p?larfb

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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p?larfb

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

Syntax

void pslarfb (char *side , char *trans , char *direct , char *storev , MKL_INT *m , MKL_INT *n , MKL_INT *k , float *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , float *t , float *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , float *work );

void pdlarfb (char *side , char *trans , char *direct , char *storev , MKL_INT *m , MKL_INT *n , MKL_INT *k , double *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , double *t , double *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , double *work );

void pclarfb (char *side , char *trans , char *direct , char *storev , MKL_INT *m , MKL_INT *n , MKL_INT *k , MKL_Complex8 *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , MKL_Complex8 *t , MKL_Complex8 *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , MKL_Complex8 *work );

void pzlarfb (char *side , char *trans , char *direct , char *storev , MKL_INT *m , MKL_INT *n , MKL_INT *k , MKL_Complex16 *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , MKL_Complex16 *t , MKL_Complex16 *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , MKL_Complex16 *work );

Include Files

mkl_scalapack.h

Description

The p?larfbfunction 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)

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)

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) 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)

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

if storev = 'C': Columnwise

if storev = 'R': Rowwise.

m

(global)

The number of rows in the distributed matrix sub(C). (m ≥ 0).

n

(global)

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

k

(global)

The order of the matrix T.

v

(local).

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)

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) array of size dlen_. The array descriptor for the distributed matrix V.

c

(local).

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) 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) array of size dlen_. The array descriptor for the distributed matrix C.

work

(local).

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 function blacs_gridinfo.

Output Parameters

t

(local).

Array of size mb_v * mb_vif storev = 'R', and nb_v * nb_vif 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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