p?gelqf

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?gelqf

Computes the LQ factorization of a general rectangular matrix.

Syntax

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

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

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

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

Include Files

Description

The p?gelqf routine computes the 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 in the distributed submatrix sub(A) (m≥ 0).

n

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

a

(local)

REAL for psgelqf

DOUBLE PRECISION for pdgelqf

COMPLEX for pcgelqf

DOUBLE COMPLEX for pzgelqf

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

Contains the local pieces of the distributed matrix sub(A) to be factored.

ia, ja

(global) INTEGER. The row and column indices in the global array A indicating the first row and the first column of the submatrix A(ia:ia+m-1,ja:ja+n-1), respectively.

desca

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

work

(local)

REAL for psgelqf

DOUBLE PRECISION for pdgelqf

COMPLEX for pcgelqf

DOUBLE COMPLEX for pzgelqf

Workspace array of size of lwork.

lwork

(local or global) INTEGER, size of work, must be at least lwork≥mb_a*(mp0 + nq0 + mb_a), 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.

NOTE:

mod(x,y) is the integer remainder of x/y.

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

The elements on and below the diagonal of sub(A) contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower trapezoidal 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 psgelqf

DOUBLE PRECISION for pdgelqf

COMPLEX for pcgelqf

DOUBLE COMPLEX for pzgelqf

Array of size LOCr(ia+min(m, n)-1).

Contains the scalar factors of elementary reflectors. tau is tied to the distributed matrix A.

work(1)

On exit, work(1) contains the minimum value of lwork required for optimum performance.

info

(global) INTEGER.

= 0: the execution is successful.

< 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),

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) is stored on exit in A(ia+i-1,ja+i:ja+n-1), and tau in tau(ia+i-1).

Parent topic: Orthogonal Factorizations: ScaLAPACK Computational Routines

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