ZLAVHE
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZLAVHE performs one of the matrix-vector operations
x := A*x or x := A^H*x,
where x is an N element vector and A is one of the factors
from the symmetric factorization computed by ZHETRF.
ZHETRF produces a factorization of the form
U * D * U^H or L * D * L^H,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, U^H (or L^H) is the conjugate transpose of
U (or L), and D is Hermitian and block diagonal with 1 x 1 and
2 x 2 diagonal blocks. The multipliers for the transformations
and the upper or lower triangular parts of the diagonal blocks
are stored in the leading upper or lower triangle of the 2-D
array A.
If TRANS = 'N' or 'n', ZLAVHE multiplies either by U or U * D
(or L or L * D).
If TRANS = 'C' or 'c', ZLAVHE multiplies either by U^H or D * U^H
(or L^H or D * L^H ).
x := A*x or x := A^H*x,
where x is an N element vector and A is one of the factors
from the symmetric factorization computed by ZHETRF.
ZHETRF produces a factorization of the form
U * D * U^H or L * D * L^H,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, U^H (or L^H) is the conjugate transpose of
U (or L), and D is Hermitian and block diagonal with 1 x 1 and
2 x 2 diagonal blocks. The multipliers for the transformations
and the upper or lower triangular parts of the diagonal blocks
are stored in the leading upper or lower triangle of the 2-D
array A.
If TRANS = 'N' or 'n', ZLAVHE multiplies either by U or U * D
(or L or L * D).
If TRANS = 'C' or 'c', ZLAVHE multiplies either by U^H or D * U^H
(or L^H or D * L^H ).
Arguments
| UPLO |
CHARACTER*1
On entry, UPLO specifies whether the triangular matrix
stored in A is upper or lower triangular. UPLO = 'U' or 'u' The matrix is upper triangular. UPLO = 'L' or 'l' The matrix is lower triangular. Unchanged on exit. |
| TRANS |
CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'C' or 'c' x := A^H*x. Unchanged on exit. |
| DIAG |
CHARACTER*1
On entry, DIAG specifies whether the diagonal blocks are
assumed to be unit matrices: DIAG = 'U' or 'u' Diagonal blocks are unit matrices. DIAG = 'N' or 'n' Diagonal blocks are non-unit. Unchanged on exit. |
| N |
INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero. Unchanged on exit. |
| NRHS |
INTEGER
On entry, NRHS specifies the number of right hand sides,
i.e., the number of vectors x to be multiplied by A. NRHS must be at least zero. Unchanged on exit. |
| A |
COMPLEX*16 array, dimension( LDA, N )
On entry, A contains a block diagonal matrix and the
multipliers of the transformations used to obtain it, stored as a 2-D triangular matrix. Unchanged on exit. |
| LDA |
INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling ( sub ) program. LDA must be at least max( 1, N ). Unchanged on exit. |
| IPIV |
INTEGER array, dimension( N )
On entry, IPIV contains the vector of pivot indices as
determined by ZSYTRF or ZHETRF. If IPIV( K ) = K, no interchange was done. If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter- changed with row IPIV( K ) and a 1 x 1 pivot block was used. If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged with row | IPIV( K ) | and a 2 x 2 pivot block was used. If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged with row | IPIV( K ) | and a 2 x 2 pivot block was used. |
| B |
COMPLEX*16 array, dimension( LDB, NRHS )
On entry, B contains NRHS vectors of length N.
On exit, B is overwritten with the product A * B. |
| LDB |
INTEGER
On entry, LDB contains the leading dimension of B as
declared in the calling program. LDB must be at least max( 1, N ). Unchanged on exit. |
| INFO |
INTEGER
INFO is the error flag.
On exit, a value of 0 indicates a successful exit. A negative value, say -K, indicates that the K-th argument has an illegal value. |