p?larzc

Syntax

Include Files

• C: mkl_scalapack.h

Description

The p?larzc routine applies a complex elementary reflector Q^H to a complex m-by-n distributed matrix sub(C) = C(ic:ic+m-1, jc:jc+n-1), from either the left or the right. Q is represented in the form

Q = i-tau*v*v',

where tau is a complex scalar and v is a complex vector.

If tau = 0, then Q is taken to be the unit matrix.

Q is a product of k elementary reflectors as returned by p?tzrzf.

Input Parameters

side

(global) CHARACTER.

if side = 'L': form Q^H*sub(C);

if side = 'R': form sub(C)*Q^H .

m

(global) INTEGER.

The number of rows to be operated on, that is, the number of rows of the distributed submatrix sub(C). (m ≥ 0).

n

(global) INTEGER.

The number of columns to be operated on, that is, the number of columns of the distributed submatrix sub(C). (n ≥ 0).

l

(global) INTEGER.

The columns of the distributed submatrix sub(A) containing the meaningful part of the Householder reflectors.

If side = 'L', m ≥ l ≥ 0,

if side = 'R', n ≥ l ≥ 0.

v

(local).

COMPLEX for pclarzc

COMPLEX*16 for pzlarzc.

Pointer into the local memory to an array of DIMENSION (lld_v,*) containing the local pieces of the distributed vectors v representing the Householder transformation Q,

v(iv:iv+l-1, jv) if side = 'L' and incv = 1,

v(iv, jv:jv+l-1) if side = 'L' and incv = m_v,

v(iv:iv+l-1, jv) if side = 'R' and incv = 1,

v(iv, jv:jv+l-1) if side = 'R' and incv = m_v.

The vector v in the representation of Q. v is not used if tau = 0.

iv, jv

(global) INTEGER.

The row and column indices in the global array V indicating the first row and the first column of the submatrix sub(V), respectively.

descv

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

incv

(global). INTEGER.

The global increment for the elements of v. Only two values of incv are supported in this version, namely 1 and m_v.

incv must not be zero.

tau

(local)

COMPLEX for pclarzc

COMPLEX*16 for pzlarzc.

Array, DIMENSIONLOCc(jv) if incv = 1, and LOCr(iv) otherwise. This array contains the Householder scalars related to the Householder vectors.

tau is tied to the distributed matrix V.

c

(local).

COMPLEX for pclarzc

COMPLEX*16 for pzlarzc.

Pointer into the local memory to an array of DIMENSION(lld_c, LOCc(jc+n-1) ), containing the local pieces of 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 sub(C), respectively.

descc

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

work

(local).

If incv = 1,

  if side = 'L' ,

    if ivcol = iccol,

      lwork ≥ nqc0

    else

      lwork ≥ mpc0 + max(1, nqc0)

    end if

  else if side = 'R' ,

    lwork ≥ nqc0 + max(max(1, mpc0), numroc(numroc(n+icoffc, nb_v, 0, 0, npcol),

           nb_v, 0, 0, lcmq))

  end if

else if incv = m_v,

  if side = 'L' ,

    lwork ≥ mpc0 + max(max(1, nqc0), numroc(numroc(m+iroffc, mb_v, 0, 0, nprow),

           mb_v, 0, 0, lcmp))

  else if side = 'R',

    if ivrow = icrow,

      lwork ≥ mpc0

    else

      lwork ≥ nqc0 + max(1, mpc0)

    end if

  end if

         end if

Here lcm is the least common multiple of nprow and npcol;

lcm = ilcm(nprow, npcol), lcmp = lcm/nprow, lcmq= lcm/npcol,

iroffc = mod(ic-1, mb_c), icoffc= mod(jc-1, nb_c),

icrow = indxg2p(ic, mb_c, myrow, rsrc_c, nprow),

iccol = indxg2p(jc, nb_c, mycol, csrc_c, npcol),

mpc0 = numroc(m+iroffc, mb_c, myrow, icrow, nprow),

nqc0 = numroc(n+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.

Output Parameters

c

(local).

On exit, sub(C) is overwritten by the Q^H*sub(C) if side = 'L', or sub(C)*Q^H if side = 'R'.