diff --git a/homework_2/Makefile b/homework_2/Makefile
index c573b2e..d890a86 100644
--- a/homework_2/Makefile
+++ b/homework_2/Makefile
@@ -25,8 +25,9 @@ TARGET          := distbitonic
 # Source directories list(space seperated). Makefile-relative path, UNDER current directory.
 SRC_DIR_LIST    := src
 # Include directories list(space seperated). Makefile-relative path.
-INC_DIR_LIST    := inc \
-                   src \
+INC_DIR_LIST    := include \
+				   /usr/lib/x86_64-linux-gnu/openmpi/include/ \
+                   src
 
 # Exclude files list(space seperated). Filenames only.
 # EXC_FILE_LIST := bad.cpp old.cpp
@@ -77,8 +78,8 @@ DOCKER          :=
 CSIZE           := size
 CFLAGS          := $(DEB_CFLAGS)
 CXXFLAGS		:= $(DEB_CXXFLAGS)
-CXX             := g++
-CC              := gcc
+CXX             := g++ #mpic++
+CC              := gcc #mpicc
 
 #
 # =========== Main body and Patterns ===========
@@ -180,11 +181,15 @@ hpc-clean:
 # make IMAGE=hpcimage v0
 # make IMAGE=hpcimage v1_cilk
 #
+dist_v05: CC := mpicc
+dist_v05: CXX := mpic++
 dist_v05: CFLAGS := $(DEB_CFLAGS) -DCODE_VERSION=50
 dist_v05: CXXFLAGS := $(DEB_CXXFLAGS) -DCODE_VERSION=50
 dist_v05: TARGET := dist_v05
 dist_v05: $(BUILD_DIR)/$(TARGET)
 
+dist_v1: CC := mpicc
+dist_v1: CXX := mpic++
 dist_v1: CFLAGS := $(DEB_CFLAGS) -DCODE_VERSION=100
 dist_v1: CXXFLAGS := $(DEB_CXXFLAGS) -DCODE_VERSION=100
 dist_v1: TARGET := dist_v1
diff --git a/homework_2/exersize.md b/homework_2/exersize.md
index a61f4a1..b8bf998 100644
--- a/homework_2/exersize.md
+++ b/homework_2/exersize.md
@@ -1,4 +1,4 @@
-Parallel & Distributed Computer Systems
+Parallel & Distributed Computer Systems HW2
 
 December 6, 2024
 
diff --git a/homework_2/include/config.h b/homework_2/include/config.h
new file mode 100644
index 0000000..433c74d
--- /dev/null
+++ b/homework_2/include/config.h
@@ -0,0 +1,39 @@
+/*!
+ * \file    config,h
+ * \brief   Build configuration file.
+ *
+ * \author
+ *    Christos Choutouridis AEM:8997
+ *    <cchoutou@ece.auth.gr>
+ */
+
+#ifndef CONFIG_H_
+#define CONFIG_H_
+
+#include <iostream>
+#include <string>
+
+/*
+ * Defines for different version of the exercise
+ */
+#define  V50     (50)
+#define  V100    (100)
+
+
+// Fail-safe version selection
+#if !defined CODE_VERSION
+#define CODE_VERSION   V1
+#endif
+
+
+/*!
+ * Session option for each invocation of the executable
+ */
+struct session_t {
+    bool        timing          {false};
+    bool        verbose         {false};    //!< Flag to enable verbose output to stdout
+};
+
+extern session_t session;
+
+#endif /* CONFIG_H_ */
diff --git a/homework_2/include/matrix.hpp b/homework_2/include/matrix.hpp
new file mode 100644
index 0000000..33b3266
--- /dev/null
+++ b/homework_2/include/matrix.hpp
@@ -0,0 +1,804 @@
+/**
+ * \file    matrix.hpp
+ * \brief   A matrix abstraction implementation
+ *
+ * \author
+ *    Christos Choutouridis AEM:8997
+ *    <cchoutou@ece.auth.gr>
+ */
+#ifndef MATRIX_HPP_
+#define MATRIX_HPP_
+
+#include <type_traits>
+#include <utility>
+#include <algorithm>
+#include <vector>
+#include <tuple>
+
+namespace mtx {
+
+using std::size_t;
+
+/*
+ * Small helper to strip types
+ */
+template<typename T>
+struct remove_cvref {
+    typedef std::remove_cv_t<std::remove_reference_t<T>> type;
+};
+template<typename T>
+using remove_cvref_t = typename remove_cvref<T>::type;
+
+/*!
+ * Enumerator to denote the storage type of the array to use.
+ */
+enum class MatrixType {
+   DENSE,      /*!< Matrix is dense */
+   SPARSE,     /*!< Matrix is sparse */
+};
+
+/*!
+ * Enumerator to denote the storage type of the array to use.
+ */
+enum class MatrixOrder {
+   COLMAJOR,     /*!< Matrix is column major */
+   ROWMAJOR,     /*!< Matrix is row major */
+};
+
+/*
+ * Forward type declarations
+ */
+
+template<typename MatrixType> struct MatCol;
+template<typename MatrixType> struct MatRow;
+template<typename MatrixType> struct MatVal;
+
+ /*!
+ * A 2-D matrix functionality over a 1-D array
+ *
+ * This is a very thin abstraction layer over a native array.
+ * This is tested using compiler explorer and our template produce
+ * almost identical assembly.
+ *
+ * The penalty hit we have is due to the fact that we use a one dimension array
+ * and we have to calculate the actual position from an (i,j) pair.
+ * The use of 1D array was our intention from the beginning, so the penalty
+ * was pretty much unavoidable.
+ *
+ * \tparam DataType  The underling data type of the array
+ * \tparam IndexType The underling type for the index variables and sizes
+ * \tparam Type      The storage type of the array
+ *    \arg  FULL              For full matrix
+ *    \arg  SYMMETRIC         For symmetric matrix (we use only the lower part)
+ */
+template<typename DataType,
+         typename IndexType = size_t,
+         MatrixType Type    = MatrixType::DENSE,
+         MatrixOrder Order  = MatrixOrder::ROWMAJOR,
+         bool Symmetric     = false>
+struct Matrix {
+
+   using dataType    = DataType;                   //!< meta:export of underling data type
+   using indexType   = IndexType;                  //!< meta:export of underling index type
+   static constexpr MatrixOrder matrixOrder = Order; //!< meta:export of array order
+   static constexpr MatrixType matrixType = Type;  //!< meta:export of array type
+   static constexpr bool symmetric = Symmetric;    //!< meta:export symmetric flag
+
+   /*!
+    * \name Obj lifetime
+    */
+   //! @{
+
+   //! Construct an empty matrix with dimensions rows x columns
+   Matrix(IndexType rows = IndexType{}, IndexType columns = IndexType{}) noexcept
+       : vector_storage_(capacity(rows, columns)),
+         raw_storage_(nullptr),
+         use_vector_(true),
+         rows_(rows),
+         cols_(columns) {
+       data_ = vector_storage_.data();
+    }
+
+   //! Construct a matrix by copying existing data with dimensions rows x columns
+   Matrix(DataType* data, IndexType major_start, IndexType major_length, IndexType minor_length) noexcept
+      :  vector_storage_(),
+         raw_storage_ (data + major_start * minor_length),
+         use_vector_ (false) {
+      if constexpr (Order == MatrixOrder::ROWMAJOR) {
+         rows_ = major_length;
+         cols_ = minor_length;
+      }
+      else {
+         rows_ = minor_length;
+         cols_ = major_length;
+      }
+      data_ = raw_storage_;
+   }
+
+   //! Construct a matrix using an initializer list
+   Matrix(IndexType rows, IndexType columns, std::initializer_list<DataType> list)
+      : vector_storage_(list),
+        raw_storage_(nullptr),
+        use_vector_(true),
+        rows_(rows),
+        cols_(columns) {
+      if (list.size() != capacity(rows, columns)) {
+          throw std::invalid_argument("Matrix initializer list size does not match matrix dimensions.");
+      }
+      data_ = vector_storage_.data();
+   }
+
+   //! move ctor
+   Matrix(Matrix&& m) noexcept { moves(std::move(m)); }
+   //! move
+   Matrix& operator=(Matrix&& m) noexcept { moves(std::move(m)); return *this; }
+   Matrix(const Matrix& m)             = delete;  //!< No copy ctor
+   Matrix& operator=(const Matrix& m)  = delete;  //!< No copy
+   //Matrix(const Matrix& m);
+   //Matrix& operator=(const Matrix& m) { copy(m); }
+
+   //! @}
+
+   //! \name Data exposure
+   //! @{
+
+
+   //! Get/Set the size of each dimension
+   IndexType rows() const noexcept { return rows_; }
+   IndexType columns() const noexcept { return cols_; }
+
+   //! Get the interface size of the Matrix (what appears to be the size)
+   IndexType size() const {
+      return rows_ * cols_;
+   }
+   //! Set the interface size of the Matrix (what appears to be the size)
+   IndexType resize(IndexType rows, IndexType columns) {
+      if (use_vector_) {
+         rows_ = rows;
+         cols_ = columns;
+         vector_storage_.resize(capacity(rows_, cols_));
+         data_ = vector_storage_.data();
+      }
+      return capacity(rows_, cols_);
+   }
+
+   //! Actual memory capacity of the symmetric matrix
+   static constexpr IndexType capacity(IndexType M, IndexType N) {
+      if constexpr (Symmetric)
+         return (M+1)*N/2;
+      else
+         return M*N;
+   }
+
+   /*
+    * virtual 2D accessors
+    */
+   DataType get (IndexType i, IndexType j) {
+      if constexpr (Symmetric) {
+         auto T = [](size_t i)->size_t { return i*(i+1)/2; };          // Triangular number of i
+         if constexpr (Order == MatrixOrder::COLMAJOR) {
+            // In column major we use the lower triangle of the matrix
+            if (i>=j)   return data_[j*rows_ - T(j) + i];  // Lower, use our notation
+            else        return data_[i*rows_ - T(i) + j];  // Upper, use opposite index
+         }
+         else {
+            // In row major we use the upper triangle of the matrix
+            if (i<=j)   return data_[i*cols_ - T(i) + j];  // Upper, use our notation
+            else        return data_[j*cols_ - T(j) + i];  // Lower, use opposite index
+         }
+      }
+      else {
+         if constexpr (Order == MatrixOrder::COLMAJOR)
+            return data_[i + j*rows_];
+         else
+            return data_[i*cols_ + j];
+      }
+   }
+
+   /*!
+    * \fn DataType set(DataType, IndexType, IndexType)
+    * \param v
+    * \param i
+    * \param j
+    * \return
+    */
+   DataType set (DataType v, IndexType i, IndexType j) {
+      if constexpr (Symmetric) {
+         auto T = [](size_t i)->size_t { return i*(i+1)/2; };          // Triangular number of i
+         if constexpr (Order == MatrixOrder::COLMAJOR) {
+            // In column major we use the lower triangle of the matrix
+            if (i>=j)   return data_[j*rows_ - T(j) + i] = v;  // Lower, use our notation
+            else        return data_[i*rows_ - T(i) + j] = v;  // Upper, use opposite index
+         }
+         else {
+            // In row major we use the upper triangle of the matrix
+            if (i<=j)   return data_[i*cols_ - T(i) + j] = v;  // Upper, use our notation
+            else        return data_[j*cols_ - T(j) + i] = v;  // Lower, use opposite index
+         }
+      }
+      else {
+         if constexpr (Order == MatrixOrder::COLMAJOR)
+            return data_[i + j*rows_] = v;
+         else
+            return data_[i*cols_ + j] = v;
+      }
+   }
+//   DataType operator()(IndexType i, IndexType j) { return get(i, j); }
+   /*!
+    * Return a proxy MatVal object with read and write capabilities.
+    * @param i    The row number
+    * @param j    The column number
+    * @return     tHE MatVal object
+    */
+   MatVal<Matrix> operator()(IndexType i, IndexType j) noexcept {
+      return MatVal<Matrix>(this, get(i, j), i, j);
+   }
+
+   // a basic serial iterator support
+   DataType* data() noexcept { return data_; }
+   DataType* begin() noexcept { return data_; }
+   const DataType* begin() const noexcept { return data_; }
+   DataType* end() noexcept { return data_ + capacity(rows_, cols_); }
+   const DataType* end() const noexcept { return data_ + capacity(rows_, cols_); }
+
+//   IndexType begin_idx() noexcept { return 0; }
+//   IndexType end_idx()   noexcept { return capacity(rows_, cols_); }
+
+   const DataType* data() const noexcept { return data_; }
+   const IndexType begin_idx() const noexcept { return 0; }
+   const IndexType end_idx()   const noexcept { return capacity(rows_, cols_); }
+   //! @}
+
+   /*!
+    * \name Safe iteration API
+    *
+    * This api automates the iteration over the array based on
+    * MatrixType
+    */
+   //! @{
+   template<typename F, typename... Args>
+   void for_each_in (IndexType begin, IndexType end, F&& lambda, Args&&... args) {
+      for (IndexType it=begin ; it<end ; ++it) {
+         std::forward<F>(lambda)(std::forward<Args>(args)..., it);
+      }
+   }
+   //! @}
+
+   //
+   void swap(Matrix& src) noexcept {
+      std::swap(vector_storage_, src.vector_storage_);
+      std::swap(raw_storage_, src.raw_storage_);
+      std::swap(data_, src.data_);
+      std::swap(use_vector_, src.use_vector_);
+      std::swap(rows_, src.rows_);
+      std::swap(cols_, src.cols_);
+   }
+
+private:
+   //! move helper
+   void moves(Matrix&& src) noexcept {
+      vector_storage_ = std::move(src.vector_storage_);
+      raw_storage_    = std::move(src.raw_storage_);
+      data_           = std::move(src.data_);
+      use_vector_     = std::move(src.use_vector_);
+      rows_           = std::move(src.rows_);
+      cols_           = std::move(src.cols_);
+   }
+
+   // Storage
+   std::vector<DataType>
+               vector_storage_;  //!< Internal storage (if used).
+   DataType*   raw_storage_;     //!< External storage (if used).
+   DataType*   data_;            //!< Pointer to active storage.
+   bool        use_vector_;      //!< True if using vector storage, false for raw pointer.
+   IndexType   rows_{};          //!< the virtual size of rows.
+   IndexType   cols_{};          //!< the virtual size of columns.
+};
+
+
+/**
+ * A simple sparse matrix specialization.
+ *
+ * We use CSC format and provide get/set functionalities for each (i,j) item
+ * on the matrix. We also provide a () overload using a proxy MatVal object.
+ * This way the user can:
+ * \code
+ *    auto v = A(3,4);
+ *    A(3, 4) = 7;
+ * \endcode
+ *
+ * We also provide getCol() and getRow() functions witch return a viewer/iterator to rows and
+ * columns of the matrix. In the case of a symmetric matrix instead of a row we return the
+ * equivalent column. This way we gain speed due to CSC format nature.
+ *
+ * @tparam DataType  The type for values
+ * @tparam IndexType The type for indexes
+ * @tparam Type      The Matrix type (FULL or SYMMETRIC)
+ */
+template<typename DataType, typename IndexType,
+         MatrixOrder Order,
+         bool Symmetric>
+struct Matrix<DataType, IndexType, MatrixType::SPARSE, Order, Symmetric> {
+
+   using dataType    = DataType;                   //!< meta:export of underling data type
+   using indexType   = IndexType;                  //!< meta:export of underling index type
+   static constexpr MatrixOrder matrixOrder = Order; //!< meta:export of array order
+   static constexpr MatrixType matrixType = MatrixType::SPARSE;  //!< meta:export of array type
+   static constexpr bool symmetric = Symmetric;    //!< meta:export symmetric flag
+
+   friend struct MatCol<Matrix>;
+   friend struct MatRow<Matrix>;
+   friend struct MatVal<Matrix>;
+
+   /*!
+    * \name Obj lifetime
+    */
+   //! @{
+
+   //! Default ctor with optional memory allocations
+   Matrix(IndexType n=IndexType{}) noexcept:
+      values{},
+      rows{},
+      col_ptr((n)? n+1:2, IndexType{}),
+      N(n),
+      NNZ(0) { }
+
+   //! A ctor using csc array data
+   Matrix(IndexType n, IndexType nnz, const IndexType* row, const IndexType* col) noexcept:
+      values(nnz, 1),
+      rows(row, row+nnz),
+      col_ptr(col, col+n+1),
+      N(n),
+      NNZ(nnz) { }
+
+   //! ctor using csc array data with value array
+   Matrix(IndexType n, IndexType nnz, const DataType* v, const IndexType* row, const IndexType* col) noexcept:
+      values(v, v+nnz),
+      rows(row, row+nnz),
+      col_ptr(col, col+n+1),
+      N(n),
+      NNZ(nnz) { }
+
+   //! ctor vectors of row/col and default value for values array
+   Matrix(IndexType n, IndexType nnz, const DataType v,
+          const std::vector<IndexType>& row, const std::vector<IndexType>& col) noexcept:
+      values(nnz, v),
+      rows (row),
+      col_ptr(col),
+      N(n),
+      NNZ(nnz) { }
+
+   //! move ctor
+   Matrix(Matrix&& m) noexcept { moves(std::move(m)); }
+   //! move
+   Matrix& operator=(Matrix&& m) noexcept { moves(std::move(m)); return *this; }
+   Matrix(const Matrix& m)             = delete;  //!< make sure there are no copies
+   Matrix& operator=(const Matrix& m)  = delete;  //!< make sure there are no copies
+   //! @}
+
+   //! \name Data exposure
+   //! @{
+
+   //! \return the dimension of the matrix
+   IndexType size()     noexcept { return N; }
+   //! After construction size configuration tool
+   IndexType resize(IndexType n) {
+      col_ptr.resize(n+1);
+      return N = n;
+   }
+   //! \return the NNZ of the matrix
+   IndexType capacity() noexcept { return NNZ; }
+   //! After construction NNZ size configuration tool
+   IndexType capacity(IndexType nnz) noexcept {
+      values.reserve(nnz);
+      rows.reserve(nnz);
+      return NNZ;
+   }
+   // getters for row arrays of the struct (unused)
+   std::vector<DataType>&  getValues() noexcept { return values; }
+   std::vector<IndexType>& getRows() noexcept { return rows; }
+   std::vector<IndexType>& getCols() noexcept { return col_ptr; }
+
+   /*!
+    * Return a proxy MatVal object with read and write capabilities.
+    * @param i    The row number
+    * @param j    The column number
+    * @return     tHE MatVal object
+    */
+   MatVal<Matrix> operator()(IndexType i, IndexType j) noexcept {
+      return MatVal<Matrix>(this, get(i, j), i, j);
+   }
+
+   /*!
+    * A read item functionality using binary search to find the correct row
+    *
+    * @param i    The row number
+    * @param j    The column number
+    * @return     The value of the item or DataType{} if is not present.
+    */
+   DataType get(IndexType i, IndexType j) noexcept {
+      IndexType idx; bool found;
+      std::tie(idx, found) =find_idx(rows, col_ptr[j], col_ptr[j+1], i);
+      return (found) ? values[idx] : 0;
+   }
+
+   /*!
+    * A write item functionality.
+    *
+    * First we search if the matrix has already a value in (i, j) position.
+    * If so we just change it to a new value. If not we add the item on the matrix.
+    *
+    * @note
+    *    When change a value, we don't increase the NNZ value of the struct. We expect the user has already
+    *    change the NNZ value to the right one using @see capacity() function. When adding a value we
+    *    increase the NNZ.
+    *
+    * @param i    The row number
+    * @param j    The column number
+    * @return     The new value of the item .
+    */
+   DataType set(DataType v, IndexType i, IndexType j) {
+      IndexType idx; bool found;
+      std::tie(idx, found) = find_idx(rows, col_ptr[j], col_ptr[j+1], i);
+      if (found)
+         return values[idx] = v;    // we don't change NNZ even if we write "0"
+      else {
+         values.insert(values.begin()+idx, v);
+         rows.insert(rows.begin()+idx, i);
+         std::transform(col_ptr.begin()+j+1, col_ptr.end(), col_ptr.begin()+j+1, [](IndexType it) {
+            return ++it;
+         });
+         ++NNZ;                     // we increase the NNZ even if we write "0"
+         return v;
+      }
+   }
+
+   /*!
+    * Get a view of a CSC column
+    * @param j    The column to get
+    * @return     The MatCol object @see MatCol
+    */
+   MatCol<Matrix> getCol(IndexType j) noexcept {
+      return MatCol<Matrix>(this, col_ptr[j], col_ptr[j+1]);
+   }
+
+   /*!
+    * Get a view of a CSC row
+    *
+    * In case of a SYMMETRIC matrix we can return a column instead.
+    *
+    * @param j    The row to get
+    * @return     On symmetric matrix MatCol otherwise a MatRow
+    */
+
+   MatCol<Matrix> getRow(IndexType i) noexcept {
+      if constexpr (Symmetric)
+         return getCol(i);
+      else
+         return MatRow<Matrix>(this, i);
+   }
+
+   // values only iterator support
+   DataType* begin() noexcept { return values.begin(); }
+   DataType* end()   noexcept { return values.end(); }
+   //! @}
+
+   //! A small iteration helper
+   template<typename F, typename... Args>
+   void for_each_in (IndexType begin, IndexType end, F&& lambda, Args&&... args) {
+      for (IndexType it=begin ; it<end ; ++it) {
+         std::forward<F>(lambda)(std::forward<Args>(args)..., it);
+      }
+   }
+
+private:
+   /*!
+    * A small binary search implementation using index for begin-end instead of iterators.
+    *
+    * \param   v     Reference to vector to search
+    * \param   begin The vector's index to begin
+    * \param   end   The vector's index to end
+    * \param   match What to search
+    * \return  An <index, status> pair.
+    *                index    is the index of the item or end if not found
+    *                status   is true if found, false otherwise
+    */
+   std::pair<IndexType, bool> find_idx(const std::vector<IndexType>& v, IndexType begin, IndexType end, IndexType match) {
+      if (v.capacity() != 0 && begin < end) {
+         IndexType b = begin, e = end-1;
+         while (b <= e) {
+            IndexType m = (b+e)/2;
+            if       (v[m] == match)   return  std::make_pair(m, true);
+            else if  (b >= e)          return  std::make_pair(end, false);
+            else {
+               if    (v[m] <  match)   b = m +1;
+               else                    e = m -1;
+            }
+         }
+      }
+      return std::make_pair(end, false);
+   }
+
+   // move helper
+   void moves(Matrix&& src) noexcept {
+      values  = std::move(src.values);
+      rows    = std::move(src.rows);
+      col_ptr = std::move(src.col_ptr);
+      N       = std::move(src.N);   // redundant for primitives
+      NNZ     = std::move(src.NNZ); //
+   }
+   //! \name Data
+   //! @{
+   std::vector<DataType>   values {};     //!< vector to store the values of the matrix
+   std::vector<IndexType>  rows{};        //!< vector to store the row information
+   std::vector<IndexType>  col_ptr{1,0};  //!< vector to store the column pointers
+   IndexType   N{0};                      //!< The dimension of the matrix (square)
+   IndexType   NNZ{0};                    //!< The NNZ (capacity of the matrix)
+   //! @}
+};
+
+
+/*!
+ * A view/iterator hybrid object for Matrix columns.
+ *
+ * This object provides access to a column of a Matrix. The public functionalities
+ * allow data access using indexes instead of iterators. We prefer indexes over iterators
+ * because we can apply the same index to different inner vector of Matrix without conversion.
+ *
+ * @tparam DataType
+ * @tparam IndexType
+ */
+template<typename MatrixType>
+struct MatCol {
+   using owner_t = MatrixType;
+
+   using DataType  = typename MatrixType::dataType;
+   using IndexType = typename MatrixType::indexType;
+
+   /*!
+    * ctor using column pointers for begin-end. own is pointer to Matrix.
+    */
+   MatCol(owner_t* own, const IndexType begin, const IndexType end) noexcept :
+      owner_(own), index_(begin), begin_(begin), end_(end) {
+      vindex_ = vIndexCalc(index_);
+   }
+   MatCol()                        = default;
+   MatCol(const MatCol&)           = delete;   //!< make sure there are no copies
+   MatCol& operator=(const MatCol&)= delete;   //!< make sure there are no copies
+   MatCol(MatCol&&)                = default;
+   MatCol& operator=(MatCol&&)     = default;
+
+   //! a simple dereference operator, like an iterator
+   DataType operator* () {
+      return get();
+   }
+   //! Increment operator acts on index(), like an iterator
+   MatCol& operator++ ()    { advance(); return *this; }
+   MatCol& operator++ (int) { MatCol& p = *this; advance(); return p; }
+
+   //! () operator acts as member access (like a view)
+   DataType operator()(IndexType x) {
+      return (x == index())? get() : DataType{};
+   }
+   //! = operator acts as member assignment (like a view)
+   DataType operator= (DataType v) { return owner_->values[index_] = v; }
+   // iterator like handlers
+   // these return a virtual index value based on the items position on the full matrix
+   // but the move of the index is just a ++ away.
+   IndexType       index()       noexcept { return vindex_; }
+   const IndexType index() const noexcept { return vindex_; }
+   IndexType       begin()       noexcept { return vIndexCalc(begin_); }
+   const IndexType begin() const noexcept { return vIndexCalc(begin_); }
+   IndexType       end()         noexcept { return owner_->N; }
+   const IndexType end()   const noexcept { return owner_->N; }
+
+   /*!
+    * Multiplication operator
+    *
+    * We follow only the non-zero values and multiply only the common indexes.
+    *
+    * @tparam C   Universal reference for the type right half site column
+    *
+    * @param c    The right hand site matrix
+    * @return     The value of the inner product of two vectors
+    * @note       The time complexity is \$ O(nnz1+nnz2) \$.
+    *             Where the nnz is the max NNZ elements of the column of the matrix
+    */
+   template <typename C>
+   DataType operator* (C&& c) {
+      static_assert(std::is_same<remove_cvref_t<C>, MatCol<MatrixType>>(), "");
+      DataType v{};
+      while (index() != end() && c.index() != c.end()) {
+         if      (index() < c.index())  advance(); // advance me
+         else if (index() > c.index())  ++c;       // advance other
+         else { //index() == c.index()
+            v += get() * *c;                       // multiply and advance both
+            ++c;
+            advance();
+         }
+      }
+      return v;
+   }
+
+private:
+   //! small tool to increase the index pointers to Matrix
+   void advance() noexcept {
+      ++index_;
+      vindex_ = vIndexCalc(index_);
+   }
+   //! tool to translate between col_ptr indexes and Matrix "virtual" full matrix indexes
+   IndexType vIndexCalc(IndexType idx) {
+      return (idx < end_) ? owner_->rows[idx] : end();
+   }
+   //! small get tool
+   DataType get() { return owner_->values[index_]; }
+
+   owner_t*    owner_   {nullptr};     //!< Pointer to owner Matrix. MatCol is just a view
+   IndexType   vindex_  {IndexType{}}; //!< Virtual index of full matrix
+   IndexType   index_   {IndexType{}}; //!< index to Matrix::rows
+   IndexType   begin_   {IndexType{}}; //!< beginning index of the column in Matrix::rows
+   IndexType   end_     {IndexType{}}; //!< ending index of the column in Matrix::rows
+};
+
+/*!
+ * A view/iterator hybrid object for Matrix rows.
+ *
+ * This object provides access to a column of a Matrix. The public functionalities
+ * allow data access using indexes instead of iterators. We prefer indexes over iterators
+ * because we can apply the same index to different inner vector of Matrix without conversion.
+ *
+ * @tparam DataType
+ * @tparam IndexType
+ */
+template<typename MatrixType>
+struct MatRow {
+   using owner_t = MatrixType;
+
+   using DataType  = typename MatrixType::dataType;
+   using IndexType = typename MatrixType::indexType;
+
+   /*!
+    * ctor using virtual full matrix row index. own is pointer to Matrix.
+    */
+   MatRow(owner_t* own, const IndexType row) noexcept :
+      owner_(own), vindex_(IndexType{}), row_(row), index_(IndexType{}),
+      begin_(IndexType{}), end_(owner_->NNZ) {
+      // place begin
+      while(begin_ != end_ && owner_->rows[begin_] != row_)
+         ++begin_;
+      // place index_ and vindex_
+      if (owner_->rows[index_] != row_)
+         advance();
+   }
+   MatRow()                        = default;
+   MatRow(const MatRow&)           = delete;   //!< make sure there are no copies
+   MatRow& operator=(const MatRow&)= delete;   //!< make sure there are no copies
+   MatRow(MatRow&&)                = default;
+   MatRow& operator=(MatRow&&)     = default;
+
+   //! a simple dereference operator, like an iterator
+   DataType operator* () {
+      return get();
+   }
+   //! Increment operator acts on index(), like an iterator
+   //! here the increment is a O(N) process.
+   MatRow& operator++ ()    { advance(); return *this; }
+   MatRow& operator++ (int) { MatRow& p = *this; advance(); return p; }
+
+   //! () operator acts as member access (like a view)
+   DataType operator()(IndexType x) {
+      return (x == index())? get() : DataType{};
+   }
+   //! = operator acts as member assignment (like a view)
+   DataType operator= (DataType v) { return owner_->values[index_] = v; }
+   // iterator like handlers
+   // these return a virtual index value based on the items position on the full matrix
+   // but the move of the index is just a ++ away.
+   IndexType       index()       noexcept { return vindex_; }
+   const IndexType index() const noexcept { return vindex_; }
+   IndexType       begin()       noexcept { return vIndexCalc(begin_); }
+   const IndexType begin() const noexcept { return vIndexCalc(begin_); }
+   IndexType       end()         noexcept { return owner_->N; }
+   const IndexType end()   const noexcept { return owner_->N; }
+
+   /*!
+    * Multiplication operator
+    *
+    * We follow only the non-zero values and multiply only the common indexes.
+    *
+    * @tparam C   Universal reference for the type right half site column
+    *
+    * @param c    The right hand site matrix
+    * @return     The value of the inner product of two vectors
+    * @note       The time complexity is \$ O(N+nnz2) \$ and way heavier the ColxCol multiplication.
+    *             Where the nnz is the max NNZ elements of the column of the matrix
+    */
+   template <typename C>
+   DataType operator* (C&& c) {
+      static_assert(std::is_same<remove_cvref_t<C>, MatCol<MatrixType>>(), "");
+      DataType v{};
+      while (index() != end() && c.index() != c.end()) {
+         if      (index() < c.index())  advance(); // advance me
+         else if (index() > c.index())  ++c;       // advance other
+         else { //index() == c.index()
+            v += get() * *c;                       // multiply and advance both
+            ++c;
+            advance();
+         }
+      }
+      return v;
+   }
+private:
+   //! small tool to increase the index pointers to Matrix matrix
+   //! We have to search the entire rows vector in Matrix to find the next
+   //! virtual row position.
+   //! time complexity O(N)
+   void advance() noexcept {
+      do
+         ++index_;
+      while(index_ != end_ && owner_->rows[index_] != row_);
+      vindex_ = vIndexCalc(index_);
+   }
+   //! tool to translate between col_ptr indexes and Matrix "virtual" full matrix indexes
+   IndexType vIndexCalc(IndexType idx) {
+      for(IndexType i =0 ; i<(owner_->N+1) ; ++i)
+         if (idx < owner_->col_ptr[i])
+            return i-1;
+      return end();
+   }
+   //! small get tool
+   DataType get() { return owner_->values[index_]; }
+
+   owner_t*    owner_   {nullptr};     //!< Pointer to owner Matrix. MatCol is just a view
+   IndexType   vindex_  {IndexType{}}; //!< Virtual index of full matrix
+   IndexType   row_     {IndexType{}}; //!< The virtual full matrix row of the object
+   IndexType   index_   {IndexType{}}; //!< index to Matrix::rows
+   IndexType   begin_   {IndexType{}}; //!< beginning index of the column in Matrix::rows
+   IndexType   end_     {IndexType{}}; //!< ending index of the column in Matrix::rows
+};
+
+/*!
+ * A proxy Matrix value object/view.
+ *
+ * This object acts as proxy to provide read/write access to an Matrix item.
+ *
+ * @tparam DataType     The type of the values of the Matrix matrix
+ * @tparam IndexType    The type of the indexes of the Matrix matrix
+ */
+template<typename MatrixType>
+struct MatVal {
+   using owner_t = MatrixType;
+
+   using DataType  = typename MatrixType::dataType;
+   using IndexType = typename MatrixType::indexType;
+
+   //!< ctor using all value-row-column data, plus a pointer to owner Matrix object
+   MatVal(owner_t* own, DataType v, IndexType i, IndexType j) :
+      owner_(own), v_(v), i_(i), j_(j) { }
+   MatVal()                         = default;
+   MatVal(const MatVal&)            = delete;  //!< make sure there are no copies
+   MatVal& operator=(const MatVal&) = delete;  //!< make sure there are no copies
+   MatVal(MatVal&&)                 = default;
+   MatVal& operator=(MatVal&&)      = default;
+
+   //! Operator to return the DataType value implicitly
+   operator DataType() { return v_; }
+   //! Operator to write back to owner the assigned value
+   //! for ex: A(2,3) = 5;
+   MatVal& operator=(DataType v) {
+      v_ = v;
+      owner_->set(v_, i_, j_);
+      return *this;
+   }
+private:
+   owner_t*    owner_{nullptr};  //!< Pointer to owner Matrix. MatVal is just a view.
+   DataType    v_{DataType{}};   //!< The value of the row-column pair (for speed)
+   IndexType   i_{IndexType{}};  //!< The row
+   IndexType   j_{IndexType{}};  //!< the column
+};
+
+
+} // namespace mtx
+
+
+#endif /* MATRIX_HPP_ */
diff --git a/homework_2/include/utils.hpp b/homework_2/include/utils.hpp
new file mode 100644
index 0000000..c6385ac
--- /dev/null
+++ b/homework_2/include/utils.hpp
@@ -0,0 +1,87 @@
+/**
+ * \file    utils.hpp
+ * \brief   Utilities header
+ *
+ * \author
+ *    Christos Choutouridis AEM:8997
+ *    <cchoutou@ece.auth.gr>
+ */
+#ifndef UTILS_HPP_
+#define UTILS_HPP_
+
+#include <iostream>
+#include <chrono>
+#include <unistd.h>
+
+#include "matrix.hpp"
+#include "config.h"
+
+/*!
+ * A Logger for entire program.
+ */
+struct Log {
+   struct Endl {} endl;    //!< a tag object to to use it as a new line request.
+
+   //! We provide logging via << operator
+   template<typename T>
+   Log& operator<< (T&& t) {
+      if (session.verbose) {
+         if (line_) {
+            std::cout << "[Log]: " << t;
+            line_ = false;
+         }
+         else
+            std::cout << t;
+      }
+      return *this;
+   }
+   // overload for special end line handling
+   Log& operator<< (Endl e) { (void)e;
+      if (session.verbose) {
+         std::cout << '\n';
+         line_ = true;
+      }
+      return *this;
+   }
+private:
+   bool line_ {true};
+};
+
+extern Log logger;
+
+/*!
+ * A small timing utility based on chrono.
+ */
+struct Timing{
+   using Tpoint = std::chrono::steady_clock::time_point;
+   using microseconds = std::chrono::microseconds;
+   using milliseconds = std::chrono::milliseconds;
+   using seconds = std::chrono::seconds;
+
+   //! tool to mark the starting point
+   Tpoint start () noexcept { return start_ = std::chrono::steady_clock::now(); }
+   //! tool to mark the ending point
+   Tpoint stop ()  noexcept { return stop_ = std::chrono::steady_clock::now(); }
+
+   auto dt () noexcept {
+      return std::chrono::duration_cast<std::chrono::microseconds>(stop_ - start_).count();
+   }
+   //! tool to print the time interval
+   void print_dt (const char* what) noexcept {
+      if (session.timing) {
+         auto t = stop_ - start_;
+         if       (std::chrono::duration_cast<microseconds>(t).count() < 10000)
+            std::cout << "[Timing]: " << what << ": " << std::to_string(std::chrono::duration_cast<microseconds>(t).count()) << " [usec]\n";
+         else if (std::chrono::duration_cast<milliseconds>(t).count() < 10000)
+            std::cout << "[Timing]: " << what << ": " << std::to_string(std::chrono::duration_cast<milliseconds>(t).count()) << " [msec]\n";
+         else
+            std::cout << "[Timing]: " << what << ": " << std::to_string(std::chrono::duration_cast<seconds>(t).count()) << " [sec]\n";
+      }
+   }
+private:
+   Tpoint start_;
+   Tpoint stop_;
+};
+
+
+#endif /* UTILS_HPP_ */
diff --git a/homework_2/src/main.cpp b/homework_2/src/main.cpp
index a51103c..0bfa754 100644
--- a/homework_2/src/main.cpp
+++ b/homework_2/src/main.cpp
@@ -1,3 +1,78 @@
-int main(void) {
+/*!
+ * \file    main.cpp
+ * \brief   Main application file for PDS HW2 (MPI)
+ *
+ * \author
+ *    Christos Choutouridis AEM:8997
+ *    <cchoutou@ece.auth.gr>
+ */
+#include <exception>
+#include <iostream>
+
+#include <mpi.h>
+
+#include "matrix.hpp"
+#include "utils.hpp"
+#include "config.h"
+
+// Global session data
+session_t   session;
+
+/*!
+ * A small command line argument parser
+ * \return  The status of the operation
+ */
+bool get_options(int argc, char* argv[]){
+    bool status =true;
+
+    // iterate over the passed arguments
+    for (int i=1 ; i<argc ; ++i) {
+        std::string arg(argv[i]);     // get current argument
+
+        if (arg == "-x" || arg == "--xxxxx") {
+            if (i+2 < argc) {
+//                session.corpusMtxFile = std::string(argv[++i]);
+//                session.corpusDataSet = std::string(argv[++i]);
+            }
+            else
+                status = false;
+        }
+
+        else if (arg == "-v" || arg == "--verbose")
+            session.verbose = true;
+        else if (arg == "-h" || arg == "--help") {
+            std::cout << "distbitonic - A distributed bitonic sort\n\n";
+            std::cout << "distbitonic -x <> [-v]\n";
+            std::cout << '\n';
+            std::cout << "Options:\n\n";
+            std::cout << "   -v | --verbose\n";
+            std::cout << "      Request a more verbose output to stdout.\n\n";
+            std::cout << "   -h | --help\n";
+            std::cout << "      Prints this and exit.\n\n";
+            std::cout << "Examples:\n\n";
+            std::cout << "   ...Example case...:\n";
+            std::cout << "   > distbitonic -x <xxxxx>  \n\n";
+
+            exit(0);
+        }
+        else {   // parse error
+            std::cout << "Invocation error. Try -h for details.\n";
+            status = false;
+        }
+    }
+
+    return status;
+}
+
+int main(int argc, char* argv[]) try {
+    // try to read command line
+    if (!get_options(argc, argv))
+        exit(1);
+
     return 0;
+}
+catch (std::exception& e) {
+    //we probably pollute the user's screen. Comment `cerr << ...` if you don't like it.
+    std::cerr << "Error: " << e.what() << '\n';
+    exit(1);
 }
\ No newline at end of file