?upgtr

Syntax

FORTRAN 77:

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

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

FORTRAN 95:

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

C:

lapack_int LAPACKE_<?>upgtr( int matrix_order, char uplo, lapack_int n, const <datatype>* ap, const <datatype>* tau, <datatype>* q, lapack_int ldq );

Include Files

• Fortran: mkl_lapack.fi and mkl_lapack.h
• Fortran 95: lapack.f90
• C: mkl_lapacke.h

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

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.

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, DIMENSION at least max(1, n-1).

Output Parameters

q

COMPLEX for cupgtr

DOUBLE COMPLEX for zupgtr.

Array, DIMENSION (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.

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 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.