Changed pinv() so it interprets its tol argument relative to the largest

singular value of the input matrix rather than as an absolute tolerance.

dlib/matrix/matrix_la.h

@@ -1595,8 +1595,8 @@ convergence:
 
         const double machine_eps = std::numeric_limits<typename EXP::type>::epsilon();
         // compute a reasonable epsilon below which we round to zero before doing the
-        // reciprocal.  Unless a non-zero tol is given then we just use tol.
-        const double eps = (tol!=0) ? tol :  machine_eps*std::max(m.nr(),m.nc())*max(w);
+        // reciprocal.  Unless a non-zero tol is given then we just use tol*max(w).
+        const double eps = (tol!=0) ? tol*max(w) :  machine_eps*std::max(m.nr(),m.nc())*max(w);
 
         // now compute the pseudoinverse
         return tmp(scale_columns(v,reciprocal(round_zeros(w,eps))))*trans(u);

dlib/matrix/matrix_la_abstract.h

@@ -44,7 +44,7 @@ namespace dlib
                 - singular values less than max(m.nr(),m.nc()) times the machine epsilon 
                   times the largest singular value are ignored.  
             - else
-                - singular values less than tol are ignored.
+                - singular values less than tol*max(singular value in m) are ignored.
     !*/
 
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