table of contents
PSLABRD(l) | LAPACK auxiliary routine (version 1.5) | PSLABRD(l) |
NAME¶
PSLABRD - reduce the first NB rows and columns of a real general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P,SYNOPSIS¶
- SUBROUTINE PSLABRD(
- M, N, NB, A, IA, JA, DESCA, D, E, TAUQ, TAUP, X, IX, JX, DESCX, Y, IY, JY, DESCY, WORK )
PURPOSE¶
PSLABRD reduces the first NB rows and columns of a real general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of sub( A ).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)). 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.
- NB (global input) INTEGER
- The number of leading rows and columns of sub( A ) to be reduced.
- A (local input/local output) REAL 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 ) to be reduced. On exit, the first NB rows and columns of the matrix are overwritten; the rest of the distributed matrix sub( A ) is unchanged. If m >= n, elements on and below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and elements above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. If m < n, elements below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and elements on and above the diagonal in the first NB rows, 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) REAL array, dimension
- LOCr(IA+MIN(M,N)-1) if M >= N; LOCc(JA+MIN(M,N)-1) otherwise. The distributed diagonal elements of the bidiagonal matrix B: D(i) = A(ia+i-1,ja+i-1). D is tied to the distributed matrix A.
- E (local output) REAL 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(ia+i-1,ja+i) for i = 1,2,...,n-1; if m < n, E(i) = A(ia+i,ja+i-1) for i = 1,2,...,m-1. E is tied to the distributed matrix A.
- TAUQ (local output) REAL array dimension
- LOCc(JA+MIN(M,N)-1). The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. TAUQ is tied to the distributed matrix A. See Further Details. TAUP (local output) REAL array, dimension LOCr(IA+MIN(M,N)-1). The scalar factors of the elementary reflectors which represent the orthogonal matrix P. TAUP is tied to the distributed matrix A. See Further Details. X (local output) REAL pointer into the local memory to an array of dimension (LLD_X,NB). On exit, the local pieces of the distributed M-by-NB matrix X(IX:IX+M-1,JX:JX+NB-1) required to update the unreduced part of sub( A ).
- IX (global input) INTEGER
- The row index in the global array X indicating the first row of sub( X ).
- JX (global input) INTEGER
- The column index in the global array X indicating the first column of sub( X ).
- DESCX (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix X.
- Y (local output) REAL pointer into the local memory
- to an array of dimension (LLD_Y,NB). On exit, the local pieces of the distributed N-by-NB matrix Y(IY:IY+N-1,JY:JY+NB-1) required to update the unreduced part of sub( A ).
- IY (global input) INTEGER
- The row index in the global array Y indicating the first row of sub( Y ).
- JY (global input) INTEGER
- The column index in the global array Y indicating the first column of sub( Y ).
- DESCY (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix Y.
- WORK (local workspace) REAL array, dimension (LWORK)
- LWORK >= NB_A + NQ, with NQ = NUMROC( N+MOD( IA-1, NB_Y ), NB_Y, MYCOL, IACOL, NPCOL ) IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ) INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.
FURTHER DETAILS¶
The matrices Q and P are represented as products of elementary reflectors:Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) 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 real scalars, and v and u are real vectors. If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in A(ia+i-1:ia+m-1,ja+i-1); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in A(ia+i-1,ja+i:ja+n-1); tauq is stored in TAUQ(ja+i-1) and taup in TAUP(ia+i-1).
( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 )
( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 )
( v1 v2 a a a ) ( v1 1 a a a a )
( v1 v2 a a a ) ( v1 v2 a a a a )
( v1 v2 a a a ) ( v1 v2 a a a a )
( v1 v2 a a a )
12 May 1997 | LAPACK version 1.5 |