p?gelq2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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p?gelq2

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

Syntax

void psgelq2 (MKL_INT *m , MKL_INT *n , float *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , float *tau , float *work , MKL_INT *lwork , MKL_INT *info );

void pdgelq2 (MKL_INT *m , MKL_INT *n , double *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , double *tau , double *work , MKL_INT *lwork , MKL_INT *info );

void pcgelq2 (MKL_INT *m , MKL_INT *n , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex8 *tau , MKL_Complex8 *work , MKL_INT *lwork , MKL_INT *info );

void pzgelq2 (MKL_INT *m , MKL_INT *n , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex16 *tau , MKL_Complex16 *work , MKL_INT *lwork , MKL_INT *info );

Include Files

mkl_scalapack.h

Description

The p?gelq2function 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)

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

n

(global)

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

a

(local).

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) 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) array of size dlen_. The array descriptor for the distributed matrix A.

work

(local).

This is a workspace array of size lwork.

lwork

(local or global)

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 function blacs_gridinfo.

If lwork = -1, then lwork is global input and a workspace query is assumed; the function 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).

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[0] returns the minimal and optimal lwork.

info

(local) If info = 0, the execution is successful. if info < 0: If the i-th argument is an array and the j-th entry, indexed j-1, 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-2].

Parent topic: ScaLAPACK Auxiliary Routines

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