# p?unmtr

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

## Syntax

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

call pzunmtr( side, uplo, trans, m, n, 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 = 'C': | 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 nq-1 elementary reflectors, as returned by p?hetrd.

If `uplo = 'U'`, `Q = H(nq-1)... H(2) H(1)`;

If `uplo = 'L'`, `Q = H(1) H(2)... H(nq-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.

uplo

  (global) CHARACTER.

  `= 'U'`: Upper triangle of `A(ia:*, ja:*)` contains elementary reflectors from p?hetrd;

  `= 'L'`: Lower triangle of `A(ia:*,ja:*)` contains elementary reflectors from p?hetrd

m

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

n

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

a

  (local)

  REAL for pcunmtr

  DOUBLE PRECISION for pzunmtr.

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

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

  If side='L', `lld_a ≥ max(1,LOCr(ia+m-1))`;

  If `side ='R'`, `lld_a ≥ max(1, LOCr(ia+n-1))`.

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 pcunmtr

  DOUBLE COMPLEX for pzunmtr.

  Array, DIMENSION of ltau where

  If `side = 'L'` and `uplo = 'U'`, `ltau = LOCc(m_a)`,

  if `side = 'L'` and `uplo = 'L'`, `ltau = LOCc(ja+m-2)`,

  if `side = 'R'` and `uplo = 'U'`, `ltau = LOCc(n_a)`,

  if `side = 'R'` and `uplo = 'L'`, `ltau = LOCc(ja+n-2)`.

  tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by p?hetrd. tau is tied to the distributed matrix A.

c

  (local) COMPLEX for pcunmtr

  DOUBLE COMPLEX for pzunmtr.

  Pointer into the local memory to an array of dimension `(lld_a, LOCc (ja+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 pcunmtr

  DOUBLE COMPLEX for pzunmtr.

  Workspace array of dimension lwork.

lwork

  (local or global) INTEGER, dimension of work, must be at least:

  If `uplo = 'U'`,

  `iaa= ia; jaa= ja+1, `icc= ic`; jcc= jc`;

  else `uplo = 'L'`,

  `iaa= ia+1, jaa= ja`;

  If `side = 'L'`,

  `icc= ic+1; jcc= jc`;

  else `icc= ic; jcc= jc+1`;

  end if

  end if

  If `side = 'L'`,

  `mi= m-1; ni= n`

  `lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0 + mpc0)*nb_a) + nb_a*nb_a`

  else

  If `side = 'R'`,

  `mi= m; mi = n-1`;

  `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

  Overwritten by the product 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`

Parent topic: Symmetric Eigenproblems