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Revision 1.6 - (download) (as text) (annotate)
Tue Nov 7 17:18:47 2006 UTC (13 years, 1 month ago) by redwards
Branch: MAIN
CVS Tags: rast_rel_2009_05_18, rast_rel_2008_06_18, rast_rel_2008_06_16, rast_rel_2008_12_18, rast_rel_2008_07_21, rast_rel_2010_0928, rast_2008_0924, rast_rel_2008_04_23, rast_rel_2008_09_30, rast_rel_2009_0925, rast_rel_2010_0526, rast_rel_2010_1206, rast_rel_2010_0118, mgrast_rel_2008_0924, mgrast_rel_2008_1110_v2, rast_rel_2009_02_05, mgrast_rel_2008_0625, rast_rel_2008_10_09, rast_release_2008_09_29, mgrast_rel_2008_0806, mgrast_rel_2008_0923, mgrast_rel_2008_0919, rast_rel_2009_07_09, rast_rel_2010_0827, mgrast_rel_2008_1110, rast_rel_2008_09_29, mgrast_rel_2008_0917, rast_rel_2008_10_29, rast_rel_2009_03_26, rast_rel_2008_11_24, rast_rel_2008_08_07
Changes since 1.5: +1 -1 lines
fixing log error

# Copyright (c) 2003-2006 University of Chicago and Fellowship
# for Interpretations of Genomes. All Rights Reserved.
#
# This file is part of the SEED Toolkit.
# 
# The SEED Toolkit is free software. You can redistribute
# it and/or modify it under the terms of the SEED Toolkit
# Public License. 
#
# You should have received a copy of the SEED Toolkit Public License
# along with this program; if not write to the University of Chicago
# at info@ci.uchicago.edu or the Fellowship for Interpretation of
# Genomes at veronika@thefig.info or download a copy from
# http://www.theseed.org/LICENSE.TXT.
#


=pod

=head1 FIGStatisticalModels

A package of Statistical models for applying to FIG data. 

At inception this was handling some methods developed by Jon McAuliffe, but feel free to add other methods here

=cut

package FIGStatisticalModels;
use strict;
use Exporter;

use vars qw(@EXPORT_OK);

@EXPORT_OK = qw();

=head1 new

Instantiate the object. Not necessary, but nice

=cut

sub new {
    my ($class)=@_;
    my $self={};
    return bless $self, $class;
}

=head1 mean

 Calculate the mean on an array
 e.g. my $mean=FIGStatisticalModels->mean(\@array);

 This is the arithmetical mean (i.e. sum/n)

=cut

sub mean {
 my ($self, $arr)=@_;
 return 0 unless ($arr);
 return 0 unless (@$arr);
 my $sum;
 foreach (@$arr) {$sum+=$_};
 return $sum/(scalar @$arr);
}

=head1 median

 Calculate the median for an array
 e.g. my $median=FIGStatisticalModels->median(\@array);
 
 This is the median, the middle number on a list.

=cut

sub median {
 my ($self, $arr)=@_;
 return 0 unless ($arr);
 @$arr=sort {$a <=> $b} @$arr;
 #@$arr=sort @$arr;
 my $mid=$#$arr/2;
 if ($mid == int($mid)) {
  return $$arr[$mid];
 } else {
  return ($$arr[$mid - 0.5] + $$arr[$mid + 0.5])/2;
 }
}

=head1 min

    Return the minimum value in an array.
    e.g. my $min=FIGStatisticalModels->min($array);

=cut

sub min {
    my ($self, $arr)=@_;
    return undef unless ($arr);
    my $min=1e99;
    map {($_ < $min) ? ($min = $_) : 1} @$arr;
    return $min;
}


=head1 max

    Return the maximum value in an array.
    e.g. my $max=FIGStatisticalModels->max($array);

=cut

sub max {
    my ($self, $arr)=@_;
    return undef unless ($arr);
    my $max=0;
    map {($_ > $max) ? ($max = $_) : 1} @$arr;
    return $max;
}

=head1 stdev
 
 Calculate the standard deviation on an array.

 e.g. my $stdev=FIGStatisticalModels->stdev(\@array);
      my $stdev=FIGStatisticalModels->stdev([1,2,3,4]);

=cut

sub stdev {        
 my ($self, $arr)=@_;
 return 0 unless ($arr);
 my ($n, $sum, $square)=(0,0,0);
 foreach (@$arr) {
  next unless ($_);
  $n++;
  $sum += $_;
  $square += $_ * $_;
 }
 
 #stdev = sqrt(((n.sum(x squared))-((sum x) squared))/n(n-1))
 unless ($n*($n-1)) {die "STDEV at div by zero as $sum, $square, $n\n"; return 0}
 unless ($n*($n-1)) {print STDERR "STDEV at div by zero as $sum, $square, $n\n"; return 0}
 my $stdev = (($n * $square)-($sum * $sum))/($n*($n-1));
 if ($stdev < 0) {die "STdev less than zero ($stdev) as $sum, $square, $n\n"}
 if ($stdev < 0) {print STDERR "STdev less than zero ($stdev) as $sum, $square, $n\n"}
 $stdev=sqrt($stdev);
 return $stdev;
}  


=head1 Functional Coupling Scoring

Scoring direct functional coupling. These are some methods to score the direct functional coupling using a method developed by Jon McAuliffe and Ross Overbeek. It was coded by Rob Edwards. The approach uses a generalized additive model using a thin plate regression spline smoother with 5 degrees of freedom.

Many of these notes have been extracted directly from discussions between Ross, Jon, and Rob. I am including them here for clarity and posterity.

Offline, a matrix was computed whose rows correspond to values of the logscore input on a fine grid. In the ith row, each column corresponds to a basis function of the smoother, evaluated at the ith grid point.

To get the predicted success probability for a given log score, we linearly interpolate between the two nearest grid points, then pass the interpolant and the coefficient vector to a classical linear-logistic prediction routine.

=head2 EQUATION

The formula can be expressed like this:

                                            1
                        logistic(x)  = -----------
                                       1 + exp(-x)

then for a given score (s) the probability of success is
        
                        P(success) = logistic (1.40 - 4.05 * b1(s) + 1.33 * b2(s) - 14.14 * b3(s) + 6.70 * b4(s) )


where b1, b2, b3, and b4 are the basis functions of a thin-plate regression spline with 5 fixed degrees of freedom.

=head1 fc_score2probability

Convert a functional coupling score based on E value to a probability

use: my $probabilty = $statistic_model->fc_score2probability($score);

=cut

sub fc_score2probability {
    my ($self, $score)=@_;

# Coefficient vector
# This vector describes the coefficients in the equation for the probability for success (see EQUATION above).
    # this is the old coef_vector from version 1 of this analysis
    #my $coef_vector = [1.4038457039268741, -4.0483109464656009, 1.3302963870075235, -14.1387590191618955,  6.6980442362324641];
    # this is the new coef_vector from version 2 of this analysis
    my $coef_vector = [1.047594571110132655, -0.107764949815202224, 0.451326357245773802, 0.739792463755890473,  0.703910832923400731];

# Matrix
# This is the precomputed matrix that McAuliffe Provided.
    my ($grid_min, $grid_max, $dgrid, $grid_data)=$self->spline_matrix();
    
    my $log_score;
    unless ($score) {print STDERR "Had a score of $score. Can't log it!!\n"; $log_score=$score}
    else {$log_score= log($score)}
    
    my $sc    = $self->score2success_prob($log_score, $coef_vector, $grid_data, $grid_min, $grid_max, $dgrid);
    return $sc;
}


=head1 fc_bitscore2probability

Convert a BBH bit score and optional tough call flag to a probability. This uses the fourth column of the BBH data - the bit score normalized by length - as the basis of calculating a probability of being a good match.

use: my $probability = $statistic_model->fc_bitscore2probability($bitscore, $toughcall);

Toughcall is a boolean. True is if it meets this regexp:
if ($function =~ /aminotransferase|system|component|oxidase|regulator|cytochrome|specific|permease|transcriptional|transport|dehydrogenase/i)

=cut

sub fc_bitscore2probability {
    my ($self, $bitscore, $toughcall)=@_;

# Coefficient vector
# This vector describes the coefficients in the equation for the probability for success (see EQUATION above).
# It is slightly different than the one above since it is for bit-scores not evalues
    my $coef_vector = [3.75350869822815225,  1.73322181593049818, -1.69597537007947863, -0.53396148373755736];

    my $log_score;
    unless ($bitscore) {print STDERR "Had a bitscore of $bitscore. Can't log it!!\n"; $log_score=$bitscore}
    else {$log_score= log($bitscore)}

    my $tc=0; if ($toughcall) {$tc=1} # this just converts it to a 1/0 boolean in case someone uses something weird
    my $score=$self->linear_logistic_prediction([1, $log_score, $tc, $tc*$log_score], $coef_vector);
    return $score;
}



=head1 score2success_prob

Convert a score to a probability of success

=cut

sub score2success_prob
{
    my ($self, $input_score, $coef_vector, $grid_matrix, $grid_min, $grid_max, $dgrid) = @_;

    my ($left_nbr_idx, $right_nbr_idx, $weight);

    # find the left- and right-hand interpolating values, and the weights { 1-w, w } to combine them for the interpolant

    if ($input_score < $grid_min)
    {
        # the score is smaller than the grid. Perhaps we should warn about this.
        $left_nbr_idx = 0;
        $right_nbr_idx = 1;
        $weight = 0;
    }
    elsif ($input_score >= $grid_max)
    {
        # the score is bigger than the grid. Perhaps we should warn about this.
        $right_nbr_idx = $#{$grid_matrix};
        $left_nbr_idx = $right_nbr_idx - 1;
        $weight = 1;
    }
    else
    {
        # just figure out our place in the grid. Note that this is calculated not run through a loop (though we could)
        $left_nbr_idx = int(($input_score - $grid_min) / $dgrid);
        $right_nbr_idx = $left_nbr_idx + 1;
        $weight = ( $input_score - ($grid_min + $left_nbr_idx * $dgrid) ) / $dgrid;
    }

    my @interpolant_vector;

    for (my $i = 0; $i < scalar(@$coef_vector); $i++)
    {
        $interpolant_vector[$i] =
            (1 - $weight) * ${$grid_matrix}[$left_nbr_idx][$i+1] +
            $weight * ${$grid_matrix}[$right_nbr_idx][$i+1];
    }

    return $self->linear_logistic_prediction(\@interpolant_vector, $coef_vector);
}


=head1 linear_logistic_prediction

Given the coefficients of a logistic regression fit and values for the covariates, return the corresponding predicted probability: take the inner product of covariates and coefficients, then pass the result  through the inverse link function (the logistic function,  h(u) = (1 + exp(-u))^{-1}).

=cut

sub linear_logistic_prediction
{
    my ($self, $covariate_vector, $coef_vector) = @_;

    my $inner_product = 0;
    for (my $i = 0; $i < scalar(@$coef_vector); $i++)
    {
        $inner_product += $covariate_vector->[$i] * $coef_vector->[$i];
    }

    my $res = 1 / (1 + exp(-$inner_product));

    return $res;
}



=head2 spline_matrix

This data is the matrix that was calculated offline by Jon mcAuliffe using the thin plate regression spline smoother. This matrix was provided by Jon, and I just converted it to this array form for easier coding.

=cut

sub spline_matrix {
	my $self=shift;
	my @matrix=(
		[0, 1, -5.12854483987495, 1.48365029477066, -1.66633483317743, -5.19728628264353],
		[0.001, 1, -5.1276370232775, 1.48319826316280, -1.66565720160812, -5.19610816345883],
		[0.002, 1, -5.12672920668005, 1.48274623155493, -1.66497957003881, -5.19493004427413],
		[0.003, 1, -5.1258213900826, 1.48229419994707, -1.66430193846950, -5.19375192508943],
		[0.004, 1, -5.12491357348514, 1.4818421683392, -1.66362430690020, -5.19257380590473],
		[0.005, 1, -5.12400575688769, 1.48139013673133, -1.66294667533089, -5.19139568672003],
		[0.006, 1, -5.12309794029024, 1.48093810512347, -1.66226904376158, -5.19021756753533],
		[0.007, 1, -5.12219012369279, 1.48048607351560, -1.66159141219227, -5.18903944835064],
		[0.008, 1, -5.12128230709534, 1.48003404190774, -1.66091378062296, -5.18786132916594],
		[0.009, 1, -5.12037449049789, 1.47958201029987, -1.66023614905365, -5.18668320998124],
		[0.01, 1, -5.11946667390043, 1.47912997869201, -1.65955851748434, -5.18550509079654],
		[0.011, 1, -5.11855885730298, 1.47867794708414, -1.65888088591503, -5.18432697161184],
		[0.012, 1, -5.11765104070553, 1.47822591547627, -1.65820325434572, -5.18314885242714],
		[0.013, 1, -5.11674322410808, 1.47777388386841, -1.65752562277641, -5.18197073324244],
		[0.014, 1, -5.11583540751063, 1.47732185226054, -1.6568479912071, -5.18079261405774],
		[0.015, 1, -5.11492759091317, 1.47686982065268, -1.65617035963779, -5.17961449487304],
		[0.016, 1, -5.11401977431572, 1.47641778904481, -1.65549272806848, -5.17843637568834],
		[0.017, 1, -5.11311195771827, 1.47596575743695, -1.65481509649917, -5.17725825650364],
		[0.018, 1, -5.11220414112082, 1.47551372582908, -1.65413746492986, -5.17608013731895],
		[0.019, 1, -5.11129632452337, 1.47506169422122, -1.65345983336055, -5.17490201813425],
		[0.02, 1, -5.11038850792592, 1.47460966261335, -1.65278220179124, -5.17372389894955],
		[0.021, 1, -5.10948069132846, 1.47415763100548, -1.65210457022193, -5.17254577976485],
		[0.022, 1, -5.10857287473101, 1.47370559939762, -1.65142693865262, -5.17136766058015],
		[0.023, 1, -5.10766505813356, 1.47325356778975, -1.65074930708331, -5.17018954139545],
		[0.024, 1, -5.10675724153611, 1.47280153618189, -1.65007167551400, -5.16901142221075],
		[0.025, 1, -5.10584942493866, 1.47234950457402, -1.64939404394470, -5.16783330302605],
		[0.026, 1, -5.1049416083412, 1.47189747296616, -1.64871641237539, -5.16665518384135],
		[0.027, 1, -5.10403379174375, 1.47144544135829, -1.64803878080608, -5.16547706465665],
		[0.028, 1, -5.1031259751463, 1.47099340975042, -1.64736114923677, -5.16429894547195],
		[0.029, 1, -5.10221815854885, 1.47054137814256, -1.64668351766746, -5.16312082628725],
		[0.03, 1, -5.10131034195140, 1.47008934653469, -1.64600588609815, -5.16194270710255],
		[0.031, 1, -5.10040252535394, 1.46963731492683, -1.64532825452884, -5.16076458791786],
		[0.032, 1, -5.09949470875649, 1.46918528331896, -1.64465062295953, -5.15958646873316],
		[0.033, 1, -5.09858689215904, 1.46873325171110, -1.64397299139022, -5.15840834954846],
		[0.034, 1, -5.09767907556159, 1.46828122010323, -1.64329535982091, -5.15723023036376],
		[0.035, 1, -5.09677125896414, 1.46782918849536, -1.6426177282516, -5.15605211117906],
		[0.036, 1, -5.09586344236669, 1.4673771568875, -1.64194009668229, -5.15487399199436],
		[0.037, 1, -5.09495562576923, 1.46692512527963, -1.64126246511298, -5.15369587280966],
		[0.038, 1, -5.09404780917178, 1.46647309367177, -1.64058483354367, -5.15251775362496],
		[0.039, 1, -5.09313999257433, 1.46602106206390, -1.63990720197436, -5.15133963444026],
		[0.04, 1, -5.09223217597688, 1.46556903045604, -1.63922957040505, -5.15016151525556],
		[0.041, 1, -5.09132435937943, 1.46511699884817, -1.63855193883574, -5.14898339607086],
		[0.042, 1, -5.09041654278197, 1.46466496724031, -1.63787430726644, -5.14780527688617],
		[0.043, 1, -5.08950872618452, 1.46421293563244, -1.63719667569712, -5.14662715770147],
		[0.044, 1, -5.08860090958707, 1.46376090402458, -1.63651904412782, -5.14544903851677],
		[0.045, 1, -5.08769309298962, 1.46330887241671, -1.63584141255851, -5.14427091933207],
		[0.046, 1, -5.08678527639217, 1.46285684080884, -1.63516378098920, -5.14309280014737],
		[0.047, 1, -5.08587745979471, 1.46240480920098, -1.63448614941989, -5.14191468096267],
		[0.048, 1, -5.08496964319726, 1.46195277759311, -1.63380851785058, -5.14073656177797],
		[0.049, 1, -5.08406182659981, 1.46150074598525, -1.63313088628127, -5.13955844259327],
		[0.05, 1, -5.08315401000236, 1.46104871437738, -1.63245325471196, -5.13838032340857],
		[0.051, 1, -5.08224619340491, 1.46059668276952, -1.63177562314265, -5.13720220422387],
		[0.052, 1, -5.08133837680746, 1.46014465116165, -1.63109799157334, -5.13602408503917],
		[0.053, 1, -5.08043056021, 1.45969261955378, -1.63042036000403, -5.13484596585448],
		[0.054, 1, -5.07952274361255, 1.45924058794592, -1.62974272843472, -5.13366784666978],
		[0.055, 1, -5.0786149270151, 1.45878855633805, -1.62906509686541, -5.13248972748508],
		[0.056, 1, -5.07770711041765, 1.45833652473019, -1.6283874652961, -5.13131160830038],
		[0.057, 1, -5.07679929382019, 1.45788449312232, -1.62770983372679, -5.13013348911568],
		[0.058, 1, -5.07589147722275, 1.45743246151446, -1.62703220215748, -5.12895536993098],
		[0.059, 1, -5.07498366062529, 1.45698042990659, -1.62635457058817, -5.12777725074628],
		[0.06, 1, -5.07407584402784, 1.45652839829872, -1.62567693901886, -5.12659913156158],
		[0.061, 1, -5.07316802743039, 1.45607636669086, -1.62499930744955, -5.12542101237688],
		[0.062, 1, -5.07226021083294, 1.45562433508299, -1.62432167588024, -5.12424289319218],
		[0.063, 1, -5.07135239423548, 1.45517230347513, -1.62364404431094, -5.12306477400748],
		[0.064, 1, -5.07044457763803, 1.45472027186726, -1.62296641274163, -5.12188665482279],
		[0.065, 1, -5.06953676104058, 1.45426824025940, -1.62228878117232, -5.12070853563809],
		[0.066, 1, -5.06862894444313, 1.45381620865153, -1.62161114960301, -5.11953041645339],
		[0.067, 1, -5.06772112784568, 1.45336417704366, -1.62093351803370, -5.11835229726869],
		[0.068, 1, -5.06681331124822, 1.4529121454358, -1.62025588646439, -5.11717417808399],
		[0.069, 1, -5.06590549465077, 1.45246011382793, -1.61957825489508, -5.11599605889929],
		[0.07, 1, -5.06499767805332, 1.45200808222007, -1.61890062332577, -5.11481793971459],
		[0.071, 1, -5.06408986145587, 1.45155605061220, -1.61822299175646, -5.11363982052989],
		[0.072, 1, -5.06318204485842, 1.45110401900434, -1.61754536018715, -5.11246170134519],
		[0.073, 1, -5.06227422826097, 1.45065198739647, -1.61686772861784, -5.11128358216049],
		[0.074, 1, -5.06136641166351, 1.45019995578861, -1.61619009704853, -5.11010546297579],
		[0.075, 1, -5.06045859506606, 1.44974792418074, -1.61551246547922, -5.10892734379109],
		[0.076, 1, -5.05955077846861, 1.44929589257287, -1.61483483390991, -5.1077492246064],
		[0.077, 1, -5.05864296187116, 1.44884386096501, -1.61415720234060, -5.1065711054217],
		[0.078, 1, -5.0577351452737, 1.44839182935714, -1.61347957077129, -5.105392986237],
		[0.079, 1, -5.05682732867625, 1.44793979774928, -1.61280193920198, -5.1042148670523],
		[0.08, 1, -5.0559195120788, 1.44748776614141, -1.61212430763267, -5.1030367478676],
		[0.081, 1, -5.05501169548135, 1.44703573453355, -1.61144667606337, -5.1018586286829],
		[0.082, 1, -5.0541038788839, 1.44658370292568, -1.61076904449406, -5.1006805094982],
		[0.083, 1, -5.05319606228645, 1.44613167131781, -1.61009141292475, -5.0995023903135],
		[0.084, 1, -5.052288245689, 1.44567963970995, -1.60941378135544, -5.0983242711288],
		[0.085, 1, -5.05138042909154, 1.44522760810208, -1.60873614978613, -5.0971461519441],
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		[9.941, 1, -3.94606432981057, 2.64820555294616, -3.58391284881699, 6.51439653245049],
		[9.942, 1, -3.94697214640801, 2.64865758455402, -3.5845904803863, 6.51557465163519],
		[9.943, 1, -3.94787996300547, 2.64910961616189, -3.58526811195561, 6.51675277081989],
		[9.944, 1, -3.94878777960292, 2.64956164776975, -3.58594574352492, 6.51793089000459],
		[9.945, 1, -3.94969559620036, 2.65001367937761, -3.58662337509423, 6.51910900918929],
		[9.946, 1, -3.95060341279783, 2.65046571098549, -3.58730100666354, 6.52028712837398],
		[9.947, 1, -3.95151122939528, 2.65091774259335, -3.58797863823285, 6.52146524755868],
		[9.948, 1, -3.95241904599272, 2.65136977420121, -3.58865626980216, 6.52264336674338],
		[9.949, 1, -3.95332686259018, 2.65182180580909, -3.58933390137147, 6.52382148592808],
		[9.95, 1, -3.95423467918763, 2.65227383741695, -3.59001153294077, 6.52499960511278],
		[9.951, 1, -3.95514249578508, 2.65272586902481, -3.59068916451008, 6.52617772429748],
		[9.952, 1, -3.95605031238253, 2.65317790063268, -3.59136679607939, 6.52735584348218],
		[9.953, 1, -3.95695812897998, 2.65362993224053, -3.5920444276487, 6.52853396266688],
		[9.954, 1, -3.95786594557743, 2.6540819638484, -3.59272205921801, 6.52971208185158],
		[9.955, 1, -3.95877376217489, 2.65453399545628, -3.59339969078732, 6.53089020103628],
		[9.956, 1, -3.95968157877234, 2.65498602706414, -3.59407732235663, 6.53206832022097],
		[9.957, 1, -3.96058939536978, 2.65543805867200, -3.59475495392594, 6.53324643940567],
		[9.958, 1, -3.96149721196725, 2.65589009027987, -3.59543258549525, 6.53442455859037],
		[9.959, 1, -3.96240502856469, 2.65634212188773, -3.59611021706456, 6.53560267777507],
		[9.96, 1, -3.96331284516214, 2.6567941534956, -3.59678784863387, 6.53678079695977],
		[9.961, 1, -3.9642206617596, 2.65724618510347, -3.59746548020318, 6.53795891614447],
		[9.962, 1, -3.96512847835705, 2.65769821671133, -3.59814311177249, 6.53913703532917],
		[9.963, 1, -3.9660362949545, 2.65815024831919, -3.5988207433418, 6.54031515451387],
		[9.964, 1, -3.96694411155196, 2.65860227992706, -3.59949837491111, 6.54149327369857],
		[9.965, 1, -3.9678519281494, 2.65905431153493, -3.60017600648042, 6.54267139288327],
		[9.966, 1, -3.96875974474685, 2.65950634314279, -3.60085363804973, 6.54384951206797],
		[9.967, 1, -3.96966756134431, 2.65995837475066, -3.60153126961904, 6.54502763125267],
		[9.968, 1, -3.97057537794175, 2.66041040635852, -3.60220890118834, 6.54620575043736],
		[9.969, 1, -3.97148319453922, 2.6608624379664, -3.60288653275765, 6.54738386962206],
		[9.97, 1, -3.97239101113667, 2.66131446957427, -3.60356416432696, 6.54856198880676],
		[9.971, 1, -3.97329882773411, 2.66176650118212, -3.60424179589627, 6.54974010799146],
		[9.972, 1, -3.97420664433157, 2.66221853279000, -3.60491942746558, 6.55091822717616],
		[9.973, 1, -3.97511446092902, 2.66267056439785, -3.60559705903489, 6.55209634636086],
		[9.974, 1, -3.97602227752647, 2.66312259600571, -3.6062746906042, 6.55327446554556],
		[9.975, 1, -3.97693009412393, 2.66357462761359, -3.60695232217351, 6.55445258473026],
		[9.976, 1, -3.97783791072138, 2.66402665922145, -3.60762995374282, 6.55563070391496],
		[9.977, 1, -3.97874572731882, 2.66447869082931, -3.60830758531213, 6.55680882309966],
		[9.978, 1, -3.97965354391629, 2.66493072243719, -3.60898521688144, 6.55798694228436],
		[9.979, 1, -3.98056136051374, 2.66538275404505, -3.60966284845075, 6.55916506146906],
		[9.98, 1, -3.98146917711118, 2.66583478565291, -3.61034048002006, 6.56034318065375],
		[9.981, 1, -3.98237699370864, 2.66628681726079, -3.61101811158937, 6.56152129983845],
		[9.982, 1, -3.98328481030609, 2.66673884886865, -3.61169574315868, 6.56269941902315],
		[9.983, 1, -3.98419262690354, 2.6671908804765, -3.61237337472799, 6.56387753820785],
		[9.984, 1, -3.985100443501, 2.66764291208438, -3.6130510062973, 6.56505565739255],
		[9.985, 1, -3.98600826009844, 2.66809494369224, -3.61372863786661, 6.56623377657725],
		[9.986, 1, -3.98691607669589, 2.6685469753001, -3.61440626943592, 6.56741189576195],
		[9.987, 1, -3.98782389329335, 2.66899900690797, -3.61508390100522, 6.56859001494665],
		[9.988, 1, -3.98873170989079, 2.66945103851583, -3.61576153257453, 6.56976813413135],
		[9.989, 1, -3.98963952648825, 2.66990307012370, -3.61643916414384, 6.57094625331605],
		[9.99, 1, -3.99054734308571, 2.67035510173157, -3.61711679571315, 6.57212437250075],
		[9.991, 1, -3.99145515968315, 2.67080713333943, -3.61779442728246, 6.57330249168544],
		[9.992, 1, -3.9923629762806, 2.67125916494730, -3.61847205885177, 6.57448061087015],
		[9.993, 1, -3.99327079287806, 2.67171119655517, -3.61914969042108, 6.57565873005484],
		[9.994, 1, -3.99417860947551, 2.67216322816302, -3.61982732199039, 6.57683684923954],
		[9.995, 1, -3.99508642607296, 2.67261525977089, -3.6205049535597, 6.57801496842424],
		[9.996, 1, -3.99599424267042, 2.67306729137877, -3.62118258512901, 6.57919308760894],
		[9.997, 1, -3.99690205926786, 2.67351932298662, -3.62186021669832, 6.58037120679364],
		[9.998, 1, -3.99780987586532, 2.67397135459450, -3.62253784826763, 6.58154932597834],
		[9.999, 1, -3.99871769246277, 2.67442338620237, -3.62321547983694, 6.58272744516304],
		[10, 1, -3.99962550906022, 2.67487541781022, -3.62389311140625, 6.58390556434774],
	);

# In the matrix provided, this was the first line. We're just going to return those values [0, 10, .001],

	return (0, 10, 0.001, \@matrix);
}



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