How to interpret Allen NLP Coreference resolution model output? - python

I am working on extracting people and tasks from texts (multiple sentences) and need a way to resolve coreferencing. I found this model, and it seems very promising, but once I installed the required libraries allennlp and allennlp_models and testing the model out for myself I got:
Script:
predictor = Predictor.from_path("https://storage.googleapis.com/allennlp-public-models/coref-spanbert-large-2021.03.10.tar.gz")
prediction = predictor.predict(
document="Paul Allen was born on January 21, 1953, in Seattle, Washington, to Kenneth Sam Allen and Edna Faye Allen. Allen attended Lakeside School, a private school in Seattle, where he befriended Bill Gates, two years younger, with whom he shared an enthusiasm for computers.")
print(prediction)
Output:
{'top_spans': [[0, 1], [3, 3], [5, 8], [5, 14], [8, 8], [11, 13], [11, 14], [13, 13], [16, 18], [16, 22], [20, 22], [24, 24], [26, 52], [33, 33], [36, 36], [37, 37], [38, 52], [41, 42], [47, 47], [48, 48], [49, 52]],
'antecedent_indices': [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]],
'predicted_antecedents': [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 5, 11, -1, -1, -1, 11, -1, -1],
'document': ['Paul', 'Allen', 'was', 'born', 'on', 'January', '21', ',', '1953', ',', 'in', 'Seattle', ',', 'Washington', ',', 'to', 'Kenneth', 'Sam', 'Allen', 'and', 'Edna', 'Faye', 'Allen', '.', 'Allen', 'attended', 'Lakeside', 'School', ',', 'a', 'private', 'school', 'in', 'Seattle', ',', 'where', 'he', 'befriended', 'Bill', 'Gates', ',', 'two', 'years', 'younger', ',', 'with', 'whom', 'he', 'shared', 'an', 'enthusiasm', 'for', 'computers', '.'],
'clusters': [[[0, 1], [24, 24], [36, 36], [47, 47]], [[11, 13], [33, 33]]]}
I'm having trouble interpreting the format of this output. I was expecting something like
{entity_0_spans: [LIST_OF_INDEX_TUPLES], # Paul Allen in this example
entity_1_spans: [LIST_OF_INDEX_TUPLES], # Seattle in this example
...}
or something that more closely resembles the visualisation available on the demo page:
I've looked through https://demo.allennlp.org/coreference-resolution but couldn't find a breakdown of how to use the model output yet - can anyone suggest some resources that will help me? Any pointers are much appreciated!


The information you are looking for is in 'clusters', where each list corresponds to an entity. Within each entity list, you will find the mentions referring to the same entity. The number are indices that mark the beginning and ending of each coreferential mention. E.g. Paul Allen [0,1] and Allen [24, 24].

Related

matplotlib quiver() displaying double arrows

The code below is producing double arrows. This is most noticeable in the center and along the bottom row.
Am I missing something or is this a bug of some sort? The Googlebox has yielded nothing helpful.
X = [[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22]]
Y = [[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1],
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2],
[ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3],
[ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4],
[ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5],
[ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6],
[ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7],
[ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8],
[ 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9],
[10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10],
[11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11],
[12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12],
[12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12],
[13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13],
[14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14],
[15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 15, 15],
[16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16],
[17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
17, 17, 17, 17, 17, 17, 17, 17],
[18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
18, 18, 18, 18, 18, 18, 18, 18],
[19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19,
19, 19, 19, 19, 19, 19, 19, 19],
[20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20,
20, 20, 20, 20, 20, 20, 20, 20],
[21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
21, 21, 21, 21, 21, 21, 21, 21],
[22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22,
22, 22, 22, 22, 22, 22, 22, 22],
[23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23,
23, 23, 23, 23, 23, 23, 23, 23]]
U = [[ 5.91106782e-01, 6.22366562e-01, 6.49723913e-01,
6.58423221e-01, 6.34788082e-01, 5.64001424e-01,
4.29552877e-01, 2.26181450e-01, -1.45749370e-02,
-2.33836090e-01, -3.97062982e-01, -5.07288787e-01,
-5.80344621e-01, -6.28652118e-01, -6.56798746e-01,
-6.59563028e-01, -6.18178096e-01, -5.00722193e-01,
-2.93582966e-01, -5.16521582e-02, 1.45799368e-01,
2.69658133e-01, 3.26500153e-01, 3.26768709e-01],
[ 5.77152607e-01, 5.82746773e-01, 5.76183972e-01,
5.43266956e-01, 4.66312191e-01, 3.24661378e-01,
1.07385088e-01, -1.54908642e-01, -3.91341641e-01,
-5.56849441e-01, -6.55288824e-01, -7.07393105e-01,
-7.30393353e-01, -7.34785105e-01, -7.24202206e-01,
-6.92703347e-01, -6.16664334e-01, -4.51489078e-01,
-1.96144234e-01, 3.89095593e-02, 1.80222779e-01,
2.38107484e-01, 2.33390450e-01, 1.75753839e-01],
[ 5.55201554e-01, 5.36916267e-01, 4.95331092e-01,
4.14297782e-01, 2.72441471e-01, 5.30267270e-02,
-2.23958353e-01, -4.85686407e-01, -6.72063827e-01,
-7.80930667e-01, -8.34052999e-01, -8.49154520e-01,
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-6.66861836e-01, -5.28032125e-01, -2.83307017e-01,
2.22999217e-02, 2.17035214e-01, 2.78107345e-01,
2.57213982e-01, 1.80414526e-01, 5.58040480e-02],
[ 5.30514869e-01, 4.88045325e-01, 4.08507605e-01,
2.73305715e-01, 6.32261747e-02, -2.15499555e-01,
-5.00468423e-01, -7.16424820e-01, -8.46362641e-01,
-9.11763344e-01, -9.32463829e-01, -9.17913774e-01,
-8.71699781e-01, -7.94959450e-01, -6.84618047e-01,
-5.27977847e-01, -3.00601184e-01, 3.24725025e-03,
2.84572480e-01, 4.15678719e-01, 4.08817699e-01,
3.17903989e-01, 1.68926905e-01, -2.47734503e-02],
[ 5.02548139e-01, 4.33179379e-01, 3.10308116e-01,
1.15832201e-01, -1.53873192e-01, -4.53740654e-01,
-7.02597717e-01, -8.60992569e-01, -9.43881451e-01,
-9.75369646e-01, -9.68057700e-01, -9.24950942e-01,
-8.45413757e-01, -7.27664488e-01, -5.66705523e-01,
-3.53336189e-01, -8.54415234e-02, 2.02537484e-01,
4.30399404e-01, 5.35069052e-01, 5.14397103e-01,
3.91608994e-01, 1.87450108e-01, -6.90256334e-02],
[ 4.65201575e-01, 3.63695264e-01, 1.90407737e-01,
-6.27986111e-02, -3.66107539e-01, -6.43527995e-01,
-8.36008710e-01, -9.43058071e-01, -9.89396085e-01,
-9.93329532e-01, -9.61559805e-01, -8.93929627e-01,
-7.88224158e-01, -6.41454775e-01, -4.49066265e-01,
-2.09439702e-01, 6.10838713e-02, 3.17493844e-01,
5.06540308e-01, 5.97919655e-01, 5.83094325e-01,
4.57218933e-01, 2.21129548e-01, -8.56001665e-02],
[ 4.07605489e-01, 2.67483222e-01, 4.05687053e-02,
-2.54052862e-01, -5.49121397e-01, -7.74824152e-01,
-9.12683654e-01, -9.80602627e-01, -9.99708951e-01,
-9.81982007e-01, -9.30930539e-01, -8.45440583e-01,
-7.22549396e-01, -5.57873670e-01, -3.47081454e-01,
-9.50528305e-02, 1.70316784e-01, 4.02869279e-01,
5.66564552e-01, 6.47406192e-01, 6.37165072e-01,
5.16241932e-01, 2.63738110e-01, -8.10456144e-02],
[ 3.16982526e-01, 1.36224084e-01, -1.31317283e-01,
-4.28869103e-01, -6.80165940e-01, -8.50494619e-01,
-9.46930042e-01, -9.87780174e-01, -9.87413002e-01,
-9.53497923e-01, -8.88237499e-01, -7.90275139e-01,
-6.55616984e-01, -4.77864944e-01, -2.52458286e-01,
9.81222811e-03, 2.71633461e-01, 4.87237886e-01,
6.32706314e-01, 7.04459838e-01, 6.96319353e-01,
5.81475147e-01, 3.21122831e-01, -5.36729232e-02],
[ 1.89851174e-01, -1.85511352e-02, -2.92612142e-01,
-5.56206782e-01, -7.55569048e-01, -8.83561174e-01,
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-5.83859882e-01, -3.91508312e-01, -1.49024508e-01,
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7.13492616e-01, 7.76382012e-01, 7.69585148e-01,
6.63495229e-01, 4.05530281e-01, 8.00655892e-03],
[ 4.93393011e-02, -1.59077638e-01, -4.07446556e-01,
-6.27159359e-01, -7.86840781e-01, -8.87988595e-01,
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8.05054050e-01, 8.57357453e-01, 8.51220724e-01,
7.58939184e-01, 5.22126402e-01, 1.20841224e-01],
[-6.08161695e-02, -2.48600589e-01, -4.63433277e-01,
-6.50364713e-01, -7.86735731e-01, -8.73048406e-01,
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-8.17468539e-01, -7.15217876e-01, -5.74265632e-01,
-3.86590763e-01, -1.44298331e-01, 1.42640838e-01,
4.27841719e-01, 6.54596037e-01, 8.04151106e-01,
8.90457558e-01, 9.29136623e-01, 9.21288722e-01,
8.45538031e-01, 6.51467861e-01, 2.89354206e-01],
[-1.11855856e-01, -2.76262916e-01, -4.66494984e-01,
-6.36195917e-01, -7.62707033e-01, -8.42791922e-01,
-8.79618811e-01, -8.76344309e-01, -8.34510258e-01,
-7.53704299e-01, -6.31437753e-01, -4.62760383e-01,
-2.41283252e-01, 3.19831190e-02, 3.28392442e-01,
5.90402526e-01, 7.76991386e-01, 8.90488023e-01,
9.51679598e-01, 9.75365138e-01, 9.63233139e-01,
9.01562554e-01, 7.57051594e-01, 4.78793525e-01],
[-1.02763752e-01, -2.49208456e-01, -4.25698141e-01,
-5.90445663e-01, -7.17037110e-01, -7.97411218e-01,
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7.23466314e-01, 8.64328407e-01, 9.44675955e-01,
9.84485357e-01, 9.95247332e-01, 9.78583745e-01,
9.26839981e-01, 8.22017325e-01, 6.32198023e-01],
[-4.76297792e-02, -1.80235400e-01, -3.48835361e-01,
-5.15498990e-01, -6.48860867e-01, -7.34607790e-01,
-7.70573611e-01, -7.57371172e-01, -6.92888223e-01,
-5.71674412e-01, -3.88941513e-01, -1.47948226e-01,
1.31928638e-01, 4.12166625e-01, 6.47847253e-01,
8.14343231e-01, 9.16397002e-01, 9.71963635e-01,
9.96490008e-01, 9.98129614e-01, 9.78410399e-01,
9.33624383e-01, 8.55392368e-01, 7.29066548e-01],
[ 3.44453327e-02, -8.45500183e-02, -2.44567678e-01,
-4.13390951e-01, -5.55986626e-01, -6.50278759e-01,
-6.88905719e-01, -6.69887784e-01, -5.89049719e-01,
-4.40034407e-01, -2.23153205e-01, 4.24368019e-02,
3.17706147e-01, 5.60575371e-01, 7.45372080e-01,
8.69074149e-01, 9.43218293e-01, 9.82237250e-01,
9.96859104e-01, 9.92775230e-01, 9.71548772e-01,
9.31926675e-01, 8.70952635e-01, 7.84147337e-01],
[ 1.24531829e-01, 2.14951720e-02, -1.24142269e-01,
-2.88285785e-01, -4.36332137e-01, -5.38600278e-01,
-5.79503157e-01, -5.52137571e-01, -4.50556205e-01,
-2.72020914e-01, -3.08257107e-02, 2.33881288e-01,
4.76396240e-01, 6.69624907e-01, 8.08474102e-01,
9.00042790e-01, 9.55065954e-01, 9.83283570e-01,
9.91629328e-01, 9.84084754e-01, 9.62320925e-01,
9.26691302e-01, 8.77415997e-01, 8.15482847e-01],
[ 2.08997618e-01, 1.24559020e-01, 8.48684407e-04,
-1.46598137e-01, -2.88661918e-01, -3.91618296e-01,
-4.29961569e-01, -3.89309376e-01, -2.63943288e-01,
-6.30136416e-02, 1.78668276e-01, 4.12249396e-01,
6.04758495e-01, 7.48714864e-01, 8.50152685e-01,
9.17783980e-01, 9.59112226e-01, 9.79804775e-01,
9.83901943e-01, 9.74114572e-01, 9.52212374e-01,
9.19706766e-01, 8.78912089e-01, 8.33903997e-01],
[ 2.82249691e-01, 2.18162184e-01, 1.22747194e-01,
5.37550368e-03, -1.12692673e-01, -1.99604825e-01,
-2.22963823e-01, -1.62177004e-01, -1.79584651e-02,
1.81399471e-01, 3.89284568e-01, 5.68595908e-01,
7.06857534e-01, 8.07907267e-01, 8.79716132e-01,
9.28814854e-01, 9.59433518e-01, 9.74181247e-01,
9.74926863e-01, 9.63345918e-01, 9.41247109e-01,
9.11068122e-01, 8.76727946e-01, 8.44239721e-01],
[ 3.46009504e-01, 3.03334542e-01, 2.40609727e-01,
1.64792336e-01, 9.10650256e-02, 4.46918062e-02,
5.47680721e-02, 1.36260477e-01, 2.74393229e-01,
4.32734135e-01, 5.78349795e-01, 6.96327399e-01,
7.86097123e-01, 8.52735284e-01, 9.01501863e-01,
9.35893510e-01, 9.57589073e-01, 9.67107013e-01,
9.64733890e-01, 9.51264330e-01, 9.28488288e-01,
8.99692809e-01, 8.70252069e-01, 8.47561147e-01],
[ 4.06955125e-01, 3.86836289e-01, 3.60008319e-01,
3.33800629e-01, 3.19793639e-01, 3.32294319e-01,
3.80910459e-01, 4.60529276e-01, 5.54085368e-01,
6.45433976e-01, 7.25560042e-01, 7.91585217e-01,
8.44113209e-01, 8.85113897e-01, 9.16480279e-01,
9.39239758e-01, 9.53365969e-01, 9.58045905e-01,
9.52421824e-01, 9.36509635e-01, 9.12084965e-01,
8.83417478e-01, 8.57475919e-01, 8.42768229e-01],
[ 4.75102487e-01, 4.79444876e-01, 4.91103049e-01,
5.17028392e-01, 5.61580652e-01, 6.19364889e-01,
6.75394533e-01, 7.20462603e-01, 7.57762648e-01,
7.92301360e-01, 8.25331968e-01, 8.55937836e-01,
8.83019438e-01, 9.05962858e-01, 9.24460078e-01,
9.38025098e-01, 9.45636106e-01, 9.45638264e-01,
9.36251692e-01, 9.16741704e-01, 8.89028586e-01,
8.58882429e-01, 8.35359426e-01, 8.27878351e-01],
[ 5.62693753e-01, 5.93592734e-01, 6.42845488e-01,
7.09881932e-01, 7.82737342e-01, 8.39735853e-01,
8.68496463e-01, 8.76464004e-01, 8.77560033e-01,
8.80145097e-01, 8.86486243e-01, 8.95793855e-01,
9.06385360e-01, 9.16670844e-01, 9.25375659e-01,
9.31289596e-01, 9.32857010e-01, 9.27783629e-01,
9.13322352e-01, 8.87929386e-01, 8.54220866e-01,
8.20792210e-01, 7.99707058e-01, 8.00713493e-01],
[ 6.75223956e-01, 7.28299137e-01, 7.98132045e-01,
8.70828514e-01, 9.28100696e-01, 9.58357163e-01,
9.63664076e-01, 9.54511170e-01, 9.41109289e-01,
9.29563623e-01, 9.22166117e-01, 9.18823138e-01,
9.18280235e-01, 9.18945445e-01, 9.19301773e-01,
9.17852346e-01, 9.12687865e-01, 9.00755102e-01,
8.77918913e-01, 8.41778780e-01, 7.97438172e-01,
7.59412209e-01, 7.43766496e-01, 7.58426057e-01],
[ 7.48028585e-01, 8.00967465e-01, 8.60639839e-01,
9.17314355e-01, 9.62374525e-01, 9.89077372e-01,
9.96239777e-01, 9.88737117e-01, 9.73767736e-01,
9.57273913e-01, 9.42647501e-01, 9.30980153e-01,
9.21800247e-01, 9.13829662e-01, 9.05516974e-01,
8.95103386e-01, 8.80063037e-01, 8.55819040e-01,
8.15680432e-01, 7.57286053e-01, 6.94667063e-01,
6.54674360e-01, 6.55242773e-01, 6.95951505e-01],
[ 5.88142228e-01, 6.56524283e-01, 7.39388262e-01,
8.26540072e-01, 9.05382649e-01, 9.63084972e-01,
9.93428420e-01, 9.99593348e-01, 9.90003898e-01,
9.72940215e-01, 9.53944608e-01, 9.35599844e-01,
9.18217361e-01, 9.00665492e-01, 8.80954002e-01,
8.56210996e-01, 8.21553193e-01, 7.67628947e-01,
6.82523479e-01, 5.74145986e-01, 4.89341942e-01,
4.69017002e-01, 5.14459717e-01, 6.05048760e-01]]
V = [[-7.64071106e-01, -7.61939824e-01, -7.56999777e-01,
fig, ax = plt.subplots(figsize=(6, 6), dpi=300);
ax.quiver(X, Y, U, V, pivot='middle');
ax.set_aspect('equal');
Output:
I've tried the above. I expect single arrows as usual.
I don't know what additional details to add to get rid of the

Didn't you ask for exactly that, repeating values 1 and 12?
#(...)
X = [[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
[ 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22],
#(...)
Y = [[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1],
#(...)
U = [[ 5.91106782e-01, 6.22366562e-01, 6.49723913e-01, (...)
[ 5.77152607e-01, 5.82746773e-01, 5.76183972e-01, (...)
You even have a quadruple arrow at coordinate (1,1). Just pair X and Y, and see that X=1 Y=1 occurs 4 times! But values of U in those 4 occurences of X=1 Y=1 are all different. So those 4 arrows that starts for (1,1) are not exactly identical.
So does X=11 Y=1.
X=2 Y=1 occurs twice.
Etc.
You said "especially in the center". No, not really. It occurs on line Y=1, on column X=1, and, indeed on line Y=12 and column X=11 that both pass not far from the center.

How to connect many short eulerian cycles into only a few longer ones?

I want to connect eulerian cycles into longer ones without exceed a value.
So, I have this eulerian cycles and their length in a list. The maximal length of a cycle can be for example 500. The length of all cycles added up is 6176.778566350282. By connecting them cleverly together there could be probably only 13 or 14 cycles. But I don't really know how I could do that. I tried to just add one cycle to another but there I got 21 cycles out. The problem is that if you have a cycle of these numbers for example: [8, 21, 9, 22, 8, 23, 9, 24, 8] and you want to integrate this cycle [10, 11, 12, 10] it will not work because in the first cycle there is no edge of the number 10. I just started then a new cycle with this numbers [10, 11, 12, 10] and saved [8, 21, 9, 22, 8, 23, 9, 24, 8] as one of the 21 result cycles. But with this method I don't really get a good result. What would be a cleverer way to solve this problem?
This is an example how the list of the short eulerian cycles looks like:
[([0, 1, 2, 0], 36.36630772776802), ([0, 3, 1, 4, 0], 93.83277865587606), ([0, 5, 1, 6, 0], 45.79353710664728), ([0, 7, 1, 8, 0], 49.60782827778143), ([0, 9, 1, 10, 0], 73.2674533926481), ([0, 11, 1, 12, 0], 75.52124688926921), ([0, 13, 1, 14, 0], 57.88021234723078), ([0, 15, 1, 16, 0], 62.21469065955568), ([0, 17, 1, 18, 0], 81.43809748917617), ([0, 19, 1, 20, 0], 98.88867905572438), ([0, 21, 1, 22, 0], 95.3596513800762), ([0, 23, 1, 24, 0], 116.15359042770964), ([2, 3, 4, 2], 49.106297391220245), ([2, 5, 3, 6, 2], 71.5422470782724), ([2, 7, 3, 8, 2], 50.237654764168), ([2, 9, 3, 10, 2], 71.36355688043689), ([2, 11, 3, 12, 2], 44.474596239420634), ([2, 13, 3, 14, 2], 103.42527218232905), ([2, 15, 3, 16, 2], 65.92444557445982), ([2, 17, 3, 18, 2], 83.30561323888043), ([2, 19, 3, 20, 2], 144.20150278029047), ([2, 21, 3, 22, 2], 131.70030082856), ([2, 23, 3, 24, 2], 141.63032737825358), ([4, 5, 6, 4], 42.10300780814433), ([4, 7, 5, 8, 4], 88.13162862262575), ([4, 9, 5, 10, 4], 29.40312423743285), ([4,
11, 5, 12, 4], 35.06685249446684), ([4, 13, 5, 14, 4], 83.54113932583394), ([4, 15, 5, 16, 4], 57.669814210895076), ([4, 17, 5, 18, 4], 85.16088821443248), ([4, 19, 5, 20, 4], 115.83839679838714), ([4, 21, 5, 22, 4], 96.32509817470469), ([4, 23, 5, 24, 4], 95.72504474795447), ([6, 7, 8, 6], 39.680511478789455), ([6, 9, 7, 10, 6], 78.55998969220359), ([6, 11, 7, 12, 6], 75.38181527864062), ([6, 13, 7, 14, 6], 65.59514045044449), ([6, 15, 7, 16, 6], 64.00893982862813), ([6, 17, 7, 18, 6], 82.99423226082924), ([6, 19, 7, 20, 6], 107.80803412093549), ([6, 21, 7, 22, 6], 104.34384551877056), ([6, 23, 7, 24, 6], 125.5684717784), ([8, 9, 10, 8], 52.130784276071026), ([8, 11, 9, 12, 8], 60.084249983353345), ([8, 13, 9, 14,
8], 80.8264707041123), ([8, 15, 9, 16, 8], 56.067658306081576), ([8, 17, 9, 18, 8], 87.79739969269264), ([8, 19, 9, 20, 8], 115.04095207094785),
([8, 21, 9, 22, 8], 100.28892183336735), ([8, 23, 9, 24, 8], 107.98171312085222), ([10, 11, 12, 10], 18.073592581964586), ([10, 13, 11, 14, 10],
86.59048377734861), ([10, 15, 11, 16, 10], 53.62896051047471), ([10, 17, 11, 18, 10], 79.42707393175432), ([10, 19, 11, 20, 10], 121.75438335508098), ([10, 21, 11, 22, 10], 103.13320830479722), ([10, 23, 11, 24, 10], 104.67092453129686), ([12, 13, 14, 12], 65.01056040398879), ([12, 15, 13, 16, 12], 73.92038351218434), ([12, 17, 13, 18, 12], 75.85986620162797), ([12, 19, 13, 20, 12], 99.9668143111241), ([12, 21, 13, 22, 12], 97.01425784207544), ([12, 23, 13, 24, 12], 113.28618776429398), ([14, 15, 16, 14], 53.12806382231952), ([14, 17, 15, 18, 14], 83.32318283097464), ([14,
19, 15, 20, 14], 59.489711796339975), ([14, 21, 15, 22, 14], 49.93204117686305), ([14, 23, 15, 24, 14], 59.39628730132421), ([16, 17, 18, 16], 76.30230372794964), ([16, 19, 17, 20, 16], 151.38369644764225), ([16, 21, 17, 22, 16], 137.27131752575687), ([16, 23, 17, 24, 16], 146.11467181532439), ([18, 19, 20, 18], 28.731124011957917), ([18, 21, 19, 22, 18], 51.78367537918862), ([18, 23, 19, 24, 18], 86.45013419422762), ([20, 21, 22,
20], 39.010097887844154), ([20, 23, 21, 24, 20], 63.48159687540681), ([22, 23, 24, 22], 22.283951753399037)]

I designed an elaborate branch-and-price scheme and then realized that it probably wouldn’t work well. Here’s a much simpler local search that achieves 14 cycles on your sample input.
from collections import defaultdict
from itertools import combinations
import random
# pip3 install networkx if necessary.
import networkx as nx
# The input consists of the variables maximum_length and cycles.
maximum_length = 500
cycles = [
([0, 1, 2, 0], 36.36630772776802),
([0, 3, 1, 4, 0], 93.83277865587606),
([0, 5, 1, 6, 0], 45.79353710664728),
([0, 7, 1, 8, 0], 49.60782827778143),
([0, 9, 1, 10, 0], 73.2674533926481),
([0, 11, 1, 12, 0], 75.52124688926921),
([0, 13, 1, 14, 0], 57.88021234723078),
([0, 15, 1, 16, 0], 62.21469065955568),
([0, 17, 1, 18, 0], 81.43809748917617),
([0, 19, 1, 20, 0], 98.88867905572438),
([0, 21, 1, 22, 0], 95.3596513800762),
([0, 23, 1, 24, 0], 116.15359042770964),
([2, 3, 4, 2], 49.106297391220245),
([2, 5, 3, 6, 2], 71.5422470782724),
([2, 7, 3, 8, 2], 50.237654764168),
([2, 9, 3, 10, 2], 71.36355688043689),
([2, 11, 3, 12, 2], 44.474596239420634),
([2, 13, 3, 14, 2], 103.42527218232905),
([2, 15, 3, 16, 2], 65.92444557445982),
([2, 17, 3, 18, 2], 83.30561323888043),
([2, 19, 3, 20, 2], 144.20150278029047),
([2, 21, 3, 22, 2], 131.70030082856),
([2, 23, 3, 24, 2], 141.63032737825358),
([4, 5, 6, 4], 42.10300780814433),
([4, 7, 5, 8, 4], 88.13162862262575),
([4, 9, 5, 10, 4], 29.40312423743285),
([4, 11, 5, 12, 4], 35.06685249446684),
([4, 13, 5, 14, 4], 83.54113932583394),
([4, 15, 5, 16, 4], 57.669814210895076),
([4, 17, 5, 18, 4], 85.16088821443248),
([4, 19, 5, 20, 4], 115.83839679838714),
([4, 21, 5, 22, 4], 96.32509817470469),
([4, 23, 5, 24, 4], 95.72504474795447),
([6, 7, 8, 6], 39.680511478789455),
([6, 9, 7, 10, 6], 78.55998969220359),
([6, 11, 7, 12, 6], 75.38181527864062),
([6, 13, 7, 14, 6], 65.59514045044449),
([6, 15, 7, 16, 6], 64.00893982862813),
([6, 17, 7, 18, 6], 82.99423226082924),
([6, 19, 7, 20, 6], 107.80803412093549),
([6, 21, 7, 22, 6], 104.34384551877056),
([6, 23, 7, 24, 6], 125.5684717784),
([8, 9, 10, 8], 52.130784276071026),
([8, 11, 9, 12, 8], 60.084249983353345),
([8, 13, 9, 14, 8], 80.8264707041123),
([8, 15, 9, 16, 8], 56.067658306081576),
([8, 17, 9, 18, 8], 87.79739969269264),
([8, 19, 9, 20, 8], 115.04095207094785),
([8, 21, 9, 22, 8], 100.28892183336735),
([8, 23, 9, 24, 8], 107.98171312085222),
([10, 11, 12, 10], 18.073592581964586),
([10, 13, 11, 14, 10], 86.59048377734861),
([10, 15, 11, 16, 10], 53.62896051047471),
([10, 17, 11, 18, 10], 79.42707393175432),
([10, 19, 11, 20, 10], 121.75438335508098),
([10, 21, 11, 22, 10], 103.13320830479722),
([10, 23, 11, 24, 10], 104.67092453129686),
([12, 13, 14, 12], 65.01056040398879),
([12, 15, 13, 16, 12], 73.92038351218434),
([12, 17, 13, 18, 12], 75.85986620162797),
([12, 19, 13, 20, 12], 99.9668143111241),
([12, 21, 13, 22, 12], 97.01425784207544),
([12, 23, 13, 24, 12], 113.28618776429398),
([14, 15, 16, 14], 53.12806382231952),
([14, 17, 15, 18, 14], 83.32318283097464),
([14, 19, 15, 20, 14], 59.489711796339975),
([14, 21, 15, 22, 14], 49.93204117686305),
([14, 23, 15, 24, 14], 59.39628730132421),
([16, 17, 18, 16], 76.30230372794964),
([16, 19, 17, 20, 16], 151.38369644764225),
([16, 21, 17, 22, 16], 137.27131752575687),
([16, 23, 17, 24, 16], 146.11467181532439),
([18, 19, 20, 18], 28.731124011957917),
([18, 21, 19, 22, 18], 51.78367537918862),
([18, 23, 19, 24, 18], 86.45013419422762),
([20, 21, 22, 20], 39.010097887844154),
([20, 23, 21, 24, 20], 63.48159687540681),
([22, 23, 24, 22], 22.283951753399037),
]
for cycle, length in cycles:
assert cycle[0] == cycle[-1]
assert 0 <= length <= maximum_length
# Two cycles can be merged if and only if there exists a vertex that they have
# in common. Compute the graph where each cycle is a node and each pair of
# cycles that can be merged is an edge. A set of cycles can be merged if and
# only if the total length does not exceed the maximum and the corresponding set
# of nodes induces a connected subgraph.
inverted_index = defaultdict(list)
for i, (cycle, length) in enumerate(cycles):
for v in set(cycle):
inverted_index[v].append(i)
cycle_graph = nx.Graph()
for i, (cycle, length) in enumerate(cycles):
cycle_graph.add_node(i, length=length)
for posting_list in inverted_index.values():
for e in combinations(posting_list, 2):
cycle_graph.add_edge(*e)
lengths = [round(length * 2**40) / 2**40 for (cycle, length) in cycles]
# We want to find the smallest partition of cycles into mergeable parts. This
# code implements a greedy local search. Initialize the partition where every
# cycle is in its own part. For some number of steps, move one cycle to another
# part, respecting the connectivity constraint.
def make_part_graph(part):
part_graph = cycle_graph.subgraph(part)
return nx.Graph(
part_graph,
can_move=set(part_graph.nodes()) - set(nx.articulation_points(part_graph)),
length=sum(lengths[i] for i in part_graph.nodes()),
)
def merge_cycles(indexes):
g = nx.DiGraph()
for i in indexes:
cycle, length = cycles[i]
for j in range(1, len(cycle)):
g.add_edge(cycle[j - 1], cycle[j])
cycle = []
for u, v in nx.eulerian_circuit(g):
if not cycle:
cycle.append(u)
cycle.append(v)
return cycle, sum(lengths[i] for i in indexes)
labels = list(range(len(cycles)))
cycle_subgraphs = {i: make_part_graph({i}) for i in range(len(cycles))}
for step in range(10000):
moves = []
for tail, cycle_subgraph in cycle_subgraphs.items():
for i in cycle_subgraph.graph["can_move"]:
for j in cycle_graph.neighbors(i):
head = labels[j]
if (
head != tail
and cycle_subgraphs[head].graph["length"] + lengths[i]
<= maximum_length
):
moves.append((i, tail, head))
i, tail, head = random.choice(moves)
labels[i] = head
cycle_subgraphs[tail] = make_part_graph(set(cycle_subgraphs[tail].nodes()) - {i})
cycle_subgraphs[head] = make_part_graph(set(cycle_subgraphs[head].nodes()) | {i})
for cycle_subgraph in cycle_subgraphs.values():
part = sorted(cycle_subgraph.nodes())
if not part:
continue
print(*merge_cycles(part))
Output:
[0, 23, 11, 24, 8, 23, 9, 3, 10, 2, 9, 24, 10, 23, 1, 24, 0, 21, 1, 22, 0] 495.5294363403709
[0, 19, 17, 20, 16, 19, 22, 18, 21, 3, 22, 2, 21, 19, 1, 20, 0, 5, 1, 6, 0] 479.5498888177626
[6, 23, 17, 24, 16, 10, 15, 11, 14, 10, 13, 11, 16, 23, 7, 24, 6] 411.90258788154733
[0, 9, 22, 8, 21, 9, 18, 16, 17, 18, 8, 17, 9, 16, 8, 15, 9, 12, 8, 6, 7, 8, 11, 9, 1, 10, 0] 493.488498414883
[2, 5, 3, 6, 19, 9, 10, 8, 9, 20, 23, 21, 24, 20, 8, 19, 7, 20, 6, 2] 410.00361442163285
[0, 7, 22, 6, 21, 7, 16, 12, 15, 20, 14, 19, 11, 20, 10, 19, 15, 13, 16, 6, 15, 7, 1, 8, 0] 473.1250922887857
[0, 13, 1, 14, 0, 11, 22, 10, 21, 11, 5, 12, 4, 11, 3, 12, 2, 11, 1, 12, 0, 1, 2, 0] 352.442424002953
[0, 3, 1, 4, 23, 15, 24, 14, 23, 5, 24, 4, 7, 5, 8, 4, 0] 337.0857393277802
[4, 21, 13, 7, 14, 8, 13, 9, 14, 6, 13, 22, 23, 24, 22, 20, 21, 22, 12, 21, 5, 22, 4, 9, 5, 10, 4] 430.458141050015
[2, 23, 3, 24, 2, 13, 3, 14, 2, 7, 12, 6, 11, 7, 10, 6, 4, 5, 6, 9, 7, 3, 8, 2] 491.33806710373847
[0, 15, 22, 14, 21, 15, 5, 20, 12, 10, 11, 12, 19, 13, 20, 4, 19, 5, 16, 4, 15, 1, 16, 0] 403.69534973878945
[0, 17, 22, 16, 21, 17, 11, 18, 19, 3, 20, 2, 19, 20, 18, 10, 17, 1, 18, 0] 471.0691157389365
[2, 15, 16, 14, 4, 13, 24, 18, 23, 19, 24, 12, 23, 13, 5, 14, 15, 3, 16, 2, 3, 4, 2] 451.43626807235523
[2, 17, 15, 18, 14, 12, 13, 14, 17, 13, 18, 12, 17, 7, 18, 6, 17, 5, 18, 4, 17, 3, 18, 2] 475.65434315073435

Prevent IPython from displaying long lists one element per line

In Jupyter notebooks, or in IPython, long lists are displayed one element per line. How do I display them on a single line? I don't mind if the line wraps.
In the following example, I'd like the 3rd list to be shown as a "row", not as a "column".
In [1]: [list(range(n)) for n in range(10,40,10)]
Out[1]:
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
[0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29]]
The output I am looking for is the following or similar:
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]]
My goal is to make the output easier to read for humans.

I would simply use
A = [list(range(n)) for n in range(10,40,10)]
for i in A:
print(i)

Swaping columns of numpy array in all rows but the first one

Given a numpy array
import numpy as np
a = np.arange(4*7).reshape([4, 7])
array([[ 0, 1, 2, 3, 4, 5, 6],
[ 7, 8, 9, 10, 11, 12, 13],
[14, 15, 16, 17, 18, 19, 20],
[21, 22, 23, 24, 25, 26, 27]])
I can apply slicing to swap the second and third columns by:
a[:, [0, 2, 1, 3, 4, 5, 6]]
array([[ 0, 2, 1, 3, 4, 5, 6],
[ 7, 9, 8, 10, 11, 12, 13],
[14, 16, 15, 17, 18, 19, 20],
[21, 23, 22, 24, 25, 26, 27]])
But, can I use slices to swap the second and third columns for all rows but the first one? The expected output would be:
array([[ 0, 1, 2, 3, 4, 5, 6],
[ 7, 9, 8, 10, 11, 12, 13],
[14, 16, 15, 17, 18, 19, 20],
[21, 23, 22, 24, 25, 26, 27]])

For in-situ edit, we can use flipping after slicing out the two columns -
a[1:,1:3] = a[1:,2:0:-1]
Sample run -
In [556]: a = np.arange(4*7).reshape([4, 7])
In [557]: a
Out[557]:
array([[ 0, 1, 2, 3, 4, 5, 6],
[ 7, 8, 9, 10, 11, 12, 13],
[14, 15, 16, 17, 18, 19, 20],
[21, 22, 23, 24, 25, 26, 27]])
In [559]: a[1:,1:3] = a[1:,2:0:-1]
In [560]: a
Out[560]:
array([[ 0, 1, 2, 3, 4, 5, 6],
[ 7, 9, 8, 10, 11, 12, 13],
[14, 16, 15, 17, 18, 19, 20],
[21, 23, 22, 24, 25, 26, 27]])
For columns that are two-step apart, use a stepsize of 2 to assign (LHS) and -2 to select (RHS). Hence, for column IDs 1 & 3 -
In [577]: a = np.arange(4*7).reshape([4, 7])
In [578]: a
Out[578]:
array([[ 0, 1, 2, 3, 4, 5, 6],
[ 7, 8, 9, 10, 11, 12, 13],
[14, 15, 16, 17, 18, 19, 20],
[21, 22, 23, 24, 25, 26, 27]])
In [579]: a[1:,1:4:2] = a[1:,3:0:-2]
In [580]: a
Out[580]:
array([[ 0, 1, 2, 3, 4, 5, 6],
[ 7, 10, 9, 8, 11, 12, 13],
[14, 17, 16, 15, 18, 19, 20],
[21, 24, 23, 22, 25, 26, 27]])
Another method would be with explicit column numbered indexing -
a[1:,[1,2]] = a[1:,[2,1]]
Note that this creates a copy with a[1:,[2,1]] and as such would be less memory efficient than the first method.

swap elements of list in recursive call python

I want to make simple function swap random element in list.
but it doesn't work in recursive call.
in first recursive call, element swapping work,
but nested recursive call(or nested recursive call in first recursive call) doesn't work.
I don't know why only swap in first recursive call works.
below are result.
Thank you all.
def change(lst):
if len(lst)>4:
a, b = np.random.randint(0, len(lst)), np.random.randint(0, len(lst))
print(lst)
lst[a], lst[b] = lst[b], lst[a]
print(lst)
mid = int(len(lst)/2)
change(lst[:mid])
change(lst[mid:])
k = list(range(0, 20))
change(k)
print(k)
`
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
[0, 19, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1]
[0, 19, 2, 3, 4, 5, 6, 7, 8, 9]
[3, 19, 2, 0, 4, 5, 6, 7, 8, 9]
[3, 19, 2, 0, 4]
[3, 0, 2, 19, 4]
[5, 6, 7, 8, 9]
[5, 6, 8, 7, 9]
[10, 11, 12, 13, 14, 15, 16, 17, 18, 1]
[10, 11, 12, 13, 14, 15, 16, 17, 18, 1]
[10, 11, 12, 13, 14]
[10, 14, 12, 13, 11]
[15, 16, 17, 18, 1]
[15, 16, 17, 18, 1]
[0, 19, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1] <= result.

The problem is that in your recursive calls:
change(lst[:mid])
change(lst[mid:])
you use a slicing operator. The slicing operator constructs a new list, so your changes are made on a new list and are not reflected on the original list (since it is a copy).
What you can do is use indices instead:
def change(lst,frm=0,to=None):
if to is None: # set the default to the end of the list
to = len(lst)
if to-frm > 4:
a, b = np.random.randint(frm,to), np.random.randint(frm,to)
print(lst)
lst[a], lst[b] = lst[b], lst[a]
print(lst)
mid = (frm+to)//2
change(lst,frm,mid)
change(lst,mid,to)
Then we obtain:
>>> k = list(range(0, 20))
>>> change(k)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 2, 3, 4, 12, 6, 7, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 2, 3, 4, 12, 6, 7, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 2, 3, 4, 12, 6, 7, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 2, 3, 4, 12, 6, 7, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 12, 6, 7, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 12, 6, 7, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 10, 11, 5, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 5, 11, 10, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 5, 11, 10, 13, 14, 15, 16, 17, 18, 19]
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 5, 11, 10, 13, 14, 15, 16, 17, 18, 19]
>>> print(k)
[0, 1, 4, 3, 2, 7, 6, 12, 8, 9, 5, 11, 10, 13, 14, 15, 16, 17, 18, 19]

That's because you create copies of the original list by lst[:mid], lst[mid:]. A solution is to pass to change() the same list and (separately) the range to process.

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