Update sparse matrix class page

Author: ikorotkin

docs/sparse-matrix.md

@@ -15,12 +15,12 @@ sparse_matrix M;                 // Creates empty sparse matrix M
 M.reserve(2);                    // Reserves memory for 2 elements (optional)
 M.add_element(0, 1, 12.0);       // Fills row 0, column 1 with value 12.0
 M.add_element(1, 1, 42.0);       // Fills row 1, column 1 with value 42.0
-std::cout << M.dense(3) << '\n'; // Prints matrix on screen assuming it's a 3x3 matrix
+std::cout << M.dense(3) << '\n'; // Prints matrix M on screen assuming it's a 3x3 matrix
 ```
 
 ## Three-array format
 
-The three-array format defines a sparse matrix using two (unsigned) integer vectors of indices `i` and `j` and one floating point vector `A` of the corresponding non-zero elements of the matrix. Only non-zero elements of the sparse matrix should be defined. Theoretically, all three arrays can be empty. This will define a zero matrix where all elements are zeros.
+The three-array format defines a sparse matrix using two (unsigned) integer vectors of indices `i` and `j` and one floating-point vector `A` of the corresponding non-zero elements of the matrix. Only non-zero elements of the sparse matrix should be defined and stored. Theoretically, all three arrays can be empty. This will define a zero matrix where all elements are zeros.
 
 {: .note }
 All three arrays `i`, `j`, and `A` should be the same size. This can be (and will be) checked by calling the `void check()` method of the class `daecpp::sparse_matrix`.
@@ -37,7 +37,7 @@ $$
 $$
 
 This matrix contains only 3 non-zero elements: `1`, `2`, and `3`.
-Here is the matrix definition in three-array format:
+Here is the matrix $$\mathbf{M}$$ definition in three-array format:
 
 | `i` (row index) | `j` (column index) | `A` (non-zero element) |
 | --------------- | ------------------ | ---------------------- |
@@ -56,18 +56,18 @@ The row and column numeration starts from `0`.
 
 | Variable | Type | Description |
 | -------- | ---- | ----------- |
-| `A`      | `std` vector of `double` (default) or `float`      | Vector of non-zero elements `A` |
-| `i`      | `std` vector of `uint32_t` (default) or `uint64_t` | Vector of row indices `i`       |
-| `j`      | `std` vector of `uint32_t` (default) or `uint64_t` | Vector of column indices `j`    |
+| `A`      | `std::vector<float_type>` | Vector of non-zero elements `A` |
+| `i`      | `std::vector<int_type>`   | Vector of row indices `i`       |
+| `j`      | `std::vector<int_type>`   | Vector of column indices `j`    |
+
+For `float_type` and `int_type` definition, refer to the [Prerequisites](prerequisites.html#dae-cpp-types) section.
 
 {: .note }
 All three vectors are initially empty an NOT preallocated
 
 ## Sparse Matrix class methods
 
-----
-
-## `void operator()(ind_i, ind_j, A_ij)`
+## `void operator()(int_type ind_i, int_type ind_j, float_type A_ij)`
 
 <br>
 Adds next non-zero element to the sparse matrix.
@@ -90,7 +90,7 @@ M(0, 1, 2.0);    // Duplicated element is OK, it will be summed up, i.e., the va
 
 ----
 
-## `void add_element(ind_i, ind_j, A_ij)`
+## `void add_element(int_type ind_i, int_type ind_j, float_type A_ij)`
 
 <br>
 An alias to the operator `()` defined above.
@@ -114,7 +114,7 @@ M.add_element(0, 1, 2.0);  // Duplicated element will be summed up, i.e., the va
 
 ----
 
-## `void reserve(N_elements)`
+## `void reserve(int_type N_elements)`
 
 <br>
 Reserves memory for `N_elements` non-zero elements. It is strongly advised to allocate memory before filling in the sparse matrix arrays to avoid multiple copying and reallocation.
@@ -147,7 +147,7 @@ If it fails, the solver exits with error message (it is not possible to recover)
 
 ----
 
-## `auto dense(N) const`
+## `auto dense(int_type N) const`
 
 <br>
 Represents matrix in dense format. Suitable for printing using `std::cout`.
@@ -170,7 +170,7 @@ std::cout << M.dense(3) << '\n'; // Prints matrix on screen assuming it's a 3x3
 
 ----
 
-## `Eigen::SparseMatrix<float_type> convert(N) const`
+## `Eigen::SparseMatrix<float_type> convert(int_type N) const`
 
 <br>
 Converts matrix from `dae-cpp` three-array format to `Eigen::SparseMatrix` format.