p?gelq2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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p?gelq2

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

Syntax

call psgelq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

call pdgelq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

call pcgelq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

call pzgelq2(m, n, a, ia, ja, desca, tau, work, lwork, info)

Description

The p?gelq2routine computes an LQ factorization of a real/complex distributed m-by-n matrix sub(A) = A(ia:ia+m-1, ja:ja+n-1) = L*Q.

Input Parameters

m

(global) INTEGER.

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

n

(global) INTEGER.

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

a

(local).

REAL for psgelq2

DOUBLE PRECISION for pdgelq2

COMPLEX for pcgelq2

COMPLEX*16 for pzgelq2.

Pointer into the local memory to an array of size (lld_a, LOCc(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 psgelq2

DOUBLE PRECISION for pdgelq2

COMPLEX for pcgelq2

COMPLEX*16 for pzgelq2.

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, the elements on and below the diagonal of sub(A) contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m ≤ n); the elements above the diagonal, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors (see Application Notes below).

tau

(local).

REAL for psgelq2

DOUBLE PRECISION for pdgelq2

COMPLEX for pcgelq2

COMPLEX*16 for pzgelq2.

Array of size LOCr(ia+min(m, n)-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+k-1)*H(ia+k-2)*. . . *H(ia) for real flavors, Q =(H(ia+k-1))^H*(H(ia+k-2))^H...*(H(ia))^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(1: i-1) = 0 and v(i) = 1; v(i+1: n) (for real flavors) or conjg(v(i+1: n)) (for complex flavors) is stored on exit in A(ia+i-1,ja+i:ja+n-1), and tau in tau(ia+i-1).

Parent topic: ScaLAPACK Auxiliary Routines

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