Developer Guide and Reference

  • 2021.3
  • 06/28/2021
  • Public Content
Contents

Pivoted QR Decomposition

Given the matrix
X
of size LaTex Math image., the problem is to compute the QR decomposition with column pivoting LaTex Math image., where
  • Q
    is an orthogonal matrix of size LaTex Math image.
  • R
    is a rectangular upper triangular matrix of size LaTex Math image.
  • P
    is a permutation matrix of size LaTex Math image.
The library requires LaTex Math image.. In this case:
LaTex Math image.
where the matrix LaTex Math image. has the size LaTex Math image. and LaTex Math image. has the size LaTex Math image..

Batch Processing

Algorithm Input
Pivoted QR decomposition accepts the input described below. Pass the
Input ID
as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.
Input ID
Input
data
Pointer to the numeric table that represents the LaTex Math image. matrix
X
to be factorized. The input can be an object of any class derived from
NumericTable
.
Algorithm Parameters
Pivoted QR decomposition has the following parameters:
Parameter
Default Value
Description
algorithmFPType
float
The floating-point type that the algorithm uses for intermediate computations. Can be
float
or
double
.
method
defaultDense
Performance-oriented computation method, the only method supported by the algorithm.
permutedColumns
Not applicable
Pointer to the numeric table with the LaTex Math image. matrix with the information for the permutation:
  • If the
    i
    -th element is zero, the
    i
    -th column of the input matrix is a free column and may be permuted with any other free column during the computation.
  • If the
    i
    -th element is non-zero, the
    i
    -th column of the input matrix is moved to the beginning of XP before the computation and remains in its place during the computation.
By default, this parameter is an object of the
HomogenNumericTable
class, filled by zeros. However, you can define this parameter as an object of any class derived from
NumericTable
except the
PackedSymmetricMatrix
class,
CSRNumericTable
class, and
PackedTriangularMatrix
class with the
lowerPackedTriangularMatrix
layout.
Algorithm Output
Pivoted QR decomposition calculates the results described below. Pass the
Result ID
as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.
Result ID
Result
matrixQ
Pointer to the numeric table with the LaTex Math image. matrix LaTex Math image..
By default, this result is an object of the
HomogenNumericTable
class, but you can define the result as an object of any class derived from
NumericTable
except
PackedSymmetricMatrix
,
PackedTriangularMatrix
, and
CSRNumericTable
.
matrixR
Pointer to the numeric table with the LaTex Math image. upper triangular matrix LaTex Math image..
By default, this result is an object of the
HomogenNumericTable
class, but you can define the result as an object of any class derived from
NumericTable
except the
PackedSymmetricMatrix
class,
CSRNumericTable
class, and
PackedTriangularMatrix
class with the
lowerPackedTriangularMatrix
layout.
permutationMatrix
Pointer to the numeric table with the LaTex Math image. matrix such that LaTex Math image. if the column
k
of the full matrix
X
is permuted into the position
i
in
XP
.
By default, this result is an object of the
HomogenNumericTable
class, but you can define the result as an object of any class derived from
NumericTable
except the
PackedSymmetricMatrix
class,
CSRNumericTable
class, and
PackedTriangularMatrix
class with the
lowerPackedTriangularMatrix
layout.

Examples

C++ (CPU)
Batch Processing:
Java*
There is no support for Java on GPU.
Batch Processing:
Python*
Batch Processing:

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.