p?larzc

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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p?larzc

Applies (multiplies by) the conjugate transpose of an elementary reflector as returned by p?tzrzf to a general matrix.

Syntax

call pclarzc(side, m, n, l, v, iv, jv, descv, incv, tau, c, ic, jc, descc, work)

call pzlarzc(side, m, n, l, v, iv, jv, descv, incv, tau, c, ic, jc, descc, work)

Description

The p?larzcroutine 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 in the distributed matrix sub(C). (m ≥ 0).

n

(global) INTEGER.

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

l

(global) INTEGER.

The columns of the distributed matrix 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 size (lld_v,*) containing the local pieces of the global distributed matrix 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 matrix V indicating the first row and the first column of the matrix sub(V), respectively.

descv

(global and local) INTEGER array of size 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 of size LOCc(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 size (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 matrix C indicating the first row and the first column of the matrix sub(C), respectively.

descc

(global and local) INTEGER array of size 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'.

Parent topic: ScaLAPACK Auxiliary Routines

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