# QuantLib_OrthogonalProjections man page

OrthogonalProjections —

## Synopsis

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

### Public Member Functions

OrthogonalProjections(constMatrix&originalVectors,RealmultiplierCutOff,Realtolerance)

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

const std::vector<Real> &GetVector(Sizeindex) constSize 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

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

Fri Sep 23 2016 Version 1.8.1 QuantLib