# p?larz

Applies an elementary reflector as returned by p?tzrzf to a general matrix.

## Syntax

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

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

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

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

## Description

The p?larz routine applies a real/complex elementary reflector Q (or QT) to a real/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 real/complex scalar and v is a real/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*sub(C`),

if `side = 'R'`: form sub`(C)*Q`, `Q = QT` (for real flavors).

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).

REAL for pslarz

DOUBLE PRECISION for pdlarz

COMPLEX for pclarz

COMPLEX*16 for pzlarz.

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 distributed 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)

REAL for pslarz

DOUBLE PRECISION for pdlarz

COMPLEX for pclarz

COMPLEX*16 for pzlarz.

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).

REAL for pslarz

DOUBLE PRECISION for pdlarz

COMPLEX for pclarz

COMPLEX*16 for pzlarz.

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 pslarz

DOUBLE PRECISION for pdlarz

COMPLEX for pclarz

COMPLEX*16 for pzlarz.

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

end if.

Here 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*sub(C)` if `side = 'L'`, or `sub(C)*Q` if `side = 'R'`.