?ungtr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?ungtr

Generates the complex unitary matrix Q determined by ?hetrd.

Syntax

call cungtr(uplo, n, a, lda, tau, work, lwork, info)

call zungtr(uplo, n, a, lda, tau, work, lwork, info)

call ungtr(a, tau [,uplo] [,info])

Include Files

mkl.fi, lapack.f90

Description

The routine explicitly generates the n-by-n unitary matrix Q formed by ?hetrd when reducing a complex Hermitian matrix A to tridiagonal form: A = Q*T*Q^H. Use this routine after a call to ?hetrd.

Input Parameters

uplo

CHARACTER*1. Must be 'U' or 'L'.

Use the same uplo as supplied to ?hetrd.

n

INTEGER. The order of the matrix Q (n≥ 0).

a, tau, work

COMPLEX for cungtr

DOUBLE COMPLEX for zungtr.

Arrays:

a(lda,*) is the array a as returned by ?hetrd.

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

tau(*) is the array tau as returned by ?hetrd.

The dimension of tau must be at least max(1, n-1).

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

lda

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

lwork

INTEGER. The size of the work array (lwork≥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 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 ungtr interface are the following:

a: Holds the matrix A of size (n,n).
tau: Holds the vector of length (n-1).
uplo: Must be 'U' or 'L'. The default value is 'U'.

Application Notes

For better performance, try using lwork = (n-1)*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 computed matrix Q differs from an exactly unitary matrix by a matrix E such that ||E||₂ = O(ε), where ε is the machine precision.

The approximate number of floating-point operations is (16/3)n³.

The real counterpart of this routine is orgtr.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?ungtr