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 )
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. If M >= N, B is upper bidiagonal; if M < N, B is lower bidiagonal. NotesDTYPE_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)). Let K be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q.
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 ) where NB = MB_A = NB_A, IROFFA = MOD( IA-1, NB ) IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JA, NB, MYCOL, CSRC_A, NPCOL ), MpA0 = NUMROC( M+IROFFA, NB, MYROW, IAROW, NPROW ), NqA0 = NUMROC( N+IROFFA, NB, 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.
- 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) Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' where tauq and taup are complex scalars, and v and u are complex vectors;
Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' where tauq and taup are complex scalars, and v and u are complex vectors;
( 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 |