p?gerq2

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?gerq2

Computes an RQ factorization of a general rectangular matrix (unblocked algorithm).

Syntax

call psgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

call pdgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

call pcgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

call pzgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

Description

The p?gerq2routine computes an RQ factorization of a real/complex distributed m-by-n matrix sub(A) = A(ia:ia+m-1, ja:ja+n-1) = R*Q.

Input Parameters

m

(global) INTEGER. The number of rows in the distributed matrix sub(A). (m≥0).

n

(global) INTEGER. The number of columns in the distributed matrix sub(A). (n≥0).

a

(local).

REAL for psgerq2

DOUBLE PRECISION for pdgerq2

COMPLEX for pcgerq2

COMPLEX*16 for pzgerq2.

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

On entry, this array contains the local pieces of the m-by-n distributed matrix sub(A) which is to be factored.

ia, ja

(global) INTEGER. The row and column indices in the global matrix A indicating the first row and the first column of sub(A), respectively.

desca

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

work

(local).

REAL for psgerq2

DOUBLE PRECISION for pdgerq2

COMPLEX for pcgerq2

COMPLEX*16 for pzgerq2.

This is a workspace array of size lwork.

lwork

(local or global) INTEGER.

The size of the array work.

lwork is local input and must be at least lwork≥nq0 + max(1, mp0), where

iroff = mod(ia-1, mb_a), icoff = mod(ja-1, nb_a),

iarow = indxg2p(ia, mb_a, myrow, rsrc_a, nprow),

iacol = indxg2p(ja, nb_a, mycol, csrc_a, npcol), mp0 = numroc( m+iroff, mb_a, myrow, iarow, nprow),

nq0 = numroc(n+icoff, nb_a, mycol, iacol, npcol),

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

a

(local).

On exit,

if m ≤ n, the upper triangle of A(ia+m-n:ia+m-1, ja:ja+n-1) contains the m-by-m upper triangular matrix R;

if m ≥ n, the elements on and above the (m-n)-th subdiagonal contain the m-by-n upper trapezoidal matrix R; the remaining elements, with the array tau, represent the orthogonal/ unitary matrix Q as a product of elementary reflectors (see Application Notes below).

tau

(local).

REAL for psgerq2

DOUBLE PRECISION for pdgerq2

COMPLEX for pcgerq2

COMPLEX*16 for pzgerq2.

Array of size LOCr(ia+m -1). This array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix A.

work

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

info

(local) INTEGER.

If info = 0, the execution is successful.

if info < 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.

Application Notes

The matrix Q is represented as a product of elementary reflectors

Q = H(ia)*H(ia+1)*...*H(ia+k-1) for real flavors,

Q = (H(ia))^H*(H(ia+1))^H...*(H(ia+k-1))^H for complex flavors,

where k = min(m, n).

Each H(i) has the form

H(i) = I - tau*v*v',

where tau is a real/complex scalar, and v is a real/complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) for real flavors or conjg(v(1:n-k+i-1)) for complex flavors is stored on exit in A(ia+m-k+i-1, ja:ja+n-k+i-2), and tau in tau(ia+m-k+i-1).

Parent topic: ScaLAPACK Auxiliary Routines

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p?gerq2

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