def test_API(self):
domain=ripRectangle(25, 25, d0=mpisize)
omega=2.
SIGMA=15.
x=[ [0.2,0.5], [0.3,0.5] ]
Z_XY=[ complex(1.2,1.5), complex(1.3,2.5) ]
eta=1.
w0=1.
Hx0=1.
# now we do a real one
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta, w0=w0, sigma0=SIGMA)
self.assertEqual(model.getDomain(), domain)
pde=model.setUpPDE()
self.assertIsInstance(pde, LinearPDE)
self.assertEqual(pde.getNumEquations(), 2)
self.assertEqual(pde.getNumSolutions(), 2)
self.assertEqual(pde.getDomain(), domain)
# other things that should work
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta=None, w0=[2.,3.], sigma0=SIGMA, airLayerLevel=1.)
# these shouldn't work
self.assertRaises(ValueError, MT2DModelTMMode, domain, omega, x, [3.], eta=[1.,1.], w0=[2.,3.], sigma0=SIGMA)
self.assertRaises(ValueError, MT2DModelTMMode, domain, omega, x, Z_XY, eta=[1.], w0=[2.,3.], sigma0=SIGMA)
self.assertRaises(ValueError, MT2DModelTMMode, domain, omega, [(6.7,5)], Z_XY, eta=[1.,1.], w0=[2.,3.], sigma0=SIGMA)
def test_API(self):
NE=20
for x in [int(sqrt(mpisize)),2,3,5,7,1]:
NX=x
NY=mpisize//x
if NX*NY == mpisize:
break
domain=ripRectangle(n0=NE*NX-1, n1=NE*NY-1, l0=1., l1=1., d0=NX, d1=NY, diracPoints=[(0.5,1.)], diracTags=['sss'])
omega=2.
data=Data([1,2], FunctionOnBoundary(domain))
F=Data([2,3], Function(domain))
w=1.
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, data, 1.) # F is a scalar
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, [1,2], F) # data is not Data
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, Data([1,2], Function(domain)), F) # data is not on boundary
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, Scalar(1, Function(domain)), F) # data is not of shape (2,)
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, [1,2], data, F) # w is not a scalar
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, Scalar(1, Function(domain)), data, F) # w is not a scalar
# now we do a real one
acw=AcousticWaveForm(domain, omega, w, data, F)
self.assertEqual(acw.getDomain(), domain)
pde=acw.setUpPDE()
self.assertIsInstance(pde, LinearPDE)
self.assertEqual(pde.getNumEquations(), 2)
self.assertEqual(pde.getNumSolutions(), 2)
self.assertEqual(pde.getDomain(), domain)
def test_PDE(self):
omega=1.
mu0=0.123
SIGMA=15.
k=cmath.sqrt(1j*omega*mu0*SIGMA) # Ex=exp(k*z)
NE=101
domain=ripRectangle(max(NE,30*mpisize-1),max(NE,30*mpisize-1), d1=mpisize)
Z0=0.5
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
IMP=-(1j*omega*mu0)/k*cmath.exp(k*Z0)/cmath.exp(k*Z0)
Z_XY=[ IMP, IMP ]
x=[ [X1,Z0], [X2,Z0] ]
eta=None
z=domain.getX()[1]
Ex0_ex=cos(k.imag*(z-1))*exp(k.real*(z-1))
Ex1_ex=sin(k.imag*(z-1))*exp(k.real*(z-1))
Ex0_ex_z=-sin(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+cos(k.imag*(z-1))*exp(k.real*(z-1))*k.real
Ex1_ex_z=cos(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+sin(k.imag*(z-1))*exp(k.real*(z-1))*k.real
model=MT2DModelTEMode(domain, omega, x, Z_XY, eta, mu=mu0, tol=1e-9, directSolver=True, sigma0=SIGMA)
args=model.getArguments(SIGMA)
Ex=args[0]
Exz=args[1]
self.assertLess(Lsup(Ex[0]-Ex0_ex), 1e-4 * Lsup(Ex0_ex))
self.assertLess(Lsup(Ex[1]-Ex1_ex), 1e-4 * Lsup(Ex1_ex))
self.assertLess(Lsup(Exz[0]-Ex0_ex_z), 1e-2 * Lsup(Ex0_ex_z))
self.assertLess(Lsup(Exz[1]-Ex1_ex_z), 1e-2 * Lsup(Ex1_ex_z))
argsr=model.getArguments(0.)
ref=model.getDefect(0., *argsr)
# this should be almost zero:
args=model.getArguments(SIGMA)
d=model.getDefect(SIGMA, *args)
self.assertTrue( d > 0.)
self.assertTrue( ref > 0.)
self.assertLess( d, 3e-3 * ref ) # d should be zero (some sort of)
z=ReducedFunction(domain).getX()[1]
Ex0_ex=cos(k.imag*(z-1))*exp(k.real*(z-1))
Ex1_ex=sin(k.imag*(z-1))*exp(k.real*(z-1))
Ex0_ex_z=-sin(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+cos(k.imag*(z-1))*exp(k.real*(z-1))*k.real
Ex1_ex_z=cos(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+sin(k.imag*(z-1))*exp(k.real*(z-1))*k.real
# and this should be zero
d0=model.getDefect(SIGMA, Ex0_ex*[1.,0]+ Ex1_ex*[0,1.], Ex0_ex_z*[1.,0]+ Ex1_ex_z*[0,1.])
self.assertTrue( d0 <= 1e-8 * ref ) # d should be zero (some sort of)
# and this too
dg=model.getGradient(SIGMA, Ex0_ex*[1.,0]+ Ex1_ex*[0,1.], Ex0_ex_z*[1.,0]+ Ex1_ex_z*[0,1.])
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==())
self.assertLess(Lsup(dg), 1e-10)
def test_API(self):
NE=20
for x in [int(sqrt(mpisize)),2,3,5,7,1]:
NX=x
NY=mpisize//x
if NX*NY == mpisize:
break
domain=ripRectangle(n0=NE*NX-1, n1=NE*NY-1, l0=1., l1=1., d0=NX, d1=NY, diracPoints=[(0.5,1.)], diracTags=['sss'])
omega=2.
data=Data([1,2], FunctionOnBoundary(domain))
F=Data([2,3], Function(domain))
w=1.
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, data, 1.) # F is a scalar
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, [1,2], F) # data is not Data
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, Data([1,2], Function(domain)), F) # data is not on boundary
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, w, Scalar(1, Function(domain)), F) # data is not of shape (2,)
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, [1,2], data, F) # w is not a scalar
self.assertRaises(ValueError, AcousticWaveForm, domain, omega, Scalar(1, Function(domain)), data, F) # w is not a scalar
# now we do a real one
acw=AcousticWaveForm(domain, omega, w, data, F)
self.assertEqual(acw.getDomain(), domain)
pde=acw.setUpPDE()
self.assertIsInstance(pde, LinearPDE)
self.assertEqual(pde.getNumEquations(), 2)
self.assertEqual(pde.getNumSolutions(), 2)
self.assertEqual(pde.getDomain(), domain)
def test_API(self):
domain=ripRectangle(25, 25, d0=mpisize)
omega=2.
SIGMA=15.
x=[ [0.2,0.5], [0.3,0.5] ]
Z_XY=[ complex(1.2,1.5), complex(1.3,2.5) ]
eta=1.
w0=1.
Hx0=1.
# now we do a real one
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta, w0=w0, sigma0=SIGMA)
self.assertEqual(model.getDomain(), domain)
pde=model.setUpPDE()
self.assertIsInstance(pde, LinearPDE)
self.assertEqual(pde.getNumEquations(), 2)
self.assertEqual(pde.getNumSolutions(), 2)
self.assertEqual(pde.getDomain(), domain)
# other things that should work
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta=None, w0=[2.,3.], sigma0=SIGMA, airLayerLevel=1.)
# these shouldn't work
self.assertRaises(ValueError, MT2DModelTMMode, domain, omega, x, [3.], eta=[1.,1.], w0=[2.,3.], sigma0=SIGMA)
self.assertRaises(ValueError, MT2DModelTMMode, domain, omega, x, Z_XY, eta=[1.], w0=[2.,3.], sigma0=SIGMA)
self.assertRaises(ValueError, MT2DModelTMMode, domain, omega, [(6.7,5)], Z_XY, eta=[1.,1.], w0=[2.,3.], sigma0=SIGMA)
def test_PDE(self):
omega=1.
mu0=0.123
SIGMA=15.
k=cmath.sqrt(1j*omega*mu0*SIGMA) # Ex=exp(k*z)
NE=101
domain=ripRectangle(max(NE,30*mpisize-1),max(NE,30*mpisize-1), d1=mpisize)
Z0=0.5
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
IMP=-(1j*omega*mu0)/k*cmath.exp(k*Z0)/cmath.exp(k*Z0)
Z_XY=[ IMP, IMP ]
x=[ [X1,Z0], [X2,Z0] ]
eta=None
z=domain.getX()[1]
Ex0_ex=cos(k.imag*(z-1))*exp(k.real*(z-1))
Ex1_ex=sin(k.imag*(z-1))*exp(k.real*(z-1))
Ex0_ex_z=-sin(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+cos(k.imag*(z-1))*exp(k.real*(z-1))*k.real
Ex1_ex_z=cos(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+sin(k.imag*(z-1))*exp(k.real*(z-1))*k.real
model=MT2DModelTEMode(domain, omega, x, Z_XY, eta, mu=mu0, tol=1e-9, directSolver=True, sigma0=SIGMA)
args=model.getArguments(SIGMA)
Ex=args[0]
Exz=args[1]
self.assertLess(Lsup(Ex[0]-Ex0_ex), 1e-4 * Lsup(Ex0_ex))
self.assertLess(Lsup(Ex[1]-Ex1_ex), 1e-4 * Lsup(Ex1_ex))
self.assertLess(Lsup(Exz[0]-Ex0_ex_z), 1e-2 * Lsup(Ex0_ex_z))
self.assertLess(Lsup(Exz[1]-Ex1_ex_z), 1e-2 * Lsup(Ex1_ex_z))
argsr=model.getArguments(0.)
ref=model.getDefect(0., *argsr)
# this should be almost zero:
args=model.getArguments(SIGMA)
d=model.getDefect(SIGMA, *args)
self.assertTrue( d > 0.)
self.assertTrue( ref > 0.)
self.assertLess( d, 3e-3 * ref ) # d should be zero (some sort of)
z=ReducedFunction(domain).getX()[1]
Ex0_ex=cos(k.imag*(z-1))*exp(k.real*(z-1))
Ex1_ex=sin(k.imag*(z-1))*exp(k.real*(z-1))
Ex0_ex_z=-sin(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+cos(k.imag*(z-1))*exp(k.real*(z-1))*k.real
Ex1_ex_z=cos(k.imag*(z-1))*k.imag*exp(k.real*(z-1))+sin(k.imag*(z-1))*exp(k.real*(z-1))*k.real
# and this should be zero
d0=model.getDefect(SIGMA, Ex0_ex*[1.,0]+ Ex1_ex*[0,1.], Ex0_ex_z*[1.,0]+ Ex1_ex_z*[0,1.])
self.assertTrue( d0 <= 1e-8 * ref ) # d should be zero (some sort of)
# and this too
dg=model.getGradient(SIGMA, Ex0_ex*[1.,0]+ Ex1_ex*[0,1.], Ex0_ex_z*[1.,0]+ Ex1_ex_z*[0,1.])
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==())
self.assertLess(Lsup(dg), 1e-10)
def test_Differential(self):
INC=0.001
omega=5.
mu0=0.123
SIGMA=15.
k=cmath.sqrt(1j*omega*mu0*SIGMA) # Ex=exp(k*z)
NE=101
domain=ripRectangle(max(NE,50*mpisize-1), max(NE,50*mpisize-1), d1=mpisize)
Z0=0.5
IMP=-(1j*omega*mu0)/k*(cmath.exp(k*Z0)-cmath.exp(-k*Z0))/(cmath.exp(k*Z0)+cmath.exp(-k*Z0))
Z_XY=[ IMP, IMP ]
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
x=[ [X1,Z0], [X2,Z0] ]
eta=None
z=domain.getX()[1]
Ex0_ex=cos(k.imag*z)*(exp(k.real*z)-exp(-k.real*z))
Ex0_ex_z=-sin(k.imag*z)*k.imag*(exp(k.real*z)-exp(-k.real*z))+cos(k.imag*z)*(exp(k.real*z)+exp(-k.real*z))*k.real
Ex1_ex=sin(k.imag*z)*(exp(k.real*z)+exp(-k.real*z))
Ex1_ex_z=cos(k.imag*z)*k.imag*(exp(k.real*z)+exp(-k.real*z))+sin(k.imag*z)*(exp(k.real*z)-exp(-k.real*z))*k.real
model=MT2DModelTEMode(domain, omega, x, Z_XY, eta, mu=mu0, sigma0=SIGMA, tol=1e-9, directSolver=True, airLayerLevel=1.)
# this is the base line:
xx=domain.getX()[0]
SIGMA0=3.*(xx+0.3)
args0=model.getArguments(SIGMA0)
d0=model.getDefect(SIGMA0, *args0)
dg0=model.getGradient(SIGMA0, *args0)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==())
X=Function(domain).getX()
# test 1
p=INC
SIGMA1=SIGMA0+p
args1=model.getArguments(SIGMA1)
d1=model.getDefect(SIGMA1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 2
p=exp(-length(X-(0.2,0.2))**2/10)*INC
SIGMA1=SIGMA0+p
args1=model.getArguments(SIGMA1)
d1=model.getDefect(SIGMA1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 3
p=sin(length(X)*3*3.14)*INC
SIGMA1=SIGMA0+p
args1=model.getArguments(SIGMA1)
d1=model.getDefect(SIGMA1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
def test_Differential(self):
INC=0.001
omega=5.
mu0=0.123
SIGMA=15.
k=cmath.sqrt(1j*omega*mu0*SIGMA) # Ex=exp(k*z)
NE=101
domain=ripRectangle(max(NE,50*mpisize-1), max(NE,50*mpisize-1), d1=mpisize)
Z0=0.5
IMP=-(1j*omega*mu0)/k*(cmath.exp(k*Z0)-cmath.exp(-k*Z0))/(cmath.exp(k*Z0)+cmath.exp(-k*Z0))
Z_XY=[ IMP, IMP ]
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
x=[ [X1,Z0], [X2,Z0] ]
eta=None
z=domain.getX()[1]
Ex0_ex=cos(k.imag*z)*(exp(k.real*z)-exp(-k.real*z))
Ex0_ex_z=-sin(k.imag*z)*k.imag*(exp(k.real*z)-exp(-k.real*z))+cos(k.imag*z)*(exp(k.real*z)+exp(-k.real*z))*k.real
Ex1_ex=sin(k.imag*z)*(exp(k.real*z)+exp(-k.real*z))
Ex1_ex_z=cos(k.imag*z)*k.imag*(exp(k.real*z)+exp(-k.real*z))+sin(k.imag*z)*(exp(k.real*z)-exp(-k.real*z))*k.real
model=MT2DModelTEMode(domain, omega, x, Z_XY, eta, mu=mu0, sigma0=SIGMA, tol=1e-9, directSolver=True, airLayerLevel=1.)
# this is the base line:
xx=domain.getX()[0]
SIGMA0=3.*(xx+0.3)
args0=model.getArguments(SIGMA0)
d0=model.getDefect(SIGMA0, *args0)
dg0=model.getGradient(SIGMA0, *args0)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==())
X=Function(domain).getX()
# test 1
p=INC
SIGMA1=SIGMA0+p
args1=model.getArguments(SIGMA1)
d1=model.getDefect(SIGMA1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 2
p=exp(-length(X-(0.2,0.2))**2/10)*INC
SIGMA1=SIGMA0+p
args1=model.getArguments(SIGMA1)
d1=model.getDefect(SIGMA1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 3
p=sin(length(X)*3*3.14)*INC
SIGMA1=SIGMA0+p
args1=model.getArguments(SIGMA1)
d1=model.getDefect(SIGMA1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
def test_numeric2DnoscaleF(self):
domain=ripRectangle(n0=10, n1=20, l0=1., l1=1., diracPoints=[(0.5,1.)], diracTags=['sss'])
omega=1.5
# test solution is u = a * z where a is complex
a=complex(3.45, 0.56)
sigma=complex(1e-3, 0.056)
data=Data([a.real, a.imag], FunctionOnBoundary(domain))
z=FunctionOnBoundary(domain).getX()[1]
w=whereZero(z-1.)
# F = - a*omega* sigma
F=Data( [-(a*omega**2*sigma).real, -(a*omega**2*sigma).imag ],Function(domain))
acw=AcousticWaveForm(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-8, saveMemory=True, scaleF=False)
# this should be zero:
sigma_comps=[sigma.real, sigma.imag]
args=acw.getArguments(sigma_comps)
d=acw.getDefect(sigma_comps, *args)
self.assertTrue(isinstance(d, float))
self.assertLess(Lsup(d), 1e-10)
#self.assertTrue(d >= 0)
dg=acw.getGradient(sigma_comps, *args)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==(2,))
self.assertTrue(dg.getFunctionSpace()==Solution(domain))
self.assertLess(Lsup(dg), 1e-8)
# this shouldn't be zero:
sigma0=Data([2*sigma.real, sigma.imag/2], Function(domain) )
args=acw.getArguments(sigma0)
d0=acw.getDefect(sigma0, *args)
self.assertTrue(isinstance(d0, float))
self.assertGreaterEqual(d0, 0)
self.assertGreater(d0, 1e-10)
dg0=acw.getGradient(sigma0, *args)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==(2,))
self.assertTrue(dg0.getFunctionSpace()==Solution(domain))
self.assertTrue(Lsup(dg0) > 1e-10)
# test the gradient numerically:
h=0.001
X=Function(domain).getX()
p=h*sin(length(X)*np.pi)*Lsup(length(sigma0))
sigma1=sigma0+p*[1,0]
args=acw.getArguments(sigma1)
d1=acw.getDefect(sigma1, *args)
self.assertLess( abs( d1-d0-integrate(dg0[0]*p) ), 1e-2*abs(d1-d0) )
sigma2=sigma0+p*[0,1]
args=acw.getArguments(sigma2)
d2=acw.getDefect(sigma2, *args)
self.assertLess( abs(d2-d0-integrate(dg0[1]*p)), 1e-2*abs(d2-d0) )
def test_Differential(self):
INC=0.001
omega=5.
mu0=0.123
RHO=0.15
SIGMA=1/RHO
k=cmath.sqrt(1j*omega*mu0*1/RHO) # Hx=exp(k*z)
L=1
NE=101
domain=ripRectangle(max(NE,50*mpisize-1), max(NE,50*mpisize-1), d1=mpisize)
Z0=0.5
IMP=RHO*k*(cmath.exp(k*(Z0-L))-cmath.exp(-k*(Z0-L)))/(cmath.exp(k*(Z0-L))+cmath.exp(-k*(Z0-L)))
Z_XY=[ IMP, IMP ]
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
x=[ [X1,Z0], [X2,Z0] ]
eta=None
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta, mu=mu0, tol=1e-9, sigma0=SIGMA, directSolver=True)
# this is the base line:
xx=domain.getX()[0]
RHO0=3.*(xx+0.3)
args0=model.getArguments(RHO0)
d0=model.getDefect(RHO0, *args0)
dg0=model.getGradient(RHO0, *args0)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==())
X=Function(domain).getX()
# test 1
p=INC
RHO1=RHO0+p
args1=model.getArguments(RHO1)
d1=model.getDefect(RHO1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 2
p=exp(-length(X-(0.2,0.2))**2/10)*INC
RHO1=RHO0+p
args1=model.getArguments(RHO1)
d1=model.getDefect(RHO1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 3
p=sin(length(X)*3*3.14)*INC
RHO1=RHO0+p
args1=model.getArguments(RHO1)
d1=model.getDefect(RHO1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
def test_Differential(self):
INC=0.001
omega=5.
mu0=0.123
RHO=0.15
SIGMA=1/RHO
k=cmath.sqrt(1j*omega*mu0*1/RHO) # Hx=exp(k*z)
L=1
NE=101
domain=ripRectangle(max(NE,50*mpisize-1), max(NE,50*mpisize-1), d1=mpisize)
Z0=0.5
IMP=RHO*k*(cmath.exp(k*(Z0-L))-cmath.exp(-k*(Z0-L)))/(cmath.exp(k*(Z0-L))+cmath.exp(-k*(Z0-L)))
Z_XY=[ IMP, IMP ]
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
x=[ [X1,Z0], [X2,Z0] ]
eta=None
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta, mu=mu0, tol=1e-9, sigma0=SIGMA, directSolver=True)
# this is the base line:
xx=domain.getX()[0]
RHO0=3.*(xx+0.3)
args0=model.getArguments(RHO0)
d0=model.getDefect(RHO0, *args0)
dg0=model.getGradient(RHO0, *args0)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==())
X=Function(domain).getX()
# test 1
p=INC
RHO1=RHO0+p
args1=model.getArguments(RHO1)
d1=model.getDefect(RHO1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 2
p=exp(-length(X-(0.2,0.2))**2/10)*INC
RHO1=RHO0+p
args1=model.getArguments(RHO1)
d1=model.getDefect(RHO1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
# test 3
p=sin(length(X)*3*3.14)*INC
RHO1=RHO0+p
args1=model.getArguments(RHO1)
d1=model.getDefect(RHO1, *args1)
self.assertLess( abs( d1-d0-integrate(dg0*p) ), 1e-2*abs(d1-d0) )
def test_numeric2DscaleF(self):
NE=40
for x in [int(sqrt(mpisize)),2,3,5,7,1]:
NX=x
NY=mpisize//x
if NX*NY == mpisize:
break
domain=ripRectangle(n0=NE*NX-1, n1=NE*NY-1, l0=1., l1=1., d0=NX, d1=NY, diracPoints=[(0.5,1.)], diracTags=['sss'])
#domain=ripRectangle(100,100, diracPoints=[(0.5,1.)], diracTags=['sss'])
omega=2.
# test solution is u = a * z where a is complex
a=complex(3.45, 0.56)
sigma=complex(1e-3, 0.056)
data=Data([a.real, a.imag], FunctionOnBoundary(domain))
mydata=data.copy()
z=FunctionOnBoundary(domain).getX()[1]
w=whereZero(z-1.)
# source:
F=Data( [1,0],Function(domain))
acw=AcousticWaveForm(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-8, saveMemory=True, scaleF=True)
# check rescaled data
surv=acw.getSurvey()
self.assertAlmostEqual( integrate(length(surv[0])**2 * surv[1]), 1.)
mydata_scale=sqrt( integrate(w*length(mydata)**2) )
self.assertAlmostEqual( acw.getSourceScaling(z*[1, 0.]) , a/mydata_scale )
self.assertAlmostEqual( acw.getSourceScaling(mydata) , 1./mydata_scale )
# this should be zero:
sigma_comps=[sigma.real, sigma.imag]
args=acw.getArguments(sigma_comps)
d=acw.getDefect(sigma_comps, *args)
self.assertTrue(isinstance(d, float))
self.assertLess(abs(d), 1e-10)
dg=acw.getGradient(sigma_comps, *args)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==(2,))
self.assertTrue(dg.getFunctionSpace()==Solution(domain))
self.assertLess(Lsup(dg), 1e-10)
# this shuld be zero' too
sigma_comps=[2*sigma.real, sigma.imag/2.]
args=acw.getArguments(sigma_comps)
d=acw.getDefect(sigma_comps, *args)
self.assertTrue(isinstance(d, float))
self.assertLess(abs(d), 1e-10)
dg=acw.getGradient(sigma_comps, *args)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==(2,))
self.assertTrue(dg.getFunctionSpace()==Solution(domain))
self.assertLess(Lsup(dg), 1e-10)
# this shouldn't be zero:
sigma0=[2*sigma.real, 10*a.imag]*(27*Function(domain).getX()[0]-Function(domain).getX()[1])
args=acw.getArguments(sigma0)
d0=acw.getDefect(sigma0, *args)
self.assertTrue(isinstance(d0, float))
self.assertTrue(d0 >= 0)
self.assertTrue(d0 > 1e-10)
dg0=acw.getGradient(sigma0, *args)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==(2,))
self.assertTrue(dg0.getFunctionSpace()==Solution(domain))
self.assertTrue(Lsup(dg0) > 1e-10)
# test the gradient numerrically:
h=0.002
X=Function(domain).getX()
# .. increment:
p=h*exp(-(length(X-[0.6,0.6])/10)**2)*Lsup(length(sigma0))
sigma1=sigma0+p*[1,0]
args=acw.getArguments(sigma1)
d1=acw.getDefect(sigma1, *args)
self.assertLess( abs( d1-d0-integrate(dg0[0]*p) ), 1e-2*abs(d1-d0) )
sigma2=sigma0+p*[0,1]
args=acw.getArguments(sigma2)
d2=acw.getDefect(sigma2, *args)
self.assertLess( abs(d2-d0-integrate(dg0[1]*p)), 1e-2*abs(d2-d0) )
def test_PDE(self):
omega=10.
mu0=0.123
RHO=0.15
SIGMA=1/RHO
k=cmath.sqrt(1j*omega*mu0/RHO) # Hx=exp(k*z)
NE=151
L=1
domain=ripRectangle(NE,NE, d0=mpisize)
Z0=0.5
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
IMP=RHO*k*cmath.exp(k*(Z0-L))/cmath.exp(k*(Z0-L))
Z_XY=[ IMP, IMP ]
x=[ [X1,Z0], [X2,Z0] ]
eta=None
z=domain.getX()[1]
Hx0_ex=cos(k.imag*(z-L))*exp(k.real*(z-L))
Hx1_ex=sin(k.imag*(z-L))*exp(k.real*(z-L))
Hx0_ex_z=-sin(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+cos(k.imag*(z-L))*exp(k.real*(z-L))*k.real
Hx1_ex_z=cos(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+sin(k.imag*(z-L))*exp(k.real*(z-L))*k.real
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta, mu=mu0, sigma0=SIGMA, tol=1e-9, directSolver=True, airLayerLevel=1.)
args=model.getArguments(RHO)
Hx=args[0]
g_Hx=args[1]
Hxz=g_Hx[:,1]
self.assertLess(Lsup(Hx[0]-Hx0_ex), 1e-4 * Lsup(Hx0_ex))
self.assertLess(Lsup(Hx[1]-Hx1_ex), 1e-4 * Lsup(Hx1_ex))
self.assertLess(Lsup(Hxz[0]-Hx0_ex_z), 1e-2 * Lsup(Hx0_ex_z))
self.assertLess(Lsup(Hxz[1]-Hx1_ex_z), 1e-2 * Lsup(Hx1_ex_z))
argsr=model.getArguments(1.)
ref=model.getDefect(1., *argsr)
# this should be almost zero:
args=model.getArguments(RHO)
d=model.getDefect(RHO, *args)
self.assertTrue( d > 0.)
self.assertTrue( ref > 0.)
self.assertTrue( d <= 3e-3 * ref ) # d should be zero (some sort of)
z=ReducedFunction(domain).getX()[1]
Hx0_ex=cos(k.imag*(z-L))*exp(k.real*(z-L))
Hx1_ex=sin(k.imag*(z-L))*exp(k.real*(z-L))
Hx0_ex_z=-sin(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+cos(k.imag*(z-L))*exp(k.real*(z-L))*k.real
Hx1_ex_z=cos(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+sin(k.imag*(z-L))*exp(k.real*(z-L))*k.real
g_Hx = Data(0, (2,2), Hx0_ex_z.getFunctionSpace())
g_Hx[0,1] = Hx0_ex_z
g_Hx[1,1] = Hx1_ex_z
# and this should be zero
d0=model.getDefect(RHO, Hx0_ex*[1.,0]+ Hx1_ex*[0,1.], g_Hx)
self.assertLess( d0, 1e-8 * ref ) # d should be zero (some sort of)
# and this too
dg=model.getGradient(RHO, Hx0_ex*[1.,0]+Hx1_ex*[0,1.], g_Hx)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==())
self.assertLess(Lsup(dg), 1e-10)
def test_numeric2DnoscaleF(self):
for x in [int(sqrt(mpisize)),2,3,5,7,1]:
NX=x
NY=mpisize//x
if NX*NY == mpisize:
break
domain=ripRectangle(n0=10*NX-1, n1=20*NY-1, l0=1., l1=1., d0=NX, d1=NY, diracPoints=[(0.5,1.)], diracTags=['sss'])
omega=1.5
# test solution is u = a * z where a is complex
a=complex(3.45, 0.56)
sigma=complex(1e-3, 0.056)
data=Data([a.real, a.imag], FunctionOnBoundary(domain))
z=FunctionOnBoundary(domain).getX()[1]
w=whereZero(z-1.)
# F = - a*omega* sigma
F=Data( [-(a*omega**2*sigma).real, -(a*omega**2*sigma).imag ],Function(domain))
acw=AcousticWaveForm(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-8, saveMemory=True, scaleF=False)
# this should be zero:
sigma_comps=[sigma.real, sigma.imag]
args=acw.getArguments(sigma_comps)
d=acw.getDefect(sigma_comps, *args)
self.assertTrue(isinstance(d, float))
self.assertLess(Lsup(d), 1e-10)
#self.assertTrue(d >= 0)
dg=acw.getGradient(sigma_comps, *args)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==(2,))
self.assertTrue(dg.getFunctionSpace()==Solution(domain))
self.assertLess(Lsup(dg), 5e-10)
# this shouldn't be zero:
sigma0=Data([2*sigma.real, sigma.imag/2], Function(domain) )
args=acw.getArguments(sigma0)
d0=acw.getDefect(sigma0, *args)
self.assertTrue(isinstance(d0, float))
self.assertGreaterEqual(d0, 0)
self.assertGreater(d0, 1e-10)
dg0=acw.getGradient(sigma0, *args)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==(2,))
self.assertTrue(dg0.getFunctionSpace()==Solution(domain))
self.assertTrue(Lsup(dg0) > 1e-10)
# test the gradient numerically:
h=0.001
X=Function(domain).getX()
p=h*sin(length(X)*np.pi)*Lsup(length(sigma0))
sigma1=sigma0+p*[1,0]
args=acw.getArguments(sigma1)
d1=acw.getDefect(sigma1, *args)
self.assertLess( abs( d1-d0-integrate(dg0[0]*p) ), 1e-2*abs(d1-d0) )
sigma2=sigma0+p*[0,1]
args=acw.getArguments(sigma2)
d2=acw.getDefect(sigma2, *args)
self.assertLess( abs(d2-d0-integrate(dg0[1]*p)), 1e-2*abs(d2-d0) )
def test_numeric2DscaleF(self):
NE=40
for x in [int(sqrt(mpisize)),2,3,5,7,1]:
NX=x
NY=mpisize//x
if NX*NY == mpisize:
break
domain=ripRectangle(n0=NE*NX-1, n1=NE*NY-1, l0=1., l1=1., d0=NX, d1=NY, diracPoints=[(0.5,1.)], diracTags=['sss'])
#domain=ripRectangle(100,100, diracPoints=[(0.5,1.)], diracTags=['sss'])
omega=2.
# test solution is u = a * z where a is complex
a=complex(3.45, 0.56)
sigma=complex(1e-3, 0.056)
data=Data([a.real, a.imag], FunctionOnBoundary(domain))
mydata=data.copy()
z=FunctionOnBoundary(domain).getX()[1]
w=whereZero(z-1.)
# source:
F=Data( [1,0],Function(domain))
acw=AcousticWaveForm(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-8, saveMemory=True, scaleF=True)
# check rescaled data
surv=acw.getSurvey()
self.assertAlmostEqual( integrate(length(surv[0])**2 * surv[1]), 1.)
mydata_scale=sqrt( integrate(w*length(mydata)**2) )
self.assertAlmostEqual( acw.getSourceScaling(z*[1, 0.]) , a/mydata_scale )
self.assertAlmostEqual( acw.getSourceScaling(mydata) , 1./mydata_scale )
# this should be zero:
sigma_comps=[sigma.real, sigma.imag]
args=acw.getArguments(sigma_comps)
d=acw.getDefect(sigma_comps, *args)
self.assertTrue(isinstance(d, float))
self.assertLess(abs(d), 1e-10)
dg=acw.getGradient(sigma_comps, *args)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==(2,))
self.assertTrue(dg.getFunctionSpace()==Solution(domain))
self.assertLess(Lsup(dg), 1e-10)
# this shuld be zero' too
sigma_comps=[2*sigma.real, sigma.imag/2.]
args=acw.getArguments(sigma_comps)
d=acw.getDefect(sigma_comps, *args)
self.assertTrue(isinstance(d, float))
self.assertLess(abs(d), 1e-10)
dg=acw.getGradient(sigma_comps, *args)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==(2,))
self.assertTrue(dg.getFunctionSpace()==Solution(domain))
self.assertLess(Lsup(dg), 1e-10)
# this shouldn't be zero:
sigma0=[2*sigma.real, 10*a.imag]*(27*Function(domain).getX()[0]-Function(domain).getX()[1])
args=acw.getArguments(sigma0)
d0=acw.getDefect(sigma0, *args)
self.assertTrue(isinstance(d0, float))
self.assertTrue(d0 >= 0)
self.assertTrue(d0 > 1e-10)
dg0=acw.getGradient(sigma0, *args)
self.assertTrue(isinstance(dg0, Data))
self.assertTrue(dg0.getShape()==(2,))
self.assertTrue(dg0.getFunctionSpace()==Solution(domain))
self.assertTrue(Lsup(dg0) > 1e-10)
# test the gradient numerrically:
h=0.002
X=Function(domain).getX()
# .. increment:
p=h*exp(-(length(X-[0.6,0.6])/10)**2)*Lsup(length(sigma0))
sigma1=sigma0+p*[1,0]
args=acw.getArguments(sigma1)
d1=acw.getDefect(sigma1, *args)
self.assertLess( abs( d1-d0-integrate(dg0[0]*p) ), 1e-2*abs(d1-d0) )
sigma2=sigma0+p*[0,1]
args=acw.getArguments(sigma2)
d2=acw.getDefect(sigma2, *args)
self.assertLess( abs(d2-d0-integrate(dg0[1]*p)), 1e-2*abs(d2-d0) )
def test_PDE(self):
omega=10.
mu0=0.123
RHO=0.15
SIGMA=1/RHO
k=cmath.sqrt(1j*omega*mu0/RHO) # Hx=exp(k*z)
NE=151
L=1
domain=ripRectangle(NE,NE, d0=mpisize)
Z0=0.5
H=1./NE
X1=(int(0.3/H)+0.5)*H
X2=(int(0.6/H)+0.5)*H
IMP=RHO*k*cmath.exp(k*(Z0-L))/cmath.exp(k*(Z0-L))
Z_XY=[ IMP, IMP ]
x=[ [X1,Z0], [X2,Z0] ]
eta=None
z=domain.getX()[1]
Hx0_ex=cos(k.imag*(z-L))*exp(k.real*(z-L))
Hx1_ex=sin(k.imag*(z-L))*exp(k.real*(z-L))
Hx0_ex_z=-sin(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+cos(k.imag*(z-L))*exp(k.real*(z-L))*k.real
Hx1_ex_z=cos(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+sin(k.imag*(z-L))*exp(k.real*(z-L))*k.real
model=MT2DModelTMMode(domain, omega, x, Z_XY, eta, mu=mu0, sigma0=SIGMA, tol=1e-9, directSolver=True, airLayerLevel=1.)
args=model.getArguments(RHO)
Hx=args[0]
g_Hx=args[1]
Hxz=g_Hx[:,1]
self.assertLess(Lsup(Hx[0]-Hx0_ex), 1e-4 * Lsup(Hx0_ex))
self.assertLess(Lsup(Hx[1]-Hx1_ex), 1e-4 * Lsup(Hx1_ex))
self.assertLess(Lsup(Hxz[0]-Hx0_ex_z), 1e-2 * Lsup(Hx0_ex_z))
self.assertLess(Lsup(Hxz[1]-Hx1_ex_z), 1e-2 * Lsup(Hx1_ex_z))
argsr=model.getArguments(1.)
ref=model.getDefect(1., *argsr)
# this should be almost zero:
args=model.getArguments(RHO)
d=model.getDefect(RHO, *args)
self.assertTrue( d > 0.)
self.assertTrue( ref > 0.)
self.assertTrue( d <= 3e-3 * ref ) # d should be zero (some sort of)
z=ReducedFunction(domain).getX()[1]
Hx0_ex=cos(k.imag*(z-L))*exp(k.real*(z-L))
Hx1_ex=sin(k.imag*(z-L))*exp(k.real*(z-L))
Hx0_ex_z=-sin(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+cos(k.imag*(z-L))*exp(k.real*(z-L))*k.real
Hx1_ex_z=cos(k.imag*(z-L))*k.imag*exp(k.real*(z-L))+sin(k.imag*(z-L))*exp(k.real*(z-L))*k.real
g_Hx = Data(0, (2,2), Hx0_ex_z.getFunctionSpace())
g_Hx[0,1] = Hx0_ex_z
g_Hx[1,1] = Hx1_ex_z
# and this should be zero
d0=model.getDefect(RHO, Hx0_ex*[1.,0]+ Hx1_ex*[0,1.], g_Hx)
self.assertLess( d0, 1e-8 * ref ) # d should be zero (some sort of)
# and this too
dg=model.getGradient(RHO, Hx0_ex*[1.,0]+Hx1_ex*[0,1.], g_Hx)
self.assertTrue(isinstance(dg, Data))
self.assertTrue(dg.getShape()==())
self.assertLess(Lsup(dg), 1e-10)
