# cunmhr.f - Man Page

SRC/cunmhr.f

## Synopsis

### Functions/Subroutines

subroutine **cunmhr** (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)**CUNMHR**

## Function/Subroutine Documentation

### subroutine cunmhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

**CUNMHR**

**Purpose:**

CUNMHR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of IHI-ILO elementary reflectors, as returned by CGEHRD: Q = H(ilo) H(ilo+1) . . . H(ihi-1).

**Parameters***SIDE*SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right.

*TRANS*TRANS is CHARACTER*1 = 'N': apply Q (No transpose) = 'C': apply Q**H (Conjugate transpose)

*M*M is INTEGER The number of rows of the matrix C. M >= 0.

*N*N is INTEGER The number of columns of the matrix C. N >= 0.

*ILO*ILO is INTEGER

*IHI*IHI is INTEGER ILO and IHI must have the same values as in the previous call of CGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and IHI = 0, if N = 0.

*A*A is COMPLEX array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by CGEHRD.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.

*TAU*TAU is COMPLEX array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEHRD.

*C*C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

*LDC*LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).

*WORK*WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. 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.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **177** of file **cunmhr.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cunmhr(3) is an alias of cunmhr.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK