p?larfc

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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p?larfc

Applies the conjugate transpose of an elementary reflector to a general matrix.

Syntax

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

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

Description

The p?larfcroutine 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.

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).

v

(local).

COMPLEX for pclarfc

COMPLEX*16 for pzlarfc.

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+m-1, jv) if side = 'L' and incv = 1,

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

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

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

The array v is 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 pclarfc

COMPLEX*16 for pzlarfc.

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 pclarfc

COMPLEX*16 for pzlarfc.

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).

COMPLEX for pclarfc

COMPLEX*16 for pzlarfc.

Workspace array of size lwork.

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,

where lcm is the least common multiple of nprow and npcol and 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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