Data commit

Task/Determinant-and-permanent/FreeBASIC/determinant-and-permanent.basic

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+sub make_S( M() as double, S() as double, i as uinteger, j as uinteger )
+    'removes row j, column i from the matrix, stores result in S()
+    dim as uinteger ii, jj, size=ubound(M), ix, jx
+    for ii = 1 to size-1
+        if ii<i then ix = ii else ix = ii + 1
+        for jj = 1 to size-1
+            if jj<j then jx = jj else jx = jj + 1
+            S(ii, jj) = M(ix, jx)
+        next jj
+    next ii
+end sub
+
+function deperminant( M() as double, det as boolean ) as double
+    'calculates the determinant or the permanent of a square matrix M
+    'det = true  for determinant, false for permanent
+    'assumes a square matrix
+    dim as uinteger size = ubound(M,1), i
+    dim as integer sign
+    dim as double S(1 to size-1, 1 to size-1)
+    dim as double ret = 0.0, inc
+    if size = 1 then return M(1,1)                                       'matrices of size < 3 are easy to calculate
+    if size = 2 and det then return M(1,1)*M(2,2) - M(1,2)*M(2,1)
+    if size = 2         then return M(1,1)*M(2,2) + M(1,2)*M(2,1)
+    for i = 1 to size
+            if det then sign = (-1)^(i+1) else sign = 1                 'this bit is what distinguishes a determinant from a permanent
+            make_S( M(), S(), i, 1 )
+            inc = sign*M(i,1)*deperminant( S(), det )                   'recursively call on submatrices
+            ret += inc
+    next i
+    return ret
+end function
+
+dim as double A(1 to 2, 1 to 2) = {{1,2},{3,4}}
+
+dim as double B(1 to 4, 1 to 4) = {_
+    {1,2,3,4}, {4,5,6,7}, {7,8,9,10}, {10,11,12,13} }
+
+dim as double C(1 to 5, 1 to 5) = {_
+     {  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 } }
+
+print deperminant( A(), true ), deperminant( A(), false )
+print deperminant( B(), true ), deperminant( B(), false )
+print deperminant( C(), true ), deperminant( C(), false )