square_root_inverse

cpp/Matrix.cpp

@@ -569,6 +569,23 @@ void svd(const Matrix& A, Matrix& U, Vector& s, Matrix& V) {
   svd(U,s,V); // call in-place version
 }
 
+/* ************************************************************************* */
+// TODO, would be faster with Cholesky
+Matrix inverse_square_root(const Matrix& A) {
+  size_t m = A.size2(), n = A.size1();
+	if (m!=n)
+		throw invalid_argument("inverse_square_root: A must be square");
+
+	// Perform SVD, TODO: symmetric SVD?
+	Matrix U,V;
+	Vector S;
+	svd(A,U,S,V);
+
+	// invert and sqrt diagonal of S
+  for(size_t i = 0; i<m; i++) S(i) = pow(S(i),-0.5);
+  return vector_scale(S, V); // V*S;
+}
+
 /* ************************************************************************* */
 
 } // namespace gtsam

cpp/Matrix.h

@@ -238,6 +238,9 @@ void svd(const Matrix& A, Matrix& U, Vector& S, Matrix& V);
 // in-place version
 void svd(Matrix& A, Vector& S, Matrix& V);
 
+/** Use SVD to calculate inverse square root of a matrix */
+Matrix inverse_square_root(const Matrix& A);
+
 // macro for unit tests
 #define EQUALITY(expected,actual)\
   { if (!assert_equal(expected,actual)) \