Lattice from matrix

[XinYu73]

say I have a lattice matrix

array([[ 8.48144648e+00,  6.58925087e-16, -3.37011015e+02],
       [ 0.00000000e+00,  1.04253452e+01,  6.38368280e-16],
       [ 0.00000000e+00,  0.00000000e+00,  1.86096030e+02]])

matrix2para gives

array([337.11772326,  10.42534517, 186.0960304 ,   1.57079633, 3.14159265,   1.57079633])

in this case, a and c are almost collinear， which leads following code giving the wrong answer due to machine precision

# in para2matrix
        # Generate an upper-diagonal matrix
        a3 = a * cos_beta
        a2 = (a * (cos_gamma - (cos_beta * cos_alpha))) / sin_alpha
        matrix[2][2] = c
        matrix[1][2] = b * cos_alpha
        matrix[1][1] = b * sin_alpha
        matrix[0][2] = a3
        matrix[0][1] = a2
        tmp = a ** 2 - a3 ** 2 - a2 ** 2
        if tmp > 0:
            matrix[0][0] = np.sqrt(a ** 2 - a3 ** 2 - a2 ** 2)
        else:
            print(tmp)

I suggest that we should use

if tmp >0:
      matrix[0][0] = np.sqrt(a ** 2 - a3 ** 2 - a2 ** 2)
elif np.abs(temp) <1e-5:
    matrix[0][0] = 0
else:
    return 0

[qzhu2017]

@XinYu73 Can you give me a full example for this case? I am a bit confused why we need this. In this case, it will return a matrix with the first column as [0, 0, 0]. It will still fail for the later process.