table of contents
PDSYTD2(l) | LAPACK auxiliary routine (version 1.5) | PDSYTD2(l) |
NAME¶
PDSYTD2 - reduce a real symmetric matrix sub( A ) to symmetric tridiagonal form T by an orthogonal similarity transformationSYNOPSIS¶
- SUBROUTINE PDSYTD2(
- UPLO, N, A, IA, JA, DESCA, D, E, TAU, WORK, LWORK, INFO )
- CHARACTER
- UPLO
- INTEGER
- IA, INFO, JA, LWORK, N
- INTEGER
- DESCA( * )
- DOUBLE
- PRECISION A( * ), D( * ), E( * ), TAU( * ), WORK( * )
PURPOSE¶
PDSYTD2 reduces a real symmetric matrix sub( A ) to symmetric tridiagonal form T by an orthogonal similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1).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¶
- UPLO (global input) CHARACTER
- Specifies whether the upper or lower triangular part of the
symmetric matrix sub( A ) is stored:
- 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.
- A (local input/local output) DOUBLE PRECISION 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 symmetric distributed matrix sub( A ). If UPLO = 'U', the leading N-by-N upper triangular part of sub( A ) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of sub( A ) contains the lower triangular part of the matrix, and its strictly upper triangular part is not referenced. On exit, if UPLO = 'U', the diagonal and first superdiagonal of sub( A ) are over- written by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = 'L', the diagonal and first subdiagonal of sub( A ) are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the orthogonal matrix Q 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+N-1)
- The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). D is tied to the distributed matrix A.
- E (local output) DOUBLE PRECISION array, dimension LOCc(JA+N-1)
- if UPLO = 'U', LOCc(JA+N-2) otherwise. The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. E is tied to the distributed matrix A.
- TAU (local output) DOUBLE PRECISION, array, dimension
- LOCc(JA+N-1). This array contains the scalar factors TAU of the elementary reflectors. TAU is tied to the distributed matrix A.
- WORK (local workspace/local output) DOUBLE PRECISION 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 >= 3*N.
- INFO (local output) INTEGER
- = 0: successful exit
FURTHER DETAILS¶
If UPLO = 'U', the matrix Q is represented as a product of elementary reflectorsQ = H(n-1) . . . H(2) H(1).
H(i) = I - tau * v * v'
Q = H(1) H(2) . . . H(n-1).
H(i) = I - tau * v * v'
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
12 May 1997 | LAPACK version 1.5 |