determinant of a matrix

[ray]

What is the best way of calculating the determinant of a (square) matrix in APL?

(Take BEST in any way you like!)

Ray Cannon

[JohnS|Dyalog]

See Roger's code in: http://dfns.dyalog.com/n_det.htm

[Roger|Dyalog]

I was curious about how the code in http://dfns.dyalog.com/c_det.htm does on the Hilbert matrix, so I ran a benchmark.

Code: Select all

   H←{÷1+∘.+⍨⍳⍵}    ⍝ Hilbert matrix of order ⍵
   H 5
1        0.5      0.333333 0.25     0.2     
0.5      0.333333 0.25     0.2      0.166667
0.333333 0.25     0.2      0.166667 0.142857
0.25     0.2      0.166667 0.142857 0.125   
0.2      0.166667 0.142857 0.125    0.111111


Now the determinants.

Code: Select all

   )copy dfns det
saved ...
   ¯18 ⍕ ⍪ det∘H¨ ⍳10
 1.000000000000000__E0    1.000000000000000000e0
 1.000000000000000__E0    1.000000000000000000e0 
 8.333333333333331__E¯2   8.333333333333333333e_2
 4.629629629629614__E¯4   4.629629629629629630e_4
 1.653439153439349__E¯7   1.653439153439153439e_7
 3.749295132519431__E¯12  3.749295132515087164e_12
 5.367299886702431__E¯18  5.367299887358687733e_18
 4.835802601799728__E¯25  4.835802623926116932e_25
 2.737050086319325__E¯33  2.737050113791513017e_33
 9.720261264884943__E¯43  9.720234311924999863e_43

On the right hand side I have put the values calculated in J using extended precision (exact) arithmetic.