?upgtr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?upgtr

Generates the complex unitary matrix Q determined by ?hptrd.

Syntax

call cupgtr(uplo, n, ap, tau, q, ldq, work, info)

call zupgtr(uplo, n, ap, tau, q, ldq, work, info)

call upgtr(ap, tau, q [,uplo] [,info])

Include Files

mkl.fi, lapack.f90

Description

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

Input Parameters

uplo

CHARACTER*1. Must be 'U' or 'L'. Use the same uplo as supplied to ?hptrd.

n

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

ap, tau

COMPLEX for cupgtr

DOUBLE COMPLEX for zupgtr.

Arrays ap and tau, as returned by ?hptrd.

The dimension of ap must be at least max(1, n(n+1)/2).

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

ldq

INTEGER. The leading dimension of the output array q;

at least max(1, n).

work

COMPLEX for cupgtr

DOUBLE COMPLEX for zupgtr.

Workspace array, size at least max(1, n-1).

Output Parameters

q

COMPLEX for cupgtr

DOUBLE COMPLEX for zupgtr.

Array, size (ldq,*) .

Contains the computed matrix Q.

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

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 upgtr interface are the following:

ap: Holds the array A of size (n*(n+1)/2).
tau: Holds the vector with the number of elements n - 1.
q: Holds the matrix Q of size (n,n).
uplo: Must be 'U' or 'L'. The default value is 'U'.

Application Notes

The computed matrix Q differs from an exactly orthogonal 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 opgtr.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?upgtr