?upgtr

Syntax

lapack_int LAPACKE_cupgtr (int matrix_layout, char uplo, lapack_int n, const lapack_complex_float* ap, const lapack_complex_float* tau, lapack_complex_float* q, lapack_int ldq);

lapack_int LAPACKE_zupgtr (int matrix_layout, char uplo, lapack_int n, const lapack_complex_double* ap, const lapack_complex_double* tau, lapack_complex_double* q, lapack_int ldq);

Include Files

• mkl.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

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

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

n

The order of the matrix Q (n≥ 0).

ap, tau

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

The leading dimension of the output array q;

at least max(1, n).

Output Parameters

q

Array, size (size max(1, ldq*n)) .

Contains the computed matrix Q.

Return Values

This function returns a value info.

If info=0, the execution is successful.

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

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.