def demo4():
theta = RiemannTheta_Function()
z = np.array([1.j, .5 * 1.j, 1.j])
omegas = []
I = 1.j
t_vals = np.linspace(1, 0, 10000)
for t in t_vals:
a = np.array([[-0.5 * t + I, 0.5 * t * (1 - I), -0.5 * t * (1 + I)],
[0.5 * t * (1 - I), I, 0], [-0.5 * t * (1 + I), 0, I]])
omegas.append(a)
print "z = (i, i, i), calculating z for 10,000 different Omegas"
print
print "Omegas = [-0.5*(1-t) + i 0.5*t*(1-i) -0.5*(1-t)*(1 + i)]"
print " [0.5*(1-t)*(1-i) i 0]"
print " [-0.5*(1-t)*(1+i) 0 i]"
print "for 0 <= t <= 1"
print
print "Beginning Computation on the GPU"
start = time.clock()
v = theta.multiple_omega_process1(z, omegas, 3)
print "Computation Finished, elapsed time: " + str(time.clock() - start)
print
print v
print
print "================================="
print "Beginning Computation on the CPU"
start = time.clock()
u = []
for i in range(10000):
U, V = theta.exp_and_osc_at_point(z, omegas[i])
u.append(V)
print "Computation Finished, elapsed time: " + str(time.clock() - start)
print
print np.array(v)
def demo1():
theta = RiemannTheta_Function()
Omega = np.array([[1.j, .5], [.5, 1.j]])
print
print "Calculating 3,600 points of the Riemann Theta Function in C..."
print
print "Omega = [i .5]"
print " [.5 i]"
print
print "z = (x + iy, 0) where (0 < x < 1) and (0 < y < 5)"
SIZE = 60
x = np.linspace(0, 1, SIZE)
y = np.linspace(0, 5, SIZE)
X, Y = p.meshgrid(x, y)
Z = X + Y * 1.0j
Z = Z.flatten()
start = time.clock()
U, V = theta.exp_and_osc_at_point([[z, 0] for z in Z],
Omega,
gpu=False,
batch=True)
done = time.clock() - start
print "Time to perform the calculation: " + str(done)
print
Z = (V.reshape(60, 60)).imag
print "\Plotting the imaginary part of the function..."
plt.contourf(X, Y, Z, 7, antialiased=True)
plt.show()
def demo3():
theta = RiemannTheta_Function()
Omega = np.array([[1.j, .5], [.5, 1.j]])
print
print "Calculating 1,000,000 points of the Riemann Theta Function on GPU..."
print
print "Omega = [i .5]"
print " [.5 i]"
print
print "z = (x + iy, 0) where (0 < x < 1) and (0 < y < 5)"
SIZE = 1000
x = np.linspace(0, 1, SIZE)
y = np.linspace(0, 5, SIZE)
X, Y = p.meshgrid(x, y)
Z = X + Y * 1.0j
Z = Z.flatten()
Z = [[z, 0] for z in Z]
print "Starting computation on the GPU"
start = time.clock()
U, V = theta.exp_and_osc_at_point(Z, Omega, batch=True)
done = time.clock() - start
print "Time to perform the calculation: " + str(done)
print
print "Starting computation on the CPU"
start = time.clock()
U, V = theta.exp_and_osc_at_point(Z, Omega, batch=True, gpu=False)
done = time.clock() - start
print "Time to perform the calculation: " + str(done)
print
def demo4():
theta = RiemannTheta_Function()
z = np.array([1.j, .5*1.j, 1.j])
omegas = []
I = 1.j
t_vals = np.linspace(1, 0, 10000)
for t in t_vals:
a = np.array([[-0.5*t + I, 0.5*t*(1-I), -0.5*t*(1 + I)],
[0.5*t*(1-I), I, 0],
[-0.5*t*(1+I), 0, I]])
omegas.append(a)
print "z = (i, i, i), calculating z for 10,000 different Omegas"
print
print "Omegas = [-0.5*(1-t) + i 0.5*t*(1-i) -0.5*(1-t)*(1 + i)]"
print " [0.5*(1-t)*(1-i) i 0]"
print " [-0.5*(1-t)*(1+i) 0 i]"
print "for 0 <= t <= 1"
print
print "Beginning Computation on the GPU"
start = time.clock()
v = theta.multiple_omega_process1(z, omegas, 3)
print "Computation Finished, elapsed time: " + str(time.clock() - start)
print
print v
print
print "================================="
print "Beginning Computation on the CPU"
start = time.clock()
u = []
for i in range(10000):
U,V = theta.exp_and_osc_at_point(z,omegas[i])
u.append(V)
print "Computation Finished, elapsed time: " + str(time.clock() - start)
print
print np.array(v)
def demo1():
theta = RiemannTheta_Function()
Omega = np.array([[1.j, .5], [.5, 1.j]])
print
print "Calculating 3,600 points of the Riemann Theta Function in C..."
print
print "Omega = [i .5]"
print " [.5 i]"
print
print "z = (x + iy, 0) where (0 < x < 1) and (0 < y < 5)"
SIZE = 60
x = np.linspace(0,1,SIZE)
y = np.linspace(0,5,SIZE)
X,Y = p.meshgrid(x,y)
Z = X + Y*1.0j
Z = Z.flatten()
start = time.clock()
U,V = theta.exp_and_osc_at_point([[z,0] for z in Z], Omega, gpu=False, batch=True)
done = time.clock() - start
print "Time to perform the calculation: " + str(done)
print
Z = (V.reshape(60,60)).imag
print "\Plotting the imaginary part of the function..."
plt.contourf(X,Y,Z,7,antialiased=True)
plt.show()
def demo3():
theta = RiemannTheta_Function()
Omega = np.array([[1.j, .5], [.5, 1.j]])
print
print "Calculating 1,000,000 points of the Riemann Theta Function on GPU..."
print
print "Omega = [i .5]"
print " [.5 i]"
print
print "z = (x + iy, 0) where (0 < x < 1) and (0 < y < 5)"
SIZE = 1000
x = np.linspace(0,1,SIZE)
y = np.linspace(0,5,SIZE)
X,Y = p.meshgrid(x,y)
Z = X + Y*1.0j
Z = Z.flatten()
Z = [[z,0] for z in Z]
print "Starting computation on the GPU"
start = time.clock()
U,V = theta.exp_and_osc_at_point(Z, Omega, batch=True)
done = time.clock() - start
print "Time to perform the calculation: " + str(done)
print
print "Starting computation on the CPU"
start = time.clock()
U,V = theta.exp_and_osc_at_point(Z, Omega, batch=True, gpu=False)
done = time.clock() - start
print "Time to perform the calculation: " + str(done)
print
