butools.reptrans.SimilarityMatrixForVectors¶

butools.reptrans.SimilarityMatrixForVectors()¶

Matlab:	B = SimilarityMatrixForVectors(vecA, vecB)
Mathematica:	B = SimilarityMatrixForVectors[vecA, vecB]
Python/Numpy:	B = SimilarityMatrixForVectors(vecA, vecB)

Returns the similarity transformation matrix that converts a given column vector to an other column vector. It works even with zero entries.

Parameters:	vecA : column vector, shape(M,1) The original column vector vecB : column vector, shape(M,1) The target column vector
Returns:	B : matrix, shape(M,M) The matrix by which \(B\cdot vecA = vecB\) holds

Examples

For Matlab:

>>> vecA = [0.0; 0.3; -1.5; 0.0];
>>> vecB = [1.0; 0.2; 0.0; 1.0];
>>> B = SimilarityMatrixForVectors(vecA, vecB);
>>> disp(B);
            0       3.3333            0            0
      0.66667      0.66667            0            0
            0            0            0            0
     -0.83333     -0.83333     -0.83333     -0.83333
>>> err = norm(B*vecA-vecB);
>>> disp(err);
     0

For Mathematica:

>>> vecA = {{0.0},{0.3},{-1.5},{0.0}};
>>> vecB = {{1.0},{0.2},{0.0},{1.0}};
>>> B = SimilarityMatrixForVectors[vecA, vecB];
>>> Print[B];
{{0., 3.3333333333333335, 0., 0.},
 {0.6666666666666667, 0.6666666666666667, 0., 0.},
 {0., 0., 0., 0.},
 {-0.8333333333333334, -0.8333333333333334, -0.8333333333333334, -0.8333333333333334}}
>>> err = Norm[B.vecA-vecB];
>>> Print[err];
0.

For Python/Numpy:

>>> vecA = ml.matrix([[0.0],[0.3],[-1.5],[0.0]])
>>> vecB = ml.matrix([[1.0],[0.2],[0.0],[1.0]])
>>> B = SimilarityMatrixForVectors(vecA, vecB)
>>> print(B)
[[ 0.       3.33333  0.       0.     ]
 [ 0.66667  0.66667  0.       0.     ]
 [ 0.       0.       0.       0.     ]
 [-0.83333 -0.83333 -0.83333 -0.83333]]
>>> err = la.norm(B*vecA-vecB)
>>> print(err)
0.0