# FactorizationQR

Computes the QR factorization of a general m-by-n matrix: A = Q * R. LAPACK function [GEQRF](https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-fortran/2025-2/geqrf.html).

Computing for type matrix<double>

```
bool  matrix::FactorizationQR(
   bool            reduced,      // calculation mode reduced or complete
   matrix&         Q,            // orthogonal matrix Q
   matrix&         R             // upper triangular matrix R
   );

```

Computing for type matrix<float>

```
bool  matrix::FactorizationQR(
   bool            reduced,      // calculation mode reduced or complete
   matrixf&        Q,            // orthogonal matrix Q
   matrixf&        R             // upper triangular matrix R
   );

```

Computing for type matrix<complex>

```
bool  matrix::FactorizationQR(
   bool            reduced,      // calculation mode reduced or complete
   matrixc&        Q,            // unitary matrix Q
   matrixc&        R             // upper triangular matrix R
   );

```

Computing for type matrix<complexf>

```
bool  matrix::FactorizationQR(
   bool            reduced,      // calculation mode reduced or complete
   matrixcf&       Q,            // unitary matrix Q
   matrixcf&       R             // upper triangular matrix R
   );

```

Parameters

reduced

[in]  Calculation mode. If reduced is true then matrices Q, R calculated with dimensions (M, K), (K, N). If reduced is false it means complete calculation of matrices Q, R with dimensions (M,M), (M,N).

Q

[out]  Orthogonal or unitary matrix Q.

R

[out]  Upper triangular matrix R.

Return Value

Return true if successful, otherwise false in case of an [error](/en/docs/constants/errorswarnings/errorcodes).

Note

If reduced is true

If m >= n, matrix Q is of m-by-n sizes, matrix R is of n-by-n sizes.

If m < n, matrix Q is of m-by-m sizes, matrix R is of m-by-n sizes.

If reduced is false, matrix Q is of m-by-m sizes, matrix R is of m-by-n sizes.