p?gerq2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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p?gerq2

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

Syntax

void psgerq2 (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 pdgerq2 (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 pcgerq2 (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 pzgerq2 (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?gerq2function computes an RQ factorization of a real/complex distributed m-by-n matrix sub(A) = A(ia:ia+m-1, ja:ja+n-1) = R*Q.

Input Parameters

m

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

n

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

a

(local).

Pointer into the local memory to an array of size lld_a * LOC_c(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,

if m ≤ n, the upper triangle of A(ia+m-n:ia+m-1, ja:ja+n-1) contains the m-by-m upper triangular matrix R;

if m ≥ n, the elements on and above the (m-n)-th subdiagonal contain the m-by-n upper trapezoidal matrix R; the remaining elements, 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+m -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)*H(ia+1)*...*H(ia+k-1) for real flavors,

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

Parent topic: ScaLAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?gerq2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes

See Also