def main():
opt = read_args()
print opt.scheme, opt.nspots, opt.nvols, opt.n
print
if opt.cpu:
utils.tic("CPU Create:")
F = create_cpu(nspots=opt.nspots, nvols=opt.nvols)
utils.toc()
idx = F.idx
if opt.run and opt.npaths:
mc = F.option.monte_carlo()
print mc
if opt.run:
print run(1.0/opt.n, F, opt.scheme)[idx]
F.grid.reset()
if opt.gpu:
utils.tic("GPU Create 1:")
FG = create_gpu(nspots=opt.nspots, nvols=opt.nvols)
utils.toc()
idx = FG.idx
if opt.run:
print run(1.0/opt.n, FG, opt.scheme, FG.grid.domain[0])[idx],
print
def main():
opt = read_args()
print opt.scheme, opt.nspots, opt.nvols, opt.n
print
if opt.cpu:
utils.tic("CPU Create:")
F = create_cpu(nspots=opt.nspots, nvols=opt.nvols)
utils.toc()
idx = F.idx
if opt.run and opt.npaths:
mc = F.option.monte_carlo()
print mc
if opt.run:
print run(1.0 / opt.n, F, opt.scheme)[idx]
F.grid.reset()
if opt.gpu:
utils.tic("GPU Create 1:")
FG = create_gpu(nspots=opt.nspots, nvols=opt.nvols)
utils.toc()
idx = FG.idx
if opt.run:
print run(1.0 / opt.n, FG, opt.scheme, FG.grid.domain[0])[idx],
print
def impl(V, L1, R1x, L2, R2x, dt, n, initial=None, callback=None):
V = V.copy()
# L1i = flatten_tensor(L1)
L1i = L1.copy()
R1 = np.array(R1x).T
# L2i = flatten_tensor(L2)
L2i = L2.copy()
R2 = np.array(R2x)
m = 2
# L = (As + Ass - H.interest_rate*np.eye(nspots))*-dt + np.eye(nspots)
L1i.data *= -dt
L1i.data[m, :] += 1
R1 *= -dt
L2i.data *= -dt
L2i.data[m, :] += 1
R2 *= -dt
offsets1 = (abs(min(L1i.offsets)), abs(max(L1i.offsets)))
offsets2 = (abs(min(L2i.offsets)), abs(max(L2i.offsets)))
dx = np.gradient(spots)[:, np.newaxis]
dy = np.gradient(vars)
Y, X = np.meshgrid(vars, spots)
gradgrid = dt * coeffs[(0, 1)](0, X, Y) / (dx * dy)
gradgrid[:, 0] = 0
gradgrid[:, -1] = 0
gradgrid[0, :] = 0
gradgrid[-1, :] = 0
print_step = max(1, int(n / 10))
to_percent = 100.0 / n
utils.tic("Impl:\t")
for k in xrange(n):
if not k % print_step:
if np.isnan(V).any():
print "Impl fail @ t = %f (%i steps)" % (dt * k, k)
return crumbs
print int(k * to_percent),
if callback is not None:
callback(V, ((n - k) * dt))
Vsv = np.gradient(np.gradient(V)[0])[1] * gradgrid
# Vsv = 0.0
V = spl.solve_banded(offsets2, L2i.data, (V + Vsv - R2).flat, overwrite_b=True).reshape(V.shape)
V = spl.solve_banded(offsets1, L1i.data, (V - R1).T.flat, overwrite_b=True).reshape(V.shape[::-1]).T
crumbs.append(V.copy())
utils.toc(": \t")
return crumbs
def douglas(V, L1, R1x, L2, R2x, dt, n, initial=None, callback=None):
V = V.copy()
theta = 0.5
# dt *= 0.5
# L1e = flatten_tensor(L1)
L1e = L1.copy()
L1i = L1e.copy()
R1 = np.array(R1x).T
# L2e = flatten_tensor(L2)
L2e = L2.copy()
L2i = L2e.copy()
R2 = np.array(R2x)
# print "L var"
# fp(L2e.data, 2)
# print "FDE op var"
# fp(F.operators[1].data, 2)
# print "diff"
# fp(F.operators[1].data - L2e.data, 2, 'f')
# assert np.allclose(F.operators[1].data, L2e.data)
m = 2
# L = (As + Ass - H.interest_rate*np.eye(nspots))*-dt + np.eye(nspots)
L1i.data *= -theta * dt
L1i.data[m, :] += 1
# R1 *= dt
L2i.data *= -theta * dt
L2i.data[m, :] += 1
# R2 *= dt
offsets1 = (abs(min(L1i.offsets)), abs(max(L1i.offsets)))
offsets2 = (abs(min(L2i.offsets)), abs(max(L2i.offsets)))
dx = np.gradient(spots)[:, np.newaxis]
dy = np.gradient(vars)
X, Y = [dim.T for dim in np.meshgrid(spots, vars)]
gradgrid = coeffs[(0, 1)](0, X, Y) / (dx * dy)
gradgrid[:, 0] = 0
gradgrid[:, -1] = 0
gradgrid[0, :] = 0
gradgrid[-1, :] = 0
print_step = max(1, int(n / 10))
to_percent = 100.0 / n
utils.tic("Douglas:\t")
R = R1 + R2
normal_shape = V.shape
transposed_shape = V.T.shape
for k in xrange(n):
if not k % print_step:
if np.isnan(V).any():
print "Douglas fail @ t = %f (%i steps)" % (dt * k, k)
return crumbs
print int(k * to_percent),
if callback is not None:
callback(V, ((n - k) * dt))
Vsv = np.gradient(np.gradient(V)[0])[1] * gradgrid
# V12 = (V
# + Vsv
# + (1-theta)*dt*L1e.dot(V.T.flat).reshape(transposed_shape).T
# + (1-theta)*dt*L2e.dot(V.flat).reshape(normal_shape)
# + dt * R)
# V1 = spl.solve_banded(offsets2, L2i.data, V12.flat, overwrite_b=True).reshape(normal_shape)
# V = spl.solve_banded(offsets1, L1i.data, V1.T.flat, overwrite_b=True).reshape(transposed_shape).T
V1 = (L1e.dot(V.T.flat).reshape(transposed_shape)).T
V2 = L2e.dot(V.flat).reshape(normal_shape)
Y0 = V + dt * (Vsv + V1 + V2 + R)
V1 = Y0 - theta * dt * L1e.dot(V.T.flat).reshape(transposed_shape).T
Y1 = spl.solve_banded(offsets1, L1i.data, V1.T.flat, overwrite_b=True).reshape(transposed_shape).T
V2 = Y1 - theta * dt * L2e.dot(V.flat).reshape(normal_shape)
Y2 = spl.solve_banded(offsets2, L2i.data, V2.flat, overwrite_b=True).reshape(normal_shape)
V = Y2
crumbs.append(V.copy())
utils.toc(": \t")
return crumbs
tenor=H.tenor,
).analytical
utils.tic("Heston Analytical:\t")
hs = hs_call_vector(
spots,
H.strike,
H.interest_rate.value,
np.sqrt(vars),
H.tenor,
H.mean_reversion,
H.mean_variance,
H.vol_of_variance,
H.correlation,
)
utils.toc()
hs = np.nan_to_num(hs)
if max(hs.flat) > spots[-1] * 2:
BADANALYTICAL = True
print "Warning: Analytical solution looks like trash."
if len(sys.argv) > 1:
if sys.argv[1] == "0":
print "Bail out with arg 0."
sys.exit()
def mu_s(t, *dim):
return H.interest_rate.value * dim[0]
def implicit_manual(V,
L1,
R1x,
L2,
R2x,
dt,
n,
spots,
vars,
coeffs,
crumbs=[],
callback=None):
V = V.copy()
# L1i = flatten_tensor(L1)
L1i = L1.copy()
R1 = np.array(R1x)
# L2i = flatten_tensor(L2)
L2i = L2.copy()
R2 = np.array(R2x)
m = 2
# L = (As + Ass - H.interest_rate*np.eye(nspots))*-dt + np.eye(nspots)
L1i.data *= -dt
L1i.data[m, :] += 1
R1 *= dt
L2i.data *= -dt
L2i.data[m, :] += 1
R2 *= dt
offsets1 = (abs(min(L1i.offsets)), abs(max(L1i.offsets)))
offsets2 = (abs(min(L2i.offsets)), abs(max(L2i.offsets)))
dx = np.gradient(spots)[:, np.newaxis]
dy = np.gradient(vars)
X, Y = [dim.T for dim in np.meshgrid(spots, vars)]
gradgrid = dt * coeffs[(0, 1)](0, X, Y) / (dx * dy)
gradgrid[:, 0] = 0
gradgrid[:, -1] = 0
gradgrid[0, :] = 0
gradgrid[-1, :] = 0
print_step = max(1, int(n / 10))
to_percent = 100.0 / n
utils.tic("Impl:")
for k in xrange(n):
if not k % print_step:
if np.isnan(V).any():
print "Impl fail @ t = %f (%i steps)" % (dt * k, k)
return crumbs
print int(k * to_percent),
if callback is not None:
callback(V, ((n - k) * dt))
Vsv = np.gradient(np.gradient(V)[0])[1] * gradgrid
V = spl.solve_banded(offsets2,
L2i.data, (V + Vsv + R2).flat,
overwrite_b=True).reshape(V.shape)
V = spl.solve_banded(offsets1,
L1i.data, (V + R1).T.flat,
overwrite_b=True).reshape(V.shape[::-1]).T
crumbs.append(V.copy())
utils.toc()
return crumbs
