◆ RowEchelonTransformRow()

bool RowEchelonTransformRow	(	size_type	iPivotColumn,
		size_type	iPivotRow,
		size_type	iTransformRow,
		transform_row_params_t...	transform_row_params
	)

protected

Performs a Gaussian row transformation to nullify a specified element located in the same column as a specified pivot element during a row echelon form transformation of the current matrix which is performed by the RowEchelonMe method.

Template Parameters

transform_row_params_t... is a template type parameter pack for arguments to the function that are provided by a caller of the RowEchelonMe method with the latter passing them as-is to the RowEchelonTransformRow method.

Parameters

iPivotColumn	is an index of a column that contains a pivot element in the row `iPivotRow`, and that is the same column that has an element to nullify, in the `iTransformRow` row.
iPivotRow	is an index of a row that has a pivot element in the column `iPivotColumn`.
iTransformRow	is an index of a row containing an element to nulltify in the column `iPivotColumn`. Using the Gaussian elimination the method transforms the whole row to nullify the element.
transform_row_params	is a pack of parameters provided by a caller of the RowEchelonMe method, which, in turn, passes them as is to the discussed `RowEchelonTransformRow` method. These parameters are always optional and it is safe to omit them for any type of a matrix element. But if the parameters are provided, there meaning and semantics are dependent upon an algebraic structure implemented by a `value_type` class of matrix elements. See the RowEchelonMe method for further details upon this.

Returns: If an element to be transformed is already zero (before the call), the function does not do anything and returns false. Otherwise, the transformation is performed, and the function returns true.

Note: In any way passing arguments to the RowEchelonMe method is optional and it is safe to omit them in a call to the RowEchelonMe method for any kind of matrix elements.; This documentation uses terms pivot row, pivot column, and pivot element as they are defined for row echelon form.; A nullifying of a matrix element is an assigning a value value_type(Chusov::Math::additive_identity) to the element. A value value_type(Chusov::Math::additive_identity) is called a zero value (or element) here.