p?unmhr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 7/13/2023

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p?unmhr

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

Syntax

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

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

Include Files

Description

This routine overwrites the general complex 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` = 'H':	`Q`^H*sub(`C`)	sub(`C`)*`Q`^H

where Q is a complex unitary 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^H is applied from the left.

='R': Q or Q^H is applied from the right.

trans

(global) CHARACTER

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

='C', conjugate transpose, Q^H 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 the distributed matrix sub (C) (n≥0).

ilo, ihi

(global) INTEGER

These must be the same parameters ilo and ihi, respectively, as supplied to p?gehrd. Q is equal to the unit matrix except in the distributed submatrixQ(ia+ilo:ia+ihi-1,ja+ilo:ja+ihi-1).

If side ='L', then 1≤ilo≤ihi≤max(1,m).

If side = 'R', then 1≤ilo≤ihi≤max(1,n)

ilo and ihi are relative indexes.

a

(local)

COMPLEX for pcunmhr

DOUBLE COMPLEX for pzunmhr.

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)

COMPLEX for pcunmhr

DOUBLE COMPLEX for pzunmhr.

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)

COMPLEX for pcunmhr

DOUBLE COMPLEX for pzunmhr.

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)

COMPLEX for pcunmhr

DOUBLE COMPLEX for pzunmhr.

Workspace array with size lwork.

lwork

(local or global)

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

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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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?unmhr

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also