(-0.137 + 0.187j) / 2.)
A_orig = toeplitz(a_fill)
a_zpad = np.zeros(40, dtype=complex)
a_zpad[0:4] = a_fill
#a_orig[:,:,0] = toeplitz([1.4+0j, 0.432+0.132j])
#a_orig[:,:,1] = toeplitz([2, (-0.137+0.187j)/2.])
#a_orig[:,:,2] = toeplitz([25, 2j])
#print "a_orig=", a_orig[:,:,0], a_orig[:,:,1]
a[:, 0] = [1.4 + 0j, 0.432 + 0.132j]
a[:, 1] = [2, (-0.137 + 0.187j) / 2.]
#a[:,2]=[25, 2j]
#l1 = block_toeplitz_decomp(a)
l2 = toeplitz_decomp(np.array(a_fill))
#print "l1", l1
#print l1[:,:,2]
#print l2, l3
print l2, l2.shape
A = np.dot(l2, np.conj(l2).T)
#At = np.dot(l1[:,:,0],np.conj(l1[:,:,0]).T)
#Ap = np.dot(l1[:,:,1],np.conj(l1[:,:,1]).T)
#print "At=",aj, aj.shape, np.sum(a_orig,2).shape
#print np.dot(l3,np.conj(l3).T)
print("Consistency check, these numbers should be small:", np.sum(A - A_orig))
#print("Consistency check, these numbers should be small:",np.sum(aj-np.sum(a_orig)))
#print("Consistency check for block decomp., these numbers should be small:",np.sum(a_orig[:,:,0]-At)-np.sum(a_orig[:,:,1]-Ap))
def block_toeplitz_par(a,b):
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
n=a.shape[1]/b
g1=np.zeros(shape=(b,n*b), dtype=complex)
g2=np.zeros(shape=(b,n*b), dtype=complex)
#for simulated data that the first matrix is toeplitz
#c=toeplitz_decomp(np.array(a[0:b,0]).reshape(-1,).tolist())
if rank==0:
#c=myBlockChol(a[0:b,0:b],1)
c=toeplitz_decomp(np.array(a[0:b,0]).reshape(-1,).tolist())
for j in xrange(0,n):
g2[:,j*b:(j+1)*b]= -np.dot(inv(c),a[0:b,j*b:(j+1)*b])
g1[:,j*b:(j+1)*b]= -g2[:,j*b:(j+1)*b]
g1=comm.bcast(g1 ,root=0)
g2=comm.bcast(g2,root=0)
size_node_temp=(n//size)*b
size_node=size_node_temp
if rank==size-1:
size_node = (n//size)*b + (n%size)*b
start = rank*size_node_temp
end = min(start+size_node, n*b)
l=np.zeros(shape=(n*b,n*b), dtype=complex)
empty=0
if rank==0:
l[0:b,:] = g1
for i in xrange( 1, n):
global_start_g1=0
global_end_g1=(n-i)*b
global_start_g2=i*b
global_end_g2=n*b
start_g1=start
if (global_end_g1<end and start<global_end_g1):
end_g1=min(end,global_end_g1)
elif (global_end_g1<end and start>=global_end_g1):
empty=1
end_g1=start
else:
end_g1=end
start_g2=start_g1+global_start_g2
end_g2=end_g1+global_start_g2
g2[:,0:start_g2]=0
g2[:,end_g2:n*b]=0
for j in xrange(0,b):
if rank==0:
g0_1=np.copy(g1[j,start_g1+j])
g0_2=np.copy(g2[:,start_g2+j])
else:
g0_1=np.zeros(shape=(1,1), dtype=complex)
g0_2=np.zeros(shape=(b,1), dtype=complex)
g0_1=comm.bcast(g0_1 ,root=0)
g0_2=comm.bcast(g0_2,root=0)
if empty:
continue
if g0_2.all()==0:
g2[:,start_g2:end_g2]=-g2[:,start_g2:end_g2]
continue
sigma=np.dot(np.conj(g0_2.T),g0_2)
alpha=-np.sign(g0_1)*np.sqrt(g0_1**2.0 - sigma)
z=g0_1+alpha
x2=-np.copy(g0_2)/np.conj(z)
beta=(2*z*np.conj(z))/(np.conj(z)*z-sigma)
if rank==0 :
g1[j,start_g1+j]=-alpha
g2[:,start_g2+j]=0
v=np.copy(g1[j,start_g1+j+1:end_g1]+np.dot(np.conj(x2.T),g2[:,start_g2+j+1:end_g2]))
g1[j,start_g1+j+1:end_g1]=g1[j,start_g1+j+1:end_g1]-beta*v
v=np.reshape(v,(1,v.shape[0]))
x2=np.reshape(x2,(1,x2.shape[0]))
g2[:,start_g2+j+1:end_g2]=-g2[:,start_g2+j+1:end_g2]-beta*np.dot(x2.T,v)
else:
v=np.copy(g1[j,start_g1:end_g1]+np.dot(np.conj(x2.T),g2[:,start_g2:end_g2]))
g1[j,start_g1:end_g1]=g1[j,start_g1:end_g1]-beta*v
v=np.reshape(v,(1,v.shape[0]))
x2=np.reshape(x2,(1,x2.shape[0]))
g2[:,start_g2:end_g2]=-g2[:,start_g2:end_g2]-beta*np.dot(x2.T,v)
a_fill = (1.4+0j, 0.432+0.132j, (0.229-0.318j)/4., (-0.137+0.187j)/2.)
A_orig = toeplitz(a_fill)
a_zpad = np.zeros(40,dtype=complex)
a_zpad[0:4] = a_fill
#a_orig[:,:,0] = toeplitz([1.4+0j, 0.432+0.132j])
#a_orig[:,:,1] = toeplitz([2, (-0.137+0.187j)/2.])
#a_orig[:,:,2] = toeplitz([25, 2j])
#print "a_orig=", a_orig[:,:,0], a_orig[:,:,1]
a[:,0] = [1.4+0j, 0.432+0.132j]
a[:,1] = [2, (-0.137+0.187j)/2.]
#a[:,2]=[25, 2j]
#l1 = block_toeplitz_decomp(a)
l2 = toeplitz_decomp(np.array(a_fill))
#print "l1", l1
#print l1[:,:,2]
#print l2, l3
print l2,l2.shape
A = np.dot(l2,np.conj(l2).T)
#At = np.dot(l1[:,:,0],np.conj(l1[:,:,0]).T)
#Ap = np.dot(l1[:,:,1],np.conj(l1[:,:,1]).T)
#print "At=",aj, aj.shape, np.sum(a_orig,2).shape
#print np.dot(l3,np.conj(l3).T)
print("Consistency check, these numbers should be small:",np.sum(A-A_orig))
#print("Consistency check, these numbers should be small:",np.sum(aj-np.sum(a_orig)))
