[Toon-members] TooN SymEigen.h test/eigen-sqrt.cc

[Damian Eads]

CVSROOT:        /sources/toon
Module name:    TooN
Changes by:     Damian Eads <eads>      09/08/28 01:14:23

Modified files:
        .              : SymEigen.h 
Added files:
        test           : eigen-sqrt.cc 

Log message:
        Updated example to include inverse square root. Put it in a test source 
file.

CVSWeb URLs:
http://cvs.savannah.gnu.org/viewcvs/TooN/SymEigen.h?cvsroot=toon&r1=1.23&r2=1.24
http://cvs.savannah.gnu.org/viewcvs/TooN/test/eigen-sqrt.cc?cvsroot=toon&rev=1.1

Patches:
Index: SymEigen.h
===================================================================
RCS file: /sources/toon/TooN/SymEigen.h,v
retrieving revision 1.23
retrieving revision 1.24
diff -u -b -r1.23 -r1.24
--- SymEigen.h  27 Aug 2009 21:06:05 -0000      1.23
+++ SymEigen.h  28 Aug 2009 01:14:22 -0000      1.24
@@ -129,20 +129,37 @@
 are the eigenvalues of \f$M\f$. These quantities are often of use directly, 
and can
 be obtained as follows:
 @code
+// construct M
 Matrix<3> M(3,3);
 M[0]=makeVector(4,0,2);
 M[1]=makeVector(0,5,3);
 M[2]=makeVector(2,3,6);
+ 
 // create the eigen decomposition of M
 SymEigen<3> eigM(M);
+cout << "A=" << M << endl;
+cout << "(E,v)=eig(A)" << endl;
 // print the smallest eigenvalue
-cout << eigM.get_evalues()[0] << endl;
+cout << "v[0]=" << eigM.get_evalues()[0] << endl;
 // print the associated eigenvector
-cout << eigM.get_evectors()[0] << endl;
+cout << "E[0]=" << eigM.get_evectors()[0] << endl;
address@hidden
+
+Further, provided the eigenvalues are nonnegative, the square root of
+a matrix and its inverse can also be obtained,
address@hidden
 // print the square root of the matrix.
-cout << eigM.get_sqrtm() << endl;
+cout << "R=sqrtm(A)=" << eigM.get_sqrtm() << endl;
 // print the square root of the matrix squared.
-cout << eigM.get_sqrtm().T() * eigM.get_sqrtm() << endl;
+cout << "(should equal A), R^T*R="
+     << eigM.get_sqrtm().T() * eigM.get_sqrtm() << endl;
+// print the inverse of the matrix.
+cout << "A^-1=" << eigM.get_pinv() << endl;
+// print the inverse square root of the matrix.
+cout << "C=isqrtm(A)=" << eigM.get_isqrtm() << endl;
+// print the inverse square root of the matrix squared.
+cout << "(should equal A^-1), C^T*C="
+     << eigM.get_isqrtm().T() * eigM.get_isqrtm() << endl;
 @endcode
 
 This decomposition is very similar to the SVD (q.v.), and can be used to solve

Index: test/eigen-sqrt.cc
===================================================================
RCS file: test/eigen-sqrt.cc
diff -N test/eigen-sqrt.cc
--- /dev/null   1 Jan 1970 00:00:00 -0000
+++ test/eigen-sqrt.cc  28 Aug 2009 01:14:23 -0000      1.1
@@ -0,0 +1,39 @@
+#include <iostream>
+#include <TooN/TooN.h>
+#include <TooN/SymEigen.h>
+
+using namespace std;
+using namespace TooN;
+
+int main() {
+  // construct M
+  double d1[][3] = {{1,2,3},{2,5,6},{3,6,7}};
+ Matrix<3> M(3,3);
+ M[0]=makeVector(4,0,2);
+ M[1]=makeVector(0,5,3);
+ M[2]=makeVector(2,3,6);
+ 
+ Vector<3> dg(makeVector(2,4,9));
+ // create the eigen decomposition of M
+ SymEigen<3> eigM(M);
+ cout << "A=" << M << endl;
+ cout << "(E,v)=eig(A)" << endl;
+ // print the smallest eigenvalue
+ cout << "v[0]=" << eigM.get_evalues()[0] << endl;
+ // print the associated eigenvector
+ cout << "E[0]=" << eigM.get_evectors()[0] << endl;
+ // print the square root of the matrix.
+ cout << "R=sqrtm(A)=" << eigM.get_sqrtm() << endl;
+ // print the square root of the matrix squared.
+ cout << "(should equal A), R^T*R="
+      << eigM.get_sqrtm().T() * eigM.get_sqrtm() << endl;
+ // print the inverse of the matrix.
+ cout << "A^-1=" << eigM.get_pinv() << endl;
+ // print the inverse square root of the matrix.
+ cout << "C=isqrtm(A)=" << eigM.get_isqrtm() << endl;
+ // print the inverse square root of the matrix squared.
+ cout << "(should equal A^-1), C^T*C="
+      << eigM.get_isqrtm().T() * eigM.get_isqrtm() << endl;
+
+  return 0;
+}