p?orm2l/p?unm2l

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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p?orm2l/p?unm2l

Multiplies a general matrix by the orthogonal/unitary matrix from a QL factorization determined by p?geqlf (unblocked algorithm).

Syntax

call psorm2l(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

call pdorm2l(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

call pcunm2l(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

call pzunm2l(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

Description

The p?orm2l/p?unm2lroutine overwrites the general real/complex m-by-n distributed matrix sub (C)=C(ic:ic+m-1,jc:jc+n-1) with

Q*sub(C) if side = 'L' and trans = 'N', or

Q^T*sub(C) / Q^H*sub(C) if side = 'L' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors), or

sub(C)*Q if side = 'R' and trans = 'N', or

sub(C)*Q^T / sub(C)*Q^H if side = 'R' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors).

where Q is a real orthogonal or complex unitary distributed matrix defined as the product of k elementary reflectors

Q = H(k)*...*H(2)*H(1) as returned by p?geqlf . Q is of order m if side = 'L' and of order n if side = 'R'.

Input Parameters

side

(global) CHARACTER.

= 'L': apply Q or Q^T for real flavors (Q^H for complex flavors) from the left,

= 'R': apply Q or Q^T for real flavors (Q^H for complex flavors) from the right.

trans

(global) CHARACTER.

= 'N': apply Q (no transpose)

= 'T': apply Q^T (transpose, for real flavors)

= 'C': apply Q^H (conjugate transpose, for complex 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.

k

(global) INTEGER.

The number of elementary reflectors whose product defines the matrix Q.

If side = 'L', m ≥ k ≥ 0;

if side = 'R', n ≥ k ≥ 0.

a

(local)

REAL for psorm2l

DOUBLE PRECISION for pdorm2l

COMPLEX for pcunm2l

COMPLEX*16 for pzunm2l.

Pointer into the local memory to an array of size (lld_a, LOCc(ja+k-1)).

On entry, the j-th row must contain the vector that defines the elementary reflector H(j), ja ≤ j ≤ ja+k-1, as returned by p?geqlf in the k columns of its distributed matrix argument A(ia:*,ja:ja+k-1). The argument A(ia:*,ja:ja+k-1) is modified by the routine but restored on exit.

If side = 'L', lld_a ≥ max(1, LOCr(ia+m-1)),

if side = 'R', lld_a ≥ max(1, LOCr(ia+n-1)).

ia

(global) INTEGER.

The row index in the global matrix A indicating the first row of sub(A).

ja

(global) INTEGER.

The column index in the global matrix A indicating the first column of sub(A).

desca

(global and local) INTEGER array of size dlen_. The array descriptor for the distributed matrix A.

tau

(local)

REAL for psorm2l

DOUBLE PRECISION for pdorm2l

COMPLEX for pcunm2l

COMPLEX*16 for pzunm2l.

Array of size LOCc(ja+n-1). tau(j) contains the scalar factor of the elementary reflector H(j), as returned by p?geqlf. This array is tied to the distributed matrix A.

c

(local)

REAL for psorm2l

DOUBLE PRECISION for pdorm2l

COMPLEX for pcunm2l

COMPLEX*16 for pzunm2l.

Pointer into the local memory to an array of size (lld_c, LOCc(jc+n-1)).On entry, the local pieces of the distributed matrix sub (C).

ic

(global) INTEGER.

The row index in the global matrix C indicating the first row of sub(C).

jc

(global) INTEGER.

The column index in the global matrix C indicating the first column of sub(C).

descc

(global and local) INTEGER array of size dlen_. The array descriptor for the distributed matrix C.

work

(local)

REAL for psorm2l

DOUBLE PRECISION for pdorm2l

COMPLEX for pcunm2l

COMPLEX*16 for pzunm2l.

Workspace array of size lwork.

On exit, work(1) returns the minimal and optimal lwork.

lwork

(local or global) INTEGER.

The size of the array work.

lwork is local input and must be at least

if side = 'L', lwork ≥ mpc0 + max(1, nqc0),

if side = 'R', lwork ≥ nqc0 + max(max(1, mpc0), numroc(numroc(n+icoffc, nb_a, 0, 0, npcol), nb_a, 0, 0, lcmq)),

where

lcmq = lcm/npcol,

lcm = iclm(nprow, 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),

Mqc0 = numroc(m+icoffc, nb_c, mycol, icrow, nprow),

Npc0 = numroc(n+iroffc, mb_c, myrow, iccol, npcol),

ilcm, indxg2p, and numroc are ScaLAPACK tool functions; myrow, mycol, nprow, and npcol can be determined by calling the subroutine blacs_gridinfo.

If lwork = -1, then lwork is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by pxerbla.

Output Parameters

c

On exit, c is overwritten by Q*sub(C), or Q^T*sub(C)/ Q^H*sub(C), or sub(C)*Q, or sub(C)*Q^T / sub(C)*Q^H

work

On exit, work(1) returns the minimal and optimal lwork.

info

(local) INTEGER.

= 0: successful exit

< 0: if the i-th argument is an array and the j-th entry had an illegal value,

then info = - (i*100 +j),

if the i-th argument is a scalar and had an illegal value,

then info = -i.

NOTE:

The distributed submatrices A(ia:*, ja:*) and C(ic:ic+m-1,jc:jc+n-1) must verify some alignment properties, namely the following expressions should be true:

If side = 'L', ( mb_a.eq.mb_c .AND. iroffa.eq.iroffc .AND. iarow.eq.icrow )

If side = 'R', ( mb_a.eq.nb_c .AND. iroffa.eq.iroffc ).

Parent topic: ScaLAPACK Auxiliary Routines

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