Created
April 22, 2017 14:18
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test choSolver against lapack
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#from scipy.linalg import cho_solve | |
from scipy.linalg.lapack import dpotrs | |
import numpy as np | |
def choBackSubstitution(L,y,lower=True,modify=False): | |
if not modify: | |
x = np.copy(y) | |
else: | |
x = y | |
if lower: | |
i = 0 | |
while i < L.shape[0]: | |
x[i] /= L[i,i] | |
x[i+1:] -= L[i+1:,i]*x[i] | |
i += 1 | |
else: | |
i = L.shape[0] - 1 | |
while i >= 0: | |
x[i] /= L[i,i] | |
x[:i] -= L[:i,i]*x[i] | |
i -= 1 | |
return x | |
def choSolve(L,b,modify=False): | |
return choBackSubstitution(L.T,choBackSubstitution(L,b,True,modify),False,modify) | |
N = 5000 | |
y = np.random.uniform(size=N) | |
a = np.random.uniform(size=[N,N]) | |
a = a.T.dot(a) | |
L = np.linalg.cholesky(a) | |
%load_ext line_profiler | |
%lprun -f choBackSubstitution choSolve(L,y,False) | |
#with y vec mod (no copy) | |
%timeit -n 10 choSolve(L,y,False) | |
#built in | |
#%timeit cho_solve((L,True),y) | |
%timeit -n 10 dpotrs(L,y,1,0) | |
#x1 = cho_solve((L,True),y) | |
x1 = dpotrs(L,y,1,0) | |
x2 = choSolve(L,y,False) | |
#x1 = dpotrs(L,y,1,1) | |
print("same:",np.alltrue(np.isclose(x1[0],x2))) | |
times1 = [] | |
times2 = [] | |
Ns = 10**np.linspace(1,4,20) | |
from time import clock | |
for N in Ns: | |
N = int(N) | |
y = np.random.uniform(size=N) | |
a = np.random.uniform(size=[N,N]) | |
a = a.T.dot(a) | |
L = np.linalg.cholesky(a) | |
t1 = clock() | |
#x1 = cho_solve((L,True),y) | |
x1 = dpotrs(L,y,1,0) | |
times1.append(clock()-t1) | |
t1 = clock() | |
x2 = choSolve(L,y,False) | |
times2.append(clock()-t1) | |
import pylab as plt | |
plt.plot(Ns,times1,label='scipy.linalg.cho_solve') | |
plt.plot(Ns,times2,label='my choSolve') | |
plt.yscale('log') | |
plt.xscale('log') | |
plt.legend() | |
plt.show() |
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