误差理论与测量平差基础：四大基础平差法Python程序实现（准确高精度）

发布于 2020-11-26 636 次阅读

条件平差

附有参数的条件平差

间接平差

附有限制条件的间接平差

综合程序：

#!/usr/bin/python3
#-*- coding: utf-8 -*-

import numpy as np

def limitAdjustment(A,W,P=None):
    A=np.mat(A)
    W=np.mat(W)

    if P is None:
        P = np.identity(A.shape[1])
    else:
        P=np.mat(P)

    print("-P\n",P)
    Q = np.linalg.inv(P)
    print("\n-Q\n",Q)
    invP = np.linalg.inv(P)
    Naa = A*invP*np.transpose(A)
    K = -np.linalg.inv(Naa)*W
    v = invP*np.transpose(A)*K
    r = A.shape[0]
    sigama = np.sqrt((np.transpose(v)*P*v)[0,0]/A.shape[0])
    print("K:\n{} \n -V:\n {}\n\n -sigama: {}".format(K,v,sigama))
    #改正数协因数阵
    Qvv = Q*np.transpose(A)*np.linalg.inv(Naa)*A*Q
    #平差值协因数阵
    Qadjhh = Q - Qvv
    print("------\nQvv:\n{} \n -QL^L^:\n {}".format(Qvv,Qadjhh))

    return v

def infiniteParaLimitAdjustment(A,B,W,P=None,r=None):
    """
    附有参数的条件平差模型 - 多次检验正确

    """
    A = np.mat(A)
    B = np.mat(B)
    if P is None:
        P = np.identity(A.shape[1])
    else:
        P=np.mat(P)
    Q = np.linalg.inv(P)
    Naa = A*Q*np.transpose(A)
    invNaa = np.linalg.inv(Naa)
    tranB = np.transpose(B)
    Nbb = tranB*invNaa*B

    x = -np.linalg.inv(Nbb)*tranB*invNaa*W
    K = -invNaa*(B*x+W)
    V = Q*np.transpose(A)*K
    print("- P\n{}\n -Q\n{} \n- Naa\n{} \n - invNaa \n{}\n- Nbb\n{} \n-x\n{}\n-v\n{}".format(P,Q,Naa,invNaa,Nbb,x,V))
    if r is not None:
        print("\n-sigama: ",np.sqrt((np.transpose(V)*P*V)[0,0]/r))
    print("\n ----平差后协因数\n - Qx^x^=invNbb\n{}\n - Qvv:".format(np.linalg.inv(Nbb)))

    return x,V

def indirectAdjustment(B,L,P=None,r=None):
    """
    间接平差
    """
    # jianjie adjustment
    matrixB = np.mat(B)
    matrixL = np.mat(L)
    print("- matrixL\n",matrixL)

    if P is None:
        P = np.identity(matrixB.shape[0])

    else:
        P=np.mat(P)

    print("-matrixP\n",P)
    Q = np.linalg.inv(P)
    print("-matrixQ\n",Q)
    NBB = np.linalg.inv(np.transpose(matrixB)*P*matrixB)

    W = np.transpose(matrixB)*P*matrixL
    print("-"*20,"\n")
    print(NBB)
    print("-W-\n")
    print(W)
    x = NBB*W
    V = matrixB*x-matrixL
    print("matrixX\n",x,"\nmatrixV\n",V)

    if r is not None:
        print("\n-sigama: ",np.sqrt((np.transpose(V)*P*V)[0,0]/r))
    invNBB = np.linalg.inv(NBB)
    Q_adjLL = matrixB*invNBB*np.transpose(matrixB)
    print("\n ----平差后协因数\n - Qx^x^=invNbb\n{}\n - Qvv:\n{}\n -QL^L^\n{}".format(invNBB,Q-Q_adjLL,Q_adjLL))

    print()
    return x,V

def infiniteLimitIndiractment():
    pass

def test_limitAdjustment():
    A=[1,1,1]
    W=[-6/1000]
    P=[3,3,2]

    L=[[4.557],[4.277],[-8.84]]
    P=np.diag(P)
    v=limitAdjustment(A,W,P)
    adjL = np.mat(L)+v
    equation = adjL[0,0]+adjL[1,0]+adjL[2,0]
    print("-AdjL\n{}\n -检核闭合差\n{}".format(adjL,equation))

def test_indirectAdjustment():
    L = [[0],[-23],[0],[14],[0]]
    conr = [3.5,2.7,4.0,3.0,2.5]
    P = np.diag(conr)
    B = [[1,0,0],
            [-1,1,0],
            [0,1,0],
            [0,1,-1],
            [0,0,1]
            ]

    indirectAdjustment(B,L,P,3)

def test_infiniteParaLimitAdjustment():
    A = [[1,-1,0,0],
        [0,0,1,-1],
        [1,0,0,0],
        [0,0,1,0]]
    B = [[0],[0],[-1],[1]]
    W = [[-20],[20],[0],[30]]
    P = np.diag([3,0.5,1,0.5])
    x,v=infiniteParaLimitAdjustment(A,B,W,P)
    L=np.mat([[1.95],[1.97],[3.08],[3.06]])
    adjL=L+v/1000
    print("平差值-adjX\n{} \n - adjL\n{}".format(59.95+x/1000,adjL))
    #print("\n- other\n{} - {}".format(adjL[0,0]**2+adjL[1,0]**2-adjL[2,0]**2,adjL[0,0]*adjL[1,0]-(L[0,0]*L[1,0]+x)[0,0]))

def test_infiniteLimitIndiractment():
    pass

if __name__=="__main__":
    test_limitAdjustment()
    #test_infiniteParaLimitAdjustment()

    #test_indirectAdjustment()

执行检验：

Linu下执行脚本：

# 条件平差
root@ws-tkpjiq-0:~/linuxLearn/adjustment# python3 limitAdjustment.py 
- P
[[3.  0.  0.  0. ]
 [0.  0.5 0.  0. ]
 [0.  0.  1.  0. ]
 [0.  0.  0.  0.5]]
 -Q
[[0.33333333 0.         0.         0.        ]
 [0.         2.         0.         0.        ]
 [0.         0.         1.         0.        ]
 [0.         0.         0.         2.        ]] 
- Naa
[[2.33333333 0.         0.33333333 0.        ]
 [0.         3.         0.         1.        ]
 [0.33333333 0.         0.33333333 0.        ]
 [0.         1.         0.         1.        ]] 
 - invNaa 
[[ 0.5  0.  -0.5  0. ]
 [ 0.   0.5  0.  -0.5]
 [-0.5  0.   3.5  0. ]
 [ 0.  -0.5  0.   1.5]]
- Nbb
[[5.]] 
-x
[[-5.]]
-v
[[ -5.]
 [-25.]
 [-25.]
 [ -5.]]

 ----平差后协因数
 - Qx^x^=invNbb
[[0.2]]
 - Qvv:
平差值-adjX
[[59.945]] 
 - adjL
[[1.945]
 [1.945]
 [3.055]
 [3.055]]

 # 间接平差
root@ws-tkpjiq-0:~/linuxLearn/adjustment# python3 limitAdjustment.py 
- matrixL
 [[  0]
 [-23]
 [  0]
 [ 14]
 [  0]]
-matrixP
 [[3.5 0.  0.  0.  0. ]
 [0.  2.7 0.  0.  0. ]
 [0.  0.  4.  0.  0. ]
 [0.  0.  0.  3.  0. ]
 [0.  0.  0.  0.  2.5]]
-matrixQ
 [[0.28571429 0.         0.         0.         0.        ]
 [0.         0.37037037 0.         0.         0.        ]
 [0.         0.         0.25       0.         0.        ]
 [0.         0.         0.         0.33333333 0.        ]
 [0.         0.         0.         0.         0.4       ]]
-------------------- 

[[0.18882384 0.06322512 0.03448643]
 [0.06322512 0.14518361 0.07919106]
 [0.03448643 0.07919106 0.2250133 ]]
-W-

[[ 62.1]
 [-20.1]
 [-42. ]]
matrixX
 [[ 9.00670569]
 [-2.31793507]
 [-8.90069186]] 
matrixV
 [[ 9.00670569]
 [11.67535923]
 [-2.31793507]
 [-7.41724321]
 [-8.90069186]]

 ----平差后协因数
 - Qx^x^=invNbb
[[ 6.20000000e+00 -2.70000000e+00  1.46991901e-16]
 [-2.70000000e+00  9.70000000e+00 -3.00000000e+00]
 [ 4.68434010e-17 -3.00000000e+00  5.50000000e+00]]
 - Qvv:
[[-5.91428571e+00  8.90000000e+00  2.70000000e+00  2.70000000e+00
  -1.46991901e-16]
 [ 8.90000000e+00 -2.09296296e+01 -1.24000000e+01 -1.54000000e+01
   3.00000000e+00]
 [ 2.70000000e+00 -1.24000000e+01 -9.45000000e+00 -1.27000000e+01
   3.00000000e+00]
 [ 2.70000000e+00 -1.54000000e+01 -1.27000000e+01 -2.08666667e+01
   8.50000000e+00]
 [-4.68434010e-17  3.00000000e+00  3.00000000e+00  8.50000000e+00
  -5.10000000e+00]]
 -QL^L^
[[ 6.20000000e+00 -8.90000000e+00 -2.70000000e+00 -2.70000000e+00
   1.46991901e-16]
 [-8.90000000e+00  2.13000000e+01  1.24000000e+01  1.54000000e+01
  -3.00000000e+00]
 [-2.70000000e+00  1.24000000e+01  9.70000000e+00  1.27000000e+01
  -3.00000000e+00]
 [-2.70000000e+00  1.54000000e+01  1.27000000e+01  2.12000000e+01
  -8.50000000e+00]
 [ 4.68434010e-17 -3.00000000e+00 -3.00000000e+00 -8.50000000e+00
   5.50000000e+00]]

root@ws-tkpjiq-0:~/linuxLearn/adjustment# python3 limitAdjustment.py 
- matrixL
 [[  0]
 [-23]
 [  0]
 [ 14]
 [  0]]
-matrixP
 [[3.5 0.  0.  0.  0. ]
 [0.  2.7 0.  0.  0. ]
 [0.  0.  4.  0.  0. ]
 [0.  0.  0.  3.  0. ]
 [0.  0.  0.  0.  2.5]]
-matrixQ
 [[0.28571429 0.         0.         0.         0.        ]
 [0.         0.37037037 0.         0.         0.        ]
 [0.         0.         0.25       0.         0.        ]
 [0.         0.         0.         0.33333333 0.        ]
 [0.         0.         0.         0.         0.4       ]]
-------------------- 

[[0.18882384 0.06322512 0.03448643]
 [0.06322512 0.14518361 0.07919106]
 [0.03448643 0.07919106 0.2250133 ]]
-W-

[[ 62.1]
 [-20.1]
 [-42. ]]
matrixX
 [[ 9.00670569]
 [-2.31793507]
 [-8.90069186]] 
matrixV
 [[ 9.00670569]
 [11.67535923]
 [-2.31793507]
 [-7.41724321]
 [-8.90069186]]

-sigama:  18.58820435488333

 ----平差后协因数
 - Qx^x^=invNbb
[[ 6.20000000e+00 -2.70000000e+00  1.46991901e-16]
 [-2.70000000e+00  9.70000000e+00 -3.00000000e+00]
 [ 4.68434010e-17 -3.00000000e+00  5.50000000e+00]]
 - Qvv:
[[-5.91428571e+00  8.90000000e+00  2.70000000e+00  2.70000000e+00
  -1.46991901e-16]
 [ 8.90000000e+00 -2.09296296e+01 -1.24000000e+01 -1.54000000e+01
   3.00000000e+00]
 [ 2.70000000e+00 -1.24000000e+01 -9.45000000e+00 -1.27000000e+01
   3.00000000e+00]
 [ 2.70000000e+00 -1.54000000e+01 -1.27000000e+01 -2.08666667e+01
   8.50000000e+00]
 [-4.68434010e-17  3.00000000e+00  3.00000000e+00  8.50000000e+00
  -5.10000000e+00]]
 -QL^L^
[[ 6.20000000e+00 -8.90000000e+00 -2.70000000e+00 -2.70000000e+00
   1.46991901e-16]
 [-8.90000000e+00  2.13000000e+01  1.24000000e+01  1.54000000e+01
  -3.00000000e+00]
 [-2.70000000e+00  1.24000000e+01  9.70000000e+00  1.27000000e+01
  -3.00000000e+00]
 [-2.70000000e+00  1.54000000e+01  1.27000000e+01  2.12000000e+01
  -8.50000000e+00]
 [ 4.68434010e-17 -3.00000000e+00 -3.00000000e+00 -8.50000000e+00
   5.50000000e+00]]

#条件平差
root@ws-tkpjiq-0:~/linuxLearn/adjustment# python3 limitAdjustment.py 
-P
 [[3 0 0]
 [0 3 0]
 [0 0 2]]

-Q
 [[0.33333333 0.         0.        ]
 [0.         0.33333333 0.        ]
 [0.         0.         0.5       ]]
K:
[[0.00514286]] 
 -V:
 [[0.00171429]
 [0.00171429]
 [0.00257143]]

 -sigama: 0.005554920598635309
------
Qvv:
[[0.0952381  0.0952381  0.14285714]
 [0.0952381  0.0952381  0.14285714]
 [0.14285714 0.14285714 0.21428571]] 
 -QL^L^:
 [[ 0.23809524 -0.0952381  -0.14285714]
 [-0.0952381   0.23809524 -0.14285714]
 [-0.14285714 -0.14285714  0.28571429]]
-AdjL
[[ 4.55871429]
 [ 4.27871429]
 [-8.83742857]]
 -检核闭合差
0.0
root@ws-tkpjiq-0:~/linuxLearn/adjustment#

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