p?ormhr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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p?ormhr

Multiplies a general matrix by the orthogonal transformation matrix from a reduction to Hessenberg form determined by p?gehrd.

Syntax

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

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

Include Files

Description

The p?ormhr routine overwrites the general real distributed m-by-n matrix sub(C)= C(iс:iс+m-1,jс:jс+n-1) with

	`side` ='L'	`side` ='R'
`trans` = 'N':	`Q`*sub(`C`)	sub(`C`)*`Q`
`trans` = 'T':	`Q`^T*sub(`C`)	sub(`C`)*`Q`^T

where Q is a real orthogonal distributed matrix of order nq, with nq = m if side = 'L' and nq = n if side = 'R'.

Q is defined as the product of ihi-ilo elementary reflectors, as returned by p?gehrd.

Q = H(ilo) H(ilo+1)... H(ihi-1).

Input Parameters

side

(global) CHARACTER

='L': Q or Q^T is applied from the left.

='R': Q or Q^T is applied from the right.

trans

(global) CHARACTER

='N', no transpose, Q is applied.

='T', transpose, Q^T is applied.

m

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

n

(global) INTEGER. The number of columns in he distributed matrix sub (C) (n≥0).

ilo, ihi

(global) INTEGER.

ilo and ihi must have the same values as in the previous call of p?gehrd. Q is equal to the unit matrix except for the distributed submatrix Q(ia+ilo:ia+ihi-1,ja+ilo:ja+ihi-1).

If side = 'L', 1≤ilo≤ihi≤max(1,m);

If side = 'R', 1≤ilo≤ihi≤max(1,n);

ilo and ihi are relative indexes.

a

(local)

REAL for psormhr

DOUBLE PRECISION for pdormhr

Pointer into the local memory to an array of size (lld_a,LOCc(ja+m-1)) if side = 'L', and (lld_a,LOCc(ja+n-1)) if side = 'R'.

Contains the vectors which define the elementary reflectors, as returned by p?gehrd.

ia, ja

(global) INTEGER. The row and column indices in the global matrix A indicating the first row and the first column of the submatrix A, respectively.

desca

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

tau

(local)

REAL for psormhr

DOUBLE PRECISION for pdormhr

Array of size LOCc(ja+m-2) if side = 'L', and LOCc(ja+n-2) if side = 'R'.

tau(j) contains the scalar factor of the elementary reflector H(j) as returned by p?gehrd. tau is tied to the distributed matrix A.

c

(local)

REAL for psormhr

DOUBLE PRECISION for pdormhr

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

Contains the local pieces of the distributed matrix sub(C).

ic, jc

(global) INTEGER. The row and column indices in the global matrix C indicating the first row and the first column of the submatrix C, respectively.

descc

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

work

(local)

REAL for psormhr

DOUBLE PRECISION for pdormhr

Workspace array with size lwork.

lwork

(local or global) INTEGER.

The size of the array work.

lwork must be at least iaa = ia + ilo; jaa = ja+ilo-1;

If side = 'L',

mi = ihi-ilo; ni = n; icc = ic + ilo; jcc = jc; lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0+mpc0)*nb_a) + nb_a*nb_a

else if side = 'R',

mi = m; ni = ihi-ilo; icc = ic; jcc = jc + ilo; lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0+max(npa0+numroc(numroc(ni+icoffc, nb_a, 0, 0, NPCOL), nb_a, 0, 0, lcmq), mpc0))*nb_a) + nb_a*nb_a

end if

where lcmq = lcm/NPCOL with lcm = ilcm(NPROW, NPCOL),

iroffa = mod(iaa-1, mb_a),

icoffa = mod(jaa-1, nb_a),

iarow = indxg2p(iaa, mb_a, MYROW, rsrc_a, NPROW),

npa0 = numroc(ni+iroffa, mb_a, MYROW, iarow, NPROW),

iroffc = mod(icc-1, mb_c), icoffc = mod(jcc-1, nb_c),

icrow = indxg2p(icc, mb_c, MYROW, rsrc_c, NPROW),

iccol = indxg2p(jcc, nb_c, MYCOL, csrc_c, NPCOL),

mpc0 = numroc(mi+iroffc, mb_c, MYROW, icrow, NPROW),

nqc0 = numroc(ni+icoffc, nb_c, MYCOL, iccol, NPCOL),

NOTE:

mod(x,y) is the integer remainder of x/y.

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

sub(C) is overwritten by Q*sub(C), or Q'*sub(C), or sub(C)*Q', or sub(C)*Q.

work(1)

On exit work(1) contains the minimum value of lwork required for optimum performance.

info

(global) INTEGER.

= 0: the execution is successful.

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

Parent topic: Nonsymmetric Eigenvalue Problems: ScaLAPACK Computational Routines

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