◆ construct_permutation_scaling_matrix()

void Chusov::Math::construct_permutation_scaling_matrix	(	ValueType *restrict	column_matrix,
		std::size_t	n,
		const std::size_t *restrict	permutation_indices,
		ValueType	scaling
	)

noexcept

Constructs a permutation matrix as a two-dimensional array of columns of elements from a vector of integral indices of elements within each column of a matrix.

Template Parameters

ValueType A type of a matrix element.

Parameters

[out]	column_matrix	A pointer to a buffer, in which elements of the resulting permutation matrix are constructed element-by-element. This buffer must be sufficient in size to hold \(n^2\) elements of the type `ValueType` in order to hold a two-dimensional array of column-major square matrix of size `nXn`.
	n	A number of columns and rows of the resulting permutation matrix constructed in the buffer addressed by `column_matrix`.
[in]	permutation_indices	An array of integral indices of non-zero elements within each column of the constructed permutation matrix. All elements of the array are assumed unique and their values are assumed less than `n`, though these preconditions are not validated by the function.
	scaling	A value assigned to non-zero elements of the permutation matrix. For a strictly permutation matrix the value of `scaling` should have the semantics of 1 (multiplicative identity).

Exceptions

Any	exception thrown by default, copy- or move-construction of `ValueType` elements.

The function uses a map \(f: \mathbb{N}_0 \to T^n\), where \(T\) is a set of values implemented by the type ValueType, to produce vectors to constitute columns of the resulting permutation matrix, such that each i^th column will have one permutation_indices[i]-th scalar copy-constructed in place addressed by &column_matrix[i * n + permutation_indices[i]] from scaling, and the other elements of that column will be default-constructed. Then the resulting matrix, elements of which are sequentially constructed in the place of column_matrix, will be \(M=\left(\begin{array}{cccc} f(p_0) & f(p_1) & \cdots & f(p_{n-1}) \end{array}\right)\), where p_i == permutation_indices[i].

The elements of the resulting permutation matrix are sequentially constructed in the uninitialized buffer pointed to by column_matrix such that neither destructors of existing data nor any assignment takes place. In order to properly replace elements of an existing matrix with a permutation matrix, use set_permutation_scaling_matrix.