def derivative(self, x, **kwargs):
"""
Parameters:
x - value between 0 and 1
"""
x = x*self.L
expC = np.exp(np.polyval(self.C1, x)/np.polyval(self.C2, x))
C1x = np.polyder(self.C1)
C2x = np.polyder(self.C2)
if kwargs['dim'] == 'x':
Cx = (np.polyval(C1x, x)*np.polyval(self.C2, x) -
np.polyval(self.C1, x)*np.polyval(C2x, x))/np.polyval(self.C2, x)**2
return 1000*Cx*expC
elif kwargs['dim'] == 'xx':
C1xx = np.polyder(C1x)
C2xx = np.polyder(C2x)
Cx = (np.polyval(C1x, x)*np.polyval(self.C2, x) -
np.polyval(self.C1, x)*np.polyval(C2x, x))/np.polyval(self.C2, x)**2
Cxx = (np.polyval(C1xx, x)*np.polyval(self.C2, x)**2 +
2*np.polyval(self.C1, x)*np.polyval(C2x, x)**2 -
2*np.polyval(C1x, x)*np.polyval(self.C2, x)*np.polyval(C2x, x) -
np.polyval(self.C1, x)*np.polyval(self.C2, x)*np.polyval(C2xx, x)) / np.polyval(self.C2, x)**3
return 1000*(Cx**2 + Cxx)*expC
else:
FunctionBase.derivative(self)
return
def derivative(self, x, **kwargs):
if kwargs.get('dim') == 'x':
coef = self.data.v('coef', x=x)
H = self.data.v('grid', 'low', 'z', x=x) - self.data.v('grid', 'high', 'z', x=x)
coefx = self.data.d('coef', x=x, dim='x')
Hx = self.data.d('grid', 'low', 'z', x=x, dim='x') - self.data.d('grid', 'high', 'z', x=x, dim='x')
val = coefx * ((H / self.H0) ** self.m) + coef * (self.m * Hx * (H / self.H0) ** self.m / H)
elif kwargs.get('dim') == 'xx':
coef = self.data.v('coef', x=x)
H = self.data.v('grid', 'low', 'z', x=x) - self.data.v('grid', 'high', 'z', x=x)
coefx = self.data.d('coef', x=x, dim='x')
Hx = self.data.d('grid', 'low', 'z', x=x, dim='x') - self.data.d('grid', 'high', 'z', x=x, dim='x')
coefxx = self.data.d('coef', x=x, dim='xx')
Hxx = self.data.d('grid', 'low', 'z', x=x, dim='xx') - self.data.d('grid', 'high', 'z', x=x, dim='xx')
val = coefxx * (H / self.H0) ** self.m + 2. * coefx * self.m * Hx * H ** (
self.m - 1) / self.H0 ** self.m + coef * self.m * (self.m - 1) * Hx ** 2 * H ** (
self.m - 2) / self.H0 ** self.m + coef * self.m * Hxx * H ** (self.m - 1) / self.H0 ** self.m
elif 'z' in kwargs.get('dim'):
val = 0.
else:
val = None
FunctionBase.derivative(self)
return val
def derivative(self, x, f, **kwargs):
if kwargs['dim'] == 'x':
x = np.asarray(x*self.L)
f = [1-bool(j) for j in toList(f)]
f = np.asarray(f).reshape(1,len(f))
sx = self.ssea/2.*(np.tanh((x-self.xc)/self.xl)**2-1)/self.xl
sx = sx.reshape(len(sx),1)*f
else:
sx = None
FunctionBase.derivative(self)
return sx
def derivative(self, x, f, **kwargs):
if kwargs['dim'] == 'x':
x = np.asarray(x*self.L)
f = [1-bool(j) for j in toList(f)]
f = np.asarray(f).reshape(1, len(f))
sx = -self.ssea/self.Ls*np.exp(-x/self.Ls)
sx = sx.reshape(len(sx), 1)*f
else:
sx = None
FunctionBase.derivative(self)
return sx
def derivative(self, x, **kwargs):
"""
Parameters:
x - value between 0 and 1
"""
if kwargs['dim'] == 'x':
x = x * self.L
return -self.C0 / self.Lc * exp(-x / self.Lc)
elif kwargs['dim'] == 'xx':
x = x * self.L
return self.C0 / (self.Lc**2) * exp(-x / self.Lc)
else:
FunctionBase.derivative(self)
return
def derivative(self, x, **kwargs):
"""
Parameters:
x - value between 0 and 1
"""
x = x * self.L
Cx = np.polyder(self.C)
if kwargs['dim'] == 'x':
return np.polyval(Cx, x)
elif kwargs['dim'] == 'xx':
Cxx = np.polyder(Cx)
return np.polyval(Cxx, x)
else:
FunctionBase.derivative(self)
return
def derivative(self, x, **kwargs):
"""
Parameters:
x - value between 0 and 1
"""
if kwargs['dim'] == 'x':
x = x * self.L
return self.C1 * (1 - np.tanh(
(x - self.xc) / self.xl)**2) / self.xl
elif kwargs['dim'] == 'xx':
x = x * self.L
return -self.C1 * 2. * np.tanh(
(x - self.xc) / self.xl) * (1 - np.tanh(
(x - self.xc) / self.xl)**2.) / self.xl**2
else:
FunctionBase.derivative(self)
return
def derivative(self, x, z, f, **kwargs):
if kwargs.get('dim') == 'z':
z = z.reshape((1, len(z), 1))
coef = self.data.v('coef', x=x, z=z, f=f)
H = self.data.v('grid', 'low', 'z', x=x, z=z, f=f) - self.data.v(
'grid', 'high', 'z', x=x, z=z, f=f)
z0_dimless = self.data.v('z0*', x=x, z=z, f=f)
zs_dimless = self.data.v('zs*', x=x, z=z, f=f)
Avz = coef / H * (-2. * (-z) - 1. - z0_dimless +
zs_dimless) * (H / self.H0)**self.m
elif kwargs.get('dim') == 'zz':
coef = self.data.v('coef', x=x, z=z, f=f)
H = self.data.v('grid', 'low', 'z', x=x, z=z, f=f) - self.data.v(
'grid', 'high', 'z', x=x, z=z, f=f)
Avz = -2. * coef / H**2. * (H / self.H0)**self.m
else:
Avz = None
FunctionBase.derivative(
self) # derivatives in other directions not implemented
return Avz
def derivative(self, x, **kwargs):
"""
Parameters:
x - value between 0 and 1
"""
x = x * self.L
Cx = np.polyder(self.C)
Cx_lin = np.polyder(self.C_lin)
p = np.zeros(len(x))
if kwargs['dim'] == 'x':
p[np.where(x <= self.XL)] = np.polyval(Cx,
x[np.where(x <= self.XL)])
p[np.where(x > self.XL)] = np.polyval(
Cx_lin, x[np.where(x > self.XL)] - self.XL)
return p
elif kwargs['dim'] == 'xx':
Cxx = np.polyder(Cx)
p[np.where(x <= self.XL)] = np.polyval(Cxx,
x[np.where(x <= self.XL)])
return p
else:
FunctionBase.derivative(self)
return