1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
#!/usr/bin/perl
use strict;
use warnings;
use utf8;
use Math::Trig;
my ($file, $mode) = @ARGV;
defined($file) or die "USAGE: $0 filename [mode]\n";
defined($mode) or $mode = "";
my $obs = ($mode eq "") ? "<Q1|c|Q0>" : "<Q0|c'|Q1>";
my $label1 = "site $obs time";
my @cdaggerI = loadVector($file, $label1);
my $sites = scalar(@cdaggerI);
my $label2 = "<Q0|c;c'|Q0>";
my @cIcDaggerJ = loadMatrix($file, $label2, $mode);
for (my $mForK = 0; $mForK < $sites; ++$mForK) {
doOneMomentumK($mForK, $sites, \@cdaggerI, \@cIcDaggerJ);
}
sub doOneMomentumK
{
my ($mForK, $sites, $cdaggerI, $cIcDaggerJ) = @_;
my $momentumK = findMomentumK($mForK, $sites);
my @numerator = ftVector($cdaggerI, $momentumK);
#print STDERR "$0: numerator= @numerator\n";
my @den = ftMatrix($cIcDaggerJ, $momentumK);
#print STDERR "$0: denominator= @den\n";
die "$0: Denominator isn't real\n" if (abs($den[1]) > 1e-5);
print $mForK." ";
if ($mode eq "") {
$_ = $numerator[0]*$numerator[0] + $numerator[1]*$numerator[1];
print "$_\n";
} else {
print $numerator[0]/$den[0]." ".$numerator[1]/$den[0]."\n";
}
}
sub ftMatrix
{
my ($a, $momentumK) = @_;
my $n = scalar(@$a);
return (1, 0) if ($n == 0);
my $center = $n/2;
my ($sumR, $sumI) = (0, 0);
for (my $i = 0; $i < $n; ++$i) {
my $ptr = $a->[$i];
my $m = scalar(@$ptr);
($n == $m) or die "$0: Matrix not square\n";
for (my $j = 0; $j < $m; ++$j) {
my $arg = $momentumK*($i - $j);
my $value = ($i < $j) ? $a->[$i]->[$j] : $a->[$j]->[$i];
$sumR += $value*cos($arg);
$sumI += $value*sin($arg);
}
}
return ($sumR, $sumI);
}
sub ftVector
{
my ($a, $momentumK) = @_;
my $n = scalar(@$a);
my $center = $n/2;
my ($sumR, $sumI) = (0, 0);
for (my $i = 0; $i < $n; ++$i) {
my $arg = $momentumK*($i - $center);
my $value = $a->[$i];
$sumR += $value*cos($arg);
$sumI += $value*sin($arg);
}
return ($sumR, $sumI);
}
sub loadVector
{
my ($file, $label) = @_;
open(FILE, "<", $file) or die "$0: Cannot open $file : $!\n";
while (<FILE>) {
last if (/^\Q$label/);
}
my @a;
while (<FILE>) {
chomp;
next if (/^#/);
my @temp = split;
last if (scalar(@temp) != 3);
last unless ($temp[0] =~ /^\d+$/);
$a[$temp[0]] = $temp[1];
}
close(FILE);
print STDERR "$0: Found ".scalar(@a)." sites for \"$label\" in $file\n";
return @a;
}
sub loadMatrix
{
my ($file, $label, $mode) = @_;
return () if ($mode eq "");
open(FILE, "<", $file) or die "$0: Cannot open $file : $!\n";
while (<FILE>) {
last if (/^\Q$label/);
}
$_ = <FILE>;
chomp;
my @sizes = split;
die "$0: No matrix dimensions found for $label in $file\n" unless (scalar(@sizes) == 2);
my @a;
my ($rows, $cols) = @sizes;
for (my $i = 0; $i < $rows; ++$i) {
$_ = <FILE>;
chomp;
next if (/^#/);
my @temp = split;
(scalar(@temp) == $cols) or die "$0: row $i not with $cols columns\n";
$a[$i] = \@temp;
}
close(FILE);
print STDERR "$0: Found matrix with ".scalar(@a)." rows for \"$label\" in $file\n";
return @a;
}
sub findMomentumK
{
my ($m, $total) = @_;
return 2*pi*$m/$total;
}
|
