delete trailing white spaces

Source/lsmrBase.cxx

@@ -322,7 +322,7 @@ Solve( unsigned int m, unsigned int n, const double * b, double * x )
   std::fill( v, v+n, zero);
   std::fill( w, v+n, zero);
   std::fill( x, x+n, zero);
-  
+
   this->Scale( m, (-1.0), u );
   this->Aprod1( m, n, x, u );
   this->Scale( m, (-1.0), u );

Source/lsmrBase.h

@@ -445,7 +445,7 @@ class lsmrBase
    */
   unsigned int GetStoppingReason() const;
 
-  /** 
+  /**
    *   Returns an string giving the reason for termination.
    *   Expands on GetStoppingReason
    *

Source/lsmrDense.cxx

@@ -75,5 +75,3 @@ Aprod2(unsigned int m, unsigned int n, double * x, const double * y ) const
     x[col] +=  sum;
     }
 }
-
-

Source/lsmrDense.h

@@ -24,9 +24,9 @@
 /** \class lsmrDense
  *
  * Specific implementation of the solver for a type of dense Matrix.
- *  
+ *
  */
-class lsmrDense : public lsmrBase 
+class lsmrDense : public lsmrBase
 {
 public:
 
@@ -57,4 +57,4 @@ class lsmrDense : public lsmrBase
   double ** A;
 };
 
-#endif 
+#endif

Source/lsqrBase.cxx

@@ -118,14 +118,14 @@ lsqrBase::GetFinalEstimateOfNormRbar() const
 }
 
 
-double 
+double
 lsqrBase::GetFinalEstimateOfNormOfResiduals() const
 {
   return this->Arnorm;
 }
 
 
-double 
+double
 lsqrBase::GetFinalEstimateOfNormOfX() const
 {
   return this->xnorm;
@@ -209,7 +209,7 @@ lsqrBase::D2Norm( double a, double b ) const
     {
     return zero;
     }
-  
+
   const double sa = a / scale;
   const double sb = b / scale;
 
@@ -239,12 +239,12 @@ lsqrBase::Dnrm2( unsigned int n, const double *x ) const
 
   for ( unsigned int i = 0; i < n; i++ )
     {
-    if ( x[i] != 0.0 ) 
+    if ( x[i] != 0.0 )
       {
       double dx = x[i];
       const double absxi = std::abs(dx);
 
-      if ( magnitudeOfLargestElement < absxi ) 
+      if ( magnitudeOfLargestElement < absxi )
         {
         // rescale the sum to the range of the new element
         dx = magnitudeOfLargestElement / absxi;
@@ -266,7 +266,7 @@ lsqrBase::Dnrm2( unsigned int n, const double *x ) const
 }
 
 
-/** 
+/**
  *
  *  The array b must have size m
  *
@@ -281,16 +281,16 @@ Solve( unsigned int m, unsigned int n, const double * b, double * x )
     {
     (*this->nout) << "Enter LSQR " << std::endl;
     (*this->nout) << m << ", " << n << std::endl;
-    (*this->nout) << this->damp << ", " << this->wantse << std::endl; 
-    (*this->nout) << this->atol << ", " << this->conlim << std::endl; 
-    (*this->nout) << this->btol << ", " << this->itnlim << std::endl; 
+    (*this->nout) << this->damp << ", " << this->wantse << std::endl;
+    (*this->nout) << this->atol << ", " << this->conlim << std::endl;
+    (*this->nout) << this->btol << ", " << this->itnlim << std::endl;
     }
 
   this->damped = ( this->damp > zero );
 
   this->itn = 0;
   this->istop = 0;
-  
+
   unsigned int nstop = 0;
   this->maxdx = 0;
 
@@ -363,7 +363,7 @@ Solve( unsigned int m, unsigned int n, const double * b, double * x )
 
     return;
     }
-  
+
   double rhobar = alpha;
   double phibar = beta;
 
@@ -372,7 +372,7 @@ Solve( unsigned int m, unsigned int n, const double * b, double * x )
 
   double test1 = 0.0;
   double test2 = 0.0;
-  
+
 
   if ( this->nout )
     {
@@ -416,7 +416,7 @@ Solve( unsigned int m, unsigned int n, const double * b, double * x )
   //
   do {
 
-    this->itn++; 
+    this->itn++;
 
     //----------------------------------------------------------------
     //  Perform the next step of the bidiagonalization to obtain the
@@ -488,7 +488,7 @@ Solve( unsigned int m, unsigned int n, const double * b, double * x )
     double t3     =     one / rho;
     double dknorm =    zero;
 
-    if ( this->wantse ) 
+    if ( this->wantse )
       {
       for ( unsigned int i = 0; i < n; i++ )
         {
@@ -649,7 +649,7 @@ Solve( unsigned int m, unsigned int n, const double * b, double * x )
         }
       }
 
-    } while ( istop == 0); 
+    } while ( istop == 0);
 
   //===================================================================
   // End of iteration loop.

Source/lsqrBase.h

@@ -26,44 +26,44 @@
  *  \brief implement a solver for a set of linear equations.
  *
  *   LSQR  finds a solution x to the following problems:
- *  
+ *
  *   1. Unsymmetric equations:    Solve  A*x = b
- *  
+ *
  *   2. Linear least squares:     Solve  A*x = b
  *                                in the least-squares sense
- *  
+ *
  *   3. Damped least squares:     Solve  (   A    )*x = ( b )
  *                                       ( damp*I )     ( 0 )
  *                                in the least-squares sense
- *  
+ *
  *   where A is a matrix with m rows and n columns, b is an m-vector,
  *   and damp is a scalar.  (All quantities are real.)
  *   The matrix A is treated as a linear operator.  It is accessed
  *   by means of subroutine calls with the following purpose:
- *  
+ *
  *   call Aprod1(m,n,x,y)  must compute y = y + A*x  without altering x.
  *   call Aprod2(m,n,x,y)  must compute x = x + A'*y without altering y.
- *  
+ *
  *   LSQR uses an iterative method to approximate the solution.
  *   The number of iterations required to reach a certain accuracy
  *   depends strongly on the scaling of the problem.  Poor scaling of
  *   the rows or columns of A should therefore be avoided where
  *   possible.
- *  
+ *
  *   For example, in problem 1 the solution is unaltered by
  *   row-scaling.  If a row of A is very small or large compared to
  *   the other rows of A, the corresponding row of ( A  b ) should be
  *   scaled up or down.
- *  
+ *
  *   In problems 1 and 2, the solution x is easily recovered
  *   following column-scaling.  Unless better information is known,
  *   the nonzero columns of A should be scaled so that they all have
  *   the same Euclidean norm (e.g., 1.0).
- *  
+ *
  *   In problem 3, there is no freedom to re-scale if damp is
  *   nonzero.  However, the value of damp should be assigned only
  *   after attention has been paid to the scaling of A.
- *  
+ *
  *   The parameter damp is intended to help regularize
  *   ill-conditioned systems, by preventing the true solution from
  *   being very large.  Another aid to regularization is provided by
@@ -74,13 +74,13 @@
  *   of the solver that is available at
  *   http://www.stanford.edu/group/SOL/software.html
  *   distributed under a BSD license.
- *   
+ *
  *   This class is a replacement for the lsqr code taken from netlib.
  *   That code had to be removed because it is copyrighted by ACM and
  *   its license was incompatible with a BSD license.
- *  
+ *
  */
-class lsqrBase 
+class lsqrBase
 {
 public:
 
@@ -102,7 +102,7 @@ class lsqrBase
    * The size of the vector y is m.
    */
   virtual void Aprod2(unsigned int m, unsigned int n, double * x, const double * y ) const = 0;
-  
+
   /**
    * returns sqrt( a**2 + b**2 )
    * with precautions to avoid overflow.
@@ -114,20 +114,20 @@ class lsqrBase
    * with precautions to avoid overflow.
    */
   double Dnrm2( unsigned int n, const double *x ) const;
-  
+
   /**
    * Scale a vector by multiplying with a constant
    */
   void Scale( unsigned int n, double factor, double *x ) const;
- 
+
   /**  A logical variable to say if the array se(*) of standard error estimates
    * should be computed.  If m > n  or  damp > 0,  the system is overdetermined
    * and the standard errors may be useful.  (See the first LSQR reference.)
    * Otherwise (m <= n  and  damp = 0) they do not mean much.  Some time and
    * storage can be saved by setting wantse = .false. and using any convenient
    * array for se(*), which won't be touched.  If you call this method with the
    * flag ON, then you MUST provide a working memory array to store the standard
-   * error estimates, via the method SetStandardErrorEstimates() 
+   * error estimates, via the method SetStandardErrorEstimates()
    */
   void SetStandardErrorEstimatesFlag( bool );
 
@@ -137,8 +137,8 @@ class lsqrBase
    */
   void SetToleranceA( double );
 
-  /** An estimate of the relative error in the data 
-   *  defining the rhs b.  For example, if b is     
+  /** An estimate of the relative error in the data
+   *  defining the rhs b.  For example, if b is
    *  accurate to about 6 digits, set btol = 1.0e-6.
    */
   void SetToleranceB( double );
@@ -181,9 +181,9 @@ class lsqrBase
    *   of damp in the range 0 to sqrt(eps)*norm(A)
    *   will probably have a negligible effect.
    *   Larger values of damp will tend to decrease
-   *   the norm of x and reduce the number of 
+   *   the norm of x and reduce the number of
    *   iterations required by LSQR.
-   * 
+   *
    *   The work per iteration and the storage needed
    *   by LSQR are the same for all values of damp.
    *
@@ -198,47 +198,47 @@ class lsqrBase
    */
   void SetMaximumNumberOfIterations( unsigned int );
 
-  /** 
+  /**
    * If provided, a summary will be printed out to this stream during
    * the execution of the Solve function.
    */
   void SetOutputStream( std::ostream & os );
 
-  /** Provide the array where the standard error estimates will be stored. 
+  /** Provide the array where the standard error estimates will be stored.
    *  You MUST provide this working memory array if you turn on the computation
    *  of standard error estimates with teh method SetStandardErrorEstimatesFlag().
    */
   void SetStandardErrorEstimates( double * array );
 
-  /** 
+  /**
    *   Returns an integer giving the reason for termination:
-   * 
+   *
    *     0       x = 0  is the exact solution.
    *             No iterations were performed.
-   * 
+   *
    *     1       The equations A*x = b are probably compatible.
    *             Norm(A*x - b) is sufficiently small, given the
    *             values of atol and btol.
-   * 
+   *
    *     2       damp is zero.  The system A*x = b is probably
    *             not compatible.  A least-squares solution has
    *             been obtained that is sufficiently accurate,
    *             given the value of atol.
-   * 
+   *
    *     3       damp is nonzero.  A damped least-squares
    *             solution has been obtained that is sufficiently
    *             accurate, given the value of atol.
-   * 
+   *
    *     4       An estimate of cond(Abar) has exceeded conlim.
    *             The system A*x = b appears to be ill-conditioned,
    *             or there could be an error in Aprod1 or Aprod2.
-   * 
+   *
    *     5       The iteration limit itnlim was reached.
    *
    */
   unsigned int GetStoppingReason() const;
 
-  /** 
+  /**
    *   Returns an string giving the reason for termination.
    *   Expands on GetStoppingReason
    *
@@ -250,7 +250,7 @@ class lsqrBase
   unsigned int GetNumberOfIterationsPerformed() const;
 
 
-  /** 
+  /**
    *   An estimate of the Frobenius norm of Abar.
    *   This is the square-root of the sum of squares
    *   of the elements of Abar.
@@ -263,7 +263,7 @@ class lsqrBase
   double GetFrobeniusNormEstimateOfAbar() const;
 
 
-  /** 
+  /**
    *   An estimate of cond(Abar), the condition
    *   number of Abar.  A very high value of Acond
    *   may again indicate an error in Aprod1 or Aprod2.
@@ -297,7 +297,7 @@ class lsqrBase
 
   /**
    *    Execute the solver
-   * 
+   *
    *    solves Ax = b or min ||Ax - b|| with or without damping,
    *
    *    m is the size of the input  vector b
@@ -338,4 +338,4 @@ class lsqrBase
   double * se;
 };
 
-#endif 
+#endif

Source/lsqrDense.cxx

@@ -77,7 +77,7 @@ Aprod2(unsigned int m, unsigned int n, double * x, const double * y ) const
 }
 
 
-/* 
+/*
 
   returns x = (I - 2*z*z')*x.
 
@@ -111,5 +111,3 @@ HouseholderTransformation(unsigned int n, const double * z, double * x ) const
     *xp++ -= scalarProduct * (*zp++);
     }
 }
-
-