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Tutorial

Going through the tutorials should answer many questions for users new to FLENS:

How to compile a small C++ code that uses FLENS?
What matrix/vector types are defined and how to use them?
What are matrix/views?
How can I compute matrix-vector operations?
How to solve a system of linear equations, compute eigenvalues, etc.?

We also try to give insight of concepts used in the design of FLENS.

Matrices, Vectors and Basic Linear Algebra Operations

Page 1	Full Storage Schemes and General Matrices What is a general matrix? Concept of dividing a matrix type into matrix interface and storage scheme. Simple example on how-to use a general matrix. What are matrix-views and how to use them. How are matrix types and matrix views realized in FLENS?
Page 2	Array Storage and Dense Vectors What is a dense vector? Example for using dense vectors. Working with vector views. Vector views referencing matrix rows, columns or diagonals of a matrix.
Page 3	Accessing Raw Data Pointers and Strides Accessing raw data pointers and strides. Concepts for implementing numerical algorithms that require workspace buffers: Design patterns. Creating matrix/vector views from local buffers (Stack buffer). Creating matrix/vector views from global buffers (Data segment buffer).
Page 4	Triangular/Trapezoidal Matrices with Full Storage Why using a full storage for triangular matrices? `TrMatrix` is not a triangular matrix. And it is a good thing. Zeros are not explicitly stored. Accidently accessing the elements from the wrong triangular part causes an assertion error. Sometimes you have to modify the upper triangualr part of a lower `TrMatrix` (and vice versa). We just help you don't do it by accident. How (and why) `GeMatrix` and `TrMatrix` can share the same data: `TrMatrix` views from `GeMatrix` `GeMatrix` views from `TrMatrix`
Page 5	Symmetric and Hermitian Matrices with Full Storage How (and why) `GeMatrix` and `TrMatrix` can share the same data: `TrMatrix` views from `SyMatrix` and `HeMatrix`. `SyMatrix` and `HeMatrix` views from `TrMatrix`.
Page 6	Basic Linear Algebra Operations (BLAS) Who gives you High Performance? It's BLAS, not the Compiler! Benchmarks comparing FLENS/ulmBLAS with others. Vector operations. Matrix-vector operations. Matrix-matrix operations. High level and low level interfaces for linear algebra operations. Using overloaded operators and why you still have full control.
Page 7	Using Operators for BLAS Why usage of operators has a bad reputation in high performance computing. What users coming form Matlab should be aware of. How FLENS provides a transparent and efficient solution. How other C++ libraries deal with issues in the respect.
Page 8	Coding a High Performance LU Factorization with FLENS That's what Matlab does when you solve a system of linear equations. It's the algorithm! Deriving algorithms that are based on matrix/vector operations. Unblocked algorithm for the LU factorization. Blocked algorithm for the LU factorization. Implementation of the unblocked and blocked algorithm Matrix/vector views are a big help! Benchmarks
Page 9	Numerical Linear Algebra (FLENS-LAPACK, LAPACK) Using FLENS-LAPACK. Examples on: Solving a system of linear equations. Computing \(LU\) and \(QR\) factorizations. Computing eigenvalues and eigenvectors.

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