さまざまな言語で数値計算
Only Do What Only You Can Do
ヤコビの反復法
ヤコビの反復法を使って, 連立一次方程式の解を求める .
例として, 連立一次方程式
を考える.
この方程式を上から順に対角線上の変数について解くと
となる.
$x,y,z,u$ に適当な値を入れて右辺を計算し,
得られた値を新たな $x,y,z,u$ として計算を繰り返す.
漸化式で書くと
VBScript
Option Explicit Private Const N = 4 Private a: a = Array(Array(9,2,1,1),Array(2,8,-2,1),Array(-1,-2,7,-2),Array(1,-1,-2,6)) Private b: b = Array(20,16,8,17) Private c: c = Array(0,0,0,0) 'ヤコビの反復法 jacobi a,b,c WScript.StdOut.WriteLine "X" disp_vector c 'ヤコビの反復法 Private Sub jacobi(ByVal a, ByVal b, ByRef x0) Do While(True) Dim x1: x1 = Array(0,0,0,0) Dim finish: finish = True Dim i, j For i = 0 To (N - 1) x1(i) = 0 For j = 0 To (N - 1) If i <> j Then x1(i) = x1(i) + a(i)(j) * x0(j) End If Next x1(i) = (b(i) - x1(i)) / a(i)(i) If (Abs(x1(i) - x0(i)) > 0.0000000001) Then finish = False End If Next For i = 0 To (N - 1) x0(i) = x1(i) Next If (finish) Then Exit Sub End If disp_vector x0 Loop End Sub '１次元配列を表示 Private Sub disp_vector(ByVal row()) Dim col For Each col In row WScript.StdOut.Write Right(Space(14) & FormatNumber(col, 10, -1, 0, 0), 14) & vbTab Next WScript.StdOut.WriteLine End Sub
Z:\>cscript //nologo Z:\1001.vbs 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
JScript
var N = 4 var a = [[9,2,1,1],[2,8,-2,1],[-1,-2,7,-2],[1,-1,-2,6]] var b = [20,16,8,17] var c = [0,0,0,0] // ヤコビの反復法 jacobi(a,b,c) WScript.StdOut.WriteLine("X") disp_vector(c) // ヤコビの反復法 function jacobi(a, b, x0) { while (true) { x1 = [] var finish = true for (i = 0; i < N; i++) { x1[i] = 0 for (j = 0; j < N; j++) if (j != i) x1[i] += a[i][j] * x0[j] x1[i] = (b[i] - x1[i]) / a[i][i] if (Math.abs(x1[i] - x0[i]) > 0.0000000001) finish = false } for (i = 0; i < N; i++) x0[i] = x1[i] if (finish) return disp_vector(x0) } } // １次元配列を表示 function disp_vector(row) { for (var i = 0; i < N; i++) WScript.StdOut.Write((" " + row[i].toFixed(10)).slice(-14) + "\t") WScript.StdOut.WriteLine() }
Z:\>cscript //nologo Z:\1001.js 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
PowerShell
set-variable -name N -value 3 -option constant # １次元配列を表示 function disp_vector($row) { foreach ($col in $row) { Write-Host ([String]::Format("{0,14:F10}", $col)) -nonewline } Write-Host } # ヤコビの反復法 function jacobi($a, $b, $x0) { while ($true) { $x1 = 0.0, 0.0, 0.0, 0.0 $finish = $true foreach ($i in 0..$N) { $x1[$i] = 0 foreach ($j in 0..$N) { if ($j -ne $i) { $x1[$i] += $a[$i][$j] * $x0[$j] } } $x1[$i] = ($b[$i] - $x1[$i]) / $a[$i][$i] if ([Math]::Abs($x1[$i] - $x0[$i]) -gt 0.0000000001) { $finish = $false } } foreach ($i in 0..$N) { $x0[$i] = $x1[$i] } if ($finish) { return } disp_vector $x0 } } $a = (9.0,2.0,1.0,1.0), (2.0,8.0,-2.0,1.0), (-1.0,-2.0,7.0,-2.0), (1.0,-1.0,-2.0,6.0) $b = 20.0, 16.0, 8.0, 17.0 $c = 0.0, 0.0, 0.0, 0.0 # ヤコビの反復法 jacobi $a $b $c Write-Host "X" disp_vector $c
Z:\>powershell -file Z:\1001.ps1 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Perl
use constant N => 3; my @a = ([9,2,1,1],[2,8,-2,1],[-1,-2,7,-2],[1,-1,-2,6]); my @b = (20,16,8,17); my @c = (0,0,0,0); # ヤコビの反復法 jacobi(\@a, \@b, \@c); print "X\n"; disp_vector(\@c); # ヤコビの反復法 sub jacobi { my ($a, $b, $x0) = @_; while (1) { my @x1 = (); my $finish = 1; for $i (0..N) { $x1[$i] = 0; for $j (0..N) { if ($j != $i) { $x1[$i] += $$a[$i][$j] * $$x0[$j]; } } $x1[$i] = ($$b[$i] - $x1[$i]) / $$a[$i][$i]; $finish = 0 if (abs($x1[$i] - $$x0[$i]) > 0.0000000001) } for $i (0..N) { $$x0[$i] = $x1[$i]; } return if ($finish); disp_vector($x0); } } # １次元配列を表示 sub disp_vector { my ($row) = @_; foreach $col (@$row) { printf("%14.10f\t", $col); } print "\n"; }
Z:\>perl Z:\1001.pl 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
PHP
<?php define("N", 3); $a = [[9,2,1,1],[2,8,-2,1],[-1,-2,7,-2],[1,-1,-2,6]]; $b = [20,16,8,17]; $c = [0,0,0,0]; # ヤコビの反復法 jacobi($a, $b, $c); print "X\n"; disp_vector($c); # ヤコビの反復法 function jacobi($a, $b, &$x0) { while (true) { $x1 = array(); $finish = true; foreach (range(0, N) as $i) { $x1[$i] = 0; foreach (range(0, N) as $j) { if ($j != $i) $x1[$i] += $a[$i][$j] * $x0[$j]; } $x1[$i] = ($b[$i] - $x1[$i]) / $a[$i][$i]; if (abs($x1[$i] - $x0[$i]) > 0.0000000001) $finish = false; } foreach (range(0, N) as $i) { $x0[$i] = $x1[$i]; } if ($finish) return; disp_vector($x0); } } # １次元配列を表示 function disp_vector($row) { foreach ($row as $col) printf("%14.10f\t", $col); print "\n"; } ?>
Z:\>php Z:\1001.php 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Python
# coding: Shift_JIS N = 4 # １次元配列を表示 def disp_vector(row): for col in row: print "%14.10f\t" % col, print "" # ヤコビの反復法 def jacobi(a, b, x0): while True: x1 = range(N) finish = True for i in range(0, N, 1): x1[i] = 0 for j in range(0, N, 1): if (j != i): x1[i] += a[i][j] * x0[j] x1[i] = (b[i] - x1[i]) / a[i][i] if (abs(x1[i] - x0[i]) > 0.0000000001): finish = False for i in range(0, N, 1): x0[i] = x1[i] if (finish): return disp_vector(x0) a = [[ 9.0, 2.0, 1.0, 1.0], [2.0, 8.0, -2.0, 1.0], [-1.0, -2.0, 7.0, -2.0], [1.0, -1.0, -2.0, 6.0]] b = [20.0, 16.0, 8.0, 17.0] c = [ 0.0, 0.0, 0.0, 0.0] # ヤコビの反復法 jacobi(a,b,c) print "X" disp_vector(c)
Z:\>python Z:\1001.py 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Ruby
# coding: Shift_JIS N = 3 # １次元配列を表示 def disp_vector(row) row.each do |col| printf("%14.10f\t", col) end puts "" end # ヤコビの反復法 def jacobi(a, b, x0) while true x1 = [] finish = true (0..N).each do |i| x1[i] = 0 (0..N).each do |j| if (j != i) x1[i] += a[i][j] * x0[j] end end x1[i] = (b[i] - x1[i]) / a[i][i] if ((x1[i] - x0[i]).abs > 0.0000000001) finish = false end end (0..N).each do |i| x0[i] = x1[i] end return if finish disp_vector(x0) end end a = [[ 9.0, 2.0, 1.0, 1.0], [2.0, 8.0, -2.0, 1.0], [-1.0, -2.0, 7.0, -2.0], [1.0, -1.0, -2.0, 6.0]] b = [20.0, 16.0, 8.0, 17.0] c = [ 0.0, 0.0, 0.0, 0.0] # ヤコビの反復法 jacobi(a,b,c) puts "X" disp_vector(c)
Z:\>ruby Z:\1001.rb 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Groovy
N = 3 def a = [[ 9.0, 2.0, 1.0, 1.0], [2.0, 8.0, -2.0, 1.0], [-1.0, -2.0, 7.0, -2.0], [1.0, -1.0, -2.0, 6.0]] as double[][] def b = [20.0, 16.0, 8.0, 17.0] as double[] def c = [ 0.0, 0.0, 0.0, 0.0] as double[] // ヤコビの反復法 jacobi(a,b,c) println("X") disp_vector(c) // ヤコビの反復法 def jacobi(a, b, x0) { def x1 = [ 0.0, 0.0, 0.0, 0.0] as double[] while (true) { def finish = true for (i in 0..N ) { x1[i] = 0 for (j in 0..N ) { if (j != i) x1[i] += a[i][j] * x0[j] } x1[i] = (b[i] - x1[i]) / a[i][i] if (Math.abs(x1[i] - x0[i]) > 0.0000000001) finish = false } for (i in 0..N ) x0[i] = x1[i] if (finish) return disp_vector(x0) } } // １次元配列を表示 def disp_vector(row) { for (col in row) printf ("%14.10f\t" , col) println() }
Z:\>groovy Groovy1001.groovy 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Pascal
program Pas1001(arg); {$MODE delphi} uses SysUtils, Math; const N = 3; type TwoDimArray = array [0..N,0..N] of Double; // １次元配列を表示 procedure disp_vector(row:array of Double); var i:Integer; begin for i := Low(row) to High(row) do write(format('%14.10f'#9, [row[i]])); writeln(); end; // ヤコビの反復法 procedure jacobi(a:TwoDimArray; b:array of Double; var x0:array of Double); var x1:array [0..N] of Double = (0.0, 0.0, 0.0, 0.0); finish:Boolean; i, j:Integer; begin while (true) do begin finish := true; for i := Low(x0) to High(x0) do begin x1[i] := 0.0; for j := Low(x0) to High(x0) do if j <> i then x1[i] := x1[i] + a[i,j] * x0[j]; x1[i] := (b[i] - x1[i]) / a[i,i]; if (Abs(x1[i] - x0[i]) > 0.0000000001) then finish := false; end; for i := Low(x0) to High(x0) do x0[i] := x1[i]; if finish then exit; disp_vector(x0); end; end; var a:TwoDimArray = (( 9.0, 2.0, 1.0, 1.0), (2.0, 8.0, -2.0, 1.0), (-1.0, -2.0, 7.0, -2.0), (1.0, -1.0, -2.0, 6.0)); b:array [0..N] of Double = (20.0, 16.0, 8.0, 17.0); c:array [0..N] of Double = ( 0.0, 0.0, 0.0, 0.0); begin // ヤコビの反復法 jacobi(a,b,c); writeln('X'); disp_vector(c); end.
Z:\>fpc -v0 -l- Pas1001.pp Z:\>Pas1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Ada
with TEXT_IO, Ada.Long_Float_Text_IO; use TEXT_IO, Ada.Long_Float_Text_IO; procedure Ada1001 is N:Constant Integer := 3; type Long_Float_Array is array (0..N) of Long_Float; type Long_Float_TwoDimArray is array (0..N, 0..N) of Long_Float; a:Long_Float_TwoDimArray := (( 9.0, 2.0, 1.0, 1.0), (2.0, 8.0, -2.0, 1.0), (-1.0, -2.0, 7.0, -2.0), (1.0, -1.0, -2.0, 6.0)); b:Long_Float_Array := (20.0, 16.0, 8.0, 17.0); c:Long_Float_Array := ( 0.0, 0.0, 0.0, 0.0); -- １次元配列を表示 procedure disp_vector(row:Long_Float_Array) is begin for i in row'Range loop Put(row(i), Fore=>3, Aft=>10, Exp=>0); Put(Ascii.HT); end loop; New_Line; end disp_vector; -- ヤコビの反復法 procedure jacobi(a:Long_Float_TwoDimArray; b:Long_Float_Array; x0:in out Long_Float_Array) is x1:Long_Float_Array := ( 0.0, 0.0, 0.0, 0.0); finish:Boolean; begin while true loop finish := true; for i in x0'Range loop x1(i) := 0.0; for j in x0'Range loop if j /= i then x1(i) := x1(i) + a(i,j) * x0(j); end if; end loop; x1(i) := (b(i) - x1(i)) / a(i,i); if (Abs(x1(i) - x0(i)) > 0.0000000001) then finish := false; end if; end loop; for i in x0'Range loop x0(i) := x1(i); end loop; if finish then exit; end if; disp_vector(x0); end loop; end jacobi; begin -- ヤコビの反復法 jacobi(a,b,c); Put_Line("X"); disp_vector(c); end Ada1001;
xxxxxx@yyyyyy /Z $ gnatmake Ada1001.adb xxxxxx@yyyyyy /Z $ Ada1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
VB.NET
Option Explicit Module VB1001 Private Const N As Integer = 3 Public Sub Main() Dim a(,) As Double = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}} Dim b() As Double = {20,16,8,17} Dim c() As Double = {0,0,0,0} 'ヤコビの反復法 jacobi(a,b,c) Console.WriteLine("X") disp_vector(c) End Sub '１次元配列の表示 Private Sub disp_vector(ByVal row() As Double) For Each col As Double In row Console.Write(String.Format("{0,14:F10}{1}", col, vbTab)) Next Console.WriteLine() End Sub 'ヤコビの反復法 Private Sub jacobi(ByVal a(,) As Double, ByVal b() As Double, ByVal x0() As Double) Do While(True) Dim x1() As Double = {0,0,0,0} Dim finish As Boolean = True For i As Integer = 0 To N x1(i) = 0 For j As Integer = 0 To N If j <> i Then x1(i) += a(i,j) * x0(j) End If Next x1(i) = (b(i) - x1(i)) / a(i,i) If (Math.Abs(x1(i) - x0(i)) > 0.0000000001) Then finish = False Next For i As Integer = 0 To N x0(i) = x1(i) Next If finish Then Return disp_vector(x0) Loop End Sub End Module
Z:\>vbc -nologo VB1001.vb Z:\>VB1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
C#
using System; public class CS1001 { private const int N = 4; public static void Main() { double[,] a = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}}; double[] b = {20,16,8,17}; double[] c = {0,0,0,0}; // ヤコビの反復法 jacobi(a,b,c); Console.WriteLine("X"); disp_vector(c); } // ヤコビの反復法 private static void jacobi(double[,] a, double[] b, double[] x0) { while (true) { double[] x1 = new double[N]; bool finish = true; for (int i = 0; i < N; i++) { x1[i] = 0; for (int j = 0; j < N; j++) if (j != i) x1[i] += a[i,j] * x0[j]; x1[i] = (b[i] - x1[i]) / a[i,i]; if (Math.Abs(x1[i] - x0[i]) > 0.0000000001) finish = false; } for (int i = 0; i < N; i++) x0[i] = x1[i]; if (finish) return; disp_vector(x0); } } // １次元配列を表示 private static void disp_vector(double[] row) { foreach (double col in row) Console.Write(string.Format("{0,14:F10}\t", col)); Console.WriteLine(); } }
Z:\>csc -nologo CS1001.cs Z:\>CS1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Java
import java.lang.*; public class Java1001 { private static final int N = 4; public static void main(String []args) { double[][] a = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}}; double[] b = {20,16,8,17}; double[] c = {0,0,0,0}; // ヤコビの反復法 jacobi(a,b,c); System.out.println("X"); disp_vector(c); } // ヤコビの反復法 private static void jacobi(double[][] a, double[] b, double[] x0) { while (true) { double[] x1 = new double[N]; boolean finish = true; for (int i = 0; i < N; i++) { x1[i] = 0; for (int j = 0; j < N; j++) if (j != i) x1[i] += a[i][j] * x0[j]; x1[i] = (b[i] - x1[i]) / a[i][i]; if (Math.abs(x1[i] - x0[i]) > 0.0000000001) finish = false; } for (int i = 0; i < N; i++) x0[i] = x1[i]; if (finish) return; disp_vector(x0); } } // １次元配列を表示 private static void disp_vector(double[] row) { for (double col: row) System.out.print(String.format("%14.10f\t", col)); System.out.println(); } }
Z:\>javac Java1001.java Z:\>java Java1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
C++
#include <iostream> #include <iomanip> #include <math.h> using namespace std; const int N = 4; // ヤコビの反復法 void jacobi(double a[N][N], double b[N], double c[N]); // １次元配列を表示 void disp_vector(double row[N]); int main() { double a[N][N] = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}}; double b[N] = {20,16,8,17}; double c[N] = {0,0,0,0}; // ヤコビの反復法 jacobi(a,b,c); cout << "X" << endl; disp_vector(c); return 0; } // ヤコビの反復法 void jacobi(double a[N][N], double b[N], double x0[N]) { while (true) { double x1[N]; bool finish = true; for (int i = 0; i < N; i++) { x1[i] = 0; for (int j = 0; j < N; j++) if (j != i) x1[i] += a[i][j] * x0[j]; x1[i] = (b[i] - x1[i]) / a[i][i]; if (fabs(x1[i] - x0[i]) > 0.0000000001) finish = false; } for (int i = 0; i < N; i++) x0[i] = x1[i]; if (finish) return; disp_vector(x0); } } // １次元配列を表示 void disp_vector(double row[N]) { for (int i = 0; i < N; i++) cout << setw(14) << fixed << setprecision(10) << row[i] << "\t"; cout << endl; }
Z:\>bcc32 -q CP1001.cpp cp1001.cpp: Z:\>CP1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Objective-C
#import <Foundation/Foundation.h> #import <math.h> const int N = 4; // ヤコビの反復法 void jacobi(double a[N][N], double b[N], double c[N]); // １次元配列を表示 void disp_vector(double row[N]); int main() { double a[4][4] = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}}; double b[4] = {20,16,8,17}; double c[4] = {0,0,0,0}; // ヤコビの反復法 jacobi(a,b,c); printf("X\n"); disp_vector(c); return 0; } // ヤコビの反復法 void jacobi(double a[N][N], double b[N], double x0[N]) { while (YES) { double x1[N]; BOOL finish = YES; int i, j; for (i = 0; i < N; i++) { x1[i] = 0; for (j = 0; j < N; j++) if (j != i) x1[i] += a[i][j] * x0[j]; x1[i] = (b[i] - x1[i]) / a[i][i]; if (fabs(x1[i] - x0[i]) > 0.0000000001) finish = NO; } for (i = 0; i < N; i++) { x0[i] = x1[i]; } if (finish) return; disp_vector(x0); } } // １次元配列を表示 void disp_vector(double row[N]) { int i; for (i = 0; i < N; i++) { printf("%14.10f\t", row[i]); } printf("\n"); }
xxxxxx@yyyyyy /Z $ gcc -o OC1001 OC1001.m -lobjc -lgnustep-base -I $INCLUDE -L $LIB $CFLAGS xxxxxx@yyyyyy /Z $ OC1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
D
import std.stdio; import std.math; const int N = 4; void main(string[] args) { double[N][N] a = [[9,2,1,1],[2,8,-2,1],[-1,-2,7,-2],[1,-1,-2,6]]; double[N] b = [20,16,8,17]; double[N] c = [0,0,0,0]; // ヤコビの反復法 jacobi(a,b,c); writefln("X"); disp_vector(c); } // ヤコビの反復法 void jacobi(double[N][N] a, double[N] b, ref double[N] x0) { while (true) { double[N] x1; bool finish = true; foreach(i; 0..N) { x1[i] = b[i]; foreach(j; 0..N) if (j != i) x1[i] -= a[i][j] * x0[j]; x1[i] /= a[i][i]; if (fabs(x1[i] - x0[i]) > 0.0000000001) finish = false; } foreach(i; 0..N) x0[i] = x1[i]; if (finish) return; disp_vector(x0); } } // １次元配列を表示 void disp_vector(double[] row) { foreach(col; row) writef("%14.10f\t", col); writefln(""); }
Z:\>dmd D1001.d Z:\>D1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Go
package main import "fmt" import "math" const N = 4 func main() { var a [N][N]float64 = [N][N]float64{{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}} var b = []float64{20,16,8,17} var c = []float64{0,0,0,0} // ヤコビの反復法 jacobi(a,b,c) fmt.Println("X") disp_vector(c) } // ヤコビの反復法 func jacobi(a[N][N]float64, b[]float64, x0[]float64) { for { var x1 = []float64{0,0,0,0} var finish = true for i := 0; i < N; i++ { x1[i] = b[i] for j := 0; j < N; j++ { if (j != i) { x1[i] -= a[i][j] * x0[j] } } x1[i] /= a[i][i] if (math.Fabs(x1[i] - x0[i]) > 0.0000000001) { finish = false } } for i := 0; i < N; i++ { x0[i] = x1[i] } if (finish) { return } disp_vector(x0) } } // １次元配列を表示 func disp_vector(row[]float64) { for _, col := range row { fmt.Printf("%14.10f\t", col) } fmt.Println("") }
Z:\>8g GO1001.go Z:\>8l -o GO1001.exe GO1001.8 Z:\>GO1001 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Scala
object Scala1001 { val N = 3 def main(args: Array[String]) { var a:Array[Array[Double]] = Array(Array(9,2,1,1),Array(2,8,-2,1),Array(-1,-2,7,-2),Array(1,-1,-2,6)) var b:Array[Double] = Array(20,16,8,17) var c:Array[Double] = Array(0,0,0,0) // ヤコビの反復法 jacobi(a,b,c) println("X") disp_vector(c) } // ヤコビの反復法 def jacobi(a:Array[Array[Double]], b:Array[Double], x0:Array[Double]) = { var finish:Boolean = false while (!finish) { var x1:Array[Double] = Array(0,0,0,0) finish = true for (i <- 0 to N) { x1(i) = 0 for (j <- 0 to N) if (j != i) x1(i) += a(i)(j) * x0(j) x1(i) = (b(i) - x1(i)) / a(i)(i) if (Math.abs(x1(i) - x0(i)) > 0.0000000001) finish = false } for (i <- 0 to N) x0(i) = x1(i) if (!finish) disp_vector(x0) } } // １次元配列を表示 def disp_vector(row:Array[Double]) = { row.foreach { col => print("%14.10f\t".format(col)) } println() } }
Z:\>scala Scala1001.scala 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
F#
module Fs1001 open System let N = 3 // １次元配列を表示 let disp_vector (row:float[]) = row |> Array.iter (fun x -> printf "%14.10f" x) printfn "" // ヤコビの反復法 let jacobi (a:float[][]) (b:float[]) (x0:float[]) = let mutable finish:bool = false while not finish do let x1:float[] = [| 0.0;0.0;0.0;0.0 |] finish <- true for i in [0..N] do x1.[i] <- 0.0 for j in [0..N] do if j <> i then x1.[i] <- x1.[i] + a.[i].[j] * x0.[j] x1.[i] <- (b.[i] - x1.[i]) / a.[i].[i] if Math.Abs(x1.[i] - x0.[i]) > 0.0000000001 then finish <- false for i in [0..N] do x0.[i] <- x1.[i] if not finish then disp_vector x0 let a:float[][] = [| [| 9.0;2.0;1.0;1.0 |]; [|2.0;8.0;-2.0;1.0 |]; [|-1.0;-2.0;7.0;-2.0 |]; [|1.0;-1.0;-2.0;6.0 |] |] let b:float[] = [| 20.0;16.0;8.0;17.0 |] let c:float[] = [| 0.0;0.0;0.0;0.0 |] // ヤコビの反復法 jacobi a b c printfn "X" disp_vector c exit 0
Z:\>fsi --nologo --quiet Fs1001.fs 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Clojure
(def N 4) (def a [[9.0 2.0 1.0 1.0] [2.0 8.0 -2.0 1.0] [-1.0 -2.0 7.0 -2.0] [1.0 -1.0 -2.0 6.0]]) (def b [20.0 16.0 8.0 17.0]) (def x0 [0.0 0.0 0.0 0.0]) ;１次元配列を表示 (defn disp_vector [row] (doseq [col row] (print (format "%14.10f\t" col))) (println)) ;２次元配列を表示 (defn disp_matrix [matrix] (doseq [row matrix] (doseq [col row] (print (format "%14.10f\t" col))) (println))) ;ヤコビの反復法 (defn row_loop [row a b x0 x1] (def a1 (map (fn [a b] [a b]) (nth a row) x0)) (def a2 (concat (take row a1) (drop (+ row 1) a1))) (def a3 (map (fn [x] (* (first x) (second x))) a2)) (def s (apply + a3)) (def x (/ (- (nth b row) s) (nth (nth a row) row))) (def xs (cons x x1)) (if (>= row (- N 1)) (reverse xs) (row_loop (inc row) a b x0 xs))) (defn jacobi [a b x0 xs] (def x1 (row_loop 0 a b x0 [])) (def cnt (count (filter (fn [x] (>= x 0.0000000001)) (map (fn [x] (. Math abs (- (first x) (second x)))) (map (fn [a b] [a b]) x0 x1))))) (if (< cnt 1) (vector (reverse xs) x1) (jacobi a b x1 (cons x1 xs)))) ;ヤコビの反復法 (def xs (jacobi a b x0 [])) (disp_matrix (first xs)) (println "X") (disp_vector (second xs))
Z:\>java -cp C:\ProgramFiles\clojure-1.5.1\clojure-1.5.1.jar clojure.main Clj1001.clj 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000
Haskell
import Text.Printf import Control.Monad n = 4::Int -- ２次元配列を表示 disp_matrix::[[Double]]->IO() disp_matrix matrix = do forM_ matrix $ \row -> do forM_ row $ \elem -> do printf "%14.10f\t" elem putStrLn "" -- １次元配列を表示 disp_vector::[Double]->IO() disp_vector vector = do forM_ vector $ \elem -> do printf "%14.10f\t" elem putStrLn "" -- ヤコビの反復法 row_loop::Int->[[Double]]->[Double]->[Double]->[Double]->[Double] row_loop row a b x0 x1 = let a1 = zip (a!!row) x0 a2 = take row a1 ++ drop (row + 1) a1 a3 = map (\(x, y) -> x * y) $ a2 s = sum a3 x = ((b!!row) - s) / a!!row!!row xs = x:x1 in if row >= (n - 1) then reverse xs else (row_loop (row+1) a b x0 xs) jacobi::[[Double]]->[Double]->[Double]->[[Double]]->([[Double]],[Double]) jacobi a b x0 xs = let x1 = (row_loop 0 a b x0 []) cnt = length $ filter (>= 0.0000000001) $ map (\(x,y) -> abs(x - y)) $ zip x0 x1 in if cnt < 1 then (reverse xs, x1) else (jacobi a b x1 (x1:xs)) main = do let a = [[9,2,1,1],[2,8,-2,1],[-1,-2,7,-2],[1,-1,-2,6::Double]] let b = [20,16,8,17::Double] let x0 = [0,0,0,0::Double] -- ヤコビの反復法 let (xs, x1) = jacobi a b x0 [] disp_matrix xs putStrLn "X" disp_vector x1
Z:\>runghc Hs1001.hs 2.2222222222 2.0000000000 1.1428571429 2.8333333333 1.3359788360 1.3759920635 2.8412698413 3.1772486772 1.2477219283 1.9791666667 2.6346371882 3.7870921517 1.0688819252 1.8733422960 2.9686056521 3.8334531858 1.0501396189 1.9957492835 2.9260675555 3.9569452792 1.0139431776 1.9743638243 2.9936469635 3.9662907960 1.0101482880 1.9991395970 2.9850360597 3.9912857623 1.0028221093 1.9948112226 2.9987141438 3.9931772381 1.0020540192 1.9998258539 2.9969712901 3.9982362335 1.0005711965 1.9989497885 2.9997397420 3.9986190691 1.0004157346 1.9999647527 2.9993869874 3.9996430127 1.0001156105 1.9997874366 2.9999473236 3.9997204988 1.0000841449 1.9999928659 2.9998759259 3.9999277456 1.0000233996 1.9999569771 2.9999893383 3.9999434288 1.0000170310 1.9999985561 2.9999748873 3.9999853757 1.0000047361 1.9999912921 2.9999978421 3.9999885500 1.0000034471 1.9999997077 2.9999949172 3.9999970400 1.0000009586 1.9999982375 2.9999995632 3.9999976825 1.0000006977 1.9999999408 2.9999989712 3.9999994009 1.0000001940 1.9999996433 2.9999999116 3.9999995309 1.0000001412 1.9999999880 2.9999997918 3.9999998787 1.0000000393 1.9999999278 2.9999999821 3.9999999051 1.0000000286 1.9999999976 2.9999999579 3.9999999755 1.0000000079 1.9999999854 2.9999999964 3.9999999808 1.0000000058 1.9999999995 2.9999999915 3.9999999950 1.0000000016 1.9999999970 2.9999999993 3.9999999961 1.0000000012 1.9999999999 2.9999999983 3.9999999990 1.0000000003 1.9999999994 2.9999999999 3.9999999992 1.0000000002 2.0000000000 2.9999999997 3.9999999998 1.0000000001 1.9999999999 3.0000000000 3.9999999998 1.0000000000 2.0000000000 2.9999999999 4.0000000000 X 1.0000000000 2.0000000000 3.0000000000 4.0000000000