numpy.triu_indices#

numpy.triu_indices(n,k=0,m=None)[source]#

Return the indices for the upper-triangle of an (n, m) array.

Parameters:
nint

The size of the arrays for which the returned indices willbe valid.

kint, optional

Diagonal offset (seetriu for details).

mint, optional

The column dimension of the arrays for which the returnedarrays will be valid.By defaultm is taken equal ton.

Returns:
indstuple, shape(2) of ndarrays, shape(n)

The row and column indices, respectively. The row indices are sortedin non-decreasing order, and the correspdonding column indices arestrictly increasing for each row.

See also

tril_indices

similar function, for lower-triangular.

mask_indices

generic function accepting an arbitrary mask function.

triu,tril

Examples

>>>importnumpyasnp

Compute two different sets of indices to access 4x4 arrays, one for theupper triangular part starting at the main diagonal, and one starting twodiagonals further right:

>>>iu1=np.triu_indices(4)>>>iu1(array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))

Note that row indices (first array) are non-decreasing, and the correspondingcolumn indices (second array) are strictly increasing for each row.

Here is how they can be used with a sample array:

>>>a=np.arange(16).reshape(4,4)>>>aarray([[ 0,  1,  2,  3],       [ 4,  5,  6,  7],       [ 8,  9, 10, 11],       [12, 13, 14, 15]])

Both for indexing:

>>>a[iu1]array([ 0,  1,  2, ..., 10, 11, 15])

And for assigning values:

>>>a[iu1]=-1>>>aarray([[-1, -1, -1, -1],       [ 4, -1, -1, -1],       [ 8,  9, -1, -1],       [12, 13, 14, -1]])

These cover only a small part of the whole array (two diagonals rightof the main one):

>>>iu2=np.triu_indices(4,2)>>>a[iu2]=-10>>>aarray([[ -1,  -1, -10, -10],       [  4,  -1,  -1, -10],       [  8,   9,  -1,  -1],       [ 12,  13,  14,  -1]])
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