Data commit

Task/Conjugate-transpose/11l/conjugate-transpose.11l

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+-V eps = 1e-10
+
+F to_str(m)
+   V r = ‘’
+   L(row) m
+      V i = L.index
+      r ‘’= I i == 0 {‘[’} E ‘ ’
+      L(val) row
+         V j = L.index
+         I j != 0
+            r ‘’= ‘ ’
+         r ‘’= ‘(#2.4, #2.4)’.format(val.real, val.imag)
+      r ‘’= I i == m.len - 1 {‘]’} E "\n"
+   R r
+
+F conjugateTransposed(m)
+   V r = [[0i] * m.len] * m.len
+   L(i) 0 .< m.len
+      L(j) 0 .< m.len
+         r[j][i] = conjugate(m[i][j])
+   R r
+
+F mmul(m1, m2)
+   V r = [[0i] * m1.len] * m1.len
+   L(i) 0 .< m1.len
+      L(j) 0 .< m1.len
+         L(k) 0 .< m1.len
+            r[i][j] += m1[i][k] * m2[k][j]
+   R r
+
+F isHermitian(m)
+   L(i) 0 .< m.len
+      L(j) 0 .< m.len
+         I m[i][j] != conjugate(m[j][i])
+            R 0B
+   R 1B
+
+F isEqual(m1, m2)
+   L(i) 0 .< m1.len
+      L(j) 0 .< m1.len
+         I m1[i][j] != m2[i][j]
+            R 0B
+   R 1B
+
+F isNormal(m)
+   V h = conjugateTransposed(m)
+   R isEqual(mmul(m, h), mmul(h, m))
+
+F isIdentity(m)
+   L(i) 0 .< m.len
+      L(j) 0 .< m.len
+         I i == j
+            I abs(m[i][j] - 1.0) > :eps
+               R 0B
+         E
+            I abs(m[i][j]) > :eps
+               R 0B
+   R 1B
+
+F isUnitary(m)
+   V h = conjugateTransposed(m)
+   R isIdentity(mmul(m, h)) & isIdentity(mmul(h, m))
+
+F test(m)
+   print(‘Matrix’)
+   print(‘------’)
+   print(to_str(m))
+   print(‘’)
+   print(‘Conjugate transposed’)
+   print(‘--------------------’)
+   print(to_str(conjugateTransposed(m)))
+   print(‘’)
+   print(‘Hermitian: ’(I isHermitian(m) {‘true’} E ‘false’))
+   print(‘Normal: ’(I isNormal(m) {‘true’} E ‘false’))
+   print(‘Unitary: ’(I isUnitary(m) {‘true’} E ‘false’))
+
+V M2 = [[3.0 + 0.0i, 2.0 + 1.0i],
+        [2.0 - 1.0i, 1.0 + 0.0i]]
+
+V M3 = [[1.0 + 0.0i, 1.0 + 0.0i, 0.0 + 0.0i],
+        [0.0 + 0.0i, 1.0 + 0.0i, 1.0 + 0.0i],
+        [1.0 + 0.0i, 0.0 + 0.0i, 1.0 + 0.0i]]
+
+V SR2 = 1 / sqrt(2.0)
+V SR2i = SR2 * 1i
+V M4 = [[SR2 + 0.0i, SR2 + 0.0i, 0.0 + 0.0i],
+        [0.0 + SR2i, 0.0 - SR2i, 0.0 + 0.0i],
+        [0.0 + 0.0i, 0.0 + 0.0i, 0.0 + 1.0i]]
+
+test(M2)
+print("\n")
+test(M3)
+print("\n")
+test(M4)