table of contents
PZGEBD2(l) | LAPACK auxiliary routine (version 1.5) | PZGEBD2(l) |
NAME¶
PZGEBD2 - reduce a complex general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper or lower bidiagonal form B by an unitary transformationSYNOPSIS¶
- SUBROUTINE PZGEBD2(
- M, N, A, IA, JA, DESCA, D, E, TAUQ, TAUP, WORK, LWORK, INFO )
- INTEGER
- IA, INFO, JA, LWORK, M, N
- INTEGER
- DESCA( * )
- DOUBLE
- PRECISION D( * ), E( * )
- COMPLEX*16
- A( * ), TAUP( * ), TAUQ( * ), WORK( * )
PURPOSE¶
PZGEBD2 reduces a complex general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper or lower bidiagonal form B by an unitary transformation: Q' * sub( A ) * P = B.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.
- N (global input) INTEGER
- The number of columns to be operated on, i.e. the number of columns of the distributed submatrix sub( A ). 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, this array contains the local pieces of the general distributed matrix sub( A ). On exit, if M >= N, the diagonal and the first superdiagonal of sub( A ) are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. If M < N, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the orthogonal matrix P 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.
- D (local output) DOUBLE PRECISION array, dimension
- LOCc(JA+MIN(M,N)-1) if M >= N; LOCr(IA+MIN(M,N)-1) otherwise. The distributed diagonal elements of the bidiagonal matrix B: D(i) = A(i,i). D is tied to the distributed matrix A.
- E (local output) DOUBLE PRECISION array, dimension
- LOCr(IA+MIN(M,N)-1) if M >= N; LOCc(JA+MIN(M,N)-2) otherwise. The distributed off-diagonal elements of the bidiagonal distributed matrix B: if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. E is tied to the distributed matrix A.
- TAUQ (local output) COMPLEX*16 array dimension
- LOCc(JA+MIN(M,N)-1). The scalar factors of the elementary reflectors which represent the unitary matrix Q. TAUQ is tied to the distributed matrix A. See Further Details. TAUP (local output) COMPLEX*16 array, dimension LOCr(IA+MIN(M,N)-1). The scalar factors of the elementary reflectors which represent the unitary matrix P. TAUP is tied to the distributed matrix A. 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( MpA0, NqA0 )
- INFO (local output) INTEGER
- = 0: successful exit
FURTHER DETAILS¶
The matrices Q and P are represented as products of elementary reflectors:Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
( v1 v2 v3 v4 v5 )
( MB_A.EQ.NB_A .AND. IROFFA.EQ.ICOFFA )
12 May 1997 | LAPACK version 1.5 |