Applies an elementary reflector as returned by p?tzrzf to a general matrix.
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)
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.
(global) CHARACTER.
if side = 'L': form Q*sub(C),
if side = 'R': form sub(C)*Q, Q = QT (for real flavors).
(global) INTEGER.
The number of rows to be operated on, that is, the number of rows of the distributed submatrix sub(C). (m ≥ 0).
(global) INTEGER.
The number of columns to be operated on, that is, the number of columns of the distributed submatrix sub(C). (n ≥ 0).
(global). INTEGER.
The columns of the distributed submatrix sub(A) containing the meaningful part of the Householder reflectors. If side = 'L', m ≥ l ≥ 0,
if side = 'R', n ≥ l ≥ 0.
(local).
REAL for pslarz
DOUBLE PRECISION for pdlarz
COMPLEX for pclarz
COMPLEX*16 for pzlarz.
Pointer into the local memory to an array of DIMENSION (lld_v,*) containing the local pieces of the distributed vectors 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.
(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.
(global and local) INTEGER array, DIMENSION (dlen_). The array descriptor for the distributed matrix V.
(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.
(local)
REAL for pslarz
DOUBLE PRECISION for pdlarz
COMPLEX for pclarz
COMPLEX*16 for pzlarz.
Array, DIMENSION 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.
(local).
REAL for pslarz
DOUBLE PRECISION for pdlarz
COMPLEX for pclarz
COMPLEX*16 for pzlarz.
Pointer into the local memory to an array of DIMENSION (lld_c, LOCc(jc+n-1) ), containing the local pieces of sub(C).
(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.
(global and local) INTEGER array, DIMENSION (dlen_). The array descriptor for the distributed matrix C.
(local).
REAL for pslarz
DOUBLE PRECISION for pdlarz
COMPLEX for pclarz
COMPLEX*16 for pzlarz.
Array, DIMENSION (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.
(local).
On exit, sub(C) is overwritten by the Q*sub(C) if side = 'L', or sub(C)*Q if side = 'R'.