def calcIdealAngles2 (desiredh, chi, phi, UBmatrix, wavelength, stars):
"Calculates the twotheta, theta, and omega values for a desired h vector. Uses chi and phi from calcScatteringPlane."
#Accepts the desired h vector, chi, phi, the UB matrix, the wavelength, and the stars dictionary
desiredhp = np.dot(UBmatrix, desiredh)
#Old code (scipy.optimize.fsolve) produced inaccurate results with far-off estimates
#solutions = scipy.optimize.fsolve(equations, x0, args=(h1p, h2p, wavelength))
q = calcq (desiredh[0], desiredh[1], desiredh[2], stars)
twotheta = 2.0 * np.arcsin(wavelength * q / 4.0 / np.pi)
x0 = [0.0]
p = NLSP(secondequations, x0, args=(desiredhp, chi, phi, wavelength, twotheta))
r = p.solve('nlp:ralg')
omega = r.xf[0]
theta = twotheta/2.0 + omega # ------ ALTERNATE SOLUTION FOR THETA ------
#theta = r.xf[1] # ------ SOLVER POTENTIALLY INACCURATE FOR THETA ------
solutions = [twotheta, theta, omega]
return np.degrees(solutions) #% 360
def calcIdealAngles2(desiredh, chi, phi, UBmatrix, wavelength, stars):
"Calculates the twotheta, theta, and omega values for a desired h vector. Uses chi and phi from calcScatteringPlane."
#Accepts the desired h vector, chi, phi, the UB matrix, the wavelength, and the stars dictionary
desiredhp = np.dot(UBmatrix, desiredh)
#Old code (scipy.optimize.fsolve) produced inaccurate results with far-off estimates
#solutions = scipy.optimize.fsolve(equations, x0, args=(h1p, h2p, wavelength))
q = calcq(desiredh[0], desiredh[1], desiredh[2], stars)
twotheta = 2.0 * np.arcsin(wavelength * q / 4.0 / np.pi)
x0 = [0.0]
p = NLSP(secondequations,
x0,
args=(desiredhp, chi, phi, wavelength, twotheta))
r = p.solve('nlp:ralg')
omega = r.xf[0]
theta = twotheta / 2.0 + omega # ------ ALTERNATE SOLUTION FOR THETA ------
#theta = r.xf[1] # ------ SOLVER POTENTIALLY INACCURATE FOR THETA ------
solutions = [twotheta, theta, omega]
return np.degrees(solutions) #% 360
def calcRefineUB(observations, wavelength):
#observations are an array of dictionaries for each observed reflection
hvectors = []
Uv = []
for i in range(0, len(observations)):
h = [observations[i]['h'], observations[i]['k'], observations[i]['l']]
hvectors.append(h)
'''
sys.stderr.write('i %3.4f \n'%(observations[i]['h'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['k'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['l'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['twotheta'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['theta'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['chi'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['phi'],))
'''
theta = np.radians(observations[i]['theta'])
chi = np.radians(observations[i]['chi'])
phi = np.radians(observations[i]['phi'])
twotheta = np.radians(observations[i]['twotheta'])
omega = theta - twotheta / 2.0
u1p = np.cos(omega) * np.cos(chi) * np.cos(phi) - np.sin(
omega) * np.sin(phi)
u2p = np.cos(omega) * np.cos(chi) * np.sin(phi) + np.sin(
omega) * np.cos(phi)
u3p = np.cos(omega) * np.sin(chi)
uv1p = 2.0 * np.sin(twotheta / 2) / wavelength * u1p
uv2p = 2.0 * np.sin(twotheta / 2) / wavelength * u2p
uv3p = 2.0 * np.sin(twotheta / 2) / wavelength * u3p
Uv.append(uv1p)
Uv.append(uv2p)
Uv.append(uv3p)
x0 = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
p = NLSP(UBRefinementEquations, x0, args=(hvectors, Uv))
r = p.solve('nlp:ralg')
a = r.xf[0]
b = r.xf[1]
c = r.xf[2]
d = r.xf[3]
e = r.xf[4]
f = r.xf[5]
g = r.xf[6]
h = r.xf[7]
j = r.xf[8]
UB = [[a, b, c], [d, e, f], [g, h, j]]
return UB
def calcRefineUB(observations, wavelength):
#observations are an array of dictionaries for each observed reflection
hvectors = []
Uv = []
for i in range(0, len(observations)):
h = [observations[i]['h'], observations[i]['k'], observations[i]['l']]
hvectors.append(h)
'''
sys.stderr.write('i %3.4f \n'%(observations[i]['h'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['k'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['l'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['twotheta'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['theta'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['chi'],))
sys.stderr.write('i %3.4f \n'%(observations[i]['phi'],))
'''
theta = np.radians(observations[i]['theta'])
chi = np.radians(observations[i]['chi'])
phi = np.radians(observations[i]['phi'])
twotheta = np.radians(observations[i]['twotheta'])
omega = theta - twotheta/2.0
u1p = np.cos(omega)*np.cos(chi)*np.cos(phi) - np.sin(omega)*np.sin(phi)
u2p = np.cos(omega)*np.cos(chi)*np.sin(phi) + np.sin(omega)*np.cos(phi)
u3p = np.cos(omega)*np.sin(chi)
uv1p = 2.0*np.sin(twotheta/2) / wavelength * u1p
uv2p = 2.0*np.sin(twotheta/2) / wavelength * u2p
uv3p = 2.0*np.sin(twotheta/2) / wavelength * u3p
Uv.append(uv1p)
Uv.append(uv2p)
Uv.append(uv3p)
x0 = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
p = NLSP(UBRefinementEquations, x0, args=(hvectors, Uv))
r = p.solve('nlp:ralg')
a = r.xf[0]
b = r.xf[1]
c = r.xf[2]
d = r.xf[3]
e = r.xf[4]
f = r.xf[5]
g = r.xf[6]
h = r.xf[7]
j = r.xf[8]
UB = [[a, b, c], [d, e, f], [g, h, j]]
return UB
def test(complexity=0, **kwargs):
f = lambda x: (x[0]**3 + x[1]**3 - 9, x[0] - 0.5 * x[1], cos(x[2]) + x[0] -
1.5)
#optional: gradient
def df(x):
df = zeros((3, 3))
df[0, 0] = 3 * x[0]**2
df[0, 1] = 3 * x[1]**2
df[1, 0] = 1
df[1, 1] = -0.5
df[2, 0] = 1
df[2, 2] = -sin(x[2])
return df
x0 = [8, 15, 80]
#w/o gradient:
#p = NLSP(f, x0)
p = NLSP(f, x0, df=df, maxFunEvals=1e5, iprint=-1, ftol=1e-6, contol=1e-35)
p.lb = [-inf, -inf, 150]
p.ub = [inf, inf, 158]
# you could try also comment/uncomment nonlinear constraints:
p.c = lambda x: (x[2] - 150.8)**2 - 1.5
# optional: gradient
p.dc = lambda x: asfarray((0, 0, 2 * (x[2] - 150.8)))
# also you could set it via p=NLSP(f, x0, ..., c = c, dc = dc)
r = p.solve('nssolve', **kwargs)
return r.istop > 0, r, p
def calcIdealAngles3(h, UBmatrix, wavelength, phi, stars):
"Calculates the chi and theta for a desired vector h in the fixed phi mode."
#Accepts ta desired vector h, the UB matrix, the wavelength, and the fixed phi
hp = np.dot(UBmatrix, h)
q = calcq(h[0], h[1], h[2], stars)
twotheta = 2 * np.arcsin(wavelength * q / 4 / np.pi)
x0 = [0.0, 0.0]
p0 = NLSP(phiEquations, x0, args=(hp, wavelength, phi, twotheta))
r0 = p0.solve('nlp:ralg')
#r0.xf is the final array
twotheta = np.degrees(twotheta)
chi = np.degrees(r0.xf[0]) # xf[0] = chi
omega = np.degrees(r0.xf[1]) # xf[1] = omega
theta = twotheta / 2.0 + omega
return twotheta, theta, omega, chi
def calcIdealAngles3(h, UBmatrix, wavelength, phi, stars):
"Calculates the chi and theta for a desired vector h in the fixed phi mode."
# Accepts ta desired vector h, the UB matrix, the wavelength, and the fixed phi
hp = N.dot(UBmatrix, h)
q = calcq(h[0], h[1], h[2], stars)
twotheta = 2 * N.arcsin(wavelength * q / 4 / N.pi)
x0 = [0.0, 0.0]
p0 = NLSP(phiEquations, x0, args=(hp, wavelength, phi, twotheta))
r0 = p0.solve("nlp:ralg")
# r0.xf is the final array
twotheta = N.degrees(twotheta)
chi = N.degrees(r0.xf[0]) # xf[0] = chi
omega = N.degrees(r0.xf[1]) # xf[1] = omega
theta = twotheta / 2.0 + omega
return twotheta, theta, omega, chi
def calcScatteringPlane(h1, h2, UBmatrix, wavelength, stars):
"Calculates the chi and phi for the scattering plane defined by h1 and h2. Used with calcIdealAngles2."
# Accepts two scattering plane vectors, h1 and h2, the UB matrix, and the wavelength
h1p = N.dot(UBmatrix, h1)
h2p = N.dot(UBmatrix, h2)
x0 = [0.0, 0.0, 0.0, 0.0]
q = calcq(h1[0], h1[1], h1[2], stars)
twotheta1 = 2.0 * N.arcsin(wavelength * q / 4.0 / N.pi)
q = calcq(h2[0], h2[1], h2[2], stars)
twotheta2 = 2.0 * N.arcsin(wavelength * q / 4.0 / N.pi)
p0 = NLSP(scatteringEquations, x0, args=(h1p, h2p, wavelength, twotheta1, twotheta2))
r0 = p0.solve("nlp:ralg")
chi = N.degrees(r0.xf[0]) # xf is the final array, xf[0] = chi
phi = N.degrees(r0.xf[1]) # xf[1] = phi
return chi, phi
def calcScatteringPlane(h1, h2, UBmatrix, wavelength, stars):
"Calculates the chi and phi for the scattering plane defined by h1 and h2. Used with calcIdealAngles2."
#Accepts two scattering plane vectors, h1 and h2, the UB matrix, and the wavelength
h1p = N.dot(UBmatrix, h1)
h2p = N.dot(UBmatrix, h2)
x0 = [0.0, 0.0, 0.0, 0.0]
q = calcq(h1[0], h1[1], h1[2], stars)
twotheta1 = 2.0 * N.arcsin(wavelength * q / 4.0 / N.pi)
q = calcq(h2[0], h2[1], h2[2], stars)
twotheta2 = 2.0 * N.arcsin(wavelength * q / 4.0 / N.pi)
p0 = NLSP(scatteringEquations,
x0,
args=(h1p, h2p, wavelength, twotheta1, twotheta2))
r0 = p0.solve('nlp:ralg')
chi = N.degrees(r0.xf[0]) #xf is the final array, xf[0] = chi
phi = N.degrees(r0.xf[1]) # xf[1] = phi
return chi, phi
def test(complexity=0, **kwargs):
f = lambda x: (x[0]**3+x[1]**3-9, x[0]-0.5*x[1], cos(x[2])+x[0]-1.5)
#optional: gradient
def df(x):
df = zeros((3,3))
df[0,0] = 3*x[0]**2
df[0,1] = 3*x[1]**2
df[1,0] = 1
df[1,1] = -0.5
df[2,0] = 1
df[2,2] = -sin(x[2])
return df
x0 = [8,15, 80]
#w/o gradient:
#p = NLSP(f, x0)
p = NLSP(f, x0, df = df, maxFunEvals = 1e5, iprint = -1, ftol = 1e-6, contol=1e-35)
p.lb = [-inf, -inf, 150]
p.ub = [inf, inf, 158]
# you could try also comment/uncomment nonlinear constraints:
p.c = lambda x: (x[2] - 150.8)**2-1.5
# optional: gradient
p.dc = lambda x: asfarray((0, 0, 2*(x[2]-150.8)))
# also you could set it via p=NLSP(f, x0, ..., c = c, dc = dc)
r = p.solve('nssolve', **kwargs)
return r.istop>0, r, p
"""
Solving system of equations:
x**3 + y**3 - 9 = 0
x - 0.5*y = 0
cos(z) + x - 1.5 = 0
"""
from FuncDesigner import *
from openopt import NLSP
x, y, z = oovars(3)
equations = (x**3 + y**3 - 9, x - 0.5 * y, cos(z) + x - 1.5)
# alternatively, since FD 0.32: you can use equations and require custom tolerances
equations = (x**3 + y**3 - 9 == 0, (x - 0.5 * y == 0)(tol=1e-9),
(cos(z) + x == 1.5)(tol=1e-9))
# if no tol is assigned for an equation, p.ftol (default 10^-6) will be used for that one
startPoint = {x: 8, y: 15, z: 80}
p = NLSP(equations, startPoint)
# optional: we could set some constraints
p.constraints = [z < 70, z > 50, z + sin(x) < 60]
r = p.solve(
'nssolve'
) # nssolve is name of solver involved, see OOF doc for more arguments
xs, ys, zs = r(x, y, z)
print('Solution: x = %f y = %f z = %f' % (xs, ys, zs))
#Solution: x = 0.999999 y = 2.000000 z = 57.595865
"""
Solving system of equations:
x**3 + y**3 - 9 = 0
x - 0.5*y = 0
cos(z) + x - 1.5 = 0
"""
from FuncDesigner import *
from openopt import NLSP
x, y, z = oovars(3)
equations = (x**3 + y**3 - 9, x - 0.5*y, cos(z) + x - 1.5)
# alternatively, since FD 0.32: you can use equations and require custom tolerances
equations = (x**3 + y**3 - 9==0, (x - 0.5*y==0)(tol=1e-9), (cos(z) + x == 1.5) (tol=1e-9))
# if no tol is assigned for an equation, p.ftol (default 10^-6) will be used for that one
startPoint = {x:8, y:15, z:80}
p = NLSP(equations, startPoint)
# optional: we could set some constraints
p.constraints = [z<70, z>50, z + sin(x) < 60]
r = p.solve('nssolve') # nssolve is name of solver involved, see OOF doc for more arguments
xs, ys, zs = r(x, y, z)
print('Solution: x = %f y = %f z = %f' % (xs, ys, zs))
#Solution: x = 0.999999 y = 2.000000 z = 57.595865