QR Decomposition
QR decomposition is a matrix factorization technique that decomposes a matrix into
a product of an orthogonal matrix
Q
and an upper triangular matrix R
.QR decomposition is used in solving linear inverse and least squares problems.
It also serves as a basis for algorithms that find eigenvalues and eigenvectors.
Performance Considerations
To get the best overall performance of the QR decomposition, for input, output, and auxiliary data,
use homogeneous numeric tables of the same type as specified in the
algorithmFPType
class template parameter.Online Processing
QR decomposition in the online processing mode is at least as computationally complex as in the batch processing mode
and has high memory requirements for storing auxiliary data between calls to the
compute()s
method.
On the other hand, the online version of QR decomposition may enable you to hide the latency of reading data from a slow data source.
To do this, implement load prefetching of the next data block in parallel with the compute()
method for the current block.Online processing mostly benefits QR decomposition when the matrix Q is not required.
In this case, memory requirements for storing auxiliary data goes down from
to
.
to
.Distributed Processing
Using QR decomposition in the distributed processing mode requires gathering local-node
numeric tables on the master node.
When the amount of local-node work is small, that is, when the local-node data set is small,
the network data transfer may become a bottleneck. To avoid this situation, ensure that local nodes have a sufficient amount of work.
For example, distribute the input data set across a smaller number of nodes.
numeric tables on the master node.
When the amount of local-node work is small, that is, when the local-node data set is small,
the network data transfer may become a bottleneck. To avoid this situation, ensure that local nodes have a sufficient amount of work.
For example, distribute the input data set across a smaller number of nodes.Optimization Notice |
|---|
Intel’s compilers may or may not optimize to the same degree for
non-Intel microprocessors for optimizations that are not unique to
Intel microprocessors. These optimizations include SSE2, SSE3, and
SSSE3 instruction sets and other optimizations. Intel does not
guarantee the availability, functionality, or effectiveness of any
optimization on microprocessors not manufactured by Intel.
Microprocessor-dependent optimizations in this product are intended
for use with Intel microprocessors. Certain optimizations not
specific to Intel microarchitecture are reserved for Intel
microprocessors. Please refer to the applicable product User and
Reference Guides for more information regarding the specific
instruction sets covered by this notice. Notice revision #20110804 |