# p?unmhr

Multiplies a general matrix by the unitary transformation matrix from a reduction to Hessenberg form determined by p?gehrd.

## Syntax

call pcunmhr(side, trans, m, n, ilo, ihi, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

call pzunmhr(side, trans, m, n, ilo, ihi, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

## Description

The routine overwrites the general complex distributed m-by-n matrix `sub(C) = C(ic:ic+m-1,jc:jc+n-1)` with

| side ='L' | side ='R'
trans = 'N': | Q*sub(C) | sub(C)*Q
trans = 'H': | QH*sub(C) | sub(C)*QH

where Q is a complex unitary distributed 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 p?gehrd.

`Q = H(ilo) H(ilo+1)... H(ihi-1)`.

## Input Parameters

side

  (global) CHARACTER

  `='L'`: Q or QH is applied from the left.

  `='R'`: Q or QH is applied from the right.

trans

  (global) CHARACTER

  `='N'`, no transpose, Q is applied.

  `='C'`, conjugate transpose, QH is applied.

m

  (global) INTEGER. The number of rows in the distributed submatrix sub (C) `(m≥0)`.

n

  (global) INTEGER. The number of columns in the distributed submatrix sub (C) `(n≥0)`.

ilo, ihi

  (global) INTEGER

  These must be the same parameters ilo and ihi, respectively, as supplied to p?gehrd. Q is equal to the unit matrix except in the distributed submatrix Q `(ia+ilo:ia+ihi-1,ia+ilo:ja+ihi-1)`.

  If `side ='L'`, then `1≤ilo≤ihi≤max(1,m)`.

  If `side = 'R'`, then `1≤ilo≤ihi≤max(1,n)`

  ilo and ihi are relative indexes.

a

  (local)

  COMPLEX for pcunmhr

  DOUBLE COMPLEX for pzunmhr.

  Pointer into the local memory to an array of dimension `(lld_a, LOC c(ja+m-1))` if `side='L'`, and `(lld_a, LOCc(ja+n-1))` if `side = 'R'`.

  Contains the vectors which define the elementary reflectors, as returned by p?gehrd.

ia, ja

  (global) INTEGER. The row and column indices in the global array a indicating the first row and the first column of the submatrix A, respectively.

desca

  (global and local) INTEGER array, dimension (dlen_). The array descriptor for the distributed matrix A.

tau

  (local)

  COMPLEX for pcunmhr

  DOUBLE COMPLEX for pzunmhr.

  Array, DIMENSION `LOCc(ja+m-2)`, if `side = 'L'`, and `LOCc(ja+n-2)` if `side = 'R'`.

  This array contains the scalar factors tau(j) of the elementary reflectors H(j) as returned by p?gehrd. tau is tied to the distributed matrix A.

c

  (local)

  COMPLEX for pcunmhr

  DOUBLE COMPLEX for pzunmhr.

  Pointer into the local memory to an array of dimension `(lld_c, LOCc(jc+n-1))`.

  Contains the local pieces of the distributed matrix sub(C).

ic, jc

  (global) INTEGER. The row and column indices in the global array c indicating the first row and the first column of the submatrix C, respectively.

descc

  (global and local) INTEGER array, dimension (dlen_). The array descriptor for the distributed matrix C.

work

  (local)

  COMPLEX for pcunmhr

  DOUBLE COMPLEX for pzunmhr.

  Workspace array with dimension lwork.

lwork

  (local or global)

  The dimension of the array work.

  lwork must be at least `iaa = ia + ilo;` `jaa = ja+ilo-1;`

  If `side = 'L'`, `mi = ihi-ilo`; `ni = n`; `icc = ic + ilo`; `jcc = jc`; `lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0+mpc0)*nb_a) + nb_a*nb_a`

  else if `side = 'R'`,

  `mi = m`; `ni = ihi-ilo`; `icc = ic`; `jcc = jc + ilo`; `lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0 + max(npa0+numroc(numroc(ni+icoffc, nb_a, 0, 0, NPCOL), nb_a, 0, 0, lcmq ), mpc0))*nb_a) + nb_a*nb_a`

  end if

  where `lcmq = lcm/NPCOL` with `lcm = ilcm(NPROW, NPCOL)`,

  `iroffa = mod(iaa-1, mb_a),`

  `icoffa = mod(jaa-1, nb_a)`,

  `iarow = indxg2p(iaa, mb_a, MYROW, rsrc_a, NPROW)`,

  `npa0 = numroc(ni+iroffa, mb_a, MYROW, iarow, NPROW)`,

  `iroffc = mod(icc-1, mb_c)`,

  `icoffc = mod(jcc-1, nb_c)`,

  `icrow = indxg2p(icc, mb_c, MYROW, rsrc_c, NPROW)`,

  `iccol = indxg2p(jcc, nb_c, MYCOL, csrc_c, NPCOL)`,

  `mpc0 = numroc(mi+iroffc, mb_c, MYROW, icrow, NPROW)`,

  `nqc0 = numroc(ni+icoffc, nb_c, MYCOL, iccol, NPCOL)`,

  ilcm, indxg2p and numroc are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine blacs_gridinfo.

  If `lwork = -1`, then lwork is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by pxerbla.

## Output Parameters

c

  C is overwritten by Q* sub(C) or Q'*sub(C) or sub(C)*Q' or sub(C)*Q.

`work(1)`

  On exit `work(1)` contains the minimum value of lwork required for optimum performance.

info

  (global) INTEGER.

  `= 0`: the execution is successful.

  `< 0`: if the i-th argument is an array and the j-entry had an illegal value, then `info = - (i* 100+j)`, if the i-th argument is a scalar and had an illegal value, then `info = -i`.

Parent topic: Nonsymmetric Eigenvalue Problems