?ungrq

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?ungrq

Generates the complex matrix Q of the RQ factorization formed by ?gerqf.

Syntax

call cungrq(m, n, k, a, lda, tau, work, lwork, info)

call zungrq(m, n, k, a, lda, tau, work, lwork, info)

call ungrq(a, tau [,info])

Include Files

mkl.fi, lapack.f90

Description

The routine generates an m-by-n complex matrix with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors H(i) of order n: Q = H(1)^H* H(2)^H*...*H(k)^H as returned by the routines gerqf. Use this routine after a call to cgerqf/zgerqf.

Input Parameters

m

INTEGER. The number of rows of the matrix Q (m≥0).

n

INTEGER. The number of columns of the matrix Q (n≥m ).

k

INTEGER. The number of elementary reflectors whose product defines the matrix Q (m≥k≥0).

a, tau, work

REAL for cungrq

DOUBLE PRECISION for zungrq

Arrays: a(lda,*), tau(*), work(lwork).

On entry, the (m - k + i)th row of a must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by cgerqf/zgerqf in the last k rows of its array argument a;

tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by cgerqf/zgerqf;

The second dimension of a must be at least max(1, n).

The size of tau must be at least max(1, k).

work is a workspace array, its dimension max(1, lwork).

lda

INTEGER. The leading dimension of a; at least max(1, m).

lwork

INTEGER. The size of the work array; at least max(1, m).

If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

See Application Notes for the suggested value of lwork.

Output Parameters

a

Overwritten by the m last rows of the n-by-n unitary matrix Q.

work(1)

If info = 0, on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine ungrq interface are the following:

a: Holds the matrix A of size (m,n).
tau: Holds the vector of length (k).

Application Notes

For better performance, try using lwork =m*blocksize, where blocksize is a machine-dependent value (typically, 16 to 64) required for optimum performance of the blocked algorithm.

If it is not clear how much workspace to supply, use a generous value of lwork for the first run, or set lwork = -1.

In first case the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array work on exit. Use this value (work(1)) for subsequent runs.

If lwork = -1, then the routine returns immediately and provides the recommended workspace in the first element of the corresponding array (work). This operation is called a workspace query.

Note that if lwork is less than the minimal required value and is not equal to -1, then the routine returns immediately with an error exit and does not provide any information on the recommended workspace.

The real counterpart of this routine is orgrq.

Parent topic: Orthogonal Factorizations: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?ungrq