?unmhr

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?unmhr

Multiplies an arbitrary complex matrix C by the complex unitary matrix Q determined by ?gehrd.

Syntax

lapack_int LAPACKE_cunmhr (int matrix_layout, char side, char trans, lapack_int m, lapack_int n, lapack_int ilo, lapack_int ihi, const lapack_complex_float* a, lapack_int lda, const lapack_complex_float* tau, lapack_complex_float* c, lapack_int ldc);

lapack_int LAPACKE_zunmhr (int matrix_layout, char side, char trans, lapack_int m, lapack_int n, lapack_int ilo, lapack_int ihi, const lapack_complex_double* a, lapack_int lda, const lapack_complex_double* tau, lapack_complex_double* c, lapack_int ldc);

Include Files

mkl.h

Description

The routine multiplies a matrix C by the unitary matrix Q that has been determined by a preceding call to cgehrd/zgehrd. (The routine ?gehrd reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation, A = Q*H*Q^H, and represents the matrix Q as a product of ihi-ilo elementary 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.)

With ?unmhr, you can form one of the matrix products Q*C, Q^H*C, C*Q, or C*Q^H, overwriting the result on C (which may be any complex rectangular matrix). A common application of this routine is to transform a matrix V of eigenvectors of H to the matrix QV of eigenvectors of A.

Input Parameters

matrix_layout

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

side

Must be 'L' or 'R'.

If side = 'L', then the routine forms Q*C or Q^H*C.

If side = 'R', then the routine forms C*Q or C*Q^H.

trans

Must be 'N' or 'C'.

If trans = 'N', then Q is applied to C.

If trans = 'T', then Q^H is applied to C.

m

The number of rows in C (m≥ 0).

n

The number of columns in C (n≥ 0).

ilo, ihi

These must be the same parameters ilo and ihi, respectively, as supplied to ?gehrd .

If m > 0 and side = 'L', then 1 ≤ilo≤ihi≤m.

If m = 0 and side = 'L', then ilo = 1 and ihi = 0.

If n > 0 and side = 'R', then 1 ≤ilo≤ihi≤n.

If n = 0 and side = 'R', then ilo =1 and ihi = 0.

a, tau, c

Arrays:

a(size max(1,lda*n) for side='R' and size max(1,lda*m) for side='L') 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, m-1)

if side = 'L' and at least max (1, n-1) if side = 'R'.

c(size max(1, ldc*n) for column major layout and max(1, ldc*m for row major layout) contains the m-by-n matrix C.

lda

The leading dimension of a; at least max(1, m) if side = 'L' and at least max (1, n) if side = 'R'.

ldc

The leading dimension of c; at least max(1, m) for column major layout and at least max(1, n) for row major layout.

Output Parameters

c: C is overwritten by Q*C, or Q^H*C, or C*Q^H, or C*Q as specified by side and trans.

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)*||C||₂, where ε is the machine precision.

The approximate number of floating-point operations is

8n(ihi-ilo)² if side = 'L';

8m(ihi-ilo)² if side = 'R'.

The real counterpart of this routine is ormhr.

Parent topic: Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?unmhr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

Application Notes