p?geqrf

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?geqrf

Computes the QR factorization of a general m-by-n matrix.

Syntax

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

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

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

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

Include Files

Description

The p?geqrf routine forms the QR factorization of a general m-by-n distributed matrix sub(A)= A(ia:ia+m-1, ja:ja+n-1) as

A=Q*R.

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 psgeqrf

DOUBLE PRECISION for pdgeqrf

COMPLEX for pcgeqrf

DOUBLE COMPLEX for pzgeqrf.

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 matrix 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 psgeqrf

DOUBLE PRECISION for pdgeqrf.

COMPLEX for pcgeqrf.

DOUBLE COMPLEX for pzgeqrf

Workspace array of size lwork.

lwork

(local or global) INTEGER, size of work, must be at least lwork≥nb_a * (mp0+nq0+nb_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), and numroc, indxg2p 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

The elements on and above the diagonal of sub(A) contain the min(m,n)-by-n upper trapezoidal matrix R (R is upper triangular if m≥n); the elements below 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 psgeqrf

DOUBLE PRECISION for pdgeqrf

COMPLEX for pcgeqrf

DOUBLE COMPLEX for pzgeqrf.

Array of size LOCc(ja+min(m,n)-1).

Contains the scalar factor 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(ja)*H(ja+1)*...*H(ja+k-1),

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

Parent topic: Orthogonal Factorizations: ScaLAPACK Computational Routines

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