# QuantLib_OrthogonalProjections man page

OrthogonalProjections

## Synopsis

`#include <ql/math/matrixutilities/basisincompleteordered.hpp>`

### Public Member Functions

**OrthogonalProjections** (const **Matrix** &originalVectors, **Real** multiplierCutOff, **Real** tolerance)

const std::valarray< bool > & **validVectors** () const

const std::vector< **Real** > & **GetVector** (**Size** index) const**Size numberValidVectors** () const

## Detailed Description

Given a collection of vectors, w_i, find a collection of vectors x_i such that x_i is orthogonal to w_j for i != j, and <x_i, w_i> = <w_i, w_i>

This is done by performing GramSchmidt on the other vectors and then projecting onto the orthogonal space.

This class is tested in

MatricesTest::testOrthogonalProjection();

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

The man pages GetVector(3), numberValidVectors(3), OrthogonalProjections(3) and validVectors(3) are aliases of QuantLib_OrthogonalProjections(3).