cunmhr.f −

**Functions/Subroutines**

subroutine **cunmhr** (SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)

CUNMHR

**subroutine cunmhr (characterSIDE, characterTRANS, integerM, integerN, integerILO, integerIHI, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( ldc, * )C, integerLDC, complex, dimension( * )WORK, integerLWORK, integerINFO)
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.

**Date:**

November 2011

Definition at line 179 of file cunmhr.f.

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