p?larfb

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?larfb

Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix.

Syntax

call pslarfb(side, trans, direct, storev, m, n, k, v, iv, jv, descv, t, c, ic, jc, descc, work)

call pdlarfb(side, trans, direct, storev, m, n, k, v, iv, jv, descv, t, c, ic, jc, descc, work)

call pclarfb(side, trans, direct, storev, m, n, k, v, iv, jv, descv, t, c, ic, jc, descc, work)

call pzlarfb(side, trans, direct, storev, m, n, k, v, iv, jv, descv, t, c, ic, jc, descc, work)

Description

The p?larfbroutine applies a real/complex block reflector Q or its transpose Q^T/conjugate transpose Q^H to a real/complex distributed m-by-n matrix sub(C) = C(ic:ic+m-1, jc:jc+n-1) from the left or the right.

Input Parameters

side

(global) CHARACTER.

if side = 'L': apply Q or Q^T for real flavors (Q^H for complex flavors) from the Left;

if side = 'R': apply Q or Q^Tfor real flavors (Q^H for complex flavors) from the Right.

trans

(global) CHARACTER.

if trans = 'N': no transpose, apply Q;

for real flavors, if trans='T': transpose, apply Q^T

for complex flavors, if trans = 'C': conjugate transpose, apply Q^H;

direct

(global) CHARACTER. Indicates how Q is formed from a product of elementary reflectors.

if direct = 'F': Q = H(1)*H(2)*...*H(k) (Forward)

if direct = 'B': Q = H(k)*...*H(2)*H(1) (Backward)

storev

(global) CHARACTER.

Indicates how the vectors that define the elementary reflectors are stored:

if storev = 'C': Columnwise

if storev = 'R': Rowwise.

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).

k

(global) INTEGER.

The order of the matrix T.

v

(local).

REAL for pslarfb

DOUBLE PRECISION for pdlarfb

COMPLEX for pclarfb

COMPLEX*16 for pzlarfb.

Pointer into the local memory to an array of size

( lld_v, LOCc(jv+k-1)) if storev = 'C',

(lld_v, LOCc(jv+m-1)) if storev = 'R' and side = 'L',

(lld_v, LOCc(jv+n-1)) if storev = 'R' and side = 'R'.

It contains the local pieces of the distributed vectors V representing the Householder transformation.

if storev = 'C' and side = 'L', lld_v ≥ max(1,LOCr(iv+m-1));

if storev = 'C' and side = 'R', lld_v ≥ max(1,LOCr(iv+n-1));

if storev = 'R', lld_v≥LOCr(jv+k-1).

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.

c

(local).

REAL for pslarfb

DOUBLE PRECISION for pdlarfb

COMPLEX for pclarfb

COMPLEX*16 for pzlarfb.

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).

REAL for pslarfb

DOUBLE PRECISION for pdlarfb

COMPLEX for pclarfb

COMPLEX*16 for pzlarfb.

Workspace array of size lwork.

If storev = 'C',

if side = 'L',

lwork≥ ( nqc0 + mpc0 ) * k

else if side = 'R',

lwork ≥ ( nqc0 + max( npv0 + numroc( numroc( n +

icoffc, nb_v, 0, 0, npcol ), nb_v, 0, 0, lcmq ),

mpc0 ) ) * k

end if

else if storev = 'R' ,

if side = 'L' ,

lwork≥ ( mpc0 + max( mqv0 + numroc( numroc( m +

iroffc, mb_v, 0, 0, nprow ), mb_v, 0, 0, lcmp ),

nqc0 ) ) * k

else if side = 'R',

lwork ≥ ( mpc0 + nqc0 ) * k

end if

end if,

where

lcmq = lcm / npcol with lcm = iclm( nprow, npcol ),

iroffv = mod( iv-1, mb_v ), icoffv = mod( jv-1, nb_v ),

ivrow = indxg2p( iv, mb_v, myrow, rsrc_v, nprow ),

ivcol = indxg2p( jv, nb_v, mycol, csrc_v, npcol ),

MqV0 = numroc( m+icoffv, nb_v, mycol, ivcol, npcol ),

NpV0 = numroc( n+iroffv, mb_v, myrow, ivrow, nprow ),

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 ),

NpC0 = numroc( n+icoffc, 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

t

(local).

REAL for pslarfb

DOUBLE PRECISION for pdlarfb

COMPLEX for pclarfb

COMPLEX*16 for pzlarfb.

Array of size ( mb_v, mb_v) if storev = 'R', and ( nb_v, nb_v) if storev = 'C'. The triangular matrix t is the representation of the block reflector.

c

(local).

On exit, sub(C) is overwritten by the Q*sub(C), or Q'*sub(C), or sub(C)*Q, or sub(C)*Q'. Q' is transpose (conjugate transpose) of Q.

Parent topic: ScaLAPACK Auxiliary Routines

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