?ungql

Syntax

FORTRAN 77:

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

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

Fortran 95:

call ungql(a, tau [,info])

C:

lapack_int LAPACKE_<?>ungql( int matrix_order, lapack_int m, lapack_int n, lapack_int k, <datatype>* a, lapack_int lda, const <datatype>* tau );

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi and mkl_lapack.h include files, the Fortran 95 interfaces are specified in the lapack.f90 include file, and the C interfaces are specified in the mkl_lapacke.h include file.

Description

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

Input Parameters

The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

m

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

n

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

k

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

a, tau, work

COMPLEX for cungql

DOUBLE COMPLEX for zungql

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

On entry, the (n - k + i)th column of a must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by cgeqlf/zgeqlf in the last k columns of its array argument a;

tau(i) must contain the scalar factor of the elementaryreflector H(i), as returned by cgeqlf/zgeqlf;

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

The dimension 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, n).

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-by-n 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.

Fortran 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 Fortran 95 Interface Conventions.

Specific details for the routine ungql 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 =n*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 ?orgql.