Multiplies a general matrix by the unitary matrix Q of the QL factorization formed by p?geqlf.

## Syntax

void pcunmql (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 pzunmql (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

This function overwrites the general complex m-by-n distributed matrix sub(C) = C(:+m-1,:+n-1) with

 side ='L' side ='R' trans = 'N': Q*sub(C) sub(C)*Q trans = 'C': QH*sub(C) sub(C)*QH

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

Q = H(k)' ... H(2)' H(1)'

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

## Input Parameters

side

(global)

='L': Q or QH is applied from the left.

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

trans

(global)

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

='C', conjugate transpose, QH is applied.

m

(global) The number of rows in the distributed matrix sub(C) (m0).

n

(global) The number of columns in the distributed matrix sub(C)(n0).

k

(global) The number of elementary reflectors whose product defines the matrix Q. Constraints:

If side = 'L', mk≥0

If side = 'R', nk≥0.

a

(local)

Pointer into the local memory to an array of size lld_a*LOCc(ja+k-1). The j-th column of the matrix stored in amust contain the vector that defines the elementary reflector H(j), jajja+k-1, as returned by p?geqlf in the k columns of its distributed matrix argument A(ia:*, ja:ja+k-1). A(ia:*, ja:ja+k-1) is modified by the function but restored on exit.

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

If side = 'R', lld_amax(1, LOCr(ia+n-1)).

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, respectively.

desca

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

tau

(local)

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

Contains the scalar factor tau[j] of elementary reflectors H(j+1) as returned by p?geqlf (0 ≤ j < LOCc(ia+n-1)). tau is tied to the distributed matrix A.

c

(local)

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

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

ic, jc

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

work

(local)

Workspace array of size of lwork.

lwork

(local or global) size of work, must be at least:

If side = 'L',

lworkmax((nb_a* (nb_a-1))/2, (nqc0+mpc0)*nb_a + nb_a*nb_a

else if side ='R',

lworkmax((nb_a*(nb_a-1))/2, (nqc0+maxnpa0)+ numroc(numroc(n+icoffc, nb_a, 0, 0, NPCOL), nb_a, 0, 0, lcmq), mpc0))*nb_a) + nb_a*nb_a

end if

where

lcmp = lcm/NPCOL with lcm = ilcm (NPROW, NPCOL),

iroffa = mod(ia-1, mb_a),

icoffa = mod(ja-1, nb_a),

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

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

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+iroffc, mb_c, MYROW, icrow, NPROW),

nqc0 = numroc(n+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 function blacs_gridinfo.

### Note

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

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

Overwritten by the product Q* sub(C), or Q' sub (C), or sub(C)* Q', or sub(C)* Q

work[0]

On exit work[0] contains the minimum value of lwork 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.