Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/22/2024
Public

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?ungtr

Generates the complex unitary matrix Q determined by ?hetrd.

Syntax

lapack_int LAPACKE_cungtr (int matrix_layout, char uplo, lapack_int n, lapack_complex_float* a, lapack_int lda, const lapack_complex_float* tau);

lapack_int LAPACKE_zungtr (int matrix_layout, char uplo, lapack_int n, lapack_complex_double* a, lapack_int lda, const lapack_complex_double* tau);

Include Files

  • mkl.h

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*QH. Use this routine after a call to ?hetrd.

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 ?hetrd.

n

The order of the matrix Q (n 0).

a, tau

Arrays:

a (size max(1, lda*n)) is the array a as returned by ?hetrd.

tau is the array tau as returned by ?hetrd.

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

lda

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

Output Parameters

a

Overwritten by the unitary 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 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.