Added sqrtm to compute matrix square root

src/matadi/math.py

@@ -267,4 +267,17 @@ def unimodular(T):
    This operation preserves the isochoric (volume-preserving) part of the tensor
    while removing the volumetric part.
    """
-   return (det(T) ** (-1 / 3)) * T
+   return (det(T) ** (-1 / 3)) * T
+
+def sqrtm(C, eps = 8e-5):
+    """
+    Compute the matrix square root of a tensor C using eigendecomposition.
+    """
+    w = eigvals(C, eps=eps)
+    eye = SX.eye(3)
+
+    M1 = (C - w[1] * eye) * (C - w[2] * eye) / (w[0] - w[1]) / (w[0] - w[2])
+    M2 = (C - w[2] * eye) * (C - w[0] * eye) / (w[1] - w[2]) / (w[1] - w[0])
+    M3 = (C - w[0] * eye) * (C - w[1] * eye) / (w[2] - w[0]) / (w[2] - w[1])
+
+    return sqrt(w[0]) * M1 + sqrt(w[1]) * M2 + sqrt(w[2]) * M3