Session 1, Page 13

Matrix Views that are not only cool but sooo usefull!

I did not introduce other matrix types of FLENS so far. Still the next example uses two more matrix types:

a type for triangular matrices and
a type for symmetric matrices.

Actually these are

triangular matrix views and
symmetric matrix views.

First some notes about triangular matrix views:

We have a general matrix storing all elements
Now its common in numerics that you want to treat a triangular part thereof as triangular matrix
Maybe LU decomposition rings a bell.
Sometimes you want that diagonal elements are assumed to be one
That is what we call a unit triangular matrix

About symmetric matrix views:

they treat a triangular part of a general matrix as symmetric matrix.
I guess it will become evident when you look at the example and its output:

s01_t09_matvecviews.cc

  #include <flens/flens.h>
  #include <iostream>
  
  using namespace flens;
  using namespace std;
  
  typedef GeMatrix<FullStorage<double, ColMajor> >   GEMatrix;
  
  int
  main()
  {
      GEMatrix A(5,5);
      A = 1, 2, 3, 4, 5,
          6, 7, 8, 9, 0,
          9, 7, 5, 3, 1,
          0, 9, 1, 8, 2,
          7, 3, 6, 4, 5;
  
      GEMatrix::TriangularView U = upper(A);
      GEMatrix::TriangularView L = lowerUnit(A);
  
      GEMatrix::SymmetricView SU = upper(A);
      GEMatrix::SymmetricView SL = lower(A);
  
      cout << "U =  " << U << endl;
      cout << "L =  " << L << endl;
      cout << "SU = " << SU << endl;
      cout << "SL = " << SL << endl;
  
      return 0;
  }

and here the output

Output of s01_t09_matvecviews

  U =  [5, 5]
     1.000000   2.000000   3.000000   4.000000   5.000000;
            0   7.000000   8.000000   9.000000   0.000000;
            0          0   5.000000   3.000000   1.000000;
            0          0          0   8.000000   2.000000;
            0          0          0          0   5.000000;
  
  
  L =  [5, 5]
            1          0          0          0          0;
     6.000000          1          0          0          0;
     9.000000   7.000000          1          0          0;
     0.000000   9.000000   1.000000          1          0;
     7.000000   3.000000   6.000000   4.000000          1;
  
  
  SU = [5, 5]
     1.000000   2.000000   3.000000   4.000000   5.000000;
     2.000000   7.000000   8.000000   9.000000   0.000000;
     3.000000   8.000000   5.000000   3.000000   1.000000;
     4.000000   9.000000   3.000000   8.000000   2.000000;
     5.000000   0.000000   1.000000   2.000000   5.000000;
  
  
  SL = [5, 5]
     1.000000   6.000000   9.000000   0.000000   7.000000;
     6.000000   7.000000   7.000000   9.000000   3.000000;
     9.000000   7.000000   5.000000   1.000000   6.000000;
     0.000000   9.000000   1.000000   8.000000   4.000000;
     7.000000   3.000000   6.000000   4.000000   5.000000;

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