Visible to Intel only — GUID: GUID-8ADD959A-F854-41F7-9B16-53C6A1886D21
Visible to Intel only — GUID: GUID-8ADD959A-F854-41F7-9B16-53C6A1886D21
p?larzc
Applies (multiplies by) the conjugate transpose of an elementary reflector as returned by p?tzrzf to a general matrix.
Syntax
call pclarzc(side, m, n, l, v, iv, jv, descv, incv, tau, c, ic, jc, descc, work)
call pzlarzc(side, m, n, l, v, iv, jv, descv, incv, tau, c, ic, jc, descc, work)
Description
The p?larzcroutine applies a complex elementary reflector QH to a 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 complex scalar and v is a 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 QH*sub(C);
if side = 'R': form sub(C)*QH .
- 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).
-
COMPLEX for pclarzc
COMPLEX*16 for pzlarzc.
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 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)
COMPLEX for pclarzc
COMPLEX*16 for pzlarzc.
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).
COMPLEX for pclarzc
COMPLEX*16 for pzlarzc.
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).
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;
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 QH*sub(C) if side = 'L', or sub(C)*QH if side = 'R'.