table of contents
PCLAHRD(l) | LAPACK auxiliary routine (version 1.5) | PCLAHRD(l) |
NAME¶
PCLAHRD - reduce the first NB columns of a complex general N-by-(N-K+1) distributed matrix A(IA:IA+N-1,JA:JA+N-K) so that elements below the k-th subdiagonal are zeroSYNOPSIS¶
- SUBROUTINE PCLAHRD(
- N, K, NB, A, IA, JA, DESCA, TAU, T, Y, IY, JY, DESCY, WORK )
PURPOSE¶
PCLAHRD reduces the first NB columns of a complex general N-by-(N-K+1) distributed matrix A(IA:IA+N-1,JA:JA+N-K) so that elements below the k-th subdiagonal are zero. The reduction is performed by an unitary similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.ARGUMENTS¶
- N (global input) INTEGER
- The number of rows and columns to be operated on, i.e. the order of the distributed submatrix sub( A ). N >= 0.
- K (global input) INTEGER
- The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero.
- NB (global input) INTEGER
- The number of columns to be reduced.
- A (local input/local output) COMPLEX pointer into
- the local memory to an array of dimension (LLD_A, LOCc(JA+N-K)). On entry, this array contains the the local pieces of the N-by-(N-K+1) general distributed matrix A(IA:IA+N-1,JA:JA+N-K). On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced distributed matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix Q as a product of elementary reflectors. The other columns of A(IA:IA+N-1,JA:JA+N-K) are unchanged. 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.
- TAU (local output) COMPLEX array, dimension LOCc(JA+N-2)
- The scalar factors of the elementary reflectors (see Further Details). TAU is tied to the distributed matrix A.
- T (local output) COMPLEX array, dimension (NB_A,NB_A)
- The upper triangular matrix T.
- Y (local output) COMPLEX pointer into the local memory
- to an array of dimension (LLD_Y,NB_A). On exit, this array contains the local pieces of the N-by-NB distributed matrix Y. LLD_Y >= LOCr(IA+N-1).
- 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) COMPLEX array, dimension (NB)
FURTHER DETAILS¶
The matrix Q is represented as a product of nb elementary reflectorsQ = H(1) H(2) . . . H(nb).
H(i) = I - tau * v * v'
( a h a a a )
( a h a a a )
( a h a a a )
( h h a a a )
( v1 h a a a )
( v1 v2 a a a )
( v1 v2 a a a )
12 May 1997 | LAPACK version 1.5 |