rectangular form if not self.polar: re, im = other.as_real_imag() for element in self.psets: if And(element.args[0]._contains(re), element.args[1]._contains(im)): return True return False # self in polar form elif self.polar: if sympify(other).is_zero: r, theta = S.Zero, S.Zero else: r, theta = Abs(other), arg(other) for element in self.psets: if And(element.args[0]._contains(r), element.args[1]._contains(theta)): return True return False
def bode_phase_numerical_data(system, initial_exp=-5, final_exp=5, **kwargs): """ Returns the numerical data of the Bode phase plot of the system. It is internally used by ``bode_phase_plot`` to get the data for plotting Bode phase plot. Users can use this data to further analyse the dynamics of the system or plot using a different backend/plotting-module. Parameters ========== system : SISOLinearTimeInvariant The system for which the Bode phase plot data is to be computed. initial_exp : Number, optional The initial exponent of 10 of the semilog plot. Defaults to -5. final_exp : Number, optional The final exponent of 10 of the semilog plot. Defaults to 5. Returns ======= tuple : (x, y) x = x-axis values of the Bode phase plot. y = y-axis values of the Bode phase plot. Raises ====== NotImplementedError When a SISO LTI system is not passed. When time delay terms are present in the system. ValueError When more than one free symbol is present in the system. The only variable in the transfer function should be the variable of the Laplace transform. Examples ======== >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import bode_phase_numerical_data >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s) >>> bode_phase_numerical_data(tf1) # doctest: +SKIP ([1e-05, 1.4472354033813751e-05, 2.035581932165858e-05,..., 47577.3248186011, 67884.09326036123, 100000.0], [-2.5000000000291665e-05, -3.6180885085e-05, -5.08895483066e-05,...,-3.1415085799262523, -3.14155265358979]) See Also ======== bode_magnitude_plot, bode_phase_numerical_data """ _check_system(system) expr = system.to_expr() _w = Dummy("w", real=True) w_expr = expr.subs({system.var: I * _w}) phase = arg(w_expr) return LineOver1DRangeSeries(phase, (_w, 10**initial_exp, 10**final_exp), xscale='log', **kwargs).get_points()
def test_torch_complexes(): assert torch_code(re(x)) == "torch.real(x)" assert torch_code(im(x)) == "torch.imag(x)" assert torch_code(arg(x)) == "torch.angle(x)"
def bode_phase_numerical_data(system, initial_exp=-5, final_exp=5, freq_unit='rad/sec', phase_unit='rad', **kwargs): """ Returns the numerical data of the Bode phase plot of the system. It is internally used by ``bode_phase_plot`` to get the data for plotting Bode phase plot. Users can use this data to further analyse the dynamics of the system or plot using a different backend/plotting-module. Parameters ========== system : SISOLinearTimeInvariant The system for which the Bode phase plot data is to be computed. initial_exp : Number, optional The initial exponent of 10 of the semilog plot. Defaults to -5. final_exp : Number, optional The final exponent of 10 of the semilog plot. Defaults to 5. freq_unit : string, optional User can choose between ``'rad/sec'`` (radians/second) and '``'Hz'`` (Hertz) as frequency units. phase_unit : string, optional User can choose between ``'rad'`` (radians) and ``'deg'`` (degree) as phase units. Returns ======= tuple : (x, y) x = x-axis values of the Bode phase plot. y = y-axis values of the Bode phase plot. Raises ====== NotImplementedError When a SISO LTI system is not passed. When time delay terms are present in the system. ValueError When more than one free symbol is present in the system. The only variable in the transfer function should be the variable of the Laplace transform. When incorrect frequency or phase units are given as input. Examples ======== >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import bode_phase_numerical_data >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s) >>> bode_phase_numerical_data(tf1) # doctest: +SKIP ([1e-05, 1.4472354033813751e-05, 2.035581932165858e-05,..., 47577.3248186011, 67884.09326036123, 100000.0], [-2.5000000000291665e-05, -3.6180885085e-05, -5.08895483066e-05,...,-3.1415085799262523, -3.14155265358979]) See Also ======== bode_magnitude_plot, bode_phase_numerical_data """ _check_system(system) expr = system.to_expr() freq_units = ('rad/sec', 'Hz') phase_units = ('rad', 'deg') if freq_unit not in freq_units: raise ValueError( 'Only "rad/sec" and "Hz" are accepted frequency units.') if phase_unit not in phase_units: raise ValueError('Only "rad" and "deg" are accepted phase units.') _w = Dummy("w", real=True) if freq_unit == 'Hz': repl = I * _w * 2 * pi else: repl = I * _w w_expr = expr.subs({system.var: repl}) if phase_unit == 'deg': phase = arg(w_expr) * 180 / pi else: phase = arg(w_expr) x, y = LineOver1DRangeSeries(phase, (_w, 10**initial_exp, 10**final_exp), xscale='log', **kwargs).get_points() return x, y
def test_tensorflow_complexes(): assert tensorflow_code(re(x)) == "tensorflow.math.real(x)" assert tensorflow_code(im(x)) == "tensorflow.math.imag(x)" assert tensorflow_code(arg(x)) == "tensorflow.math.angle(x)"