table of contents
PZGGRQF(l) | LAPACK routine (version 1.5) | PZGGRQF(l) |
NAME¶
PZGGRQF - compute a generalized RQ factorization of an M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1)SYNOPSIS¶
- SUBROUTINE PZGGRQF(
- M, P, N, A, IA, JA, DESCA, TAUA, B, IB, JB, DESCB, TAUB, WORK, LWORK, INFO )
- INTEGER
- IA, IB, INFO, JA, JB, LWORK, M, N, P
- INTEGER
- DESCA( * ), DESCB( * )
- COMPLEX*16
- A( * ), B( * ), TAUA( * ), TAUB( * ), WORK( * )
PURPOSE¶
PZGGRQF computes a generalized RQ factorization of an M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) and a P-by-N matrix sub( B ) = B(IB:IB+P-1,JB:JB+N-1):sub( A ) = R*Q, sub( B ) = Z*T*Q,
N-M M ( R21 ) N
N
( 0 ) P-N P N-P
N
sub( A )*inv( sub( B ) ) = (R*inv(T))*Z'
DTYPE_A = 1.
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
array A.
array A.
the rows of the array.
the columns of the array.
row of the array A is distributed. CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
array. LLD_A >= MAX(1,LOCr(M_A)).
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). An upper bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
ARGUMENTS¶
- M (global input) INTEGER
- The number of rows to be operated on i.e the number of rows of the distributed submatrix sub( A ). M >= 0.
- P (global input) INTEGER
- The number of rows to be operated on i.e the number of rows of the distributed submatrix sub( B ). P >= 0.
- N (global input) INTEGER
- The number of columns to be operated on i.e the number of columns of the distributed submatrices sub( A ) and sub( B ). N >= 0.
- A (local input/local output) COMPLEX*16 pointer into the
- local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). On entry, the local pieces of the M-by-N distributed matrix sub( A ) which is to be factored. On exit, if M <= N, the upper triangle of A( IA:IA+M-1, JA+N-M: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 TAUA, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). IA (global input) INTEGER The row index in the global array A indicating the first row of sub( A ).
- JA (global input) INTEGER
- The column index in the global array A indicating the first column of sub( A ).
- DESCA (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix A.
- TAUA (local output) COMPLEX*16, array, dimension LOCr(IA+M-1)
- This array contains the scalar factors of the elementary reflectors which represent the unitary matrix Q. TAUA is tied to the distributed matrix A (see Further Details). B (local input/local output) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_B, LOCc(JB+N-1)). On entry, the local pieces of the P-by-N distributed matrix sub( B ) which is to be factored. On exit, the elements on and above the diagonal of sub( B ) contain the min(P,N) by N upper trapezoidal matrix T (T is upper triangular if P >= N); the elements below the diagonal, with the array TAUB, represent the unitary matrix Z as a product of elementary reflectors (see Further Details). IB (global input) INTEGER The row index in the global array B indicating the first row of sub( B ).
- JB (global input) INTEGER
- The column index in the global array B indicating the first column of sub( B ).
- DESCB (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix B.
- TAUB (local output) COMPLEX*16, array, dimension
- LOCc(JB+MIN(P,N)-1). This array contains the scalar factors TAUB of the elementary reflectors which represent the unitary matrix Z. TAUB is tied to the distributed matrix B (see Further Details). WORK (local workspace/local output) COMPLEX*16 array, dimension (LWORK) On exit, WORK(1) returns the minimal and optimal LWORK.
- LWORK (local or global input) INTEGER
- The dimension of the array WORK. LWORK is local input and
must be at least LWORK >= MAX( MB_A * ( MpA0 + NqA0 + MB_A ), MAX(
(MB_A*(MB_A-1))/2, (PpB0 + NqB0)*MB_A ) + MB_A * MB_A, NB_B * ( PpB0 +
NqB0 + NB_B ) ), where
- INFO (global output) INTEGER
- = 0: successful exit
FURTHER DETAILS¶
The matrix Q is represented as a product of elementary reflectorsQ = H(ia)' H(ia+1)' . . . H(ia+k-1)', where k = min(m,n).
H(i) = I - taua * v * v'
Z = H(jb) H(jb+1) . . . H(jb+k-1), where k = min(p,n).
H(i) = I - taub * v * v'
12 May 1997 | LAPACK version 1.5 |