numpy - Constraining the least squares fitting in python -

i want solve following in least-squares sense:

h = dot(a, b) + dot(a.conj(), c) 

where complex matrices h, b , c known. remaining complex matrix a (with complex conjugate) being searched.

i tried computing (python) numpy function:

x, res, r, singval = np.linalg.lstsq(np.vstack((b, c)), h) 

however results not in shape want( --> array((a, a.conj())).

how can solve this?

the easiest way found separating value of a real , imaginary part:

a = u + 1j*v 

therefore:

h = dot(u, b+c) + 1j*dot(v, b-c) 

and use of scipy.optimize.lstsqr, model defined as:

def model(b, c, uv):     u = uv[:len(uv)//2]     v = uv[len(uv)//2:]     h = np.dot(u, b+c) + 1j*np.dot(v, b+c)     return h.view(float) 

and residuals as:

def residuals(params, b, c, h):     uv = params     diff = model(b, c, uv) - h.view(float)     return diff.flatten() 

and result obtained follows:

params, cov = optimize.leastsq(residuals, x0 = np.ones(len(uv), dtype = float),                                 args=(b, c, h))