table of contents
PCGGQRF(l) | LAPACK routine (version 1.5) | PCGGQRF(l) |
NAME¶
PCGGQRF - compute a generalized QR factorization of an N-by-M matrix sub( A ) = A(IA:IA+N-1,JA:JA+M-1) and an N-by-P matrix sub( B ) = B(IB:IB+N-1,JB:JB+P-1)SYNOPSIS¶
- SUBROUTINE PCGGQRF(
- N, M, P, 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
- A( * ), B( * ), TAUA( * ), TAUB( * ), WORK( * )
PURPOSE¶
PCGGQRF computes a generalized QR factorization of an N-by-M matrix sub( A ) = A(IA:IA+N-1,JA:JA+M-1) and an N-by-P matrix sub( B ) = B(IB:IB+N-1,JB:JB+P-1):sub( A ) = Q*R, sub( B ) = Q*T*Z,
( 0 ) N-M N M-N
M
P-N N ( T21 ) P
P
inv( sub( B ) )*sub( A )= Z'*(inv(T)*R)
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¶
- N (global input) INTEGER
- The number of rows to be operated on i.e the number of rows of the distributed submatrices sub( A ) and sub( B ). N >= 0.
- M (global input) INTEGER
- The number of columns to be operated on i.e the number of columns of the distributed submatrix sub( A ). M >= 0.
- P (global input) INTEGER
- The number of columns to be operated on i.e the number of columns of the distributed submatrix sub( B ). P >= 0.
- A (local input/local output) COMPLEX pointer into the
- local memory to an array of dimension (LLD_A, LOCc(JA+M-1)). On entry, the local pieces of the N-by-M distributed matrix sub( A ) which is to be factored. On exit, the elements on and above the diagonal of sub( A ) contain the min(N,M) by M upper trapezoidal matrix R (R is upper triangular if N >= M); the elements below the diagonal, with the array TAUA, represent the unitary matrix Q as a product of min(N,M) 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, array, dimension
- LOCc(JA+MIN(N,M)-1). This array contains the scalar factors TAUA 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 pointer into the local memory to an array of dimension (LLD_B, LOCc(JB+P-1)). On entry, the local pieces of the N-by-P distributed matrix sub( B ) which is to be factored. On exit, if N <= P, the upper triangle of B(IB:IB+N-1,JB+P-N:JB+P-1) contains the N by N upper triangular matrix T; if N > P, the elements on and above the (N-P)-th subdiagonal contain the N by P upper trapezoidal matrix T; the remaining elements, 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, array, dimension LOCr(IB+N-1)
- This array contains the scalar factors 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 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( NB_A * ( NpA0 + MqA0 + NB_A ), MAX(
(NB_A*(NB_A-1))/2, (PqB0 + NpB0)*NB_A ) + NB_A * NB_A, MB_B * ( NpB0 +
PqB0 + MB_B ) ), where
- INFO (global output) INTEGER
- = 0: successful exit
FURTHER DETAILS¶
The matrix Q is represented as a product of elementary reflectorsQ = H(ja) H(ja+1) . . . H(ja+k-1), where k = min(n,m).
H(i) = I - taua * v * v'
Z = H(ib)' H(ib+1)' . . . H(ib+k-1)', where k = min(n,p).
H(i) = I - taub * v * v'
12 May 1997 | LAPACK version 1.5 |