def shermanMorrison(x, Ainv, m, up=True):
'''
Does a rank-1 adjustment of Ainv using the Sherman-Morrison formula
(A + xx^H)^(-1) = A^(-1) - (A^(-1)xx^(H)A^(-1)) / (1 + x^(H)A^(-1)x)
if (1 + x^(H)A^(-1)x) != 0.
Ainv is a matrix of size m*m
x is a column vector of length m
If up == True: A rank update is performed,
otherwise we do a rank degrade.
'''
factor = 1
if up != True:
factor = -1
xH = x.conjugate()
Ainvx = mynp.dot(Ainv, x)
xHAinv = mynp.dot(xH, Ainv)
xHAinvx = mynp.dot(
xH, mynp.dot(Ainv, x)
) # memory layout impose this product rather than reusing xHAinv (the result here is a scalar)
numerator = mynp.outer(Ainvx, xHAinv)
denominator = 1 + factor * xHAinvx
if abs(denominator) == 0:
raise Exception('Denominator is 0 in Sherman Morrison formula')
return Ainv - ((factor / denominator) * numerator)
def shermanMorrison(x, Ainv, m, up = True):
'''
Does a rank-1 adjustment of Ainv using the Sherman-Morrison formula
(A + xx^H)^(-1) = A^(-1) - (A^(-1)xx^(H)A^(-1)) / (1 + x^(H)A^(-1)x)
if (1 + x^(H)A^(-1)x) != 0.
Ainv is a matrix of size m*m
x is a column vector of length m
If up == True: A rank update is performed,
otherwise we do a rank degrade.
'''
factor = 1
if up != True:
factor = -1
xH = x.conjugate()
Ainvx = mynp.dot(Ainv, x)
xHAinv = mynp.dot(xH, Ainv)
xHAinvx = mynp.dot(xH, mynp.dot(Ainv, x)) # memory layout impose this product rather than reusing xHAinv (the result here is a scalar)
numerator = mynp.outer(Ainvx, xHAinv)
denominator = 1 + factor * xHAinvx
if abs(denominator) == 0:
raise Exception('Denominator is 0 in Sherman Morrison formula')
return Ainv - ( (factor/denominator) * numerator )
def calcBeamPatternLinearArray(self, w, M, spacing, thetas, steering_angle=0, takePowerAndNormalize=False):
x_el = np.linspace( -(M-1)/(2.0/spacing), (M-1)/(2.0/spacing), M )
W_matrix = np.exp(-1j * np.outer(2*np.pi*(np.sin(thetas) - np.sin(steering_angle)), x_el))
W = np.dot(W_matrix , w)
if takePowerAndNormalize:
W = W*W.conj()
W = W / W.max()
return W
def calcBeamPatternLinearArray(self,
w,
M,
spacing,
thetas,
steering_angle=0,
takePowerAndNormalize=False):
x_el = np.linspace(-(M - 1) / (2.0 / spacing),
(M - 1) / (2.0 / spacing), M)
W_matrix = np.exp(
-1j *
np.outer(2 * np.pi *
(np.sin(thetas) - np.sin(steering_angle)), x_el))
W = np.dot(W_matrix, w)
if takePowerAndNormalize:
W = W * W.conj()
W = W / W.max()
return W
def testComplexCholeskySolver(self):
N = 32
x = np.random.normal(loc=0.0, scale=1.0, size=(N,)) + 1j * np.random.normal(loc=0.0, scale=1.0, size=(N,))
A = np.outer(x, x.conj()).astype("complex128")
A = A + 0.5 * np.eye(N)
b = np.ones(N, dtype=np.complex128)
# A = np.array([[3+0j,5+1j],[5-1j,14+0j]])
# b = np.array([1+0j,1+0j])
yi = mklcSolveCholeskyC(A, b)
print yi
print "Numpy reference:"
C = np.linalg.solve(A, b)
print C
print "hello"