Re: [Numpy-discussion] Optical autocorrelation calculated with numpy is slow
Charles R Harris wrote: > That should work. The first two integrals are actually the same, but > need to be E(t)*E(t).conj(). The second integral needs twice the real > part of E(t)*E(t-tau).conj(). Numpy correlate should really have the > conjugate built in, but it doesn't. > > Chuck > It worked, thanks. João Silva ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Optical autocorrelation calculated with numpy is slow
On Tue, Mar 31, 2009 at 8:54 PM, Jochen S wrote: > On Tue, Mar 31, 2009 at 7:13 AM, João Luís Silva wrote: > >> Hi, >> > > >> I wrote a script to calculate the *optical* autocorrelation of an >> electric field. It's like the autocorrelation, but sums the fields >> instead of multiplying them. I'm calculating >> >> I(tau) = integral( abs(E(t)+E(t-tau))**2,t=-inf..inf) >> > > An autocorrelation is just a convolution, which is a multiplication in > frequency space. Thus you can do: > FT_E = fft(E) > FT_ac=FT_E*FT_E.conj() > ac = fftshift(ifft(FT_ac)) > > where E is your field and ac is your autocorrelation. Also what sort of > autocorrelation are you talking about. For instance SHG autocorrelation is > an intensity autocorrelation thus the first line should be: > FT_E = fft(abs(E)**2) > Sorry I was reading over your example to quickly earlier, you're obviously using intensity autocorrelation so what you should be doing is: FT_E=fft(abs(E)**2) FT_ac = FT_E*FT_E.conj() ac = fftshift(ifft(FT_ac)) > > HTH > Jochen > > >> with script appended at the end. It's too slow for my purposes (takes ~5 >> seconds, and scales ~O(N**2)). numpy's correlate is fast enough, but >> isn't what I need as it multiplies instead of add the fields. Could you >> help me get this script to run faster (without having to write it in >> another programming language) ? >> >> Thanks, >> João Silva >> >> # >> >> import numpy as np >> #import matplotlib.pyplot as plt >> >> n = 2**12 >> n_autocorr = 3*n-2 >> >> c = 3E2 >> w0 = 2.0*np.pi*c/800.0 >> t_max = 100.0 >> t = np.linspace(-t_max/2.0,t_max/2.0,n) >> >> E = np.exp(-(t/10.0)**2)*np.exp(1j*w0*t)#Electric field >> >> dt = t[1]-t[0] >> t_autocorr=np.linspace(-dt*n_autocorr/2.0,dt*n_autocorr/2.0,n_autocorr) >> E1 = np.zeros(n_autocorr,dtype=E.dtype) >> E2 = np.zeros(n_autocorr,dtype=E.dtype) >> Ac = np.zeros(n_autocorr,dtype=np.float64) >> >> E2[n-1:n-1+n] = E[:] >> >> for i in range(2*n-2): >> E1[:] = 0.0 >> E1[i:i+n] = E[:] >> >> Ac[i] = np.sum(np.abs(E1+E2)**2) >> >> Ac *= dt >> >> #plt.plot(t_autocorr,Ac) >> #plt.show() >> >> # >> >> ___ >> Numpy-discussion mailing list >> Numpy-discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion >> > > ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Optical autocorrelation calculated with numpy is slow
On Tue, Mar 31, 2009 at 7:13 AM, João Luís Silva wrote: > Hi, > > I wrote a script to calculate the *optical* autocorrelation of an > electric field. It's like the autocorrelation, but sums the fields > instead of multiplying them. I'm calculating > > I(tau) = integral( abs(E(t)+E(t-tau))**2,t=-inf..inf) > An autocorrelation is just a convolution, which is a multiplication in frequency space. Thus you can do: FT_E = fft(E) FT_ac=FT_E*FT_E.conj() ac = fftshift(ifft(FT_ac)) where E is your field and ac is your autocorrelation. Also what sort of autocorrelation are you talking about. For instance SHG autocorrelation is an intensity autocorrelation thus the first line should be: FT_E = fft(abs(E)**2) HTH Jochen > with script appended at the end. It's too slow for my purposes (takes ~5 > seconds, and scales ~O(N**2)). numpy's correlate is fast enough, but > isn't what I need as it multiplies instead of add the fields. Could you > help me get this script to run faster (without having to write it in > another programming language) ? > > Thanks, > João Silva > > # > > import numpy as np > #import matplotlib.pyplot as plt > > n = 2**12 > n_autocorr = 3*n-2 > > c = 3E2 > w0 = 2.0*np.pi*c/800.0 > t_max = 100.0 > t = np.linspace(-t_max/2.0,t_max/2.0,n) > > E = np.exp(-(t/10.0)**2)*np.exp(1j*w0*t)#Electric field > > dt = t[1]-t[0] > t_autocorr=np.linspace(-dt*n_autocorr/2.0,dt*n_autocorr/2.0,n_autocorr) > E1 = np.zeros(n_autocorr,dtype=E.dtype) > E2 = np.zeros(n_autocorr,dtype=E.dtype) > Ac = np.zeros(n_autocorr,dtype=np.float64) > > E2[n-1:n-1+n] = E[:] > > for i in range(2*n-2): > E1[:] = 0.0 > E1[i:i+n] = E[:] > > Ac[i] = np.sum(np.abs(E1+E2)**2) > > Ac *= dt > > #plt.plot(t_autocorr,Ac) > #plt.show() > > # > > ___ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Optical autocorrelation calculated with numpy is slow
On Mon, Mar 30, 2009 at 12:23 PM, Anne Archibald wrote: > 2009/3/30 João Luís Silva : > > Hi, > > > > I wrote a script to calculate the *optical* autocorrelation of an > > electric field. It's like the autocorrelation, but sums the fields > > instead of multiplying them. I'm calculating > > > > I(tau) = integral( abs(E(t)+E(t-tau))**2,t=-inf..inf) > > You may be in trouble if there's cancellation, but can't you just > rewrite this as E(t)**2+E(t-tau)**2-2*E(t)*E(t-tau)? Then you have two > O(n) integrals and one standard autocorrelation... > That should work. The first two integrals are actually the same, but need to be E(t)*E(t).conj(). The second integral needs twice the real part of E(t)*E(t-tau).conj(). Numpy correlate should really have the conjugate built in, but it doesn't. Chuck ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Optical autocorrelation calculated with numpy is slow
2009/3/30 João Luís Silva : > Hi, > > I wrote a script to calculate the *optical* autocorrelation of an > electric field. It's like the autocorrelation, but sums the fields > instead of multiplying them. I'm calculating > > I(tau) = integral( abs(E(t)+E(t-tau))**2,t=-inf..inf) You may be in trouble if there's cancellation, but can't you just rewrite this as E(t)**2+E(t-tau)**2-2*E(t)*E(t-tau)? Then you have two O(n) integrals and one standard autocorrelation... Anne > with script appended at the end. It's too slow for my purposes (takes ~5 > seconds, and scales ~O(N**2)). numpy's correlate is fast enough, but > isn't what I need as it multiplies instead of add the fields. Could you > help me get this script to run faster (without having to write it in > another programming language) ? > > Thanks, > João Silva > > # > > import numpy as np > #import matplotlib.pyplot as plt > > n = 2**12 > n_autocorr = 3*n-2 > > c = 3E2 > w0 = 2.0*np.pi*c/800.0 > t_max = 100.0 > t = np.linspace(-t_max/2.0,t_max/2.0,n) > > E = np.exp(-(t/10.0)**2)*np.exp(1j*w0*t) #Electric field > > dt = t[1]-t[0] > t_autocorr=np.linspace(-dt*n_autocorr/2.0,dt*n_autocorr/2.0,n_autocorr) > E1 = np.zeros(n_autocorr,dtype=E.dtype) > E2 = np.zeros(n_autocorr,dtype=E.dtype) > Ac = np.zeros(n_autocorr,dtype=np.float64) > > E2[n-1:n-1+n] = E[:] > > for i in range(2*n-2): > E1[:] = 0.0 > E1[i:i+n] = E[:] > > Ac[i] = np.sum(np.abs(E1+E2)**2) > > Ac *= dt > > #plt.plot(t_autocorr,Ac) > #plt.show() > > # > > ___ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
[Numpy-discussion] Optical autocorrelation calculated with numpy is slow
Hi, I wrote a script to calculate the *optical* autocorrelation of an electric field. It's like the autocorrelation, but sums the fields instead of multiplying them. I'm calculating I(tau) = integral( abs(E(t)+E(t-tau))**2,t=-inf..inf) with script appended at the end. It's too slow for my purposes (takes ~5 seconds, and scales ~O(N**2)). numpy's correlate is fast enough, but isn't what I need as it multiplies instead of add the fields. Could you help me get this script to run faster (without having to write it in another programming language) ? Thanks, João Silva # import numpy as np #import matplotlib.pyplot as plt n = 2**12 n_autocorr = 3*n-2 c = 3E2 w0 = 2.0*np.pi*c/800.0 t_max = 100.0 t = np.linspace(-t_max/2.0,t_max/2.0,n) E = np.exp(-(t/10.0)**2)*np.exp(1j*w0*t)#Electric field dt = t[1]-t[0] t_autocorr=np.linspace(-dt*n_autocorr/2.0,dt*n_autocorr/2.0,n_autocorr) E1 = np.zeros(n_autocorr,dtype=E.dtype) E2 = np.zeros(n_autocorr,dtype=E.dtype) Ac = np.zeros(n_autocorr,dtype=np.float64) E2[n-1:n-1+n] = E[:] for i in range(2*n-2): E1[:] = 0.0 E1[i:i+n] = E[:] Ac[i] = np.sum(np.abs(E1+E2)**2) Ac *= dt #plt.plot(t_autocorr,Ac) #plt.show() # ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
