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  Python implementation Bursa transition model
     
  Add Date : 2018-11-21      
         
         
         
  The core issue

1. Because it is the same accuracy and mutually independent observations, final weight matrix should be used for the matrix P (3m * 3m), m is the number of known points.

p = np.eye (n) # Unit weight matrix 3n * 3n

2. The program implements all known points of XYZ coordinate read into the corresponding columns of the matrix, the coefficient matrix B also need this operation (V = BX-L). When numpy process can be expressed as:

for i in range (vector_count):
        matrix_source.append (vector3d_list_source [i] .X)
        matrix_source.append (vector3d_list_source [i] .Y)
        matrix_source.append (vector3d_list_source [i] .Z)
        matrix_dest.append (vector3d_list_dest [i] .X)
        matrix_dest.append (vector3d_list_dest [i] .Y)
        matrix_dest.append (vector3d_list_dest [i] .Z)
        matrix_B.append ([1, 0, 0, 0, -vector3d_list_source [i] .Z, vector3d_list_source [i] .Y, vector3d_list_source [i] .X])
        matrix_B.append ([0, 1, 0, vector3d_list_source [i] .Z, 0, -vector3d_list_source [i] .X, vector3d_list_source [i] .Y])
        matrix_B.append ([0, 0, 1, -vector3d_list_source [i] .Y, vector3d_list_source [i] .X, 0, vector3d_list_source [i] .Z])
    matrix_source = np.array (matrix_source) .reshape (1, -1) .T
    matrix_dest = np.array (matrix_dest) .reshape (1, -1) .T
    matrix_B = np.array (matrix_B)
    L = matrix_dest - matrix_source

3. The value of the parameter matrix (column matrix)

X = np.dot (np.linalg.inv (np.dot (matrix_B.T, matrix_B)), np.dot (matrix_B.T, L))

4. The error equation

V = np.dot (matrix_B, X) - L # error equation

5. Accuracy Assessment

standard_deviation = math.sqrt (np.dot (np.dot (V.T, p), V) / r) # conversion error
     
         
         
         
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