inverse tensor

lib/gpt/core/foundation/tensor.py

@@ -48,6 +48,24 @@ def component_simple_map(operator, numpy_operator, extra_params, first, second):
     return res
 
 
+def identity(t):
+    e = gpt.tensor(t.otype)
+    if len(e.array.shape) == 2:
+        e.array = numpy.eye(dtype=e.array.dtype, N=e.array.shape[0])
+    elif len(e.array.shape) == 4:
+        n1 = e.array.shape[0]
+        n2 = e.array.shape[2]
+        for i in range(n1):
+            for j in range(n1):
+                if i == j:
+                    e.array[i, j] = numpy.eye(dtype=e.array.dtype, N=n2)
+                else:
+                    e.array[i, j] = numpy.zeros(dtype=e.array.dtype, shape=(n2, n2))
+    else:
+        raise Exception(f"Unknown shape of tensor.identity {e.array.shape}")
+    return e
+
+
 def adj(l):
     if l.transposable():
         return l.adj()

lib/gpt/core/matrix/inv.py

@@ -17,10 +17,31 @@
 #    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 #
 import gpt, cgpt
+import numpy as np
+
+
+def deflate(A):
+    if len(A.shape) == 4:
+        n1 = A.shape[0]
+        n2 = A.shape[2]
+        return n1, n2, np.swapaxes(A, 1, 2).reshape(n1 * n2, n1 * n2)
+    return None, None, A
+
+
+def inflate(n1, n2, A):
+    if n1 is None:
+        return A
+    return np.swapaxes(A.reshape(n1, n2, n1, n2), 1, 2)
 
 
 def inv(A):
     A = gpt.eval(A)
+
+    if isinstance(A, gpt.tensor):
+        n1, n2, a = deflate(A.array)
+        a = inflate(n1, n2, np.linalg.inv(a))
+        return gpt.tensor(a, A.otype)
+
     assert isinstance(A, gpt.lattice)
 
     to_list = gpt.util.to_list

tests/core/matrix.py

@@ -89,6 +89,11 @@ def mod0p1(x):
         g.message(f"test M*M^-1 = 1 for {m.otype.__name__}: {eps2}")
         assert eps2 < eps**2
 
+        eps2 = g.norm2(
+            g.matrix.inv(m[0, 0, 0, 0]) * m[0, 0, 0, 0] - g.identity(m[0, 0, 0, 0])
+        ) / g.norm2(g.identity(m[0, 0, 0, 0]))
+        assert eps2 < eps**2 * 10
+
         m2 = g.matrix.exp(g.matrix.log(m))
         eps2 = g.norm2(m - m2) / g.norm2(m)
         g.message(f"exp(log(m)) == m: {eps2}")