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#### 8.4.5 Matrix views

A matrix view is a temporary object, stored on the stack, which can be used to operate on a subset of matrix elements. Matrix views can be defined for both constant and non-constant matrices using separate types that preserve constness. A matrix view has the type `gsl_matrix_view` and a constant matrix view has the type `gsl_matrix_const_view`. In both cases the elements of the view can by accessed using the `matrix` component of the view object. A pointer `gsl_matrix *` or `const gsl_matrix *` can be obtained by taking the address of the `matrix` component with the `&` operator. In addition to matrix views it is also possible to create vector views of a matrix, such as row or column views.

— Function: gsl_matrix_view gsl_matrix_submatrix (gsl_matrix * m, size_t k1, size_t k2, size_t n1, size_t n2)
— Function: gsl_matrix_const_view gsl_matrix_const_submatrix (const gsl_matrix * m, size_t k1, size_t k2, size_t n1, size_t n2)

These functions return a matrix view of a submatrix of the matrix m. The upper-left element of the submatrix is the element (k1,k2) of the original matrix. The submatrix has n1 rows and n2 columns. The physical number of columns in memory given by tda is unchanged. Mathematically, the (i,j)-th element of the new matrix is given by,

```          m'(i,j) = m->data[(k1*m->tda + k2) + i*m->tda + j]
```

where the index i runs from 0 to `n1-1` and the index j runs from 0 to `n2-1`.

The `data` pointer of the returned matrix struct is set to null if the combined parameters (i,j,n1,n2,tda) overrun the ends of the original matrix.

The new matrix view is only a view of the block underlying the existing matrix, m. The block containing the elements of m is not owned by the new matrix view. When the view goes out of scope the original matrix m and its block will continue to exist. The original memory can only be deallocated by freeing the original matrix. Of course, the original matrix should not be deallocated while the view is still in use.

The function `gsl_matrix_const_submatrix` is equivalent to `gsl_matrix_submatrix` but can be used for matrices which are declared `const`.

— Function: gsl_matrix_view gsl_matrix_view_array (double * base, size_t n1, size_t n2)
— Function: gsl_matrix_const_view gsl_matrix_const_view_array (const double * base, size_t n1, size_t n2)

These functions return a matrix view of the array base. The matrix has n1 rows and n2 columns. The physical number of columns in memory is also given by n2. Mathematically, the (i,j)-th element of the new matrix is given by,

```          m'(i,j) = base[i*n2 + j]
```

where the index i runs from 0 to `n1-1` and the index j runs from 0 to `n2-1`.

The new matrix is only a view of the array base. When the view goes out of scope the original array base will continue to exist. The original memory can only be deallocated by freeing the original array. Of course, the original array should not be deallocated while the view is still in use.

The function `gsl_matrix_const_view_array` is equivalent to `gsl_matrix_view_array` but can be used for matrices which are declared `const`.

— Function: gsl_matrix_view gsl_matrix_view_array_with_tda (double * base, size_t n1, size_t n2, size_t tda)
— Function: gsl_matrix_const_view gsl_matrix_const_view_array_with_tda (const double * base, size_t n1, size_t n2, size_t tda)

These functions return a matrix view of the array base with a physical number of columns tda which may differ from the corresponding dimension of the matrix. The matrix has n1 rows and n2 columns, and the physical number of columns in memory is given by tda. Mathematically, the (i,j)-th element of the new matrix is given by,

```          m'(i,j) = base[i*tda + j]
```

where the index i runs from 0 to `n1-1` and the index j runs from 0 to `n2-1`.

The new matrix is only a view of the array base. When the view goes out of scope the original array base will continue to exist. The original memory can only be deallocated by freeing the original array. Of course, the original array should not be deallocated while the view is still in use.

The function `gsl_matrix_const_view_array_with_tda` is equivalent to `gsl_matrix_view_array_with_tda` but can be used for matrices which are declared `const`.

— Function: gsl_matrix_view gsl_matrix_view_vector (gsl_vector * v, size_t n1, size_t n2)
— Function: gsl_matrix_const_view gsl_matrix_const_view_vector (const gsl_vector * v, size_t n1, size_t n2)

These functions return a matrix view of the vector v. The matrix has n1 rows and n2 columns. The vector must have unit stride. The physical number of columns in memory is also given by n2. Mathematically, the (i,j)-th element of the new matrix is given by,

```          m'(i,j) = v->data[i*n2 + j]
```

where the index i runs from 0 to `n1-1` and the index j runs from 0 to `n2-1`.

The new matrix is only a view of the vector v. When the view goes out of scope the original vector v will continue to exist. The original memory can only be deallocated by freeing the original vector. Of course, the original vector should not be deallocated while the view is still in use.

The function `gsl_matrix_const_view_vector` is equivalent to `gsl_matrix_view_vector` but can be used for matrices which are declared `const`.

— Function: gsl_matrix_view gsl_matrix_view_vector_with_tda (gsl_vector * v, size_t n1, size_t n2, size_t tda)
— Function: gsl_matrix_const_view gsl_matrix_const_view_vector_with_tda (const gsl_vector * v, size_t n1, size_t n2, size_t tda)

These functions return a matrix view of the vector v with a physical number of columns tda which may differ from the corresponding matrix dimension. The vector must have unit stride. The matrix has n1 rows and n2 columns, and the physical number of columns in memory is given by tda. Mathematically, the (i,j)-th element of the new matrix is given by,

```          m'(i,j) = v->data[i*tda + j]
```

where the index i runs from 0 to `n1-1` and the index j runs from 0 to `n2-1`.

The new matrix is only a view of the vector v. When the view goes out of scope the original vector v will continue to exist. The original memory can only be deallocated by freeing the original vector. Of course, the original vector should not be deallocated while the view is still in use.

The function `gsl_matrix_const_view_vector_with_tda` is equivalent to `gsl_matrix_view_vector_with_tda` but can be used for matrices which are declared `const`.

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