def get_freestream(circle_center, r, vel, aoa):
aoa = sp.rad(aoa)
zeta = sp.symbols('zeta', real=False)
function1 = vel * zeta * (sp.cos(aoa) - 1j * sp.sin(aoa))
function2 = vel * (r**2 / (zeta - circle_center)) * (sp.cos(aoa) +
1j * sp.sin(aoa))
return function1 + function2
def rotation_matrix(theta: int,
axis='z',
unit: str = 'rad',
numpy: bool = False):
"""
Create a z-axis rotation matrix given an angle.
Parameters
----------
theta : int
Rotation about the z-axis
axis : {'x', 'y', 'z'}
Axis of rotation
unit : {'rad', 'deg'}, optional
Radians or degrees. By default 'rad'.
numpy : bool, optional
If True, return a Numpy array, otherwise return a sympy matrix.
By default False.
Returns
-------
{np.array, sp.Matrix}
If `numpy` is True, will return rotation matrix as np.array. Otherwise,
will return a sp.Matrix.
"""
sin = sp.sin
cos = sp.cos
if unit == 'deg':
theta = sp.rad(theta)
R = sp.Matrix([[sp.cos(theta), -sp.sin(theta), 0],
[sp.sin(theta), sp.cos(theta), 0], [0, 0, 1]])
return sp.matrix2numpy(R, dtype='float32') if numpy else R
def apply_grad_cartesian_tensor(grad_X, zmat_dist):
"""Apply the gradient for transformation to cartesian space onto zmat_dist.
Args:
grad_X (:class:`numpy.ndarray`): A ``(3, n, n, 3)`` array.
The mathematical details of the index layout is explained in
:meth:`~chemcoord.Cartesian.get_grad_zmat()`.
zmat_dist (:class:`~chemcoord.Zmat`):
Distortions in Zmatrix space.
Returns:
:class:`~chemcoord.Cartesian`: Distortions in cartesian space.
"""
columns = ['bond', 'angle', 'dihedral']
C_dist = zmat_dist.loc[:, columns].values.T
try:
C_dist = C_dist.astype('f8')
C_dist[[1, 2], :] = np.radians(C_dist[[1, 2], :])
except (TypeError, AttributeError):
C_dist[[1, 2], :] = sympy.rad(C_dist[[1, 2], :])
cart_dist = np.tensordot(grad_X, C_dist, axes=([3, 2], [0, 1])).T
from chemcoord.cartesian_coordinates.cartesian_class_main import Cartesian
return Cartesian(atoms=zmat_dist['atom'],
coords=cart_dist,
index=zmat_dist.index)
def __init__(self, vel, aoa): # initially create freestream
self.vel, self.aoa = vel, sp.rad(
aoa) # create variables, aoa is converted into radians
self.z = sp.symbols('z', real=False) # create z complex number
self.x, self.y = sp.symbols(
'x, y', real=True
) # create x,y variables. real and imaginery parts of the z
def getConfigurationMatrixCart(self):
angle = sp.rad(self.angleCart)
M = sp.Matrix([[sp.cos(angle), -sp.sin(angle), 0,
sp.N(self.x)],
[sp.sin(angle),
sp.cos(angle), 0,
sp.N(self.y)], [0, 0, 1, self.offset], [0, 0, 0, 1]])
print("caa cart>>", M)
return M
def convertToRadians(expr):
newExpr = None
if trigUnit == TrigUnit.Degrees:
newExpr = sympy.rad(expr)
elif trigUnit == TrigUnit.Gradients:
newExpr = expr * sympy.pi / 200
else:
newExpr = expr
return newExpr
def __updateDistanceRos__(self, xName, yName, angle, distance, timePerRev):
#now = time()
#future = now+distance/157*timePerRev
#print( "update: now, future", now, future )
#cutoff = now
#while now-cutoff < future-cutoff:
# print( now-cutoff, future-cutoff, now-cutoff < future-cutoff )
# setattr( self, xName, sp.N( sp.cos( sp.rad(angle))* (now-cutoff)/(future-cutoff)*distance) )
# setattr( self, yName, sp.N( sp.sin( sp.rad(angle))* (now-cutoff)/(future-cutoff)*distance) )
# print( "getAttr", getattr( self, xName ) )
# print( "getAttr", getattr( self, yName ) )
# print( "------>", sp.N( sp.cos( sp.rad(angle))* (now-cutoff)/(future-cutoff)*distance) )
# print( "------>", sp.N( sp.sin( sp.rad(angle))* (now-cutoff)/(future-cutoff)*distance) )
# rclpy.sleep(0.1)
# now = time()
setattr(self, xName, sp.N(sp.cos(sp.rad(angle)) * distance))
setattr(self, yName, sp.N(sp.sin(sp.rad(angle)) * distance))
def grad_V(values=None, get_calculated=False,
calculated=[]): # pylint:disable=dangerous-default-value
if get_calculated:
return calculated
elif values is not None:
substitutions = list(zip(symbolic_expressions, values))
new_zmat = zmolecule.subs(substitutions)
if isfile(input_path(len(calculated))):
result = {}
while len(result.keys()) < 3:
try:
result = molcas.parse_output(output_path(len(calculated)))
except FileNotFoundError:
pass
sleep(0.5)
else:
result = molcas.calculate(
molecule=new_zmat, forces=True,
el_calc_input=input_path(len(calculated)),
start_orb=start_orb_path(len(calculated) - 1) if calculated else start_orb,
hamiltonian=hamiltonian, basis=basis,
charge=charge, title=title,
multiplicity=multiplicity,
num_procs=num_procs, mem_per_proc=mem_per_proc, **kwargs)
energy, grad_energy_X = result['energy'], result['gradient']
grad_energy_C = _get_grad_energy_C(new_zmat, grad_energy_X)
zm_values_rad = zmolecule.loc[:, value_cols].values
zm_values_rad[:, [1, 2]] = sympy.rad(zm_values_rad[:, [1, 2]])
energy_symb = np.sum(zm_values_rad * grad_energy_C)
grad_energy_symb = sympy.Matrix([
energy_symb.diff(arg) for arg in symbolic_expressions])
grad_energy_symb = np.array(grad_energy_symb.subs(substitutions))
grad_energy_symb = grad_energy_symb.astype('f8').flatten()
new_zmat.metadata['energy'] = energy
new_zmat.metadata['symbols'] = substitutions
calculated.append({'energy': energy, 'structure': new_zmat,
'symbols': substitutions})
with open(md_out, 'a') as f:
f.write(_get_table_row(calculated, grad_energy_symb))
if is_converged(calculated, etol=etol):
raise ConvergenceFinished(successful=True)
elif len(calculated) >= max_iter:
raise ConvergenceFinished(successful=False)
return grad_energy_symb
else:
raise ValueError
def new_vortex_position(trailing_edge, center, angle, distance, a):
"""
:param center: center of airfoil
:param a: joukowski parameter
:param trailing_edge: current trailing edge of the airfoil
:param angle: vortex position angle
:param distance: vortex position distance relative to the chord length
:return: z coordinate zeta coordinate
"""
z = trailing_edge + distance * sp.exp(-1j * sp.rad(angle)).evalf()
zeta = mapzeta(z, a)
zeta = check_in_zeta(zeta, center, a)
return [z, zeta]
def pxpzhat0_values(self, contour_values_: Union[List[float],
Tuple[float]],
sub_: Dict) -> List[Tuple[float, float]]:
r"""Generate initial values for :math:`\hat{p}_x`, :math:`\hat{p}_z`."""
pxpzhat_values_ = [(float(0), float(0))] * len(contour_values_)
for i_, Ci_ in enumerate(contour_values_):
tmp_sub_ = omitdict(sub_, [rxhat, Ci])
tmp_sub_[Ci] = rad(Ci_)
# pzhat for pxhat=1 which is true when rxhat=0
pzhat_ = self.pzhat_lambda(tmp_sub_, 0, 1).n()
eqn_ = self.pxhatsqrd_Ci_polylike_eqn(tmp_sub_, pzhat_)
x_ = float(self.pxhat_Ci_soln(eqn_, tmp_sub_, rxhat.subs(sub_)))
y_ = float(self.pzhat_lambda(tmp_sub_, 0, 1).n())
pxpzhat_values_[i_] = (x_, y_)
return pxpzhat_values_
def __updateAngleRos__(self, angleName, angle, maxAngle, timePerRev):
"""
Continuously updates the angles s.t. ros can turn the coordinate
systems in real time.
"""
#now = time()
#future = now+angle/maxAngle*timePerRev
#cutoff = now
#while now-cutoff < future-cutoff:
# #print( now-cutoff, future-cutoff, now-cutoff < future-cutoff )
# setattr( self, angleName, sp.N(sp.rad(sp.N((now-cutoff)/(future-cutoff)*angle)) ) )
# #print( "getAttr", getattr( self, angleName ) )
# #print( "------>", sp.N(sp.rad(sp.N((now-cutoff)/(future-cutoff)*angle)) ))
# rclpy.sleep(0.1)
# now = time()
setattr(self, angleName, sp.N(sp.rad(angle)))
for i in range(len(vortex_velocity)):
new_x = x_vortex_z[i] + float(sp.re(vortex_velocity[i])) * t_step
new_y = y_vortex_z[i] - float(sp.im(vortex_velocity[i])) * t_step
x_vortex_z[i] = float(new_x)
y_vortex_z[i] = float(new_y)
zeta1_temp, zeta2_temp = joukowiski.maptozeta(new_x, new_y, a)
x_vortex_zeta[i] = float(sp.re(zeta1_temp))
y_vortex_zeta[i] = float(sp.im(zeta1_temp))
##################
distance = 0.015
theta = 0
x1_z, y1_z = 2 * a + distance * sp.cos(
sp.rad(theta)).evalf(), distance * sp.sin(sp.rad(theta)).evalf()
zeta1, zeta2 = joukowiski.maptozeta(x1_z, y1_z, a)
vortex_center = zeta1 # vortex center coordinates
x_vortex_zeta.append(float(sp.re(zeta1)))
y_vortex_zeta.append(float(sp.im(zeta1)))
x_vortex_z.append(float(x1_z))
y_vortex_z.append(float(y1_z))
'''
vortex_center = 0
x1_z, y1_z = 0.0, 0.0
if len(x_vortex_z) == 0:
distance = 2*a*0.015
theta = 2 # degrees
def __init__(self, vel, aoa):
self.vel, self.aoa = vel, sp.rad(aoa)
self.z = sp.symbols('z', real = False)
self.x, self.y = sp.symbols('x, y', real = True)
import function_file as ff # -------------- parameters ------------------ # # -------------------------------------------- # plunging parameters pl_amplitude = 0 pl_frequency = 0 # joukowski paramters center = -0.2 + 1j * 0.2 joukowski_parameter = 2 radius = np.sqrt(center.imag**2 + (joukowski_parameter - center.real)**2) velocity = 5.0 aoa = 2.0 # degree aoa = sp.rad(aoa).evalf() # time time_step = 0.05 current_time = 0.00 iteration = 5 # new vortex distance = 0.015 # portion of the chord length angle = 0 # degrees # data store circulation = [] vortex_strength = [] vortex_z = [] vortex_zeta = []
import sympy as sp
import sympy_helpers as sph
from argparse import ArgumentParser
import os
import codegen
R_W_IMU = sp.rot_axis1(sp.rad(-90)) * sp.rot_axis3(sp.rad(-90))
R_W_ACC = sp.rot_axis1(sp.rad(90)) * sp.rot_axis3(sp.rad(-90))
v_IMU = sp.MatrixSymbol("v_IMU", 3, 1)
v_ACC = sp.MatrixSymbol("v_ACC", 3, 1)
v_W = sp.MatrixSymbol("v_W", 3, 1)
def main(args):
exprs = {"IMU_to_W": [sp.Eq(v_W, R_W_IMU * v_IMU)],
"ACC_to_W": [sp.Eq(v_W, R_W_ACC * v_ACC)],
"W_to_IMU": [sp.Eq(v_IMU, R_W_IMU.T * v_W)],
"W_to_ACC": [sp.Eq(v_ACC, R_W_ACC.T * v_W)]}
out = codegen.gen_code(exprs, args.prefix, "trans")
os.makedirs(args.out_dir, exist_ok=True)
for fid in out:
path = os.path.join(args.out_dir, fid[0])
with open(path, "w") as f:
f.write(fid[1])
if __name__ == "__main__":
parser = ArgumentParser()
parser.add_argument("--outdir", dest="out_dir", type=str,
import intelligent_robotics as ir
import sympy
sympy.init_printing()
theta1,theta2 = ir.dynamicsymbols('theta1,theta2')
l1,l1g,l2,l2g,IG1,IG2,m1,m2 = sympy.symbols('l1,l1g,l2,l2g,IG1,IG2,m1,m2')
"""#### DH Parameter
"""
T01 = ir.DH(0,0,l1,theta1)
T12 = ir.DH(0,-sympy.rad(90),0,theta2)
T23 = ir.DH(l2,sympy.rad(90),0,0)
T01, T12, T23
w_0_0 = sympy.Matrix([[0],[0],[0]])
w_1_1 = ir.get_angular_vel_R(T01,w_0_0,theta1.diff())
w_2_2 = ir.get_angular_vel_R(T12,w_1_1,theta2.diff())
w_3_3 = ir.get_angular_vel_R(T23,w_2_2,0)
w_1_1,w_2_2,w_3_3
v_0_0 = sympy.Matrix([[0],[0],[0]])
v_1_1 = ir.get_linear_vel_R(T01,w_0_0,v_0_0)
v_2_2 = ir.get_linear_vel_R(T12,w_1_1,v_1_1)
sp.I # Unidad imaginaria
# Potencias y raices
sp.Pow(x, potencia) # Calcular la potencia n-esima
sp.sqrt(num) # Calcular la raiz cuadrada
sp.cbrt(num) # Calcular la raiz cubica
sp.Pow(x, sp.Rational(1, n)) # Calcular la raiz n-esima
# Exponentes y logaritmos
sp.exp(num) # Calcular la exponencial
sp.log(num) # Calcular el logaritmo natural
sp.log(base, num) # Calcular el logaritmo en la base especificada
# Conversión de angulos
sp.deg(num) # Convertir ángulos de radianes a grados.
sp.rad(num) # Convertir ángulos de grados a radianes.
# Funciones para trigonometría (Angulos en radianes)
sp.sin(num) # Seno
sp.cos(num) # Coseno
sp.tan(num) # tangente
sp.cot(num) # cotangente
sp.sec(num) # secante
sp.csc(num) # cosecante
sp.asin(num) # Arcoseno
sp.acos(num) # Arcocoseno
sp.atan(num) # Arcotangente
sp.atan2(catetoY,
catetoX) # Arcotangente de un triangulo segun los catetos (Angulo)
sp.acot(num) # Arcocotangente
sp.asec(num) # Arcosecante
print(vx, vy)
x0_f, y0_f = 0, 0
x1_f, y1_f = 0, 0
center = Particle((0, 0), 1)
p0 = Particle((x_0, y_0), 3)
p1 = Particle((x_1, y_1), 3)
a = Vec2d(0, 0)
b = Vec2d(0, 0)
v = Vec2d(vx, vy)
print(a, b, v)
p0.speed = v.get_length()
p0.angle = rad(v.get_angle() + 90)
p1.speed = 0
p1.angle = 0
print(p0.angle)
font = pygame.font.Font(None, 32)
clock = pygame.time.Clock()
radius = 30.75 * 2
running = True
moving = False
collide = False
t = 1
while running:
clock.tick(1)
def test_issue_7263():
assert abs((simplify(30.8**2 - 82.5**2 * sin(rad(11.6))**2)).evalf() - \
673.447451402970) < 1e-12
def dx(self):
return cos(rad(self.rotation))
def dy(self):
return sin(rad(self.rotation))
#taking all values for incident angle
all_values = np.linspace(0.00001, 90.0, 100)
#***************************************************Normal Graph [ delta vs i ] *****************************************************
# ------------------------------------------------Delta vs incident angle ( in varying mu )---------------------------------------------------------
# for mu =1.5 & A = 60
y_list = []
x_list = []
for v in all_values:
try:
#only possible values should be taken
y_list.append(
float(f.evalf(subs={
i: sp.rad(v),
A: sp.rad(60),
mu: 1.5
})))
x_list.append(v)
except:
pass
# for mu =1.33 & A = 60
y1_list = []
x1_list = []
for v in all_values:
try:
y1_list.append(
float(f.evalf(subs={
i: sp.rad(v),
def test_issue_7263():
assert abs((simplify(30.8**2 - 82.5**2 * sin(rad(11.6))**2)).evalf() - \
673.447451402970) < 1e-12
def rotate_vector(self, theta, deg: bool = False):
# def rotate_vector(self, theta: Union[int, float], deg: bool = False):
if deg:
theta = rad(theta)
self.vector = self.rotation_matrix.subs(self.t, theta) * self.vector