def d(arg, v, **kw):#, *args, **kw):
N = len(v)
# if len(args) == 1:
# derivativeSide = args[0]
# assert derivativeSide in ('left', 'right', 'both')
# else:
# derivativeSide = 'both'
stencil = kw.get('stencil', 3)
if stencil not in (2, 3):
raise FuncDesignerException('for d1 only stencil = 2 and 3 are implemented')
timestep = v[1]-v[0]
if not all(abs(v[1:] - v [:-1] - timestep) < 1e-10):
raise FuncDesignerException('unimplemented for non-uniform step yet')
if stencil == 2:
r1 = -3*arg[0] + 4*arg[1] - arg[2]
r2 = (arg[2:N] - arg[0:N-2]) / 2.0
r3 = 3*arg[N-1] - 4*arg[N-2] + arg[N-3]
return hstack((r1, r2, r3)) / timestep
elif stencil == 3:
r1 = -22 * arg[0] + 36 * arg[1] - 18 * arg[2] + 4 * arg[3]
r2 = -22 * arg[1] + 36 * arg[2] - 18 * arg[3] + 4 * arg[4] # TODO: mb rework it?
r3 = arg[0:N-4] -8*arg[1:N-3] + 8*arg[3:N-1] - arg[4:N]
r4 = 22 * arg[N-5] - 36 * arg[N-4] + 18 * arg[N-3] - 4 * arg[N-2] # TODO: mb rework it?
r5 = 22 * arg[N-4] - 36 * arg[N-3] + 18 * arg[N-2] - 4 * arg[N-1]
return hstack((r1, r2, r3, r4, r5)) / (12*timestep)
# if derivativeSide == 'both':
# r = hstack((r1, r2, r3))
# elif derivativeSide == 'left':
# r = hstack((r1, r2))
# else: # derivativeSide == 'right'
# r = hstack((r2, r3))
return r
def d(arg, v, **kw): #, *args, **kw):
N = len(v)
# if len(args) == 1:
# derivativeSide = args[0]
# assert derivativeSide in ('left', 'right', 'both')
# else:
# derivativeSide = 'both'
stencil = kw.get('stencil', 3)
if stencil not in (2, 3):
raise FuncDesignerException(
'for d1 only stencil = 2 and 3 are implemented')
timestep = v[1] - v[0]
if not all(abs(v[1:] - v[:-1] - timestep) < 1e-10):
raise FuncDesignerException('unimplemented for non-uniform step yet')
if stencil == 2:
r1 = -3 * arg[0] + 4 * arg[1] - arg[2]
r2 = (arg[2:N] - arg[0:N - 2]) / 2.0
r3 = 3 * arg[N - 1] - 4 * arg[N - 2] + arg[N - 3]
return hstack((r1, r2, r3)) / timestep
elif stencil == 3:
r1 = -22 * arg[0] + 36 * arg[1] - 18 * arg[2] + 4 * arg[3]
r2 = -22 * arg[1] + 36 * arg[2] - 18 * arg[3] + 4 * arg[
4] # TODO: mb rework it?
r3 = arg[0:N - 4] - 8 * arg[1:N - 3] + 8 * arg[3:N - 1] - arg[4:N]
r4 = 22 * arg[N - 5] - 36 * arg[N - 4] + 18 * arg[N - 3] - 4 * arg[
N - 2] # TODO: mb rework it?
r5 = 22 * arg[N - 4] - 36 * arg[N - 3] + 18 * arg[N - 2] - 4 * arg[N -
1]
return hstack((r1, r2, r3, r4, r5)) / (12 * timestep)
# if derivativeSide == 'both':
# r = hstack((r1, r2, r3))
# elif derivativeSide == 'left':
# r = hstack((r1, r2))
# else: # derivativeSide == 'right'
# r = hstack((r2, r3))
return r
def d2(arg, v, **kw): #, *args, **kw):
N = len(v)
timestep = v[1] - v[0]
if not all(abs(v[1:] - v[:-1] - timestep) < 1e-10):
raise FuncDesignerException('unimplemented for non-uniform step yet')
stencil = kw.get('stencil', 1)
if stencil not in (1, ):
raise FuncDesignerException('for d2 only stencil = 1 is implemented')
if stencil == 1:
r1 = arg[0] - 2 * arg[1] + arg[2]
r2 = arg[0:N - 2] - 2 * arg[1:N - 1] + arg[2:N]
r3 = arg[N - 1] - 2 * arg[N - 2] + arg[N - 3]
return hstack((r1, r2, r3)) / timestep**2
def d2(arg, v, **kw):#, *args, **kw):
N = len(v)
timestep = v[1]-v[0]
if not all(abs(v[1:] - v [:-1] - timestep) < 1e-10):
raise FuncDesignerException('unimplemented for non-uniform step yet')
stencil = kw.get('stencil', 1)
if stencil not in (1, ):
raise FuncDesignerException('for d2 only stencil = 1 is implemented')
if stencil == 1:
r1 = arg[0] - 2*arg[1] + arg[2]
r2 = arg[0:N-2] - 2 * arg[1:N-1] + arg[2:N]
r3 = arg[N-1] - 2*arg[N-2] + arg[N-3]
return hstack((r1, r2, r3)) / timestep**2