Generates the complex unitary matrix Q determined by ?gehrd.


lapack_int LAPACKE_cunghr (int matrix_layout, lapack_int n, lapack_int ilo, lapack_int ihi, lapack_complex_float* a, lapack_int lda, const lapack_complex_float* tau);

lapack_int LAPACKE_zunghr (int matrix_layout, lapack_int n, lapack_int ilo, lapack_int ihi, lapack_complex_double* a, lapack_int lda, const lapack_complex_double* tau);

Include Files

  • mkl.h


The routine is intended to be used following a call to cgehrd/zgehrd, which reduces a complex matrix A to upper Hessenberg form H by a unitary similarity transformation: A = Q*H*QH. ?gehrd represents the matrix Q as a product of ihi-iloelementary reflectors. Here ilo and ihi are values determined by cgebal/zgebal when balancing the matrix; if the matrix has not been balanced, ilo = 1 and ihi = n.

Use the routine unghr to generate Q explicitly as a square matrix. The matrix Q has the structure:


where Q22 occupies rows and columns ilo to ihi.

Input Parameters


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


The order of the matrix Q (n 0).

ilo, ihi

These must be the same parameters ilo and ihi, respectively, as supplied to ?gehrd . (If n > 0, then 1 iloihin. If n = 0, then ilo = 1 and ihi = 0.)

a, tau


a (size max(1, lda*n)) contains details of the vectors which define the elementary reflectors, as returned by ?gehrd.

tau contains further details of the elementary reflectors, as returned by ?gehrd .

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


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

Output Parameters


Overwritten by the n-by-n 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 the exact result by a matrix E such that ||E||2 = O(ε), where ε is the machine precision.

The approximate number of real floating-point operations is (16/3)(ihi-ilo)3.

The real counterpart of this routine is orghr.

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