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Incorrect results with banded alignment #28

Description

@quim0

For some sequences, when I activate the band in extd2_sse, KSW2 reports an alignment score higher than the optimal one. My understanding is that this is incorrect, because the banded alignment should always be worst or equal to the optimal solution (as the band is a subset of the full alignment matrix).

Here is an example that generates this error:

ksw2-test -t extd2_sse -s -A 2 -B 4 -O 4,24 -E 2,1 -w 200 "AATGACGTCTCATTCATTAGAGTTATAGGGTTTGCTAAGCTAGTTTTGTTCTCCTGATATGTGCGACTAACTCTGATAGTTCCTGGGATGCGCCAGAAATACAAGATGACGTTTGCGCGCTATCCAACCACACGGAGGGAAGTCCGGATGCTTTGTAAAACTCGTGGGACCCGACGCGCTTAACAGTAGACTCACCGAAGGCAACCTGAAGTCAACTACCATACTGCGTATCAAGGGGCGTTGTAGGTGACTTCCGTAAGAAACCGTTAACTATAAGTACAACAAGCGGGTGTCACATACAACAACCACCGCTGCGAAATCTCGTTTGTACACGACTGTATTCGATCCGTCGCGCAGATGCCTTGCGGGGACGTCACGGTATCCCAATCTTACCACAGAGACTGCCTTCCCCCATTGAAGCTCCGCTGGTAGGCCCTGATTGCATGATAAAGTAAACATATAGCCATGCGTACCCGCTGCATCTCGACTAATAAGGGGCTCCTTGCCACACCTTCACCGCGTAGATAGCGGTTCTCTTGATAGTCTACATGGGTCGGGAAAGTTGCCACTACCGCATATGTGAAGTGGCAGTCAGCCCACGCCATTAGATCACCCACAGGACCGCAATCAGACAACTAAAACAGTGGATAGACAGTATGGACGGCTTCAACAACGGACAAACTAGTTCTTACTCACGAATACCCTAATCCAGCGATCTTGATGTCGCACGCAGGCTTATTACACATCAACTGCGCGAGTTCTCTTTATGCTGCCTGCGACGGCCTTTCTCCTTGGGGTGC"  AATGACGTCTCATTCATTAGAGTTATAGGGTTTGCTAAGCTAGTTTTGTTCTCCTGATATGTGCGACTAACTCTGATGTTCCTGGGATGCGCCAGAAATACAAGATGACGTTTGCGCGCTATCCAACCACGCGGAGGGTAAGTACCGGATGCTTGTAAAACTGTGGGACCCGACGCGCTTAGAAGTAGACTCACCGAAGGCAACCTGAAGTCAACTACCATACTGTCGTACAAGGGGCGTTGAAGGTGACTTCCGTAAGAAACCGTTAACTATAAGTACACAAGCGGGTCGTCACATACACAACCCACCGCTGCGAAATTGGTAGAAGACGGGTAAACCGTTCGATTAAGAGCAGTATCCCAATTATTGCCCATTCGGGGCGCGGAGTTAACACATGATAGCCGACTTAGGCAAATAGTAGTCTCGTTTGTCACACGACTGTATTCGATCCGCGCGCAGATGCTTGCGGGGACGTCAGGTATGCCAATCTTACCACAGAGAGTGCTTCCCCCATTGAAGCTCGCTGGTAGGCCCTGATTGCATGATAAAGCAAACATATAGCCATCGTACCCGCTGCATCTCGACTAATAAGGGGCTCCTTGCCACACCTTCACCGCGTAGATAGCGGTTCGCTTGATAGTTTACATGGGTCGGGAA
AGTTACCACTACAGCTGCCTATCGTTCGCGGGAGCCATCGTGTTCATTGAGTAAGTTTGCCATGTCTAACGTAGTCGGACGGATTGGGGAATCTCCACCCTACTGAACTCGCATATGTGAAGTGGCAGTCAGCCCAGGCCATTAGATCACCCACAGGACCGCAATCAGACAACTAAAACCGTGGATAGACAGTATGGACGGCTTCAACACGGACAAACTAGTTCTTACTCACGAATACCCTAATCCAGGATCTTGTGTCCACTGCAGGCTTATTACACATCAACTGCGCGAGTTCCTTTATGCTGCCTGCGACGGCCTTTCTCCTTGGGGTGCACTCGGAACC"

KSW2 reported score when using -w 200: 1084
KSW2 reported score without using the band: 1078

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