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package SmotifTF::GeometricalCalculations; |
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use 5.8.8; |
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use strict; |
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use warnings; |
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BEGIN { |
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use Exporter (); |
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100
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our ( $VERSION, @ISA, @EXPORT, @EXPORT_OK, %EXPORT_TAGS); |
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$VERSION = "0.01"; |
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@ISA = qw(Exporter); |
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# name of the functions to export |
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@EXPORT_OK = qw( |
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calc_geom |
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check_file |
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exist_pdb_code_on_obsoletes |
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exist_pdb_code_on_uncompressed |
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exist_pdb_code_on_alternate |
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exist_pdb_code_on_remodelled |
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get_full_path_name_for_pdb_code |
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get_full_path_name_for_pdb_code_old |
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_getReadingFileHandle |
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get_from_file |
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translate |
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convert |
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COM |
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COM2 |
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calculate_axis |
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get_axis |
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calc_I |
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calc_evec |
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projectpoint |
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det |
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find_eigs |
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matmul |
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matvec |
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vecvec |
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find_roots |
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rotateaxis |
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rotate |
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cross |
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dot |
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unit |
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norm |
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vecadd |
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max |
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min |
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dbin |
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angbin |
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pearson |
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find_rmsd |
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superpose |
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dihedral |
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findcb |
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findo |
57
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pointsonsphere |
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norm2 |
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); |
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@EXPORT = qw( |
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); # symbols to export on request |
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} |
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our @EXPORT_OK; |
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our $DEBUG = 0; |
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67
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1
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1
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1152
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use Math::Trig; |
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17766
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1
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161
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68
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1
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1
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814
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use Storable qw(dclone); |
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1
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3097
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1
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85
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69
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1
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9
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use Carp; |
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1
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66
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70
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1
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1
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9514
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use IO::Uncompress::Gunzip qw(gunzip); |
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48894
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1
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66
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71
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1
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1
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7
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use File::Spec::Functions qw(catfile); |
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2
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1
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40
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72
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73
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1
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1
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741
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use Config::Simple; |
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10806
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1
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10
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74
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# accessing a block of an ini-file; |
75
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my $config_file = $ENV{'SMOTIFTF_CONFIG_FILE'}; |
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croak "Environmental variable SMOTIFTF_CONFIG_FILE should be set" unless $config_file; |
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78
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my $cfg = new Config::Simple($config_file); |
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my $PDB = $cfg->param( -block => 'pdb' ); |
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my $PDB_PATH = $PDB->{'pdb_path'}; |
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my $USER_SPECIFIC_PDB_PATH = $PDB->{'user_specific_pdb_path'}; |
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my $REMODELLED_PDB_PATH = $PDB->{'remodeled_pdb_path'}; |
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84
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my $host = ""; |
85
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86
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=head1 NAME |
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88
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GeometricalCalculations |
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90
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=head1 VERSION |
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92
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Version 0.01 |
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=cut |
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96
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our $VERSION = '0.01'; |
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98
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99
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=head1 SYNOPSIS |
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101
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This module consists of subroutines that carry out geometrical calculations |
102
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using the atomic coordinates obtained from a protein structure. |
103
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104
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=head2 calc_geom |
105
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106
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subroutine to calculate delta, theta, and rho angles for an smotif |
107
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108
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Input 1: $lvec - vector between the anchor points of the bracing secondary structures |
109
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Input 2: $e1 - axis vector for 1st secondary structure |
110
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Input 3: $e2 - axis vector for 2nd secondary structure |
111
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112
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=cut |
113
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sub calc_geom { |
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0
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0
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my ( $lvec, $e1, $e2 ) = @_; |
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0
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my $rad = 180 / 3.14159265; |
116
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0
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my $delta = ( Math::Trig::acos( dot( @$e1, @$lvec ) ) ) * $rad; |
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0
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my $theta = ( Math::Trig::acos( dot( @$e1, @$e2 ) ) ) * $rad; |
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0
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my $rho = 0; |
119
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0
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my @normal = unit( cross( @$lvec, @$e1 ) ); |
120
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0
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my @target = cross( @$e1, @normal ); |
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my $check = norm(@target); |
122
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0
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0
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if ( $check ne 0 ) { |
123
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my $proj = dot( @$e1, @$e2 ); |
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0
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my @proj = ( |
125
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$$e2[0] - $proj * $$e1[0], |
126
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$$e2[1] - $proj * $$e1[1], |
127
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$$e2[2] - $proj * $$e1[2] |
128
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); |
129
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my $dproj = norm(@proj); |
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0
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0
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if ( $dproj ne 0 ) { |
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0
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$rho = Math::Trig::acos( dot( @proj, @normal ) / $dproj ) * $rad; |
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0
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0
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if ( dot( @proj, @target ) < 0 ) { $rho = 360 - $rho } |
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0
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133
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} |
134
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} |
135
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0
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return ( $delta, $theta, $rho ); |
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} |
137
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138
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=head2 check_file |
139
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140
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subroutine to check if pdb file exists in the PDB flat-file database |
141
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=cut |
142
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sub check_file { |
143
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144
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0
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0
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my ($name) = @_; |
145
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0
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0
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croak unless $name; |
146
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147
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0
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my $pdb_file_name = "pdb" . $name . '.ent'; |
148
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0
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my $filename = "$PDB_PATH/uncompressed/$pdb_file_name"; |
149
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my $filename2 = "$PDB_PATH/obsoletes/$pdb_file_name"; |
150
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my $check = 1; |
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open( FILE1, $filename ) or open( FILE1, $filename2 ) or $check = 0; |
152
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0
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return $check; |
153
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} |
154
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155
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=head2 _getReadingFileHandle |
156
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subroutine to get a reading file handle |
157
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for a file. |
158
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159
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input: file path name to the file |
160
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=cut |
161
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sub _getReadingFileHandle { |
162
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1
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1
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566
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use IO::Uncompress::Gunzip qw(gunzip); |
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2
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1
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793
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163
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164
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my $file = shift; |
165
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die "path_name files is required" unless $file; |
166
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167
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my $fh; |
168
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if ( $file =~ /\.gz$/ ) { |
169
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$fh = new IO::Uncompress::Gunzip $file || die("Cannot open $file"); |
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} |
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else { |
172
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open( $fh, "< $file" ) || die("Cannot open $file"); |
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} |
174
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0
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return $fh; |
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} |
176
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177
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=head2 exist_pdb_code_on_obsoletes |
178
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check if a four-letters pdb code exist in PDB obsoletes folder |
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it will return the full path name if a match is found. |
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return undef if not file was found |
181
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182
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exist_pdb_code_on_obsoletes |
183
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input : pdb_code (4fab) |
184
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return : full path name |
185
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186
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=cut |
187
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sub exist_pdb_code_on_obsoletes { |
188
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0
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0
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my ($pdb_code) = @_; |
189
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0
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0
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croak "exist_pdb_code_on_obsoletes: pdb_code is required" unless $pdb_code; |
190
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191
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0
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chomp $pdb_code; |
192
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0
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0
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croak "$pdb_code does not look like a four-letter PDB_CODE" |
193
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unless $pdb_code =~ /[A-z0-9]{4}/; |
194
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195
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0
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my $pdb_file_name = "pdb" . $pdb_code . '.ent'; |
196
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0
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my $pdb_file_name_gz = "pdb" . $pdb_code . '.ent.gz'; |
197
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198
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0
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my $uncompressed = "$PDB_PATH/obsoletes/$pdb_file_name"; |
199
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0
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my $compressed = "$PDB_PATH/obsoletes/$pdb_file_name_gz"; |
200
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201
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# try uncompressed pdb filename existence |
202
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0
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0
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if ( -e $uncompressed ) { |
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0
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203
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0
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return $uncompressed; |
204
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} |
205
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206
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# try compressed file |
207
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elsif ( -e $compressed ) { |
208
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0
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|
return $compressed; |
209
|
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} |
210
|
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else { |
211
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0
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|
return undef; |
212
|
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} |
213
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|
} |
214
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215
|
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|
=head2 exist_pdb_code_on_uncompressed |
216
|
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217
|
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|
check if a four-letters pdb code exist in uncompressed PDB folder |
218
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it will return the full path name if a match is found. |
219
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|
Return undef if not file was found |
220
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221
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input : pdb_code (4fab) |
222
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return : full path name |
223
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224
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|
=cut |
225
|
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|
|
sub exist_pdb_code_on_uncompressed { |
226
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0
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0
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|
my ($pdb_code) = @_; |
227
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0
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0
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croak "exist_pdb_code_on_uncompressed: pdb_code is required" unless $pdb_code; |
228
|
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229
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0
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|
chomp $pdb_code; |
230
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0
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0
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|
croak "$pdb_code does not look like a four-letter PDB_CODE" |
231
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|
unless $pdb_code =~ /[A-z0-9]{4}/; |
232
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233
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0
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|
my $pdb_file_name = "pdb" . $pdb_code . '.ent'; |
234
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0
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|
my $pdb_file_name_gz = "pdb" . $pdb_code . '.ent.gz'; |
235
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|
236
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0
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|
my $uncompressed = "$PDB_PATH/uncompressed/$pdb_file_name"; |
237
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0
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|
my $compressed = "$PDB_PATH/uncompressed/$pdb_file_name_gz"; |
238
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|
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|
239
|
|
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|
|
|
# try uncompressed pdb filename existence |
240
|
0
|
0
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|
|
if ( -e $uncompressed ) { |
|
|
0
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241
|
0
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|
return $uncompressed; |
242
|
|
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|
|
|
} |
243
|
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|
244
|
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|
|
# try compressed file |
245
|
|
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|
|
|
|
elsif ( -e $compressed ) { |
246
|
0
|
|
|
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|
return $compressed; |
247
|
|
|
|
|
|
|
} |
248
|
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|
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|
else { |
249
|
0
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|
return undef; |
250
|
|
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|
|
|
|
} |
251
|
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|
|
|
} |
252
|
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|
253
|
|
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|
|
|
=head2 exist_pdb_code_on_alternate |
254
|
|
|
|
|
|
|
|
255
|
|
|
|
|
|
|
check if a four-letters pdb code exist in user defined alternate |
256
|
|
|
|
|
|
|
PDB folder |
257
|
|
|
|
|
|
|
it will return the full path name if a match is found. |
258
|
|
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|
Return undef if not file was found |
259
|
|
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|
|
|
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|
260
|
|
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|
|
|
|
input : pdb_code (4fab) |
261
|
|
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|
|
|
|
return : full path name |
262
|
|
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|
|
|
|
|
263
|
|
|
|
|
|
|
=cut |
264
|
|
|
|
|
|
|
sub exist_pdb_code_on_alternate { |
265
|
0
|
|
|
0
|
|
|
my ($pdb_code, $chain) = @_; |
266
|
0
|
0
|
|
|
|
|
croak "exist_pdb_code_on_alternate: pdb_code is required" unless $pdb_code; |
267
|
0
|
0
|
|
|
|
|
croak "exist_pdb_code_on_alternate: chain_id is required" unless $chain; |
268
|
|
|
|
|
|
|
|
269
|
0
|
|
|
|
|
|
chomp $pdb_code; |
270
|
0
|
0
|
|
|
|
|
croak "$pdb_code does not look like a four-letter PDB_CODE" |
271
|
|
|
|
|
|
|
unless $pdb_code =~ /[A-z0-9]{4}/; |
272
|
|
|
|
|
|
|
|
273
|
0
|
|
|
|
|
|
my $pdb_file_name = 'pdb' . $pdb_code . $chain . '.ent'; |
274
|
0
|
|
|
|
|
|
my $pdb_file_name_gz = 'pdb' . $pdb_code . $chain . '.ent.gz'; |
275
|
|
|
|
|
|
|
|
276
|
0
|
|
|
|
|
|
my $uncompressed = catfile ($USER_SPECIFIC_PDB_PATH, $pdb_file_name); |
277
|
0
|
|
|
|
|
|
my $compressed = catfile ($USER_SPECIFIC_PDB_PATH, $pdb_file_name_gz); |
278
|
|
|
|
|
|
|
|
279
|
|
|
|
|
|
|
# try uncompressed pdb filename existence |
280
|
0
|
0
|
|
|
|
|
if ( -e $uncompressed ) { |
|
|
0
|
|
|
|
|
|
281
|
0
|
|
|
|
|
|
return $uncompressed; |
282
|
|
|
|
|
|
|
} |
283
|
|
|
|
|
|
|
|
284
|
|
|
|
|
|
|
# try compressed file |
285
|
|
|
|
|
|
|
elsif ( -e $compressed ) { |
286
|
0
|
|
|
|
|
|
return $compressed; |
287
|
|
|
|
|
|
|
} |
288
|
|
|
|
|
|
|
else { |
289
|
0
|
|
|
|
|
|
return undef; |
290
|
|
|
|
|
|
|
} |
291
|
|
|
|
|
|
|
} |
292
|
|
|
|
|
|
|
|
293
|
|
|
|
|
|
|
=head2 exist_pdb_code_on_remodelled |
294
|
|
|
|
|
|
|
|
295
|
|
|
|
|
|
|
check if a four-letters pdb code exist in user defined remodelled |
296
|
|
|
|
|
|
|
PDB folder |
297
|
|
|
|
|
|
|
it will return the full path name if a match is found. |
298
|
|
|
|
|
|
|
Return undef if not file was found |
299
|
|
|
|
|
|
|
|
300
|
|
|
|
|
|
|
input : pdb_code (4fab) |
301
|
|
|
|
|
|
|
return : full path name |
302
|
|
|
|
|
|
|
|
303
|
|
|
|
|
|
|
=cut |
304
|
|
|
|
|
|
|
sub exist_pdb_code_on_remodelled { |
305
|
0
|
|
|
0
|
|
|
my ($pdb_code, $chain) = @_; |
306
|
0
|
0
|
|
|
|
|
croak "exist_pdb_code_on_alternate: pdb_code is required" unless $pdb_code; |
307
|
0
|
0
|
|
|
|
|
croak "exist_pdb_code_on_alternate: Chain ID is required" unless $chain; |
308
|
|
|
|
|
|
|
|
309
|
0
|
|
|
|
|
|
chomp $pdb_code; |
310
|
0
|
0
|
|
|
|
|
croak "$pdb_code does not look like a four-letter PDB_CODE" |
311
|
|
|
|
|
|
|
unless $pdb_code =~ /[A-z0-9]{4}/; |
312
|
|
|
|
|
|
|
|
313
|
0
|
|
|
|
|
|
my $pdb_file_name = 'pdb' . $pdb_code . $chain . '.ent'; |
314
|
0
|
|
|
|
|
|
my $pdb_file_name_gz = 'pdb' . $pdb_code . $chain . '.ent.gz'; |
315
|
|
|
|
|
|
|
|
316
|
0
|
|
|
|
|
|
my $uncompressed = catfile ($REMODELLED_PDB_PATH, $pdb_file_name); |
317
|
0
|
|
|
|
|
|
my $compressed = catfile ($REMODELLED_PDB_PATH, $pdb_file_name_gz); |
318
|
|
|
|
|
|
|
|
319
|
|
|
|
|
|
|
# try uncompressed pdb filename existence |
320
|
0
|
0
|
|
|
|
|
if ( -e $uncompressed ) { |
|
|
0
|
|
|
|
|
|
321
|
0
|
|
|
|
|
|
return $uncompressed; |
322
|
|
|
|
|
|
|
} |
323
|
|
|
|
|
|
|
|
324
|
|
|
|
|
|
|
# try compressed file |
325
|
|
|
|
|
|
|
elsif ( -e $compressed ) { |
326
|
0
|
|
|
|
|
|
return $compressed; |
327
|
|
|
|
|
|
|
} |
328
|
|
|
|
|
|
|
else { |
329
|
0
|
|
|
|
|
|
return undef; |
330
|
|
|
|
|
|
|
} |
331
|
|
|
|
|
|
|
} |
332
|
|
|
|
|
|
|
|
333
|
|
|
|
|
|
|
=head2 get_full_path_name_for_pdb_code |
334
|
|
|
|
|
|
|
Return a fullpath name for a given four-letter PDB code |
335
|
|
|
|
|
|
|
It will look in remodelled_PDB directory |
336
|
|
|
|
|
|
|
|
337
|
|
|
|
|
|
|
die if not match found |
338
|
|
|
|
|
|
|
|
339
|
|
|
|
|
|
|
=cut |
340
|
|
|
|
|
|
|
sub get_full_path_name_for_pdb_code { |
341
|
1
|
|
|
1
|
|
668
|
use Data::Dumper; |
|
1
|
|
|
|
|
4568
|
|
|
1
|
|
|
|
|
244
|
|
342
|
0
|
|
|
0
|
|
|
my ($pdb_code, $chain) = @_; |
343
|
|
|
|
|
|
|
|
344
|
0
|
0
|
|
|
|
|
if ($DEBUG){ |
345
|
0
|
|
|
|
|
|
my ($package, $filename, $line) = caller; |
346
|
0
|
|
|
|
|
|
print "package = $package\n"; |
347
|
0
|
|
|
|
|
|
print "filename = $filename\n"; |
348
|
0
|
|
|
|
|
|
print "line = $line\n"; |
349
|
0
|
|
|
|
|
|
print Dumper(\@_); |
350
|
|
|
|
|
|
|
} |
351
|
|
|
|
|
|
|
|
352
|
0
|
0
|
|
|
|
|
croak "get_full_path_name_for_pdb_code: pdb_code is required" unless $pdb_code; |
353
|
0
|
0
|
|
|
|
|
croak "get_full_path_name_for_pdb_code: Chain ID is required" unless $chain; |
354
|
|
|
|
|
|
|
|
355
|
0
|
|
|
|
|
|
chomp $pdb_code; |
356
|
0
|
0
|
|
|
|
|
croak "$pdb_code does not look like a four-letter PDB_CODE" |
357
|
|
|
|
|
|
|
unless $pdb_code =~ /[A-z0-9]{4}/; |
358
|
|
|
|
|
|
|
|
359
|
0
|
|
|
|
|
|
my $path; |
360
|
|
|
|
|
|
|
|
361
|
0
|
|
|
|
|
|
$path = exist_pdb_code_on_remodelled($pdb_code, $chain); |
362
|
0
|
0
|
|
|
|
|
return $path if $path; |
363
|
|
|
|
|
|
|
|
364
|
0
|
|
|
|
|
|
$path = exist_pdb_code_on_alternate($pdb_code, $chain); |
365
|
0
|
0
|
|
|
|
|
return $path if $path; |
366
|
|
|
|
|
|
|
|
367
|
0
|
0
|
|
|
|
|
croak "Could not find $pdb_code $chain on $REMODELLED_PDB_PATH" |
368
|
|
|
|
|
|
|
unless $path; |
369
|
|
|
|
|
|
|
} |
370
|
|
|
|
|
|
|
|
371
|
|
|
|
|
|
|
=head2 get_full_path_name_for_pdb_code_old |
372
|
|
|
|
|
|
|
Return a fullpath name for a given four-letter PDB code |
373
|
|
|
|
|
|
|
It will look in obsoletes and uncompressed directories |
374
|
|
|
|
|
|
|
|
375
|
|
|
|
|
|
|
die if not match found |
376
|
|
|
|
|
|
|
|
377
|
|
|
|
|
|
|
=cut |
378
|
|
|
|
|
|
|
sub get_full_path_name_for_pdb_code_old { |
379
|
1
|
|
|
1
|
|
9
|
use Data::Dumper; |
|
1
|
|
|
|
|
1
|
|
|
1
|
|
|
|
|
197
|
|
380
|
0
|
|
|
0
|
|
|
my ($pdb_code) = @_; |
381
|
|
|
|
|
|
|
|
382
|
0
|
0
|
|
|
|
|
if ($DEBUG){ |
383
|
0
|
|
|
|
|
|
my ($package, $filename, $line) = caller; |
384
|
0
|
|
|
|
|
|
print "package = $package\n"; |
385
|
0
|
|
|
|
|
|
print "filename = $filename\n"; |
386
|
0
|
|
|
|
|
|
print "line = $line\n"; |
387
|
0
|
|
|
|
|
|
print Dumper(\@_); |
388
|
|
|
|
|
|
|
} |
389
|
|
|
|
|
|
|
|
390
|
0
|
0
|
|
|
|
|
croak "get_full_path_name_for_pdb_code_old: pdb_code is required" unless $pdb_code; |
391
|
|
|
|
|
|
|
|
392
|
0
|
|
|
|
|
|
chomp $pdb_code; |
393
|
0
|
0
|
|
|
|
|
croak "$pdb_code does not look like a four-letter PDB_CODE" |
394
|
|
|
|
|
|
|
unless $pdb_code =~ /[A-z0-9]{4}/; |
395
|
|
|
|
|
|
|
|
396
|
0
|
|
|
|
|
|
my $path; |
397
|
0
|
|
|
|
|
|
$path = exist_pdb_code_on_uncompressed($pdb_code); |
398
|
0
|
0
|
|
|
|
|
return $path if $path; |
399
|
|
|
|
|
|
|
|
400
|
0
|
|
|
|
|
|
$path = exist_pdb_code_on_obsoletes($pdb_code); |
401
|
0
|
0
|
|
|
|
|
return $path if $path; |
402
|
|
|
|
|
|
|
|
403
|
0
|
|
|
|
|
|
$path = exist_pdb_code_on_alternate($pdb_code); |
404
|
0
|
0
|
|
|
|
|
return $path if $path; |
405
|
|
|
|
|
|
|
|
406
|
0
|
0
|
|
|
|
|
croak "Could not find $pdb_code on $PDB_PATH or $USER_SPECIFIC_PDB_PATH" |
407
|
|
|
|
|
|
|
unless $path; |
408
|
|
|
|
|
|
|
} |
409
|
|
|
|
|
|
|
|
410
|
|
|
|
|
|
|
=head2 get_from_file |
411
|
|
|
|
|
|
|
|
412
|
|
|
|
|
|
|
subroutine to read PDB file and obtain coordinates of backbone atoms. |
413
|
|
|
|
|
|
|
|
414
|
|
|
|
|
|
|
Input 1: @$data - smotif info (pdb ID, chain ID, start residue, ss1 length, ss2 length, loop length) |
415
|
|
|
|
|
|
|
Input/Output 2: @$landmarks - output array with smotif landmarks (0, loop start, ss2 start, ss2 end) |
416
|
|
|
|
|
|
|
Input 3: $string - backbone atom (CA, CB, C, N, or O) |
417
|
|
|
|
|
|
|
Input/Output 4: $seq - smotif sequence |
418
|
|
|
|
|
|
|
|
419
|
|
|
|
|
|
|
$VAR1 = [ |
420
|
|
|
|
|
|
|
'/usr/local/databases/pdb//uncompressed/pdb2kl8.ent.gz', |
421
|
|
|
|
|
|
|
'A', |
422
|
|
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2, |
423
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7, |
424
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17, |
425
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3, |
426
|
|
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0, |
427
|
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'EH' |
428
|
|
|
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|
]; |
429
|
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|
|
430
|
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431
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|
=cut |
432
|
|
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|
|
sub get_from_file { |
433
|
0
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0
|
|
|
my ( $data, $landmarks, $string, $seq ) = @_; |
434
|
|
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|
|
435
|
|
|
|
|
|
|
# data contains pdbid, chain, start, ss1, ss2 |
436
|
1
|
|
|
1
|
|
5
|
use Data::Dumper; |
|
1
|
|
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2
|
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1
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|
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|
38
|
|
437
|
1
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1
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|
4
|
use File::Basename; |
|
1
|
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1
|
|
|
1
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|
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|
6076
|
|
438
|
|
|
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|
|
|
#print Dumper($data); |
439
|
|
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|
|
|
|
|
440
|
0
|
|
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|
my $chain = $$data[1]; |
441
|
0
|
|
|
|
|
|
my $startres = $$data[2]; |
442
|
0
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|
|
my $endres = $$data[2] + $$data[5] + $$data[3] + $$data[4] - 1; |
443
|
0
|
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|
|
@$landmarks = |
444
|
|
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|
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|
|
( $$data[3], $$data[3] + $$data[5], $$data[3] + $$data[5] + $$data[4] ); |
445
|
|
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|
446
|
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|
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|
|
# $$data[0] has values like this: |
447
|
|
|
|
|
|
|
# 2kl8/pdb2kl8.ent |
448
|
0
|
|
|
|
|
|
my $pdb_code; |
449
|
|
|
|
|
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|
|
450
|
0
|
0
|
|
|
|
|
if ( $$data[0] =~ /\// ) { |
451
|
|
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|
|
|
|
# $pdb_code = ( split( /\//, $$data[0] ) )[0]; |
452
|
0
|
|
|
|
|
|
my $filename = basename $$data[0]; |
453
|
0
|
0
|
|
|
|
|
if ( $filename =~ /pdb(\w{4}).*/ ) { |
|
|
0
|
|
|
|
|
|
454
|
0
|
|
|
|
|
|
$pdb_code = $1; |
455
|
|
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|
|
|
|
} |
456
|
|
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|
|
|
|
elsif ( $filename =~ /(\w{4}).*/ ) { |
457
|
0
|
|
|
|
|
|
$pdb_code = $1; |
458
|
|
|
|
|
|
|
} |
459
|
|
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|
|
else {} |
460
|
|
|
|
|
|
|
} |
461
|
|
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|
|
|
|
else { |
462
|
0
|
|
|
|
|
|
$pdb_code = $$data[0]; |
463
|
0
|
|
|
|
|
|
$pdb_code =~ s/^pdb//g; # removing leading pdb string |
464
|
0
|
|
|
|
|
|
$pdb_code =~ s/\.(\w+)$//g; # removing file extension |
465
|
|
|
|
|
|
|
} |
466
|
|
|
|
|
|
|
|
467
|
|
|
|
|
|
|
#unless ( $$data[0] ) { |
468
|
|
|
|
|
|
|
# use Data::Dumper; |
469
|
|
|
|
|
|
|
# print "pdb_code $pdb_code\n"; |
470
|
|
|
|
|
|
|
# print Dumper($data); |
471
|
|
|
|
|
|
|
# #croak "get_from_file: pdb_code is required"; |
472
|
|
|
|
|
|
|
#} |
473
|
|
|
|
|
|
|
|
474
|
|
|
|
|
|
|
|
475
|
0
|
|
|
|
|
|
my $full_path_name = get_full_path_name_for_pdb_code($pdb_code, $chain); |
476
|
0
|
|
|
|
|
|
my $fh = _getReadingFileHandle($full_path_name); |
477
|
|
|
|
|
|
|
|
478
|
0
|
|
|
|
|
|
my $done = 0; |
479
|
0
|
|
|
|
|
|
my @coords = (); |
480
|
0
|
|
|
|
|
|
my $prevres = 0; |
481
|
0
|
|
|
|
|
|
my $len = length($string); |
482
|
0
|
|
|
|
|
|
my $id = $prevres; |
483
|
0
|
0
|
|
|
|
|
if ( $string ne 'CB' ) |
484
|
|
|
|
|
|
|
{ #certain residues (GLY) will not have CBs, so this case has to be treated separately |
485
|
0
|
|
0
|
|
|
|
while ( defined( my $line = <$fh> ) and ( $done == 0 ) ) { |
486
|
0
|
|
|
|
|
|
chomp($line); |
487
|
0
|
0
|
|
|
|
|
if ( $line =~ |
488
|
|
|
|
|
|
|
/ATOM\s+-*\d+\s+$string\s+(\w+)\s$chain\s*(-*\d+\w?\s)/ ) |
489
|
|
|
|
|
|
|
{ |
490
|
0
|
|
|
|
|
|
$id = $2; |
491
|
0
|
|
|
|
|
|
my $amino = $1; |
492
|
0
|
0
|
|
|
|
|
if ( $id =~ /(-*\d+)\D/ ) { $id = $1 } |
|
0
|
|
|
|
|
|
|
493
|
0
|
0
|
|
|
|
|
if ( $id ne $prevres ) { |
494
|
0
|
0
|
|
|
|
|
if ( $id > $endres ) { |
|
|
0
|
|
|
|
|
|
495
|
0
|
|
|
|
|
|
$done = 1; |
496
|
|
|
|
|
|
|
} |
497
|
|
|
|
|
|
|
elsif ( $id >= $startres ) { |
498
|
0
|
|
|
|
|
|
push( |
499
|
|
|
|
|
|
|
@coords, |
500
|
|
|
|
|
|
|
[ |
501
|
|
|
|
|
|
|
substr( $line, 30, 8 ), |
502
|
|
|
|
|
|
|
substr( $line, 38, 8 ), |
503
|
|
|
|
|
|
|
substr( $line, 46, 8 ) |
504
|
|
|
|
|
|
|
] |
505
|
|
|
|
|
|
|
); |
506
|
|
|
|
|
|
|
|
507
|
|
|
|
|
|
|
#print "$line\t$amino\n"; |
508
|
0
|
|
|
|
|
|
$$seq = $$seq . translate($amino); |
509
|
|
|
|
|
|
|
|
510
|
|
|
|
|
|
|
#print "$line\n"; |
511
|
|
|
|
|
|
|
} |
512
|
|
|
|
|
|
|
} |
513
|
0
|
|
|
|
|
|
$prevres = $id; |
514
|
|
|
|
|
|
|
} |
515
|
|
|
|
|
|
|
} |
516
|
|
|
|
|
|
|
} |
517
|
|
|
|
|
|
|
else { |
518
|
0
|
|
|
|
|
|
$$seq = ''; |
519
|
0
|
|
|
|
|
|
my $prevline = <$fh>; |
520
|
0
|
|
0
|
|
|
|
while ( defined( my $line = <$fh> ) and ( $done == 0 ) ) { |
521
|
0
|
|
|
|
|
|
chomp($line); |
522
|
0
|
0
|
|
|
|
|
if ( $line =~ /ATOM\s+-*\d+\s+CB\s+(\w+)\s$chain\s*(-*\d+\w?\s)/ ) { |
|
|
0
|
|
|
|
|
|
523
|
0
|
|
|
|
|
|
$id = $2; |
524
|
0
|
|
|
|
|
|
my $amin = substr( $1, -3, 3 ); |
525
|
0
|
0
|
|
|
|
|
if ( $id =~ /(-*\d+)\D/ ) { $id = $1 } |
|
0
|
|
|
|
|
|
|
526
|
0
|
0
|
|
|
|
|
if ( $id ne $prevres ) { |
527
|
0
|
0
|
|
|
|
|
if ( $id > $endres ) { |
|
|
0
|
|
|
|
|
|
528
|
0
|
|
|
|
|
|
$done = 1; |
529
|
|
|
|
|
|
|
} |
530
|
|
|
|
|
|
|
elsif ( $id >= $startres ) { |
531
|
0
|
|
|
|
|
|
push( |
532
|
|
|
|
|
|
|
@coords, |
533
|
|
|
|
|
|
|
[ |
534
|
|
|
|
|
|
|
substr( $line, 30, 8 ), |
535
|
|
|
|
|
|
|
substr( $line, 38, 8 ), |
536
|
|
|
|
|
|
|
substr( $line, 46, 8 ) |
537
|
|
|
|
|
|
|
] |
538
|
|
|
|
|
|
|
); |
539
|
0
|
|
|
|
|
|
$$seq = $$seq . translate($amin); |
540
|
|
|
|
|
|
|
|
541
|
|
|
|
|
|
|
#print "$line\t$startres\t$endres\n"; |
542
|
|
|
|
|
|
|
} |
543
|
|
|
|
|
|
|
} |
544
|
0
|
|
|
|
|
|
$prevres = $id; |
545
|
|
|
|
|
|
|
} |
546
|
|
|
|
|
|
|
elsif ( |
547
|
|
|
|
|
|
|
$prevline =~ /ATOM\s+-*\d+\s+O\s+(\w+)\s$chain\s*(-*\d+\w?\s)/ ) |
548
|
|
|
|
|
|
|
{ |
549
|
0
|
|
|
|
|
|
$id = $2; |
550
|
0
|
|
|
|
|
|
my $amin = substr( $1, -3, 3 ); |
551
|
0
|
0
|
|
|
|
|
if ( $id =~ /(-*\d+)\D/ ) { $id = $1 } |
|
0
|
|
|
|
|
|
|
552
|
0
|
0
|
|
|
|
|
if ( $id ne $prevres ) { |
553
|
0
|
0
|
|
|
|
|
if ( $id > $endres ) { |
|
|
0
|
|
|
|
|
|
554
|
0
|
|
|
|
|
|
$done = 1; |
555
|
|
|
|
|
|
|
} |
556
|
|
|
|
|
|
|
elsif ( $id >= $startres ) { |
557
|
0
|
|
|
|
|
|
push( @coords, 0 ); |
558
|
0
|
|
|
|
|
|
$$seq = $$seq . translate($amin); |
559
|
|
|
|
|
|
|
} |
560
|
|
|
|
|
|
|
} |
561
|
0
|
|
|
|
|
|
$prevres = $id; |
562
|
|
|
|
|
|
|
} |
563
|
0
|
|
|
|
|
|
$prevline = $line; |
564
|
|
|
|
|
|
|
} |
565
|
|
|
|
|
|
|
} |
566
|
0
|
|
|
|
|
|
close($fh); |
567
|
0
|
|
|
|
|
|
return @coords; |
568
|
|
|
|
|
|
|
} |
569
|
|
|
|
|
|
|
|
570
|
|
|
|
|
|
|
=head2 |
571
|
|
|
|
|
|
|
|
572
|
|
|
|
|
|
|
translate |
573
|
|
|
|
|
|
|
subroutine to convert from 3-letter codes to 1-letter codes |
574
|
|
|
|
|
|
|
|
575
|
|
|
|
|
|
|
=cut |
576
|
|
|
|
|
|
|
sub translate { |
577
|
0
|
|
|
0
|
|
|
my ($inp) = @_; |
578
|
0
|
|
|
|
|
|
my $out; |
579
|
0
|
0
|
|
|
|
|
if ( $inp eq 'ALA' ) { $out = 'A' } |
|
0
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
580
|
0
|
|
|
|
|
|
elsif ( $inp eq 'CYS' ) { $out = 'C' } |
581
|
0
|
|
|
|
|
|
elsif ( $inp eq 'ASP' ) { $out = 'D' } |
582
|
0
|
|
|
|
|
|
elsif ( $inp eq 'GLU' ) { $out = 'E' } |
583
|
0
|
|
|
|
|
|
elsif ( $inp eq 'PHE' ) { $out = 'F' } |
584
|
0
|
|
|
|
|
|
elsif ( $inp eq 'GLY' ) { $out = 'G' } |
585
|
0
|
|
|
|
|
|
elsif ( $inp eq 'HIS' ) { $out = 'H' } |
586
|
0
|
|
|
|
|
|
elsif ( $inp eq 'ILE' ) { $out = 'I' } |
587
|
0
|
|
|
|
|
|
elsif ( $inp eq 'LYS' ) { $out = 'K' } |
588
|
0
|
|
|
|
|
|
elsif ( $inp eq 'LEU' ) { $out = 'L' } |
589
|
0
|
|
|
|
|
|
elsif ( $inp eq 'MET' ) { $out = 'M' } |
590
|
0
|
|
|
|
|
|
elsif ( $inp eq 'ASN' ) { $out = 'N' } |
591
|
0
|
|
|
|
|
|
elsif ( $inp eq 'PRO' ) { $out = 'P' } |
592
|
0
|
|
|
|
|
|
elsif ( $inp eq 'GLN' ) { $out = 'Q' } |
593
|
0
|
|
|
|
|
|
elsif ( $inp eq 'ARG' ) { $out = 'R' } |
594
|
0
|
|
|
|
|
|
elsif ( $inp eq 'SER' ) { $out = 'S' } |
595
|
0
|
|
|
|
|
|
elsif ( $inp eq 'THR' ) { $out = 'T' } |
596
|
0
|
|
|
|
|
|
elsif ( $inp eq 'VAL' ) { $out = 'V' } |
597
|
0
|
|
|
|
|
|
elsif ( $inp eq 'TRP' ) { $out = 'W' } |
598
|
0
|
|
|
|
|
|
else { $out = 'Y' } |
599
|
0
|
|
|
|
|
|
return $out; |
600
|
|
|
|
|
|
|
} |
601
|
|
|
|
|
|
|
|
602
|
|
|
|
|
|
|
=head2 convert |
603
|
|
|
|
|
|
|
|
604
|
|
|
|
|
|
|
subroutine to convert from 1-letter codes to 3-letter codes |
605
|
|
|
|
|
|
|
|
606
|
|
|
|
|
|
|
=cut |
607
|
|
|
|
|
|
|
sub convert { |
608
|
0
|
|
|
0
|
|
|
my ($aa) = @_; |
609
|
0
|
0
|
|
|
|
|
if ( $aa eq 'A' ) { return 'ALA' } |
|
0
|
|
|
|
|
|
|
610
|
0
|
0
|
|
|
|
|
if ( $aa eq 'C' ) { return 'CYS' } |
|
0
|
|
|
|
|
|
|
611
|
0
|
0
|
|
|
|
|
if ( $aa eq 'D' ) { return 'ASP' } |
|
0
|
|
|
|
|
|
|
612
|
0
|
0
|
|
|
|
|
if ( $aa eq 'E' ) { return 'GLU' } |
|
0
|
|
|
|
|
|
|
613
|
0
|
0
|
|
|
|
|
if ( $aa eq 'F' ) { return 'PHE' } |
|
0
|
|
|
|
|
|
|
614
|
0
|
0
|
|
|
|
|
if ( $aa eq 'G' ) { return 'GLY' } |
|
0
|
|
|
|
|
|
|
615
|
0
|
0
|
|
|
|
|
if ( $aa eq 'H' ) { return 'HIS' } |
|
0
|
|
|
|
|
|
|
616
|
0
|
0
|
|
|
|
|
if ( $aa eq 'I' ) { return 'ILE' } |
|
0
|
|
|
|
|
|
|
617
|
0
|
0
|
|
|
|
|
if ( $aa eq 'K' ) { return 'LYS' } |
|
0
|
|
|
|
|
|
|
618
|
0
|
0
|
|
|
|
|
if ( $aa eq 'L' ) { return 'LEU' } |
|
0
|
|
|
|
|
|
|
619
|
0
|
0
|
|
|
|
|
if ( $aa eq 'M' ) { return 'MET' } |
|
0
|
|
|
|
|
|
|
620
|
0
|
0
|
|
|
|
|
if ( $aa eq 'N' ) { return 'ASN' } |
|
0
|
|
|
|
|
|
|
621
|
0
|
0
|
|
|
|
|
if ( $aa eq 'P' ) { return 'PRO' } |
|
0
|
|
|
|
|
|
|
622
|
0
|
0
|
|
|
|
|
if ( $aa eq 'Q' ) { return 'GLN' } |
|
0
|
|
|
|
|
|
|
623
|
0
|
0
|
|
|
|
|
if ( $aa eq 'R' ) { return 'ARG' } |
|
0
|
|
|
|
|
|
|
624
|
0
|
0
|
|
|
|
|
if ( $aa eq 'S' ) { return 'SER' } |
|
0
|
|
|
|
|
|
|
625
|
0
|
0
|
|
|
|
|
if ( $aa eq 'T' ) { return 'THR' } |
|
0
|
|
|
|
|
|
|
626
|
0
|
0
|
|
|
|
|
if ( $aa eq 'V' ) { return 'VAL' } |
|
0
|
|
|
|
|
|
|
627
|
0
|
0
|
|
|
|
|
if ( $aa eq 'W' ) { return 'TRP' } |
|
0
|
|
|
|
|
|
|
628
|
0
|
0
|
|
|
|
|
if ( $aa eq 'Y' ) { return 'TYR' } |
|
0
|
|
|
|
|
|
|
629
|
|
|
|
|
|
|
} |
630
|
|
|
|
|
|
|
|
631
|
|
|
|
|
|
|
=head2 COM |
632
|
|
|
|
|
|
|
|
633
|
|
|
|
|
|
|
subroutine to find the centre of mass of a set of points, presented in 3 vectors |
634
|
|
|
|
|
|
|
|
635
|
|
|
|
|
|
|
=cut |
636
|
|
|
|
|
|
|
sub COM { |
637
|
0
|
|
|
0
|
|
|
my ( $start, $end, $ca, $n, $c ) = @_; |
638
|
0
|
|
|
|
|
|
my @tots = ( 0, 0, 0 ); |
639
|
0
|
|
|
|
|
|
my $count = 3 * ( $end - $start ); |
640
|
0
|
|
|
|
|
|
for ( my $a = $start ; $a < $end ; $a++ ) { |
641
|
|
|
|
|
|
|
|
642
|
|
|
|
|
|
|
# print $$ca[$a][0], "\n"; |
643
|
0
|
|
|
|
|
|
$tots[0] = $tots[0] + $$ca[$a][0] + $$n[$a][0] + $$c[$a][0]; |
644
|
0
|
|
|
|
|
|
$tots[1] = $tots[1] + $$ca[$a][1] + $$n[$a][1] + $$c[$a][1]; |
645
|
0
|
|
|
|
|
|
$tots[2] = $tots[2] + $$ca[$a][2] + $$n[$a][2] + $$c[$a][2]; |
646
|
|
|
|
|
|
|
} |
647
|
0
|
|
|
|
|
|
return ( $tots[0] / $count, $tots[1] / $count, $tots[2] / $count ); |
648
|
|
|
|
|
|
|
} |
649
|
|
|
|
|
|
|
|
650
|
|
|
|
|
|
|
=head2 COM2 |
651
|
|
|
|
|
|
|
|
652
|
|
|
|
|
|
|
subroutine to find the centre of mass of a set of points, presented as a single vector |
653
|
|
|
|
|
|
|
|
654
|
|
|
|
|
|
|
=cut |
655
|
|
|
|
|
|
|
sub COM2 { |
656
|
0
|
|
|
0
|
|
|
my ( $start, $end, $c ) = @_; |
657
|
0
|
|
|
|
|
|
my @tots = ( 0, 0, 0 ); |
658
|
0
|
|
|
|
|
|
my $count = $end - $start; |
659
|
0
|
|
|
|
|
|
for ( my $a = $start ; $a < $end ; $a++ ) { |
660
|
0
|
|
|
|
|
|
$tots[0] += $$c[$a][0]; |
661
|
0
|
|
|
|
|
|
$tots[1] += $$c[$a][1]; |
662
|
0
|
|
|
|
|
|
$tots[2] += $$c[$a][2]; |
663
|
|
|
|
|
|
|
} |
664
|
0
|
|
|
|
|
|
return ( $tots[0] / $count, $tots[1] / $count, $tots[2] / $count ); |
665
|
|
|
|
|
|
|
} |
666
|
|
|
|
|
|
|
|
667
|
|
|
|
|
|
|
=head2 calculate_axis |
668
|
|
|
|
|
|
|
|
669
|
|
|
|
|
|
|
subroutine to calculate the principal axis of a set of points |
670
|
|
|
|
|
|
|
(corresponds to the principal eigenvector for the moment matrix) |
671
|
|
|
|
|
|
|
|
672
|
|
|
|
|
|
|
=cut |
673
|
|
|
|
|
|
|
sub calculate_axis { |
674
|
0
|
|
|
0
|
|
|
my ( $type, $ca, $n, $c ) = @_; |
675
|
0
|
|
|
|
|
|
my @ca2 = @$ca; |
676
|
0
|
|
|
|
|
|
my @n2 = @$n; |
677
|
0
|
|
|
|
|
|
my @c2 = @$c; |
678
|
0
|
|
|
|
|
|
my $count = scalar(@ca2); |
679
|
0
|
|
|
|
|
|
my @com = COM( 0, $count, \@ca2, \@n2, \@c2 ); |
680
|
0
|
|
|
|
|
|
for ( my $a = 0 ; $a < $count ; $a++ ) { |
681
|
0
|
|
|
|
|
|
$ca2[$a][0] -= $com[0]; |
682
|
0
|
|
|
|
|
|
$ca2[$a][1] -= $com[1]; |
683
|
0
|
|
|
|
|
|
$ca2[$a][2] -= $com[2]; |
684
|
0
|
|
|
|
|
|
$n2[$a][0] -= $com[0]; |
685
|
0
|
|
|
|
|
|
$n2[$a][1] -= $com[1]; |
686
|
0
|
|
|
|
|
|
$n2[$a][2] -= $com[2]; |
687
|
0
|
|
|
|
|
|
$c2[$a][0] -= $com[0]; |
688
|
0
|
|
|
|
|
|
$c2[$a][1] -= $com[1]; |
689
|
0
|
|
|
|
|
|
$c2[$a][2] -= $com[2]; |
690
|
|
|
|
|
|
|
} |
691
|
0
|
|
|
|
|
|
my @p = ( [@ca2], [@n2], [@c2] ); |
692
|
|
|
|
|
|
|
|
693
|
|
|
|
|
|
|
#find moment of inertia matrix |
694
|
0
|
|
|
|
|
|
my @I = calc_I( $type, $count, @p ); |
695
|
|
|
|
|
|
|
|
696
|
|
|
|
|
|
|
#find principal eigenvector |
697
|
0
|
|
|
|
|
|
my @eigs = find_eigs(@I); |
698
|
0
|
|
|
|
|
|
my @evec = calc_evec( $eigs[2], @I ); |
699
|
|
|
|
|
|
|
|
700
|
|
|
|
|
|
|
#check direction of axis by looking at max eigenvec, difference |
701
|
0
|
|
|
|
|
|
my $i = 2; |
702
|
0
|
0
|
0
|
|
|
|
if ( ( abs( $evec[0] ) >= abs( $evec[1] ) ) |
|
|
0
|
|
|
|
|
|
703
|
|
|
|
|
|
|
and ( abs( $evec[0] ) >= abs( $evec[2] ) ) ) |
704
|
|
|
|
|
|
|
{ #x-coord is max |
705
|
0
|
|
|
|
|
|
$i = 0; |
706
|
|
|
|
|
|
|
} |
707
|
|
|
|
|
|
|
elsif ( abs( $evec[1] ) >= abs( $evec[2] ) ) { #y-coord is max |
708
|
0
|
|
|
|
|
|
$i = 1; |
709
|
|
|
|
|
|
|
} |
710
|
0
|
0
|
|
|
|
|
if ( ( $evec[$i] * ( $p[0][-1][$i] - $p[0][0][$i] ) ) < 0 ) { |
711
|
0
|
|
|
|
|
|
return ( -$evec[0], -$evec[1], -$evec[2] ); |
712
|
|
|
|
|
|
|
} |
713
|
|
|
|
|
|
|
else { |
714
|
0
|
|
|
|
|
|
return @evec; |
715
|
|
|
|
|
|
|
} |
716
|
|
|
|
|
|
|
} |
717
|
|
|
|
|
|
|
|
718
|
|
|
|
|
|
|
=head2 get_axis |
719
|
|
|
|
|
|
|
subroutine to find the axis vector of a secondary structure, |
720
|
|
|
|
|
|
|
using at least 4 residues for a helix or 2 for a strand |
721
|
|
|
|
|
|
|
|
722
|
|
|
|
|
|
|
Input 1: Type of secondary structure (H=Helix, E=strand) |
723
|
|
|
|
|
|
|
Input 2: Option to indicate whether the secondary structure is the first (1) or second (2) part of the smotif |
724
|
|
|
|
|
|
|
Input 3: Initial residue number of the secondary structure |
725
|
|
|
|
|
|
|
Input 4: Final residue number of the secondar structure |
726
|
|
|
|
|
|
|
Input 5-7: Vectors containing the coordinates of C-alpha atoms, N atoms, and C atoms of the smotif |
727
|
|
|
|
|
|
|
|
728
|
|
|
|
|
|
|
=cut |
729
|
|
|
|
|
|
|
sub get_axis { |
730
|
0
|
|
|
0
|
|
|
my ( $type, $ss, $first, $last, $ca, $n, $c ) = @_; |
731
|
0
|
|
|
|
|
|
my $ang = 0; |
732
|
0
|
|
|
|
|
|
my @newaxis; |
733
|
|
|
|
|
|
|
my @oldaxis; |
734
|
0
|
|
|
|
|
|
my $j; |
735
|
0
|
|
|
|
|
|
my @use_ca; |
736
|
0
|
|
|
|
|
|
my @use_n; |
737
|
0
|
|
|
|
|
|
my @use_c; |
738
|
0
|
|
|
|
|
|
my $count = $last - $first; |
739
|
0
|
|
|
|
|
|
my $beg = 0; |
740
|
0
|
|
|
|
|
|
my $end = 0; |
741
|
0
|
|
|
|
|
|
my $lim = 5 * 3.14159265 / 180; |
742
|
0
|
|
|
|
|
|
my $term = 8; |
743
|
0
|
|
|
|
|
|
my $stop = 3; |
744
|
|
|
|
|
|
|
|
745
|
0
|
0
|
|
|
|
|
if ( $type eq 'H' ) { |
746
|
0
|
|
|
|
|
|
$stop = 9; |
747
|
0
|
|
|
|
|
|
$term = 100; |
748
|
|
|
|
|
|
|
} |
749
|
0
|
0
|
|
|
|
|
if ( $ss == 1 ) |
750
|
|
|
|
|
|
|
{ #first ss of motif, measure axis from the loop side (end of ss) |
751
|
0
|
|
|
|
|
|
$beg = max( $last - $stop, $first ); |
752
|
0
|
|
|
|
|
|
$end = $last; |
753
|
|
|
|
|
|
|
} |
754
|
|
|
|
|
|
|
else { |
755
|
0
|
|
|
|
|
|
$beg = $first |
756
|
|
|
|
|
|
|
; #second ss of motif, measure axis from the loop side (beginning of ss) |
757
|
0
|
|
|
|
|
|
$end = min( $first + $stop, $last ); |
758
|
|
|
|
|
|
|
} |
759
|
0
|
|
|
|
|
|
for ( my $aa = $beg ; $aa < $end ; $aa++ ) { |
760
|
0
|
|
|
|
|
|
push( @use_ca, [ ( $$ca[$aa][0], $$ca[$aa][1], $$ca[$aa][2] ) ] ); |
761
|
0
|
|
|
|
|
|
push( @use_n, [ ( $$n[$aa][0], $$n[$aa][1], $$n[$aa][2] ) ] ); |
762
|
0
|
|
|
|
|
|
push( @use_c, [ ( $$c[$aa][0], $$c[$aa][1], $$c[$aa][2] ) ] ); |
763
|
|
|
|
|
|
|
} |
764
|
0
|
|
|
|
|
|
@newaxis = calculate_axis( $type, \@use_ca, \@use_n, \@use_c ); |
765
|
0
|
|
|
|
|
|
$j = $stop; |
766
|
0
|
|
|
|
|
|
@oldaxis = @newaxis; |
767
|
0
|
|
0
|
|
|
|
while ( ( $j < $count ) and ( $ang < $lim ) and ( $j < $term ) ) |
|
|
|
0
|
|
|
|
|
768
|
|
|
|
|
|
|
{ #so long as the ss does not curve too much, keep measuring axis |
769
|
0
|
|
|
|
|
|
$j++; |
770
|
0
|
|
|
|
|
|
@use_ca = (); |
771
|
0
|
|
|
|
|
|
@use_n = (); |
772
|
0
|
|
|
|
|
|
@use_c = (); |
773
|
|
|
|
|
|
|
|
774
|
|
|
|
|
|
|
#extend ss from the appropriate side |
775
|
0
|
0
|
|
|
|
|
if ( $ss == 1 ) { |
776
|
0
|
|
|
|
|
|
$beg = max( $last - $j, $first ); |
777
|
0
|
|
|
|
|
|
$end = $last; |
778
|
|
|
|
|
|
|
} |
779
|
|
|
|
|
|
|
else { |
780
|
0
|
|
|
|
|
|
$beg = $first; |
781
|
0
|
|
|
|
|
|
$end = min( $first + $j, $last ); |
782
|
|
|
|
|
|
|
} |
783
|
0
|
|
|
|
|
|
for ( my $aa = $beg ; $aa < $end ; $aa++ ) { |
784
|
0
|
|
|
|
|
|
push( @use_ca, [ ( $$ca[$aa][0], $$ca[$aa][1], $$ca[$aa][2] ) ] ); |
785
|
0
|
|
|
|
|
|
push( @use_n, [ ( $$n[$aa][0], $$n[$aa][1], $$n[$aa][2] ) ] ); |
786
|
0
|
|
|
|
|
|
push( @use_c, [ ( $$c[$aa][0], $$c[$aa][1], $$c[$aa][2] ) ] ); |
787
|
|
|
|
|
|
|
} |
788
|
0
|
|
|
|
|
|
@oldaxis = @newaxis; |
789
|
0
|
|
|
|
|
|
@newaxis = calculate_axis( $type, \@use_ca, \@use_n, \@use_c ); |
790
|
0
|
|
|
|
|
|
$ang = Math::Trig::acos( dot( @newaxis, @oldaxis ) ); |
791
|
|
|
|
|
|
|
} |
792
|
0
|
|
|
|
|
|
return @oldaxis; |
793
|
|
|
|
|
|
|
} |
794
|
|
|
|
|
|
|
|
795
|
|
|
|
|
|
|
=head2 calc_I |
796
|
|
|
|
|
|
|
|
797
|
|
|
|
|
|
|
subroutine to calculate the matrix of moments from a set of backbone coordinates |
798
|
|
|
|
|
|
|
Input 1: Secondary structure type |
799
|
|
|
|
|
|
|
Input 2: Number of backbone atoms; |
800
|
|
|
|
|
|
|
Input 3: 3-D vector containing the coordinates of C-alpha, N, and C-atoms |
801
|
|
|
|
|
|
|
|
802
|
|
|
|
|
|
|
=cut |
803
|
|
|
|
|
|
|
sub calc_I { |
804
|
0
|
|
|
0
|
|
|
my ( $type, $count, @p ) = @_; |
805
|
0
|
|
|
|
|
|
my @I = ( [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ); |
806
|
0
|
|
|
|
|
|
my @pt; |
807
|
0
|
0
|
|
|
|
|
if ( $type eq 'H' ) { #helix, calculate based on each point |
808
|
0
|
|
|
|
|
|
for ( my $atom = 0 ; $atom < 3 ; $atom++ ) { |
809
|
0
|
|
|
|
|
|
for ( my $a = 0 ; $a < $count ; $a++ ) { |
810
|
0
|
|
|
|
|
|
@pt = ( $p[$atom][$a][0], $p[$atom][$a][1], $p[$atom][$a][2] ); |
811
|
0
|
|
|
|
|
|
$I[0][0] = $I[0][0] + ( $pt[1]**2 ) + ( $pt[2]**2 ); |
812
|
0
|
|
|
|
|
|
$I[1][1] = $I[1][1] + ( $pt[0]**2 ) + ( $pt[2]**2 ); |
813
|
0
|
|
|
|
|
|
$I[2][2] = $I[2][2] + ( $pt[0]**2 ) + ( $pt[1]**2 ); |
814
|
0
|
|
|
|
|
|
$I[0][1] = $I[0][1] - $pt[0] * $pt[1]; |
815
|
0
|
|
|
|
|
|
$I[0][2] = $I[0][2] - $pt[0] * $pt[2]; |
816
|
0
|
|
|
|
|
|
$I[1][2] = $I[1][2] - $pt[1] * $pt[2]; |
817
|
|
|
|
|
|
|
} |
818
|
|
|
|
|
|
|
} |
819
|
|
|
|
|
|
|
} |
820
|
|
|
|
|
|
|
else { #strand, calculate based on midpts of successive atoms |
821
|
0
|
|
|
|
|
|
for ( my $atom = 0 ; $atom < 3 ; $atom++ ) { |
822
|
0
|
|
|
|
|
|
for ( my $a = 0 ; $a < $count - 1 ; $a++ ) { |
823
|
0
|
|
|
|
|
|
@pt = ( |
824
|
|
|
|
|
|
|
0.5 * ( $p[$atom][$a][0] + $p[$atom][ $a + 1 ][0] ), |
825
|
|
|
|
|
|
|
0.5 * ( $p[$atom][$a][1] + $p[$atom][ $a + 1 ][1] ), |
826
|
|
|
|
|
|
|
0.5 * ( $p[$atom][$a][2] + $p[$atom][ $a + 1 ][2] ) |
827
|
|
|
|
|
|
|
); |
828
|
0
|
|
|
|
|
|
$I[0][0] = $I[0][0] + ( $pt[1]**2 ) + ( $pt[2]**2 ); |
829
|
0
|
|
|
|
|
|
$I[1][1] = $I[1][1] + ( $pt[0]**2 ) + ( $pt[2]**2 ); |
830
|
0
|
|
|
|
|
|
$I[2][2] = $I[2][2] + ( $pt[0]**2 ) + ( $pt[1]**2 ); |
831
|
0
|
|
|
|
|
|
$I[0][1] = $I[0][1] - $pt[0] * $pt[1]; |
832
|
0
|
|
|
|
|
|
$I[0][2] = $I[0][2] - $pt[0] * $pt[2]; |
833
|
0
|
|
|
|
|
|
$I[1][2] = $I[1][2] - $pt[1] * $pt[2]; |
834
|
|
|
|
|
|
|
} |
835
|
|
|
|
|
|
|
} |
836
|
|
|
|
|
|
|
} |
837
|
0
|
|
|
|
|
|
$I[1][0] = $I[0][1]; |
838
|
0
|
|
|
|
|
|
$I[2][0] = $I[0][2]; |
839
|
0
|
|
|
|
|
|
$I[2][1] = $I[1][2]; |
840
|
0
|
|
|
|
|
|
return @I; |
841
|
|
|
|
|
|
|
} |
842
|
|
|
|
|
|
|
|
843
|
|
|
|
|
|
|
=head2 calc_evec |
844
|
|
|
|
|
|
|
|
845
|
|
|
|
|
|
|
subroutine to calculate the eigenvector of a 3x3 matrix for a given eigenvalue |
846
|
|
|
|
|
|
|
Input 1: Eigenvalue |
847
|
|
|
|
|
|
|
Input 2: 3x3 matrix |
848
|
|
|
|
|
|
|
|
849
|
|
|
|
|
|
|
=cut |
850
|
|
|
|
|
|
|
sub calc_evec { |
851
|
0
|
|
|
0
|
|
|
my ( $eval, @M ) = @_; |
852
|
|
|
|
|
|
|
|
853
|
|
|
|
|
|
|
#subtract off diagonals |
854
|
0
|
|
|
|
|
|
my @I = @{ Storable::dclone( \@M ) }; |
|
0
|
|
|
|
|
|
|
855
|
0
|
|
|
|
|
|
$I[0][0] = $I[0][0] - $eval; |
856
|
0
|
|
|
|
|
|
$I[1][1] = $I[1][1] - $eval; |
857
|
0
|
|
|
|
|
|
$I[2][2] = $I[2][2] - $eval; |
858
|
0
|
|
|
|
|
|
my @evec = ( 0, 0, 0 ); |
859
|
|
|
|
|
|
|
|
860
|
|
|
|
|
|
|
#Find co-factors of first row |
861
|
0
|
|
|
|
|
|
$evec[0] = $I[1][1] * $I[2][2] - $I[1][2] * $I[2][1]; |
862
|
0
|
|
|
|
|
|
$evec[1] = $I[1][2] * $I[2][0] - $I[1][0] * $I[2][2]; |
863
|
0
|
|
|
|
|
|
$evec[2] = $I[1][0] * $I[2][1] - $I[1][1] * $I[2][0]; |
864
|
0
|
0
|
|
|
|
|
if ( $evec[0]**2 + $evec[1]**2 + $evec[2]**2 < 0.01 ) { |
865
|
|
|
|
|
|
|
|
866
|
|
|
|
|
|
|
#Find co-factors of second row |
867
|
0
|
|
|
|
|
|
$evec[0] = $I[0][2] * $I[2][1] - $I[0][1] * $I[2][2]; |
868
|
0
|
|
|
|
|
|
$evec[1] = $I[0][0] * $I[2][2] - $I[0][2] * $I[2][0]; |
869
|
0
|
|
|
|
|
|
$evec[2] = $I[0][1] * $I[2][0] - $I[0][0] * $I[2][1]; |
870
|
0
|
0
|
|
|
|
|
if ( $evec[0]**2 + $evec[1]**2 + $evec[2]**2 < 0.01 ) { |
871
|
0
|
|
|
|
|
|
$evec[0] = $I[0][1] * $I[1][2] - $I[0][2] * $I[1][1]; |
872
|
0
|
|
|
|
|
|
$evec[1] = $I[0][2] * $I[1][0] - $I[0][0] * $I[1][2]; |
873
|
0
|
|
|
|
|
|
$evec[2] = $I[0][0] * $I[1][1] - $I[0][1] * $I[1][0]; |
874
|
|
|
|
|
|
|
} |
875
|
|
|
|
|
|
|
} |
876
|
0
|
|
|
|
|
|
return unit(@evec); |
877
|
|
|
|
|
|
|
} |
878
|
|
|
|
|
|
|
|
879
|
|
|
|
|
|
|
=head2 |
880
|
|
|
|
|
|
|
|
881
|
|
|
|
|
|
|
subroutine to project a point onto an axis, given a point on the line |
882
|
|
|
|
|
|
|
Input 1: Cooridnates of the point |
883
|
|
|
|
|
|
|
Input 2: Vector representing the axis |
884
|
|
|
|
|
|
|
Input 3: A point on the line |
885
|
|
|
|
|
|
|
|
886
|
|
|
|
|
|
|
=cut |
887
|
|
|
|
|
|
|
sub projectpoint { |
888
|
0
|
|
|
0
|
|
|
my ( $p, $v, $c ) = @_; |
889
|
0
|
|
|
|
|
|
my @newp = ( 0, 0, 0 ); |
890
|
0
|
|
|
|
|
|
my @padj = ( $$p[0] - $$c[0], $$p[1] - $$c[1], $$p[2] - $$c[2] ); |
891
|
0
|
|
|
|
|
|
my $proj = dot( @padj, @$v ); |
892
|
0
|
|
|
|
|
|
$newp[0] = $proj * $$v[0] + $$c[0]; |
893
|
0
|
|
|
|
|
|
$newp[1] = $proj * $$v[1] + $$c[1]; |
894
|
0
|
|
|
|
|
|
$newp[2] = $proj * $$v[2] + $$c[2]; |
895
|
0
|
|
|
|
|
|
return @newp; |
896
|
|
|
|
|
|
|
} |
897
|
|
|
|
|
|
|
|
898
|
|
|
|
|
|
|
=head2 det |
899
|
|
|
|
|
|
|
|
900
|
|
|
|
|
|
|
subroutine to find the determinant of a 3x3 matrix |
901
|
|
|
|
|
|
|
|
902
|
|
|
|
|
|
|
=cut |
903
|
|
|
|
|
|
|
sub det { |
904
|
0
|
|
|
0
|
|
|
my (@m) = @_; |
905
|
0
|
|
|
|
|
|
my $d = |
906
|
|
|
|
|
|
|
$m[0][0] * ( $m[1][1] * $m[2][2] - $m[1][2] * $m[2][1] ) - |
907
|
|
|
|
|
|
|
$m[0][1] * ( $m[1][0] * $m[2][2] - $m[1][2] * $m[2][0] ) + |
908
|
|
|
|
|
|
|
$m[0][2] * ( $m[1][0] * $m[2][1] - $m[1][1] * $m[2][0] ); |
909
|
0
|
|
|
|
|
|
return $d; |
910
|
|
|
|
|
|
|
} |
911
|
|
|
|
|
|
|
|
912
|
|
|
|
|
|
|
=head2 find_eigs |
913
|
|
|
|
|
|
|
|
914
|
|
|
|
|
|
|
subroutine to find the eigenvalues (ordered) of a 3x3 matrix |
915
|
|
|
|
|
|
|
=cut |
916
|
|
|
|
|
|
|
sub find_eigs { |
917
|
|
|
|
|
|
|
|
918
|
|
|
|
|
|
|
#return eigenvalues |
919
|
0
|
|
|
0
|
|
|
my (@I) = @_; |
920
|
0
|
|
|
|
|
|
my $a = -1 * ( $I[0][0] + $I[1][1] + $I[2][2] ); |
921
|
0
|
|
|
|
|
|
my $b = |
922
|
|
|
|
|
|
|
$I[0][0] * $I[2][2] + |
923
|
|
|
|
|
|
|
$I[1][1] * $I[2][2] + |
924
|
|
|
|
|
|
|
$I[0][0] * $I[1][1] - |
925
|
|
|
|
|
|
|
$I[0][2] * $I[2][0] - |
926
|
|
|
|
|
|
|
$I[1][2] * $I[2][1] - |
927
|
|
|
|
|
|
|
$I[0][1] * $I[1][0]; |
928
|
0
|
|
|
|
|
|
my $c = -1 * det(@I); |
929
|
0
|
|
|
|
|
|
my @eigs = find_roots( $a, $b, $c ); |
930
|
0
|
|
|
|
|
|
my @temp; |
931
|
0
|
0
|
0
|
|
|
|
if ( ( $eigs[0] > $eigs[1] ) and ( $eigs[0] > $eigs[2] ) ) { |
|
|
0
|
|
|
|
|
|
932
|
0
|
|
|
|
|
|
$temp[0] = $eigs[0]; |
933
|
0
|
0
|
|
|
|
|
if ( $eigs[1] > $eigs[2] ) { |
934
|
0
|
|
|
|
|
|
$temp[1] = $eigs[1]; |
935
|
0
|
|
|
|
|
|
$temp[2] = $eigs[2]; |
936
|
|
|
|
|
|
|
} |
937
|
|
|
|
|
|
|
else { |
938
|
0
|
|
|
|
|
|
$temp[1] = $eigs[2]; |
939
|
0
|
|
|
|
|
|
$temp[2] = $eigs[1]; |
940
|
|
|
|
|
|
|
} |
941
|
|
|
|
|
|
|
} |
942
|
|
|
|
|
|
|
elsif ( $eigs[1] > $eigs[2] ) { |
943
|
0
|
|
|
|
|
|
$temp[0] = $eigs[1]; |
944
|
0
|
0
|
|
|
|
|
if ( $eigs[0] > $eigs[2] ) { |
945
|
0
|
|
|
|
|
|
$temp[1] = $eigs[0]; |
946
|
0
|
|
|
|
|
|
$temp[2] = $eigs[2]; |
947
|
|
|
|
|
|
|
} |
948
|
|
|
|
|
|
|
else { |
949
|
0
|
|
|
|
|
|
$temp[1] = $eigs[2]; |
950
|
0
|
|
|
|
|
|
$temp[2] = $eigs[0]; |
951
|
|
|
|
|
|
|
} |
952
|
|
|
|
|
|
|
} |
953
|
|
|
|
|
|
|
else { |
954
|
0
|
|
|
|
|
|
$temp[0] = $eigs[2]; |
955
|
0
|
0
|
|
|
|
|
if ( $eigs[0] > $eigs[1] ) { |
956
|
0
|
|
|
|
|
|
$temp[1] = $eigs[0]; |
957
|
0
|
|
|
|
|
|
$temp[2] = $eigs[1]; |
958
|
|
|
|
|
|
|
} |
959
|
|
|
|
|
|
|
else { |
960
|
0
|
|
|
|
|
|
$temp[1] = $eigs[1]; |
961
|
0
|
|
|
|
|
|
$temp[2] = $eigs[0]; |
962
|
|
|
|
|
|
|
} |
963
|
|
|
|
|
|
|
} |
964
|
0
|
|
|
|
|
|
return @temp; |
965
|
|
|
|
|
|
|
} |
966
|
|
|
|
|
|
|
|
967
|
|
|
|
|
|
|
=head2 matmul |
968
|
|
|
|
|
|
|
|
969
|
|
|
|
|
|
|
subroutine to multiply two matrices |
970
|
|
|
|
|
|
|
Input 1: Matrix 1 |
971
|
|
|
|
|
|
|
Input 2: Matrix 2 |
972
|
|
|
|
|
|
|
Input 3: Number of rows in matrix 1 |
973
|
|
|
|
|
|
|
Input 4: Number of columns in matrix 1, also the number of rows in matrix 2 |
974
|
|
|
|
|
|
|
Input 5: Numer of columns in matrix 2 |
975
|
|
|
|
|
|
|
|
976
|
|
|
|
|
|
|
=cut |
977
|
|
|
|
|
|
|
sub matmul { |
978
|
0
|
|
|
0
|
|
|
my ( $m, $n, $dim1, $dim2, $dim3 ) = @_; |
979
|
0
|
|
|
|
|
|
my @o; |
980
|
|
|
|
|
|
|
my @row; |
981
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim3 ; $aa++ ) { |
982
|
0
|
|
|
|
|
|
push( @row, 0 ); |
983
|
|
|
|
|
|
|
} |
984
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim1 ; $aa++ ) { |
985
|
0
|
|
|
|
|
|
push( @o, [@row] ); |
986
|
|
|
|
|
|
|
} |
987
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim1 ; $aa++ ) { |
988
|
0
|
|
|
|
|
|
for ( my $bb = 0 ; $bb < $dim3 ; $bb++ ) { |
989
|
0
|
|
|
|
|
|
for ( my $cc = 0 ; $cc < $dim2 ; $cc++ ) { |
990
|
0
|
|
|
|
|
|
$o[$aa][$bb] += $$m[$aa][$cc] * $$n[$cc][$bb]; |
991
|
|
|
|
|
|
|
} |
992
|
|
|
|
|
|
|
} |
993
|
|
|
|
|
|
|
} |
994
|
0
|
|
|
|
|
|
return @o; |
995
|
|
|
|
|
|
|
} |
996
|
|
|
|
|
|
|
|
997
|
|
|
|
|
|
|
=head2 matvec |
998
|
|
|
|
|
|
|
|
999
|
|
|
|
|
|
|
subroutine to multiply a vector by a matrix |
1000
|
|
|
|
|
|
|
|
1001
|
|
|
|
|
|
|
Input 1: Matrix |
1002
|
|
|
|
|
|
|
Input 2: Vector |
1003
|
|
|
|
|
|
|
Input 3: Number of rows in the matrix |
1004
|
|
|
|
|
|
|
Input 4: Number of columns in the matrix, also the number of elements in the vector |
1005
|
|
|
|
|
|
|
|
1006
|
|
|
|
|
|
|
=cut |
1007
|
|
|
|
|
|
|
sub matvec { |
1008
|
0
|
|
|
0
|
|
|
my ( $m, $n, $dim1, $dim2 ) = @_; |
1009
|
0
|
|
|
|
|
|
my @o; |
1010
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim1 ; $aa++ ) { |
1011
|
0
|
|
|
|
|
|
push( @o, 0 ); |
1012
|
|
|
|
|
|
|
} |
1013
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim1 ; $aa++ ) { |
1014
|
0
|
|
|
|
|
|
for ( my $cc = 0 ; $cc < $dim2 ; $cc++ ) { |
1015
|
0
|
|
|
|
|
|
$o[$aa] += $$m[$aa][$cc] * $$n[$cc]; |
1016
|
|
|
|
|
|
|
} |
1017
|
|
|
|
|
|
|
} |
1018
|
0
|
|
|
|
|
|
return @o; |
1019
|
|
|
|
|
|
|
} |
1020
|
|
|
|
|
|
|
|
1021
|
|
|
|
|
|
|
=head2 vecvec |
1022
|
|
|
|
|
|
|
|
1023
|
|
|
|
|
|
|
subroutine to find the outer product of two vectors of the same length |
1024
|
|
|
|
|
|
|
Input 1: Vector 1 |
1025
|
|
|
|
|
|
|
Input 2: Vector 2 |
1026
|
|
|
|
|
|
|
Input 3: Dimension of vector 1, also dimension of vector 2 |
1027
|
|
|
|
|
|
|
|
1028
|
|
|
|
|
|
|
=cut |
1029
|
|
|
|
|
|
|
sub vecvec { |
1030
|
0
|
|
|
0
|
|
|
my ( $m, $n, $dim1 ) = @_; |
1031
|
0
|
|
|
|
|
|
my @o; |
1032
|
|
|
|
|
|
|
my @row; |
1033
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim1 ; $aa++ ) { |
1034
|
0
|
|
|
|
|
|
push( @row, 0 ); |
1035
|
|
|
|
|
|
|
} |
1036
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim1 ; $aa++ ) { |
1037
|
0
|
|
|
|
|
|
push( @o, [@row] ); |
1038
|
|
|
|
|
|
|
} |
1039
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim1 ; $aa++ ) { |
1040
|
0
|
|
|
|
|
|
for ( my $bb = 0 ; $bb < $dim1 ; $bb++ ) { |
1041
|
0
|
|
|
|
|
|
$o[$aa][$bb] = $$m[$aa] * $$n[$bb]; |
1042
|
|
|
|
|
|
|
} |
1043
|
|
|
|
|
|
|
} |
1044
|
0
|
|
|
|
|
|
return @o; |
1045
|
|
|
|
|
|
|
} |
1046
|
|
|
|
|
|
|
|
1047
|
|
|
|
|
|
|
=head2 find_roots |
1048
|
|
|
|
|
|
|
|
1049
|
|
|
|
|
|
|
subroutine to find the roots of a cubic equation of the form x^3+ax^2+bx+cx=0 |
1050
|
|
|
|
|
|
|
|
1051
|
|
|
|
|
|
|
=cut |
1052
|
|
|
|
|
|
|
sub find_roots { |
1053
|
0
|
|
|
0
|
|
|
my ( $a, $b, $c ) = @_; |
1054
|
0
|
|
|
|
|
|
my $p = $b - ( $a**2 ) / 3; |
1055
|
0
|
|
|
|
|
|
my $q = $c + ( 2 * $a**3 - 9 * $a * $b ) / 27; |
1056
|
0
|
|
|
|
|
|
my $urad = ( ( $q**2 ) / 4 + ( $p**3 ) / 27 ); |
1057
|
0
|
|
|
|
|
|
my $mag = sqrt( 0.25 * ( $q**2 ) - $urad ); |
1058
|
0
|
|
|
|
|
|
my $newmag = $mag**( 1 / 3 ); |
1059
|
0
|
|
|
|
|
|
my $ang = Math::Trig::acos( -0.5 * $q / $mag ); |
1060
|
0
|
|
|
|
|
|
my $m = abs( cos( $ang / 3 ) ); |
1061
|
0
|
|
|
|
|
|
my $n = abs( sin( $ang / 3 ) * ( 3**(0.5) ) ); |
1062
|
0
|
|
|
|
|
|
my $x1 = 2 * $newmag * $m - ( $a / 3 ); |
1063
|
0
|
|
|
|
|
|
my $x2 = -1 * $newmag * ( $m + $n ) - ( $a / 3 ); |
1064
|
0
|
|
|
|
|
|
my $x3 = -1 * $newmag * ( $m - $n ) - ( $a / 3 ); |
1065
|
0
|
|
|
|
|
|
return ( $x1, $x2, $x3 ); |
1066
|
|
|
|
|
|
|
} |
1067
|
|
|
|
|
|
|
|
1068
|
|
|
|
|
|
|
=head2 rotateaxis |
1069
|
|
|
|
|
|
|
|
1070
|
|
|
|
|
|
|
subroutine to rotate a point (pt) around an axis (vec) by a given angle (ang) |
1071
|
|
|
|
|
|
|
=cut |
1072
|
|
|
|
|
|
|
sub rotateaxis { |
1073
|
0
|
|
|
0
|
|
|
my ( $pt, $vec, $ang ) = @_; |
1074
|
0
|
|
|
|
|
|
my @res = ( $$pt[0], $$pt[1], $$pt[2] ); |
1075
|
0
|
|
|
|
|
|
my $cos = cos( $$ang * 3.1415926 / 180 ); |
1076
|
0
|
|
|
|
|
|
my $sin = sin( $$ang * 3.1415926 / 180 ); |
1077
|
0
|
|
|
|
|
|
my $uv = $$vec[0]**2 + $$vec[1]**2; |
1078
|
0
|
|
|
|
|
|
my $vw = $$vec[1]**2 + $$vec[2]**2; |
1079
|
0
|
|
|
|
|
|
my $uw = $$vec[0]**2 + $$vec[2]**2; |
1080
|
0
|
|
|
|
|
|
$res[0] = |
1081
|
|
|
|
|
|
|
( $$vec[0] * dot( @$pt, @$vec ) ) - |
1082
|
|
|
|
|
|
|
( $$vec[0] * ( $$vec[1] * $$pt[1] + $$vec[2] * $$pt[2] ) - $$pt[0] * $vw ) |
1083
|
|
|
|
|
|
|
* $cos + |
1084
|
|
|
|
|
|
|
( $$vec[1] * $$pt[2] - $$vec[2] * $$pt[1] ) * $sin; |
1085
|
0
|
|
|
|
|
|
$res[1] = |
1086
|
|
|
|
|
|
|
( $$vec[1] * dot( @$pt, @$vec ) ) - |
1087
|
|
|
|
|
|
|
( $$vec[1] * ( $$vec[0] * $$pt[0] + $$vec[2] * $$pt[2] ) - $$pt[1] * $uw ) |
1088
|
|
|
|
|
|
|
* $cos + |
1089
|
|
|
|
|
|
|
( $$vec[2] * $$pt[0] - $$vec[0] * $$pt[2] ) * $sin; |
1090
|
0
|
|
|
|
|
|
$res[2] = |
1091
|
|
|
|
|
|
|
( $$vec[2] * dot( @$pt, @$vec ) ) - |
1092
|
|
|
|
|
|
|
( $$vec[2] * ( $$vec[0] * $$pt[0] + $$vec[1] * $$pt[1] ) - $$pt[2] * $uv ) |
1093
|
|
|
|
|
|
|
* $cos + |
1094
|
|
|
|
|
|
|
( $$vec[0] * $$pt[1] - $$vec[1] * $$pt[0] ) * $sin; |
1095
|
0
|
|
|
|
|
|
return @res; |
1096
|
|
|
|
|
|
|
} |
1097
|
|
|
|
|
|
|
|
1098
|
|
|
|
|
|
|
=head2 rotate |
1099
|
|
|
|
|
|
|
|
1100
|
|
|
|
|
|
|
subroutine to rotate a point (pt) such that one axis (u) aligns with another (v) |
1101
|
|
|
|
|
|
|
|
1102
|
|
|
|
|
|
|
=cut |
1103
|
|
|
|
|
|
|
sub rotate { |
1104
|
0
|
|
|
0
|
|
|
my ( $pt, $u, $v ) = @_; |
1105
|
|
|
|
|
|
|
|
1106
|
|
|
|
|
|
|
#rotate a point (pt) such that vector u aligns with vector v |
1107
|
0
|
|
|
|
|
|
my @res = ( $$pt[0], $$pt[1], $$pt[2] ); |
1108
|
0
|
|
|
|
|
|
my $cos = dot( @$u, @$v ) / ( norm(@$u) * norm(@$v) ); |
1109
|
0
|
0
|
|
|
|
|
if ( $cos ne 1 ) { #if vectors are already aligned |
1110
|
0
|
|
|
|
|
|
my @n = unit( cross( @$u, @$v ) ); |
1111
|
0
|
|
|
|
|
|
my $ocos = 1 - $cos; |
1112
|
0
|
|
|
|
|
|
my $sin = sin( Math::Trig::acos($cos) ); |
1113
|
0
|
|
|
|
|
|
$res[0] = |
1114
|
|
|
|
|
|
|
( ( $ocos * $n[0] * $n[0] ) + $cos ) * $$pt[0] + |
1115
|
|
|
|
|
|
|
( ( $ocos * $n[0] * $n[1] ) - $n[2] * $sin ) * $$pt[1] + |
1116
|
|
|
|
|
|
|
( ( $ocos * $n[0] * $n[2] ) + $n[1] * $sin ) * $$pt[2]; |
1117
|
0
|
|
|
|
|
|
$res[1] = |
1118
|
|
|
|
|
|
|
( ( $ocos * $n[0] * $n[1] ) + $n[2] * $sin ) * $$pt[0] + |
1119
|
|
|
|
|
|
|
( ( $ocos * $n[1] * $n[1] ) + $cos ) * $$pt[1] + |
1120
|
|
|
|
|
|
|
( ( $ocos * $n[1] * $n[2] ) - $n[0] * $sin ) * $$pt[2]; |
1121
|
0
|
|
|
|
|
|
$res[2] = |
1122
|
|
|
|
|
|
|
( ( $ocos * $n[0] * $n[2] ) - $n[1] * $sin ) * $$pt[0] + |
1123
|
|
|
|
|
|
|
( ( $ocos * $n[1] * $n[2] ) + $n[0] * $sin ) * $$pt[1] + |
1124
|
|
|
|
|
|
|
( ( $ocos * $n[2] * $n[2] ) + $cos ) * $$pt[2]; |
1125
|
|
|
|
|
|
|
} |
1126
|
0
|
|
|
|
|
|
return @res; |
1127
|
|
|
|
|
|
|
} |
1128
|
|
|
|
|
|
|
|
1129
|
|
|
|
|
|
|
=head2 cross |
1130
|
|
|
|
|
|
|
|
1131
|
|
|
|
|
|
|
subroutine to find the cross product of two 3-d vectors |
1132
|
|
|
|
|
|
|
Input 1: Concatenated vector whose first three elements represent vector 1 and whose last three represent vector 2 |
1133
|
|
|
|
|
|
|
|
1134
|
|
|
|
|
|
|
=cut |
1135
|
|
|
|
|
|
|
sub cross { |
1136
|
0
|
|
|
0
|
|
|
my (@v) = @_; |
1137
|
0
|
|
|
|
|
|
my @res = ( 0, 0, 0 ); |
1138
|
0
|
|
|
|
|
|
$res[0] = $v[1] * $v[5] - $v[2] * $v[4]; |
1139
|
0
|
|
|
|
|
|
$res[1] = $v[2] * $v[3] - $v[0] * $v[5]; |
1140
|
0
|
|
|
|
|
|
$res[2] = $v[0] * $v[4] - $v[1] * $v[3]; |
1141
|
0
|
|
|
|
|
|
return @res; |
1142
|
|
|
|
|
|
|
} |
1143
|
|
|
|
|
|
|
|
1144
|
|
|
|
|
|
|
=head2 dot2 |
1145
|
|
|
|
|
|
|
|
1146
|
|
|
|
|
|
|
subroutine to find the dot product of two vectors |
1147
|
|
|
|
|
|
|
Input 1: Concatenated vector whose first half represents vector 1 and whose second half represents vector 2 |
1148
|
|
|
|
|
|
|
|
1149
|
|
|
|
|
|
|
=cut |
1150
|
|
|
|
|
|
|
sub dot { |
1151
|
0
|
|
|
0
|
|
|
my (@v) = @_; |
1152
|
0
|
|
|
|
|
|
my $max = scalar(@v) / 2; |
1153
|
0
|
|
|
|
|
|
my $res = 0; |
1154
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $max ; $aa++ ) { |
1155
|
0
|
|
|
|
|
|
$res += $v[$aa] * $v[ $aa + $max ]; |
1156
|
|
|
|
|
|
|
} |
1157
|
0
|
|
|
|
|
|
return $res; |
1158
|
|
|
|
|
|
|
} |
1159
|
|
|
|
|
|
|
|
1160
|
|
|
|
|
|
|
=head2 unit |
1161
|
|
|
|
|
|
|
|
1162
|
|
|
|
|
|
|
subroutine to return the unit vector corresponding to a given vector |
1163
|
|
|
|
|
|
|
=cut |
1164
|
|
|
|
|
|
|
sub unit { |
1165
|
0
|
|
|
0
|
|
|
my (@v) = @_; |
1166
|
0
|
|
|
|
|
|
my $norm = norm(@v); |
1167
|
0
|
|
|
|
|
|
my $max = scalar(@v); |
1168
|
0
|
|
|
|
|
|
for ( my $a = 0 ; $a < $max ; $a++ ) { |
1169
|
0
|
|
|
|
|
|
$v[$a] = $v[$a] / $norm; |
1170
|
|
|
|
|
|
|
} |
1171
|
0
|
|
|
|
|
|
return @v; |
1172
|
|
|
|
|
|
|
} |
1173
|
|
|
|
|
|
|
|
1174
|
|
|
|
|
|
|
=head2 norm |
1175
|
|
|
|
|
|
|
|
1176
|
|
|
|
|
|
|
subroutine to return the 2-norm of a given vector |
1177
|
|
|
|
|
|
|
|
1178
|
|
|
|
|
|
|
=cut |
1179
|
|
|
|
|
|
|
sub norm { |
1180
|
0
|
|
|
0
|
|
|
my (@v) = @_; |
1181
|
0
|
|
|
|
|
|
my $res = 0; |
1182
|
0
|
|
|
|
|
|
foreach (@v) { |
1183
|
0
|
|
|
|
|
|
$res += $_**2; |
1184
|
|
|
|
|
|
|
} |
1185
|
0
|
|
|
|
|
|
return sqrt($res); |
1186
|
|
|
|
|
|
|
} |
1187
|
|
|
|
|
|
|
|
1188
|
|
|
|
|
|
|
=head2 vecadd |
1189
|
|
|
|
|
|
|
|
1190
|
|
|
|
|
|
|
subroutine to add two vectors |
1191
|
|
|
|
|
|
|
Input 1: Scalar factor to multiply the second vector |
1192
|
|
|
|
|
|
|
Input 2: Concatenated vector whose first half represents the first vector |
1193
|
|
|
|
|
|
|
and whose second half represents the second vector |
1194
|
|
|
|
|
|
|
|
1195
|
|
|
|
|
|
|
=cut |
1196
|
|
|
|
|
|
|
sub vecadd { |
1197
|
0
|
|
|
0
|
|
|
my ( $scale, @v1 ) = @_; |
1198
|
|
|
|
|
|
|
|
1199
|
|
|
|
|
|
|
#v1+scale*v2 |
1200
|
0
|
|
|
|
|
|
my $dim = scalar(@v1) / 2; |
1201
|
0
|
|
|
|
|
|
my @res; |
1202
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $dim ; $aa++ ) { |
1203
|
0
|
|
|
|
|
|
push( @res, $v1[$aa] + $scale * $v1[ $dim + $aa ] ); |
1204
|
|
|
|
|
|
|
} |
1205
|
0
|
|
|
|
|
|
return @res; |
1206
|
|
|
|
|
|
|
} |
1207
|
|
|
|
|
|
|
|
1208
|
|
|
|
|
|
|
=head2 max |
1209
|
|
|
|
|
|
|
|
1210
|
|
|
|
|
|
|
subroutine to find the maximum of an array |
1211
|
|
|
|
|
|
|
|
1212
|
|
|
|
|
|
|
=cut |
1213
|
|
|
|
|
|
|
sub max { |
1214
|
0
|
|
|
0
|
|
|
my (@a) = @_; |
1215
|
0
|
|
|
|
|
|
my $m = $a[0]; |
1216
|
0
|
|
|
|
|
|
foreach (@a) { |
1217
|
0
|
0
|
|
|
|
|
if ( $_ > $m ) { $m = $_ } |
|
0
|
|
|
|
|
|
|
1218
|
|
|
|
|
|
|
} |
1219
|
0
|
|
|
|
|
|
return $m; |
1220
|
|
|
|
|
|
|
} |
1221
|
|
|
|
|
|
|
|
1222
|
|
|
|
|
|
|
=head2 min |
1223
|
|
|
|
|
|
|
|
1224
|
|
|
|
|
|
|
subroutine to find the minimum of an array |
1225
|
|
|
|
|
|
|
|
1226
|
|
|
|
|
|
|
=cut |
1227
|
|
|
|
|
|
|
sub min { |
1228
|
0
|
|
|
0
|
|
|
my (@a) = @_; |
1229
|
0
|
|
|
|
|
|
my $m = $a[0]; |
1230
|
0
|
|
|
|
|
|
foreach (@a) { |
1231
|
0
|
0
|
|
|
|
|
if ( $_ < $m ) { $m = $_ } |
|
0
|
|
|
|
|
|
|
1232
|
|
|
|
|
|
|
} |
1233
|
0
|
|
|
|
|
|
return $m; |
1234
|
|
|
|
|
|
|
} |
1235
|
|
|
|
|
|
|
|
1236
|
|
|
|
|
|
|
=head2 dbin |
1237
|
|
|
|
|
|
|
|
1238
|
|
|
|
|
|
|
subroutine to Fbin a value from 0-40 using a given binsize |
1239
|
|
|
|
|
|
|
|
1240
|
|
|
|
|
|
|
=cut |
1241
|
|
|
|
|
|
|
sub dbin { |
1242
|
0
|
|
|
0
|
|
|
my ( $val, $binsize ) = @_; |
1243
|
0
|
|
|
|
|
|
my $binval = 41; |
1244
|
0
|
0
|
|
|
|
|
if ( $val <= 40 ) { |
1245
|
0
|
|
|
|
|
|
$binval = $binsize * ( int( $val / $binsize ) + 1 ); |
1246
|
|
|
|
|
|
|
} |
1247
|
0
|
|
|
|
|
|
return $binval; |
1248
|
|
|
|
|
|
|
} |
1249
|
|
|
|
|
|
|
|
1250
|
|
|
|
|
|
|
=head2 angbin |
1251
|
|
|
|
|
|
|
|
1252
|
|
|
|
|
|
|
subroutine to bin a value using a given bin size |
1253
|
|
|
|
|
|
|
|
1254
|
|
|
|
|
|
|
=cut |
1255
|
|
|
|
|
|
|
sub angbin { |
1256
|
0
|
|
|
0
|
|
|
my ( $val, $binsize ) = @_; |
1257
|
0
|
|
|
|
|
|
my $binval = $binsize * ( int( $val / $binsize ) + 1 ); |
1258
|
0
|
|
|
|
|
|
return $binval; |
1259
|
|
|
|
|
|
|
} |
1260
|
|
|
|
|
|
|
|
1261
|
|
|
|
|
|
|
=head2 pearson |
1262
|
|
|
|
|
|
|
|
1263
|
|
|
|
|
|
|
subroutine to find the Pearson correlation coefficient between two data sets |
1264
|
|
|
|
|
|
|
|
1265
|
|
|
|
|
|
|
=cut |
1266
|
|
|
|
|
|
|
sub pearson { |
1267
|
0
|
|
|
0
|
|
|
my ( $x, $y ) = @_; |
1268
|
0
|
|
|
|
|
|
my $xm = 0; |
1269
|
0
|
|
|
|
|
|
my $ym = 0; |
1270
|
0
|
|
|
|
|
|
my $xsd = 0; |
1271
|
0
|
|
|
|
|
|
my $ysd = 0; |
1272
|
0
|
|
|
|
|
|
my $count = scalar(@$x); |
1273
|
0
|
|
|
|
|
|
foreach (@$x) { |
1274
|
0
|
|
|
|
|
|
$xm += $_; |
1275
|
0
|
|
|
|
|
|
$xsd += $_ * $_; |
1276
|
|
|
|
|
|
|
} |
1277
|
0
|
|
|
|
|
|
foreach (@$y) { |
1278
|
0
|
|
|
|
|
|
$ym += $_; |
1279
|
0
|
|
|
|
|
|
$ysd += $_ * $_; |
1280
|
|
|
|
|
|
|
} |
1281
|
0
|
|
|
|
|
|
$xm /= $count; |
1282
|
0
|
|
|
|
|
|
$ym /= $count; |
1283
|
0
|
|
|
|
|
|
$xsd = sqrt( ( $xsd / $count ) - ( $xm * $xm ) ); |
1284
|
0
|
|
|
|
|
|
$ysd = sqrt( ( $ysd / $count ) - ( $ym * $ym ) ); |
1285
|
0
|
|
|
|
|
|
my $r = 0; |
1286
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $count ; $aa++ ) { |
1287
|
0
|
|
|
|
|
|
$r += ( ( $$x[$aa] - $xm ) * ( $$y[$aa] - $ym ) / ( $xsd * $ysd ) ); |
1288
|
|
|
|
|
|
|
} |
1289
|
0
|
|
|
|
|
|
$r /= $count; |
1290
|
0
|
|
|
|
|
|
return $r; |
1291
|
|
|
|
|
|
|
} |
1292
|
|
|
|
|
|
|
|
1293
|
|
|
|
|
|
|
=head2 find_rmsd |
1294
|
|
|
|
|
|
|
|
1295
|
|
|
|
|
|
|
subroutine to find the RMSD between two sets of points, |
1296
|
|
|
|
|
|
|
using the method described by Theobald |
1297
|
|
|
|
|
|
|
|
1298
|
|
|
|
|
|
|
Input 1: Number of points to consider |
1299
|
|
|
|
|
|
|
Input 2: Vector with the first set of coordinates |
1300
|
|
|
|
|
|
|
Input 3: Vector with the second set of coordinates |
1301
|
|
|
|
|
|
|
|
1302
|
|
|
|
|
|
|
=cut |
1303
|
|
|
|
|
|
|
sub find_rmsd { |
1304
|
0
|
|
|
0
|
|
|
my ( $c, $x, $y ) = @_; |
1305
|
0
|
|
|
|
|
|
my @R = ( [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ); |
1306
|
0
|
|
|
|
|
|
my @xcom = COM2( 0, $c, \@$x ); |
1307
|
0
|
|
|
|
|
|
my @ycom = COM2( 0, $c, \@$y ); |
1308
|
0
|
|
|
|
|
|
my $e0 = 0; |
1309
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $c ; $aa++ ) { |
1310
|
0
|
|
|
|
|
|
for ( my $bb = 0 ; $bb < 3 ; $bb++ ) { |
1311
|
0
|
|
|
|
|
|
for ( my $cc = 0 ; $cc < 3 ; $cc++ ) { |
1312
|
0
|
|
|
|
|
|
$R[$bb][$cc] += |
1313
|
|
|
|
|
|
|
( $$x[$aa][$bb] - $xcom[$bb] ) * |
1314
|
|
|
|
|
|
|
( $$y[$aa][$cc] - $ycom[$cc] ); |
1315
|
|
|
|
|
|
|
} |
1316
|
0
|
|
|
|
|
|
$e0 += |
1317
|
|
|
|
|
|
|
( ( $$x[$aa][$bb] - $xcom[$bb] )**2 + |
1318
|
|
|
|
|
|
|
( $$y[$aa][$bb] - $ycom[$bb] )**2 ); |
1319
|
|
|
|
|
|
|
} |
1320
|
|
|
|
|
|
|
} |
1321
|
|
|
|
|
|
|
|
1322
|
|
|
|
|
|
|
#calculate cross-coefficients |
1323
|
0
|
|
|
|
|
|
my $xx = $R[0][0]**2; |
1324
|
0
|
|
|
|
|
|
my $xy = $R[0][1]**2; |
1325
|
0
|
|
|
|
|
|
my $xz = $R[0][2]**2; |
1326
|
0
|
|
|
|
|
|
my $yx = $R[1][0]**2; |
1327
|
0
|
|
|
|
|
|
my $yy = $R[1][1]**2; |
1328
|
0
|
|
|
|
|
|
my $yz = $R[1][2]**2; |
1329
|
0
|
|
|
|
|
|
my $zx = $R[2][0]**2; |
1330
|
0
|
|
|
|
|
|
my $zy = $R[2][1]**2; |
1331
|
0
|
|
|
|
|
|
my $zz = $R[2][2]**2; |
1332
|
0
|
|
|
|
|
|
my $D = ( $xy + $xz - $yx - $zx )**2; |
1333
|
0
|
|
|
|
|
|
my $temp = -$xx + $yy + $zz + $yz + $zy; |
1334
|
0
|
|
|
|
|
|
my $temp2 = 2 * ( $R[1][1] * $R[2][2] - $R[1][2] * $R[2][1] ); |
1335
|
0
|
|
|
|
|
|
my $E = ( $temp - $temp2 ) * ( $temp + $temp2 ); |
1336
|
0
|
|
|
|
|
|
my $xzpzx = $R[0][2] + $R[2][0]; |
1337
|
0
|
|
|
|
|
|
my $xzmzx = $R[0][2] - $R[2][0]; |
1338
|
0
|
|
|
|
|
|
my $yzpzy = $R[1][2] + $R[2][1]; |
1339
|
0
|
|
|
|
|
|
my $yzmzy = $R[1][2] - $R[2][1]; |
1340
|
0
|
|
|
|
|
|
my $xypyx = $R[0][1] + $R[1][0]; |
1341
|
0
|
|
|
|
|
|
my $xymyx = $R[0][1] - $R[1][0]; |
1342
|
0
|
|
|
|
|
|
my $xmymz = $R[0][0] - $R[1][1] - $R[2][2]; |
1343
|
0
|
|
|
|
|
|
my $xmypz = $R[0][0] - $R[1][1] + $R[2][2]; |
1344
|
0
|
|
|
|
|
|
my $xpymz = $R[0][0] + $R[1][1] - $R[2][2]; |
1345
|
0
|
|
|
|
|
|
my $xpypz = $R[0][0] + $R[1][1] + $R[2][2]; |
1346
|
0
|
|
|
|
|
|
my $F = |
1347
|
|
|
|
|
|
|
( -( $xzpzx * $yzmzy ) + ( $xymyx * $xmymz ) ) * |
1348
|
|
|
|
|
|
|
( -( $xzmzx * $yzpzy ) + ( $xymyx * $xmypz ) ); |
1349
|
0
|
|
|
|
|
|
my $G = |
1350
|
|
|
|
|
|
|
( -( $xzpzx * $yzpzy ) - ( $xypyx * $xpymz ) ) * |
1351
|
|
|
|
|
|
|
( -( $xzmzx * $yzmzy ) - ( $xypyx * $xpypz ) ); |
1352
|
0
|
|
|
|
|
|
my $H = |
1353
|
|
|
|
|
|
|
( ( $xypyx * $yzpzy ) + ( $xzpzx * $xmypz ) ) * |
1354
|
|
|
|
|
|
|
( -( $xymyx * $yzmzy ) + ( $xzpzx * $xpypz ) ); |
1355
|
0
|
|
|
|
|
|
my $I = |
1356
|
|
|
|
|
|
|
( ( $xypyx * $yzmzy ) + ( $xzmzx * $xmymz ) ) * |
1357
|
|
|
|
|
|
|
( -( $xymyx * $yzpzy ) + ( $xzmzx * $xpymz ) ); |
1358
|
0
|
|
|
|
|
|
my $c0 = $D + $E + $F + $G + $H + $I; |
1359
|
0
|
|
|
|
|
|
my $c1 = |
1360
|
|
|
|
|
|
|
8 * |
1361
|
|
|
|
|
|
|
( ( $R[0][0] * ( $R[1][2] * $R[2][1] - $R[1][1] * $R[2][2] ) ) + |
1362
|
|
|
|
|
|
|
( $R[0][1] * ( $R[1][0] * $R[2][2] - $R[1][2] * $R[2][0] ) ) + |
1363
|
|
|
|
|
|
|
( $R[0][2] * ( $R[1][1] * $R[2][0] - $R[1][0] * $R[2][1] ) ) ); |
1364
|
0
|
|
|
|
|
|
my $c2 = -2 * ( $xx + $xy + $xz + $yx + $yy + $yz + $zx + $zy + $zz ); |
1365
|
0
|
|
|
|
|
|
my $lam = 0.5 * $e0; |
1366
|
0
|
|
|
|
|
|
my $prec = 0.00001; |
1367
|
0
|
|
|
|
|
|
my $lamold = $lam + 1; |
1368
|
|
|
|
|
|
|
|
1369
|
|
|
|
|
|
|
#Use Newton's method to find the largest eigenvalue |
1370
|
0
|
|
|
|
|
|
while ( abs( $lam - $lamold ) > $prec ) { |
1371
|
0
|
|
|
|
|
|
$lamold = $lam; |
1372
|
0
|
|
|
|
|
|
my $t = 4 * ( $lam**3 ) + 2 * $c2 * $lam + $c1; |
1373
|
0
|
0
|
|
|
|
|
if ( $t ne 0 ) { |
1374
|
0
|
|
|
|
|
|
$lam -= |
1375
|
|
|
|
|
|
|
( $lam**4 + $c2 * ( $lam**2 ) + $c1 * $lam + $c0 ) / |
1376
|
|
|
|
|
|
|
( 4 * ( $lam**3 ) + 2 * $c2 * $lam + $c1 ); |
1377
|
|
|
|
|
|
|
} |
1378
|
|
|
|
|
|
|
} |
1379
|
0
|
|
|
|
|
|
my $rms = sqrt( abs( ( $e0 - 2 * $lam ) / $c ) ); |
1380
|
0
|
|
|
|
|
|
return $rms; |
1381
|
|
|
|
|
|
|
} |
1382
|
|
|
|
|
|
|
|
1383
|
|
|
|
|
|
|
=head2 superpose |
1384
|
|
|
|
|
|
|
|
1385
|
|
|
|
|
|
|
subroutine to superpose one set of points onto another |
1386
|
|
|
|
|
|
|
|
1387
|
|
|
|
|
|
|
Input 1: Number of points to superpose |
1388
|
|
|
|
|
|
|
Input 2: Vector of points to be used as the superposition template |
1389
|
|
|
|
|
|
|
Input 3: Vector of points to be aligned and superposed |
1390
|
|
|
|
|
|
|
Input 4: Vector of extra points to be superposed (not aligned, since they are "carried along") |
1391
|
|
|
|
|
|
|
|
1392
|
|
|
|
|
|
|
=cut |
1393
|
|
|
|
|
|
|
sub superpose { |
1394
|
0
|
|
|
0
|
|
|
my ( $c, $x, $y, $extra ) = @_; |
1395
|
0
|
|
|
|
|
|
my @R = ( [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ); |
1396
|
0
|
|
|
|
|
|
my @xcom = COM2( 0, $c, \@$x ); |
1397
|
0
|
|
|
|
|
|
my @ycom = COM2( 0, $c, \@$y ); |
1398
|
0
|
|
|
|
|
|
my $e0 = 0; |
1399
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $c ; $aa++ ) { |
1400
|
0
|
|
|
|
|
|
for ( my $bb = 0 ; $bb < 3 ; $bb++ ) { |
1401
|
0
|
|
|
|
|
|
for ( my $cc = 0 ; $cc < 3 ; $cc++ ) { |
1402
|
0
|
|
|
|
|
|
$R[$bb][$cc] += |
1403
|
|
|
|
|
|
|
( $$x[$aa][$bb] - $xcom[$bb] ) * |
1404
|
|
|
|
|
|
|
( $$y[$aa][$cc] - $ycom[$cc] ); |
1405
|
|
|
|
|
|
|
} |
1406
|
0
|
|
|
|
|
|
$e0 += |
1407
|
|
|
|
|
|
|
( ( $$x[$aa][$bb] - $xcom[$bb] )**2 + |
1408
|
|
|
|
|
|
|
( $$y[$aa][$bb] - $ycom[$bb] )**2 ); |
1409
|
|
|
|
|
|
|
} |
1410
|
|
|
|
|
|
|
} |
1411
|
|
|
|
|
|
|
|
1412
|
|
|
|
|
|
|
#calculate cross-coefficients |
1413
|
0
|
|
|
|
|
|
my $xx = $R[0][0]**2; |
1414
|
0
|
|
|
|
|
|
my $xy = $R[0][1]**2; |
1415
|
0
|
|
|
|
|
|
my $xz = $R[0][2]**2; |
1416
|
0
|
|
|
|
|
|
my $yx = $R[1][0]**2; |
1417
|
0
|
|
|
|
|
|
my $yy = $R[1][1]**2; |
1418
|
0
|
|
|
|
|
|
my $yz = $R[1][2]**2; |
1419
|
0
|
|
|
|
|
|
my $zx = $R[2][0]**2; |
1420
|
0
|
|
|
|
|
|
my $zy = $R[2][1]**2; |
1421
|
0
|
|
|
|
|
|
my $zz = $R[2][2]**2; |
1422
|
0
|
|
|
|
|
|
my $D = ( $xy + $xz - $yx - $zx )**2; |
1423
|
0
|
|
|
|
|
|
my $temp = -$xx + $yy + $zz + $yz + $zy; |
1424
|
0
|
|
|
|
|
|
my $temp2 = 2 * ( $R[1][1] * $R[2][2] - $R[1][2] * $R[2][1] ); |
1425
|
0
|
|
|
|
|
|
my $E = ( $temp - $temp2 ) * ( $temp + $temp2 ); |
1426
|
0
|
|
|
|
|
|
my $xzpzx = $R[0][2] + $R[2][0]; |
1427
|
0
|
|
|
|
|
|
my $xzmzx = $R[0][2] - $R[2][0]; |
1428
|
0
|
|
|
|
|
|
my $yzpzy = $R[1][2] + $R[2][1]; |
1429
|
0
|
|
|
|
|
|
my $yzmzy = $R[1][2] - $R[2][1]; |
1430
|
0
|
|
|
|
|
|
my $xypyx = $R[0][1] + $R[1][0]; |
1431
|
0
|
|
|
|
|
|
my $xymyx = $R[0][1] - $R[1][0]; |
1432
|
0
|
|
|
|
|
|
my $xmymz = $R[0][0] - $R[1][1] - $R[2][2]; |
1433
|
0
|
|
|
|
|
|
my $xmypz = $R[0][0] - $R[1][1] + $R[2][2]; |
1434
|
0
|
|
|
|
|
|
my $xpymz = $R[0][0] + $R[1][1] - $R[2][2]; |
1435
|
0
|
|
|
|
|
|
my $xpypz = $R[0][0] + $R[1][1] + $R[2][2]; |
1436
|
0
|
|
|
|
|
|
my $F = |
1437
|
|
|
|
|
|
|
( -( $xzpzx * $yzmzy ) + ( $xymyx * $xmymz ) ) * |
1438
|
|
|
|
|
|
|
( -( $xzmzx * $yzpzy ) + ( $xymyx * $xmypz ) ); |
1439
|
0
|
|
|
|
|
|
my $G = |
1440
|
|
|
|
|
|
|
( -( $xzpzx * $yzpzy ) - ( $xypyx * $xpymz ) ) * |
1441
|
|
|
|
|
|
|
( -( $xzmzx * $yzmzy ) - ( $xypyx * $xpypz ) ); |
1442
|
0
|
|
|
|
|
|
my $H = |
1443
|
|
|
|
|
|
|
( ( $xypyx * $yzpzy ) + ( $xzpzx * $xmypz ) ) * |
1444
|
|
|
|
|
|
|
( -( $xymyx * $yzmzy ) + ( $xzpzx * $xpypz ) ); |
1445
|
0
|
|
|
|
|
|
my $I = |
1446
|
|
|
|
|
|
|
( ( $xypyx * $yzmzy ) + ( $xzmzx * $xmymz ) ) * |
1447
|
|
|
|
|
|
|
( -( $xymyx * $yzpzy ) + ( $xzmzx * $xpymz ) ); |
1448
|
0
|
|
|
|
|
|
my $c0 = $D + $E + $F + $G + $H + $I; |
1449
|
0
|
|
|
|
|
|
my $c1 = |
1450
|
|
|
|
|
|
|
8 * |
1451
|
|
|
|
|
|
|
( ( $R[0][0] * ( $R[1][2] * $R[2][1] - $R[1][1] * $R[2][2] ) ) + |
1452
|
|
|
|
|
|
|
( $R[0][1] * ( $R[1][0] * $R[2][2] - $R[1][2] * $R[2][0] ) ) + |
1453
|
|
|
|
|
|
|
( $R[0][2] * ( $R[1][1] * $R[2][0] - $R[1][0] * $R[2][1] ) ) ); |
1454
|
0
|
|
|
|
|
|
my $c2 = -2 * ( $xx + $xy + $xz + $yx + $yy + $yz + $zx + $zy + $zz ); |
1455
|
0
|
|
|
|
|
|
my $lam = 0.5 * $e0; |
1456
|
0
|
|
|
|
|
|
my $prec = 0.00001; |
1457
|
0
|
|
|
|
|
|
my $lamold = $lam + 1; |
1458
|
|
|
|
|
|
|
|
1459
|
|
|
|
|
|
|
#Use Newton's method to find largest eigenvalue |
1460
|
0
|
|
|
|
|
|
while ( abs( $lam - $lamold ) > $prec ) { |
1461
|
0
|
|
|
|
|
|
$lamold = $lam; |
1462
|
0
|
|
|
|
|
|
my $t = 4 * ( $lam**3 ) + 2 * $c2 * $lam + $c1; |
1463
|
0
|
0
|
|
|
|
|
if ( $t ne 0 ) { |
1464
|
0
|
|
|
|
|
|
$lam -= |
1465
|
|
|
|
|
|
|
( $lam**4 + $c2 * ( $lam**2 ) + $c1 * $lam + $c0 ) / |
1466
|
|
|
|
|
|
|
( 4 * ( $lam**3 ) + 2 * $c2 * $lam + $c1 ); |
1467
|
|
|
|
|
|
|
} |
1468
|
|
|
|
|
|
|
} |
1469
|
0
|
|
|
|
|
|
my $rms = sqrt( abs( ( $e0 - 2 * $lam ) / $c ) ); |
1470
|
0
|
0
|
|
|
|
|
if ( $rms > 0 ) { |
1471
|
|
|
|
|
|
|
|
1472
|
|
|
|
|
|
|
#find eigenvector of 4x4 quaternion matrix for largest eigenvalue |
1473
|
0
|
|
|
|
|
|
my @evec = ( 0, 0, 0, 0 ); |
1474
|
0
|
|
|
|
|
|
my @M; |
1475
|
0
|
|
|
|
|
|
push( @M, [ ( $xpypz - $lam, $yzmzy, -$xzmzx, $xymyx ) ] ); |
1476
|
0
|
|
|
|
|
|
push( @M, [ ( $yzmzy, $xmymz - $lam, $xypyx, $xzpzx ) ] ); |
1477
|
0
|
|
|
|
|
|
push( @M, [ ( -$xzmzx, $xypyx, -$xmypz - $lam, $yzpzy ) ] ); |
1478
|
0
|
|
|
|
|
|
push( @M, [ ( $xymyx, $xzpzx, $yzpzy, -$xpymz - $lam ) ] ); |
1479
|
|
|
|
|
|
|
|
1480
|
|
|
|
|
|
|
#Find co-factors of first row |
1481
|
0
|
|
|
|
|
|
$evec[0] = det( |
1482
|
|
|
|
|
|
|
( |
1483
|
0
|
|
|
|
|
|
[ @{ $M[1] }[ 1 .. 3 ] ], |
1484
|
0
|
|
|
|
|
|
[ @{ $M[2] }[ 1 .. 3 ] ], |
1485
|
0
|
|
|
|
|
|
[ @{ $M[3] }[ 1 .. 3 ] ] |
1486
|
|
|
|
|
|
|
) |
1487
|
|
|
|
|
|
|
); |
1488
|
0
|
|
|
|
|
|
$evec[1] = -1 * det( |
1489
|
|
|
|
|
|
|
( |
1490
|
0
|
|
|
|
|
|
[ ( $M[1][0], @{ $M[1] }[ 2 .. 3 ] ) ], |
1491
|
0
|
|
|
|
|
|
[ ( $M[2][0], @{ $M[2] }[ 2 .. 3 ] ) ], |
1492
|
0
|
|
|
|
|
|
[ ( $M[3][0], @{ $M[3] }[ 2 .. 3 ] ) ] |
1493
|
|
|
|
|
|
|
) |
1494
|
|
|
|
|
|
|
); |
1495
|
0
|
|
|
|
|
|
$evec[2] = det( |
1496
|
|
|
|
|
|
|
( |
1497
|
0
|
|
|
|
|
|
[ ( @{ $M[1] }[ 0 .. 1 ], $M[1][3] ) ], |
1498
|
0
|
|
|
|
|
|
[ ( @{ $M[2] }[ 0 .. 1 ], $M[2][3] ) ], |
1499
|
0
|
|
|
|
|
|
[ ( @{ $M[3] }[ 0 .. 1 ], $M[3][3] ) ] |
1500
|
|
|
|
|
|
|
) |
1501
|
|
|
|
|
|
|
); |
1502
|
0
|
|
|
|
|
|
$evec[3] = -1 * det( |
1503
|
|
|
|
|
|
|
( |
1504
|
0
|
|
|
|
|
|
[ @{ $M[1] }[ 0 .. 2 ] ], |
1505
|
0
|
|
|
|
|
|
[ @{ $M[2] }[ 0 .. 2 ] ], |
1506
|
0
|
|
|
|
|
|
[ @{ $M[3] }[ 0 .. 2 ] ] |
1507
|
|
|
|
|
|
|
) |
1508
|
|
|
|
|
|
|
); |
1509
|
0
|
0
|
|
|
|
|
if ( |
1510
|
|
|
|
|
|
|
abs( $evec[0] ) + |
1511
|
|
|
|
|
|
|
abs( $evec[1] ) + |
1512
|
|
|
|
|
|
|
abs( $evec[2] ) + |
1513
|
|
|
|
|
|
|
abs( $evec[3] ) < 0.001 ) |
1514
|
|
|
|
|
|
|
{ |
1515
|
|
|
|
|
|
|
|
1516
|
|
|
|
|
|
|
#Find co-factors of second row |
1517
|
0
|
|
|
|
|
|
$evec[0] = -1 * det( |
1518
|
|
|
|
|
|
|
( |
1519
|
0
|
|
|
|
|
|
[ @{ $M[0] }[ 1 .. 3 ] ], |
1520
|
0
|
|
|
|
|
|
[ @{ $M[2] }[ 1 .. 3 ] ], |
1521
|
0
|
|
|
|
|
|
[ @{ $M[3] }[ 1 .. 3 ] ] |
1522
|
|
|
|
|
|
|
) |
1523
|
|
|
|
|
|
|
); |
1524
|
0
|
|
|
|
|
|
$evec[1] = det( |
1525
|
|
|
|
|
|
|
( |
1526
|
0
|
|
|
|
|
|
[ ( $M[0][0], @{ $M[0] }[ 2 .. 3 ] ) ], |
1527
|
0
|
|
|
|
|
|
[ ( $M[2][0], @{ $M[2] }[ 2 .. 3 ] ) ], |
1528
|
0
|
|
|
|
|
|
[ ( $M[3][0], @{ $M[3] }[ 2 .. 3 ] ) ] |
1529
|
|
|
|
|
|
|
) |
1530
|
|
|
|
|
|
|
); |
1531
|
0
|
|
|
|
|
|
$evec[2] = -1 * det( |
1532
|
|
|
|
|
|
|
( |
1533
|
0
|
|
|
|
|
|
[ ( @{ $M[0] }[ 0 .. 1 ], $M[0][3] ) ], |
1534
|
0
|
|
|
|
|
|
[ ( @{ $M[2] }[ 0 .. 1 ], $M[2][3] ) ], |
1535
|
0
|
|
|
|
|
|
[ ( @{ $M[3] }[ 0 .. 1 ], $M[3][3] ) ] |
1536
|
|
|
|
|
|
|
) |
1537
|
|
|
|
|
|
|
); |
1538
|
0
|
|
|
|
|
|
$evec[3] = det( |
1539
|
|
|
|
|
|
|
( |
1540
|
0
|
|
|
|
|
|
[ @{ $M[0] }[ 0 .. 2 ] ], |
1541
|
0
|
|
|
|
|
|
[ @{ $M[2] }[ 0 .. 2 ] ], |
1542
|
0
|
|
|
|
|
|
[ @{ $M[3] }[ 0 .. 2 ] ] |
1543
|
|
|
|
|
|
|
) |
1544
|
|
|
|
|
|
|
); |
1545
|
0
|
0
|
|
|
|
|
if ( $evec[0]**2 + $evec[1]**2 + $evec[2]**2 + $evec[3]**2 < 0.001 ) |
1546
|
|
|
|
|
|
|
{ |
1547
|
|
|
|
|
|
|
|
1548
|
|
|
|
|
|
|
#Find co-factors of third row |
1549
|
0
|
|
|
|
|
|
$evec[0] = det( |
1550
|
|
|
|
|
|
|
( |
1551
|
0
|
|
|
|
|
|
[ @{ $M[0] }[ 1 .. 3 ] ], |
1552
|
0
|
|
|
|
|
|
[ @{ $M[1] }[ 1 .. 3 ] ], |
1553
|
0
|
|
|
|
|
|
[ @{ $M[3] }[ 1 .. 3 ] ] |
1554
|
|
|
|
|
|
|
) |
1555
|
|
|
|
|
|
|
); |
1556
|
0
|
|
|
|
|
|
$evec[1] = -1 * det( |
1557
|
|
|
|
|
|
|
( |
1558
|
0
|
|
|
|
|
|
[ ( $M[0][0], @{ $M[0] }[ 2 .. 3 ] ) ], |
1559
|
0
|
|
|
|
|
|
[ ( $M[1][0], @{ $M[1] }[ 2 .. 3 ] ) ], |
1560
|
0
|
|
|
|
|
|
[ ( $M[3][0], @{ $M[3] }[ 2 .. 3 ] ) ] |
1561
|
|
|
|
|
|
|
) |
1562
|
|
|
|
|
|
|
); |
1563
|
0
|
|
|
|
|
|
$evec[2] = det( |
1564
|
|
|
|
|
|
|
( |
1565
|
0
|
|
|
|
|
|
[ ( @{ $M[0] }[ 0 .. 1 ], $M[0][3] ) ], |
1566
|
0
|
|
|
|
|
|
[ ( @{ $M[1] }[ 0 .. 1 ], $M[1][3] ) ], |
1567
|
0
|
|
|
|
|
|
[ ( @{ $M[3] }[ 0 .. 1 ], $M[3][3] ) ] |
1568
|
|
|
|
|
|
|
) |
1569
|
|
|
|
|
|
|
); |
1570
|
0
|
|
|
|
|
|
$evec[3] = -1 * det( |
1571
|
|
|
|
|
|
|
( |
1572
|
0
|
|
|
|
|
|
[ @{ $M[0] }[ 0 .. 2 ] ], |
1573
|
0
|
|
|
|
|
|
[ @{ $M[1] }[ 0 .. 2 ] ], |
1574
|
0
|
|
|
|
|
|
[ @{ $M[3] }[ 0 .. 2 ] ] |
1575
|
|
|
|
|
|
|
) |
1576
|
|
|
|
|
|
|
); |
1577
|
0
|
0
|
|
|
|
|
if ( $evec[0]**2 + $evec[1]**2 + $evec[2]**2 + $evec[3]**2 < |
1578
|
|
|
|
|
|
|
0.001 ) |
1579
|
|
|
|
|
|
|
{ |
1580
|
|
|
|
|
|
|
|
1581
|
|
|
|
|
|
|
#Find co-factors of fourth row |
1582
|
0
|
|
|
|
|
|
$evec[0] = -1 * det( |
1583
|
|
|
|
|
|
|
( |
1584
|
0
|
|
|
|
|
|
[ @{ $M[0] }[ 1 .. 3 ] ], |
1585
|
0
|
|
|
|
|
|
[ @{ $M[1] }[ 1 .. 3 ] ], |
1586
|
0
|
|
|
|
|
|
[ @{ $M[2] }[ 1 .. 3 ] ] |
1587
|
|
|
|
|
|
|
) |
1588
|
|
|
|
|
|
|
); |
1589
|
0
|
|
|
|
|
|
$evec[1] = det( |
1590
|
|
|
|
|
|
|
( |
1591
|
0
|
|
|
|
|
|
[ ( $M[0][0], @{ $M[0] }[ 2 .. 3 ] ) ], |
1592
|
0
|
|
|
|
|
|
[ ( $M[1][0], @{ $M[1] }[ 2 .. 3 ] ) ], |
1593
|
0
|
|
|
|
|
|
[ ( $M[2][0], @{ $M[2] }[ 2 .. 3 ] ) ] |
1594
|
|
|
|
|
|
|
) |
1595
|
|
|
|
|
|
|
); |
1596
|
0
|
|
|
|
|
|
$evec[2] = -1 * det( |
1597
|
|
|
|
|
|
|
( |
1598
|
0
|
|
|
|
|
|
[ ( @{ $M[0] }[ 0 .. 1 ], $M[0][3] ) ], |
1599
|
0
|
|
|
|
|
|
[ ( @{ $M[1] }[ 0 .. 1 ], $M[1][3] ) ], |
1600
|
0
|
|
|
|
|
|
[ ( @{ $M[2] }[ 0 .. 1 ], $M[2][3] ) ] |
1601
|
|
|
|
|
|
|
) |
1602
|
|
|
|
|
|
|
); |
1603
|
0
|
|
|
|
|
|
$evec[3] = det( |
1604
|
|
|
|
|
|
|
( |
1605
|
0
|
|
|
|
|
|
[ @{ $M[0] }[ 0 .. 2 ] ], |
1606
|
0
|
|
|
|
|
|
[ @{ $M[1] }[ 0 .. 2 ] ], |
1607
|
0
|
|
|
|
|
|
[ @{ $M[2] }[ 0 .. 2 ] ] |
1608
|
|
|
|
|
|
|
) |
1609
|
|
|
|
|
|
|
); |
1610
|
|
|
|
|
|
|
} |
1611
|
|
|
|
|
|
|
} |
1612
|
|
|
|
|
|
|
} |
1613
|
0
|
|
|
|
|
|
my @quat = unit(@evec); |
1614
|
0
|
|
|
|
|
|
my $scal = $quat[0]; |
1615
|
0
|
|
|
|
|
|
my @vec = @quat[ 1 .. 3 ]; |
1616
|
0
|
|
|
|
|
|
foreach (@vec) { $_ = -1 * $_ } |
|
0
|
|
|
|
|
|
|
1617
|
|
|
|
|
|
|
|
1618
|
|
|
|
|
|
|
#Form rotation matrix |
1619
|
0
|
|
|
|
|
|
foreach my $coord (@$y) { |
1620
|
0
|
|
|
|
|
|
my @new = ( |
1621
|
0
|
|
|
|
|
|
${$coord}[0] - $ycom[0], |
1622
|
0
|
|
|
|
|
|
${$coord}[1] - $ycom[1], |
1623
|
0
|
|
|
|
|
|
${$coord}[2] - $ycom[2] |
1624
|
|
|
|
|
|
|
); |
1625
|
0
|
|
|
|
|
|
my $s1 = -1 * dot( @vec, @new ); |
1626
|
0
|
|
|
|
|
|
my @svec = vecadd( $scal, cross( @vec, @new ), @new ); |
1627
|
0
|
|
|
|
|
|
my @rotpt = |
1628
|
|
|
|
|
|
|
vecadd( -1 * $s1, vecadd( $scal, cross( @vec, @svec ), @svec ), |
1629
|
|
|
|
|
|
|
@vec ); |
1630
|
0
|
|
|
|
|
|
$coord = [ vecadd( 1, @xcom, @rotpt ) ]; |
1631
|
|
|
|
|
|
|
} |
1632
|
0
|
|
|
|
|
|
foreach my $coord (@$extra) { |
1633
|
0
|
|
|
|
|
|
my @new = ( |
1634
|
0
|
|
|
|
|
|
${$coord}[0] - $ycom[0], |
1635
|
0
|
|
|
|
|
|
${$coord}[1] - $ycom[1], |
1636
|
0
|
|
|
|
|
|
${$coord}[2] - $ycom[2] |
1637
|
|
|
|
|
|
|
); |
1638
|
0
|
|
|
|
|
|
my $s1 = -1 * dot( @vec, @new ); |
1639
|
0
|
|
|
|
|
|
my @svec = vecadd( $scal, cross( @vec, @new ), @new ); |
1640
|
0
|
|
|
|
|
|
my @rotpt = |
1641
|
|
|
|
|
|
|
vecadd( -1 * $s1, vecadd( $scal, cross( @vec, @svec ), @svec ), |
1642
|
|
|
|
|
|
|
@vec ); |
1643
|
0
|
|
|
|
|
|
$coord = [ vecadd( 1, @xcom, @rotpt ) ]; |
1644
|
|
|
|
|
|
|
} |
1645
|
|
|
|
|
|
|
} |
1646
|
|
|
|
|
|
|
else { |
1647
|
0
|
|
|
|
|
|
@$y = @{ Storable::dclone( \@$x ) }; |
|
0
|
|
|
|
|
|
|
1648
|
|
|
|
|
|
|
} |
1649
|
0
|
|
|
|
|
|
return $rms; |
1650
|
|
|
|
|
|
|
} |
1651
|
|
|
|
|
|
|
|
1652
|
|
|
|
|
|
|
=head2 dihedral |
1653
|
|
|
|
|
|
|
|
1654
|
|
|
|
|
|
|
subroutine to calculate the dihedral angle generated by four atoms |
1655
|
|
|
|
|
|
|
|
1656
|
|
|
|
|
|
|
=cut |
1657
|
|
|
|
|
|
|
sub dihedral { |
1658
|
0
|
|
|
0
|
|
|
my ( $c1, $c2, $c3, $c4 ) = @_; |
1659
|
0
|
|
|
|
|
|
my @v21 = unit( vecadd( -1, @$c1, @$c2 ) ); |
1660
|
0
|
|
|
|
|
|
my @v23 = unit( vecadd( -1, @$c3, @$c2 ) ); |
1661
|
0
|
|
|
|
|
|
my @v34 = unit( vecadd( -1, @$c4, @$c3 ) ); |
1662
|
0
|
|
|
|
|
|
my @v21orth = unit( vecadd( -1 * dot( @v21, @v23 ), @v21, @v23 ) ); |
1663
|
0
|
|
|
|
|
|
my @v34orth = unit( vecadd( -1 * dot( @v34, @v23 ), @v34, @v23 ) ); |
1664
|
0
|
|
|
|
|
|
my $ang = Math::Trig::acos( dot( @v21orth, @v34orth ) ) * 180 / 3.14159265; |
1665
|
0
|
|
|
|
|
|
my @dirvec = cross( @v21orth, @v34orth ); |
1666
|
0
|
0
|
|
|
|
|
if ( dot( @v23, @dirvec ) < 0 ) { $ang *= -1 } |
|
0
|
|
|
|
|
|
|
1667
|
0
|
|
|
|
|
|
return $ang; |
1668
|
|
|
|
|
|
|
} |
1669
|
|
|
|
|
|
|
|
1670
|
|
|
|
|
|
|
=head2 findcb |
1671
|
|
|
|
|
|
|
|
1672
|
|
|
|
|
|
|
subroutine to calculate the coordinates of a beta-carbon, given statistically observed tetrahedral geometry###### |
1673
|
|
|
|
|
|
|
|
1674
|
|
|
|
|
|
|
Input 1: C-alpha coordinates |
1675
|
|
|
|
|
|
|
Input 2: C coordinates |
1676
|
|
|
|
|
|
|
Input 3: N coordinates |
1677
|
|
|
|
|
|
|
=cut |
1678
|
|
|
|
|
|
|
sub findcb { |
1679
|
0
|
|
|
0
|
|
|
my ( $ca, $c, $n ) = @_; |
1680
|
0
|
|
|
|
|
|
my @v3 = unit( vecadd( -1, @$c, @$n ) ); |
1681
|
0
|
|
|
|
|
|
my @v1 = unit( vecadd( -1, @$ca, @$c ) ); |
1682
|
0
|
|
|
|
|
|
my @v2 = unit( vecadd( -1, @$ca, @$n ) ); |
1683
|
0
|
|
|
|
|
|
my @v4 = unit( vecadd( 1, @v1, @v2 ) ); |
1684
|
0
|
|
|
|
|
|
my $ang = 53.2; |
1685
|
0
|
|
|
|
|
|
my @dist = rotateaxis( \@v4, \@v3, \$ang ); |
1686
|
0
|
|
|
|
|
|
@dist = ( $dist[0] * 1.53, $dist[1] * 1.53, $dist[2] * 1.53 ); |
1687
|
0
|
|
|
|
|
|
my @cb = vecadd( 1, @$ca, @dist ); |
1688
|
0
|
|
|
|
|
|
return @cb; |
1689
|
|
|
|
|
|
|
} |
1690
|
|
|
|
|
|
|
|
1691
|
|
|
|
|
|
|
=head2 findo |
1692
|
|
|
|
|
|
|
|
1693
|
|
|
|
|
|
|
=cut |
1694
|
|
|
|
|
|
|
sub findo { |
1695
|
0
|
|
|
0
|
|
|
my ( $ca, $c, $n ) = @_; |
1696
|
0
|
|
|
|
|
|
my @c_to_ca = unit( vecadd( -1, @$ca, @$c ) ); |
1697
|
0
|
|
|
|
|
|
my @c_to_n = unit( vecadd( -1, @$n, @$c ) ); |
1698
|
0
|
|
|
|
|
|
my @normal = unit( cross( @c_to_n, @c_to_ca ) ); |
1699
|
|
|
|
|
|
|
|
1700
|
|
|
|
|
|
|
#rotate c-ca bond around normal counterclockwise 121 degrees |
1701
|
0
|
|
|
|
|
|
my $ang = 121; |
1702
|
0
|
|
|
|
|
|
my @out = rotateaxis( \@c_to_ca, \@normal, \$ang ); |
1703
|
0
|
|
|
|
|
|
my @o = vecadd( 1.23, @$c, @out ); |
1704
|
0
|
|
|
|
|
|
return @o; |
1705
|
|
|
|
|
|
|
} |
1706
|
|
|
|
|
|
|
|
1707
|
|
|
|
|
|
|
=head2 pointsonsphere |
1708
|
|
|
|
|
|
|
|
1709
|
|
|
|
|
|
|
subroutine to distribute points evenly on a sphere |
1710
|
|
|
|
|
|
|
Input 1: Number of points to distribute |
1711
|
|
|
|
|
|
|
Input 2: Radius of sphere |
1712
|
|
|
|
|
|
|
|
1713
|
|
|
|
|
|
|
=cut |
1714
|
|
|
|
|
|
|
sub pointsonsphere { |
1715
|
0
|
|
|
0
|
|
|
my ( $n, $rad ) = @_; |
1716
|
0
|
|
|
|
|
|
my @pts; |
1717
|
0
|
|
|
|
|
|
my $increment = 3.14159265359 * ( 3 - sqrt(5) ); |
1718
|
0
|
|
|
|
|
|
my $offset = 2 / $n; |
1719
|
0
|
|
|
|
|
|
for ( my $aa = 0 ; $aa < $n ; $aa++ ) { |
1720
|
0
|
|
|
|
|
|
my $y = $aa * $offset - 1 + 0.5 * $offset; |
1721
|
0
|
|
|
|
|
|
my $r = sqrt( 1 - $y * $y ); |
1722
|
0
|
|
|
|
|
|
my $phi = $aa * $increment; |
1723
|
0
|
|
|
|
|
|
push( @pts, |
1724
|
|
|
|
|
|
|
[ ( $rad * $r * cos($phi), $rad * $y, $rad * $r * sin($phi) ) ] ); |
1725
|
|
|
|
|
|
|
} |
1726
|
0
|
|
|
|
|
|
return @pts; |
1727
|
|
|
|
|
|
|
} |
1728
|
|
|
|
|
|
|
|
1729
|
|
|
|
|
|
|
=head2 norm2 |
1730
|
|
|
|
|
|
|
|
1731
|
|
|
|
|
|
|
subroutine to find the square of the 2-norm of a vector |
1732
|
|
|
|
|
|
|
=cut |
1733
|
|
|
|
|
|
|
sub norm2 { |
1734
|
0
|
|
|
0
|
|
|
my (@v) = @_; |
1735
|
0
|
|
|
|
|
|
my $res = 0; |
1736
|
0
|
|
|
|
|
|
foreach (@v) { |
1737
|
0
|
|
|
|
|
|
$res += $_**2; |
1738
|
|
|
|
|
|
|
} |
1739
|
0
|
|
|
|
|
|
return $res; |
1740
|
|
|
|
|
|
|
} |
1741
|
|
|
|
|
|
|
|
1742
|
|
|
|
|
|
|
=head1 AUTHORS |
1743
|
|
|
|
|
|
|
|
1744
|
|
|
|
|
|
|
Fiserlab Members , C<< >> |
1745
|
|
|
|
|
|
|
|
1746
|
|
|
|
|
|
|
=head1 BUGS |
1747
|
|
|
|
|
|
|
|
1748
|
|
|
|
|
|
|
Please report any bugs or feature requests to C, or through |
1749
|
|
|
|
|
|
|
the web interface at L. |
1750
|
|
|
|
|
|
|
|
1751
|
|
|
|
|
|
|
=head1 SUPPORT |
1752
|
|
|
|
|
|
|
|
1753
|
|
|
|
|
|
|
You can find documentation for this module with the perldoc command. |
1754
|
|
|
|
|
|
|
|
1755
|
|
|
|
|
|
|
perldoc GeometricalCalculations |
1756
|
|
|
|
|
|
|
|
1757
|
|
|
|
|
|
|
=over 4 |
1758
|
|
|
|
|
|
|
|
1759
|
|
|
|
|
|
|
=item * RT: CPAN's request tracker (report bugs here) |
1760
|
|
|
|
|
|
|
|
1761
|
|
|
|
|
|
|
L |
1762
|
|
|
|
|
|
|
|
1763
|
|
|
|
|
|
|
=item * AnnoCPAN: Annotated CPAN documentation |
1764
|
|
|
|
|
|
|
|
1765
|
|
|
|
|
|
|
L |
1766
|
|
|
|
|
|
|
|
1767
|
|
|
|
|
|
|
=item * CPAN Ratings |
1768
|
|
|
|
|
|
|
|
1769
|
|
|
|
|
|
|
L |
1770
|
|
|
|
|
|
|
|
1771
|
|
|
|
|
|
|
=item * Search CPAN |
1772
|
|
|
|
|
|
|
|
1773
|
|
|
|
|
|
|
L |
1774
|
|
|
|
|
|
|
|
1775
|
|
|
|
|
|
|
=back |
1776
|
|
|
|
|
|
|
|
1777
|
|
|
|
|
|
|
=head1 LICENSE AND COPYRIGHT |
1778
|
|
|
|
|
|
|
|
1779
|
|
|
|
|
|
|
Copyright 2015 Fiserlab Members . |
1780
|
|
|
|
|
|
|
|
1781
|
|
|
|
|
|
|
This program is free software; you can redistribute it and/or modify it |
1782
|
|
|
|
|
|
|
under the terms of the the Artistic License (2.0). You may obtain a |
1783
|
|
|
|
|
|
|
copy of the full license at: |
1784
|
|
|
|
|
|
|
|
1785
|
|
|
|
|
|
|
L |
1786
|
|
|
|
|
|
|
|
1787
|
|
|
|
|
|
|
Any use, modification, and distribution of the Standard or Modified |
1788
|
|
|
|
|
|
|
Versions is governed by this Artistic License. By using, modifying or |
1789
|
|
|
|
|
|
|
distributing the Package, you accept this license. Do not use, modify, |
1790
|
|
|
|
|
|
|
or distribute the Package, if you do not accept this license. |
1791
|
|
|
|
|
|
|
|
1792
|
|
|
|
|
|
|
If your Modified Version has been derived from a Modified Version made |
1793
|
|
|
|
|
|
|
by someone other than you, you are nevertheless required to ensure that |
1794
|
|
|
|
|
|
|
your Modified Version complies with the requirements of this license. |
1795
|
|
|
|
|
|
|
|
1796
|
|
|
|
|
|
|
This license does not grant you the right to use any trademark, service |
1797
|
|
|
|
|
|
|
mark, tradename, or logo of the Copyright Holder. |
1798
|
|
|
|
|
|
|
|
1799
|
|
|
|
|
|
|
This license includes the non-exclusive, worldwide, free-of-charge |
1800
|
|
|
|
|
|
|
patent license to make, have made, use, offer to sell, sell, import and |
1801
|
|
|
|
|
|
|
otherwise transfer the Package with respect to any patent claims |
1802
|
|
|
|
|
|
|
licensable by the Copyright Holder that are necessarily infringed by the |
1803
|
|
|
|
|
|
|
Package. If you institute patent litigation (including a cross-claim or |
1804
|
|
|
|
|
|
|
counterclaim) against any party alleging that the Package constitutes |
1805
|
|
|
|
|
|
|
direct or contributory patent infringement, then this Artistic License |
1806
|
|
|
|
|
|
|
to you shall terminate on the date that such litigation is filed. |
1807
|
|
|
|
|
|
|
|
1808
|
|
|
|
|
|
|
Disclaimer of Warranty: THE PACKAGE IS PROVIDED BY THE COPYRIGHT HOLDER |
1809
|
|
|
|
|
|
|
AND CONTRIBUTORS "AS IS' AND WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES. |
1810
|
|
|
|
|
|
|
THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR |
1811
|
|
|
|
|
|
|
PURPOSE, OR NON-INFRINGEMENT ARE DISCLAIMED TO THE EXTENT PERMITTED BY |
1812
|
|
|
|
|
|
|
YOUR LOCAL LAW. UNLESS REQUIRED BY LAW, NO COPYRIGHT HOLDER OR |
1813
|
|
|
|
|
|
|
CONTRIBUTOR WILL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, OR |
1814
|
|
|
|
|
|
|
CONSEQUENTIAL DAMAGES ARISING IN ANY WAY OUT OF THE USE OF THE PACKAGE, |
1815
|
|
|
|
|
|
|
EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
1816
|
|
|
|
|
|
|
|
1817
|
|
|
|
|
|
|
|
1818
|
|
|
|
|
|
|
=cut |
1819
|
|
|
|
|
|
|
|
1820
|
|
|
|
|
|
|
1; # End of GeometricalCalculations |