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I generated a lower triangular matrix, and I want to complete the matrix using the values in the lower triangular matrix to form a square matrix, symmetrical around the diagonal zeros.
lower_triangle = numpy.array([
[0,0,0,0],
[1,0,0,0],
[2,3,0,0],
[4,5,6,0]])
I want to generate the following complete matrix, maintaining the zero diagonal:
complete_matrix = numpy.array([
[0, 1, 2, 4],
[1, 0, 3, 5],
[2, 3, 0, 6],
[4, 5, 6, 0]])
Thanks.
408
Input : mat[4][4] = {{1, 0, 0, 0}, {1, 4, 0, 0}, {4, 6, 2, 0}, {0, 4, 7, 6}}; Output : Matrix is in lower triangular form. Input : mat[4][4] = {{1, 0, 0, 0}, {4, 3, 0, 1}, {7, 9, 2, 0}, {8, 5, 3, 6}}; Output : Matrix is not in lower triangular form.
A square matrix is called lower triangular if all the entries above the main diagonal are zero. Upper Triangular Matrix. A square matrix is called upper triangular if all the entries below the main diagonal are zero. A matrix of the form. L=[ℓ1,10ell2,1ℓ2,2ell3,1ℓ3,2⋱vdots⋮⋱⋱elln,1ℓn,2…
Python NumPy triu() is an inbuilt function that is used to return a copy of the array matrix with an element of the upper part of the triangle with respect to k.
You can simply add it to its transpose:
>>> m
array([[0, 0, 0, 0],
[1, 0, 0, 0],
[2, 3, 0, 0],
[4, 5, 6, 0]])
>>> m + m.T
array([[0, 1, 2, 4],
[1, 0, 3, 5],
[2, 3, 0, 6],
[4, 5, 6, 0]])
You can use the numpy.triu_indices or numpy.tril_indices:
>>> a=np.array([[0, 0, 0, 0],
... [1, 0, 0, 0],
... [2, 3, 0, 0],
... [4, 5, 6, 0]])
>>> irows,icols = np.triu_indices(len(a),1)
>>> a[irows,icols]=a[icols,irows]
>>> a
array([[0, 1, 2, 4],
[1, 0, 3, 5],
[2, 3, 0, 6],
[4, 5, 6, 0]])
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