Gauss-Jordan matrix inversion: Difference between revisions

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 '''A''' &nbsp; being an &nbsp; '''n''' &times; '''n''' &nbsp; matrix.
 <br><br>
+=={{header|11l}}==
+{{trans|Nim}}
+<lang 11l>V Eps = 1e-10
+F transformToRref(&mat)
+   V lead = 0
+   L(r) 0 .< mat.len
+      I lead >= mat[0].len
+         R
+      V i = r
+      L mat[i][lead] == 0
+         i++
+         I i == mat.len
+            i = r
+            lead++
+            I lead == mat[0].len
+               R
+      swap(&mat[i], &mat[r])
+      V d = mat[r][lead]
+      I abs(d) > Eps
+         L(&item) mat[r]
+            item /= d
+      L(i) 0 .< mat.len
+         I i != r
+            V m = mat[i][lead]
+            L(c) 0 .< mat[0].len
+               mat[i][c] -= mat[r][c] * m
+      lead++
+F inverse(mat)
+   V augmat = [[0.0] * (2 * mat.len)] * mat.len
+   L(i) 0 .< mat.len
+      L(j) 0 .< mat.len
+         augmat[i][j] = mat[i][j]
+      augmat[i][mat.len + i] = 1
+   transformToRref(&augmat)
+   V result = [[0.0] * mat.len] * mat.len
+   L(i) 0 .< mat.len
+      L(j) 0 .< mat.len
+         I augmat[i][j] != Float(i == j)
+            X ValueError(‘matrix is singular’)
+         result[i][j] = augmat[i][mat.len + j]
+   R result
+F print_mat(mat)
+   L(row) mat
+      V line = ‘’
+      L(val) row
+         I !line.empty
+            line ‘’= ‘ ’
+         line ‘’= ‘#3.5’.format(val)
+      print(line)
+F runTest(mat)
+   print(‘Matrix:’)
+   print_mat(mat)
+   print()
+   print(‘Inverse:’)
+   print_mat(inverse(mat))
+   print()
+   print()
+V m1 = [[Float(1), 2, 3],
+        [Float(4), 1, 6],
+        [Float(7), 8, 9]]
+V m2 = [[Float( 2), -1,  0],
+        [Float(-1),  2, -1],
+        [Float( 0), -1,  2]]
+V m3 = [[Float(-1), -2,  3,  2],
+        [Float(-4), -1,  6,  2],
+        [Float( 7), -8,  9,  1],
+        [Float( 1), -2,  1,  3]]
+runTest(m1)
+runTest(m2)
+runTest(m3)</lang>
+{{out}}
+<pre>
+Matrix:
+.00000   2.00000   3.00000
+.00000   1.00000   6.00000
+.00000   8.00000   9.00000
+Inverse:
+ -0.81250   0.12500   0.18750
+.12500  -0.25000   0.12500
+.52083   0.12500  -0.14583
+Matrix:
+.00000  -1.00000   0.00000
+ -1.00000   2.00000  -1.00000
+.00000  -1.00000   2.00000
+Inverse:
+.75000   0.50000   0.25000
+.50000   1.00000   0.50000
+.25000   0.50000   0.75000
+Matrix:
+ -1.00000  -2.00000   3.00000   2.00000
+ -4.00000  -1.00000   6.00000   2.00000
+.00000  -8.00000   9.00000   1.00000
+.00000  -2.00000   1.00000   3.00000
+Inverse:
+ -0.91304   0.24638   0.09420   0.41304
+ -1.65217   0.65217   0.04348   0.65217
+ -0.69565   0.36232   0.07971   0.19565
+ -0.56522   0.23188  -0.02899   0.56522
+</pre>
 =={{header|360 Assembly}}==