Computes an RQ factorization of a general rectangular matrix (unblocked algorithm).
call psgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)
call pdgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)
call pcgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)
call pzgerq2(m, n, a, ia, ja, desca, tau, work, lwork, info)
The p?gerq2 routine computes an RQ factorization of a real/complex distributed m-by-n matrix sub(A) = A(ia:ia+m-1, ja:ja+n-1) = R*Q.
(global). INTEGER.
The number of rows to be operated on, that is, the number of rows of the distributed submatrix sub(A). (m≥0).
(global).INTEGER. The number of columns to be operated on, that is, the number of columns of the distributed submatrix sub(A). (n≥0).
(local).
REAL for psgerq2
DOUBLE PRECISION for pdgerq2
COMPLEX for pcgerq2
COMPLEX*16 for pzgerq2.
Pointer into the local memory to an array of DIMENSION (lld_a,LOCc(ja+n-1)).
On entry, this array contains the local pieces of the m-by-n distributed matrix sub(A) which is to be factored.
(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.
(global and local) INTEGER array, DIMENSION (dlen_). The array descriptor for the distributed matrix A.
(local).
REAL for psgerq2
DOUBLE PRECISION for pdgerq2
COMPLEX for pcgerq2
COMPLEX*16 for pzgerq2.
This is a workspace array of DIMENSION (lwork).
(local or global). INTEGER.
The dimension of the array work.
lwork is local input and must be at least lwork≥nq0 + max(1, mp0), where
iroff = mod(ia-1, mb_a), icoff = mod(ja-1, nb_a),
iarow = indxg2p(ia, mb_a, myrow, rsrc_a, nprow),
iacol = indxg2p(ja, nb_a, mycol, csrc_a, npcol), mp0 = numroc( m+iroff, mb_a, myrow, iarow, nprow),
nq0 = numroc(n+icoff, nb_a, mycol, iacol, npcol),
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.
(local).
On exit,
if m ≤ n, the upper triangle of A(ia+m-n:ia+m-1, ja:ja+n-1) contains the m-by-m upper triangular matrix R;
if m ≥ n, the elements on and above the (m-n)-th subdiagonal contain the m-by-n upper trapezoidal matrix R; the remaining elements, with the array tau, represent the orthogonal/ unitary matrix Q as a product of elementary reflectors (see Application Notes below).
(local).
REAL for psgerq2
DOUBLE PRECISION for pdgerq2
COMPLEX for pcgerq2
COMPLEX*16 for pzgerq2.
Array, DIMENSION LOCr(ia+m -1). This array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix A.
On exit, work(1) returns the minimal and optimal lwork.
(local). INTEGER.
If info = 0, the execution is successful.
if info < 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.
The matrix Q is represented as a product of elementary reflectors
Q = H(ia)*H(ia+1)*...*H(ia+k-1) for real flavors,
Q = (H(ia))H*(H(ia+1))H...*(H(ia+k-1))H for complex flavors,
where k = min(m, n).
Each H(i) has the form
H(i) = I - tau*v*v',
where tau is a real/complex scalar, and v is a real/complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) for real flavors or conjg(v(1:n-k+i-1)) for complex flavors is stored on exit in A(ia+m-k+i-1, ja:ja+n-k+i-2), and tau in TAU(ia+m-k+i-1).