?ungtr

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?ungtr

Generates the complex unitary matrix Q determined by ?hetrd .

Syntax

lapack_intLAPACKE_cungtr ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_float*a , lapack_intlda , constlapack_complex_float*tau );

lapack_intLAPACKE_zungtr ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_double*a , lapack_intlda , constlapack_complex_double*tau );

Include Files

mkl.h

Description

cungtr zungtr ungtr

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

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 , work

COMPLEX for cungtr DOUBLE COMPLEX for zungtr . Arrays:

a (size max(1, lda * n )) 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

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

lwork

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.

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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

The computed matrix \(Q\) differs from an exactly unitary matrix by a matrix \(E\) such that \(||E||_{2} = O(\varepsilon)\) , where \(\varepsilon\) is the machine precision.

The approximate number of floating-point operations is \((16/3)n^{3}\) .

The real counterpart of this routine is orgtr .

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?ungtr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes