September 2017 Update

Task/Matrix-arithmetic/Phix/matrix-arithmetic.phix

@@ -0,0 +1,88 @@
+function minor(sequence a, integer x, integer y)
+integer l = length(a)-1
+sequence result = repeat(repeat(0,l),l)
+    for i=1 to l do
+        for j=1 to l do
+            result[i][j] = a[i+(i>=x)][j+(j>=y)]
+        end for
+    end for
+    return result
+end function
+
+function det(sequence a)
+    if length(a)=1 then
+        return a[1][1]
+    end if
+    integer sgn = 1
+    integer res = 0
+    for i=1 to length(a) do
+        res += sgn*a[1][i]*det(minor(a,1,i))
+        sgn *= -1
+    end for
+    return res
+end function
+
+function perm(sequence a)
+    if length(a)=1 then
+        return a[1][1]
+    end if
+    integer res = 0
+    for i=1 to length(a) do
+        res += a[1][i]*perm(minor(a,1,i))
+    end for
+    return res
+end function
+
+constant tests = {
+{{1,  2},
+ {3,  4}},
+--Determinant: -2, permanent: 10
+{{2, 9, 4},
+ {7, 5, 3},
+ {6, 1, 8}},
+--Determinant: -360, permanent: 900
+{{ 1,  2,  3,  4},
+ { 4,  5,  6,  7},
+ { 7,  8,  9, 10},
+ {10, 11, 12, 13}},
+--Determinant: 0, permanent: 29556
+{{ 0,  1,  2,  3,  4},
+ { 5,  6,  7,  8,  9},
+ {10, 11, 12, 13, 14},
+ {15, 16, 17, 18, 19},
+ {20, 21, 22, 23, 24}},
+--Determinant: 0, permanent: 6778800
+{{5}},
+--Determinant: 5, permanent: 5
+{{1,0,0},
+ {0,1,0},
+ {0,0,1}},
+--Determinant: 1, permanent: 1
+{{0,0,1},
+ {0,1,0},
+ {1,0,0}},
+--Determinant: -1, Permanent: 1
+{{4,3},
+ {2,5}},
+--Determinant: 14, Permanent: 26
+{{2,5},
+ {4,3}},
+--Determinant: -14, Permanent: 26
+{{4,4},
+ {2,2}},
+--Determinant: 0, Permanent: 16
+{{7,    2,      -2,     4},
+ {4,    4,      1,      7},
+ {11,   -8,     9,      10},
+ {10,   5,      12,     13}},
+--det:  -4319   permanent:      10723
+
+{{-2,   2,      -3},
+ {-1,   1,      3},
+ {2 ,   0,      -1}}
+--det:  18      permanent:      10
+}
+for i=1 to length(tests) do
+    sequence ti = tests[i]
+    ?{det(ti),perm(ti)}
+end for