table of contents
PSTZRZF(l) | LAPACK routine (version 1.5) | PSTZRZF(l) |
NAME¶
PSTZRZF - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper triangular form by means of orthogonal transformationsSYNOPSIS¶
- SUBROUTINE PSTZRZF(
- M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )
- INTEGER
- IA, INFO, JA, LWORK, M, N
- INTEGER
- DESCA( * )
- REAL
- A( * ), TAU( * ), WORK( * )
PURPOSE¶
PSTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper triangular form by means of orthogonal transformations.sub( A ) = ( R 0 ) * 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.
- 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) REAL 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, the leading M-by-M upper triangular part of sub( A ) contains the upper trian- gular matrix R, and elements M+1 to N of the first M rows of sub( A ), with the array TAU, represent the orthogonal matrix Z as a product of M elementary reflectors.
- 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.
- TAU (local output) REAL, array, dimension LOCr(IA+M-1)
- This array contains the scalar factors of the elementary reflectors. TAU is tied to the distributed matrix A.
- WORK (local workspace/local output) REAL 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 >= MB_A * ( Mp0 + Nq0 + MB_A ), where
- INFO (global output) INTEGER
- = 0: successful exit
FURTHER DETAILS¶
The factorization is obtained by Householder's method. The kth transformation matrix, Z( k ), which is used to introduce zeros into the (m - k + 1)th row of sub( A ), is given in the formZ( k ) = ( I 0 ),
( 0 T( k ) )
T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
( 0 )
( z( k ) )
Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
12 May 1997 | LAPACK version 1.5 |