p?geqpf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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p?geqpf

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

Syntax

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

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

void pcgeqpf (MKL_INT *m , MKL_INT *n , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , MKL_Complex8 *tau , MKL_Complex8 *work , MKL_INT *lwork , float *rwork , MKL_INT *lrwork , MKL_INT *info );

void pzgeqpf (MKL_INT *m , MKL_INT *n , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , MKL_Complex16 *tau , MKL_Complex16 *work , MKL_INT *lwork , double *rwork , MKL_INT *lrwork , MKL_INT *info );

Include Files

mkl_scalapack.h

Description

The p?geqpf function 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) The number of rows in the matrix sub(A) (m≥ 0).

n

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

a

(local)

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

work

(local).

Workspace array of size lwork.

lwork

(local or global) 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_gridinfofunction.

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.

rwork

(local).

Workspace array of size lrwork (complex flavors only).

lrwork

(local or global) 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_gridinfofunction.

If lrwork = -1, then lrwork 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

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

ipiv[i] = k, the local (i+1)-th column of sub(A)*P was the global k-th column of sub(A) (0 ≤ i < LOCc(ja+n-1). ipiv is tied to the distributed matrix A.

tau

(local)

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[0]

On exit, work[0] contains the minimum value of lwork required for optimum performance.

rwork[0]

On exit, rwork[0] contains the minimum value of lrwork required for optimum performance.

info

(global)

= 0, the execution is successful.

< 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(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+1)-th column of P is the i-th canonical unit vector (0 ≤ j < LOCc(ja+n-1).

Parent topic: Orthogonal Factorizations: ScaLAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?geqpf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes

See Also