如何從MatLab上的無理數產生近似分數？

Question

我有一個笨拙的PHP代碼，我用它來得到無理數的近似分數，如pi，phi，2,3的平方根等等。我想獲得一個公式，我可以在MatLab上使用該公式，並獲取數據表並根據近似分數繪製一個圖。也許有人已經可以從這個搶，但我會提供的PHP代碼爲補充的情況下：

$n = phi(); # irrational number (imaginary/complex number?) 
$x = 500; # how many numbers to check 
$max = 50; # how many instances to show 
$precision = 0.0001; 

# check every i against every j and make a comparison how near their values are to each other 
for ($i=1; $i<$x; $i++) { 
    for ($j=1; $j<$x; $j++) { 
     # compared value is stored on array. very distant numbers needs to be discarded ($precision) or array gets easily too big, limit 64k 
     if (($d = abs(($n - ($i/$j)))) && $d > $precision) continue; 
     $c[] = array($i, $j, $d); 
    } 
} 

# sort comparison chart by third index (2) 
array_qsort($c, 2); 

# print max best values from the sorted comparison chart 
$count = count($c); 
echo "closest fraction numbers for $n from $count calculated values are:<br />\n<br />\n"; 
$r = 0; 
foreach ($c as $abc) { 
    $r++; 
    $d = $abc[0]/$abc[1]; 
    echo $abc[0] . '/' . $abc[1] . ' = ' . $d . ' (' . round($abc[2]*(1/$precision), 10) . ')' . "<br />\n"; 
    if ($r > $max) break; 
} 

Answer 1

有更高效的算法，這裏是一個：

function [a, b, c] = approxfrac(r, precision) 
a = floor(r); 
r = r - a; 
if r==0, 
    b=0; 
    c=1; 
    return 
end 
p1 = 0; q1 = 1; 
p2 = 1; q2 = 1; 
b = p1+p2; 
c = q1+q2; 
while abs(r-b/c) > precision, 
    if r>b/c, 
     p1 = b; q1 = c; 
    else 
     p2 = b; q2 = c; 
    end 
    b = p1+p2; 
    c = q1+q2; 
end 
end 

Answer 2

有該功能：rat