def inversedot(m, v):
return dot(la.inverse(m), v)
n, nn = m.shape
if 1:
for i in range(n):
sys.stdout.write('% ')
for j in range(n):
if m[i, j] > 0: sys.stdout.write('+ ')
elif m[i, j] < 0: sys.stdout.write('- ')
else: sys.stdout.write(' ')
sys.stdout.write('\n')
cyclic = False
for i in range(4):
for j in range(n - 4, n):
if m[i, j] != 0:
cyclic = True
print '% cyclic:', cyclic
if not cyclic:
a = zeros((n, 11), Float)
for i in range(n):
for j in range(max(-5, -i), min(6, n - i)):
a[i, j + 5] = m[i, i + j]
for i in range(n):
sys.stdout.write('% ')
for j in range(11):
if a[i, j] > 0: sys.stdout.write('+ ')
elif a[i, j] < 0: sys.stdout.write('- ')
else: sys.stdout.write(' ')
sys.stdout.write('\n')
al, indx, d = band.bandec(a, 5, 5)
print a
band.banbks(a, 5, 5, al, indx, v)
return v
else:
#return inversedot_woodbury(m, v)
bign = 3 * n
a = zeros((bign, 11), Float)
u = zeros(bign, Float)
for i in range(bign):
u[i] = v[i % n]
for j in range(-7, 4):
a[i, j + 7] = m[i % n, (i + j + 7 * n) % n]
#print a
if 1:
for i in range(bign):
sys.stdout.write('% ')
for j in range(11):
if a[i, j] > 0: sys.stdout.write('+ ')
elif a[i, j] < 0: sys.stdout.write('- ')
else: sys.stdout.write(' ')
sys.stdout.write('\n')
#print u
al, indx, d = band.bandec(a, 5, 5)
band.banbks(a, 5, 5, al, indx, u)
#print u
return u[n + 2: 2 * n + 2]
def inversedot_woodbury(m, v):
a = zeros((n, 11), Float)
for i in range(n):
for j in range(max(-7, -i), min(4, n - i)):
a[i, j + 7] = m[i, i + j]
print a
al, indx, d = band.bandec(a, 7, 3)
VtZ = identity(4, Float)
Z = zeros((n, 4), Float)
for i in range(4):
u = zeros(n, Float)
for j in range(4):
u[j] = m[j, n - 4 + i]
band.banbks(a, 7, 3, al, indx, u)
for k in range(n):
Z[k, i] = u[k]
#Z[:,i] = u
for j in range(4):
VtZ[j, i] += u[n - 4 + j]
print Z
print VtZ
H = la.inverse(VtZ)
print H
band.banbks(a, 7, 3, al, indx, v)
return(v - dot(Z, dot(H, v[n - 4:])))