p?geqpf

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?geqpf

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

Syntax

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

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

call pcgeqpf(m, n, a, ia, ja, desca, ipiv, tau, work, lwork, rwork, lrwork, info)

call pzgeqpf(m, n, a, ia, ja, desca, ipiv, tau, work, lwork, rwork, lrwork, info)

Include Files

Description

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

sub(A)*P=Q*R.

Input Parameters

m

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

n

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

a

(local)

REAL for psgeqpf

DOUBLE PRECISION for pdgeqpf

COMPLEX for pcgeqpf

DOUBLE COMPLEX for pzgeqpf.

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 psgeqpf

DOUBLE PRECISION for pdgeqpf.

COMPLEX for pcgeqpf.

DOUBLE COMPLEX for pzgeqpf

Workspace array of size lwork.

lwork

(local or global) INTEGER, size of work, must be at least

For real flavors:

lwork≥max(3,mp0+nq0) + LOCc (ja+n-1) + nq0.

For complex flavors:

lwork≥max(3,mp0+nq0) .

Here

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),

LOCc (ja+n-1) = numroc(ja+n-1, nb_a, MYCOL,csrc_a, NPCOL), and numroc, indxg2p are ScaLAPACK tool functions.

You can determine MYROW, MYCOL, NPROW and NPCOL by calling the blacs_gridinfosubroutine.

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.

rwork

(local).

REAL for pcgeqpf.

DOUBLE PRECISION for pzgeqpf.

Workspace array of size lrwork (complex flavors only).

lrwork

(local or global) INTEGER, size of rwork (complex flavors only). The value of lrwork must be at least

lwork≥LOCc (ja+n-1) + nq0 .

Here

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),

LOCc (ja+n-1) = numroc(ja+n-1, nb_a, MYCOL,csrc_a, NPCOL), and numroc, indxg2p are ScaLAPACK tool functions.

You can determine MYROW, MYCOL, NPROW and NPCOL by calling the blacs_gridinfosubroutine.

If lrwork = -1, then lrwork 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).

ipiv

(local) INTEGER. Array of size LOCc(ja+n-1).

ipiv(i) = k, the local i-th column of sub(A)*P was the global k-th column of sub(A). ipiv is tied to the distributed matrix A.

tau

(local)

REAL for psgeqpf

DOUBLE PRECISION for pdgeqpf

COMPLEX for pcgeqpf

DOUBLE COMPLEX for pzgeqpf.

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

Contains the scalar factor tau 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.

rwork(1)

On exit, rwork(1) contains the minimum value of lrwork 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(1)*H(2)*...*H(k)

where k = min(m,n).

Each H(i) has the form

H = 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).

The matrix P is represented in ipiv as follows: if ipiv(j)= i then the j-th column of P is the i-th canonical unit vector.

Parent topic: Orthogonal Factorizations: ScaLAPACK Computational Routines

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