p?larfb

Syntax

Include Files

• C: mkl_scalapack.h

Description

The p?larfb routine 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 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).

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 DIMENSION

( 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 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.

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 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).

REAL for pslarfb

DOUBLE PRECISION for pdlarfb

COMPLEX for pclarfb

COMPLEX*16 for pzlarfb.

Workspace array, DIMENSION (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, DIMENSION( 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.