p?orm2r/p?unm2r

Multiplies a general matrix by the orthogonal/unitary matrix from a QR factorization determined by p?geqrf (unblocked algorithm).

Syntax

FORTRAN:

call psorm2r(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

call pdorm2r(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

call pcunm2r(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

call pzunm2r(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)

C:

void psorm2r (char *side , char *trans , MKL_INT *m , MKL_INT *n , MKL_INT *k , float *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , float *tau , float *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , float *work , MKL_INT *lwork , MKL_INT *info );

void pdorm2r (char *side , char *trans , MKL_INT *m , MKL_INT *n , MKL_INT *k , double *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , double *tau , double *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , double *work , MKL_INT *lwork , MKL_INT *info );

void pcunm2r (char *side , char *trans , MKL_INT *m , MKL_INT *n , MKL_INT *k , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex8 *tau , MKL_Complex8 *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , MKL_Complex8 *work , MKL_INT *lwork , MKL_INT *info );

void pzunm2r (char *side , char *trans , MKL_INT *m , MKL_INT *n , MKL_INT *k , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex16 *tau , MKL_Complex16 *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , MKL_Complex16 *work , MKL_INT *lwork , MKL_INT *info );

Include Files

  • C: mkl_scalapack.h

Description

The p?orm2r/p?unm2r routine overwrites the general real/complex m-by-n distributed matrix sub (C)=C(ic:ic+m-1, jc:jc+n-1) with

Q*sub(C) if side = 'L' and trans = 'N', or

QT*sub(C) / QH*sub(C) if side = 'L' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors), or

sub(C)*Q if side = 'R' and trans = 'N', or

sub(C)*QT / sub(C)*QH if side = 'R' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors).

where Q is a real orthogonal or complex unitary matrix defined as the product of k elementary reflectors

Q = H(k)*...*H(2)*H(1) as returned by p?geqrf . Q is of order m if side = 'L' and of order n if side = 'R'.

Input Parameters

side

(global) CHARACTER.

= 'L': apply Q or QT for real flavors (QH for complex flavors) from the left,

= 'R': apply Q or QT for real flavors (QH for complex flavors) from the right.

trans

(global) CHARACTER.

= 'N': apply Q (no transpose)

= 'T': apply QT (transpose, for real flavors)

= 'C': apply QH (conjugate transpose, for complex flavors)

m

(global) INTEGER.

The number of rows to be operated on, that is, the number of rows of the distributed submatrix sub(C). m 0.

n

(global) INTEGER.

The number of columns to be operated on, that is, the number of columns of the distributed submatrix sub(C). n 0.

k

(global) INTEGER.

The number of elementary reflectors whose product defines the matrix Q.

If side = 'L', m k 0;

if side = 'R', n k 0.

a

(local)

REAL for psorm2r

DOUBLE PRECISION for pdorm2r

COMPLEX for pcunm2r

COMPLEX*16 for pzunm2r.

Pointer into the local memory to an array, size(lld_a, LOCc(ja+k-1).

On entry, the j-th column must contain the vector that defines the elementary reflector H(j), ja j ja+k-1, as returned by p?geqrf in the k columns of its distributed matrix argument A(ia:*,ja:ja+k-1). The argument A(ia:*,ja:ja+k-1) is modified by the routine but restored on exit.

If side = 'L', lld_a max(1, LOCr(ia+m-1)),

if side = 'R', lld_a max(1, LOCr(ia+n-1)).

ia

(global) INTEGER.

The row index in the global array A indicating the first row of sub(A).

ja

(global) INTEGER.

The column index in the global array A indicating the first column of sub(A).

desca

(global and local) INTEGER array of size (dlen_). The array descriptor for the distributed matrix A.

tau

(local)

REAL for psorm2r

DOUBLE PRECISION for pdorm2r

COMPLEX for pcunm2r

COMPLEX*16 for pzunm2r.

Array, size LOCc(ja+k-1). This array contains the scalar factors tau(j) of the elementary reflector H(j), as returned by p?geqrf. This array is tied to the distributed matrix A.

c

(local)

REAL for psorm2r

DOUBLE PRECISION for pdorm2r

COMPLEX for pcunm2r

COMPLEX*16 for pzunm2r.

Pointer into the local memory to an array, size(lld_c, LOCc(jc+n-1)).

On entry, the local pieces of the distributed matrix sub (C).

ic

(global) INTEGER.

The row index in the global array C indicating the first row of sub(C).

jc

(global) INTEGER.

The column index in the global array C indicating the first column of sub(C).

descc

(global and local) INTEGER array of size (dlen_).

The array descriptor for the distributed matrix C.

work

(local)

REAL for psorm2r

DOUBLE PRECISION for pdorm2r

COMPLEX for pcunm2r

COMPLEX*16 for pzunm2r.

Workspace array, size (lwork).

lwork

(local or global) INTEGER.

The dimension of the array work.

lwork is local input and must be at least

if side = 'L', lwork mpc0 + max(1, nqc0),

if side = 'R', lwork nqc0 + max(max(1, mpc0), numroc(numroc(n+icoffc, nb_a, 0, 0, npcol), nb_a, 0, 0, lcmq)),

where

lcmq = lcm/npcol ,

lcm = iclm(nprow, npcol),

iroffc = mod(ic-1, mb_c),

icoffc = mod(jc-1, nb_c),

icrow = indxg2p(ic, mb_c, myrow, rsrc_c, nprow),

iccol = indxg2p(jc, nb_c, mycol, csrc_c, npcol),

Mqc0 = numroc(m+icoffc, nb_c, mycol, icrow, nprow),

Npc0 = numroc(n+iroffc, mb_c, myrow, iccol, npcol),

ilcm, indxg2p and numroc 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

c

On exit, c is overwritten by Q*sub(C), or QT*sub(C)/ QH*sub(C), or sub(C)*Q, or sub(C)*QT / sub(C)*QH

work

On exit, work(1) returns the minimal and optimal lwork.

info

(local) INTEGER.

= 0: successful exit

< 0: if the i-th argument is an array and the j-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.

Note

The distributed submatrices A(ia:*, ja:*) and C(ic:ic+m-1, jc:jc+n-1) must verify some alignment properties, namely the following expressions should be true:

If side = 'L', (mb_a.eq.mb_c .AND. iroffa.eq.iroffc .AND. iarow.eq.icrow)

If side = 'R', (mb_a.eq.nb_c .AND. iroffa.eq.iroffc).

For more complete information about compiler optimizations, see our Optimization Notice.