p?orml2/p?unml2

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?orml2/p?unml2

Multiplies a general matrix by the orthogonal/unitary matrix from an LQ factorization determined by p?gelqf (unblocked algorithm).

Syntax

void psorml2 (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 pdorml2 (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 pcunml2 (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 pzunml2 (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

mkl_scalapack.h

Description

The p?orml2/p?unml2function 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

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

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

Q = H(k)*...*H(2)*H(1) (for real flavors)

Q = (H(k))^H*...*(H(2))^H*(H(1))^H (for complex flavors)

as returned by p?gelqf . Q is of order m if side = 'L' and of order n if side = 'R'.

Input Parameters

side

(global)

= 'L': apply Q or Q^T for real flavors (Q^H for complex flavors) from the left,

= 'R': apply Q or Q^T for real flavors (Q^H for complex flavors) from the right.

trans

(global)

= 'N': apply Q (no transpose)

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

= 'C': apply Q^H (conjugate transpose, for complex flavors)

m

(global)

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

n

(global)

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

k

(global)

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)

Pointer into the local memory to an array of size

lld_a * LOCc(ja+m-1) if side='L',

lld_a * LOCc(ja+n-1) if side='R',

where lld_a ≥ max (1, LOCr(ia+k-1)).

On entry, the i-th row of the matrix stored in amust contain the vector that defines the elementary reflector H(i), ia ≤ i ≤ ia+k-1, as returned by p?gelqf in the k rows of its distributed matrix argument A(ia:ia+k-1, ja:*). The argument A(ia:ia+k-1, ja:*) is modified by the function but restored on exit.

ia

(global)

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

ja

(global)

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

desca

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

tau

(local)

Array of size LOCc(ia+k-1). tau[i] contains the scalar factor of the elementary reflector H(i+1), i = 0, 1, ..., LOCc(ja+k-1)-1, as returned by p?gelqf. This array is tied to the distributed matrix A.

c

(local)

Pointer into the local memory to an array of size lld_c * LOCc(jc+n-1). On entry, the local pieces of the distributed matrix sub (C).

ic

(global)

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

jc

(global)

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

descc

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

work

(local)

Workspace array of size lwork.

lwork

(local or global)

The size of the array work.

lwork is local input and must be at least

if side = 'L', lwork ≥ mqc0 + max(max( 1, npc0), numroc(numroc(m+icoffc, mb_a, 0, 0, nprow), mb_a, 0, 0, lcmp)),

if side = 'R', lwork ≥ npc0 + max(1, mqc0),

where

lcmp = lcm / nprow,

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),

Mpc0 = numroc(m+icoffc, mb_c, mycol, icrow, nprow),

Nqc0 = numroc(n+iroffc, nb_c, myrow, iccol, npcol),

ilcm, 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

c

On exit, c is overwritten by Q*sub(C), or Q^T*sub(C)/ Q^H*sub(C), or sub(C)*Q, or sub(C)*Q^T / sub(C)*Q^H

work

On exit, work[0] returns the minimal and optimal lwork.

info

(local)

= 0: successful exit

< 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.

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', (nb_a == mb_c && icoffa == iroffc)

If side = 'R', (nb_a == nb_c && icoffa == icoffc && iacol == iccol).

Parent topic: ScaLAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?orml2/p?unml2

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also