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FactorizationQRTallSkinny

Computes a blocked Tall-Skinny QR factorization of an m-by-n (m>n) matrix: A = Q * R. LAPACK function LATSQR.

Computing for type matrix<double>

bool  matrix::FactorizationQRTallSkinny(
   long&           mb,           // row block size to be used in the blocked QR
   long&           nb,           // column block size to be used in the blocked QR
   matrix&         Q,            // orthogonal matrix Q
   matrix&         R             // upper triangular matrix R
   );

Computing for type matrix<float>

bool  matrix::FactorizationQRTallSkinny(
   long&           mb,           // row block size to be used in the blocked QR
   long&           nb,           // column block size to be used in the blocked QR
   matrixf&        Q,            // orthogonal matrix Q
   matrixf&        R             // upper triangular matrix R
   );

Computing for type matrix<complex>

bool  matrix::FactorizationQRTallSkinny(
   long&           mb,           // row block size to be used in the blocked QR
   long&           nb,           // column block size to be used in the blocked QR
   matrixc&        Q,            // unitary matrix Q
   matrixc&        R             // upper triangular matrix R
   );

Computing for type matrix<complexf>

bool  matrix::FactorizationQRTallSkinny(
   long&           mb,           // row block size to be used in the blocked QR
   long&           nb,           // column block size to be used in the blocked QR
   matrixcf&       Q,            // unitary matrix Q
   matrixcf&       R             // upper triangular matrix R
   );

Parameters

mb

[in,out] The row block size to be used in the blocked QR. MB > N. If 0 is passed in the parameter, the optimal MB value will be calculated using the ILAENV function and returned.

nb

[in,out] The column block size to be used in the blocked QR. N >= NB >= 1. If 0 is passed in the parameter, the optimal NB value will be calculated using the ILAENV function and returned.

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.

Note

Although the LAPACK routine ILAENV computes suitable values for MB and NB automatically, these parameters can be tuned manually to match the CPU cache size, which may provide a significant performance improvement. A useful rule of thumb is:

NB = min(N, 32 or 64)

MB = max(2*N, cache_target_rows)

MB = min(M-1, MB)

где cache_target_rows выбирается так, чтобы блок MB x N помещался в L2/L3 cache: MB ≈ cache_bytes / (8 * N) для double precision.