# p?ormql

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

## Syntax

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

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

## Description

The routine overwrites the general real m-by-n distributed matrix `sub(C) = C (ic:ic+m-1,jc:jc+n-1)` with

| side ='L' | side ='R'
trans = 'N': | Q*sub(C) | sub(C)*Q
trans = 'T': | QT*sub(C) | sub(C)*QT

where Q is a real orthogonal 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) CHARACTER

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

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

trans

  (global) CHARACTER

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

  `='T'`, transpose, QT 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)`.

k

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

  If `side = 'L'`, `m≥k≥0`

  If `side = 'R'`, `n≥k≥0`.

a

  (local)

  REAL for psormql

  DOUBLE PRECISION for pdormql.

  Pointer into the local memory to an array of dimension `(lld_a, LOCc(ja+k-1))`. The j-th column must contain the vector which defines the elementary reflector `H(j), ja≤j≤ja+k-1`, as returned by p?gelqf 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 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, ja

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

desca

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

tau

  (local)

  REAL for psormql

  DOUBLE PRECISION for pdormql.

  Array, DIMENSION `LOCc(ja+n-1) )`.

  Contains the scalar factor tau (j) of elementary reflectors H(j) as returned by p?geqlf. tau is tied to the distributed matrix A.

c

  (local)

  REAL for psormql

  DOUBLE PRECISION for pdormql.

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

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

ic, jc

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

descc

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

work

  (local)

  REAL for psormql

  DOUBLE PRECISION for pdormql.

  Workspace array of dimension of lwork.

lwork

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

  If `side = 'L'`,

  `lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0+mpc0)*nb_a + nb_a*nb_a`

  else if `side ='R'`,

  `lwork ≥ max((nb_a*(nb_a-1))/2, (nqc0+max npa0)+ 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)`,

  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

  Overwritten by the product 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-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: Orthogonal Factorizations